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< 0.05). We speculated that the presence of CNTs played a positive role toward the attachment and proliferation of MSCs. Since PLGA was a biodegradable polymer matrix, it may release CNTs into bone over an extended period. The cytotoxicity of CNTs was an actively debated issue. Previous researches have shown that CNTs have no adverse effects on proliferation, and differentiation of MSCs The ALP activity was an indicator of the commitment of MSCs toward the osteoblastic lineage. The results from the ALP activity confirmed the observations made on the cell proliferation measurements. All groups on day 21 showed the maximum ALP productions (). Hence, it was significantly higher in osteoblastic differentiation on PLGA/c-MWCNTs film compared to PLGA and PLGA/MWCNTs films on each culture time (*P |
< 0.05 and **P |
< 0.01). The results suggested that the differentiation of MSCs toward osteoblasts markedly depended on the surface properties of substrate. It had been suggested that the nanostructures of biomaterials were crucial to the differentiation of cells ), consistent with the ALP activity described previously. PLGA/c-MWCNT nanocomposite films supported MSCs growth and differentiation, which was consistent with the results mentioned above.MSCs were derived from rat bone marrow and cultured on PLGA/c-MWCNT nanocomposite films with high tensile strength for the first time. SEM and AFM confirmed that the carboxyl-functionalized MWCNTs could offer better possibilities for their dispersion in the PLGA matrix. The MWCNT and c-MWCNT modified PLGA nanocomposite films possessed higher tensile strength than the FDA-approved PLGA, especially the PLGA/c-MWCNTs. Addition of c-MWCNTs allowed a better hydrophilicity in the PLGA matrix according to the results of XPS, water contact angle, and the degradation in vitro. In addition, the PLGA/c-MWCNT nanocomposite films promoted the attachment, proliferation, and ALP secretion of rat MSCs. MSCs attaching on PLGA/c-MWCNT nanocomposite films expressed elevated levels of bone marker ALP. Hence, the performance of these PLGA/c-MWCNT nanocomposite films warrants future work aimed in vivo characterization and fabrication of 3-D scaffolds for bone regeneration.Supplementary data associated with this article can be found, in the online version, at Incidence of load combination methods on time-variant oil tanker reliability in intact conditionsReliability analysis of an oil tanker in intact conditions is performed to investigate the incidence of load combination methods on hull girder sagging/hogging time-variant failure probability. Particularly, Turkstra rule, Ferry Borges and Castanheta method and Poisson square wave model are applied to evaluate the statistical distribution of bending moment, with reference to both one voyage and 1-year period. Statistical properties of time-variant ultimate strength are determined by Monte Carlo simulation, up to 25-year ship lifetime; bending capacity is determined by means of a modified incremental-iterative method, to account for corrosion wastage of structural members contributing to hull girder strength, welding residual stresses and material properties randomness. After determining the still water load combination factors, based on statistical properties of still water, wave and total vertical bending moments, with reference to 1-year time interval, reliability analysis is performed by Monte Carlo simulation, based on limit state formulations relative to different load combination methods. Finally, the VLCC double hull oil tanker, benchmarked in the 2012 ISSC report, is assumed as a reference ship and obtained results are fully discussed.Structural reliability analysis was started at the end of the 1940s by , who suggested that statistical distributions of load factors should be taken into account for a more rational design of engineering structures, based on safety and serviceability levels. Following the first attempts in developing probability-based formats for ship structural design, carried out by , the earliest applications of reliability analysis to ship structural design mainly focused on global safety and serviceability levels of ship structures under vertical bending moments (). In this respect, the main difficulty in estimating the hull girder failure probability was encountered when combining still water and wave vertical loads, as they are characterized by different time variability and relevant maxima do not occur simultaneously, so that the maximum of the combined process may be smaller than the sum of individual load maxima (). Furthermore, when structures are subjected to the combined action of two or more stochastic load processes, reliability analysis becomes a time-variant problem, that reduces to a time-invariant one if external Ioads are resembled by relevant extreme values, with reference to a given time interval, based on load-combination analysis (). From this point of view, several load combination methods of vertical still water and wave bending moments have been applied to ship structural design in the last decades (), with reference to both deterministic methods, such as peak coincidence, root of sum of squares ( rules, and stochastic techniques, such as In the same years, the other main source of uncertainties, mainly related to hull girder ultimate bending capacity, has been widely investigated to derive probabilistic values of hull girder strength, in terms of nominal mean values, coefficients of variation and distribution types ( focused on time-variant reliability of an oil tanker experiencing structural degradation, due to corrosion wastage. carried out the reliability assessment of a Floating Production, Storage and Offloading (FPSO) vessel by a modified Smith method, accounting for corrosion growth and crack propagation by Paris-Erdogan equation. presented a new approach to reduce uncertainties in the performance assessment of ship structures, updating the wave-induced load effects by Bayesian methods with data acquired from structural health monitoring and comparing time-variant reliability indexes before and after the improvement process. applied fast integration techniques to estimate the long-term vertical wave bending moment, with reference to a time-variant reliability analysis. Finally, investigated the statistical properties of time-variant ultimate and residual strength of a bulk carrier, accounting for structural degradation and neutral axis rotation, in case of asymmetrically damaged cross-sections. They also investigated the incidence of different reliability analysis techniques, namely First, Second-Order Reliability Analysis and Importance Sampling simulation, on time-variant hull girder failure probability in pure bending intact and damage conditions (). Finally, real-time reliability of ship structures recently became a popular topic. In this respect, investigated the optimal mission-oriented routing of ships and developed a risk-informed approach for ship structures, assessing the risk levels by reliability analysis of hull girder amidships cross-section and accounting for corrosion wastage, different damage levels and plasticity propagation.Hence, following the improvements in the assessment of hull girder failure probability with reference to the statistical analysis of vertical bending moments and hull girder capacity, the International Association of Classification Societies (IACS) developed the new ultimate hull girder strength check criterion for oil tankers (), actually embodied in the Harmonized Common Structural Rules for Oil Tankers and Bulk Carriers (), calibrating partial safety factors by structural reliability analysis. Particularly, reliability analysis was based on rule and the characteristic value of still water bending moment (SWBM), with reference to one voyage, was combined with the extreme vertical wave bending moment (VWBM) one, with 1-year return period, for which a Gumbel type distribution has been applied. Besides, the ultimate bending capacity has been determined by the single-step method, based on the net scantling approach, disregarding time-variant corrosion wastage and accounting for model uncertainties due to material properties randomness, by means of an uncertainty factor, following the normal distribution with 1.05 mean value and 0.1 standard deviation, to reflect differences between the single-step method and more advanced techniques, such as non-linear FE analysis. Similarly, model uncertainty factors for still water and wave vertical bending moments were derived to account for differences between sagging and hogging conditions and nonlinearities due to large amplitude motions in harsh weather conditions. Hence, following the outcomes stressed within the calibration process of partial safety factors for ultimate strength check criterion of oil tankers, the same format, mainly based on deterministic rule, has been recently applied in the calibration process of the residual strength check criterion for oil tankers and bulk carriers, after collision or grounding events. In this respect, the structural reliability analysis model for intact condition has been partly modified to account for lower exposure times to wave loads and milder weather conditions in coastal areas, where collision and grounding events generally occur, with respect to 25-year time interval and North Atlantic climate adopted for intact condition.Anyway, following the outcomes stressed by rule may furnish quite unconservative results and underestimate the structural failure probability, if the combined random load processes have the same order of magnitude, as for vertical still water and wave bending moments. Furthermore, performed the reliability analysis of an oil tanker by different wave load formulations, concluding that failure probabilities change significantly with the applied format, so that relevant choice becomes a matter of standardisation in order to allow different ship structures to be consistently compared each other. Hence, based on actual state of art, some concerns arise with reference to the evaluation of hull girder stochastic properties and the application of load combination methods to reliability analysis. In this respect, the paper provides a comprehensive format to investigate the statistical properties of time-variant hull girder strength and focuses on the incidence of load combination methods on sagging/hogging failure probabilities of a double hull oil tanker in intact condition. Stochastic modelling of extreme still water and wave vertical bending moments, as well as the basics of the modified ultimate strength method to account for corrosion wastage, welding residual stresses and material properties randomness are preliminarily discussed. Subsequently, three main aspects are fully investigated:Hull girder ultimate strength is assessed by Monte Carlo simulation, accounting for corrosion wastages of structural elements contributing to hull girder strength, welding residual stresses and material properties randomness.Sagging/hogging failure probability is investigated by Monte Carlo simulation, based on two different limit state formulations, the former mainly derived by the IACS format with reference to deterministic rule, the latter accounting for stochastic load combination among vertical still water and wave bending moments.A comparative analysis among deterministic rule and load combination methods, based on ) models for still water loads, is performed to investigate the incidence of extreme value statistics on the attained failure probability level.Finally, the double hull VLCC oil tanker, analysed for the first time in the report and subsequently benchmarked in the study, is assumed as a test case for reliability analysis, carried out by a dedicated programme developed in Matlab (The first systematic study on the stochastic properties of SWBM was performed by , who carried out a statistical analysis on a data set consisting of about 2000 voyages of 100 ships from 39 ship-owners, to establish the variability of still water loads during normal operations of oceangoing ships. They concluded that the SWBM follows the normal distribution, with mean and standard deviation mainly depending on ship types and loading conditions that, in turn, were kept constant during each voyage, assuming the probabilistic model at departure as representative of any random point in time, till arrival in port (). This hypothesis revealed to be adequate in many cases, namely ballast and partial/ballast load conditions for double and single hull oil tankers respectively, even if found that SWBM of double-hull oil tankers in partial or full load conditions could significantly vary during each voyage and recommended, for practical applications, to take relevant mean and standard deviation equal to the average values between departure and arrival conditions.Furthermore, if the SWBM is regarded as a random variable, it may exceed the maximum value reported in the loading manual that should not obviously be surpassed, which implies that relevant distribution should be truncated to avoid unrealistic sagging/hogging bending moments ( concluded that the truncation of SWBM distribution has negligible effects on oil tankers.In this respect, in actual analysis the one voyage SWBM is assumed to follow the normal distribution, with mean and standard deviation equal to 70% and 20% of the maximum bending moment reported in the loading manual, with reference to both full load and ballast load conditions, corresponding to sagging and hogging bending moments respectively, as suggested by . Besides, no truncation of relevant distribution is applied, which implies that the exceedance probability of maximum values reported in the loading manual is less than 7%.The extreme value distribution of SWBM mainly depends on the ship operational profile. In this respect, the ship is assumed to operate at sea for 85% of life, in full (42.5%) and ballast (42.5%) load conditions, while it stays in port for the remaining fraction of time, in accordance to the typical operational profile of oil tankers, assumed in the calibration process of the hull girder ultimate strength capacity criterion (). Moreover, based on the stochastic analysis carried out by , voyage duration tv is assumed to follow the Weibull distribution, with mean value and standard deviation equal to 23.5 and 11.3 days, respectively. Besides, the extreme value distribution of SWBM is determined by Ferry Borges and Castanheta (FBC) and Poisson square wave (PSW) models, assuming that bending moments in different voyages are independent random variables. model, still water loads are regarded as a sequence of rectangular pulses with fixed duration. Hence, denoting by FMsw the one voyage distribution of SWBM for any load condition, the extreme distribution FMsw, max, with reference to the specified time interval T, is determined as follows:having denoted by nsw,T the number of voyages in the time interval T, depending on the mean voyage duration E[tv] and the effective time fraction pe of the load condition (Hence, the characteristic SWBM Msw,T that, on average, is exceeded once in a sample of size nsw,T, is derived (According to the Poisson square wave model (), the voyage duration is regarded as an exponential random variable. Hence, the SWBM extreme distribution FMsw, max is approximated as follows (It is noticed that, if the number of load repetitions nsw,T in the time interval T is sufficiently high, Eq. can be resembled by the Gumbel law, with scale and shape parameters depending on the SWBM characteristic value and one voyage hazard function (). Finally, the characteristic value Msw,T is determined by letting the mean number of events upcrossing the level Msw,T equal to one (The short-term VWBM can be regarded as a stationary narrow-band Gaussian process, with peak values following the Rayleigh distribution (). Relevant long-term statistics are derived by averaging the short-term ones (), based on the North Atlantic wave climate (), with reference to areas 8, 9, 15 and 16 of Global Wave Statistics (). Hence, the long-term response peak distribution is fitted by the Weibull law (having denoted by w and k relevant scale and shape parameters, respectively. The latter, mainly depending on ship type, is quite close to 1 () and follows the uniform distribution in the range 0.88–1.00 and 0.82–0.95 for full (sagging) and ballast (hogging) load conditions, respectively (). In actual analysis the shape parameter is assumed equal to 1, so leading to slightly higher characteristic values of VWBM (), while the scale parameter w is determined by the rule VWBM Mwv, rule () that, in turn, is related to an exceedance probability level q=10−8, based on 20-year ship lifetime:The extreme value distribution of VWBM FMwv, max is regarded as an exponential random process (). Hence, it can be approximated as follows (Wen, 1990; having denoted by nwv,T the number of wave load peak values in the period T, depending on the effective time fraction of load condition pe and the mean wave period E[tw], equal to 8 s for North Atlantic area:Finally, the characteristic value of VWBM Mwv,T is derived by letting the mean number of events upcrossing the level Mwv,T equal to one (Global longitudinal loads acting on oceangoing ships are assessed by combining vertical still water and wave bending moments. In this respect, when two random processes are superimposed, maxima of individual load processes do not occur simultaneously, which implies that the maximum of the combined load process is smaller than the sum of individual load maxima (). Hence, combination between still water and wave vertical bending moments can be performed by deterministic or stochastic methods. The former, such as rule, are mainly based on combining the mean value of a given variable with the characteristic extreme value of the remaining one with reference to a given time interval, while the latter directly combine the characteristic loads, with reference to a given return period, by means of load combination factors, to be assessed by superimposing the time-variant random processes ( load combination method the SWBM is modelled as a sequence of rectangular pulses of fixed duration, while in the Poisson square wave model the SWBM is modelled as an exponential random process. rule is a deterministic procedure to design structures subjected to the combined effects of several load events. It assumes that the maximum load occurs when either component of the individual processes reaches its maximum value, while an arbitrary point in time value characterizes the other ones. Hence, with reference to vertical still water and wave bending moments, the total extreme bending moment Mmax, with reference to a given period T, is determined according to the following governing equation, assuming that the wave load is dominating compared to the still water one (having denoted by Msw,v the one voyage SWBM and by Mwv, max the extreme VWBM in the time interval T. The method generally provides sufficiently accurate results, if either of two variables dominates, while it furnishes unconservative estimates of the total load characteristic value if the two variables have the same magnitude, as it commonly happens for ship structures (). Nevertheless, the method has been applied by the International Association of Classification Societies (IACS) in two comprehensive studies, devoted to partial safety factor calibration for hull girder ultimate () strength check criteria, based on reliability analysis of several reference ships. load combination method can be applied if the SWBM is modelled as a sequence of rectangular pulses with fixed duration. In this respect, the one voyage distribution FMC,v of maximum bending moment is determined as follows:having denoted by fMs the one voyage SWBM density function and by nwv,v the wave load peak numbers in one voyage:Hence, the distribution of total bending moment in the time interval T is derived (from which the characteristic value of maximum bending moment Mc,T that is exceeded, on average, once in a sample of size nsw,T, as defined in Eq. Hence, the reducing effect of combined loads’ characteristic maximum value is derived introducing the still water load combination factor ψsw (Poisson square wave load combination method can be applied if voyage duration is an exponential random process. In this respect, the one voyage distribution FMC,v of maximum bending moment is determined as follows (Huang and Moan, 2008):FMc,v(m)=∫−∞∞FMwv(m−x)fMs(x)1+nwv,v[1−FMwv(m−x)]dxfrom which the distribution of maximum bending moment can be derived with reference to nsw,T load repetitions in the time interval T (FMc,max(m)≈exp{-nsw,T∫−∞∞[1−FMwv(x)]fMs(m-x)dx}Hence, after determining the maximum bending moment distribution, relevant characteristic value Mc,T is derived by letting the mean number of events upcrossing the characteristic bending moment Mc,T in the time period T equal to one (So the characteristic value, corresponding to an exceedance probability level equal to 1-e−1, is derived:Finally, the still water load combination factor ψsw is determined according to Eq. ), even if modified incremental iterative methods have been recently proposed to account for neutral axis rotation, due to asymmetrically damaged cross-sections (In actual analysis, following the outcomes stressed by , statistical properties of hull girder sagging/hogging bending capacity are determined by Monte Carlo simulation, accounting for uncertainties due to: (i) corrosion wastage of all structural elements contributing to hull girder strength, (ii) welding residual stresses and (iii) material properties randomness.The corrosion wastage model, developed by , is applied to estimate the time-variant thickness reduction tr(T) of any structural element contributing to hull girder strength, assuming that ship life is subdivided into two phases, the former without corrosion wastage due to coating protection, the latter characterized by a constant annual corrosion rate: Tc is the coating life, while C1 is the annual corrosion rate that follows the Weibull distribution, with scale and shape parameters based on wastage statistics, developed by , with reference to 34 structural elements of single and double-hull oil tankers, FSO and FPSO units. In actual analysis severe corrosion rates, corresponding to 95% and upper bound of measured data, are assumed with reference to a mean coating life of 7.5 years. In this respect, current corrosion model is mainly based on the following basic assumptions: (i) the annual corrosion rate is constant and depends on element type and location; (ii) the coating life is the same for all structural elements; (iii) corrosion wastage is null until the ship age reaches the coating life and then increases linearly over time. First of all, it must be pointed out that corrosion progression is generally characterized by a time-dependent rate that decreases or increases over time for statically and dynamically loaded structures, respectively. In the former case, corroded material stays on steel surface, protecting it from further contact with corrosive environment, so as the corrosion wastage process decreases or approximately stabilizes over time. In the latter case, instead, ablation due to ship speed and crack propagation due to cyclic loading continually expose new material to corrosive attack, so as corrosion process accelerates (). Really, as ship structures are characterized by different corrosion rates and progressions over time, mainly depending on element type and location, the linear corrosion rate applied by reveals to be a reasonable choice for practical design purposes, considering the scatter of corrosion progress characteristics. Besides, corrosion progression over time also depends on degradation performances of anticorrosion coatings that, in turn, are mainly conditioned by: (i) coating systems, (ii) details of application (surface preparation, stripe coats, film thickness, humidity and salt control) and (iii) maintenance and repair over time, which implies that coating life may be regarded as a random variable, generally ranging between 5 and 10 years (). Nevertheless, if coating life increases, corrosion rate mean value is expected to decrease accordingly, to keep constant the thickness reduction after 25-year ship lifetime, based on gauged thickness measurements, as highlighted by , which implies that variations of coating life may lead to slight different distributions of hull girder ultimate bending capacities over time, even if relevant values after 25-year ship lifetime are expected to be almost the same. Besides, it is conceivable that replacement of some structural elements, due to severe corrosion degradation, may occur during the ship lifetime (). Anyway, no replacement has been considered, on safe side, even if it is predictable that relevant incidence on main outcomes of current analysis is almost negligible.Finally, following the outcomes stressed by , who investigated the incidence of different correlation models on time-variant hull girder ultimate strength statistical properties a partial correlation model is applied, assuming that full correlation exists among corrosion wastages of structural elements belonging to the same group of compartments, namely double-bottom, hopper tank, double-side and cargo oil tank, while no correlation exists for elements belonging to different categories.Welding residual stresses in the attached platings of longitudinal stiffeners are based on . The incidence of welding residual stresses on hull girder reliability, the edge function ϕ, namely the structural to plating yield stress ratio for both positive (shortening) and negative (lengthening) relative strains ε (φ=max{-1;min[1,ε,σrε+1−σr1+σr];min[0,ε1+σr]}having denoted by σr the welding residual stress ratio, depending on the random weld tension block parameter η and the plating breadth to gross thickness ratio b/tg (, i.e. giving the same values for compressive loads, lower values for tensile loads. Besides, the weld tension block parameter η is assumed to follow the normal distribution, with mean value μη and standard deviation ση depending on the plating breadth to gross thickness ratio, according to the following formulas proposed by , valid if the breadth to gross thickness ratio b/tg is less than 120:It is noticed that the above mentioned condition is generally fulfilled for typical platings of oil tankers, characterized by a ratio lower than 100. Finally, it is assumed that no correlation exists among welding residual stresses in attached platings of different longitudinal stiffeners and no relaxation over time is applied. In this respect, it must be pointed out that welding residual stresses are generally relaxed to some extent by stretching of stiffened platings under cyclic loadings. Particularly, found that welding residual stresses in tee-stiffened platings are reduced by about 20% and 40%, in presence of cyclic axial stresses, with amplitude equal to 25% and 50% of material yield strength respectively, so producing a corresponding ultimate strength capacity increase between 1.5% and 7.0%, after partial relief by shakedown. Hence, as the increase of ultimate strength of typical stiffened plates of ship structures is expected to be lower than 10% after shakedown, in current analysis welding residual stress relaxation is not considered, on safe side.Material properties randomness, with reference to both Young modulus and yield strength, is taken into account. Particularly, the Young modulus is assumed to follow the normal distribution, with 210 GPa mean value and 5% variation coefficient (). In turn, the yield strength is assumed to follow the lognormal distribution, with mean value equal to 1.1 times the Rule one and 8% (6%) variation coefficient for mild (high-tensile) steel (). Besides, generation of random variables is performed assuming that no correlation exists among material mechanical properties of different elements. Finally, it must be pointed out that in current analysis material mechanical properties are regarded as time-independent random variables, even if a certain decrease of Young modulus and yield strength mean values occurs over time, due to corrosion degradation of platings and support structures. Nevertheless, it is predictable that the decrease over time of material mechanical properties due to corrosion degradation is quite limited, if corrosion wastage is less than 20% of as-built thickness, as investigated by It is well known that reliability analysis techniques are generally subdivided into four level methods (), depending on the level of accuracy in estimating the statistical properties of random variables. (). Particularly, Level I techniques correspond to the deterministic partial safety factor method. Level II methods consider both mean value and standard deviation of each random variable, as for reliability index. Level III methods, based on the joint probability density function of all random variables, employ either analytical approximations, as for First and Second-Order reliability analysis, or numerical techniques, such as Monte Carlo simulation. Finally, Level IV methods evaluate structural reliability on the basis of economic criteria, related to costs and benefits associated with construction, consequences of failure and maintenance/repair operations (Particularly, actual reliability analysis is performed by Monte Carlo simulation, based on two different limit state formulations relative to deterministic and stochastic load combination methods. In both cases the limit state function, determined by superimposing the still water and wave vertical bending moments with relevant uncertainty factors, defines two domains of safety, namely the safe g(x,t)>0 and unsafe g(x,t)<0 regions in the space of random variables.The time-variant limit state formulation g(x,t) based on the deterministic where: Mu(t) is the time-variant ultimate bending capacity, accounting for random corrosion wastages of all structural elements contributing to hull girder strength, welding residual stresses and material properties randomness; Xr is the model uncertainty factor for hull girder ultimate bending capacity; Mwv, max is the maximum wave bending moment with reference to 1-year return period; Xst and Xnl are the wave bending moment uncertainty factors, due to linear and non-linear response calculations, respectively; Msw,v is the SWBM relative to one voyage; Xsw is the still water uncertainty factor. In this respect, statistical properties of all random variables are listed in , with reference to distribution type, mean value and standard deviation. It is noticed that all random variables follow the normal distribution, with the only exception of VWBM that is modelled as an exponential random process, according to Eq. , and the ultimate hull girder bending capacity, whose distribution will be directly investigated by Monte Carlo simulation.The time-variant limit state formulation g(x,t) for stochastic load combination methods is assumed on the basis of g(x,t)=Mu(t)Xr−(Mwv,maxXstXnl+ψswMsw,maxXsw)replacing the one voyage SWBM Msw,v with the extreme one Msw, max, relative to 1-year return period, and adding the still water load combination factor ψsw that, in turn, depends on the applied load combination method, namely Ferry Borges and Castanheta (FBC) and Poisson square wave (PSW) models, as reported in Reliability analysis is performed for the ISSC double hull VLCC oil tanker, analysed for the first time in the Report and subsequently benchmarked in the comparative study on sagging/hogging ultimate strength capacities of six reference ships, based on different techniques, namely incremental iterative method, modified Paik-Mansour formula and full FE elasto-plastic analysis. The hull was extensively studied in the past. In this respect, investigated the residual strength capacity by the incremental-iterative method, under combined vertical and horizontal bending moments, accounting for randomness due to yield strength, plate thickness and damage extension. investigated the incidence of welding residual stresses and material properties randomness on hull girder ultimate strength. investigated, by the incremental-iterative method, the incidence of damage size on residual strength capacity, due to collision and grounding events, and proposed some analytical formulations between hull girder capacity reduction and damage dimensions, based on systematic variations of damage extent along the ship side and bottom. Finally, determined the ultimate strength capacity by the FE method, within a comparative analysis among numerical and experimental results for several reference ships.The main data of the ISSC double hull oil tanker are reported in the section scheme is shown. It is noticed that ultimate sagging/hogging capacities refer to the gross-scantling section, with no corrosion wastage and welding residual stresses. In this respect, the bending moment versus curvature distribution is reported in as reference test-case. It is noticed that continuous line refers to the bending moment distribution while the dashed one to the inelastic neutral axis vertical shift Δz=zCL(χ)-zCL(0) from the elastic neutral axis position (). Actual results, obtained by a dedicated programme developed in Matlab (), comply well with those ones reported in and provided by several Working Organizations involved in the Input data for reliability analysis are reported in . Statistical properties of ultimate strength capacity and VWBM extreme distribution are the same for both deterministic Turkstra rule and stochastic load combination methods. On the contrary, SWBM follows the one voyage distribution, based on Turkstra rule, and the extreme value one if stochastic load combination methods are applied. It is noticed that the still water load combination factor ψsw depends on the load combination method, namely Ferry Borges and Castanheta and Poisson square wave models, as it is subsequently investigated.Characteristic values of sagging/hogging SWBM and VWBM are reported in , with reference to 1-year return period, for Ferry Borges and Castanheta (FBC) and Poisson square wave (PSW) models. It is noticed that still water load combination factors, lying in the range 0.84–0.87 and 0.89–0.92 for full load (sagging) and ballast load (hogging) conditions respectively, are slightly overestimated by the FBC model, with reference to the PSW one. Anyway, actual results are well in accordance with those ones provided by for a set of five oil tankers, with reference to 1-year return period. Finally, the one voyage distributions FMC,v of maximum sagging/hogging bending moments are reported in (a) and (b). Continuous and dashed lines refer to Ferry Borges and Castaneta (FSC) and Poisson square wave (PSW) models, respectively. It is noticed that the one voyage distribution based on Turkstra rule is not reported, as the latter method is based on a deterministic combination of still water and vertical wave bending loads, which implies that statistics of maximum bending moments are not available. From (a) and (b), it can be gathered that characteristic values of maximum sagging/hogging bending moments at probability level 1-1/nsW,T, equal to 0.848 in current analysis, are slightly higher for Ferry Borges and Castaneta than Poisson square wave model. In this respect, it is predictable that hull girder failure probability, based on the former method, will be slightly higher than the latter one.Statistical properties of time-variant hull girder sagging/hogging bending capacity are investigated by Monte Carlo simulation. In this respect, the minimum iteration number nmin is preliminarily determined based on having denoted by nreq(n) the required iteration number, depending on the confidence level p of hull girder capacity mean value and maximum percentage error E: COV(n) is the hull girder sagging/hogging coefficient of variation, while zc(p) is a coefficient derived by the normal distribution and depending on the assumed confidence level p. If Eq. is satisfied and Monte Carlo simulation is run for nmin iterations, the target function mean value will not differ more than E from the true one, with reference to probability level p. In actual analysis Monte Carlo simulation was performed by a dedicated programme developed in Matlab (), varying the iteration number from 100 up to 1500, for both sagging and hogging conditions, with reference to 95% confidence level, 1% percentage error and 25-year ship lifetime. Based on actual results reported in , n=1000 iterations are widely sufficient to satisfy the Driels and Shin (2004) rule. Hence, time-variant hull girder sagging/hogging ultimate bending capacities are reported in , with 2.5-year step. It is noticed that mean values and variation coefficients are time-invariant up to 7.5 years, due to coating protection. In all cases a z-test has been performed to check that hull girder capacity follows the normal distribution, as Lindeberg-Feller Central Limit Theorem cannot be applied when correlation among input variables exists (). Finally, frequency histograms and relevant best-fit normal distributions are reported in (a) and (b) for sagging and hogging capacities at 25-year ship lifetime. It is noticed that rule is applied to estimate the optimum bin size length:having denoted by IQR(x) the interquartile range of data set x and by n the iteration number.Time-variant sagging/hogging failure probability pf(t) is determined by Monte Carlo simulation:having denoted by n the simulation number and by I[g(xi,t)] the indicator function at time t with reference to the i-th data set:I[g(xi,t)]={0ifg(xi,t)>0(safedomain)1ifg(xi,t)≤0(unsafedomain)Hence, the failure probability standard error s is estimated as follows (In this respect, before performing reliability analysis, a preliminary convergence test is carried out, varying the iteration number from 106 to 1010 simulations, with reference to rule, Ferry Borges and Castanheta (FBC) and Poisson square wave (PSW) models, paying attention to truncate in any simulation negative values of sagging/hogging bending capacities that, in turn, are positive defined. Actual results, reported in for full load (sagging) and ballast load (hogging) conditions up to 7.5-year ship lifetime, suggest than 109 simulations are widely sufficient to achieve convergence in terms of failure probability. It is noticed that actual reliability analysis was performed by a dedicated programme developed in Matlab () that requires about 10 min to perform 109 simulations on a standard 16 GB RAM computer desktop.Time-variant annual failure probabilities and standard errors, based on Turkstra format ((a) and (b). Continuous and dashed lines refer to sagging and hogging conditions, respectively. Based on actual results, failure probabilities are constant up to 7.5-year ship lifetime and then they increase in time, reaching maxima equal to 1.803E-03 and 8.000E-04 for full load (sagging) and ballast load (hogging) conditions, respectively. Besides, failure probability in sagging is always higher than in hogging condition, while relevant percentage difference is almost time-independent. Similar outcomes can be stressed for the standard error distribution versus time.Time-variant annual failure probabilities and standard errors, based on FBC stochastic load combination format, are reported in (a) and (b). Continuous and dashed lines refer to full (sagging) and ballast (hogging) load conditions, as for the previously discussed case. Maximum values of sagging/hogging failure probabilities at 25-year ship lifetime are equal to 2.575E-02 and 1.624E-03 for full load (sagging) and ballast load (hogging) conditions. In both cases FBC load model provides higher failure probabilities, with reference to deterministic Turkstra rule.(a) and (b) report failure probabilities and standard errors for sagging/hogging conditions, based on PSW stochastic load combination model. Maximum values of sagging/hogging failure probabilities at 25-year ship lifetime are equal to 2.253E-02 and 1.297E-03 for full load (sagging) and ballast load (hogging) conditions. In both cases PSW load model provides slightly lower failure probabilities, with reference to the FBC one.Three different load combination methods, namely Turkstra rule, Ferry Borges and Castanheta (FBC) and Poisson square wave (PSW) models, have been applied to investigate the incidence of deterministic and stochastic load combination processes on hull girder reliability. Particularly, report a comparative analysis among hull girder sagging/hogging failure probabilities up to 7.5 and after 25-year ship lifetime. Based on actual results, maximum failure probability occurs for full load (sagging) condition, after 25-year ship lifetime. In this respect, Turkstra rule underestimates it, with reference to the PSW model, by about 20%, while the opposite holds true for FBC model that, in turn, overestimates it by about 15%. It is noticed that similar key features can be underlined for failure probability in ballast load (hogging) condition that is underestimated (overestimated) by about 38% (25%) by Turkstra rule (FBC model). Anyway, hogging failure probabilities are widely lower that sagging ones, which implies that they are unlikely to be dimensioning effective.Current trend confirms and extends to ship structures the main outcomes of previous researches carried out by , who indicated that Turkstra rule generally gives unconservative results, as regards probabilistic load combination models, and underestimates the failure probability of civil structures, such as buildings and bridges. This outcome, confirmed by current analysis, is also obtained by for a FPSO vessel. Besides, failure probabilities, based on FBC and PSW models, are each other comparable, even if the former always furnishes slightly higher failure probabilities as regards the latter. This difference is mainly due to the higher characteristic values of sagging/hogging total bending moments, based on FBC model, as regards the PSW one, as it can be also gathered by the probability functions reported in (a) and (b) for the oil tanker assumed as case study in current analysis. Nevertheless, it is well known that Turkstra rule has been widely applied in the past for reliability analysis of ship structures and calibration of partial safety factors for ultimate and residual strength check criteria of oil tankers and bulk carriers (). Hence, current results not only highlight that the choice of proper load combination method plays a fundamental role in the assessment of hull girder failure probability, but also that a slight re-calibration of partial safety factors may be needed, if Turkstra rule is replaced by probabilistic load combination models.Time-variant reliability analysis of a double hull oil tanker in intact conditions has been performed by Monte Carlo simulation, to investigate the incidence of deterministic and stochastic load combination methods on hull girder reliability. Particularly, three load combination models have been applied and compared. The former, embodied by IACS in the calibration process of ultimate and residual strength check criteria for oil tankers and bulk-carriers, is based on deterministic Turkstra rule, while the remaining two ones, namely Ferry Borges and Castanheta (FBC) and Poisson square wave (PSW) models, are based on a stochastic format for still water and total vertical bending moment extreme values. Time-variant sagging/hogging ultimate hull girder capacity has been preliminarily determined by Monte Carlo simulation, accounting for uncertainties due to corrosion wastages of all structural members contributing to hull girder strength, welding residual stresses and material properties randomness. Finally, reliability analysis has been performed by Monte Carlo simulation up to 25-year ship lifetime. The following main outcomes have been achieved:Improved edge functions for positive (shortening) and negative (lengthening) strains in platings of ordinary stiffeners have been applied and the main sources of uncertainties, mainly due to corrosion wastage, welding residual stresses and material properties randomness, have been considered in the assessment of hull girder ultimate strength capacity.Two limit state functions, the former based on IACS format with reference to deterministic Turkstra rule, the latter accounting for stochastic load combination among still water and vertical wave bending moments, have been formulated to provide uniform formats for reliability analysis.A comparative analysis among deterministic Turkstra rule and stochastic load combination methods, based on FBC and PSW models, has been performed to investigate the incidence of extreme value distributions on attained sagging/hogging failure probabilities. Actual results suggest that Turkstra deterministic format, embodied by IACS within the calibration process of partial safety factors for ultimate and residual strength check criteria of oil tankers and bulk-carriers, underestimates the failure probabilities by about 20%, with reference to PSW model. On the contrary, FBC model overestimates it by about 15%.Actual analysis highlights that the choice of load combination model plays a fundamental role in the assessment of hull girder failure probabilities. Hence, the correct estimate of still water and wave bending moment extreme value combination becomes a basic issue for a more reliable evaluation of hull girder ultimate strength. Even if actual results need to be further investigated, considering a representative sample of oil tankers and bulk carriers, it is conceivable that safety factors of ultimate strength check criterion, actually embodied in the Harmonized Common Structural Rules for Oil Tankers and Bulk Carriers (), need to be re-checked and eventually revised, regarding still water loads as exponential random processes, according to the Poisson square wave model, and applying a limit state formulation based on stochastic load combination of still water and vertical wave bending moment extreme value distributions.Supplementary data associated with this article can be found in the online version at Effects of gamma radiation sterilization and strain rate on compressive behavior of equine cortical boneGamma radiation has been widely used for sterilization of bone allograft. However, sterilization by gamma radiation damages the material properties of bone which is a major clinical concern since bone allograft is used in load bearing applications. While the degree of this damage is well investigated for quasi-static and cyclic loading conditions, there does not appear any information on mechanical behavior of gamma-irradiated cortical bone at high speed loading conditions. In this study, the effects of gamma irradiation on high strain rate compressive behavior of equine cortical bone were investigated using a Split Hopkinson Pressure Bar (SHPB). Quasi-static compression testing was also performed.Equine cortical bone tissue from 8 year old retired racehorses was divided into two groups: non-irradiated and gamma-irradiated at 30 kGy. Quasi-static and high strain rate compression tests were performed at average strain rates of 0.0045/s and 725/s, respectively.Agreeing with previous results on the embrittlement of cortical bone when gamma-irradiated, the quasi-static results showed that gamma-irradiation significantly decreased ultimate strength (9%), ultimate strain (27%) and toughness (41%), while not having significant effect on modulus of elasticity, yield strain and resilience. More importantly, contrary to what is typically observed in quasi-static loading, the gamma-irradiated bone under high speed loading showed significantly higher modulus of elasticity (45%), ultimate strength (24%) and toughness (26%) than those of non-irradiated bone, although the failure was at a similar strain.Under high speed loading, the mechanical properties of bone allografts were not degraded by irradiation, in contrast to the degradation measured in this and prior studies under quasi-static loading. This result calls into question the assumption that bone allograft is always degraded by gamma irradiation, regardless of loading conditions. However, it needs further investigation to be translated positively in a clinical setting.Bone fractures are a leading health problem with enormous social and economical consequences (). Bone allografts are widely used as a natural substitute to repair the defects in skeletal system such as bone fractures, spinal fractures and bone tumor. Due to its effectiveness and convenience, terminal sterilization of bone allografts by gamma radiation is very important to minimize disease transmission and infection (). However, the mechanical properties of gamma-irradiated cortical bone are affected by the destruction of collagen and it is made brittle by irradiation because of the destruction of collagen alpha chains (). Clinical findings have indicated that the rate of fracture in allografts sterilized with gamma radiation may be higher than that in non-irradiated allografts (). The degree of this destruction depends on dose of the radiation (). The dose employed in many of tissue banks is 30 kGy, with a tolerance of 5 kGy, which is sufficient to minimize any risk of disease transmission ( that there was no significant effect of gamma irradiation with a dose between 25 kGy and 35 kGy, there are numerous studies stating that gamma irradiation even at these doses significantly reduces the mechanical properties of allograft bone (As engineering materials, bone might also be subjected to high rates of loading in some instances such as sports accidents, traffic accidents involving vehicles, cyclists and/or pedestrians, falls from a height, sudden falls, gun shots and drilling processes in orthopedic surgery. The strength of bone is known to be dependent on the rate of loading and, over a range of loading rates consistent with normal physiological loads, the mechanical properties such as modulus of elasticity, yield strength, ultimate strength and toughness, vary modestly with rate (). Nevertheless, in high speed loading situations, ultimate strength can increase considerably while the ultimate strain, a measure of ductility, can decrease considerably (). However, there are contradictory results for modulus of elasticity in previous studies. While most studies indicated a significant increase in modulus of elasticity (), there are a few studies that indicated either smaller increase (Understanding the response of bone under high rates of loading is critical to accurately model mechanical behavior of bone, and to predict where and how bone injury might occur in case of sports or traffic accidents. For instance, development of computational models in predicting mechanical behavior of bone under high rates of loading is very important in some industries such as automotive (), sports, personal protective equipments and orthopedics (). Because, the success of the computational models is highly dependent on the bone models employed. While data exists for the mechanical behavior of non-irradiated bone at low and high strain rates to develop constitutive models, there is no data of gamma-irradiated bone at high strain rates since radiation-induced embrittlement of bone has only been studied for quasi-static and cyclic loading conditions. However, most clinical bone fractures occur under high speed loading conditions. In view of this, the present study is undertaken to examine the compressive behavior of gamma-irradiated cortical bone under high speed loading using a Split Hopkinson Pressure Bar (SHPB) and comparing compressive behavior to that of non-irradiated cortical bone. Quasi-static compression is also performed to compare the effects of gamma-irradiation on cortical bone in both quasi-static and high speed loadings.The SHPB, also called Kolsky bar, is the most commonly used method for determining the mechanical properties of various materials at high strain rates (). However, the SHPB has mainly been used to test metals, ceramics and other hard materials including cancellous (). One of the main problems in testing soft materials with the SHPB is the impedance mismatch between a soft material specimen and metallic bars. The introduction of polymeric bars in the SHPB apparatus () has overcome the impedance matching problem, thereby allowing proper reflection and transmission of strain wave by the specimen. Recent studies have shown that modifications to the traditional SHPB allow for the successful characterization of mechanical properties of soft materials including biological soft tissues at high strain rates that exceed alternate soft tissue testing techniques. In the last ten years, there have been several studies using modified SHPB for soft tissues such as muscle, ligament and brain (). Explanation of SHPB compression system and the equations of stress, strain rate and strain used for SHPB compression system are included in Cortical bone of larger animal species such as goat, sheep, cow, pig and horse is often used for comparative biomechanical studies () as it cannot be distinguished from human cortical bone due to their commonly shared secondary Haversian tissue microstructures when plexiform bone tissue is not present (). Particularly, there are distinct similarities in basic microstructure, and changes occurring in the microstructure between human and equine bone (). In our study, which is a comparative biomechanical study, fresh radius, metacarpal, tibia and metatarsal bones of eight years old retired racehorse (Veliefendi Hipodromu, Istanbul, Turkey) were obtained, and before compressive testing, its transverse section was examined to see if the plexiform bone tissue was present. A representative micrograph showing the transverse section of the equine cortical bone has been given in , the equine cortical bone has secondary osteonal growth with random arrangement of the Haversian systems and it has no plexiform bone tissue. The microstructure of the equine cortical bone also indicates that the Haversian systems and porosity have similar dimensions to those of human cortical bone.Specimen preparation consisted of the following stages: bones were first cleaned by removing excess soft tissue and their mid-shaft segments were taken out by cutting the proximal and distal epiphyses using a band saw machine (Promax PM-72151, Istanbul, Turkey). Each mid-shaft segment was further cut longitudinally into four pieces to produce anterior (A), posterior (P), medial (M) and lateral (L) beams. A table-top lathe (Quantum, D210×320, Germany) was used to machine the beams into 6 mm diameter round rods and the circumferential surfaces of the round rods were then polished by hand using a fine grid abrasive paper. The 6 mm diameter round rods were placed in a bone chuck of a low speed diamond saw (Struers-Minitom, Ballerup, Denmark) and parallel cuts were made along the longitudinal axis to obtain the 5 mm long compression testing specimens. During machining, the specimens were kept wet by a distilled water drip.After machining, each compression specimen was labeled to show whether it is obtained from left or right leg (L, R), its bone type (Rd: Radius, Mc: Metacarpal, Tb: Tibia and Mt: Metatarsal), and its quadrant (A: Anterior, P: Posterior, M: Medial and L: Lateral). For both quasi-static and high strain rate compression testing, there were two groups of specimens: non-irradiated and gamma-irradiated. Specimens were systematically assigned to the gamma-irradiated and non-irradiated test groups from either the right or the left bone of each pair such that specimens from the same diaphyseal location of left and right pairs served as matched pairs to avoid bias (). The gamma-irradiated specimens were kept wet frozen, were packed in polyethylene bags, and were surrounded with dry ice for shipment for gamma radiation sterilization by a commercial sterilizing vendor (TAEK, Ankara, Turkey). The specimens were gamma-irradiated at room temperature in oxygen and received an average dose of 30 kGy, which is commonly employed in tissue banks for allograft sterilization.All specimens were completely wrapped in Hank׳s balanced salt solution-soaked tissue paper, placed in airtight polyethylene bags and kept frozen at −20 °C until the day of testing. The specimens were removed from the freezer prior to testing and allowed to thaw at room temperature in Hank׳s balanced salt solution. All tests were carried out at room temperature and a distilled water drip was used to keep the specimens wet during testing. The apparent density of cortical bone is calculated as the mass of the bone divided by its bulk volume, including the volume associated with the vascular channels and porosity. The average apparent density of equine cortical bone samples was found to be 1.92 (±0.05) g/cm3, which is within the range for human cortical bone. The typical range of apparent density for human cortical bone is 1.80–2.00 g/cm3 (Quasi-static compression tests under displacement control at an average rate of 0.0045/s were performed with a custom-made testing machine specially designed for mechanical testing of low-strength materials at the Mechanical Engineering Department of Suleyman Demirel University in Isparta, Turkey. The custom-made testing machine was equipped with a 1000 kg load cell (Tedea Huntleigh MN:16, Malvern, USA) and two LVDTs of 10 mm stroke (Novotechnik Tr10, Germany) to measure the load and the corresponding displacement during testing. The LVDTs were attached to the lower loading platen and positioned on the upper loading platen at its nearest location to the sample using a custom-made fixture for deformation measurements (). The average deformation for each sample was calculated by averaging the readings from the two LVDTs and it was converted to strain using the sample thickness. Since the axial strain was calculated using the displacement of the upper loading platen relative to the lower platen at a point closest to the sample, the deformations in the load cell, test rig and in the overall machine structure were excluded to avoid an overestimation of the strain. Friction between the sample and compression platens was minimized by applying petroleum jelly on the surfaces of the upper and lower loading platens. A four-channel oscilloscope (Nicholet-Oddysey XE, USA) was used to record the measured data from both transducers. The modulus of elasticity was based on the slope of the initial linear portion of the stress vs. strain curve. Ultimate strain is the strain at the failure point on the stress–strain curve. However, it is well known that it is harder to identify the point of failure for a quasi-static compression test compared to a quasi-static tensile test since the specimen continues to carry the load even after it is fractured into pieces. In quasi-static tension, however, when fracture starts on the specimen, the load sharply drops to zero. In our study, strain vs. time and stress vs. time plots were jointly used to identify the failure point (). For non-irradiated and gamma-irradiated samples, after reaching the maximum stress, the strain vs. time curve changed its slope slightly with decreasing stress and had a plastic deformation, relatively little for gamma-irradiated samples. Then, a sudden stress drop and a strain jump occurred on the stress vs. time and the strain vs. time curves, respectively. The point corresponding to the strain jump and the sudden stress drop for both non-irradiated and gamma-irradiated samples was accepted as the failure point, and the strain corresponding to the failure point was accepted as the ultimate strain of the specimen.A Split Hopkinson Pressure Bar (SHPB) was employed to conduct high strain rate compression tests (). The apparatus comprises a striker, an incident and a transmitter bar made from high strength 7075-T6 Al alloy (nominal yield strength 500 MPa) and having a diameter of 19.05 mm. In the present tests striker bar of length 0.3 m was employed, while the incident and transmitted bars were 1.85 m and 1.60 m long respectively. It is very important that the specimen should be in dynamic equilibrium and deform uniformly during the testing. In order to ensure these conditions, a cardboard pulse shaper with a diameter of 4 mm and a thickness of 0.8 mm was placed on the impact surface of the incident bar. The striker bar is accelerated using an air operated gun. Before testing of bone specimens, dummy bone specimens were used to obtain a perfect alignment of the bars and proper impact velocity for the SHPB compression so that clean signals of strains on the bars without any distortions could be obtained. A pair of foil strain gages (Vishay, Micro Measurements BLH SR-4, FAE-12-100SX) was strategically attached on the incident bar while another pair of foil strain gages (Vishay, Micro Measurements BLH SR-4, FAE-12-100SX) was attached on the transmitted bar. These strain gages are used in conjunction with Wheatstone bridge circuits, the output of which is recorded on a digital oscilloscope (Nicholet-Oddysey XE, USA) to monitor the strain during the test. By using the data obtained from those strain gages, the stress, strain rate and strain values for the specimens were calculated using Eqs. . The modulus of elasticity was based on the slope of the linear portion of the stress vs. strain curve over the load range in which strain rate is nearly constant. In high strain rate compression of cortical bone, when failure starts on the specimen at about 60 µs of test duration, sharp changes occur on the reflected and transmitted bar signals (), which also coincide with the point of sudden stress drop (). Ultimate compressive strain is the strain at the failure point on the stress–strain curve, which also coincides with the point of the ultimate strength.The load–displacement data from quasi-static and high strain rate compressive tests were processed to calculate modulus of elasticity, yield strength, ultimate strength, yield strain, ultimate strain, resilience and toughness using custom written software in Matlab (Math Works, Natick, MA, USA). The strength values were obtained by dividing the load data by the cross-sectional area of each specimen. The strain values were obtained by dividing the displacement data by the initial length of the specimen. The stress value that a material can withstand before permanent deformation (non-elastic) occurs is called the yield strength. The 0.2% offset method was used to define the yield strength. The area under the stress–strain curve in the elastic region was used to determine the resilience and the total area under the stress–strain curve was used to determine the toughness.Statistical analysis was conducted using Minitab (Minitab, Inc., State College, PA). Results of the dependent variables (DVs) were expressed as mean and standard deviation (SD). The Anderson–Darling test was used to analyze the normal distribution of the DVs (P>0.05), and the test results indicated that all data sets of the DVs were normally distributed. After the data sets passed the normality test, they were analyzed with two-way analysis of variance (ANOVA), with mechanical properties as the DVs and the treatment and strain rate as the independent variables (IVs). The level of statistical significance was set at P<0.05. Multiple comparisons between the testing groups were made by Bonferroni-corrected t-test.Representative stress–strain curves obtained from quasi-static and high strain rate compression tests are shown in , and the test results are summarized in . Vertical bar charts with error bars of 95% Bonferroni Confidence Interval (CI) were used to display the mean values of the mechanical properties (a–d). The results of the statistical comparisons from post hoc tests were indicated on the vertical bar charts using letters. Means sharing the same letters are not significantly different (Bonferroni corrected t-test, adjusted P0.05, 6 <0.0085).As it is mentioned previously, it is very important that the specimen in SHPB testing should be in dynamic stress equilibrium and deform uniformly during the testing. To verify the dynamic equilibrium, the interface stresses σ1 and σ2 were calculated using Eqs. and the representative results are shown in . Since both curves of σ1 and σ2 almost coincide with each other, it can be concluded that the specimen is in a state of dynamic stress equilibrium. Strain rate vs. time curve in indicates that the constant strain rate was achieved at almost 20 μs, and remained constant up to 60 μs, which is the point of failure. The average strain was 727/s (±117/s) for the non-irradiated samples, ranging from 600/s to 850/s and 723/s (±126/s) for the gamma-irradiated samples, ranging from 575/s to 875/s.The modulus of elasticity was significantly influenced by the strain rate (p<0.05, ANOVA) and treatment (p<0.05, ANOVA). The modulus of elasticity was significantly greater for high strain rate testing compared to quasi-static testing in both treatment groups (P0.05/6<0.0085, t-test, a). More importantly, it was significantly increased with irradiation at high strain rate (P0.05/6<0.0085, t-test) but was not significantly affected by irradiation at low strain rate (P0.05/6>0.0085, t-test) (The yield strength was significantly influenced by the strain rate (p<0.05, ANOVA) but was not influenced by the treatment (p>0.05, ANOVA). The yield strength was significantly greater for high strain rate testing compared to quasi-static testing in gamma-irradiated treatment group (P0.05/6<0.0085, t-test) but was not significantly changed in non-irradiated treatment group (P0.05/6>0.0085, t-test). More importantly, it was not significantly affected by irradiation at high strain rate (P0.05/6>0.0085, t-test) but was significantly decreased with irradiation at low strain rate (P0.05/6<0.0085, t-test).The ultimate strength was significantly influenced by the strain rate (p<0.05, ANOVA) and treatment (p<0.05, ANOVA). The ultimate strength was significantly greater for high strain rate testing compared to quasi-static testing in both treatment groups (P0.05/6<0.0085, t-test, b). More importantly, it was significantly increased with irradiation at high strain rates (P0.05/6<0.0085, t-test) but was decreased with irradiation at low strain rates (P0.05/6<0.0085, t-test) (The yield strain was significantly influenced by the strain rate (p<0.05, ANOVA) but was not influenced by the treatment (p>0.05, ANOVA). The yield strain was significantly lower for high strain rate testing compared to quasi-static testing in gamma-irradiated treatment group (P0.05/6<0.0085, t-test) but was not significantly changed in non-irradiated treatment group (P0.05/6>0.0085, t-test). It was not significantly affected by irradiation at both strain rate groups (P0.05/6>0.0085, t-test).The ultimate strain was significantly influenced by the treatment (p<0.05, ANOVA) but was not influenced by the strain rate (p>0.05, ANOVA). The ultimate strain was significantly lower for high strain rate testing compared to quasi-static testing in non-irradiated treatment group (P0.05/6<0.0085, t-test) but was not significantly changed in gamma-irradiated treatment group (P0.05/6>0.0085, t-test) (c). More importantly, it was not significantly affected by irradiation at high strain rate (P0.05/6>0.0085, t-test) but was significantly decreased with irradiation at low strain rate (P0.05/6<0.0085, t-test) (The resilience was significantly influenced by the strain rate (p<0.05, ANOVA) but was not influenced by the treatment (p>0.05, ANOVA). The resilience was significantly greater for high strain rate testing compared to quasi-static testing in non-irradiated treatment group (P0.05/6<0.0085, t-test) but was not significantly changed in gamma-irradiated treatment group (P0.05/6>0.0085, t-test). It was not significantly affected by irradiation at both strain rate groups (P0.05/6>0.0085, t-test).The toughness was significantly influenced by the strain rate (p<0.05, ANOVA) but was not influenced by the treatment (p>0.05, ANOVA). The toughness was significantly greater for high strain rate testing compared to quasi-static testing in gamma-irradiated treatment group (P0.05/6<0.0085, t-test) but was not significantly changed in non-irradiated treatment group (P0.05/6>0.0085, t-test) (d). More importantly, it was significantly increased with irradiation at high strain rate (P0.05/6<0.0085, t-test) but was significantly decreased with irradiation at low strain rate (P0.05/6<0.0085, t-test) (Agreeing with most of the previously published results on the embrittlement of cortical bone when gamma-irradiated, the quasi-static results showed that gamma-irradiation significantly decreased ultimate strength (9%), ultimate strain (27%) and toughness (41%), while not having significant effect on modulus of elasticity, yield strain and resilience. As has been previously outlined, equine cortical bone is primarily composed of mineral and collagen, with mechanical properties determined primarily by the amounts, arrangement, and molecular structure of these primary constituents. Collagen structure is altered by gamma-irradiation (), resulting in significant reductions in post-yield (plastic) properties such as ultimate strength, ultimate strain and toughness, rather than the pre-yield (elastic) properties such as modulus of elasticity, yield strength and yield strain (). During loading into the plastic region for non-irradiated bone, intact collagen fibers provide a bridging and reinforcement function to the bone matrix. However, for gamma-irradiated bone, collagen fibers fail to provide bridging at the ultra-structural level, which indicates that when the integrity of the collagen matrix is damaged by gamma-irradiation, individual molecules collapse under loading (More importantly, contrary to what is typically observed in quasi-static loading, the gamma-irradiated cortical bone samples under high speed loading showed significantly higher modulus of elasticity (45%), ultimate strength (24%) and toughness (26%) than those of non-irradiated samples, although the failure was at a similar strain. Collagen has been shown to increase in modulus of elasticity and become more brittle with increasing strain rate, while the mineral phase is expected to have minimal viscoelastic response due to its very ceramic-like nature (), and also due to the rapid nature of the loading rate that has no time for peripheral damage to stably form (). In gamma-irradiated cortical bone, collagen is damaged to the extent that it is present within the bone, but it is functionally irrelevant. Since our results have shown that gamma-irradiated bone performs better than non-irradiated bone at high strain rate, the functional absence of collagen seems to be increasing the fracture resistance at high strain rate, which indicates that, in traumatic loading conditions, bone allograft may not necessarily be the weaker component. However, this result needs to be confirmed by other studies that will include damage analysis and will investigate which mechanisms could be behind it. To our knowledge, no previous work has been carried out on the mechanical properties of gamma-irradiated cortical bone under high speed loading. Therefore, no direct comparison with previous results could be performed. However, dry vs. wet bone is a good example of this behavior as both the dry and wet bone samples exhibit increase in modulus of elasticity and strength with increasing strain rate, and the dry bone, more brittle than wet bone, exhibits higher modulus of elasticity and fails at higher stresses than the wet bone (Non-irradiated cortical bone under high strain rate loading demonstrated significant differences in modulus of elasticity (19% increase), ultimate strength (20% increase), resilience (30% increase) and ultimate strain (20% decrease), while not having significant differences in yield strength, yield strain and toughness compared to those of non-irradiated cortical bone under quasi-static loading. gives the comparison of some mechanical properties of non-irradiated cortical bone between quasi-static and high strain rate compression in the current and previous studies. Applied high strain rates in the previous studies varied between 100/s and 1500/s, and the comparison results of the current study are consistent with those of the previous studies (), which may also support the validity of the results of this study for gamma-irradiated cortical bone under high speed loading. Comparing to quasi-static results, ultimate strength is higher in all of the studies, modulus of elasticity is higher in all except the study by , and ultimate strain is lower in the studies reporting ultimate strain. The current study also supports the phenomena that have been previously reported (). In particular, the results from the SHPB compression showed there is a complete loss of load carrying ability under high speed loading. Typically, the load fell to zero at a rate similar to the rate at which the load increased (). In contrast, quasi-statically loaded samples typically sustained substantial compressive loads () beyond the deformations associated with ultimate stress (There are several limitations to this study. First, all specimens were tested under compressive loading up to failure; no tension and torsion testing were performed to investigate the effects of gamma irradiation sterilization on high strain rate properties under those loading conditions. Second limitation is that all specimens of high strain rate testing, gamma-irradiated and non-irradiated, were tested at an average strain rate of 725/s. Further studies might be useful to confirm the results of this study by testing the specimens under various high strain rates ranging from 100/s to 1000/s. Third limitation is that equine cortical bone was used instead of human cortical bone. However, regardless of animal model, cortical bone has similar constituents at molecular size scale, collagen, mineral, non-collagenous proteins and proteoglycans. If the gamma irradiation did not affect one of these constituents – or interactions between them – at equine cortical bone, we do not expect the gamma irradiation to behave differently for human cortical bone. While equine bone, as other animal bones, may closely represent the mechanical and physiological human clinical situation, it must be remembered that it is only an approximation. Use of the data from animal studies should therefore focus more upon the effects of change in structure and composition on mechanical properties as opposed to using the data as a substitute for the properties of human bones (). Additional experiments might be required to extend these findings of equine cortical bone to human cortical bone. gives the comparison of some mechanical properties of non-irradiated equine cortical bone in the current study with those of non-irradiated equine and human cortical bones in the previous studies. Modulus of elasticity and ultimate strength of human cortical bone in the previous studies cover a wide range of values, and the modulus of elasticity of equine cortical bone remains in that range. However, the ultimate strength and ultimate strain of equine cortical bone are generally higher than those of human cortical bone in most other studies (). It should be remembered that the mechanical properties of bone not only vary from one species to another, but also for similar bones, or even within a same bone, which reflect local structural variations. Finally, the comparisons between the two strain rates using two different test methods may also be thought of as a limitation. However, when the effect of strain rate on materials׳ mechanical properties is investigated, it is not always possible to use the same testing machine, or test method, for all strain rates from low to high, and in most of previous studies, SHPB was used for high strain rates while hydraulic and electromechanical testers were used for low strain rates.Despite these limitations, the results of this study have several scientific implications rather than direct clinical implications. First, this study suggests that the numerical models involving bone model need to be modified to accurately reflect bone׳s mechanical behavior at high strain rates if it was sterilized with gamma-irradiation. Second, probably the most important, the results of this study call into question the assumption that bone allograft is always degraded by gamma irradiation, regardless of loading conditions. Under high speed loading, the mechanical properties of bone allograft were not degraded by irradiation, in contrast to the degradation measured in this and prior studies under quasi-static loading. However, it needs further investigation to be translated positively in a clinical setting.In a SHPB compression system, two symmetrical bars are situated in series, with the specimen between (). The first bar is the incident bar, which is struck by a striker bar during testing. The striker bar is fired from an air gun. The second bar is the transmitted bar, which collides with a stopper. By striking to the end of incident bar, a compressive stress wave is generated that immediately begins to travel towards the specimen. Upon arrival at the incident bar–specimen interface, the wave partially reflects back to the impact end. The remainder of the wave transmits through the specimen into the second bar causing deformation in the specimen (). If the two bars remain elastic and wave dispersion ignored, then the measured stress pulses can be assumed to be the same as the one acting on the specimen. Incident and transmitted bars were made of the same material with equal cross-sectional areas. In the equations below (), the following notations are used: incident (I), transmitted (T), reflected (R), specimen (s), density (ρ), modulus of elasticity (E), wave speed (c) and cross-sectional area (A) of the bars and the cross-sectional area (As) and length (l0) of the specimen (If the specimen deforms uniformly, the strain rate ε̇s is calculated asThe velocity at interface 1 and interface 2 can be written as followsBy substituting these interface velocities into equation Stresses at the ends of the specimen areIf the specimen is in dynamic stress equilibriumThen the stress, strain rate and strain are given bySome applications of analytical TEM to the characterisation of high temperature equipmentMuch of the high temperature refinery and power generation equipment currently in use in Australia is typically quite old. In many cases plant has been operating for over 20 years, and in a few cases, for 40+ years. Understanding and predicting the behaviour of service-exposed equipment, which has operated at high temperatures and pressures for extended periods, requires a detailed understanding of the material microstructures and properties. Remaining life assessment of aged plant brings to bear a raft of techniques to measure mechanical properties and to look for damage effects. Analytical transmission electron microscopy (AEM), while not a traditional tool for looking at such problems, can provide some useful insights into the microstructural degradation processes which can occur during service, such as carbide coarsening, secondary precipitation and transformation. This paper will highlight some of the potentially useful information which AEM can provide, along with some of its limitations, with reference to refiner pressure vessels, turbine generating rotors, and superheater outlet headers.The critical components of large power generation, chemical and refinery plant, operate at high temperature and pressure. Failure of such components in service may lead to loss of life and severe financial losses. Much of the pressure equipment currently in use in Australia is quite old. For example, over 50% of Australian power generating turbine rotors are over 20 years old (Maintaining, repairing and replacing these critical components requires information on the properties, the structural integrity and the microstructure. A range of low alloy steels have been utilised in pressure systems including 1.25Cr–0.5Mo, 2.25Cr–1Mo and 1Cr–1Mo–0.25V (). Chromium alloying additions afford improved scaling resistance, while Mo and V promote creep resistance through solid solution strengthening and carbide formation (). These carbide microstructures are metastable, and prolonged exposure to high temperatures and stress promotes the coarsening, secondary precipitation and transformation of carbides (). This contributes to long-term changes in the mechanical properties (A diverse range of techniques has been applied to the study of in-service materials such as ultrasonic, creep and toughness testing. While analytical transmission electron microscopy (AEM) is not a tool traditionally used in such investigations, it can provide a wealth of information. This includes grain size, the degree of grain boundary coverage with carbides, depleted zones and the nature and disposition of such carbides (. While this information cannot be directly related to remaining life, it may allow the extent of degradation to be qualitatively assessed. This can be correlated with other information such as creep data and may help explain any anomalies or inconsistencies. In the present work AEM has been used to study three pressure vessel systems: a steel destined for refiner pressure vessel service, seven in-service and retired turbine generating rotors and seven superheater outlet headers.Material from the 1.25Cr–0.5Mo refiner pressure vessel steel was in the form of a weld qualification test block. Sections were heat treated at 670, 690 and 710°C for 8 h. TEM specimens were prepared by a single stage replication technique. Charpy toughness testing and extraction of carbides for quantitative X-ray diffraction (XRD) analysis was also performed. Seven 1Cr–1Mo–0.25V turbine rotors were replicated in situ using a two stage replication technique. Replication was performed on the outer edges of rotor disks near the blade root fixings at regions corresponding to steam inlet (hot≈540°C) and steam exhaust (cold≈350°C) sections. Small sections were excised across welds of seven 2.25Cr–1Mo superheater outlet headers ostensibly for creep testing. Material was metallographically examined and replicated using a single stage technique. TEM examination was carried out using a JEOL 2000 FXII fitted with a calibrated energy dispersive X-ray (EDX) analysis system.AEM was used to understand the influence of post-weld heat treatment on the vessel microstructure prior to service. The stability of the carbide phases formed during heat treatment influences the susceptibility to subsequent carbide gasification by dissolved hydrogen (hydrogen attack). The amount of Mo remaining in solid solution after heat treatment is a key factor influencing the migration of tramp elements, most notably P, to grain boundaries, which can lead to temper embrittlement. The vessel was designed for hydrogen service at a maximum temperature of 549°C and a pressure of 2.56 MPa. The aim was to optimise the heat treatment temperature (within allowable guidelines), to minimise subsequent hydrogen attack and temper embrittlement susceptibility. This entailed maximising the formation of thermodynamically stable Fe and Cr carbides while avoiding excessive precipitation of Mo-rich phases.Full details of the materials and testing procedures can be found elsewhere (). Through-plate hardness measurement showed significant variation ( through the 10 cm wall thickness, and this was also reflected in the microstructure. The plate surface comprised bainite while the plate interior was a mixed ferrite/bainite (). Such microstructural variations are the result of differing cooling rates from the austenitising temperature.Carbides were selected at random and quantitatively analysed in the parent plate, heat affected zone (HAZ) and weld of the as-received and the three heat treated materials. Quantitative XRD of extracted carbides enabled assessment of carbide populations. Typical parent plate and HAZ microstructures are shown in , respectively. Significant microstructural differences were not apparent amongst the materials heat treated at the three different temperatures. However, compositional analysis did show a shift from almost exclusively Fe-rich M3C in the as-received parent plate, to a mixed population of M3C and M23C6 in the material heat treated at 710°C. Very limited M6C was found, and limited amounts of M2C was present within the ferrite grains of the parent plate [contained too few carbides to be statistically representative of the carbide populations. However, the quantitative XRD analysis ( showed that >90% of carbides were M3C, irrespective of region and heat treatment. By combining the carbide population statistics derived from XRD, with the average carbide compositions derived from AEM, it was possible to deduce the disposition of the various alloying elements in both the matrix and the carbide phases. Of concern was the loss of Mo from solid solution, due to precipitation of Mo-rich carbides, notably M2C, and the amount of Cr enrichment in the carbide phases. These parameters influence temper embrittlement and hydrogen attack susceptibility respectively (discussed later).Extensive M2C precipitation was not encountered at any heat treatment temperature. The Mo retained in solid solution within the ferrite matrix of the parent plate (as a percentage of the total Mo in the alloy) varied by only 7%, across the three heat treatments, and the variation for the weld was only 5%. The 690°C treatment of the parent plate resulted in the highest Mo fraction (77% of total Mo) remaining in solid solution (). Total carbide Cr levels were highest for the two highest heat treatment temperatures, and very similar values were obtained for the respective parent plate and weld regions (Hardness data (not shown) indicated that the hardness differential between the hardest region (HAZ) and the softest (parent plate) was lowest in the material heat treated at 690°C. This was deemed to be the optimum heat treatment temperature, for reasons discussed later. The suitability of this treatment was further evaluated by comparison of the fracture appearance transition temperature (FATT) derived from Charpy toughness tests of optimally heat treated material and material which had been given an embrittling heat treatment [Gould cycle ()] following optimum heat treatment. This yielded FATT values of −35±5°C for the optimally heat treated material, and −30±5°C for the embrittled material.Time in service for the rotors studied here varied between 58,000 and 150,000 h. Compositional data from test certificates was absent, and all rotors were of nominally similar composition (1Cr–1Mo–0.25V(1CMV)), though came from UK, German and Japanese manufacturers. Historical operational data was not available, though nearly all design temperatures were ≈540°C. The absence of accurate operational data for older equipment is not at all uncommon, and imposes major difficulties in accurate life assessment (). Typical steam inlet temperatures at the ‘hot’ end of the HP rotor were ≈540°C, while steam exhaust temperatures were ≈350°C at the ‘cold’ end. As rotors are precision balanced and highly stressed, excision of material was not possible, and non-destructive evaluation techniques were mandatory. Full details are given elsewhere (Despite their large size, segregation effects along and across the surface of the rotor were not evident in replicas. Comparison was made between the cold ends of the rotors and the hot ends. It was assumed that the cold end being at ≈350°C would not be heavily modified by such a low temperature. Microhardness measurements ( indicated that service exposure caused up to 7% softening in the hot sections of the rotors relative to the respective cold ends. Optical microscopy failed to show any microstructural differences, and the superior resolution of AEM was required to observe the subtle changes taking place.show the microstructure of the cold and hot sections a rotor after 136,000 h of service. The cold section [] showed an upper bainitic microstructure, containing a large population of blocky or lath-like Fe-rich M3C carbides ≈1 μm wide. Also apparent were prior austenite grain boundaries (PAGBs) delineated by features arising from failed extraction of slightly larger carbides. The hot section microstructure [] was very similar to the cold, except for the presence of a background of fine scale carbides. This was the only significant difference between the hot and cold sections of all rotors examined. The fine scale carbides [] comprised small (20–50 nm) square platelets of V-rich MC as well as short rods (20–50 nm) of Mo-rich M2C. Also present were occasional H-type carbides, comprising M2C ‘wings’ on a MC core [EDX was used to characterise the carbides. Carbide compositional and diffraction information in the literature (), combined with compositional and morphological data here, permitted unambiguous identification of carbides. Of all the carbide types, only M3C showed a significant change in composition as a function of time. Analysis of a wide range of M3C particles showed the composition to be insensitive to particle size, within the range examined. Service exposure-induced Cr enrichment occurred at the expense of Fe in the hot section M3C []. These trends were linear when plotted as function of √time and indicate a diffusion-controlled process. The relationship for Mn enrichment in M3C contained one set of outlying data (arrowed). This was from a rotor which showed consistently unusual behaviour. The relationship (excluding the outlier) was (R=correlation coefficient):The use of time-temperature parameters, such as the Larson–Miller Parameter (LMP), incorporates both the effects of time and temperature. However, application to the current data was not successful, owing to the reliance upon design temperature data here, due to an absence of operational data. The critical dependence of LMP on temperature caused large scatter when used with design temperatures.Typical header dimensions may be 1 m diameter, 10 cm wall thickness, by >10 m in length. Headers operate at typical steam outlet conditions ≈540°C and ≈13 MPa. Issues of concern to structural integrity are primarily creep-related. Material was excised in the form of one or more prismatic sections typically 4 cm long×1 cm×1 cm and incorporating weld, HAZ and parent material to permit metallographic examination, and creep specimen fabrication. Creep data from these investigations is highly commercially sensitive, and is not reported here. Replicas were prepared from the polished sections using a single stage technique. Seven headers were examined, spanning the as-installed (virgin) condition through to 190,000 h of service, with full details being given elsewhere (). All headers were generically 2.25Cr–1Mo, though one header (119, 000 h exposure) did contain a much higher Cr-level than typical (2.41%Cr).Perhaps of greatest interest was the microstructure. All headers comprised a mixed ferrite/bainite microstructure. The virgin header bainite contained a mixture of M23C6 and M7C3 [, while the ferrite contained a fine dispersion of short rod-like M2C. Some precipitation along prior austenite grain boundaries was apparent, with very narrow (≈0.5 μm) adjacent denuded zones. The level of microstructural degradation increased with service exposure. Comparison with the most thermally aged material (190,000 h) showed dramatic differences, with large faceted M6C carbides within the bainite, and highly elongated M2C needles within the ferrite []. Most prominent was the development of a very wide (≤5 μm) denuded zone along the PAGBs, caused by dissolution of the M2C in the ferrite.Carbides were identified on the basis of composition () and when plotted on a ternary diagram, the transformation of a parent plate bainitic carbide population of predominantly M7C3 and M23C6 to one of M7C3 and M6C was apparent (. Compositional trends with time were studied for all carbide types in the parent, HAZ and weld, and several interesting compositional trends were observed as a function of √time [see for full details]. Ferritic M2C in the parent plate ( showed significant Mo enrichment at the expense of Cr, with a parabolic time dependence. The relationship was:) is for a header with much higher Cr levels (2.41wt%) than the other headers.Low alloy steel forged and welded structures enter service with a microstructure that is metastable. Carbides which precipitate during normalisation or quenching are the kinetically favoured species, and are Fe-rich. However, during post-weld heat treatment, and subsequent service, these carbides transform into more thermodynamically favoured species (). The driving force for this change is the greater thermodynamic stability of alloying element carbides compared with Fe-rich carbides, according to the following sequence: Fe<Cr<Mo<V (). As well as transformation and coarsening of existing carbides, nucleation and growth of new carbides can occur. These microstructural modifications can lead to changes in mechanical properties.Had the 1.25Cr–0.5Mo pressure vessel material examined here been a vessel in service, then only the external surface would have been accessible for replication. This would have revealed a fully bainitic microstructure, which was largely unrepresentative of the bulk of the material (). This is a limitation of non-destructive surface techniques, such as replication, when applied to thick-walled vessels.The main damage effects of concern in this instance are temper embrittlement and, to a much lesser degree, hydrogen attack. The former problem is the result of migration of tramp elements such as P to grain boundaries. Modern steel making practice largely excludes many such tramp elements. However, the disposition of Mo in the alloy remains crucial as it scavenges P from solid solution, thereby impeding its migration to grain boundaries. Embrittlement phenomena in Cr–Mo steels have been the subject of several reviews (e.g. ). AEM demonstrated that 1.25Cr–0.5Mo steel used here was relatively insensitive to microstructural variation within the range of heat treatment conditions used. The absence of extensive M2C precipitation is important, not only in terms of Mo loss from solid solution and subsequent temper embrittlement susceptibility, but also in terms of creep embrittlement. Extensive M2C precipitation within the grains strengthens them with respect to the grain boundaries and near-grain boundary regions, which may be denuded of this carbide. This localises creep strain to these regions and reduces creep ductility (Although qualitative assessment of the types of carbide present in 1.25Cr–0.5Mo can be made using AEM (), the sampling statistics are too poor for quantitative assessment and quantitative XRD is required. A broad range of compositions has been reported for the various of carbide types (). The present compositional data derived from AEM enabled accurate assessment of Mo levels, since measured compositions differed slightly from the ‘typical’ values (). The AEM technique demonstrated a lack of microstructural sensitivity of 1.25Cr–0.5Mo to heat treatment temperature. The choice of 690°C as the optimum heat treatment temperature was made on the basis of producing: the highest Mo levels remaining in the solid solution to resist temper embrittlement; high carbide Cr levels to resist hydrogen attack; low hardness mismatch values across the weld to produce desirable mechanical properties. After heat treatment at this temperature, a subsequent embrittling heat treatment resulted in very small changes in FATT (+5°C). This suggests that resistance of the pressure vessel to temper embrittlement in service will be excellent.The 1CMV turbine rotor could only be surface replicated as material removal was not possible. Surface replication indicated the microstructure to be upper bainite. However, the core of the rotor would be mixed ferrite/bainite (). One of the most critical regions of a rotor from a remanent life viewpoint is the interior of the hollow bore, as it is here where creep cracking can initiate (). This region is inaccessible to the AEM technique, and so it cannot be applied for such assessments. The present rotor work was undertaken to understand in-service carbide changes and identify any features which may be potential indicators of time at temperature. The microstructural changes observed were very limited, although some carbide compositional change in the M3C was found. The challenge which remains is to relate this compositional variation with other rotor parameters such as toughness etc, so that an end-of-life criterion can be defined. Only one of the seven rotors examined here had been retired, and this was on efficiency rather than structural integrity grounds.In a similar vein to the rotor work, assessment of superheater headers was carried out. For these structures remaining creep life is a critical factor. Microstructural assessment of the parent plate showed very significant change with time at temperature, notably extensive M2C development in the ferrite and M6C growth in the bainite upon aging []. 2.25Cr–1Mo has been very widely studied and carbide transformation sequences have been well documented, albeit primarily through accelerated testing at elevated temperatures, e.g. . Data such as this from ex-service material with very prolonged exposures, is useful in that it removes the uncertainties of extrapolation inherent in accelerated testing. The microstructural degradation seen in the more aged materials was of such an extent that it permitted qualitative assessment of the extent of microstructural degradation. For instance the most aged header (190,000 h) [] would be expected to have extremely poor creep properties owing to the very extensive grain boundary denuded zones and the highly developed M2C in the ferrite. The creep rupture life for this header (data not shown) was an order of magnitude shorter than that of the next longest exposure header in this study (119,000 h), which showed far less evidence for microstructural degradation.This study identified a range of parameters which change with time at temperature: degree of PAGB precipitation, the width of the associated denuded zone, nature of M2C in ferrite, general carbide makeup, and carbide compositional parameters. In a comparative study such as this it is possible to rank headers according to their degree of degradation. This qualitative ranking has also been supported by creep data (not shown). The importance of AEM in this context, is that it provides a microstructural basis for understanding other properties, such as creep. This can be particularly important where creep data show unusual trends, or trends which are difficult to explain. In view of the cost and time necessary to carry out creep testing, such supporting data can be quite valuable. Carbide compositional parameters (e.g. ) also enable a quantitative measure of time at temperature. Enrichment processes found here are of a similar nature to those found in accelerated test results (). However, the present data are derived from service exposed material, and so the kinetics of enrichment are directly applicable to in-service material. The key issue remaining is to link such parameters with a readily defined end-of-life criterion, such as a remaining creep life falling below a certain threshold. There is certainly scope for more work in this area.AEM can provide a detailed understanding of the microstructure and composition of low alloys steels. In the case of a 1.25Cr–0.5Mo steel, AEM permitted the optimum post-weld heat treatment temperature to be defined, by showing that within the range of heat treatment temperatures used, the microstructure and fraction of Mo and Cr remaining in solid solution was relatively insensitive to heat treatment temperature. The optimum heat treatment temperature selected led to maximum retention of Mo in solid solution, a carbide product rich in Cr and a minimum hardness variation across the weld/HAZ/parent plate. Embrittlement and subsequent toughness testing demonstrated that excellent resistance to temper embrittlement was obtained.1Cr–1Mo–0.25V rotors service exposed for up to 150,000 h showed very limited microstructural changes. However, M3C did show a compositional change with time at temperature, and this may have some potential application in remanent life assessment.2.25Cr–1Mo superheater outlet headers, service exposed for up to 190,000 h, showed quite significant microstructural changes. The most severely degraded materials showed obvious features such as coarse M2C and grain boundary denuded zones. Carbide compositional parameters which change with time at temperature have also been identified. Combined, these features permit a qualitative assessment of degree of degradation. This can be an invaluable when interpreting results from other assessment technique such as creep testing. As with the rotor studies, correlation of the present data with well defined end-of-life criteria is highly desirable.Selective laser sintering and multi jet fusion: Process-induced modification of the raw materials and analyses of parts performanceAdditive manufacturing (AM) is a rapidly expanding framework of production technologies evolving in different directions, following the needs of different industries. Among powder bed fusion technologies, one of the main branches of AM, selective laser sintering (SLS) is the second oldest one. In the last few years, a direct rival has emerged: multi jet fusion (MJF). The purpose of this work is to compare these processes throughout a systematic analysis of powder and final parts made of commercially available polyamide 12 (PA12). Differences have been spotted both on the molecular and powder scale, with end capping of the MJF feedstock together with different thermal properties of the new and recycled materials. On the other hand, flowing properties are similar among the two virgin and recycled powders, with only a significant change in the fraction of fines for SLS material. The parts produced through SLS exhibit higher Young's modulus but lower elongation at break and ultimate tensile strength if compared to the ones obtained using MJF. This confirms once more that the occurrence of postcondensation has a profound influence on the final properties. Also Charpy impact strength according to ISO 179 has been tested, confirming the literature data for SLS, but also showing higher strength in the out-of-plane direction for un-notched specimens coming from MJF. Finally, the evaluation of advanced area roughness parameters such as surface roughness, skewness and kurtosis according to ISO 25178 allows the ascertainment of subtle differences arising in parts with different positioning on the build platform, possibly due to the inks employed in the MJF process.Additive manufacturing (AM) refers to advanced production methods that enable direct fabrication of parts through conversion of 3D models into real objects in a layer-wise manner, that is building layer upon layer by depositing material only where actually needed. In comparison with traditional manufacturing technologies, the waste of raw material using AM is diminished but still post-processing with subtractive methods is required to obtain final parts. AM is now available for many material classes, including metals, polymers, ceramics and composite materials.Among the available AM technologies for service providers, selective laser sintering (SLS) is the third most common, surpassed only by stereolitography and fused deposition modeling (a)) followed by illumination and melting with a CO2 laser of specific regions of the powder bed ((b)). These regions represent the cross-sections of the 3D object itself, stacked upon each other until the final part is completed ((c)). After its extraction from the unmolten powder cake, the unsintered feedstock can be further reused after the addition of certain amounts of virgin powder Nowadays, polyamide 12 (PA12) is the most commonly used material for selective laser sintering, with a market share above 90% (not stechiometrically correct). It also comes from the same source (Evonik, Marl, Germany) and is indirectly conveyed to the final customer by the machine suppliers with different trade names (Duraform, PA2200, etc.) For this reason, this material was chosen for a process comparison between selective laser sintering and multi jet fusion, a proprietary technology of Hewlett-Packard, first presented in 2014. Although the powder recoating is the same as in SLS ((d)), MJF is characterized by the use of two inks, respectively named fusion and detailing agent. The former is jetted by an ink-jet printhead exactly where the powder needs to be molten, while the latter is used around the part edges to absorb heat and thus reduce thermal bleeding and improve dimensional accuracy. This way, only the powder particles impregnated with the fusing agent melt when an IR lamp is moved at a given speed across the powder surface along the Y axis of the machine ((e)). This contrasts with the time-consuming laser scanning of the parts that happens in LS, in which parts complexity leads to higher layer time with respect to MJF. Afterwards, the powder recoating is repeated from the other direction along the X axis of the machine for the following layer ((f)). According to HP, MJF is up to ten times faster than Fused Deposition Modeling (FDM) and SLS Scope of the current work is thus to compare these two additive manufacturing technologies based on powder-bed fusion, with a combined and equal set of analyses on both feedstock and final parts. In order to obtain meaningful results, the investigation is focused on a single material type (PA12). Although partially similar, the two processes use very diverse illumination/melting (laser vs. IR lamp) and recoating (roller vs. blade) strategies, and also the powder bed temperature is different. For these reasons, plus the presence of the inks in the MJF process, the analyses of new and used powders are extremely important to ascertain their recyclability and reusability, a key point for industrialization of these technologies. A further novelty introduced by the current work are the areal parameters for surface characterization on MJF specimens, that give a better approximation in comparison with “traditional” line parameters.This study was carried out both on powders and printed parts from SLS and MJF processes using commercially available polymers. 3D Systems Duraform PA12 (short: DF) was bought from 3D System (Rock Hill, SC, USA), HP 3D High Reusability PA12 (short: HP3D) was purchased from Hewlett-Packard (Palo Alto, CA, USA). Both materials were used as received, and powder characterization was carried out both on virgin (short: DF-N, HP3D-N) and recycled (short: DF-R, HP3D-R) materials, with refresh ratio 50:50 for DF and 20:80 for HP3D (new:recycled). A fifth sample, HP3D-AA (artificially-aged), was produced in order to assess the molecular weight change according to the following procedure: 20 g of HP3D-N were placed in oven and subjected to 72 h of isothermal heating at 150 ± 2 °C under nitrogen atmosphere, followed by slow cool-down for 16 h.All powders were characterized according to various methodologies. Particle size and shape distributions was obtained through laser diffraction and/or optical microscopy. Thermal properties were evaluated using differential scanning calorimetry. A Revolution Powder Analyzer was used to assess the spreadability behavior while the molecular weight was calculated using gel permeation chromatography/size exclusion chromatograpy.Differential Scanning Calorimetry (DSC) measurements were carried out on a DSC 25 (TA Instruments – New Castle, DE, USA) with sample weights between 5 and 10 mg under nitrogen flow. Samples were heated from 25 °C to 250 °C, cooled down to 25 °C and again heated up to 250 °C. All the steps were executed with a rate of 10 °C/min, and the DSC curves were recorded and integrated for the peak onset and enthalpy. The percentage crystallinity (Xc) was calculated using Eq. , with ΔHm = 209.3 J g−1 as reference (100% crystalline PA12 Weight-average molecular weight (MW) and polydispersity (PDI) were determined using gel permeation chromatography/size exclusion chromatography (GPC/SEC). The SEC system consisted of a Waters (Milford, MA, USA) 1515 isocratic HPLC pump with a Waters 2707 autosampler. The separation was performed with a PSS PFG guard column followed by two PFG-linear-XL (7 μm, 8 × 300 mm) columns in series at 40 °C. A Waters 2414 refractive index detector (DRI) was used at 35 °C. Hexafluoroisopropanol (HFIP) with 3 g/L potassium trifluoroacetate was used as eluent with a flow rate of 0.8 mL/min. Standards and samples were prepared in concentrations of 2.5 mg/mL and were dissolved in HFIP at room temperature by stirring for 24 h. The samples were injected in a volume of 75 μL after filtering through a 0.2 μm PTFE filter (13 mm, PP housing – Grace, MD, USA). Molecular weights were calculated relative to narrow poly(methyl-methacrylate) standards (PMMA from Polymer Laboratories Ltd., UK, MP = 3800 − 685000 g/mol).A Revolution Powder Analyzer (Mercury Scientific – Newton, CT, USA) was used to measure the powders’ ability to flow, consolidate, pack and fluidize. The measurements were repeated 3 times for each of the samples, with 128 avalanches per run recorded for the flowability ((a)). Increasing drum rotational speeds from 50 to 90RPM by increments of 10RPM were used to assess the fluidized volume of the feedstock (The avalanche angle AA represents the angle at which an avalanche occurs in the rotating drum. A powder characterized by a low AA is usually associated with better flowability during processing. The surface fractal SF corresponds to the fractal dimension of the powder free surface, and measures the smoothness of the interface between the powder and the air in the drum after an avalanche occurred. Mathematically, it can be expressed as reported in Eq. with L being the length estimate, β the scale of the measurement (varying between the minimum resolution of the image and one third of the drum diameter), M is a positive value and F a constant at least equals to 1. A lower SF describes a smooth powder/air interface and hints at a good flowability with no agglomeration.Regarding fluidization, the ratio between the fluidized and the total volume (F/T ratio) at the extreme rotational speeds (50 and 90 RPM) is reported. As can be seen from (b), a high F/T ratio means that more material is fluidized: a comparison between F/T ratios can be interpreted as a direct measure of the shear-thinning (F/T increases) or thickening (F/T decrease) behavior of the powder under increasing rotational shearing.A LS230 laser diffraction device (Beckman Coulter – Brea, CA, USA) was used to assess the powder size distribution (PSD), with conventional measures taken on dispersed samples (0.03 % wt in ethanol). A DM-6 optical microscope (Leica Wetzlar – Germany) under reflected light in bright field was employed for optical particle size analyses. A XY moving stage was used to acquire pictures of dry samples dispersed on a glass substrate. The particle size distribution was successively obtained by an in-house written algorithm over at least 20,000 particles per sample.The same set of pictures acquired for PSD was also used for particle shape analysis. As reported by Miyajima et al. over at least 20,000 particles per sample. All these evaluations are carried out starting from the fitting of an ellipse with same area, orientation and centroid as the particle (Fig. (with Pparticle being the perimeter of the particle and Pellipse the one of the fitted ellipse. The perimeter of the ellipse is calculated according to Eq. The aspect ratio AR is calculated according to:with aellipse being the major axis of the fitted ellipse and bellipse the minor one.The solidity S is calculated according to:with Aparticle being the area of the particle and Conv(·) its convex hull.The ES gives a quantitative estimation about the fitting of a particle inside an ellipse: the closer it is to 1, the more similar the particle shape to an ellipse is. In this case, ES is used instead of Circularity due to the peculiarity of the PBF powders, which are typically slightly elongated. AR informs about the particle elongation: the closer it is to 1, the more isotropic the particle is. S gives an information about the overall convexity of a particle: as the shape of the particle becomes rougher, S will decrease from 1 (maximum, very smooth particle) to 0.The same sets of specimens were fabricated on industrial-grade machines used on a daily basis for parts production. Tensile testing coupons according to ISO 527-1 . 5 samples were produced per each orientation (abbreviated with the first letter, corresponding to the principal direction). For DF, no specimens were produced in the YXZ direction due to the known in-plane isotropy For SLS, a DTM 2500plus (now 3D Systems, formerly DTM – Rock Hill, SC, USA) retrofitted with digital scan-head and multi-zone heating system was employed, with a set of parameters optimized for the best surface finishing . Regarding MJF, a multi jet fusion 4200 (Hewlett-Packard – Palo Alto, CA, USA) was used, with the default parameters suggested by the supplier. The parts were produced in both cases with recycled materials, with the refresh ratio reported above.All the specimens were characterized according to different properties, after mild sand-blasting to remove the excess of powder. For the statistical evaluation, one-way ANOVA with appropriate orthogonal contrast was employed, assuming significant statistics when p < 0.05, with p being the probability value.Charpy un-notched and notched impact tests were performed on a Frank 53565 at room temperature with different pendulum hammers (0.5 J for notched, 2 J for un-notched specimens), according to ISO 179-1 Tensile tests were performed according to ISO 527-1 A Gelsight™(Gelsight – Waltham, MA, USA) benchtop device was used to acquire topographical images of surfaces with various orientations (top, bottom, side) of all cubes. The exact procedure is reported elsewhere by Vetterli et al. These values were computed using MountainMaps (Digital Surf - Besançon, France) on a cropped area of about 3 × 3 mm from the center of the cube face, after applying a robust Gaussian regression (FARG) cutoff filter of 1.6 mm to remove the main measurement error of the device Both materials are based on Vestosint powder In the first melting characteristics, DF exhibits a considerable change between virgin and recycled, by peak broadening and shifting to higher melting temperature, while HP3D peaks retains the same shape although being shifted by roughly 1 °. This is probably a consequence of the process itself, and in particular on the bed temperature: in fact, MJF employs a lower pre-heating temperature thanks to the use of the fusing agent, resulting in a very different thermal cycling for the feedstock with respect to SLS. On the other hand, the refresh ratio varies considerably between the two materials (50:50 for DF, 20:80 for HP3D; new:recycled). This implies that the thermal properties of HP3D are much more constant than those of DF.Regarding the crystallization characteristics, a difference can be seen in the transition between new and used materials: although both DF and HP3D crystallization peaks are shifted towards higher temperature upon usage, the shape of the peak changes for DF. This might have several reasons, but the most probable hypothesis is that some modification on the molecular structure exists between these two materials. In particular, reactive, open end groups are present in DF, which is characterized by molecular weight change upon residence time in the machine at high temperature or that the polymeric chain is adjusted to avoid this process to happen.The data about molecular weight is shown in DF-N is characterized by a weight average molecular weight (MW) of 49737 g/mol, that more than doubles to 134120 g/mol from the virgin to the recycled material. This is consistent from what is reported by Schmid towards the products by continuous water removal. Differently, the MW of HP3D does not increase significantly due to the process (about 17.5% from HP3D-N to HP3D-R), and even artificial aging in the oven induces only a 32% difference. From these data, it is clear that the polymeric chains of HP3D are not subjected to the chain extension reaction shown in Eq. , and can thus be considered as being end-capped. Taking into account that the post-condensation reaction provides additional entanglements between the polymeric chains (cross-linking) at molecular level The data about particle size distribution (PSD) analyzed through laser diffraction and optical microscopy are presented in PSD from both optical microscopy and laser diffraction show that both materials are expected to perform well in the process: the correct range for ensuring a compact powder bed is respected , obtained by z-stacking of optical microscope pictures, presents both virgin powders, and the comparison of DF-N ((b)) gives a qualitative confirmation about the presence of smaller particles in DF, while HP3D looks more prone to agglomeration., it can be stated that both powders present particles with similar size and shapes hinting thus a common source of these materials. A quantitative estimation of the shape factors introduced in From these data, there seems to be no difference between DF and HP3D, and also the transition between new and used materials leads to negligible changes in particles’ morphology. A smooth (ES ≈ 1.1), elliptical (AR > 1) and rather dense (S ≈ 0.9) shape characterizes both materials.RPA analyses were carried out on all the samples in order to understand the powders’ behavior at low and high drum rotating speeds. The relevant data are shown in , according to the methods introduced in The best flowing behavior is exhibited by HP3D-N, which has an average SF value that is slightly below the others. Considering the avalanche angles, the two virgin materials seem very similar, and the transition from new to recycled appears to be the same, both regarding the mean value and the standard deviation. The flowing behavior is highly influenced by flowing additives and by the parameters introduced in , mainly the fraction of fines (well expressed by the D10V from ) and the particle morphology (AR and ES from ). In this case, the higher fraction of fines in DF is probably detrimental for the overall flowing behavior, and even more for the fluidization. The transition between new and used DF goes in the opposite trend of what happens for HP3D, with a better flowing behavior for recycled than for new.A comparison for X and Y directions of HP3D is reported in Charpy impact strength for notched specimens is significantly the same in both X and Y direction (according to ISO/ASTM 52921 The comparison of Charpy impact strength between X and Z direction for DF and HP3D is shown in A highly significant (p < 0.001) difference is found between X and Z notched HP3D samples with a reduction of about 50%: this proves that the layer-to-layer adhesion is for XY directions significantly higher than Z one (according to ), even with the aid of the fusing agent. Regarding SLS notched samples, no difference between X and Z direction can be spotted: according to Schmid et al. Regarding the un-notched specimens, a different and significant (p = 0.046) trend can be observed when comparing X with Z HP3D specimens: although with a higher standard deviation, Z specimens exhibit a 75% higher mean value for the Charpy impact strength than X ones. By directly evaluating notched and un-notched specimens built in the Z direction, it appears clear that the dimension of the cross-section plays an important role: the different trend between SLS and MJF can be then explained by the presence of the fusing/detailing agent in the latter. Also in un-notched specimen, when comparing MJF with SLS, it is quite evident that HP3D exhibits higher values in all cases, up to 92% more in X-notched specimens.Finally, the following considerations can be made:the set of parameters for SLS was optimized for best surface finishing, and not for maximum mechanical performances;the presence of the fusing agent in MJF probably influences the final properties, since it remains embedded into the parts;the different part bed temperature and cool down time between the two processes definitely play a major role in defining the final properties;the higher resulting molecular weight (due to postcondensation) in SLS certainly influences the impact strength and the fracture mechanism. In the present work, no further molecular weight analyses were carried out on the produced parts.A comparison of selected stress-strain curves is shown in , while the average results regarding tensile modulus Et, maximum strength σm and elongation at break ϵb are presented in The comparison of DF against HP3D shows many differences, particularly in the Young's modulus. This is actually higher in DF than in HP3D, and is the result of several factors. Bigger crystallite size promoted by longer residence time at high temperature and slow cooldown during SLS is definitely one of them, and also occurrence of postcondensation (see Eq. The trend between XY and Z building directions is different between the two processes/materials. In SLS, Z specimens are associated with lower performance due to limited interlayer bonding The elongation at break does not change significantly among the three orientations in HP3D specimens (p = 0.175), but the mean value of the elongation at break is higher in the Y direction. This confirms what was reported by O’Connor et al. The surface analysis results are presented in . The area roughness parameters Sq, Ssk and Sku of the three faces (bottom, side and top) of the cubes positioned according to for the MJF build job are shown. A cube from SLS was also analyzed: due to the known surface properties of SLS specimen In particular, the trend of surface roughness of the bottom and top surface seems almost equal in MJF and SLS. Bottom surfaces are smoother and present a very similar values in both processes. Top ones are generally rougher and the variance is much higher. As observed in , the heat transfer mechanism in these two cases is different, being influenced by the surrounding environment, which is mainly made of colder pristine powder (bottom) and semi-molten solid layers (top).As observed in the Sq plot for the top orientation in , the excess of heat coming from the part enables to partially melt particles that belong to the t + 1 layer and leading thus to a higher roughness. The heat excess originates from the previously molten and processed layers. Also, a lower powder bed temperature for MJF with respect to SLS increases the variance between the top surface of cubes and renders the parts’ surface more susceptible to their position within the build platform. Regarding the bottom surface, the heat exchange mechanism is very different: random melting of particles belonging to the b − 1 layer is less probable due to the shielding effect of the bottom surface, which screens the heat coming from the energy source. Moreover, the ink jetting of the fusing agent definitely helps to compact the powder layer Bottom before melting occurs.A clear difference arises on the side surface when comparing MJF and SLS. The presence of the detailing agent on the XY (layer) plane enhances the control on thermal bleeding in MJF, and this can be actually quantified in the considerable reduction of the average value of Sq from 24.3 ± 1.1 (Similar trends for MJF parts were observed also by O’Connor et al. In order to better understand the surface topography of the parts obtained through MJF and SLS, the introduction of more advanced surface parameters is quite important. In fact, Ssk provides suitable information on the ratio between peaks and valleys on the surface (skewness of the height distribution, median value 0): it is clear from the data shown in that the surface characteristics of the final parts are strongly affected by the position on the build platform in MJF. Two different regions seem to exist for the bottom surfaces: MJF cubes 1 (Ssk = −0.361) and 2 (Ssk = −0.322) are characterized by a higher presence of valleys while MJF cubes 3 (Ssk = 0.011) and 4 (Ssk = 0.012) exhibit more symmetric height distribution, hence an equal number of valley and peaks. Regarding the side surfaces, all cubes present a negative value of Ssk: this means that the height distribution is once again negatively skewed and thus most of the surface features lay below the median plane. Finally, regarding the top surface, it is clear that all the cubes produced with MJF are positively skewed, confirming the assumption made on the heat transfer mechanism and enhanced thermal bleeding. Moreover, for functional surfaces a positive Ssk promises a better load carrying characteristics.Also the surface kurtosis Sku, which defines the steepness of valley and peaks (median value: 3), provides useful insights on the surface characteristics: it confirms the allegation made on the similarities between the bottom surfaces of cubes 1 and 2, and also suggests that in those cases the height distribution is spiked. By looking at the top surfaces, it seems that only cube 2 (the closest to center of the build platform) exhibits a spiked height distribution, which suggest a higher probability of random melting of particles compared to the other specimens.This study investigates the characteristics of virgin and recycled powders employed in SLS and MJF processes as well as selected properties in final parts produced on industrial systems.Regarding the raw materials, HP3D is end-capped (see Section ) and for this reason its recyclability is expected to be much higher than the one of DF. An increase of MW of only 18% was registered between HP3D-N and HP3D-R, compared to the 270% difference between DF-N and DF-R. The analysis of the thermal properties shows pronounced differences between DF-N and DF-R, while the same cannot be said for HP3D. This means that, apart from the molecular chain differences in the polymers, the process conditions play quite an important role in influencing the recyclability. The use of an IR lamp might be the reason behind the decision of end-capping the MJF feedstock: in fact, a lower time per layer makes the chain extension complicated and thus less probable to happen in MJF with respect to SLS. The evaluation of the thermal properties shall be repeated after a higher number of refreshing cycles, in order to assess the real impact of the processing conditions on the MJF feedstock. The particle size and shape distribution measured through laser diffraction and quantitative optical microscopy is similar for the two powders. However the SLS process definitely induces a change in the fraction of fines on DF, by favouring the coalescence of small particles and thus increasing the D10V. On the other hand, HP3D has less fine particles, which is definitely beneficial for flowability: this assumption is confirmed by the lowest SF of the powder/air interface for HP3D-N. New methods for the analysis of powder spreadability are ongoing investigation, and will possibily helpful in gaining a more profund understanding of the shifts in properties that has been observed in this work.Regarding the parts’ properties, Z-oriented specimens built with MJF exhibit higher Young's modulus and un-notched Charpy impact strength than X/Y-oriented ones. This happens possibly due to a bigger XY cross-section that helps the fusing agent to achieve a better interlayer adhesion than what is it possible to obtain with SLS. Nevertheless, Young's modulus of SLS parts is 20% higher due to postcondensation and different thermal history, but the elongation at break of MJF parts is about twice (X and Y) to three (Z) times higher with a similar maximum strength. From these data, it appears clear that further investigation need to be carried out with particular focus on the positioning of the part inside the build platform, especially for MJF. Surface maps were acquired using a Gelsight device, and the different area parameters were calculated based on the filtered surface. In the present work, not only the amplitude of the surface roughness is evaluated, but also the skewness and kurtosis of the height distributions are taken into account. Through the analysis of these higher area roughness parameters, it is possible to determine that the bottom surface is highly affected by the positioning inside the build chamber for MJF, with similar values of Sq for all cubes but different height distribution represented by Ssk and Sku. On the other hand, connected to the presence of the detailing agent, a clear difference has been spotted in side surfaces roughness Sq, which is much lower and consistent no matter the position of MJF parts on the build platform. Furthermore, top surfaces are different for different positions within the build area, mainly due to heat transfer mechanism connected to the well-known thermal bleeding problem of powder-bed fusion technology. This issue is common to both SLS and MJF, and the cube placed in the closes position with respect to the center of the build platform (the most isothermal region, usually) exhibits a very positively skewed and spiked height distribution, confirming once again the importance of thermal bleeding control in order to obtain a very homogeneous surface topography among parts placed in different locations on the build platform. Further work needs to be carried out in order to understand the importance of the relative rotation of parts with respect to the XY plane in MJF: analyzing tilted cubes will certainly provide more information about the influence of the inks, and on the overall isotropy of the process itself.Oil spill remediation from water surface using induction of magnetorheological behavior in oil by functionalized sawdustProtecting the environment is important for its impact on the life of humans and organisms. Oil pollution is one of the most important factors affecting the life of creatures. Here we are looking for the way to magnetize oil contamination by modified sawdust. The iron oxide nanoparticles were coated in situ on the sawdust using co-precipitation method, which magnetized the sawdust. Subsequently, the magnetic sawdust was successfully functionalized with a saline coupling agent to form a highly hydrophobic and oleophilic surface. FE-SEM, FTIR, EDXA, VSM, WCA and optical microscopy were performed to complete characterization of the products. In addition, a new magnetorheological (MR) fluid based on the crude oil and magnetized sawdust was developed and its rheological properties studied by a rheometer furnished with a magnetic field generator. The results were completely fitted using Bingham model. The strong MR response induced in the crude oil by adding the modified sawdust could exhibit a high crude oil removal capacity of about 47 times the modified sawdust weight.The awareness about environmental pollution sources and pollution prevention approaches are very important for healthy lifestyle. Several factors, whether of a human or natural origin, cause environmental pollution. Contamination of marine environments is due to the harmful effects of plastics and petroleum products (). Oil pollution can lead to the loss of microorganisms and living organisms by limiting the amount of oxygen reached from the surface as well as the presence of toxic compounds (). Environmental pollution with human origin is much broader than natural contaminants (). Contaminants can directly pollute human food sources or deprive animals and plants of healthy food. Oil pollution is one of the most important factors affecting the food chain, as well as waste of energy resources (). The volume of oil pollution can reach up to 10 million tons in transit (). Therefore, the collection and removal of contamination is of great importance. In general, oil pollution cleanup can be divided into several general categories including filtration, bilogical and mechanical methods, application of sorbent material and so on (). Adsorbent material can be referred to items such as porous media, powder particle, nanocomposite and so on. Besides, oil separation can be performed using membrane, mesh and filter (). Gravity separation and skimming are known as mechanical methods (). Over the past decade, numerous efforts have been made to prevent oil pollution with application of safe carriers to cleanup of contaminants.Adsorption is the best technology that is preferred due to its lower processing cost (). Besides, feasibility and effectiveness are two other characteristics of absorption process (). Functional groups of the sorbents are responsible for oil adsorption, C-O, O-H and C=O are the most important functional groups for oil attraction (Each of the above-mentioned methods to cleanup oil spill has advantages and disadvantages. For example, the use of membrane methods is only suitable for small oil volume. Nanoparticles are difficult to suspend and solid sorbent materials (sponges, textiles and nonwoven webs) have moderate oil sorption capacity. In addition, the time of cleaning maybe too long or the cost of a process is exorbitant which is not cost-effective (). Natural sorbents including clay, peat moss, wood residues, straw, ground corncobs and feathers are ecofriendly alternatives for oil remediation. Natural sorbents can be classified into organic and inorganic substances which are environmental friendly materials (). Sawdust, rice husk, kapok and cotton grass are some commonly used natural materials cleaning up contaminants (). Sawdust is a natural organic material, which is available and cheap in most regions of the world. Sawdust includes both macro and micro porous structures that oil can be attached and entraped into their pores (). Two factors of suitable hydrophobicity and floatability/buoyancy are very effective in oil sorption. Despite the mentioned advantages, wood dust has poor selectivity in absorbing oil. Because the inherent hydrophilicity of wood dust leads to high water uptake (). Therefore hydrophobic modification can improve oil selectivity and floatability and stabilize sawdust in oil phase (). In this study, we are trying to investigate a new method based on induction of high hydrophobicity and magnetic property in the sawdust for an effective cleaning oil pollution.Recently, high hydrophobicity and magnetism have been introduced to modify conventional sorbents in order to improve their efficiency. The use of magnetic property leads to selectively and quickly eliminate contamination from the surface and also increases the separation efficiency. To the best of our knowledge there are only few articles published about the application of magnetic sawdust as a precursor to adsorb oil. Gan et al. have functionalized sawdust with COFe2O4 as the magnetic core. They also modified the surface energy with polysiloxane layers and applied this optimized material for remediation of lubricant oil (). The maximum sorption capacity of 11.5 times of magnetic sawdust weight was reached. Xin et al. tried to apply sawdust modified with Fe3O4 nanoparticles to selectively adsorb toluene which was reduced by 97.6% (In this paper, we try to develop a recyclable, low cost and environmentally friend composite material to cleanup the crude oil from water surface using wood dust. To this, the sawdust is magnetized with iron oxide nanoparticles. Co-precipitation () used to precipitate Fe3O4 magnetic core on the surface of sawdust (sawdust@Fe3O4). Using the sol gel method, silica and 3˗(trimethoxysilyl) propyl methacrylate (MPS) were covered onto Fe3O4 as an inner shall and an outer shell, respectively to induce hydrophobicity and oleophilicity in the magnetic sawdust. For the first time, this paper proposes the use of magnetorheological property to control and remove the oil pollution.Magnetorheological (MR) fluids are smart fluids which created by suspending micrometer-sized magnetic particles in a carrier. Here the suspension of modified sawdust in the crude oil creates a stabilized magnetic fluid that exhibits a yield stress under a magnetic field due to formation of chainlike structure of magnetic particles parallel to the direction of magnetic field. Shape, internal structure and particle size play key roles in determining such rheological behavior (). This property in the MR fluid (here oil phase) will induce a better control of the oil spill and prevent the spreading of it on the water surface before collection of oil contaminant with a magnetic separator. In the first step of this work, different functionalized particles based on sawdust are prepared by change of the reactants concentration and characterized. As a second step, the effect of particles type on oil absorption, fluid viscosity and other rheological properties is investigated.Sawdust (Arbocel C320) with particle size between 160–200 μm (Spruce wood (Picea Abies) from JRS Co.) was supplied from Technische Universitaet Dresden. Ferric chloride hexahydrate (FeCl3·6H2O) (99%) and ferrous chloride tetrahydrate (FeCl2·4H2O) (99%), tetraethyl ortho silicate (TEOS), ammonia solution (25 wt%) ethanol (>99%) and toluene (>99%) were purchased from Merck. 3˗(Trimethoxysilyl) propyl methacrylate (MPS) was purchased from Sigma Aldrich. Distilled water was used during experiments. All the reagents were used as recieved.The wood particles were washed with abundant amount of DI water and then washed with ethanol solution and again washed with water then dried, cut and sieved through 150 mesh screen.Co-precipitation method was used to precipitate Fe3O4 core as magnetic agent on the surface of sawdust. Oxidation of iron chloride salts was done with ammonia solution with 10% v/v concentration based on our previous work (). In this step, 3 g of pretreated sawdust was poured in the solution of 200 mL DI water and 4.05 g FeCl3 and 1.75 g FeCl2 salts. The amount of deionized water used in this step was 200 ml.Sol-gel (Stober) method was used to functionalize the surface of sawdust@Fe3O4 (). At this stage, the modified sawdust from the previous step was divided into two equal parts, then each part was poured into a 3-neck balloon Thereafter, a solution of 160 mL ethanol, 40 mL DI water and 10 mL ammonia (25%v/v) was added to the balloon. To modify sawdust@Fe3O4, two amounts of 2 and 4 mL TEOS were added dropwise to the abovementioned suspensions, separately. During reaction, a mechanical agitator with speed of 1000 rpm was used to agitate each suspension at room temperature (under a nitrogen atmosphere) for 6 h.To coat modified magnetic sawdust with MPS saline coupling agent, at first each type of two samples obtained from the previous step was divided into three equal parts (each of them was 0.5 g) and poured into a 3-neck balloon. Then 200 mL of toluene was added to the particles as the reaction solvent. Besides, a beaker of MPS solution was prepared with addition of a known amount of MPS (2, 3 and 4 mL for each sample) in 10 mL of ethanol. The obtained solution was added to the balloon dropwise under a nitrogen atmosphere and agitated for 6 h. After reaction, the sample was dried in an oven at 60 °C. Acquired modified sawdust was named based on the amount of TEOS and MPS used during synthesizing process, thus the magnetic sawdust (MS) modified with 2 ml TEOS and 4 mL MPS was briefly named as MS2,4. presents the schematic diagram of the sawdust modification.The structure and morphology of the as-prepared modified sawdust were characterized by a field emission scanning electron microscope (FE-SEM, Hitachi 1460, and Japan). IR spectra were measured within the range 400–4000 cm−1 by FTIR spectrophotometer (Bruker Tensor II, Germany). The magnetic properties were measured using a vibration sample magnetometer (VSM, Kavir Magnet Company, Iran). An energy dispersive X-ray spectrometer (EDS) was used to determine the elemental composition (TESCAN-Vega 3). The water contact angle (WCA) of nanoparticles was determined with a DSA100 CA analyzer (Kruss, Germany) to characterize the surface property of sawdust@Fe3O4@SiO2@MPS particles. Optical microscope was also used to see modified sawdust treatment in the medium of crude oil.(C: H), a large number of magnetic nanoparticles cover the surface of sawdust and make a rough surface which hydrophobicity originate from this (). Besides, it is clear that a percentage of nanoparticles is also found to be coagulated. According to A, sawdust has internal pores that cause oil to get trapped inside it (). From image analysis it is estimated that magnetic nanoparticles precipitated on the surface are about 50 nm and less; then their size exceeds up to around 500 nm after modification with two layers (TEOS and MPS). The sorbent surface is an important factor in determining the ability to maintain oil and directly affects absorption capacity () due to the increase of both adhesion and surface area.FTIR spectra of pristine and modified sawdust samples are shown in . The peak at 3330–3350 cm−1 was assigned to stretching vibration of hydroxyl groups on the sawdust surface, which weakened in treated samples. Besides peaks at 890 cm−1 was related to cellulose (cell wall component) and 1240 cm−1 to lignin in the sawdust (). The observed peak at 570 cm−1 in all treated samples was ascribed to Fe-O bending vibration () due to sawdust functionalization with Fe3O4. The peak observed at 459 cm−1 was also assisted to the stretching vibration of Fe–O bond (). The peaks were located at 800 cm−1 and 1100 cm−1 assigned to stretching vibration of Si–C and Si–O–Si bonds in the modified sample with silica (). The spectrum of sawdust@Fe3O4@SiO2@MPS shows two bonds at 1712 and 1637 cm−1, which are associated with the stretching vibrations of the C=O and C=C groups of the acrylic moiety in MPS, respectively (). The peak at 2985 cm−1 is related to C–H stretching vibration in MPS (). These peak assignments are in agreement with those reported in other works dealing with surface treated with the MPS as an agent to obtain low-energy surfaces.B depicts the result of elemental analysis for the sawdust and treated sawdust samples. As shown in B, it is revealed that the compounds including iron oxide, silica and MPS were properly attached onto the sawdust surface. What is seen from the weight percent of iron (∼15%) in the magnetic sawdust sample (sawdust@Fe3O4), is that by coating the silica and MPS, the weight percent of iron is reduced to around 7 and 2.5%, in sawdust@Fe3O4@SiO2 and sawdust@Fe3O4@SiO2@MPS, respectively. This indicates the grafting of MPS on the magnetized sawdust surface via silica layer.Due to intermolecular force between liquid and solid when a droplet of liquid is placed on the solid it will spread, so water contact angle is a measurement of the wettability of the surface. Besides, the amount of contact angle indicates the hydrophobicity or oleophilicity. If the water contact angle is smaller than 90° the surface is hydrophilic and when it is > 90° it is hydrophobic. If the water contact angle is greater than 150°,the surface is called superhydrophobic (). When surface modification was done on the sawdust surface, the hydrophobicity was sharply enhanced (WCA of 133–148°, see ). Because, application of low surface energy modification as well as hierarchical morphological structure (micro-/nano-dual scale structure) on the surface of sawdust induces an extremely low wettable surface. The obtained results revealed that this method of sawdust modification led to high hydrophobicity and water repellency in the treated sawdust. Oil attraction on the surface of sorbents is attributed to the high hydrophobicity and water repellency due to the special coatings (). Favorable chemical stability is very important which is seen during this work.The oil absorption capacity of the modified sawdust samples was measured by the weighting method. Crude oil was added dropwise to the modified sawdust (which was dispersed on the water surface) until it was observed no more sorption and the oil would not move over the water surface under a constant magnetic field. According to , with increasing MPS content as a hydrophobic outer surface, first the oil sorption capacity increases then decreases, so an optimum point occurred at 3 mL of MPS. Since surface roughness is the another important factor in surface adsorption, increasing of MPS, initially increased the rate of adsorption, but with further rising of MPS content, the surface roughness was decreased on the sawdust surface and this resulted in lower sorption capacity. In previous studies it was reported that the roughness of the surface and the projections resulted in better sorption capacity of organic sorbents like pith baggase (The high oil sorption capacity reported here can be explained by two reasons:Surface adsorption property: According to WCA results, the functionalized sawdust with highly hydrophobic property can exhibit a selective adsorption property of the crude oil. As can be seen, the absorption capacity of heavy crude oil (API = 19.6) is higher than the light oil. This may be due to the higher weight percent of asphaltenes and resins in the heavy oil that act as natural surfactants for better stability of the ferrofluid (Magnetorheological (MR) property: Under the influence of the magnetic field, magnetic particles act as dipoles (with the north and south poles) in the fluid which causes a chainlike structure and creates a resistance to flow (). With such property, the oil that absorbed and trapped within the network of magnetic sawdust (see ) can move easily on the surface by applying an external magnetic field and quickly collected.MR fluid showed a non-Newtonian behavior in the presence of the magnetic field, and its viscosity greatly increases with a yield stress due to induce chainlike structure of magnetic particle in the direction of magnetic field (). The rheological behavior in an MR fluid can be modeled with the Bingham fluid model to describe the flow behavior. In fact, the fluid exhibits solid behavior prior to yield stress under the magnetic field, which causes the fluid viscosity to increase dramatically (). This reduces fluid mobility and stops oil leak. This factor is influenced by the size distribution, shape, magnetic field magnitude, weight percent and agglomeration of the particles (A and B, the higher the viscosity (according to viscosity data given in the following) under magnetic field, the higher the absorption capacity.In the presence of a magnetic field, for particles that possessed θ |
< 55ο, the attraction force is among them and the rest (θ |
> 55ο) repel each other (). These attractive and repulsive forces form chains of particles that are parallel to each other (see When the magnetic field is applied, the polymer-modified sawdust sticks together to form long and parallel strands. Oil is trapped inside the grid, and the sawdust moves under the external magnetic field. In fact, if we want to simulate this flow, it is like moving a fluid inside a tube that the shell moves. The external stress (slip stress) induces by magnetic force forms a plug region moving at constant velocity. Actually this behavior is the main reason of high absorption capacity of crude oil and the surface adsorption has a little effect.Saturation magnetization of nanoparticles has an important role in magnetorheological efficiency of an MR fluid. , shows the response of samples’ magnetization against applied magnetic field. The values of saturation magnetization for the modified wood dust are between 15 and 26 emu/g which indicates an appropriate magnetic behavior. Small area of hysteresis loop is attributed to small coercive force and approaching of residual magnetization to zero. Therefore it is expected that in the presence of magnetic sawdust, the crude oil can be easily magnetized, then quickly controlled and collected by an external magnetic field.To examine MR behavior of the modified sawdusts, three different MR fluids were prepared by adding sawdust@Fe3O4@SiO2@MPS in the crude oil of API 19.6°, two of them with the weight percent of 3% and the last one with 10% of the particles. shows the variation of viscosity versus shear rate for the prepared MR fluids under different external magnetic strength. According to obtained results, the MR fluids exhibit a non Newtonian behavior obeying the Bingham model in low shear rates. Generally, MR fluid can be modeled with Bingham, Casson and Herchel-Bulkly models (). Here the data is well fitted with Bingham model which is brought in the following:where in Eq. (1), τ0, is the yield stress which is a function of magnetic field and k reveals the plastic viscosity. Fitting results of this rheological model to the experimental data are presented in The stronger the applied field, the higher viscosity of the fluid which is due to formation of strong column structure as a result of strong dipole–dipole attraction between adjacent magnetic sawdust particles. In fact, this network resists to stress, which in turn increases the viscosity of the fluid. It is revealed that the reported viscosity values for sample MS4,3 is greater than sample MS4,2. If we look at the results of the EDAX test, the sample contains MS4,3 has a higher weight percentage of carbon than the sample MS4,2. This is due to using greater extent of the oleophilic MPS as the outer layer on the modified sawdust in the synthesis step. Therefore the better interactions between particles and the crude oil along with the magnetic dipoles, results in a higher viscosity value in MS4,3 when compared to MS4,2 (C in comparison to 1A and 1B, it is found that increasing the weight percent of modified sawdust affects the yield stress and increases it. As it is seen, the value of k in Eq.1 (plastic viscosity) is significantly higher than the samples with lower weight percent of the modified sawdust.In this paper, the use of a magnetorheological fluid as a smart fluid to remove oil contamination from the water surface was investigated. Sawdust with particle size ranges between 160 and 200 μm was magnetized by iron oxide (Fe3O4) and selected for this work. Subsequently, using a sol-gel method, two layers of silica as a coupling agent and MPS as an oleophilic layer were coated on this surface. Results show that as-prepared modified sawdust with the appropriate magnetization exhibited capacity of oil sorption up to 47 times of its weight in a short time. It was found that both magnetorheological property and surface adsorption are factors affecting oil sorption. The orientation of the modified sawdust particles with the magnetic field and the formation of chainlike structures cause the oil to move along with the motion of the magnetic network when the magnetic field is applied. In addition, the surface roughness due to properly covering of magnetic particles on sawdust surface as well as MPS coating is a reason of better oil adsorption onto modified sawdust surface. Besides whatever the oil is heavier the higher the oil sorption capacity will be. Since sawdust is an abundant, inexpensive, and environmental friendly material, it is appropriate to use as a precursor. Because the sawdust absorption capacity is low, it can be modified by coating with suitable compounds. The compounds used to modify sawdust are not harmful to humans and organisms. Therefore, modified sawdust with magnetic properties can be used without any restrictions. Since the sol-gel and co-precipitation methods used for such modification are inexpensive and fast, the cost of synthesis is low. Furhermore, the high speed of operation, complete cleanup of contamination and recyclabilty of the modified particles are evidence of its suitability for large-scale operations.Supplementary data associated with this article can be found, in the online version, at The following are the supplementary data to this article:Development of a large area plate-to-plate type UV imprinting toolA UV imprint lithography tool has been developed for micro/nano-scale patterning in an extremely large area, i.e., ∼300 × 400 mm2. To achieve high pattern fidelity, residual-layer thickness uniformity, and an air bubble-free layer in a large area, the UV imprint tool has several main components including a silicon rubber uniform pressurizer, a large area UV-LED module, a vacuum pump, a chuck module, etc. Contact and structural analyses have been performed using commercial FEM packages such as LS-DYNA and ANSYS. The developed tool has been tested, and its performance indices including pattern fidelity and residual-layer thickness uniformity have been measured to be ∼97% and ∼90%, respectively.Nano imprint lithography has been used for making micro/nano-scale patterns on rigid or flexible substrates In our study, a uniform pressurizing device for large-area pattern transfer was made using a large-sized silicon rubber. Nonlinear contact mechanics and structural analyses were performed using conventional FEM packages. Pattern transfer experiment was performed, and the important performance indices, including the pattern fidelity and residual-layer thickness uniformity were measured., the uniform pressurizing device uses a silicon rubber to apply hydrostatic air pressure to the target bottom substrate. It is important to decide the silicon rubber’s size to acquire an adequate area of the uniformly pressurized zone. If the silicon rubber is too small, the area of the uniformly pressurized zone will not be enough. On the other hand, if the silicon rubber is too large, it will slip down, as shown in (a). In this case, the silicon rubber is subjected to high tension. In an extreme case, material facture can occur. (b) shows the acquisition of an adequate area of the uniform pressurizing zone due to the appropriately chosen silicon rubber size. In our display application, it is important to acquire an area of 280 × 380 mm2 of the active pressurizing zone to pressurize our imprint mold pattern area. The finite element analysis program, LS-DYNA, was used for contact mechanics analysis. The element size of the silicon rubber region was 0.01 m and the total number of elements was about 6300. All four edges of the silicon rubber region and the whole region of the mold were assumed to be fixed during pressurizing simulation. The material properties of the silicon rubber are shown in . The Young’s modulus and the fracture strength were measured using a tensile test machine. shows the total active pressurizing zone for various silicon rubber sizes in the case of a silicon rubber thickness of 5 mm and initial distance between the silicon rubber and mold of 8 mm. Based on our result of contact mechanics analysis, the target area of the active pressurizing zone, 280 × 380 mm2, could be achieved in the case of a silicon rubber size between 300 × 400 and 320 × 420 mm2. shows a schematic diagram of the uniform pressurizer based on contact mechanics and structural analyses. shows the result of the pressurizing experiment performed using the silicon rubber uniform pressurizer and pressure sensing paper. For a silicon rubber size of 300 × 400 mm2 and applied air pressure of 2 bar, an area of 280 × 380 mm2 of the active pressurizing zone was achieved. The experimental result has an error of 11% in comparison with the result of our contact mechanics analysis. shows a schematic diagram of the design of the UV imprinting tool, which consists of (1) an upper module including the silicon rubber, UV-LED array module, etc., (2) an absorbing plate for fixing the bottom-substrate glass panel, (3) a chuck module for supporting the applied air pressure, and (4) a main body module for holding the vacuum pressure. To verify structural stability during imprinting, structural analysis for the chuck module was performed using ANSYS. The finite element size of the chuck module was 0.01 m and the number of finite elements was about 24,000. The most bottom region of the chuck module was assumed to be fixed. The material properties of the chuck module are shown in , a maximum displacement of 17 μm occurred at the end of the absorption plate, and a maximum stress of 28 MPa occurred on the rib that supports the deflection of the absorption plate. Since the fracture strength of SM45C is 620 MPa, we could get a safety factor of ∼22. shows the finally fabricated UV imprinting tool based on the analyses of contact mechanics and structural stability. shows the fabrication processes of the developed UV imprinting tool. The pattern fidelity and the residual-layer thickness uniformity were tested using a large-area (370 × 470 mm2) imprint mold having a 2.5 μm-high periodic pattern. The experimental conditions are shown in , UV resin was dropped on the substrate glass panel using a micropipette. The total quantity of resin dropped was about 1680 μl. shows an example of the micro pattern imprinted on the glass panel. The pattern heights were measured using a large area optical interference machine (SNU Precision Inc.). For the entire glass panel, the maximum, minimum, and average heights of the imprinted patterns were 2.5, 2.3, and 2.377 μm, respectively. The standard deviation was 67 nm. 97% pattern uniformity, which is calculated using the following equation, was achieved.Uniformity(%)=1-(standard deviation/average).On the other hand, the uniformity of the residual-layer thickness was measured for various pressurizing times and applied pressures. The residual-layer thickness was measured using Nanofocus uSurf 3-D non-contact profilometer after the partial scratch of the patterned area. First, for a fixed air pressure of 2 bar, the pressurizing time was varied from 300 to 660 s. The residual-layer thickness and its uniformity are shown in , respectively. Lesser residual-layer thickness was achieved for a high pressurizing time, as we expected. However, the increased pressurizing time reduced the residual layer uniformity. Second, for a fixed pressurizing time of 300 s, the applied pressure values were changed from 1 to 2 bar. The residual-layer thickness and its uniformity are shown in , respectively. For a higher applied pressure, lower residual-layer thickness and higher uniformity were obtained as we expected.A UV imprint lithography tool was developed for micro/nano-scale patterning in an extremely large area, e.g., 300 × 400 mm2. To get high pattern fidelity, residual-layer thickness uniformity, and an air bubble-free layer in a large area, the UV imprint tool has several important components including a silicon rubber uniform pressurizer, a large-area UV-LED module, a vacuum pump, a chuck module, etc. Contact and structural analyses have been performed using commercial FEM packages such as LS-DYNA and ANSYS. The developed tool has been tested, and its performance indices including the pattern fidelity and residual-layer thickness uniformity have been measured to be ∼97% and ∼90%, respectively. In our future work, the fabrication processes will be further optimized to achieve better residual-layer thickness uniformity, thinner residual layer, short imprint time, etc.Computational models of hair cell bundle mechanics: I. Single stereociliumA distributed parameter model for describing the response of a stereocilium to an applied force is presented. This model is based on elasticity theory, plus the geometry and material properties of the stereocilium. The stereocilia shaft above the taper is not assumed to be perfectly rigid. It is assumed to be deformable and that two separate mechanisms are involved in its deformation: bending and shear. The influence of each mode of deformation is explored in parametric studies. Results show that the magnitude of tip deflection depends on the shear compliance of the stereocilium material, the degree of base taper, and stereocilium height. Furthermore, the deformation profiles observed experimentally will occur only if there are constraints on the geometry and material properties of the stereocilium.In this paper, we propose a stereocilium model that distributes the stiffness of the stereocilium along the entire height of the structure. This distributed parameter model is based upon the theory of deformable bodies, which is used widely in engineering practice (). Model parameters describe the intrinsic physical properties of the constitutive material and the observable geometry of the stereocilium. The model output describes deformation along the entire shaft as a function of stereocilium height and has an infinite number of degrees of freedom. In the companion papers, we combine two or more of these stereocilia to model the mechanical behavior of both a single line of stereocilia and full three dimensional hair bundles.) lump the resistance to deflection into a single parameter (). This single parameter is analogous to a torsional spring located at the base of a stereocilium modeled as a rigid shaft. In such a model the applied force (or moment) may be divided by the torsional spring stiffness, K, to determine a single deflection value – either linear displacement of the tip, or angular displacement of the stereocilium. This stiffness value, K, is experimentally determined, or selected to match observed deflections for a range of bundle morphologies. The stereocilium itself is considered a rigid shaft that does not deform, so the response can be described by a single parameter (e.g. angular rotation), and the system is said to have a single degree of freedom.The use of a distributed parameter model results in more accurate deformation descriptions than earlier models (). We will show that this accuracy is insignificant for determining tip deflection of some ciliary geometries; for other geometries, the fuller description is essential. The distributed parameter model is also needed to describe deformation along the shaft with the accuracy required for mechanical analyses of whole ciliary bundles. This stereocilium model has been used previously () and is the basic element of our full bundle models.Any stereocilium has a high aspect ratio (ratio of height to radius) and a circular cross-section; its base tapers to an insertion point in the sensory epithelium (). If such a stereocilium is subjected to a point load force perpendicular to its height, applied at the top (y |
= |
L), basic elasticity theory requires that it experiences both an internal shear force and an internal bending moment (). The magnitude of this shear force is constant over the length of the shaft (), while the moment increases linearly from the top, down the shaft (). Forces applied at different points and distributed force loadings also produce internal shear and bending moments, different from that shown in In response to these two internal force loads, the stereocilium deforms (). The shear force induces a shear deformation, while the moment causes bending. Under the point force load shown, shear results in a linear deformation profile (). Deformation due to bending can be described with a third order polynomial as a function of height (). The slope of the cross-section stays parallel to the apical surface of the cell under shear (), but rotates as a second order polynomial of height under bending (The resistance to these force loads at each cross-section along the height of the stereocilia is defined by both material and geometric parameters. Materially, the resistance to shear is described by a constant value called the shear modulus, G, while the resistance to bending is described by Young’s modulus, E. Geometrically, shear is resisted by the area of the cross-section, while bending is resisted by the area moment of inertia, I. This moment of inertia measures how much material is present at a distance from the centroid of the cross-section, and for a circular cross-section is given bywhere r is the radius of the cross-section. Thus bending is greatest in regions such as the tapered stereocilium base where the radius is small.For structures with high aspect ratios (height/width) such as stereocilia, bending generally dominates the deformation. This is increasingly true as the aspect ratio increases. However, three factors support that shear also plays a significant role in stereocilium deformation:(1) A stereocilium is made up of filamentous actin (f-actin) oriented parallel to its long axis (). This internal structure resists the axially oriented tensile and compressive forces seen in bending and confers a higher resistance to bending than to shear in which fibers merely slide past each other (). Directionally biased structures such as this are said to be transversely isotropic, and they often shear more easily than structures with no directional bias (). For clarification, an isotropic material has the same deformation properties in all directions, and an anisotropic material has different deformation properties when measured in different directions. In terms of a stereocilia, a transversely isotropic material has different material properties in a direction transverse to the long axis of the stereocilia.(2) Early finite element models using isotropic stereocilia produced a paradox (). An isotropic material has a shear modulus of approximately one-half to one-third of its Young’s modulus (). Under the assumption of isotropy, a realistic Young’s modulus value of 109 N/m2 () produced bundles much stiffer than observed experimentally. A lower Young’s modulus produced realistic values of bundle stiffness, but the lack of bending resistance led to buckling of the bundle, which is not observed experimentally. Realistic deformation shapes and stiffness magnitudes could only be obtained by decoupling bending and shear, which is consistent with the behavior of transversely isotropic structure. As noted above, such structures are relatively susceptible to shear.(3) Electron microscope images of deformed stereocilia material support the hypothesis that the stereocilium undergoes significant shear (). In these images, the actin fibers and cross-links between them can be visualized. When the bundle is deflected, the cross-links appear to remain parallel to the apical surface of the hair cell, as shearing would predict (see We developed the proposed model in four steps. First, we formulated the problem from first principles of elasticity theory. Second, we non-dimensionalized the problem to reduce the number of parameters that need to be adjusted. Third, we bracketed these parameters to produce mechanical behavior that matches experimental results on ciliary bundles and the constituent material of the stereocilium. Fourth, when appropriate (e.g., to calculate stereocilium stiffness), we redimensionalized the problem to derive numbers that can be compared with experimental results.). The shaft is assumed to have a circular cross-section and a constant diameter; circular cross-sections have been observed experimentally, and the assumption of constant shaft diameter is accurate for most stereocilia (). The stereocilium tapers at its base to an insertion point; we assume this taper to be linear. Geometrically, each stereocilium can be described by its overall height, L, the height of its tapered base, L1, the radius of its shaft, r2, and the radius of its insertion point, r1 (We assume that the stereocilium is firmly held at its base. We base this on (1) experimental observations () of rootlet fibers that extend from the insertion point deep into the cuticular plate, and (2) earlier models, which showed that a rigid base and a realistically deformable base produce identical results (We model two mechanisms of tip deflection: bending and shear. Linear superposition is valid for the small deflections that a stereocilium undergoes. Thus, the total tip deflection of a stereocilium, x, is the sum of bending deformation xB and shear deformation xS (Using energy methods and Castigliano’s theorem (), the deflection from bending can be derived. This is done by computing the total strain energy is one component from bending and the other from shear, then applying the Castigliano’s theorem one can get deflection directly. The bending deflection iswhere M |
= moment, V |
= shear, I |
= the area moment of inertia, and A |
= cross-sectional area, and all are functions of stereocilium height, y (as indicated by (y)) (see for the derivation); E |
= Young’s modulus, and G |
= shear modulus, both moduli are constant in this formulation; and k |
= a shear correction factor, which is 4/3 for a circular cross-section (Normalizing the variables and parameters to make them dimensionless (non-dimensionalization), allows reduction of the number of parameters and provides insight into relevant quantities defining deformation. Two non-dimensional variables, denoted by overbars: height y¯ and displacement x¯, and four non-dimensional parameters: stereocilium height L¯, taper radius, r¯1, shaft radius r¯2, and shear modulus, G¯ are defined in . These non-dimensional variables and parameters are introduced into Eqs. , and upon integration for the specific point loaded force case depicted in , the tip deflection of the stereocilium isx¯B=3∫01(L¯-y¯)2r¯(y¯)4dy¯+(L¯3-3L¯2+3L¯-1),The function r¯(y¯) is the radius in the stereocilium, defined in the taper by the function,The two non-dimensional parameters G¯ and r¯2 may be combined into a single parameter (see Eq. ). This value represents the shear compliance and will be denoted by Sh such thatThe total non-dimensional tip deflection of the above model reduces to a function of three non-dimensional variables: the non-dimensional height L¯, the non-dimensional taper radius r¯1, and the shear compliance Sh. Eq. was numerically integrated using Simpson’s method to obtain deflection.Parametric studies of non-dimensional tip deflections were computed with variations in stereocilium height, taper, and shear compliance. Ranges for each non-dimensional parameter and for their underlying dimensional parameters are presented in presents the effects of five parameters on Sh; the range of reasonable values for these five parameters yields substantial differences in Sh. Previous work on simplified bundles indicates that values for Sh are 10−4–10−2 (); accordingly, we use this range in the parametric studies reported here.Since much of the literature addresses stereocilium stiffness, we calculated the non-dimensional stiffness of our model stereocilium by inverting the non-dimensional tip deflection. Redimensionalization yields stiffness values for the stereocilium. The linear stiffness of the stereocilium, kx is equal toRotational stiffness, kθ , is the moment (M) per unit angular deflection θ (). It is related to linear stiffness for a stereocilium of height L deflected through small angles, θ, asDeformation profiles were examined using a computer program designed to model ciliary bundles (). This program assumes the same mechanisms described above, namely shear and bending of a cantilevered beam with a tapered base. The program uses a finite element technique to solve for deflection as a function of stereocilium height.Several geometric combinations were examined to show deformation profiles. Model parameters are as shown in . Shaft radii were taken to be 0.18 μm. Taper height was 1.0 μm, with a minimum radii of 1/3 of the shaft radius (0.06 μm). Heights of 3, 5, 7, 10, 20, and 50 μm were simulated. Young’s modulus was 3 × 109 N/m2, and the shear modulus was 4 × 106 N/m2.Deformation profiles were compared with profiles of a stereocilium having an infinitely stiff shaft. To do this, the cross-sectional rotation at the top of the taper was used to define the angular rotation of the shaft. Also compared are isotropic cases where G is of the same order as E, and bending dominates. were evaluated for different non-dimensionalized values of shear compliance Sh, taper r¯1=r1/r2, and stereocilium height L¯=L/L1. Tip displacements plotted against stereocilium height (both non-dimensional) are presented in for four different degrees of taper: radius ratio r¯1=r1/r2=1.0 (untapered), 0.5, 0.3, and 0.2. Each plot shows the tip deflection due to bending (dashed line) and due to shear (solid lines) for shear compliances Sh = 101–103. The shear compliance values depicted are appropriate for a transversely isotropic material where the shear modulus is several orders of magnitude less than the tensile modulus.The contributions of bending and shear to total tip deflection increase as stereocilium height increases, but the contribution from bending increases at a higher rate than the contribution from shear. For predicted values of Sh (i.e., Sh < 103), bending dominates for tall stereocilia while shear generally dominates for the short stereocilia. Which mode dominates at any given time is strongly dependent on the value of Sh, since Sh is a linear multiplier of shear deformation (Eq. ). With each 10-fold increase in Sh, a 10-fold increase in tip deformation from shear is realized. The contribution from bending increases as the degree of taper increases. This is shown in more detail in which shows tip displacements as a function of taper (radius ratio, r¯1=r1/r2), and for non-dimensional stereocilium heights (L¯=L/L1) of 3, 5, and 10. As the radius ratio r¯1=r1/r2 increases the amount of taper decreases (when r1/r2 |
= 1 the stereocilium has a straight shaft with no taper), As r¯1=r1/r2 increases, tip displacement decreases. The contribution from bending is more sensitive than that from shear; as r¯1=r1/r2 increases tip displacement due to bending decreases by two orders of magnitude, while shear deformations decrease more gradually.Stereocilium stiffness was redimensionalized and plotted as a function of stereocilium height in . As height increases, linear stiffness decreases. For the values shown, height variations can cause linear stiffness variations of two orders of magnitude; the decrease in linear stiffness is even greater for stereocilia taller than 20 μm. The model gives linear stereocilium stiffness values (10−6 up to 10−4 N/m) that seem reasonable when compared to stiffness of whole hair bundles (10−4–10−3, ). Rotational stiffness is more robust to changes in height, varying from 0.6 × 10−15 to 1.3 × 10−15 N/m over the height range of 2–20 μm. These values fall within the range given by presents predicted deformation profiles (solid line) for stereocilia of six different heights (L |
= 3–50 μm). The predicted profiles generally resemble early qualitative descriptions of stereocilia deformations, i.e., that stereocilia bend at the base and shaft profiles are linear (). Closer examination shows that some shaft bending is visibly present in all but the shortest stereocilia. Bending of tall stereocilia is evident in published pictures of living hair bundles from toadfish horizontal canal ( shows predicted deformation profiles of stereocilia modeled with more restrictive assumptions. Stereocilia with an infinitely stiff shaft (dotted line) approximate the model of . These stereocilia are stiffer, and they depart increasingly from predictions of the proposed model with increasing stereocilium height. For a 50 μm stereocilium, assumption of an infinitely stiff shaft reduces total tip deflection by 1.7 μm. Stereocilia with isotropic material properties (dashed line) undergo negligible shear deformation. Their deformation profiles approach predictions of the present model as stereocilium height increases. Thus, adoption of restrictive assumptions (no shaft bending, no shear) significantly effects the predicted deformation profile of a stereocilium, but the magnitude of the effect depends on stereocilium height.A final observation is the noticeable shear displacement in the taper for the shortest stereocilia depicted (3 μm height). Because our proposed model does not account for known differences between the structure of the taper and the structure of the shaft (), this shear displacement in the taper may not occur in vivo. However the ankle links observed by would limit this possible shear displacement while allowing the stereocilium to bend at its base.We propose a new model for the mechanical behavior of a single stereocilium, derived from first principles of the theory of deformable bodies and experimental observations of the geometry and material properties of stereocilia. Deformable bodies theory predicts that structures with a high aspect ratio, such as a stereocilium, will bend when subjected to a point load force; thus, earlier assumptions of a perfectly rigid stereocilium shaft are unrealistic. In addition, both theory and experimental observations suggest that the stereocilium must undergo shear when deflected. The proposed model assumes that both bending and shear occur when a stereocilium is forced by a point load force at its tip.Our model indicates that most of the bending in a stereocilium occurs at the base because the base is tapered, i.e., because the cross-sectional area is smallest at that point. The observed shear is conferred by the cross-linked f-actin fiber (transversely isotropic) composition of the stereocilium. Thus, geometric factors (base taper) and material properties (degree of transverse isotropy) must be constrained to achieve biologically realistic deformation of our model stereocilium.Our model predicts that short stereocilia will deform as described in earlier experimental literature: they will bend at the base and have an approximately straight shaft (). This dominate bending at the base and not much in the shaft is probably true of most cochlear bundles. Longer stereocilia, such as those in the cristae of the semicircular canals (these can reach 50–100 μm height), will exhibit significant bending of the shaft. Such bending of stereocilia has been observed experimentally in an entire bundle (). Parametric analyses suggest that total tip deflection and the relative contributions of bending and shear to total tip deflection will depend on three factors: (1) the shear compliance of the stereocilium material, (2) the degree of base taper, and (3) stereocilium height.The use of finite element methods has allowed us to predict the deformation profile of a stereocilium when it is forced by a point load at its tip. If the goal is simply to determine total tip deflection, then profile shape is not important. However, if the stereocilium model is incorporated into a model of a (partial or complete) hair bundle, it must not only describe tip deflection accurately, but also the deflection at all points of link attachment along the length of the stereocilium. This is true because the lateral links that connect stereocilia are relatively stiff compared to the stereocilia (). Thus, small errors in predicting deformation profiles will be transmitted faithfully between stereocilia, and the in-series arrangement of stereocilia in a bundle will magnify these small errors as deflection cascades down the excitatory/inhibitory axis of the bundle.Non-linear waves in heterogeneous elastic rods via homogenizationWe consider the propagation of a planar loop on a heterogeneous elastic rod with a periodic microstructure consisting of two alternating homogeneous regions with different material properties. The analysis is carried out using a second-order homogenization theory based on a multiple scale asymptotic expansion.► We study the propagation of elastic waves in an inhomogeneous non-linear elastic rod. ► The effective properties of the rod are obtained through homogenization. ► The existence of localized loop solution is demonstrated to first order. ► Dispersive effects due to interface are shown to occur at higher order.We consider an inextensible and unshearable elastic rod of circular cross-section and infinite length, that is straight in a stress-free state.The static and dynamical solutions of such a system under fixed tension and with homogeneous material properties have been extensively studied and classified starting with the classical work of Euler and Kirchhoff, among others A classical problem in the theory of homogenization is to consider longitudinal waves in a heterogeneous elastic medium with a periodic material microstructure of two alternating homogeneous materials. For the case of small-amplitude linear elastic wave, this problem has been analyzed using a homogenization technique The goal of this paper is to investigate the effect of such heterogeneities in localized flexural waves on a straight elastic rod.Geometrically, the rod is characterized by a curve called the centerline, and parametrized by the arc length s. We assume that the rod is inextensible, that is the parametrization r(s) of the centerline is arc-length-preserving for all time, and unshearable, i.e. the cross-sections remain normal to the centerline tangent. Moreover, we assume that the rod is confined to the x–y plane and ignore the possible effect of self-contact. Let (x,y) be the coordinates of a point of the rod centerline, (F,G) the coordinates of the force acting at that point, and Φ the angle the tangent vector at (x,y) makes with the x-axis. The dynamics of the rod is then governed by the following system of equations (cf. e.g. where A and I are the cross-section area and second moment of area, ρ is the (mass) density, and E is the Young modulus. We eliminate x and y from the first two equations by differentiating them with respect to s and using the last two equations differentiated twice with respect to t. Thus we obtain the following system for (F,G,Φ):We assume that the rod is uniform with a circular cross-section of radius R, henceyields the following non-dimensionalized system (all variables are now dimensionless, but are denoted by the same symbol as their dimensional counterparts):We consider a rod with variable material properties on a small scale, so that regions of two different constant properties alternate periodically (see ). We denote the length of the unit cell by ε. This cell is composed of two subdomains with lengths αε and (1−α)ε, densities ρa and ρb, and the Young moduli Ea and Eb, respectively.Assuming that the solution to the system (5) is essentially constant over a unit cell, i.e. that ε is a small parameter with respect to a characteristic length of the solution, we introduce a fast length scale s^:and proceed with a standard multiple scale analysis (see, e.g. The periodic structure of the rod induces periodicity in terms of the fast arc length variable s^ with period 1 (size of the unit cell in terms of s^) in the dependent variables in the system,With the addition of the fast arc length variable, the spatial differential operator needs to be modified:ρΦtt=EΦs+1εΦs^s+1εEΦs+1εΦs^s^+GcosΦ−FsinΦ.F=∑i=0∞εiFi(s,s^,t),G=∑i=0∞εiGi(s,s^,t),Φ=∑i=0∞εiΦi(s,s^,t),and expand the trigonometric functions on the left-hand sides about Φ0, e.g.:Collecting terms in the system (10) expanded via , the lowest order O(ε−2) yields the following system: by F0 and integrating by parts with respect to s^, the first term vanishes by periodicity of F0, and, as expected, we conclude that F0,s^≡0, i.e. that F0 is a function of s and t only. Eqs. yield analogous results for G0 and Φ0, thusWe consistently denote variables that do not explicitly depend on the fast arc length s^ with lowercase letters, and reserve uppercase letters for variables that depend on the rod microstructure.The next order of ε in the system (10) expanded via for F1 using the following ansatz (cf. where this decomposition is made unique by imposing the following normalization condition:where the operator · averages over the unit cell:Recall that ρ is a piecewise-constant function (cf. over each subdomain, we obtain affine functions that we denote Ka and Kb, respectively. The four integration constants (two on each subdomain) are found from the following conditions:continuity of the parenthesized expression in , which we term the validation condition.Conditions (a) and (b) imply continuity and periodicity of K, respectively, yielding Ka(α)=Kb(α) and Ka(0)=Kb(1). Note that the validation condition (d) implies differentiability, since the derivative of the expression vanishes on both intervals, hence on both sides of the point s^=α. The four conditions yield the following solution:K(s^)=Ka(s^)≔(1−α)ρa−ρbαρa+(1−α)ρbs^−α2,s^∈[0,α),Kb(s^)≔αρa−ρbαρa+(1−α)ρb1+α2−s^,s^∈[α,1).L(s^)=La(s^)≔(1−α)Eb−Ea(1−α)Ea+αEbs^−α2,s^∈[0,α),Lb(s^)≔αEb−Ea(1−α)Ea+αEb1+α2−s^,s^∈[α,1).For future reference, we note that Eqs. along with the validation conditions imply that the differentiated expressions are constant over the unit cell. We can evaluate these constants using the solutions Next, we consider the system of order O(ε0):ρΦ0,tt=(E(Φ0,s+Φ1,s^))s+(E(Φ1,s+Φ2,s^))s^+G0cosΦ0−F0sinΦ0. for F1,G1,Φ1, as well as identities (27), the system (28) becomesρϕ0,tt=Ehϕ0,ss+(E(ϕ1,s+Lϕ0,ss+Φ2,s^))s^+g0cosϕ0−f0sinϕ0. on the system (29). We note that φs^≡0 for any function φ periodic on a unit cell, hence the second terms on the right-hand sides of (29) all vanish when averaged. The O(ε0) balance is thusThis is a system describing the homogenized behavior of the heterogeneous rod in the leading-order approximation. It has the form of a system of equations describing a homogeneous rod (cf. (5)), where the constant material properties are the bulk density ρh, and Eh, which is one-half of the harmonic average of the Young modulus (cf. (27)). Up to now, the analysis of the system was general. We now focus on the localized flexural waves in order to understand the effect on the microstructure in their characteristics. To do so, we solve the system (30) by a traveling wave reduction:The solutions we are looking for are loops on a straight rod with a tension T applied at infinity. We thus impose the following boundary conditions at infinity for the force:while the boundary conditions for the angle for a single loop are subject to the above boundary conditions, we haveAs expected from the Kirchhoff analogy, Eq. is the pendulum equation where the tangent angle plays the role of the angle the pendulum makes with the vertical and arc length corresponds to time correspond to a homoclinic orbit, with ϕ0=0mod2π as the homoclinic point. We therefore conclude that ℓ2>0 (a negative value of ℓ2 would have ϕ0=π for a homoclinic point), which implies the following condition on the wave speed:Note that ℓ→0 when the wave speed approaches c0≔Eh/ρh (speed of sound in a homogeneous material with the Young modulus Eh and density ρh), and ℓ→∞ for c2→T/ρh. With zero tension, the parameter ℓ≡1−c02/c2 is an increasing function of the wave speed c, and (38) yields a lower bound c0 for the wave speed. Therefore, we have 0<ℓ<1, where ℓ→0 for c→c0, and ℓ→1 for c→∞. The solution to is the well-known homoclinic orbit of the pendulum (cf. where ξ0 is an integration constant that corresponds to the position of the midpoint of the loop. The parameter ℓ can now be identified as the characteristic size of the loop. The solution . The shape of the planar rod corresponding to this tangent angle is a single loop that straightens out exponentially on the two ends, and is shown in We now go back to the O(ε0) system (29). The averaged balance (30) implies, we decompose F2, G2, and Φ2 as follows:F2(s,s^,t)=f2(s,t)+K(s^)f1,s(s,t)+M(s^)f0,ss(s,t),G2(s,s^,t)=g2(s,t)+K(s^)g1,s(s,t)+M(s^)g0,ss(s,t),Φ2(s,s^,t)=ϕ2(s,t)+L(s^)ϕ1,s(s,t)+N(s^)ϕ0,ss(s,t),We solve this equation for M analogously to , by integrating over the two subdomains separately. Recall that on each subdomain ρ is constant (cf. ). We thus obtain two quadratic functions Ma, Mb, where the integration constants are obtained fromthe validation condition: continuity of the parenthesized expression in M(s^)=Ma(s^)≔−(1−α)(ρa−ρb)2ρhs^2−αs^+α(2α−1)6,s^∈[0,α),Mb(s^)≔α(ρa−ρb)2ρhs^2−(1+α)s^+2α2+3α+16,s^∈[α,1).Noting that ϕ0 satisfies the wave equation with speed c, this leads toIntegrating the equation on the two subdomains, where E and ρ are constants, as L is affine function on each, we obtain two quadratic functions Na and Nb. The constants of integration are obtained by imposing the same four conditions as above. We note, however, that the validation condition, i.e. the continuity of (E(L+Ns^)) here does not implies differentiability, as the right-hand side of has a jump at the material interface s^=α. Therefore, the solution obtained for N is a weak solution.N(s^)=Na(s^)≔na2s^2+na1s^+na0,s^∈[0,α),Nb(s^)≔nb2s^2+nb1s^+nb0,s^∈[α,1),where the n's are constants that depend on the parameters α,ρa,ρb,Ea,Eb, and the wave speed c. (Henceforth, we omit the explicit expressions for the coefficients as they become rather cumbersome at this point.)The next order system we consider is O(ε):−(Φ1sinΦ0)tt=F1,s+F2,s^ρs+F2,s+F3,s^ρs^,ρΦ1,tt=EΦ1,s+Φ2,s^s+EΦ2,s+Φ3,s^s^+G1cosΦ0−G0Φ1sinΦ0−F1sinΦ0−F0Φ1cosΦ0.Applying the ansatz for (F1,G1,Φ1) and (F2,G2,Φ2), as well as the identity −((ϕ1+Lϕ2,s)sinϕ0)tt=f1,ssρh+f2,s+Kf1,ss+Mf0,sss+F3,s^ρs^,((ϕ1+Lϕ2,s)cosϕ0)tt=g1,ssρh+g2,s+Kg1,ss+Mg0,sss+G3,s^ρs^,ρ(ϕ1,tt+Lϕ0,stt)=Ehϕ1,ss+E(L+Ns^)Φ0,sss+Eϕ2,s+Lϕ1,ss+Nϕ0,sss+Φ3,s^s^+(g1+Kg0,s)cosϕ0−g0(ϕ1+Lϕ0,s)sinϕ0−(f1+Kf0,s)sinϕ0−f0(ϕ1+Lϕ0,s)cosϕ0.Averaging the system (50) over the unit cell, and using the following identities:ρhϕ1,tt=Ehϕ1,ss−ϕ1(g0sinϕ0+f0cosϕ0)+g1cosϕ0−f1sinϕ0.As the zeroth-order solution (f0,g0,ϕ0) is known (cf. ), this is a system of equations for (f1,g1,ϕ1). Applying a traveling wave reduction, and integrating the first two equations with zero boundary conditions at infinity, we haveEliminating f1,g1 from the reduced third equation yields satisfying the boundary conditions is given by. This is the first correction in the homogenized solution, one that captures (the leading order of) the difference with respect to the homogeneous system behavior.We now go back to the O(ε) system (50), with the following ansatz for F3,G3,Φ3:F3(s,s^,t)=f3(s,t)+K(s^)f2,s(s,t)+M(s^)f1,ss(s,t)+P(s^)f0,sss(s,t),G3(s,s^,t)=g3(s,t)+K(s^)g2,s(s,t)+M(s^)g1,ss(s,t)+P(s^)g0,sss(s,t),Φ3(s,s^,t)=ϕ3(s,t)+L(s^)ϕ2,s(s,t)+N(s^)ϕ1,ss(s,t)+Q(s^)ϕ0,sss(s,t),where P and Q satisfy the normalization conditionsUsing the ansatz for (F1,G1,Φ1) and (F2,G2,Φ2), as well as the solution and the identities (27), and (53), the system (50) becomesρLϕ0,stt=[E(L+Ns^)+(E(N+Qs^))s^]ϕ0,sss+c2ρh(K−L(1−cosϕ0))ϕ0,s.Transforming the left-hand side with the help of the averaged O(1) system (30), each of the first two equations reduces toAs L is an affine function, and M is a quadratic one, the solution for P is a cubic function each subdomain,P(s^)=Pa(s^)≔pa3s^3+pa2s^2+pa1s^+pa0,s^∈[0,α),Pb(s^)≔pb3s^3+pb2s^2+pb1s^+pb0,s^∈[α,1),where the coefficients p are determined by the usual conditions: continuity, periodicity, normalization and validation, and are functions of the material parameters Ea,Eb,ρa,ρb,α, and the wave speed c.Since ϕ0 satisfies the wave equation with wave speed c, Eq. [c2ρL−E(L+Ns^)−(E(N+Qs^))s^]ϕ0,sss=c2ρh(Kcos2ϕ0−L(1−cosϕ0))ϕ0,s. for Q because of the extra term on the right-hand side. We therefore amend the ansatz for Φ3 so as to cancel this term out. The modified ansatz isΦ3(s,s^,t)=ϕ3+Lϕ2,s+Nϕ1,ss+Qϕ0,sss+H(s,s^,t),Moreover, we impose the following normalization condition on H:so that ϕ3=Φ3 still holds, and we require H to be continuous and periodic. Analogously to the validation conditions seen above, we require EHs^ to be continuous as well. We obtain H by integrating equation twice over each of the two subdomains, and determine the integration constants from the aforementioned conditions on H. It is clear that the s^-dependence of H is cubic. Note that integrating equation with respect to s^ leaves χ and λ intact, therefore the form of the solution for H is cancels out the last two terms in the right-hand side of As previously, Q is obtained by integrating twice over each of the two subdomains, and the integration constants are found the usual way. As L is an affine function, and N is quadratic, the resulting function Q is a cubic on each subdomain:Q(s^)=Qa(s^)≔qa3s^3+qa2s^2+qa1s^+qa0,s^∈[0,α),Qb(s^)≔qb3s^3+qb2s^2+qb1s^+qb0,s^∈[α,1).Collected terms of order ε2 yield the following system:−Φ2sinΦ0−12Φ12cosΦ0tt=F2,s+F3,s^ρs+F3,s+F4,s^ρs^,Φ2cosΦ0−12Φ12sinΦ0tt=G2,s+G3,s^ρs+G3,s+G4,s^ρs^,ρΦ2,tt=E(Φ2,s+Φ3,s^)s+(E(Φ3,s+Φ4,s^))s^+G0−Φ2sinΦ0−12Φ12cosΦ0−G1Φ1sinΦ0+G2cosΦ0−F0Φ2cosΦ0−12Φ12sinΦ0−F1Φ1cosΦ0−F2sinΦ0.Using the ansatz expressions and the known identities, the averaged system (72) becomes−(ϕ2sinϕ0)tt=ρh−1f2,ss+M+Ps^ρf0,ssss+12L2(ϕ0,s2cosϕ0)tt,(ϕ2cosϕ0)tt=ρh−1g2,ss+M+Ps^ρg0,ssss+12L2(ϕ0,s2sinϕ0)tt,ρhϕ2,tt=Ehϕ2,ss−c2ρhϕ2(1−cosϕ0)−f2sinϕ0+g2cosϕ0−c2ρhL22ϕ0,s2sinϕ0+E(N+Qs^)ϕ0,ssss−ρNϕ0,sstt+EHK,s^χs+EHL,s^λs.This is a system for (f2,g2,ϕ2), which we solve using a traveling wave reduction. Integrating twice the reduced first two equations with zero boundary conditions at infinity yieldsf2=−c2ρhϕ2sinϕ0−ρhM+Ps^ρf0,ξξ−c22ρhL2ϕ0,s2cosϕ0,g2=c2ρhϕ2cosϕ0−ρhM+Ps^ρg0,ξξ−c22ρhL2ϕ0,s2sinϕ0.Eliminating f2 and g2 from the reduced Eq. +1ℓ2EHK,s^−EHL,s^(1−cosϕ0)−ρhM+Ps^ρϕ0,ξξ. One solution (satisfying the boundary conditions for ϕ1) was found to be The other solution, found by a reduction ϕ2(ξ)=u(ξ)ϕ0,ξ(ξ) of the homogeneous equation, is: is now obtained by variation of parametersϕ2,part=ϕ2,hom(1)∫W1(x)W(x)dx+ϕ2,hom(2)∫W2(x)W(x)dx,where W is the Wronskian determinant for the homogeneous basis W1(ξ)≔−ψ(ξ)ϕ2,hom(2),W2(ξ)≔ψ(ξ)ϕ2,hom(1).The explicit form of the particular solution ϕ2 is far too complex to be reproduced here, but it is found to satisfy null boundary conditions at infinity.Using a homogenization approach, we have obtained a leading-order solution ϕ0 and the first correction ϕ1 in terms of the angle variable,as well as the second correction ϕ2, given by . Whereas ϕ0 and ϕ1 depend on the material parameters, the tension T, and the wave speed c only through the characteristic length ℓ, the second-order correction explicitly depends on all material parameters Ea, Eb, ρa, ρb, α, and the wave speed c (note the dependence of ψ on various averaged quantities in , each being an expression involving the material parameters).The graphs of the three solutions are shown in . The effect of the first correction is to increase the angle ϕ within a localized region, which coincides with the extent of the loop (compare with In order to view the solution in terms of the shape of the rod in the (x,y) plane, rather than integrating the x and y equations for the combined angle ϕ=ϕ0+εϕ1+ε2ϕ2, we carry out the same multiple scale expansion as seen above for these two equations.Collected terms of order O(ε0) for the Cartesian coordinates system and averaging over the unit cell yields is the well-known loop solution on a homogeneous rod, depicted in Collecting terms of order O(ε) and applying the averaging operator yieldsThis gives the following solution in terms of the Cartesian coordinates:where the integration constants have been set by null Dirichlet boundary conditions at infinity. The graphs of the two coordinate solutions are shown in . The effect of the first correction in the x direction is to move the homogeneous solution loop to the left (see (a)). In the y direction, the “front part” of the loop, i.e. the part corresponding to values of the independent variable ξ<ξ0, experiences a shift upwards, while the ξ>ξ0 part shifts downwards (see , where relatively large values of ε have been used in order to accentuate the effect. The first-order correction conserves the arc length of the loop, since limξ→∞x1(ξ)=limξ→−∞x1(ξ).While the leading-order and first-order systems are solved analytically above, the solutions we obtained for the second-order system are numerical. Integrating the coordinates x2 and y2 from (a) and (b) The arc length of the loop is altered by the second correction: note the shift in the x-coordinate versus the arc length variable ξ in (a). In the horizontal direction, the loop gets stretched out (cf. (a)), while in the vertical direction, the tails get slightly pushed upwards, while the central part of the loop is significantly pulled downwards (cf. (b)). The effect of the second correction on the overall shape of the loop is shown in for different values of ε (compare with corresponding values of ε in We have examined planar loop traveling wave solutions on a heterogeneous, inextensible and unshearable elastic rod using a multiple scales homogenization technique, where the heterogeneity consisted in a periodic microstructure of two different material properties.The leading-order balance (30) is a system describing a homogeneous rod, and allowed us to identify the effective material properties. In the case of the density ρ, it is just the bulk density ρh=ρ, but as far as the Young modulus is concerned, the effective value is found to be Eh=E−1−1.Two lowest-order corrections have been found and shown to distort the homogeneous-type loop, breaking its symmetry. The effect of the corrections is shown in . From the effect of the second-order boundary conditions, we can infer that an initially traveling loop on a rod with periodic microstructure would eventually deform and loose its traveling wave structure as expected due to dispersion effects.Reactivity of stressed molecules: calculation of the effect of chain deformation on scission for macromolecules and middle macroradicalsThe effect of deformation ε of polyethylene molecule and radical on activation energy Ea of the reaction of its monomolecular scission was calculated using MNDO and AM1 methods. Propane, octane, and decane molecules were used as models for PE chain. Reactions of molecule and radical scission were shown to be strongly accelerated by deformation, its activation energy, in contrast to previously studied reactions, being parabolic in chain deformation. The Ea(ε) dependence for scission of molecules is shown to be linear only in the region of small (ε<3%) strains, for scission of macroradical such region is absent. Both semi-empirical methods give close results, but the AM1 method provides a better description for deformation of macroradicals. The proposed approach makes it possible to analytically describe calculated results, including the case of a reaction proceeding under the influence of constant force acting on a molecule. The possible cause for difference between the dependences of the local and integral rate constants on the load are considered.Recent experimental results show that the deformation of a reaction center can significantly (sometimes by several orders of magnitude) change its reactivity both in low-molecular-mass compounds where coefficient α depends on the nature of reaction, presence of catalysts, and the structure of material; it determines the deformation susceptibility of the process. Therefore, to predict the response of a particular process to deformation, one should learn to estimate α; and for this purpose, one should elucidate the mechanism of the effect.With this aim in view, we previously performed quantum calculations of the dependence of activation energy on the deformation of a model molecule for the processes in question. We took as model molecules low-molecular-mass compounds with the structure of the reaction center similar to that in polymer. To confine ourselves to a reasonable length of model molecule, we determined the minimum number of its units for which the calculated results become independent of this number. For example, it has been shown that even propane is sufficient to describe the abstraction of a hydrogen atom from PE by ozone and that the PE chain rupture requires consideration of octane at least The deformation of model molecules was specified by introducing different distances between their terminal skeletal atoms into the problem, without optimization of this parameter in calculations. This approach proved to be very fruitful. It provided a good description for the reaction of hydrogen atom abstraction from PE and PP by ozone . Moreover, a comparison of the calculated results with the experimental data demonstrated a reasonable quantitative agreement between them. However, when we attempted to calculate the tension susceptibility of the monomolecular rupture of PE chain The calculations were conducted using MNDO and, if it was necessary, AM1 methods in MOPAC 7.2 software. The length of the ruptured bond R was used as the reaction coordinate. The deformation was varied through change in the distance (L) between the terminal carbon atoms. In all cases, the chain was in the all-trans planar zigzag conformation.The model molecules for scission of macromolecule were heptane, octane, and decane. Similarly heptyl, octyl, and decyl radicals were used as models of PE middle macroradical. The ruptured bond was assumed to be in the middle of a molecule (between the third and forth C atoms in heptyl radical, forth and fifth C atoms in octyl radical, and fifth and sixth atoms in decyl radical), and the free valence was borne by the C atom adjacent to the one involved in the bond ruptured:The rupture of this particular bond is the most favorable because this reaction results in the formation of double bond with corresponding gain in energy. The calculation proceeded in the following way. First, the equilibrium length of the model molecule was evaluated. Then, the distance between terminal carbons, corresponding to specific strain ε from 0 to 5–8%, was fixed. The profile of potential energy surface (PES) was calculated for each ε by variation of the reaction coordinate R with the step of 0.05 A and optimization of all other coordinates.For the molecular scission, the initial state is the ground state of the molecule, the final state is biradical, and it is not known which of the two states is closer to the transition state. Unlike a system composed of two atoms, where the ground state is bonding, biradical state is loosening, and the transient state occurs at the intersection of these two terms, in more complex systems a biradical state can be one of bonding states as well. The well-known stable biradicals provide an example. In this connection, the calculation of the PES profile was carried out for both ground and biradical states. There was no such problem in reaction of radical scission.Before passing to the reactions of deformed molecules, let us consider the data on deformation. shows the dependence of energy of formation for the model molecules and radicals U0 on specific strain ε. Solid lines show parabolic fit to the calculated points. In our previous calculations presents the results of this calculation for decyl radical. The dependence U0(L) different from linear elastic for L<L0 does not allow one to accurately determine L0. In this connection, in addition to the MNDO Hamiltonian, we used in this work for calculations of radicals reaction the AM1 Hamiltonian, which provided a sufficiently good description of radical deformation (For both model molecules and radicals, Hook's law well describes the molecule deformation up to considerable ε; this was previously mentioned in Refs. ). Thus, the dependence of energy U0 in the vicinity of the initial molecule as a function of length can be described by parabolic dependence (Hook's law)where D0 is stiffness of the initial molecule (the energy of the initial equilibrium state is assumed zero). summarizes the obtained (least-square fit) values of D0 and L0 and calculated from D0 values of elastic modulus E of a chain (the cross-section 1.8×10−19 |
m2 was taken from X-ray diffraction data For model radicals, E obtained using MNDO method are 10% smaller than those obtained with AM1 Hamiltonian. This can be considered as a good agreement. For heptyl radical, as well as for heptane molecule, the obtained elastic modulus is smaller than for other radicals. Therefore, this model molecule is too small for the description of deformation and results obtained for heptyl radical can contain artifacts. The values of E for octyl and decyl radicals coincide, being close to the elastic modulus of PE chain equal to 250–270 GPa (both experimental and calculated values ). Comparing the MNDO values obtained for the radical and the molecule, we may conclude that the presence of radical fragment results in a decrease in the elastic modulus of the chain by about 10% (Hence, calculations using MNDO and AM1 semi-empirical methods give us reasonable results on deformation of both macromolecules and middle macroradicals.It should be emphasized that a connection between activation energy and deformation is quite natural for the reactions under consideration: the more energy is ‘pumped’ into the bond elongation, the less energy has to be added for its rupture. However, it is not the bond, but the whole molecule, that is being strained; this is manifested, for instance, by a deformation relaxation of the free radicals evolved. That is why, for more accurate description of the PES profile in the region of the transition state, the calculation was carried out with a fixed R and increasing L, whereby true reaction coordinate is a combination of the two parameters. It should also be noted that we always refer to PES in R–L coordinates without subtracting the energy of the initial state at a given strain. The reason for this consists in that the most important parameters for the description of reactions of deformed molecules are the coordinates of saddle point on this surface (), i.e. the point through which the reaction of a free molecule proceeds, the parameter is a sought sensitivity to strain for the reaction shows the difference between the calculated values of standard energy of formation of the ground and biradical states ΔΔU for octane molecule, plotted against R. As expected for the C–C bond length close to the equilibrium value (1.548 A according to MNDO data), the ground state is more favorable in energy than biradical, as confirmed by negative values of ΔΔU (the latter state is bonding as well). When R=1.87 A, the enthalpies of formation for these states become equal, and biradical state becomes more preferable at large R. It is important to note that intersection of the energy levels is fairly smooth, as indicated by a rather small slope of the curve at the abscissa axis intersection () as compared to the slope of ΔU(R) dependence at the same R value (35.6 vs. 503 kJ/(mol A), respectively). This testifies to the fact that the terms are passing close to each other for a rather wide range of R. Therefore, one can assume that nothing hinders this transition in a real reaction.Hence, the PES profile for scission of macromolecule must incorporate a transition from the ground state to biradical prior to the formation of the transition state and the latter is biradical. shows the dependence of the change in activation energy Ea of the rupture of PE molecule and middle radical on its deformation. This dependence is nonlinear. demonstrates that it is adequately described by a parabola, but this does not agree with numerous experimental data. In this work, the calculation is performed as the cross-section of the PES at a fixed length. But, in this case, the length L itself becomes a rightful reaction coordinate, as is confirmed by calculations at a constant R and increasing L. Another cross-section of the same PES is thus obtained. The results of such calculations for the reaction of macromolecule scission exemplified by octane as a model molecule are shown in . Apparently, both calculation variants yield close results and show that the PES of this reaction has a saddle point, just as in the case of other processes are coordinates of the saddle point, Ea0 is activation energy of the reaction for free molecule, and A, B, and C are fit parameters obtained by least-squares processing of the calculated results. When reaction occurs at L=L′=const, it passes the point with the coordinates (L′,R′) rather than the saddle point and R′ value obeys the relationship has the physical meaning of stiffness of the transition state. Then, allowing for the fact that f=2D(L′−L0) is the force acting on the molecule prior to the beginning of the reaction, the change in the activation energy for relative deformation of the reaction center ε=(L−L0)/L0=const can be described by the expression corresponds to the increase in activation energy due to the fact that the reaction passes the barrier at L=L0 rather than at The quadratic dependence of ΔEa on f and, accordingly, on ε appears in this expression. Earlier in the transition state. Then, similar to the above calculations, one can easily derive expression describing the change in the activation energy for f=const:. Let us consider some principal properties of these equations.The formation of transition state is usually accompanied by a certain loosening of atom–atom bonds. For the reaction of backbone bonds of macromolecule, this means that (which is usually the case). Then ΔEa<0 for any deformations; that is, tension activates the process. If ΔEa>0 for small deformations and ΔEa<0 for large ones. Thus, the pattern of the ΔEa(ε) dependence may change with increasing ε for such processes: from inhibition of the reaction to its acceleration.If the stiffness increases during the formation of transition state, the Ea(ε) dependence at will be a monotonically increasing function for all ε; Ea(ε) will decrease for small ε values and increase for large ones. If the formation of the transition state does not entail any significant loosening of skeletal bonds, that is, coincide with an accuracy up to the free term and the dependence of ΔEa on the force or deformation becomes linear. The force susceptibility does not depend on the reaction pathway (L=const or f=const); it is the case considered earlier are also linear in the region of small deformations, but the force susceptibility changes as the reaction path changes. The region of small deformations itself is limited by the εc value, which, as follows from both formulas, is determined by the relationshipIf the length of the reaction center does not significantly change during the formation of the transition state, that is, then the linear part will be completely absent (εc=0) and dependence of the activation energy on deformation or force will be parabolic. If the condition is also satisfied, the reactivity of such systems does not depend on deformation.The studied PE chain scission is a good illustration of this inference. For this reaction, the value εc is fairly high and amounts to 5.4%, because the parameter |
A is very high. The parameters of the initial and transition states for this reaction are presented in . At small deformations, the ΔEa(ε) dependence is virtually linear (), but subsequently the quadratic term also manifests itself.), both MNDO and AM1 methods give a parabolic dependence of ΔEa(ε) from the very beginning. The points obtained by the same method for octyl and decyl radicals are fitted by a single curve. This indicates that even the octyl radical perfectly reflects the features of the reaction of longer molecules and, thus, appears to be a representative model for the macroradical scission. almost coincide for both octyl and decyl radicals. According to Eq. , this must result in the absence of the dependence of Ea on ε if there is a weak change in the molecular stiffness D upon the formation of the transition state. But in our case, such assumption is not valid: the transition state is characterized by 4–5 or 3–3.5 times smaller chain stiffness; according to the MNDO and the AM1 method, respectively. If L0 and is equal to zero and dependence ΔEa(ε) is determined by the quadratic term. It is this case that is considered in the present work. Therefore, for the reaction of middle radical scission, the region of small deformations in which the quadratic term can be ignored (as was done in the case of other reactions), does not exist.Thus, the linear dependence of the local rate constant on the load is observed only in some cases. There can exist reactions that pass from the linear to quadratic dependence as the deformation increases; in some cases, this dependence is quadratic from the very beginning. But the dependence of Eq. type, that is, a linear ΔEa(ε) dependence, is observed in all studies of this phenomenon. The absence of a quadratic dependence in experiments may be due to several reasons.First, let us estimate the real deformations that a macromolecule may undergo in a loaded polymer. The chain elasticity modulus in PE amounts to ≈250 GPa, depending on the length of the model molecule. A highly oriented high density PE may bear a load up to 1000 MPa. If this load is uniformly distributed over all the chains, their deformation will be only 0.36%. For a 10-fold overload (that is, for the situation where only 10% of the chains bear the whole external load), the deformation of the load-bearing chains increases to 3.6%. This result should be regarded as an upper estimate, because the values used in calculations were intentionally chosen to be equal to the limiting values for ordinary (not ultra-high-strength) polymers. Actually, real loads are significantly (one or two orders of magnitude) smaller. Then, the deformation of macrochains seldom exceeds 1%; that is, in most cases, reactions proceed at ε≪εc and, therefore, fall into the region of a linear ΔEa(ε) dependence.In the general case, the macroscopic rate constant is a convolution of the local constant k(f), where f is the local force, with the distribution function F(σ,f) of the external stress σ over the polymer chains:The pattern of the distribution function F(σ,f) is unknown, but there are some approaches to its estimation. It is assumed that the majority of chains do not bear any load but the whole external load is distributed among 10% of the bonds. Accordingly, the F(σ,f) function must have the form of a steeply decreasing function f with a long ‘shoulder’ in the region of high stresses. The contribution of each group of differently loaded chains to the integral rate constant depends on the load susceptibility of the local constant of the reaction in question. For example, in the case of reactions whose rate constant is highly sensitive to the chain deformation, the contribution of the most strained bonds is maximum; in the case of reactions with a low susceptibility to deformation, the reaction of unloaded chains may make a significant contribution to the integral rate constant. Thus, the main contribution to the integral rate constant for each specific reaction is due to its relevant groups of strained chains, that is, to different portions of the distribution function. Hence, the local rate constant for different reactions is actually integrated in formula over different distribution functions. As a result, the integrated dependence k(σ) may have the same pattern even for different dependences of the local rate constants on the force. In addition, if the reaction is accompanied by the rupture of macromolecules, the load is redistributed among the intact chains during the process and, accordingly, the pattern of the F(σ,f) function changes. This complicates the problem even further. The only evident thing is that the k(f)∼exp(f2) dependence at a definite pattern of the F(σ,f) function may also yield the equation of form Finally, the third reason for the experimentally observed linear relationship between log(k) and σ may be that the researchers took the deviations from linearity for inflexion of this dependence that are due to changes in the chemical mechanism of the process (see, for instance, Ref. Thus, our analysis showed that there are reactions for which the activation energy of the local rate constant depends nonlinearly on force (for example, the reaction of monomolecular scission of PE chain considered in this work). There exists only a narrow region of small deformations, where the deviation from linearity is negligible; this occurs often but not always. According to formula , this region does not exist (that is, εc=0) for reactions where In this case, the linear portion is totally absent and the dependence of activation energy on force for such reactions is quadratic starting from the smallest deformations.In this work, a similar dependence of the activation energy for scission of middle radical on the force acting on chain (deformation) has been obtained. This relationship is quadratic, with the linear term coefficient being zero. This results in absence of the region of small deformations in which the dependence can be approximated by a linear function. This type of dependence is explained by a considerable variation of the stiffness and small change in the chain length upon the formation of the transition state.The search for such processes and their study will be the aim of further research. We expect that their revelation as a result of calculations and analysis of experimental data will enable us to make some conclusions concerning the pattern of the F(σ,f), because this function must satisfy a requirement that is contradictory at first sight: its convolution with exp(f) for one reaction and with exp(f2) for another reaction should yield exp(σ) in both cases, as follows from the presently available experimental data.Microstructural evolution of rhenium Part II: TensionThe microstructural evolution of Re under tension was investigated using EBSD, in-situ and ex-situ TEM. The samples had a texture that suppressed possible {112̅1}〈112̅6〉 twinning, while favoring <a> type 〈112̅0〉 basal dislocations during tensile straining. In-situ tensile straining was performed on rhenium both at room temperature and at 920 °C to investigate the low strain region of deformation, where it was found that <a> type b⃗=[112̅0] screw dislocations operated on the basal planes in loosely aligned slip bands. Through Schmidt factor analysis, EBSD had shown that pyramidal slip activated appreciably only at strain values above half of the failure strain. At failure stresses, <a> type b⃗=[112̅0] basal screw dislocations observed in dislocation slip bands and <c+a> type b⃗=[112̅3] pyramidal screw dislocations formed dislocation nets interfering with <a> type glide. HAADF STEM imaging was used to view the morphology of tension-induced {112̅1}〈112̅6〉 twins at higher strain values. Twin transmission with {112̅1}〈112̅6〉 twins changing twin planes between parent and matrix orientations was observed. The twin structure observed in tension were representative of classical twin structures, contrary to the {112̅1}〈112̅6〉 type twins seen in compression which consisted of twin aggregates. Our results suggest that the compression-tension asymmetry in Re is likely due to the twin favorability of the microstructure forcing the creation of many more twins during compression as compared to tension. The exceptionally-high work hardening rate in Re was found to be mainly due to large scale twin formation coupled with basal slip activity during initial straining.One of the most interesting metals of HCP crystal structure is rhenium. Rhenium is mainly used as a platinum-rhenium reforming catalyst, hydrogenation and fine chemicals for hydrocracking, as x-ray tubes and targets. However, one of its key uses is as a structural metal is as ballistic combustion chambers and nozzles The microstructural evolution of rhenium has been shown using compression In addition to ex-situ microstructural characterization, further understanding can be gained through imaging the formation and motion of dislocations and twins using in-situ straining. While there exist advanced x-ray techniques that can view interior dynamics of crystal structure during deformation of macroscopic samples The samples tested in this work were purchased from Rhenium Alloys, Inc (Ohio, USA). 10 tensile samples were cut from a sheet of 2.85 mm thick rhenium using wire EDM. The Re sheet was formed from an ingot of Re that was formed from powder and sintered at 2350 °C. The ingot was cold rolled with intermittent 1650 °C heat treatments, and a final 1650 °C anneal to remove the deformation induced through rolling. The initial texture of the tensile bars, seen in , shows heavy prismatic texture unfavorable for the most common twin variant in Re, {112̅1}〈112̅6〉 twins.The samples were all tested on an MTS Criterion Universal Test System using a strain rate of 3.3 × 10−4 second−1. Samples were square with an 8.55 mm2 initial area and had the same initial gauge length of 15 mm. Some grip slippage was seen during straining due to the high strength and relatively low coefficient of friction of Re For use in the in-situ tests, Rhenium foil was again purchased from Rhenium Alloys Inc. The method of forming the foil was the same as for the metal sheet, with the rolling steps progressing until the foil was roughly 75 µm thick. The initial foil texture was the same as for the Re sheet, promoting the observation of dislocation motion in-situ. The foil was machined using EDM into the shape required for a Gatan heating-straining in-situ holder, and jet-polished with the aforementioned solution. Samples were tested in-situ at room temperature, and once dislocation motion was fully characterized, at 920 °C to observe changes in temperature-based behavior. show a range of samples strained to different maximum engineering strains. The macroscopic tensile behavior of all samples is nearly identical. One sample strained to 8.2% strain contains an unloading and re-loading segment to understand the effect of detwinning on the inherent microstructure. As there is no change in the unloading vs. loading modulus, no de-twining is present in these tensile samples. The initial texture is shown with an EBSD IPF map and pole figure in (b,c). The slight discrepancy in yield stresses is attributed to the difference in the grain size distribution between samples as seen (e,f), showing the sensitivity of rhenium to the grain size. Samples with relatively large grains have shown lower yield stress coupled with a higher initial work hardening rate, as reported previously In order to determine the most active slip systems, a series of Schmidt factor maps the 8.6% strain sample is shown in . {112̅1}〈112̅6〉 twins are capable of accommodating up to 61% strain in tension along the c-axis, however the [0001] direction of grains with this texture is generally orthogonal to the tensile direction, resulting in low {112̅1}〈112̅6〉 twin activity. There are exceptions within the microstructure of the high Schmidt factor grains (seen as red grains in c) which will promote twinning in this system. With twinning acting secondarily to slip for samples with this texture, shows the Schmidt factors for the relevant slip systems in Re. Additionally, as twinning operates as a simple shearing mechanism with a relatively low critical resolved shear stress The initial overview of the strain effects on the sample behavior were investigated using EBSD scans of large regions of the sample. The default step size of 750 nm was used for the large area overview scans. This allowed for the highest data acquisition throughput, while still being able to observe which grains had initiated deformation twinning. While the large scans allowed for the acquisition of datasets that showed general trends in the microstructure, detailed scans were performed in order to view the twinning and dislocation (seen as grain misorientations) interactions at each level of strain. This allows for insights into the very high work hardening rates seen in (b). TEM micrographs can then be used to understand how the very small twins seen in the EBSD maps interact with individual dislocations to accommodate the applied tensile strain., were taken of each sample described previously, and were used to provide a general progression of microstructure as a function of strain. Despite an average scan step size of 750 nm for course scans, it is possible to observe small twin features common in Re, which can be as small as a few nanometers in width to a few tens of microns in length. Most grains which have Schmidt factors above 0.4 for {112̅1}〈112̅6〉 type twins will show signs of twinning, as seen in (c). For very low strains, immediately after initial yielding, there is little difference between the IPF maps of the annealed samples seen in (a) and the IPF maps for the 0.4% strained sample in . No twins are observed in large grains, with no noticeable color gradients within grains indicating local grain misorientations. With the increase in strain to 1.9%, large twins become visible within high Schmidt factor grains, with more noticeable color gradients internal to the grains appearing in the majority of these grains. This is likely due to basal dislocation slip, as seen by the coincidence of twinning and the high {0002}〈112̅0〉 basal slip Schmidt factor seen in (d). Once the deformation reaches 3.3% strain, large-scale twinning fully crossing grains has become prominent in all the grains with high twinning Schmidt factors, as seen in (c). It can be seen that after roughly one third the failure strain to 8.6%, the ratio of twinned grains relative to untwinned grains observed does not increase appreciably. This both suggests that deformation twinning is mainly activated at low strains, with dislocation plasticity accommodating the additional strain after twinning saturates, and that the high initial work hardening rate seen in (b) is mainly due to large scale twin formation.To get a more complete understanding of the strains required for each possible deformation mode to be activated, EBSD maps of the 8.6% strain sample with significant dislocation plasticity and twinning were compared to the Schmidt factors of prominent deformation modes for this texture, seen in . Having Schmidt factors for each orientation only gives insights into the favorability for which orientation to deform. However, in order to understand the interaction between applied stress and deformation internal to each grain, an understanding of the critical resolved shear stress (CRSS) in the sample must be accounted for. It has been observed by Jeffery et al. , which shows an EBSD map of of the 8.6% strain sample (after fracture) with accompanying misorientation map and {112̅1}〈112̅6〉, {0002}〈112̅0〉, {101̅0}〈12̅10〉, and {101̅1}〈12̅13〉 Schmidt factors. While it is less commonly seen in Re, the {101̅0} plane has been observed forming slip bands in polycrystalline Re by Churchman, and was also the plane along which dislocations were observed in Re deformed in compression It should be noticed immediately that while basal slip has some favorable and unfavorable grains, prism slip almost always a high Schmid factor. From this it can be concluded with the observations by Jeffery et al. that basal slip and {112̅1}〈112̅6〉 twinning are the dominant mechanisms operating in tandem during tension. If prism slip were to have lower CRSS than basal slip in rhenium, deformation would appear more uniform than it currently does due to the even distribution of prism slip Schmidt values. It can be seen from the scans in , that while most of the large grains with high {112̅1}〈112̅6〉 Schmidt factors show deformation twins, twins can appear in grains with Schmidt factors lower than 0.4, however it is less common. All grains with high twin Schmidt factors also show high basal Schmidt factors and large amounts of misorientation. This indicates that after twins have formed, basal slip is the next most favorable deformation mode. Significant misorientations are also seen in grains oriented only for pyramidal slip, making the number of active deformation modes in this sample a minimum of three, based on EBSD observations.When looking at overall trends of misorientations as a function of strain, , it can be quickly seen that the overall local misorientation maps have large bands saturated with values up to 3° as the strain increases to fracture. At low and intermediate strains, the relative amount of deformation is lower in pyramidal slip oriented grains (deep blue and purple grains marked with white arrows). Any grain with noticeable deformation twinning has both increased basal slip Schmidt factors and generally has higher local misorientations at low strains. Couple this behavior of basal slip dominating at low strains with the proclivity for deformation twins at strain values of 3.3% or below, and it is clear that dynamically changing deformation modes seems to be an important operating mechanism for accommodating deformation in Re. As twinning in the crystal saturates and basal slip activates in the twinned grains, work hardening leads to activation of pyramidal slip at higher stress levels. Initial twins form in easy basal slip grains, inducing high work hardening, which allows for the activation of pyramidal slip.While the 750 µm step sized used for the overview scan can acquire adequate measurements of overall structure of Re as a function of strain, detailed maps of each orientation using small step sizes below 200 nm are required to observe smaller features including most deformation twins within the twinning-unfavorable grains. The trend for coupled twinning and dislocation plasticity seen in the overview scans of is also apparent at smaller size scales that include only a handful of grains, seen in . Grains marked with black triangles were favorable for basal slip and grains with white triangles are pyramidal slip favored. Here the large contrast between 8.6% strain and 3.3% strain is readily apparent, as is the difference between the misorientation in pyramidal grains when compared to basally oriented grains. Again, it is seen that grains with twins have larger misorientations than those without, indicating that basal slip and twinning operate together to deform the crystal.In compression, twinning was seen to impede dislocation motion Due to the complexity of twinned structures in Re, TEM analysis gives valuable context for understanding the mechanisms causing strain accommodation within the Re microstructures. For this work conventional TEM imaging was used to determine twin morphology as well as the dislocation Burgers vectors twinning planes. HAADF STEM was used to provide detailed images of the general microstructural behavior, with more limited interference from dynamical contrast effects than typical diffraction contrast imaging , where the images for 0.4% and 1.9% strain are conventional TEM DF, with the more heavily dislocated 3.3% and after fracture samples taken in STEM. The combined use of STEM images and conventional TEM for microstructural analysis provides the most complete view of TEM images of the rhenium microstructure formed under tension, and general trends can be seen in , dislocations tend to orient themselves with respect to each other such that they form long dislocation slip bands crossing from twin to twin. Very long thin twins are seen in the more heavily strained samples, while at low strains, thin twins are much more difficult to observe. The two twin boundaries seen in the 0.4% strain sample is more commonly seen at lower strains, where wider twins have formed. As the strain increases twins tend to form with very high aspect ratios, stretching tens of microns through the crystal, while remaining only a few hundred nanometers thick. Dislocation density increases steadily as the total applied strain increases. From the 1.9% applied strain sample to the 3.3% strain sample the density of twins increases significantly more than between any other steps.As seen in the low strain overview samples, slip bands containing many dislocations are extremely prevalent in the tension samples. Often these bands span in between twin boundaries, and unlike with the twins seen in compression, dislocation slip bands appear able to pass through the twin boundaries (or the twins pass through the slip bands unimpeded). A full g⃗∙b⃗ analysis for a heavily dislocated area within the 8.6% strain sample, can be seen in . Dislocations were imaged along multiple zone-axes, allowing for the determination of both <a> type and <c+a> type dislocations and the operating plane shows the interactions of <a> type and <c+a> type dislocations. A few sets of <c+a> dislocation networks surrounding slip bands of <a> type dislocations. At the high strains at fracture, 8.6% strain, the <a> type dislocations form loosely aligned slip bands slipping in the same direction. There are two distinct slip bands oriented roughly 60° apart from each other, indicating that before fracture occurs, multiple easy basal slip systems have been activated within individual grains, with pyramidal <c+a> dislocations surrounding the basal dislocations. These <c+a> dislocations, that were not visible during the initial low-strain dislocation observations () are likely appearing in such large quantities only when the motion of basal dislocations becomes difficult. With the pyramidal dislocations surrounding the basal dislocations, the formation of pyramidal dislocations serves to further impede the motion of basal dislocations, resulting in inability for the sample to adequately accommodate further strain, ultimately contributing to stress concentrations leading to failure.With the observation of multiple active dislocation systems at high strains, STEM imaging of twins within the moderate strain, 3.3% total strain sample was used to investigate the properties of twin boundaries as well as the interactions they have with the prevalent <a> type dislocations. The common behavior of the {112̅1}〈112̅6〉 twins seen in rhenium is the ability to transmit through one another. Another key feature which was commonly seen in Re twins under compression is the formation of larger twins often comprised of many smaller twins aggregated together. shows the structure of a typical {112̅1}〈112̅6〉 twin formed under tension with a second {112̅1}〈112̅6〉 twin propagating horizontally through the larger twin.Two main factors were used when determining the orientation of the twins and matrix in . First, diffraction patterns of the six noticeable regions were taken to determine orientation relationships and the angles between incident and exiting twins was measured within the STEM image, each DP inset within the STEM image of . Due to the non-standard shape of tension samples (2.85 mm x 3 mm rectangles) these images are taken using the single tilt FEI TEM holder. As such, the closest achievable zone for the matrix was near to a 〈101̅0〉 zone, which serves as the “rotation axis” around which the {112̅1}〈112̅6〉 twin changes its orientation. The most important thing to note about the twins seen in is that they have the same classical twin morphology seen in other heavily deformation twinned metals, where a distinct twin boundary separates the matrix crystal orientation from the twinned crystal orientation. The interior of the large vertical twin contains a single heavily dislocated region separated by the horizontal twin. The horizontal twin changes the orientation of the crystal between the top and bottom of the sample by a few degrees. While this does not appear to be a large misorientation it factors into the angles between the various twins not being exactly what the misorientation between {112̅1}〈112̅6〉 twins should be in a perfect Re crystal.The horizontal twin forms an angle of 68° to the twin boundary seen of the larger vertical twin, this angle is mirrored around the twin boundary twice, allowing for the twin to exit through the twinned region parallel to its initial direction after effectively “jogging” through the crystal along the basal planes. The measured angle of 68° is relevant for two more reasons, firstly it is the misorientation between the 〈101̅0〉 zone axis and the 〈72̅5̅3〉 zone axis. Since there is a few degree misorientation accompanied by the horizontal twin boundary, this 68° misorientation also becomes relevant as the angle between a [12̅16] and a [12̅16̅] direction will result in a roughly 65° for Re. Coupled with the few degree misorientation between the top and bottom diffraction patterns leads to the conclusion that the two twins are both the very common {112̅1}〈112̅6〉 type twin.The horizontal twin appears to increase in width substantially in width within the larger vertical twin regime, meaning that the twin plane along which it was formed has changed to occupy the requisite plane within the twinned regime. This twin transmission has been accompanied by an overall “jog” of the twin relative to the basal plane normal, as was seen in the twin transmission of {112̅1}〈112̅6〉 formed during compression. However, here the change in twin plane through the vertical twin can be clearly seen (mainly due to the use of STEM imaging as compared to conventional TEM). This observation demonstrates that transmission through the twin boundary involves a change of twin plane to that of the crystal past the twin boundary, while still maintaining the large misorientation across the twin after transmitting through the twin boundary.Dislocation interactions with the {112̅1}〈112̅6〉 twins formed in tension seem to be much more easy to describe than during the {112̅1}〈112̅6〉 compression formed twins. Since the twins formed in compression had such an intricate internal structure it was not surprising that dislocations were not identified within the twins themselves, only populated on the boundaries. In this regard, it is also not surprising that the twins had difficulty in transmitting through such complicated compression induced twin boundaries. Contrary to this, as can be seen in , very long thin twins form in tension. The twins are populated along their lengths with multiple dislocations emerging from the twin boundaries, as well as dislocations crossing the interiors of the twins, bridging in between the two twin boundaries. It is also noticeable how twins appear to intersect one another or branch away, forming regions of thicker or thinner twins, seen As a further example of possible twin configurations observed in tension twinning, shows very complex possibilities of twins within tension samples of Re. shows the complex twin structures inherent to the Re microstructure. In this part of the sample strained to 3.3%, the “z” shape twinning that was seen in previous compression studies also appears within the tension sample microstructure . It can also be seen in the magnified larger twins that dislocations are highly active within the in twinned regime, in , with dislocations clearly being able to cross the interior twin boundary near the interior junction of the twin split.With the more conventional twin boundary structure seen in tension-induced {112̅1}〈112̅6〉 twins, it is unsurprising that dislocation transmission through twin boundaries is easily achieved. To this end, future work should involve the developing the understanding of the intricacies of the {112̅1}〈112̅6〉 twin boundary for twins created in tension, contrasted with compression induced twins, as well as the twin boundary orientations that either allow or do not allow the transmission of dislocations. By comparing the two sections of the 3.3% strained sample microstructure, it can be seen that if the relative area of observed twins increases, the dislocation density reduces substantially. This further validates the notion that when it is crystallographically feasible, twinning will be dominant initially followed by basal slip, and then finally by <c+a> pyramidal slip.For the in-situ dislocation analysis of Re foils, two samples were produced which yielded interpretable results; the two samples will be referred to as sample 1 and sample 2. The initial pre-straining optic axis of sample 1 was close to a [112̅3] zone axis and sample 2 [415̅3], which were used for dislocation analysis. With the rolling texture inherent to the sample, and the orientation of the grains observed during testing, the observed region had the [0001] direction oriented roughly orthogonal to the tensile direction. The initial straining was stopped once the slip bands were visible in the bottom right of (a). The cause of these slip bands was not initially clear, however evidence of these lines being due to slip bands is taken from the in-situ deformation videos of sample 1, three frames of which are taken from the video and reproduced in . The formation of the slip bands through dislocations exiting through the surface can clearly be seen in the progression between (a–c). The slip bands and active dislocations are oriented with respect to each other with three-fold symmetry because the dislocations are all basal <a> type screws, determined using slip trace analysis.After identifying a thin area with suitable dislocations for in-situ dislocation analysis, further straining was performed to determine the evolution of dislocation motion with increasing strain.As stated in the methodology, any straining of the sample will also cause large translations of the viewed area. In order to mitigate this for viewing, a low magnification was used for the dislocation motion videos. The video of dislocation motion from which the stills in are taken was edited for contrast in Adobe Premier, as well as using stabilization software in order to keep the active region in view. Finally, most of the dislocation motion was seen after the strain was applied, during relaxation of the sample, and with the sample translated back into the field of view.For the initial configuration of dislocations in sample 1, (a), it can be seen that the active dislocations marked with arrows are all spaced relatively close together with an average spacing in between each dislocation of 300 nm. The series of frames in occurs over a span of 15 s. It can be seen that the leading dislocation has moved far out from the others, where it encounters an immobile pinned dislocation and they mutually annihilate. In frames b) and c) of , the other dislocations continue on the path made by the initial dislocation, however they also do not move with the same velocity as one another. In the video () it can be seen that during this relaxation period, dislocations do no flow smoothly, but start and stop in a “semi-jerky” fashion, less than what is described by Clouet in Ti Sample 2 was a more difficult sample in characterizing the mobile dislocations, with the closest major zone axis available with the single tilt axis was the high order [51̅4̅3] zone. For this sample dislocations were again found to be <a> type basal screw dislocations. While sample 2 does not have the three-fold slip banding that is apparent in sample 1, the dislocations are of the same character as in sample 1, and as such the general behavior should be directly relatable between the two samples. A series of frames from sample 2 in a (01̅11̅) DF imaging condition are seen in . Much like in sample 1, dislocations are seen to be irregularly spaced. Here the dislocation spacing is much larger than what was seen in sample 1. This is to be expected as the total number of dislocations is much lower, likely due to the fact that this region was observed to be active earlier within the strain history than the region of interest in sample 1. Despite this lower dislocation density, the overall behavior of dislocations has not changed, with different dislocations moving at different speeds traveling in the same general direction. The dislocations shown in (d) and (e) are seen to be very slow, while the leading dislocation travels a large distance and stops between (b) and (c). Additionally, the distances that dislocations jumped in their “jerky” motion was much larger than in sample 1, likely due to the abundance of previously formed slip bands in sample 1, as well as sample 1 having a much longer deformation history.With the aim of investigating the mechanical properties of rhenium guided by the high temperature properties of this unique metal, each in-situ sample provides an opportunity for the direct comparison of dislocations at room temperature and high temperature. The effect of temperature is immediately seen when operating the sample holder within the TEM, as large thermal expansions translate the sample during the initial heating. Once thermal equilibrium is reached, the sample is strained using the same method as was performed at room temperature.. The results of high temperature in-situ testing of sample 2 gives the most insights into the effects of temperature on the dislocation motion of basal <a> type dislocations in Re.Since the available temperature for in situ TEM straining is still less than one third of the homologous temperature of Re, in situ deformation at 920 degrees C can still be considered in the relatively low temperature regime for Re. With this relatively low temperature increase, large behavior changes were not anticipated, but are worth reporting. Still frames that detail the motion at temperature of Re dislocations can be seen in . Arrows mark the position of large motions between the frames. Much like what was seen in the room temperature motion of the dislocations, the dislocations move in the same “semi-jerky” way as was seen in the room temperature tests. The only discernable difference seen between the high-temperature dislocations and the room temperature straining is the number of active dislocations, and the size of the motion bursts. At 920 °C there are far more dislocations activated during deformation. In order to see appreciable differences at temperature, the sample must be tested at well over 1000 °C, something that is beyond the capabilities of the in-situ holder.Pure rhenium samples were tested in tension in order to understand the interplay between microstructure and the exceptionally high work-hardening behavior seen uniquely in rhenium. Through the use of multiple microscopy techniques, a full description of the typical microstructure progression of Re under tension as a function of strain was described. The use of EBSD demonstrated that the overall undeformed microstructure had a very {112̅1}〈112̅6〉 twin unfavorable texture for loading under tension. This lead to the overall area fraction of twins within the post-deformation microstructure being equivalently saturated above a strain value of one third the fracture strain. This coincided with the end of the initial high work hardening rate seen in Re. Above the point of twin saturation, all changes to the deformed microstructure using EBSD was seen as increased local misorientations within the grain interiors. Grains showing extensive large twins had large misorientations in between the twins due to basal slip activity, as determined by the Schmidt factor favorably seen in the EBSD maps and later confirmed using TEM imaging. Finally, EBSD demonstrated that pyramidal slip activated appreciably only when strain increased above half of the failure strain. The high initial rate of twin formation with dislocation slip was tied to the high initial work hardening rate which quickly lowers as twinning saturates.Conventional TEM dislocation analysis was performed to understand the dislocation structures as well as the planes upon which dislocation slip operated. <a> type b⃗=[112̅0] screw dislocations operated on the basal planes in loosely aligned slip bands. Only <a> type dislocations were observed in the TEM at low strains, generally between twin boundaries. At failure, <a> type b⃗=[112̅0] basal screw dislocations were again observed in dislocation slip bands. <c+a> type b⃗=[112̅3] pyramidal screw dislocations, which formed tangled dislocation nets interfering with <a> type glide, were observed at high strains, likely due to their much higher CRSS value. The morphology of tension induced {112̅1}〈112̅6〉 twins was more representative of classical twin structures involving well-defined twin boundaries than {112̅1}〈112̅6〉 twins formed in compression. Twin transmission with {112̅1}〈112̅6〉 twins changing twin plane between parent and matrix orientations was observed. Multiple twin systems with twins growing out of twin boundaries were observed, with the TEM and STEM observations confirming the observations made using purely EBSD maps for analysis.In-situ straining was performed on rhenium both at room temperature and at elevated temperature. The samples used all had a foil texture, suppressing possible {112̅1}〈112̅6〉 twinning, while exaggerating <a> type dislocation activity. <a> type 〈112̅0〉 basal dislocations was the dominant mechanism during in-situ tensile straining. No <c+a> type {101̅1}〈112̅3〉 dislocations were observed in-situ, likely due the relatively low absolute stresses imposed upon the sample during the in-situ test. Dislocation motion was observed with video, with the general dislocation motion consisting of a “jerky” crawl of loosely aligned dislocations. The only appreciable effect that elevating temperature to 920 °C had on dislocation motion was to possibly increase the number of active dislocations.In conclusion, our results show that deformation twinning is mainly activated at low strains, with dislocation plasticity accommodating the additional strain after twinning saturates, and that the exceptionally high initial work hardening rate in Re is mainly due to large scale twin formation coupled with basal slip activity.Supplementary data associated with this article can be found in the online version at Supplementary materialSupplementary Fig. 1 g⃗∙b⃗ analysis for a dislocation slip band in the 3.3% strained sample, viewed in a JEOL 2011 microscope, using a 200kv accelerating voltage. Images were all taken using a strong 2-beam Bragg condition from a 〈112̅3〉 zone axis with the BF images (left) generally showing less dislocation contrast than the DF two beam condition (right). Using the DF images, the (11̅01) and (1̅101̅) were seen to be invisible, such that g⃗∙b⃗=0, and b⃗=[112̅0] screw dislocationsExperimental study on seismic performance of fire-exposed perforated brick masonry wallThe seismic performance of perforated brick masonry wall was investigated by subjecting six fire-exposed pieces and one unexposed piece to low reversed cyclic loading. Two of the exposed pieces were reinforced with carbon fiber cloth and steel mesh cement mortar. The effect of the fire duration, fire boundary, cooling regime, and reinforcement method on the failure characteristics of the specimens was investigated. The experimental results revealed that (i) for the same position, the temperature of the mortar was higher than that of the brick and (ii) the cracking load and ultimate load of the walls decreased progressively with increasing fire duration. Moreover, the ultimate bearing capacity of the wall reinforced by carbon fiber cloth and steel mesh cement mortar was higher than that of the wall subjected to the same fire duration. This capacity was also higher than that of the unexposed wall.Masonry structure has always played an important role in Chinese and global architecture. This structure is low cost and can be fabricated from various materials and through a simple construction process. Hence, this structure is used in various civil and public buildings. In China, reuse and reinforcement of the existing masonry buildings is important for the construction of cities. These buildings are, however, susceptible to fire damage. Nevertheless, a mature theory and method for properly assessing the safety and seismic performance of fire-exposed masonry structures is lacking. Therefore, (i) an evaluation of the mechanical properties and seismic performance as well as (ii) the development of a reinforcement method for fire-exposed perforated brick masonry structure are significant from both theoretical and engineering perspectives.To date, research on the seismic behavior of fire-exposed masonry walls remains unreported. Studies have focused mainly on the thermal performance of masonry and the effect of elevated temperatures on the mechanical properties of single brick specimens Some researchers have conducted experiments and finite element studies on the mechanical properties of fire-exposed masonry walls The effect of reinforcement on masonry walls exposed to room temperature has recently been investigated The seismic behavior of fire-exposed concrete structures has been considered in some studies A literature review has shown that mature theories and methods for evaluating the safety and seismic performance of fire-exposed masonry walls are lacking. For restored use of the fire-exposed masonry structure, the extent of damage should be assessed, and the reinforcement scheme should be determined relatively quickly. The seismic performance of the structure must be calculated to determine whether the fire-exposed masonry structure can be reused after reinforcement. However, determining whether the fire-exposed masonry structure meets the seismic requirements is impossible via current standards. Therefore, in this work, the perforated brick masonry wall was subjected to fire tests and subsequent low cycle tests to determine the effect of different reinforcement methods on the seismic performance of the fire-exposed wall.This study was based on a fire-exposed masonry structure in Shanghai. Some of the walls of the masonry structure were exposed to fire on one side, but many walls were exposed to fire on two sides. Therefore, in our study, five specimens were exposed to fire on two sides and one specimen was exposed to fire on one side. Six perforated brick masonry walls, without loading, were subjected to the fire test. KP1-type perforated brick (strength: MU10, size: 240 mm × 115 mm × 90 mm) was selected in accordance with Chinese codes GB13544-2011 . The grade of the mortar (strength of mortar: M2.5) was designed using different proportions of cement, lime putty, and sand (1:1.14:9.4). The concrete strength of the top beam and the bottom beam was C25. The fire tests were all performed in the large-scale horizontal test furnace housed in the Southeast University Key Laboratory for Concrete and Prestressed Concrete Structure of the Education Ministry of China. Perforated brick masonry walls with sizes of 1500 mm (length)×240 mm (width)×1865 mm (height) were heated in a 4000 mm (length)×3000 mm (width)×2000 mm (height) furnace; see for the specimen description and dimensions, respectively.All specimens will be constructed in accordance with Chinese codes GB 50203-2011 The fire test was based on the ISO 834 standard fire temperature curve, which was recommended by the International Organization for Standardization. Twelve thermocouples were placed in the same location of each specimen. Measurement points T1–T3 at embedded depths of 40 mm, 80 mm, and 120 mm, respectively, were designated for the same brick in the middle of the wall. Measurement points T4–T6 with embedded depths of 40 mm, 80 mm, and 120 mm, respectively, in the mortar joint were located at respective positions corresponding to T1–T3. These six measurement points allowed a comparison of the temperature at the same depth in the brick block and the mortar joint. The temperature distribution, i.e., the temperature recorded by each of the thermocouples placed at the aforementioned depths in the brick block and mortar joint, was determined. Measurement points T7–T12 corresponding to the positions of points T1–T6, respectively, were located at the bottom left of the wall. The array of 12 thermocouples is shown in Specimen S1.5 was exposed to fire on one side. Fire-resistant asbestos was used on both sides, as well as on the back of the specimen and the end of the top beam, as shown in a. Specimens D1.5, D2.5, D1.5C, D1.5S, and D1.5-W were exposed to fire on two sides. Fire-resistant asbestos was used on both sides of each specimen and the end of the top beam, as shown in b. The six specimens were divided into four groups and subjected to fire tests with different duration and cooling mode, as the horizontal test furnace can only test two wall pieces at a time. The first furnace contains specimens D1.5 and S1.5; the second furnace contains D2.5; the third furnace contains D1.5C and D1.5S; the fourth furnace contains D1.5-W.In addition to specimen D1.5-W, the rest of the specimens underwent natural cooling. When the temperature in the furnace was lowered to 200 °C, the lid of the furnace was opened, thereby allowing cooling of the specimen to room temperature. Heating of D1.5-W was stopped after the design temperature was reached. When the temperature in the furnace was lowered to 400 °C (for safety reasons), the lid of the furnace was opened, and the specimen was water-cooled. A large amount of white smoke was emitted during the water cooling process, as shown in Similar results are obtained for the six specimens exposed to high temperatures. The results revealed that the integrity of each specimen is retained. The specimens remain connected and brick peeling is absent after fire exposure. However, the surface of the fire-exposed wall becomes white, and small cracks form in the surface of some bricks. The fire-exposed mortar can be removed by hand. However, the fire has only a small influence on the asbestos-covered parts of the wall, and the appearance of these parts is virtually unchanged (see for photographs of the fire-exposed wall).The ISO 834 standard fire temperature curve and the actual furnace temperature curve are compared in ① The furnace temperature and ISO 834 standard fire temperature curve are basically consistent, especially for the second furnaces. For these furnaces, the difference in temperature between the furnace temperature and the temperatures along the ISO 834 standard fire temperature curve is ≤2 °C.② After 20 min, the temperature of the first furnace becomes lower than the temperatures along the ISO 834 standard fire temperature curve. This results possibly from the fact that the air was wet, owing to heavy rain, and the supply of natural gas was constant. The temperature difference is ≤ 10 °C and, hence, the error is small.The temperature curves of the third and fourth furnaces are similar to those of the first and second furnaces.Compare the temperature at the same depth of the brick and the mortar jointTake specimen D1.5 as an example. The corresponding temperature–time curves of measurement points T1–T6 are shown in ① The temperatures of T1, T2, and T3 are respectively smaller than those of T4, T5, and T6, respectively, indicating that the temperature at the same location of the brick is lower than that of the mortar.② The difference in the highest temperature between the brick and the mortar joint increases with increasing depth of the measurement points. The difference in the highest temperature between T4 and T1 is small, but the differences associated with T5 and T6 are 34.7% higher and 48.7% higher than those of T2 and T3, respectively.Compare the temperature at different depths of the brick and the mortar jointTake specimen D1.5 as an example. The temperature at different depths of the brick and the mortar joint are shown in . The trends may be summarized as follows:① The temperature of the measurement point decreases with increasing embedded depth of the points, and the temperature difference between T1 and T2 is considerably larger than the difference between T2 and T3. In the brick, T1 and T2 are 346.75 °C and 118.56 °C higher than T2 and T3, respectively. In the mortar joint, T4 and T5 are 237.65 °C and 135.68 °C higher than T5 and T6, respectively. This indicates that, compared with other regions, the region 80–120 mm away from the fire side is less affected by the fire.② The temperature of the measurement point increases slowly in the initial stage and rapidly in subsequent stages.Influence of the fire boundary on the temperature distribution of the wallTake D1.5 (exposed to fire on two sides) and S1.5 (exposed to fire on one side) as the research objects. shows the influence of the fire boundary on the temperature distribution of the brick and mortar. The measurement points T1–T6 are located in D1.5, and measurement points T1‘–T6‘ are located in the corresponding positions in S1.5.① At the same position, the temperature of the measurement point exposed to fire on two sides is higher than that of the point exposed to fire on one side. The corresponding temperature difference increases with increasing depth of the measurement point. In brick, the temperature difference of each measurement point is described as follows: T1, T2, and T3 are 12.9%, 52.1%, and 91.4% higher than T1‘, T2‘, and T3‘, respectively. In mortar, the temperature difference of each measurement point is described as follows: T4, T5, and T6 are 7%, 44.5%, and 139.6% higher than T4‘, T5‘, and T6‘, respectively. This indicates that the fire boundary exerts a larger influence on the temperature of the mortar than on the temperature of the brick.② In the first 40 min, the temperature difference between the walls with two sides and one side exposed to fire is insignificant, but increases gradually thereafter. This indicates that, in the D1.5 wall, heat transfer from the far side to the measuring point occurs in the later stages, rather than in the initial stage of the fire. Therefore, the temperature difference between the walls with two and one side exposed to the fire is insignificant in the first 40 min. With increasing fire duration, heat transfer from the far side to the measuring point and, hence, the temperature difference between D1.5 and S1.5 also increase.The temperature distribution along the wall shows the temperature-time curve of 12 measurement points along the specimen. The temperature of points T1–T6 is higher than that of T7–T12, respectively, indicating that the temperature of the lower part of the wall is lower than that of the upper region. This results from the fact that the gas nozzle in the fire testing furnace is located approximately halfway along the height of the furnace. Therefore, compared with the lower part of the wall, the middle part of the wall is more directly affected by fire. However, the temperature difference is, in general, very small (i.e., mean temperature difference: ≤30 °C) and similar trends are observed, indicating that the temperature distribution of the entire fire-exposed wall is uniform.After the fire test, the D1.5C and D1.5S were reinforced with carbon fiber cloth and steel mesh cement mortar, respectively. The aforementioned seven specimens were tested under a low reversed cyclic load.Reinforcement with the carbon fiber clothThe attributes of the X-shaped wall reinforced on two sides are summarized as follows: bandwidth of carbon fiber cloth: 300 mm, length and bandwidth of anchor fabric: 600 mm and 150 mm, respectively. During construction, the oblique carbon fiber cloth would be pasted first, and the vertical carbon fiber cloth will be pasted afterward. The ends of the oblique carbon fiber cloth must be anchored, as shown in The mechanical properties of the carbon fiber and the binder are shown in Reinforcement with the steel mesh cement mortarThe attributes of the wall reinforced on two sides were summarized as follows: thickness of the reinforced concrete mortar: 40 mm, diameter and spacing of transverse rebar: 6 mm and 250 mm, respectively, diameter and spacing of vertical rebar: 8 mm and 250 mm, respectively, and spacing of S-shaped binding rebar: 500 mm. shows the wall reinforced with the steel mesh cement mortar.The average compression strength of the cement mortar layer was 25.6 MPa. In addition, the yield strength and the ultimate strength of the rebar with a diameter of 6 mm were 429.3 MPa and 635.2 MPa, respectively. The yield strength and ultimate strength of the rebar with a diameter of 8 mm were 469.6 MPa and 713.2 MPa, respectively., and a schematic and a photograph of the test device are shown in . To prevent slippage or overturning, the bottom beam was anchored to the floor of the laboratory using anchor bolts. In addition, the wall was fixed by a lateral steel support, thereby preventing out-of-plane collapse of the wall during testing.The test loading system was based on Chinese codes JGJ101-2015 During the load-control stage, the wall was pushed and pulled once per load level. Level I corresponded to a load of 0.2 Pu, and each subsequent level was associated with a load increase of 0.2 Pu until a load of 0.8 Pu was reached. Thereafter, each level was associated with a load increase of 0.1 Pu until cracks formed. Displacement control was then adopted. During the displacement-control stage, the wall was pushed and pulled three times per load level. The initial loading displacement was the cracking displacement (△cr) and the displacement was increased by △cr for each subsequent level. until the load was reduced to 85% of Pu. At this point, the wall was considered destroyed, the test was stopped, and the corresponding displacement of the wall was recorded as the ultimate displacement (see for the corresponding loading diagram).This test consists of several components namely, the:horizontal displacement of the wall at all levels of loading. In the MTS measurement, this displacement was checked by a horizontal-displacement meter placed in the cross-section of the top beam. Similarly, the horizontal movement of the bottom beam was measured by horizontal displacement meters placed in the cross-section of the bottom beam.development of fracture, which was observed via visual inspection and measured with a steel ruler and measuring tape.strain experienced by the carbon fiber cloth and the steel mesh in the reinforced masonry wall.The layout of the (i) displacement meter and (ii) strain gage in the carbon fiber cloth and the steel mesh is shown in The results indicate that all seven walls undergo mainly shear compression failure. X-shaped cracks are normally produced along the diagonal of the walls. Most of the cracks are characterized by a ladder-like distribution and occur in the mortar joint (i.e., only a few cracks occur in the brick). As the load increases, the X-shaped cracks expand continuously until the wall is divided into several triangular parts, resulting in the final destruction of the wall.Owing to shear-friction failure, a horizontal seam is formed at the bottom of specimen C. The failure of D1.5C is attributed to a reduction in the area of the wall section. This reduction results from cracking of the wall by the carbon fiber cloth, and subsequent crushing of the wall. Specimen D1.5-W undergoes typical shear compression failure, i.e., when the wall reaches the cracking load, the cracks extend along the horizontal and vertical mortar joint to the diagonal of the wall. shows the final destruction of the seven walls.The test results of the walls are summarized in The bearing capacity of each specimen is presented in the form of a bar graph (see show, the cracking load and ultimate load of the perforated brick masonry wall decrease upon fire exposure of the wall. The cracking load and ultimate load of the wall can be improved through reinforcement with carbon fiber cloth and steel mesh cement mortar. However, the ultimate load is improved more than the cracking load. In fact, compared with that of wall C, the:cracking load values of unreinforced walls D1.5, S1.5, D2.5, and D1.5-W are 13.7%, 7.0%, 20.4%, and 20% lower, respectively; the corresponding ultimate load values are 14.6%, 12.1%, 34.7%, and 21.7% lower, respectively. The cracking load, ultimate load, and shear capacity of the wall decrease with increasing fire duration. For the same fire duration, the bearing capacity of the wall exposed to fire on both sides is (2.5%) lower than that of the wall exposed to fire on only one side. Similarly, the bearing capacity of the water-cooled wall is (7.1%) lower than that of wall D1.5.cracking load values of D1.5C reinforced by the carbon fiber cloth and D1.5S reinforced by the steel mesh cement mortar are 6.2% and 19.5% higher, respectively. The corresponding ultimate load values are 15.6% and 53.5% higher, respectively. Both methods of reinforcement restore the post-fire bearing capacity of the wall to the pre-fire level. The capacity improves to varying degrees, especially the capacity of D1.5S reinforced by the steel mesh cement mortar, which increases by 79.4%.ratio of the ultimate load to the cracking load of the four unreinforced walls is lower. Values of 139.1%, 133.6%, 115.4%, and 138.0% (ratio corresponding to wall C: 141.2%) are obtained for D1.5, S1.5, D2.5, and D1.5-W, respectively. The difference in the ratio is most significant for wall D2.5, where the ultimate load is only 15.4% higher than the cracking load. Therefore, consistent with the occurrence of brittle failure, the ultimate load of the fire-exposed wall is reached relatively rapidly after cracking begins. The ratio decreases with increasing fire duration. Ratios of 153.7% and 181.5% are obtained for D1.5C and D1.5S, respectively.These results indicate that both methods of reinforcement can slow the process of wall cracking and damage. However, compared with the reinforcement consisting of carbon fiber cloth, the reinforcement consisting of steel mesh cement mortar is more effective in slowing this process.The hysteresis curve of each specimen is shown in . The following conclusions can be drawn from the trends exhibited by these curves.The amount and area of hysteresis associated with unreinforced walls D1.5, S1.5, D2.5, and D1.5-W are lower than those associated with wall C. This indicates that fire exposure leads to a decrease in the energy dissipation capacity and seismic performance of the wall. The hysteresis area and ultimate load of S1.5 are greater than those of wall D1.5. Therefore, the seismic performance of the wall exposed to fire on one side is slightly better than that of the wall exposed to fire on two sides. The stiffness of D1.5-W decreases very abruptly, and the hysteresis area is smaller than that of D1.5, indicating that water cooling increases the brittleness, reduces the ductility, and lowers the seismic performance of the wall.The D1.5C walls reinforced by the carbon fiber cloth and D1.5S reinforced by the steel mesh cement mortar have large hysteresis areas. Similarly, the amount of hysteresis and ultimate load are significantly higher than those of the unreinforced walls. The D1.5S wall has high ductility. Therefore, both methods of reinforcement can yield significant improvement in the seismic performance and energy dissipation capacity of the fire-exposed walls. In addition, the seismic performance of D1.5S is better than that of D1.5C. The ductility of the steel mesh reinforcement is superior to that of the carbon fiber cloth, thereby yielding more significant improvement in the seismic performance of the wall.The skeleton curve of each specimen is shown in . The following conclusions can be drawn, based on the trends shown in these curves.Compared with that of wall C, the peak and slope of the skeleton curves of four unreinforced walls are smaller and decrease with increasing fire duration. This indicates that the fire reduces the bearing capacity and stiffness of the wall. The peak and slope of the S1.5 wall is greater than that of the D1.5 wall. Therefore, the bearing capacity of the wall exposed to fire on one side is higher than that of the wall exposed to fire on two sides. The skeleton curve of D1.5-W lies between the curves of D1.5 and D2.5. Hence, for the same duration, the seismic performance of the water-cooled wall is worse than that of the air-cooled wall, but is better than that of wall D2.5.The skeleton curve of D1.5C and D1.5S lies above and has a greater slope than the curves corresponding to the unreinforced walls. This shows that both methods of reinforcement can restore the post-fire bearing capacity and ductility of the wall to pre-fire levels. In addition, the skeleton curve of D1.5S is above the curve corresponding to D1.5C. This suggests that the seismic performance of the wall reinforced by the steel mesh cement mortar is better than that of the wall reinforced by the carbon fiber cloth.The skeleton curve of each specimen is shown in . The following conclusions are drawn, based on the trends associated with these curves. The:stiffness degradation curve of D2.5 is convex and steeper than the curves of the other walls. The curves of the other walls are concave and relatively smooth. The results show that a fire duration of 2.5 h has significant influence on the stiffness degradation curve.initial stiffness of the wall reinforced by the steel mesh cement mortar is more than 55% higher than that of the other walls. Furthermore, the corresponding stiffness degradation curve associated with subsequent loading stages is the smoothest. In the case of carbon fiber reinforcement, the initial stiffness and the rate of stiffness degradation are only slightly higher than the pre-reinforcement values. Therefore, if the initial stiffness of the wall is desired, reinforcement with the steel mesh cement mortar is more effective than reinforcement by the carbon fiber.In this work, the displacement ductility coefficient (i.e., the ratio of the ultimate displacement to the crack displacement; see ) is used to describe the ductility performance of a specimen. The following conclusions are drawn, based on the trends shown in the histogram.The ductility of the specimens after the fire is lower than that of the normal temperature specimen, and decreases progressively with increasing duration of the fire. Compared with that of wall C, the ductility of walls D1.5 and D2.5 is 23.7% and 33.5% lower, respectively, indicating that the fire reduces the ductility of the wall. Moreover, the degree of attenuation is proportional to the fire duration. The ductility coefficient of the wall exposed to fire on one side is only 5% higher than that of the wall exposed to fire on two sides. This indicates that fire exposure of one side or two sides has little effect on the ductility of the wall. The ductility of D1.5-W is lower than that of D1.5, showing that water cooling results in increased brittleness and decreased ductility of the wall.The ductility coefficients of D1.5C and D1.5S are 19.7% and 36.1%, respectively, higher than that of C, and 56.9% and 78.3% higher, respectively, than that of D1.5. Therefore, both methods of reinforcement can restore the post-fire ductility of the wall to the pre-fire level. However, compared with the carbon fiber cloth, the steel mesh cement mortar is more effective in improving the ductility.The energy dissipation capacity of the structure is characterized via the energy dissipation coefficient he (see . Under earthquake conditions, this capacity increases with increasing he (see for the he value of each specimen). The following conclusions are drawn, based on the trends shown in the histogram.The he values of D1.5 and D2.5 are 13.6% and 25.9% lower, respectively, than that of C. Furthermore, the energy dissipation capacity of the wall decreases after the fire, and worsens with increasing fire duration. The he value of S1.5 is slightly higher than that of D1.5. This indicates that the energy dissipation capacity of the wall exposed to fire on one side is stronger than that of the wall exposed to fire on two sides. Moreover, the he value of D1.5-W is lower than that of D1.5, showing that water cooling leads to a decrease in the energy dissipation capacity of the walls.The he value of D1.5C and D1.5S is higher than that of the other walls. Therefore, both types of reinforcement methods lead to an increase in the amount of energy absorbed and dissipated during an earthquake. However, the steel mesh cement mortar provides more effective (i.e., earthquake-resistant) reinforcement than the carbon fiber cloth.The strain-load curve of the carbon fiber cloth for the typical position of D1.5C is shown in . The positive load, negative load, positive strain value, and negative strain value in the figure represent the horizontal thrust, horizontal pull, tensile strain, and compression strain, respectively. The following conclusions are drawn, based on the trends in the figure.Strain gages 1 and 2 are attached to the middle of the vertical carbon fiber cloth. These gages, which recorded small strain values, are attached to the rift grain and the cross grain of the fiber, respectively. However, the value recorded by gage 2 is larger than that recorded by gage 1. The vertical carbon fiber cloth plays a small role in the experiment, and the rift grain of the cloth experiences a larger strain than the cross grain. With the use of reinforcement, cost optimization can be achieved by removing the middle section of the vertical carbon fiber. Therefore, only the upper and lower parts can be used for anchoring the diagonal carbon fiber cloth and the wall.In the initial stage of loading, the specimen remains crack-free and the carbon fiber cloth is only slightly strained. Cracking occurs with increased loading, and the strain recorded by strain gages 7 and 12 increases sharply at the position of the crack. This results in pulling of the carbon fiber cloth (as indicated by the bending of the strain-load curve), which experiences a high level of tension-induced stress. Bulging occurs in the central region of the carbon fiber cloth, whereas the bottom corner of the cloth is stuck to the wall. Therefore, the peak strain recorded by gage 12 is higher than that recorded by gage 7.The strain-load curve of the steel mesh for the typical position of D1.5S, is shown in . The following conclusions are drawn, based on the trends shown in the figure. The:transverse rebar in the steel mesh experiences a very large strain, with similar peak strain values of 2216 µε, 2459 µε, and 2839 µε recorded by strain gages 6, 7, and 8, respectively. The transverse rebar of the upper, middle, and lower parts of the steel mesh experience similar levels of strain.vertical rebar experiences a relatively small strain, as evidenced by peak strain values of 240 µε, 291 µε, 202 µε, and 282 µε recorded by strain gages 1, 5, 9, and 13, respectively. The peak strain recorded by gages 5 and 13 is slightly greater than that recorded by gages 1 and 9, respectively. The vertical bar at the bottom corner of the steel mesh experiences a slightly larger strain than the bar at other locations.transverse rebar in the steel mesh experiences a significantly larger strain than the vertical rebar. Therefore, the transverse rebar and vertical rebar yield significant improvement and slight improvement, respectively, in the bearing capacity of the wall. With the use of reinforcement, cost optimization can be achieved by increasing the spacing of the vertical rebar.The fire test is based on the ISO 834 standard fire temperature curve. The integrity of the wall without external load is maintained for fire durations of up to 2.5 h, whereas the surface of the fire-exposed wall becomes white. In addition, the strength of the mortar decreases, owing to fire exposure, and the mortar can then be removed by hand.The coefficient of thermal conductivity of the mortar is higher than that of the brick masonry. For the same position, the temperature (i) of the mortar is higher than that of the brick and (ii) difference of the highest temperature between the brick and the mortar joint increases with increasing depth of the measurement points.The temperature of the measurement point decreases with increasing embedded depth of the points. The temperature of the measurement point increases slowly in the initial stage and rapidly in subsequent stages.At the same position, the temperature of measurement points exposed to fire on two sides is higher than that of points exposed to fire on one side. This temperature difference increases with increasing depth of the measurement point. Furthermore, this fire boundary has greater influence on the mortar temperature than on the brick temperature.The cracking load and ultimate load of the walls decrease, when the fire-exposed perforated brick masonry wall is subjected to a low reversed cyclic load. These loads decrease progressively with increasing fire duration. For the same fire duration, the bearing capacity, ductility, and energy dissipation capacity of the wall exposed to fire on one side are slightly higher than those of the wall exposed to fire on two sides. Compared with air cooling, water cooling increases the brittleness, reduces the ductility, and lowers the seismic performance of the wall.The ultimate bearing capacity of the wall reinforced by carbon fiber cloth is 15.6% higher than that of wall C and is 35.1% higher than that of the wall exposed to fire for the same duration. Similarly, the ductility and energy dissipation capacity of the walls have improved, and the seismic performance of the wall can be restored to the pre-fire level. However, this reinforcement method has little effect on improving the initial stiffness of the wall.The ultimate bearing capacity of the wall reinforced by the steel mesh cement mortar is 53.5% higher and 79.4% higher than that of wall C and the wall exposed to fire for the same duration, respectively. This reinforcement method yields significant improvement in the seismic performance, stiffness, ductility, and energy dissipation capacity of the wall.The authors declared that they have no conflicts of interest to this work.Virtual Sliding Pipe Rheometer for estimating pumpability of concretePredicting the pumping pressure needed to ensure a consistent flow rate of concrete is crucial to the success of current construction processes and newly introduced, but fast-growing 3D-concrete printing techniques. The Sliding Pipe Rheometer (Sliper) has recently proved to be a reliable experimental tool in predicting pumping pressure. Building on the experimental results of an earlier investigation by means of Sliper, a single-fluid numerical model for simulating Sliper tests (virtual Sliper) was developed using Computational Fluid Dynamics (CFD). Various observations as well as numerical limitations of the model and their physical origins were analysed. It was demonstrated that lubricating layer has vital influence on concrete pumping and that single phase numerical models, not considering the lubricating layer are only applicable to some specific concrete compositions. Hence, the initial single-phase model was improved by implementing a separate lubricating layer; its properties were calculated using Chateau-Ovarlez-Trung and Krieger-Dougherty models. Experimental and numerical comparative analyses confirm the validity of the above-mentioned approach in calculating lubricating layer properties. Parameter sensitivity analysis showed that the plastic viscosity and thickness of the lubricating exert the dominant influences on pumping pressure. The virtual pumpability testing tool as developed should enable a more purposeful material design of pumpable concrete and pre-estimation of pumping processes.Concrete pumping has emerged as one of the most important processing technologies in the construction industry. It often makes possible the reduction of construction costs and considerably speeds up the construction process. Concrete pumping is also crucial to many advancements in construction-related processes such as Digital Construction (DC), often called 3D-printing with concrete. In the case of onsite DC techniques, concrete must be transported or pumped over longer distances, periodically stopping after having pumped each layer, but without any blockages or circuit breakdowns over longer time durations (see Concrete pumping occurs by pushing concrete using high pressure into pipelines made of either flexible, abrasive resistant material or steel. In other words, the force of the applied pressure causes the concrete material to deform in the direction of the force applied and so to transmit the force further. The pressure required to pump concrete depends on its composition as well as on the pumping specifications such as distance, height to pump, pipe diameter, and discharge rate. Any changes in the composition of concrete such as water-to-binder ratio, aggregate size distributions (grading), and admixtures can exert a pronounced influence on its rheological properties, indeed its behaviour during pumping. Hence, predicting the discharge pressure needed to pump a particular concrete mixture over a given distance or height at a specific rate is not trivial. Much research has been conducted on this topic, especially during the last two decades, which has led in turn to different prediction models and test approaches ) which is a relatively new device developed to overcome the conventional problems in testing the pumpability of concrete and estimating discharge pressures for various concrete types As the first part of this research, extensive laboratory investigations (considering plug/slip flow with no deformation in the plug where L is the length, D is the diameter of the pipeline, ρ is the density of concrete, H is the pumping height, and Q is the desired flow rate.Assuming a linear relationship between P and Q, see where PH = pressure induced by deadweight of concrete in the Sliper pipe, parameters a and b can be calculated from the P-Q plot of Sliper experiments using Eq. where A is the P-intercept of the P-Q curve, B is the slope of P-Q curve, and l and d are the length and diameter of Sliper pipe, 0.5 m and 0.126 m, respectively.Today’s very broad spectrum of concrete compositions, which certainly become even broader in the future, makes it necessary to perform numerous experiments to characterise their rheological properties and subsequently determine their pumpability. Moreover, considering on the one hand that concrete properties are time- and thixotropy- (resting time) dependent and that on the other hand pumping in the case of modern processes such as DC demands pumpability for longer durations, extensive experimental studies are needed to assure the pumpability of concrete, even if its composition is unaltered. Therefore, a purely experimental approach for assessing pumpability does not seem feasible in all the cases, since extensive experimental tests demand a great deal of time and economic investment.As in many other fields, numerical simulations present a promising tool in complementing experimental studies The common numerical approaches in simulating the behaviour of fresh concrete are Computational Fluid Dynamics (CFD) In CFD, concrete is modelled as a single continuum phase or as multiple continuum phases, while the modelled domain is discretized as interconnected mesh elements. This means that the rheological properties of concrete in a phase are constant throughout the modelled geometry. Numerical solution for fresh concrete’s rheological behaviour is then made possible by adding apparent viscosity, commonly following the Bingham or Herschel-Bulkley models, to the Navier-Stokes equations It is possible to simulate large volume concrete flows such as castings The approach presented in the article at hand is significantly different to those previous to it. In all the above listed literature, numerical models were primarily developed to study concrete flow characteristics, and that of LL, in a long pumping circuit. So far no numerical model is available to link the resulting rheological properties as observed in the Sliper tests to any other more commonly used experimental procedure such as the use of a rheometer or viscometer. This is a rather significant knowledge deficiency that should be overcome with the utmost urgency, considering the proven applicability of Sliper for pumping pressure prediction and its newness and unavailability in most concrete laboratories and ready-mix concrete practitioners. This paper addresses this challenge by presenting virtual Sliper – a CFD model able to predict Sliper experimental results using rheological input parameters according to the Bingham model as obtained from viscometer tests.From this point on, this paper is organised into the following segments: Experimental background (Section ), Single-phase numerical model (Section ), and User-defined, single-phase model (Section ), followed by the summary and conclusions (Section ). In both numerical model sections, the modelling schema is presented in detail, followed by results and discussion. In the initial single-phase model, Sliper simulations were carried out without considering the LL. It was demonstrated that single-phase numerical models which do not consider the LL are applicable only to some specific concrete compositions. With that in mind, an initial single-phase model was improved by implementing a separate LL using a user-defined function; its properties were calculated using Chateau-Ovarlez-Trung and Krieger-Dougherty models. Finally, the applicability of user-defined single-phase model for predicting pressured measured with Sliper is demonstrated for all concrete compositions under investigation.As the first part of this research, extensive laboratory investigations of the pumpability of fresh concrete were conducted using Sliper gives an overview of the mixtures under investigation. All these concretes were also tested using a ConTec Viscometer 5 and the flow table. The evaluation of the results emphasised the advantages of using Sliper to characterise the pumping behaviour of concrete, while a positive correlation was found between the Sliper viscosity parameter b and the plastic viscosity µ as obtained from the viscometer tests. Finally, the predicting capability of Sliper was validated under field conditions by measuring full-scale pumping pressure. The details of the mixtures tested, testing procedures, and the results obtained are presented and discussed in the previous article In the first step of the Sliper modelling experiments, concrete was assumed to be a continuous Bingham fluid, and the approach is termed as ‘Initial single-phase model (ISPM). The numerical model and the corresponding simulation results are presented in the following sections.Concrete flow was modelled by the conservation equations for mass and momentum of steady-state, incompressible flow. The continuity equation for the conservation of mass is where u→ is the velocity, ∇ is the divergence in a tensor notation, and ∇·u→ is the time rate of change of the volume of a moving fluid element in an infinitesimally small cell The momentum in the numerical model is conserved according to Eq. where g→ is the gravitational acceleration, ρ is the density and σ is the stress tensor.σ can be subdivided into normal stresses σii and the shear stresses τij as:σ=σxxτxyτxzτyxσyyτyzτzxτzyσzz=-p000p000p+σxx+pτxyτxzτyxσyy+pτyzτzxτzyσzz+pσ=-pI+τwhere p is an isotropic pressure term, -∇p is the pressure gradient, I is the unit dyadic, and τ is the shear stress tensor For incompressible flow, shear stress can be expressed as:Here η is the dynamic viscosity; see also Section The concrete flow was considered isothermal in accordance with Fresh concrete is a heterogeneous material with constituents of various sizes and shapes. Its rheological behaviour is that of a yield stress fluid, i.e., it yields non-zero shear stress at a shear rate of zero. With increasing shear rates, the shear stress increases often non-linearly, thus accounting for shear thickening or thinning effects. Hence, concrete can be classified as a non-Newtonian fluid with yield stress. The Hershel-Bulkley model represents this shear stress-shear rate (τ-γ̇) relationship (Eq. a) using three parameters: yield stress τ0, plastic viscosity μpl, and power law index n. For the sake of simplicity, the description of concrete as a Newtonian fluid with yield stress is often applied alternatively, the so-called Bingham plastic model (Eq. b). This model was proven to represent concrete’s rheological behaviour with adequate accuracy In the present research, the Bingham model was implemented by adopting the built-in Herschel-Bulkley model, also called the bi-viscous model ). The bi-viscous model emulates two viscous fluids: one with a very high, constant dynamic viscosity η0 and one with gradually decreasing dynamic viscosity ηi. The change from one behaviour to another occurs coincidently with the passing of the critical shear rate γ̇c:η=η0=τ0γ̇c2-γ̇γ̇c+k(2-n)+(n-1)γ̇γ̇cγ̇⩽γ̇cηi=τ0γ̇+kγ̇γ̇cn-1γ̇>γ̇cAssigning the power law index n equal to 1, the above equation result in Bingham model as long as shear rate is higher than critical shear rate, i.e. γ̇>γ̇c.η=η0=τ0γ̇c2-γ̇γ̇c+kγ̇⩽γ̇cηi=τ0γ̇+kγ̇>γ̇cTo complete the implementation, the critical shear rate γ̇c was assumed to be close to zero, thus prompting the solver to examine a second case in Eq. immediately after flow initiates, i.e., even at very low shear rates. Low γ̇c implies a very high dynamic viscosity η0 as long as γ̇⩽γ̇c.The numerical discretization of the computational domain plays a vital role in the overall performance of the model. The accuracy of the model significantly increases with more detailed, finer discretization but leads also to drastic increases in computational time. Hence, an optimum is to be strived for, which would represent the physical phenomena sufficiently while being cost effective. The Sliper pipe is axi-symmetric; see . The flow of the concrete can be assumed to be axi-symmetric in a macroscopic perspective. Therefore, instead of the whole pipe geometry, a quarter of it was modelled using the meshing tool ICEM CFD; see . The modelled geometry is created as an assembly of four surfaces: pipe wall (Sliper pipe), top (top surface of filled concrete), bottom (piston head of Sliper, where the pressure sensor is located) and internal walls, the inner boundaries of the Sliper quadrant under consideration.The boundary conditions applied are a no-slip moving wall for the pipe wall, symmetry for the internal walls, and a fixed wall for the top and bottom walls. Because of this relatively simple geometry, the use of the single-phase material model, and a structured grid, the computational time is relatively low. The boundary layer close to the pipe wall is important in investigating the lubricating layer phenomenon. The fineness of discretization (dimensions of finite elements) plays significant role in numerical simulations. Considering this, a numerical refinement near the wall surface was employed; see . Instead of creating fine mesh throughout the entire modelled domain, which would increase the computational time drastically, the region close to the pipe wall were modelled using a finer mesh. Since the observed thickness of lubrication layer Varies between 1 mm and 5 mm (see details in Section ), the elements size close to the pipe boundary was chosen as 0.84 mm. This resulted in the total number of 58,460 elements in the model. gives a conceptual physical description of the numerical model and experiments. Input and output parameters of the numerical model were chosen to reflect the corresponding experimental parameters closely.Concrete composition and pipe velocity V are the varying parameters in the Sliper experiments. In other words, different rheological properties were attained by mix design, and different pipe velocities were obtained by changing the weights attached to the pipe Seven concrete mixtures, namely 1, 2, 3, 5, 7, 10 and 11, were chosen from experimental study shows measured pressures from Sliper experiments and calculated pressures from ISPM simulations over corresponding flow rates.Both experimental and numerical results confirm the consensus that with an increase in flow rate the discharge pressure becomes higher as well, showing a nearly linear P-Q relationship. The pressure values calculated with ISPM showed good agreement with the Sliper measurements, both qualitatively and quantitatively, for mixtures with low water-binder ratio of 0.3, i.e., Mixtures 5, 7, 10 and 11. The representative results are shown in a on the example of Mixture 10. In contrast, for mixtures with high water-binder ratios of 0.45 and 0.6, especially for Mixtures 2 and 3 (see b), the calculated results showed little agreement with experimental findings. Correspondingly, the P-Q diagram can be roughly subdivided in two areas as showed in The primary reason for the poor agreement between the calculated and measured P-Q curves for concretes with relatively high w/b appears to be the effect of the lubricating layer, which forms at the pipe wall and has immense influence on the discharge pressures according to Still further, from the fundamentals of the numerical model developed, it can be deduced that the larger the discrepancies in Sliper and viscometer measurements for a concrete mixture, the poorer the experimental and numerical correlation (ENC) is. shows that mixtures with high w/b, i.e., Mixtures 1, 2 and 3, yielded very low values of Sliper viscosity parameter b, 0.59 Pa·s/mm, 0.14 Pa·s/mm and 0.81 Pa·s/mm, respectively, while the corresponding plastic viscosities measured by viscometer were 76 Pa·s, 38 Pa·s and 230 Pa·s, respectively. To understand the relative sensitivity of both Sliper and viscometer to mixture variation, a value denoted as ‘discrepancy’ Δ (Eq. ) was calculated. When comparing measurements from different instruments, to avoid the common variables such as geometrical factors and test conditions, a ‘relative parameter’ can be calculated. Ferraris et al. calculated relative plastic viscosity to compare measurements from various rheometers . In the next step, the discrepancy is quantified by dividing the difference in relative viscosities as obtained from Sliper and viscometer measurements with relative viscosity obtained by using Sliper Rb.The calculated discrepancy values are presented in as percentages. Very high discrepancies in cases of Mixtures 2 and 3 indicate very poor ENC. The negative sign in the discrepancy indicates that Sliper relative viscosity parameter showed higher reduction than that of relative plastic viscosity from viscometer.It is noteworthy here that Sliper measurements catch the influence of the LL much better than does the viscometer, which originates from the devices’ respective geometries and functioning principles in both experiments. In the viscometer, the whole concrete is sheared with the help of special ribs designed to prevent slippage. Although in Sliper varying from mixture to mixture, primarily the material in the vicinity of the pipe wall is deformed. The discrepancy of mixtures with poor ENC, i.e., 2, 3 and 1 all are negative and high, thus showing higher reductions in relative viscosities measured with Sliper than those with viscometer. Thus, it is evident that among the concretes under consideration, the behaviours of Mixtures 2 and 3 followed by Mixture 1 were significantly influenced by a prominent LL. Mixture 1 showed a somewhat better ENC than Mixture 3 even though it had the same w/b. This can be explained by the fact that the yield stress of M1 was with 245 Pa among the lowest of all tested concretes, and much lower than 450 Pa and 533 Pa measured for M2 and M3, respectively. The low yield stress of M1 appears to have resulted in the partial shearing of the plug during Sliper testing; see Obviously, the applicability of ISPM is strongly limited due to its not considering the LL. To overcome this limitation, ISPM was improved by implementing a user-defined function as described in the next section.A single-phase model with user-defined functions, hereinafter UDFM, enables the incorporation of the LL’s influence into the initial single-phase model. Even though it is possible to model the LL and plug as separate phases using a multi-phase model, such an approach demands relatively large amounts of computational resources, and so it increases model complexity and, accordingly, computational time. In contrast, the single-phase model calculation with UDF took approximately the same time as the simulations using the initial single-phase model.The LL forming during the flow of concrete in a pipe is assumed to be composed of cement, water, admixtures and fine aggregates; therefore, it can be broadly considered to be fine mortar. The absence of coarse aggregates in the fine mortar layer reduces its yield stress τ0 and plastic viscosity μ dramatically. From the perspective of numerical modelling, this means that the fluid elements (cells) near the wall have lower yield stress τ0 and plastic viscosity μ than more distant elements. To assign varying rheological properties appropriately across the cross-section of Sliper, the numerical model must identify the positions of all elements in a specified region near the pipe wall and assign the corresponding properties. This task was accomplished by implementing ‘user defined functions’ (UDF) in ANSYS Fluent controlling τ0 and μ values of the ‘fluid elements’ based on their distance from the pipe wall.The UDF approach improves model performance by adding four parameters to the initial model: layer thickness TLL, yield stress factor τf, viscosity factor μf and gradient factor; see . The yield stress and viscosity factors are the ratios of yield stress and plastic viscosities of mortar to the same values for concrete. Note that in the literature the terms ‘dimensionless viscosity’ and ‘dimensionless yield stresses’ or ‘relative viscosity’ and ‘relative yield stress’ have been used previously Determining the thickness and rheological properties of the LL is not trivial. Experimental investigation of LL requires special equipment such as Ultrasonic Velocity Profiler In the above models, τc(ϕ), μc(ϕ) are the yield stress and viscosity of the suspension with particle concentration (packing fraction) of ϕ. τc(0) and μc(0) are the yield stress and plastic viscosity of the suspension with particle concentration of zero; thus, the plastic viscosity of the fluid matrix, ϕm is the maximum possible packing fraction and [η] is the intrinsic viscosity are valid for monodisperse suspensions. For multidisperse suspensions such as concretes, as reported in μc(ϕ)μc(0)=1-ϕaϕa,m[ηa]ϕa,m1-ϕbϕb,m[ηb]ϕb,mwhere indices a and b indicate two phases in the suspension, e.g., fine sand and coarse sand in concrete.τco(ϕ)τi(0)=1-ϕcement1-ϕcementϕcement,m2.5ϕcement,m1-ϕsand1-ϕsandϕsand,m2.5ϕsand,m1-ϕgravel1-ϕgravelϕgravel,m2.5ϕgravel,mμco(ϕ)μi(0)=1-ϕcementϕcement,m-2.5ϕcement,m1-ϕsandϕsand,m-2.5ϕsand,m1-ϕgravelϕgravel,m-2.5ϕgravel,mwhere ϕcement, ϕsand and ϕgravel are the concentrations of cement, sand and gravel in cement paste, mortar, and fresh concrete, respectively; ϕcement,m, ϕsand,m and ϕgravel,m are the corresponding maximum concentrations; τco(0) and μco(0) are the plastic viscosity and yield stress of concrete with solid particle concentration ϕ; τi(0) and μi(0) are the plastic viscosity and yield stress of concrete with zero solid particle concentration.Within the constraints of the work at hand, upon implementation of LL through UDF, a parametric study was carried out by varying one model parameter while the other two were kept constant. The thickness of the LL (TLL) was varied from 1 mm to 5 mm based on literature and reported expert opinions . Finally, the μf values at which numerical simulations fitted the experimental results best were compared with μf values calculated using Eq. and considering the LL to be equivalent to the representative mortar. It is noteworthy that the rheological properties of the lubrication layer in pipe flow may not be necessarily equal to those of constituting mortar belonging to the corresponding concrete. The validity of this condition depends upon the concrete composition and flow characteristics. For flows with a very thin LL, the constituting of fine mortar consisting of cement paste and very fine sand is apparently realistic. However, in this first study, for sake of simplicity, the properties of the LL were assumed to be equivalent to those of constituting mortars.Though ISPM yielded good correlations for mixtures with low w/b, it does not imply the absence of LL during the pumping of these mixtures. In reality, the existence of LL for all mixtures is very probable. However, the crucial point to notice is the thickness and properties of this layer as well as flow characteristics, i.e. plug flow or plug-plus-shear flow. Kaplan et al. Disregarding the good correlation of a few mixtures in cases of ISPM, all the mixtures under investigation were simulated using UDFM. In the first step, a sensitivity analysis for the model parameters was conducted, documenting the high influence of μf on the calculated pressure. a illustrates the comparative results for the calculated pressure with viscosity factors varying from 0.001 to 0.2, while layer thickness and yield stress factor were kept constant at 5 mm and 0.2, respectively. It was also observed that the increment in viscosity factor can cause drastic drops of the pressure at higher discharge rates Q and lower pressure drops at lower discharge rates Q. Similarly, layer thickness TLL also showed considerable influence on the calculated results. b gives the comparative results of measured and calculated pressure values for layer thicknesses of 3, 4 and 5 mm.In contrast, τf variation yielded minimal influence on calculated pressures. shows the comparative results for yield stress factors of 0.08, 0.2 and 0.8 with layer thickness of 5 mm and viscosity factors of 0.001 (b). Similar low influences of yield stress on rheological behaviour of concrete have been generally reported, especially in cases of high shear flows where the final shape of the fluid body is not of primary concern . Considering the low influence of τf on calculated pressures, its value was set constant at 0.2 for all the subsequent simulations. presents the final best-fit parameters from the numerical simulations as well as μf values calculated using Eq. . It is noteworthy that Mixtures 1 and 5 contained round natural quartz aggregates while all the other mixtures contained crushed basalt aggregates. The intrinsic viscosity [η] for the round and crushed aggregates was assumed, broadly based on ; for Mixture 3 the match was very close. The only divergent case in these results was Mixture 7 for reasons yet to be determined. Mixture 1 in a peculiar case showed a positive ENC for three different TLL, viz. 5 mm, 4 mm and 1 mm, each with different μf, viz. 0.50, 0.40 and 0.12. The ambiguous results are rather another upshot of slip-plus-shear flow that occurs in case of low yield stress concrete; see Section . Nevertheless, acceptable agreement of best-fit values and predicted viscosity factors make it possible to estimate μf parameters roughly for further studies, largely independent of empirical knowledge. In addition, by assigning calculated τf and μf values, one can determine TLL for a particular composition if experimental pressure and flow rate results are available. Also, input parameters of UDFM, that Eq. does not indicate, are the thickness of LL and the gradient of LL properties. However, as repeatedly proven, once formed, the thickness of the LL remains constant throughout the pumping period Nonetheless, the dependence of any suspension’s rheological properties on their suspending fluid is influenced by theMaximum packing fraction of the particles;Packing fraction of particles or paste volume in the concrete;Particles, shape, size distribution and size range: minimum and maximum diameter;In addition, in the case of applying particle concentration models for Sliper model, TLL has also to be considered. Considering the complexity of this phenomenon, the findings presented in this study should be taken as preliminary observations on the applicability of particle concentration models for determining properties of the LL. Further studies are essential to explain how the parameters influence the applicability of such models in determining the properties of the LL. brings together the results of experimental measurements and of ISPM and UDFM simulations. The results of numerical simulation using the calibrated UDFM model showed very good agreement with experimental results for both mixtures. For other mixtures similar results were obtained as well.The layer thickness in the Sliper experiments appears to vary from 1 mm for mixtures with low water content (low w/b) to 5 mm for mixtures with high water content, in agreement with earlier research findings It is commonly understood that if a concrete mixture can develop a thick LL, of which the yield stress and plastic viscosity are always lower than those of concrete, then the pumping discharge pressures are lower in comparison to concrete with a thin lubrication layer. It is also well known that paste-rich concretes and concretes with low yield stresses are prone to develop a thicker LL. The numerical results and experimental measurements clearly support the earlier knowledge. The mixtures with low water content (low w/b) which are also exhibit higher yield stress and plastic viscosity When looked more specifically, Mixture 2 with a w/b of 0.6 is very flowable even without superplasticizer A numerical tool to simulate Sliper tests is highly relevant in predicting the pumping behaviour of concrete. Such a tool, a virtual Sliper, was developed using the single fluid CFD method, short ISPM. ISPM predicted the general trend of pressure variation with respect to the discharge rate correctly and provided acceptable agreement with experimental results in the case of concretes with low water-to-binder ratios. However, since the lubrication layer LL was not considered, the applicability of ISPM was limited to the scenarios in which formation of LL was not pronounced.Thus, an improved single-phase model with User Defined Function (UFD) was developed, which can model the lubricating layer. This approach also makes possible the estimation of the thickness, yield stress and plastic viscosity of the LL for different concrete compositions. In the framework of a parameter study performed using the UDF model it was observed that both the thickness and plastic viscosity of the LL have pronounced influences on concrete pumpability, while the yield stress parameter showed a negligible effect. Additionally, the best-fit results suggest that the assumption of a yield stress factor parameter equal to 1/5 is appropriate, while plastic viscosity factor and thickness parameters varied within the ranges from 1/1.25 to 1/20 and from 1 to 5 mm, respectively. The parameter study and the subsequent empirical fitting of the calculated results indicate the validity of calculating the viscosity of the lubricating layer as a function of concrete viscosity using the Krieger-Dougherty model.The virtual pumpability testing tool developed should enable both a more purposeful material design of pumpable concrete and estimation of pumping processes. In addition, virtual Sliper might become an inherent part of DC approaches where minimal involvement of human labour is envisioned with enhanced machine-material integration. Virtual Sliper can predict the required pumping pressures with help of supporting on-line sensors to measure transient rheological properties of concrete during pumping and printing and has the potential to play vital role in autonomous concrete construction.Improved prediction of simultaneous local and overall buckling of stiffened panelsIn this paper, improved expressions for elastic local plate buckling and overall panel buckling of uniaxially compressed T-stiffened panels are developed and validated with 55 ABAQUS eigenvalue buckling analyses of a wide range of typical panel geometries. These two expressions are equated to derive a new expression for the rigidity ratio (EIx/Db)CO that uniquely identifies “crossover” panels—those for which local and overall buckling stresses are the same. The new expression for (EIx/Db)CO is also validated using the 55 FE models. Earlier work by Chen (Ultimate strength analysis of stiffened panels using a beam-column method. PhD Dissertation, Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 2003) had produced a new step-by-step beam-column method for predicting stiffener-induced compressive collapse of stiffened panels. An alternative approach is to use orthotropic plate theory. As part of the validation of the new beam-column method, ABAQUS elasto-plastic Riks ultimate strength analyses were made for 107 stiffened panels—the 55 crossover panels and 52 others. The beam-column and orthotropic approaches were also used. A surprising result was that the orthotropic approach has a large error for crossover panels whereas the beam-column method does not. Some possible reasons for this are suggested.length of one-bay, spacing between two adjacent transverse framessectional area of plate in between adjacent stiffeners (=bt)sectional area of a single longitudinal stiffenersectional area of a single longitudinal stiffener plus effective platingspacing between two adjacent longitudinal stiffenersmoment of inertia of a single stiffener with attached platingnumber of longitudinal stiffeners in a stiffened panelmaximum initial deflection of a longitudinal stiffener (=0.0025a)ratio of flexural rigidity of plate–stiffener combination to flexural rigidity of plating (=EIx/Db)slenderness ratio of stiffener with attached plating (radius of gyration of longitudinal stiffener with attached plating (flexural rigidity of isotropic plate (=Et3/12(1−ν2))flexural rigidity of orthotropic plate in x-direction (=EIx/b)bending rigidity of orthotropic plate in y-direction (=EIy/a)torsional rigidity of orthotropic plate (=(1/6Gt3)+(GJx/b))torsional rigidity of a longitudinal stiffener for continuous stiffening (=1/6(hwtw3+bftf3))virtual aspect ratio of orthotropic plate (=(a/B)(Dy/Dx)1/4)ratio of torsional rigidity of stiffener and bending rigidity of attached plating (=GJx/Db)torsional stiffness parameter of orthotropic plate (In ships, a common portion of structure is a multi-bay longitudinally stiffened panel supported by transverse cross-frames. If there are two cross-frames, it is a three-bay panel as shown in . The cross-section of a single plate–stiffener combination is shown in Mode I: overall buckling of the plating and stiffeners as a unitMode II: buckling due to predominantly transverse compressionMode III: beam-column buckling of the stiffenersMode IV: local buckling of the stiffener webMode V: flexural–torsional buckling or “tripping” of the stiffenersThese modes are neither mutually exclusive nor independent. However, having stiffeners with good proportions can prevent the last two buckling modes cited above. Some local bending of the stiffener web could still interact with the other modes in otherwise practical panel dimensions. For a stiffened panel subjected to uniaxial compression only, overall buckling and local plate buckling are usually two distinct modes. However, there are specific geometric dimensions when these two modes occur together and interact very closely. shows a simplified design space with only two design variables, plate thickness and height of the stiffener web. The axis normal to the page is the weight of the stiffened panel, and the contours are those of constant weight per unit width. The figure shows the constraints against local plate buckling and overall panel buckling, and it is evident that the optimum design would be at the junction of these two constraints.Such an optimum panel would have the highest bifurcation buckling stress in its class of panels of equal weight per unit width This paper has five parts. The first two parts () develop improved expressions for the elastic bifurcation buckling stress of one-bay stiffened panels under uniaxial compression for local and overall buckling. For local or plate buckling, it presents an improved expression for the decrease in rotational restraint of the plating by the stiffeners due to bending of the stiffener web. For overall buckling, it considers a modified Euler buckling formula derived by Timoshenko ) examines “crossover” panels—i.e. panels whose proportions are such that the elastic local and overall bifurcation buckling stresses are equal. Bifurcation theory predicts that crossover panels have a steep post-buckling load shedding curve. By equating the improved expressions for local and overall buckling, the paper obtains an improved expression for the rigidity ratio γCO that uniquely identifies a crossover panel. The accuracy of these three new expressions is demonstrated by performing a fine mesh ABAQUS elastic eigenvalue analysis of 55 one-bay panels that cover a wide range of typical panel geometries. For each panel, the stiffener web height was adjusted iteratively until the local and overall buckling modes coincided. The mean value of the local buckling stress normalized by the ABAQUS eigenvalue is 0.965 with a COV of 6%. The mean value of the overall buckling stress normalized by the ABAQUS result is 1.007 with a COV of 4.2%. The new crossover expression normalized by the ABAQUS crossover value has a mean of 0.956 associated with a COV of 7.3%, whereas the customary expression due to Klitchieff ) presents the results of elasto-plastic finite element (ABAQUS) ultimate strength analysis of 55 crossover panels (but now three bays in length) and the predictions of two classes of closed form methods for predicting panel ultimate strength. The first class of methods is based on elastic large deflection orthotropic plate theory, saying that collapse occurs at first yield. This part of the paper shows that such methods cannot handle stiffener-induced failure of crossover panels. Two possible reasons are that orthotropic theory (1) does not allow for two simultaneous and different buckling modes and (2) does not consider the stiffener web height, but only an equivalent thickness. For the 55 panels, two representative orthotropic methods normalized by the ABAQUS ultimate strength have means of 1.274 and 1.455 with COV being around 24%. Recently, Chen Because of the variety in panel geometry, there is a corresponding variety in the pattern of plasticity at collapse. Based on these patterns, the panels were classified into four groups in the fifth part of the paper. The occurrence of plasticity converts the sudden elastic bifurcation into a smooth soft-peaked load–deflection curve, and in all but nine of the 55 panels, it prevented a steep post-buckling load–deflection curve. The authors were unable to find any common and unique property among the nine that could explain this. However, the crossover formula remains useful because it provides a rough estimate of the minimum size of stiffener needed to prevent overall buckling from preceding plate buckling.For eigenvalue buckling analysis, it was found that a one-bay panel with appropriate boundary conditions that simulate the support of the bay at transverse frames gave the same results as a three-bay panel. So, for this part of the analyses, a series of one-bay panels with three or five equally spaced longitudinal T-stiffeners was modeled and analyzed using ABAQUS. A three-stiffener model is shown in . The stiffened panel is discretized into sufficient number of elements to allow for free development of the buckling modes. The use of four-node shell elements S4 allows for finite rotations and membrane strains.Let u, v, and w be the translations along x-, y- and z-axes, respectively of the mid-node of both longitudinal (unloaded) plate edges have u constrained to be zero and the mid-node of both the loaded plate edges have v constrained to be zero, to prevent rigid body motion.the longitudinal (unloaded) edges are simply supported.the transverse (loaded) edges are simply supported. In addition, they have rotational restraint about the z-axis. The web nodes are constrained to have equal v displacement which prevents sideways bending of the web at the frames. These together simulate the support of the panel at transverse frames or bulkheads.With other dimensions unchanged, the web height of the stiffeners was carefully adjusted to get a crossover value of local and overall buckling stresses (typically within 1% or 2%, maximum 5%). shows the local plate buckling mode of the crossover panel shown in shows the overall buckling mode of the same panel. This adjustment procedure was performed to get 55 crossover panels covering a wide range of practical panel dimensions used in ship design. The first 25 panels were three-stiffener models and the other 30 panels were five-stiffener models.For the panels with five stiffeners (and some of the three stiffener ones indicated with an “∗” in ), it was found that the plate buckled at the longitudinal edges only with a low stress value, while the rest of the panel remained unbuckled. This is because the two edge subpanels are weaker than the others. In reality, the longitudinal edges would have other longitudinal structure that would provide some rotational restraint to the plating. To simulate this effect and prevent “edge buckling”, additional stiffeners were modeled along the longitudinal edges of the panel which resulted in realistic uniform local plate buckling in between the stiffeners. lists the scantlings of the crossover panels with three stiffeners and five stiffeners, respectively. In this study, the range of panels is grouped in terms of β. All the panels are within practical proportions from a design point of view. As shown in , the width B is 3600 mm for all panels.Since this study is part of ongoing research at Virginia Tech on ultimate strength of stiffened panels, the data presented in this paper are a subset of a larger database of 107 panels presented in Table 1.1 of Chen (and subsequent tables of data corresponding to a panel from these tables) are kept the same. The panels are numbered as P50–P107, excluding P57, P66 and P75 which were not crossover panels.The equation for buckling of a simply supported bare plate was derived by Bryan The expression for the buckling coefficient k depends on the type of boundary support, and for long simply supported plates, it is usually assumed that k=4. In our one-bay panels under consideration, the bare plating in between the stiffeners is simply supported on the loaded edges and is elastically restrained by the stiffeners along the longitudinal edges. Paik and Thayamballi in which ζ=GJx/Db is a non-dimensional parameter involving the St. Venant torsional stiffness Jx of the stiffener. is based on the assumption that the stiffeners remain straight until the plating in between them buckled. But if the stiffener web is slender (either tall or thin), then there will be bending of the stiffener web and the stiffeners will not provide the full theoretical rotational restraint along their line of attachment. We propose a correction factor Cr for web bending as follows:We now have an expression for local plate buckling which allows not only for rotational restraint by the stiffeners but also for possible web bending in the stiffeners:, the ABAQUS eigenvalues corresponding to local and overall buckling modes are recorded as one critical buckling stress value under the column σbkl,FEA. The local buckling stress calculated using is normalized by σbkl,FEA and the mean for the 55 panels presented in this paper is 0.965 with a COV of 6%. This verifies the accuracy of The Euler buckling stress for a column is:A stiffened panel will undergo overall buckling if the stiffeners are relatively small. From small deflection orthotropic theory, the elastic overall buckling stress is:where Π0=(a/B)(Dy/Dx)1/4 is the panel virtual aspect ratio, and is the orthotropic torsional stiffness parameter.If Π0 is small, the stiffeners become independent and the stiffener-column buckling would give good results. There are several ways in which Π0 can be small:very close spacing of stiffeners (large Dx/D)For cases when Π0 is not small, we convert the stiffener-column buckling into a panel buckling equation by applying the orthotropic buckling coefficient korth given by , σE is the Euler column buckling stress, the term in parenthesis accounts for the transverse shear force, and the term in braces accounts for the panel geometric properties. In , the overall panel buckling stress calculated using is normalized by σbkl,FEA and the mean for the 55 panels is 1.007 with a COV of 4.2% which verifies the accuracy of this analytical expression.By transformation of a system of equations established by Timoshenko Since a crossover panel undergoes simultaneous local and overall buckling, we can obtain an expression for γCO by equating Substituting σE=π2E/(a/ρ)2 and ρ2=Ix/AT in where kCr, Π0 and η have been defined earlier., we present the crossover value of γCO obtained from the eigenvalue results for the 55 crossover panels under the column γCO,FEA. Compared to it are the predictions using . The Klitchieff expression normalized by γCO,FEA has a mean of 0.739 with a high scatter (COV=14.8%) and the normalized new expression has a mean of 0.956 associated with a COV of 7.3%.For inelastic analysis, the panels being modeled should be appropriate to capture all the mechanisms that lead to collapse of the structure. Subjected to longitudinal compression, an interframe bay would deflect in an upward or downward half-sine wave (which are the plate-induced and stiffener-induced modes, respectively), while the next bay would deflect in the opposite sense. Chen . Also, due to inclusion of the inelastic properties which involve complex collapse mechanisms, it was found that edge stiffening of the panels was not necessary.In our ABAQUS models, four-node S4 shell elements were used and a fine mesh generated to adequately represent the deformations and stress gradients. Uniaxial compressive load was applied to the right hand side of the model only as concentrated nodal forces using the ∗CLOAD option. The loads were applied in two portions—one portion as a “dead load” in a previous step, and a “live load” in the current RIKS step. The material properties are the same as in the eigenvalue analyses, and an idealized “elastic-perfectly plastic” stress–strain curve is adopted.The imperfection pattern is obtained from an overall buckling mode shape of an eigenvalue buckling analysis. The selected mode shape has an upward half wave deflection in the full bay and a downward deflection in the half bay, which is shown in . The scaling factor for the initial imperfection of the stiffeners is w0=0.0025a, where a is the length of one-bay. Since there will always be some local subpanel deflection (more or less, depending on the size of stiffener and the size of subpanel) in an overall buckling mode shape, the initial deflection of plating is automatically included once the scaling factor is applied.Let a “0” on T[x, y, z] denote translation constraints and on R[x, y, z] denote rotational constraints about the x-, y- and z-coordinates in the mid-width node in each of the two transverse edges has T[1, 0, 1] to prevent rigid body motion in the y-direction.the longitudinal edges are simply supported with T[1, 1, 0] and R[1, 0, 0], with all the nodes along each edge having equal y-displacement.the transverse edge on the left hand side, which is the midlength of the mid-bay of the full three-bay model, has symmetric boundary conditions. This is simulated with T[0, 1, 1] and R[1, 0, 1].the transverse edge on the right hand side, which is the loaded edge, is simply supported with T[1, 1, 0] and R[0, 1, 0]. Only the plate nodes have equal x-displacements.the transverse cross-frame is not modeled, but is simulated with T[1, 1, 0].The governing differential equations for large deflection orthotropic plate theory are the equilibrium equation and the compatibility equation Solving the governing differential equations for large deflection orthotropic plate theory, Paik and Thayamballi The above theory has been implemented in the computer program ULSAP (ultimate strength analysis of panels) . ULSAP however is not restricted to orthotropic theory and provides independent ultimate strength algorithms for all five of the failure modes listed in ). In order to apply the beam-column method to a stiffened panel, it is necessary to account for local plate buckling, which is usually done by means of an effective breadth beThe beam-column ultimate strength is then corrected by a factor R obtained by curve fitting the finite element values of ultimate strength for 107 stiffened panels. The resulting expression for the factor R is:For panels with very small stiffeners, hw/tw<2.5, it was found that the depth of yield in the stiffener web could not be accurately ascertained. For such small stiffeners, the panel strength will be slightly higher than the bare plate ultimate strength. Therefore, for hw/tw<2.5, ULTBEAM uses the following formula to predict the ultimate strength:This procedure has been implemented in the computer program ULTBEAM. For the crossover panels in this study, the ultimate strength is also calculated using ULTBEAM and the results are tabulated under σULTBEAM in giving statistical comparisons of the ultimate strength predictions of orthotropic theory based on outer surface stress, that based on membrane stress and the beam-column method (as implemented in ULTBEAM) compared to the finite element results (ABAQUS).The correlation of the three methods with the FE solutions is plotted in . The orthotropic outer surface stress based results are optimistic for most cases. The orthotropic membrane stress approach gives a collapse stress value that is nearly equal to the material yield stress. This method is too optimistic and therefore not recommended particularly for crossover panels. We now consider what might be the reasons for the above errors in the orthotropic-based methods.Firstly, of its very nature, orthotropic plate theory is elastic, and does not consider the growth and spread of plasticity. Secondly, orthotropic plate theory is based on a regular buckled pattern of m×n half waves. If the stiffeners are small, it will correctly predict overall buckling, with m and n being small. If the stiffeners are large, it will correctly predict local plate buckling, with m being roughly B/(ns+1), where ns is the number of stiffeners. But in a crossover panel, these two buckling modes are occurring together and orthotropic plate theory does not allow for two simultaneous elastic buckling modes. shows the normalized ultimate strength value from FEA and the orthotropic strength based on surface stress plotted against λ, which is the slenderness ratio of the stiffener with attached plating. As expected, the FEA ultimate strength decreases sharply with λ, whereas the orthotropic surface stress based results remain nearly unchanged., Panel nos. P58, P59, P67, P68, P76 and P77 have been excluded. For these panels, the plate slenderness parameter β is 3.73, as seen in . This is unusually slender and permits the stiffeners to behave independently, which by itself is sufficient reason for the orthotropic plate approach to have less accuracy. and plots the percentage error in the orthotropic surface stress results compared to FEA against λ. Whereas one would expect that the accuracy of orthotropic plate theory would improve as the stiffener size decreases (larger λ), but here it is the opposite. Again, this may be because orthotropic plate theory does not allow for two simultaneous elastic buckling modes.The membrane stress based prediction is also orthotropic in nature. Orthotropic plate theory cannot distinguish between plate-induced and stiffener-induced failure. Because of the specified initial imperfection ( plots the percentage error in the orthotropic membrane stress based results for all crossover panels excluding the six panels with β=3.73 versus the ratio b2t/Z. A pronounced correlation is observed from the figure. are a gray-scale version. Ghosh’s thesis can be downloaded from the following address: http://scholar.lib.vt.edu/theses/available/etd-04212003-100603/ labeled “collapse mode”, the collapse mechanisms at the ultimate load carrying capacity of each panel are identified from these plots using the following nomenclature:C: Approximate plastic hinge in middle bay3: Plate mid-longitudinal edges yielded in middle bay3: Plate mid-longitudinal edges yielded in end bay, the collapse mechanisms are complex and varied. However, they are not unusual and are similar to those observed in non-crossover panels, as presented by Chen , we present a broader classification of the 14 different collapse mechanisms occurring in the 55 crossover panels in four groups., we see that 18 panels in Group I reaches their ultimate load with yield in the stiffeners only, while the plate midthickness in both middle and end bays is still elastic. This further illustrates that the orthotropic membrane stress prediction of ultimate strength can be optimistic. Note that while the pattern and extent of plasticity in the plating varies widely, “stiffener yield through web” is a common factor in all 55 cases. For the stiffeners in the middle bay, the yield zone reached the full depth of the web (“approximate plastic hinge”; first letter C) in 48 cases, and in the other seven cases, the yield zone extended some distance into the web. The consistent presence of stiffener web yield and the inconsistent presence of plate yield suggest that for stiffener-induced failure “stiffener web yield” (say through 2/3 of the web height to be conservative) is a better criterion for panel collapse than the “initial yield of plating” criteria that is used by the orthotropic-based methods. show the von Mises stress distribution at midthickness at the maximum load carrying capacity of one panel from each group.As part of the RIKS analysis using ABAQUS, the axial deformation or end shortening of the panel u1 was measured at a loaded edge plate node at every load increment. The normalized stress–end shortening curve was then drawn for every panel. In , we present the curves for the four panels which are a good representation of what we have seen for all the crossover panels in this study.All the crossover panels in this study collapsed due to a stiffener-induced failure of the middle bay. The first loss of stiffness as shown in is caused by progressive yield through the stiffener web at the most stressed location which is at the midlength of the middle bay. Collapse occurs with the formation of an approximate plastic hinge at that location, the depth of yield depending on the stiffener proportions, with or without yield in the plate in one or more bays. Yield locations in the plate were either at the midlength of the longitudinal edges or the four corners of the bay. In some panels yielding in the stiffeners caused by shear was observed in the end bay. Although this facilitated overall panel collapse, it is not considered to be a major cause.The post-collapse behavior is associated with gradual spread of plasticity in the panel, and to obtain equilibrium ABAQUS reduced the applied load in subsequent increments. As shown in , three out of the four panels have a stable post-collapse behavior. This was seen in 46 out of the 55 panels. The remaining nine panels (P52, P56, P62, P63, P69, P71, P104, P105, and P106) suffered from a steep drop in load carrying capacity similar to P52 shown in the figure.In this study, 55 stiffened panels with proportions suitable for use in ship design which had simultaneous local and overall elastic buckling stresses were modeled and analyzed using the finite element software, ABAQUS. Modified expressions for elastic local plate buckling and overall panel buckling expressions were derived and compared to elastic FE bifurcation buckling results. An improved expression for prediction of crossover proportions was derived and compared to the bifurcation results. Inelastic RIKS analysis for ultimate collapse stress and post-collapse behavior using ABAQUS was carried out on these panels. Ultimate stress was also calculated using orthotropic-based methods and a modified beam-column method for stiffened panels and compared to the FE results. It was found that for panels having crossover proportions, orthotropic-based methods are unsatisfactory and the beam-column method is most suitable for ultimate stress prediction. Collapse patterns were studied and classified from von Mises stress distribution at collapse and were not found to be unusual. Load–deflection diagrams showed stable inelastic post-collapse behavior for most panels and an abrupt drop in load carrying capacity in only nine of the 55.Surface generation and boundary lubrication in bulk forming of aluminium alloyThe electrical contact resistance is measured between the tool and workpiece during plane strain compression of aluminium strip coated with a non-conductive oxide film produced by anodising. Results are correlated with the observed oxide topography after the test. The purpose is to investigate the mechanism of the development of close metal-to-metal contact, the associated material transfer and their effects on the friction coefficient under boundary lubrication conditions. Initially the anodised layer provides electrical insulation between the tool and the strip but, as deformation proceeds, this layer breaks up and fresh metal is extruded through the cracks formed, causing a sharp fall in electrical resistance. Details of this behaviour are explored, showing a dependence not only on strip reduction, but also on the base oil used and the presence of boundary additives. The change in the behaviour is tracked as a transfer layer builds up on the tool.reference resistor in series with the stripreference resistor in parallel with the strippressure viscosity coefficient of the lubricantviscosity of lubricant at ambient pressureMost cold metal forming processes are performed in the ‘mixed’ lubrication regime, where there are asperity-to-asperity contacts as well as pressurised oil between the tool and workpiece surfaces. The average friction coefficient is determined by the ratio of the real to the nominal contact area and by the boundary friction stress on the contact areas It has been demonstrated that material transfer has a significant effect on sliding friction between soft and hard surface pairs. Experiments using a crossed-cylinders friction apparatus It has been shown that surface bending and stretching is responsible for the fracture of the surface oxide layer present on aluminium strip in rolling process. Fresh metal then extrudes through the micro-cracks formed in the oxide layer An innovative technique based on the measurement of contact electrical resistance in PSCTs has been recently reported by the authors, looking at how metal-to-metal contact is established, whether the oil can get into the micro-cracks in the oxide film and how fast the transfer film develops The aim of this paper is to present the methodology for measuring electrical resistance in PSCTs in more detail and use this, along with visual observations and estimates of friction, to investigate how oxide break-up affects boundary lubrication and transfer layer build-up. The effects of base oil and boundary additives are explored.Samples of width L |
= 30 mm were cut from cold-rolled and work-hardened AA1200 aluminium alloy sheet of initial thickness h0 |
= 0.4 mm. All the results presented here are for samples which were covered in an anodised non-conductive aluminium oxide film. This was produced by etching the samples in 10 wt.% sodium alkaline solution, denuding them in 20 wt.% nitric acid and then anodising in 10 wt.% sulphuric acid at an electrical voltage of 20 V. The oxide film generated was estimated from the electronic charge during anodising to be about 12 μm thick.The surface topography of the samples was observed with an optical microscope (LEICA) and the surface roughness was measured using a Zygo three-dimensional interferometric profilometer on areas of 0.71 mm × 0.52 mm. The surface topography of the as-received samples is given in (a), showing longitudinal roll marks and scattered tiny surface pits. The topography of the anodised surface is shown in (b), revealing a micro-porous oxide film, but with the longitudinal roughness from the as-received strip still visible. The strips were orientated during compression tests with the rolling marks being parallel to the elongation direction. The average root mean square roughness for both as-received and anodised surfaces is about 0.7 μm.Two base oil lubricants, Somentor 32 (‘S32’) and Primol 352 (‘P352’), were used. S32 is a predominantly paraffinic kerosene mineral oil used in cold rolling. P352 is a ‘medicinal white oil’ with a similar processing route to S32 (to give a composition of 66% paraffinics, 34% naphthenics and no aromatics), but it has a significantly higher viscosity. The oil properties are summarised in . Density and viscosity data are from the manufacturer's data sheets The electrical resistance R between the two punches (effectively the sum of the contact resistances at the interfaces between the strip and each of the punches) was measured using the electrical circuit shown in . The DC power supply of 5 V was rectified. Values of 1 kΩ and 10 Ω were chosen for the reference resistors R0 and R1, respectively, to ensure that the electric potential across the sample was below 50 mV during the tests. According to the manufacturer (personal communications with ExxonMobil), the electrical breakdown strength of the oils used in these experiments is about 10–20 MV/m. An input of 50 mV across the sample would avoid the electrical breakdown of oil films thicker than 2 nm at both interfaces. The output voltage was recorded by the PC data logger. The resistance is then given byThe average friction coefficient μ is extracted from the final load and the width of each indentation using a conventional slab model and Coulomb friction law. The normal load for a given friction coefficient is obtained by integrating von Karman's equation where p is the normal pressure, x the distance from the centre line, h the strip thickness and Y the plane strain yield stress. The variation of strip thickness with position is given by the geometry of the punches, which are assumed to be rigid. The friction coefficient is then solved by matching the measured load, taking a value of yield stress Y equal to the value of 140 MPa inferred from previous PSCTs with very low friction In preliminary tests a clip gauge was attached across the punches to measure the approach of the two punches. The output signal was amplified and logged by a PC data logger at a sampling rate between 100 and 500 Hz. The signal from the clip gauge was filtered to eliminate the noise from vibration of the loading machine using a digital filter and calibrated to give the change in thickness of the sample. The reduction in thickness of the centre of the specimen was given bywhere hc is the central thickness at the end of the test.The final reduction can also be obtained by direct thickness measurements with vernier calipers. However the reduction tends to be underestimated due to the difficulty in locating the minimum strip thickness within the cylindrical indentation. Instead, the final indentation width w is measured under an optical microscope and the final reduction is derived byassuming that the circular arc of contact can be approximated by a parabola (an approximation which is accurate to within 0.4% for a reduction of 50%).The final reduction measured by the clip gauge has good agreement with that given by measurements of the indentation width. However, to avoid problems with noise in the clip gauge measurement, the evolution of reduction during the test is estimated from the measured load using the following procedure. It is assumed that the friction coefficient is constant throughout the test. Therefore, for the fixed material and geometric conditions, the applied load is a function only of the reduction. This function is calculated using the slab model and plotted in for various friction coefficients. A few tests without lubricant or with S32 base oil were stopped at reduced loads. The reduction is calculated from the contact width after these tests and indicated in . The results confirm that a simple slab model using a friction coefficient of around 0.3 inferred from the reduction at the final load for these tests predicts the reduction correctly at an intermediate load. This procedure is followed for each test, using the reduction at final load to estimate the friction coefficient through the test and hence the dependence of reduction on load.(a) shows the results for a preliminary test at a loading velocity of 0.05 mm/min on a sample under dry conditions. The reduction is measured by the clip gauge in this test. (a) shows the reduction and resistance as a function of loading time, with the zero time set at an arbitrary load of 0.3 kN. The test continues until a maximum load of 20 kN and a final reduction of about 20% are reached. At the beginning of the test the electrical resistance is tens of MΩs, so that it is off the scale of the graph. It then drops suddenly to a few ohms at a reduction of about 10% and then gradually to a nominal zero resistance. This result is replotted in , with the electrical resistance given as a function of reduction. The indentation on the strip is observed under the optical microscope after the test. It is found that fresh metal has extruded through micro-cracks in the oxide layer, as shown in (a), in which the centre line of the indentation is somewhere beyond the left edge. (a) also shows that the crack spacing decreases outwards from the centre of the indent. A similar phenomenon was observed in cold rolling and modelled by the authors To understand what is happening when the electrical resistance drops sharply, loading is held constant at that point in a second test. The results are shown in (b). The electrical resistance falls slightly as the load is held constant and the reduction stays effectively unchanged. Examination of the indentation using the optical microscope, (b), reveals that metal has been extruded through just one line of cracks near the centre of the indent. These observations support the hypothesis that metal-to-metal contact between the fresh aluminium metal and the tool surface occurs in a step-wise manner as metal extrudes through successive cracks, depending on the mechanisms of cracking and extrusion modelled in Ref. In the rolling process a micro-crack is initiated near the entry to the bite, owing to bending of the oxide. The crack opens up with increasing bulk strain through the roll bite and reaches a maximum at the exit (a). As indentation proceeds this crack will open up, while more cracks form further out from the centre of the indent as it widens, as indicated in (b). The crack spacing decreases towards the edge of the indent because bending of the top surface is more severe with increasing entry angle (cf. (a) and (b)). The theoretical model for metal extrusion Note that there will be a no-slip region at the centre of the indent due to the compressive lateral stress induced during deformation. With a Coulomb friction coefficient of 0.3 and a thickness reduction of 0.25, a simple slab model of the process shows that the compressive lateral stress at the centre of the indent is about 6 times the strip yield stress. This stress corresponds to a compressive elastic strain of 1.2%. An estimate of the extent of the no-slip region can be made by finding the location at which this compressive elastic strain equals the plastic extensional strain in a homogeneous rigid-perfectly plastic model. This approach suggests that the no-slip will extend 40 μm either side of the centre of the indent. Furthermore, the oxide layer will not break immediately at the edge of this no-slip region. The results of Le et al. Tests were also performed under various lubrication conditions on anodised samples at a maximum load of 24 kN and a velocity of 0.5 mm/min. In this section, tests with the two base oils are described, while the effect of additives is detailed in the following section. At least five indentations were performed under each set of conditions. The punches were cleaned with acetone prior to testing with a new oil to minimise any transfer film developed in the previous tests, so that the initial tool surface condition is comparable for each series of tests. The friction coefficient for each test is derived from the final load and reduction as described in Section . The mean value of the five tests for each set of conditions is summarised in . Neither the indentation velocity nor the oil viscosity has a noticeable effect on the average friction coefficient, confirming that lubrication is in the boundary lubrication regime.(b) shows the dependence of electrical resistance on reduction for tests with S32 base oil. The electrical resistance falls sharply to a few ohms at a critical reduction of around 8–10%, similar to the critical reduction seen in the dry tests, (a) for tests with S32 base oil shows how the fresh metal (the brighter regions) has been extruded through cracks on either side of the centre line, in a similar manner to that seen with the dry tests, (a). Although a transfer film is visible on the tool surface after tests with S32 base oil, no significant change in the friction coefficient and electrical resistance is found. It is inferred that the transfer film formed on the tool surface under this conditions does not change the shear stress between the tool and oxide surface. With the thicker P352 oil the clear-cut fall in electrical resistance at a critical reduction is not observed. For most tests (7 out of the 10 tests performed) the electrical resistance always exceeded the maximum value of 100 Ω chosen for the resistance axis of (c), though there was significant variability. (b) shows the corresponding optical image for the first indent. No bright areas corresponding to metal-to-metal contact are observed; similar images from other tests confirm this observation. These observations strongly support the hypothesis that more oil will be trapped in the micro-cracks with the thicker lubricant, inhibiting the extrusion of metal through the oxide layer film. The variability of the contact resistance observed in these tests is due to an edge effect, rather than typical of the bulk of the contact. This has no significant effect on the friction coefficient because the friction coefficient is mainly determined by the contact between the tool and the fragmented oxide surface. These observations show how the combination of electrical resistance measurements and oxide fracture topography provides valuable additional information about the effect of the lubricant on the boundary lubrication process.In this section we explore the effect of additives on the plane strain compression behaviour for tests with S32 base oil and a final load of 24 kN. Both the as-received and anodised strips were tested for comparison. The tool was not polished between tests, allowing growth of a transfer layer. shows that the friction coefficient has already fallen to 0.19 for the first test, staying at this level for subsequent tests. Evidently the transfer layer has formed more quickly with this higher additive concentration although, interestingly, the final friction coefficient is similar with either 0.5 or 10 wt.% lauric acid. A similar independence of friction coefficient on stearic acid additive concentration, above a critical concentration of about 0.25 wt.%, was observed with PSCT on as-received aluminium using smooth tools . Where there was no significant variation with test number an average figure of five indentations is given, otherwise the value for the first indentation is quoted.The effect of the transfer layer on the variation of electrical resistance versus reduction with 0.5 wt.% lauric acid is shown in (a). Note that the curves have been shifted upwards progressively in steps of 10 Ω to separate them; in each case the resistance falls to a nominal zero. A comparison of (a) and the corresponding figure for the S32 base oil alone, (b), shows that the addition of 0.5 wt.% lauric acid in S32 base oil makes little difference to the way in which electrical resistance falls with increasing reduction for the first test. In subsequent tests the fall in resistance occurs at an earlier reduction when the additive is included. This finding correlates with the observed decrease in friction after the first test with the additive. The electrical resistance drops more quickly and fluctuates more severely after a transfer layer has developed on the punches. The surface topography after the first and 10th tests is shown in (a) and (b), respectively, in which the centre line of the indentation is at the left edge of the image. There is a clear increase in the area of fresh metal surface from the 1st to the 10th tests, associated with the increase in reduction. The onset of metal-to-metal contact at a lower reduction, reflected in the electrical resistance curves, appears to be due to more localised crack opening near the centre line of the indentation. The lower frictional resistance between the strip and the tool once a transfer layer has developed may facilitate the stretching of the surface and hence extrusion of metal through the micro-cracks. It is also noted that the extrusion of metal occurs nearer to the centre of the indent in the 10th test. This confirms the reduction in the extent of the no-slip zone with a lower friction. The fluctuation in electrical resistance after the transfer layer develops can be explained by a ‘blocking and sliding’ mechanism. The electrical resistance increases when the non-conductive transfer layer blocks the newly exposed metal surface and then decreases when it is displaced due to the relative sliding. The change in oxide morphology, coupled with the observed earlier onset of metal-to-metal contact, shows how there is close coupling between the friction at the interface and the oxide break-up and soap generation, which in turn determines friction.Similar electrical resistance curves are shown in (b) for the higher lauric acid concentration of 10 wt.%. From the first indent the electrical resistance falls at a small strip reduction of around 5%. Again there are severe fluctuations in the electrical resistance as the resistance falls, presumably caused by the transfer film.A comparison of the electrical resistance curves for S32 with 10 wt.% lauryl alcohol, (c), and the corresponding curves for the S32 base oil alone, (b), shows that this additive does not make a significant difference to the reduction at which the electrical resistance drops. Moreover, the change with test number is not significant compared to the experimental error in reduction. The optical micrographs for the first and 10th test in (a) for S32 base oil. Recalling that friction is not affected by inclusion of this additive in S32, this supports the hypothesis that it is changes in friction that cause the fall in critical reduction at which the electrical resistance falls.The effect of lauric acid in P352 oil on the evolution of the friction coefficient during a series of tests was observed to be similar to that with S32 base oil, though there was a tendency for more tests to be needed before a fall in friction coefficient was observed. This suggests that the development of the transfer film is retarded by the trapped oil, reducing the amount of close metal-to-metal contact. This is in line with the proposed mechanisms of material transfer in sliding of ductile materials which involve: particle detachment at metal-to-metal asperity contacts, chemical reactions between the boundary additive and reactive newly-detached particles, and chemisorption of the organo-metallic compounds to the tool surface The paper details a series of plane strain compression tests using cylindrical steel punches to indent aluminium alloy strip coated in a relatively thick electrically-insulating anodised oxide layer, using two mineral base oils and various additives as lubricants. Measurements of the electrical resistance between the two punches (i.e. effectively twice the contact resistance between the tool and strip), coupled with observations of the indented surface and estimates of friction between the tool and strip, were used to investigate the way in which the break-up of the oxide layer affects the lubrication process. The following conclusions can be drawn:Measurements of electrical resistance and observations of surface topography show that metal-to-metal contact is established after the oxide breaks and metal extrudes through the oxide.More viscous base oil inhibits the establishment of direct metal-to-metal contact and the corresponding fall of electrical resistance, perhaps due to oil trapped in micro-cracks in the oxide layer.The addition of lauric acid in a low-viscosity base oil (S32) leads to the development of a low-friction transfer film, giving rise to metal-to-metal contact at a smaller reduction and fluctuations in the electrical resistance during the tests.The addition of lauryl alcohol in S32 base oil does not significantly affect the average friction coefficient or the establishment of metal-to-metal contact.The development of a transfer film during tests with lauric acid in the thicker P352 mineral oil is slower than for the less viscous S32 base oil, revealing the role of oil entrapment and metal-to-metal contact in the material transfer process.Quantitative assessment of the saturation degree of model fine recycled concrete aggregates immersed in a filler or cement pasteWe study water transfer between different model fine recycled concrete aggregates and fresh filler or cement paste in which they are immersed. Our aim is to introduce a spread based experimental protocol for studying the time evolution of water content in initially dry aggregates when mixed with such pastes. The procedure developed hereby is tested on three model Cement Paste Sands (CPS) prepared with different water-to-cement ratios leading to very different porosities and pore structures. The results show that water content in the CPS reaches a maximum no later than 6 min after first contact with limestone filler or cement paste then remains fairly constant afterwards. The saturation degree, i.e. ratio of the water content in the CPS to their water absorption, increases with the porosity of the CPS and remains less than one whatever the paste. The corresponding reduction of water absorption capacity in a cement paste should be taken into account during mix design of a recycled concrete.In 2014, the building and public works sector has produced 223 million tons of construction and demolition wastes in France concrete wastes represent 15% A number of researchers have studied the performances of concrete incorporating Recycled Concrete Aggregates (RCA) The decreased performances of a recycled concrete are mainly due to poorer properties of RCA. RCA consist of a mixture of natural aggregates and attached cement paste. This cement paste is responsible for lower density, a higher porosity and a higher water demand of RCA compared to natural aggregates (NA) Different methods have been tested to limit the impact of water transfer between the cement paste and RCA on the fresh and hardened properties of recycled concrete. A common method consists in adding an excess of mixing water corresponding to the theoretical water absorption of RCA minus their initial moisture content. Substantial shortcomings of this method have been reported in the two extreme cases of oven dried aggregates or saturated surface dried aggregates. In a study of Poon et al. Water transfer between RCA and the cement paste at early age has to be quantified in order to be accurately accounted for in mix design. NMR spectrometry has been successfully used to measure water transfer between a cement paste and model porous media. Fourmentin et al. The present study is focused on how water transfer between fine RCA and a cement paste affect the mortar workability during mixing. For this purpose, water transfer occurring between an inert limestone filler or cement paste and a fine cement paste sand in contact with it are studied using spread measurements. A new testing protocol based on spread measurements is implemented to follow this water transfer. Materials are presented in Section . The experimental protocol and the mix design of tested mortars are presented in Section . Experimental results are shown in Section Water absorption of porous aggregates is first studied in a limestone filler paste. The use of this model inert paste eliminates the effects of chemical hydration on the evolution of workability. The filler is a Betocarb HP-OG calcareous filler by OMYA Company coming from the quarry Orgon. By using helium pycnometry, its density is found equal to 2.72 g/cm3. Water absorption by model RCA is also studied in a cement paste. For this purpose, a white cement CEM I 52.5N from Lafarge Company is used. White cement is used to enhance the contrast between the new cement paste and model RCA during microscopic investigations performed in a further study. Its absolute density is 3.11 g/cm3. The particle size distributions of the filler and the cement are roughly the same (see First, model porous RCA are prepared. Model aggregates consist of pure cement paste with known W/C ratio, W and C being respectively water and cement mass contents. Grey cement CEMI 52.5N by Lafarge is used to prepare three cement pastes with different water-to-cement ratios by weight: 0.3, 0.5 and 0.7. Water is mixed with cement in a mixer to reach the desired W/C ratio. Superplasticizer MC-Powerflow 3140 of the MC-Bauchemie Müller GmbH & Co Company is added to the most concentrated mix (W/C = 0.3) at a ratio of 0.2% by mass of dry cement to enhance its fluidity. Each time, around 4 L of fresh cement are prepared. The fresh paste is then poured in hermetic plastic bottles. The bottles with W/C equal to 0.3 and 0.5 are vibrated vertically during 30 s at a frequency of 50 Hz and amplitude between 0.05 and 0.64 mm to minimize the presence of air bubbles trapped inside the pastes. Those with W/C equal to 0.7 are not vibrated as important segregation was observed when vibrating during preliminary tests. Besides, air bubbles are easily evacuated from this mix because of its high fluidity. The plastic bottles filled with fresh paste (nominal volume of 0.5 L) are then sealed and rotated during 12 h in order to avoid segregation and bleeding of cement pastes during setting. Then, the pastes are hydrated during at least 90 days inside the bottles in sealed conditions at a temperature of 20 °C ± 2 °C. We consider that the microstructure of the cement pastes does not vary significantly after 90 days of hydration as reported in the literature Hydrated cement pastes are then used to prepare different samples. Model RCA are prepared by crushing cement pastes in a jaw crusher to produce three model Cement Paste Sands (CPS) with a grain size diameter ranging between 63 µm and 4 mm. Crushing is performed in two steps. A crushing with a jaw aperture of 9 mm is first carried out. The fraction larger than 4 mm is crushed again with a reduced jaw aperture of 4 mm during the second step. The same crushing procedure is used for the three cement paste sands. Despite cement paste strength differences, CPS with similar particle size distributions are obtained (). The crushed CPS are immersed in water during 7 days to complete the hydration of anhydrous phases made accessible to water after crushing. Then they are water sieved on the 63 µm test sieve and dried at 60 °C until constant mass.Another batch of model cement pastes is crushed to produce coarse aggregates (4–10 mm) for water absorption (WA24) measurements using standard test NF-EN 1097-6 with a drying temperature reduced to 60 °C. Excessive drying temperatures lead to a partial dehydration of hydrates and an overestimation of water absorption ). On the other hand, our preparation protocol yields homogeneous cement pastes, as will be discussed later. For these reasons, water absorptions of CPS is taken equal to that of the fraction (4–10 mm) measured experimentally.Three cubic samples (around 1 cm3) are cut using a water cooled diamond blade from each hardened cement paste for Mercury Intrusion Porosimetry (MIP) measurements. MIP measurements are performed using a (Micrometrics Autopore IV) porosimeter. We took care to cut the three samples from the top, middle and bottom of the hydrated cement bottles in order to check their homogeneity and the relevance of the mixing procedure.For microstructural investigations of the cement pastes, cubic samples measuring 1 cm3 are cut, impregnated and polished using the following procedure. After drying at 40°, samples are embedded in resin (H2020, Huntsman) under vacuum (pressure 100–200 mbar). After hardening, the thin excess of resin at the sample surface is removed carefully using 80 grit diamond discs (Struers MD System) and ground using successive decreasing abrasive size (220, 600) for no more than 30 s each time with a 25 N load on MD discs rotating at 150 rpm. The 1200 grit stage is carried out under the same conditions for 1 min. A manual lapping using 800 grit powder SiC mixed with ethanol is carried out on a glass plate. Then, fine polishing is carried out on woven discs (MD Dac) with diamond pastes using the following procedure: 30–45 min for the 6 µm step at 30 rpm, 30 min for the 3 µm step at 40 rpm and 30 min for the 1 µm step at 60 rpm. Between each step, water free lubricants are used (Struers DP Brown) to carry out thorough cleaning with ethanol, soft brushes and cotton.In the following, theoretical effective water (Weff,th) refers to total water in the mortar minus the theoretical water absorption (Weff,th = Wtot − WA24) and effective water (Weff) refers to total water minus the amount of water actually contained in the CPS (Weff = Wtot − WCPS). shows a schematic illustration of the methodology used to determine the water content of initially dry CPS at time t. First, two mortars with identical compositions (same total water content, aggregate volume and powder volume) are prepared. CPS is incorporated in dry state in the first mortar (a). The total amount of water added to this mix is the sum of the theoretical effective water (Weff,th) and the CPS water absorption (WA24). In the second mortar, the CPS is in saturated state (c). Hence, only theoretical effective water (Weff,th) is added to this mix.After the first contact between fresh paste and initially dry CPS, an amount of water to be quantified migrates from the paste to the porosity of the CPS at time t (b). In order to quantify this amount, an extra amount of water ΔW is added to the mortar made with saturated CPS in order to achieve the same spread at time t as for the mortar with initially dry CPS (d). Since all mixes are prepared with the same volumes of CPS, each having the same grading curve, measuring similar spreads indicates similar effective water contents in both the mix with saturated CPS and a water increment ΔW, and that with initially dry CPS at a time t. Then, knowing the total water content, the moisture content at time t in initially dry CPS is deduced by difference.Mortars preparation takes place in several steps. CPS3, CPS5 and CPS7 are quartered to produce CPS samples with a fixed volume and particle size distribution. For each CPS, a sample is kept in dry state and 6 samples are saturated according to a procedure described below. Samples of saturated CPS are used to prepare different mortars with a fixed mass of powder (filler or cement) and different amounts of mixing water. Mixing water includes theoretical effective water (Weff,th) plus over-saturation water (ΔW). ΔW is a fraction of the water absorption WA24 and varies between 0 and 0.5WA24. Theoretical effective water Weff,th is adjusted in a way that all mortars show no significant segregation or bleeding during the test and the spread at 6 min varies between 20 cm and 30 cm. The spread test procedure is described in the next section. Two series of mortars are investigated. The first series includes limestone filler mortars prepared with the three CPS and the second one includes cement mortars made with CPS5 only. shows the composition of mortars prepared with a CPS and a filler or cement paste.Mixes are labeled according to the nature of the paste (filler or cement), the W/C ratio of the CPS, saturation state of the CPS and the over-saturation water. For example, F3D stands for a filler paste mixed with CPS3 in dry state; C5S20 stands for a cement paste mixed with CPS5 in saturated state and over-saturated by ΔW = 0.2WA24. For a given series, the masses of CPS mCPS, filler or cement (m(F or C)), mixing water Wmix are respectively calculated as follows (t = 0):For saturated aggregates: Wmix=Weff,th+=W (ΔW takes values between 0 and 0.5WA)ρOD is the oven-dried density of model CPS measured according to NF EN 1097-6.Pre-saturation of CPS is performed in hermetic plastic bottles with an amount of water equal to their dry mass multiplied by their water absorption plus 5% during 7 days prior to the test. The bottles are rolled horizontally at least every two days to homogenize the mixture. Previous works have shown the efficiency of this procedure for complete aggregates saturation of RCA within 7 days a shows a schematic of the experimental procedure for spread measurements. The cone described in Concrete Equivalent Mortar method Spread is measured at 6, 15, 30, 45, 60, 75 and 90 min after the beginning of the mixing procedure using the same mortar sample. The time needed to place the mortar inside the cone is 1 min 30 s. Once the spread is measured, the mortar is returned to the mixing drum and covered with a plastic film until the next spread measurement in order to minimize water loss from mortars during the test duration (90 min) due to evaporation. Mortars are mixed during 4 min before any spread measurement. The mixing procedure is shown in . The mixing rate is kept at 62 rpm during all experiments. For mortars incorporating either dry or saturated CPS and a fixed total water content (F3D, F3S, F5D, F5S, F7D, F7S, C5D and C7S), three specimens are tested. For the other mortars, only one specimen is tested. In this work, a total number of 308 spread tests have been conducted. All tests are carried out in an air conditioned room at 20 ± 2 °C. Materials and apparatus used in the experiments are stored in the air conditioned room at least 24 h before the test.a shows a microstructural comparison between three CPS having different W/C ratios using Scanning Electron Microscopy in Backscattered Electrons mode (SEM BSE). Each image is acquired on a 320 × 240 µm2 field with a resolution of 0.25 µm per pixel. The grey-scale intensity being proportional to the atomic number, partially anhydrous grains and pores may be visually identified on the images This figure shows that when the W/C ratio increases, the proportion of anhydrous grains per surface area decreases. This results from a lower concentration of the cement paste and a higher water content leading to a higher hydration degree. Moreover, we observe that images appear visually darker when the W/C increases. This is due to the higher porosity of the corresponding paste. Typical grey level histograms of the three cement pastes are shown in b. A first peak at the highest grey level (around 200) is distinguished. This peak corresponds to anhydrous grains and is the highest for the most concentrated cement paste. This confirms the visual observation of higher concentration in anhydrous cement grains when W/C decreases. The second peak to the left corresponds to hydration products and porosity. This peak shifts towards lower grey levels when W/C increases. It is due to the increase of porosity with W/C ratio. gives the porosity and oven-dry density ρOD measured according to NF EN 1097-6 and using MIP. Water absorption measured according to NF EN 1097-6 is given as well. ρOD is the ratio of the dry mass to solid volume plus pore volume (including inaccessible pores). Densities measured with MIP and according to NF EN 1097-6 are very close. For mix design, we choose to work with NF EN 1097-6 oven-dry densities. Note that the porosity accessible to water is larger than the porosity accessible to mercury. This has been expected since water is known to be able to penetrate deeper in the porosity of cement paste than mercury, due to its higher wetting capacity and smaller atomic size compared to mercury. The calculated standard deviations on porosity and oven-dry density measurements using water and mercury porosimetry are less than 1.68% and 0.03 g/cm3 respectively, thus confirming the cement pastes homogeneity. shows the differential distribution curves of CPS3, CPS5 and CPS7 issued from MIP measurements in order to evaluate the pore structure of the cement pastes. The area below each curve reflects the amount of mercury intruded. As expected, the total intruded volume increases with the W/C ratio, thus indicating a higher accessible porosity of the cement pastes. MIP shows a broader pore size distribution for the cement pastes with the highest W/C ratio. For instance, the proportion of pores larger than 0.1 µm is equal to 4%, 27% and 37% for the 0.3, 0.5 and 0.7 W/C pastes respectively. Note that the 1 µm mode can only be observed in CPS7. This mode corresponds to relatively large capillaries more easily connected to the surface.a shows spread diameter versus time evolution of filler mortars containing dry or saturated CPS. Here, “time evolution” refers to the elapsed time since first contact between the constituents of the mortar. The graph suggests a spread loss over time for all mixes. This spread loss may result from water transfer to dry CPS or water losses during spread measurement operations. In the following, we assume that at a given time, water losses are similar among all mortars at the same time.a also shows that whatever the type of CPS, the spread of a mortar made with dry CPS is always larger than that of a mortar made with saturated CPS. Since the compositions of both mortars are identical, the spread difference may only be caused by an excess of effective water content in the filler paste of the mortar containing dry CPS which increases the mortar fluidity. Initially, this excess is equal to the CPS water absorption for mortars incorporating dry CPS whereas the absorption water is totally trapped in the porosity of saturated CPS and does not contribute to fluidizing mortars incorporating them. With time, capillarity causes partial transfer of absorption water from the paste to the porosity of initially dry CPS, leading to a decrease of both the volume and fluidity of paste.Since the spread of mortar made with dry CPS remains greater than the spread of the same mortar made with saturated CPS, we can deduce that dry CPS are not saturated when mixed with fresh paste, even 90 min after the beginning of mixing and for CPS7 which has the highest and coarsest porosity (47.1%). A similar result was found in reference Supposing that dry CPS becomes fully saturated at a given time, then the spread of dry CPS mortars should be equal to that of mortars made with saturated CPS. b shows that at 6 min, F3S, F5S and F7S have roughly the same spread whereas F3D, F5D and F7D have remarkably different spreads. Besides, CPS7 mortars, whether in initially dry or saturated conditions, already have close spread diameters at 6 min, suggesting that their saturation is a quick process. The spread difference between mortars incorporating dry or saturated CPS is the highest for the mortar with CPS3 and decreases with W/C of the CPS, suggesting a faster migration of water into the internal porosity of CPS when their W/C ratio increases. shows the time evolution of spread diameter of mortars containing CPS over-saturated by different fractions of their respective water absorption. It is important to note that all mortars have the same volume of CPS with similar particle size distribution and mass of filler, so that a spread difference between two mortars made with the same CPS may only be due to a difference of effective water content. The spread diameter increases as the effective water content increases. This increase is due to higher volumes of paste and higher fluidity of pastes when the amount of oversaturation water increases.For instance at t = 6 min, the spread of F5D lies between those of F5S10 and F5S30. Assuming that there is no water transfer between saturated CPS5 and the filler paste, we deduce that the amount of effective water in the paste of F5D is framed by the amounts of effective water in F5S10 and F5S30 filler paste mortars, hence lies in the interval [Weff,th + (10/100)WA24(CPS5);Weff,th + (30/100)WA24(CPS5)]. Since the initial effective water content of F5D is equal to Weff,th + WA 24(CPS5), we deduce that an amount of water lying in the interval [(70/100)WA24(CPS5); (90/100)WA24(CPS5)] has penetrated the F5D porosity, hence between 70% and 90% of the water absorption has been transferred to the porosity of dry CPS5. Similarly, we deduce that less than 50% of the water absorption has been transferred to the porosity of initially dry CPS3, whereas between 90% and 100% of its water absorption has been transferred to the porosity of initially dry CPS7. These data confirm an increase of the saturation degree of CPS with their porosity and pore size.For a quantitative assessment of water content of initially dry CPS according to our experimental protocol, it is necessary to investigate spread diameter variations when effective water varies between Weff,th and Weff,th + 0.5WA24 in mortars made with saturated CPS. At various time steps, shows the variations of spread diameter logarithm of mortars made with saturated CPS as a function of the effective water-to-filler ratio. The results suggest that the spread logarithm is approximately given by a linear function of the effective water-to-filler ratio over the range of W/F investigated (R2 between 0.93 and 0.96). Therefore we can write:. Note however that even if the fitting function describes satisfactorily the system, the slower variation of spread when Weff/F varies in the range of 0.57–0.59 is not well captured. Similar observations are made in Furthermore, the variations of spread diameter as a function of the effective water to filler ratio for the three CPS collapse into a single curve (). This means that the effective water content is the parameter governing the rheology of all the mortars containing saturated CPS and variable effective water contents. This can be explained by similar volumes and size-distributions of the three CPS incorporated in different mortars. Hence, mortars “see” the saturated aggregates with different W/C ratio as same aggregates. Knowing the Eq. fit parameters (a and b) and the spread diameter of mortars made with dry CPS at each time interval, the effective water content of mortars made with initially dry CPS can be deduced at each time t. Then, the CPS water content WCPS can be calculated knowing the total water content of the mortars (Parameters a and b are presumably specific to each CPS and time t. Upon calculating the mean value of the set of parameters a at different time steps, as well as the mean values of the set of parameters b; we observe that mean values fall inside the confidence ellipse of each set of parameters (a, b). Thus, the “spread – (Weff/S)” curves are time independent in our case. a shows the temporal evolution of water content in initially dry CPS. Here, water content is the ratio of the mass of pore water to the dry mass of aggregates. As expected, water content stays lower than the water absorption. A saturation degree smaller than 1 could be due to a concentration of filler grains in the vicinity of CPS decreasing the permeability of the fresh filler paste. An actual blocking of pore entries by filler grains cannot be excluded as well since the pore size of the three tested CPS ranges between 5 nm and 3 µm whereas the size of filler grains spreads between 0.4 µm and 40 µm. Error bars represent 95% confidence intervals. Statistical analysis at a 95% confidence level shows insignificant variation of the water content over time for the 3 CPS. Thus, the amount of water absorbed by the CPS before 6 min remains constant. This is not surprising because of the large mean pore size in the filler paste (around 6 µm) than in the porosity of the CPS, thus inducing larger capillary pressures in the porosity of the CPS than in the fresh filler paste.The saturation degree increases with the CPS W/C ratio (see b). This suggests a higher permeability of the CPS having the largest pore size, thus leading to a faster capillary absorption. This means that the assumption of total water saturation of industrial RCA in a cement paste during casting is certainly invalid since model pure cement paste aggregates with a high W/C (0.7) ratio are not fully saturated when mixed with an inert paste during 90 min. In fact, water transfer from a cement paste to industrial RCA should be slower than between a filler paste and pure cement paste aggregates with a 0.7 W/C because of a finer porosity of RCA as compared to that of a pure cement paste with a 0.7 W/C.Carrying out the same procedure as before on series II mortars, water transfer between a cement paste with a water to cement ratio equal to 0.77 and initially dry CPS5 are investigated. At each time interval, spread diameter of series II mortars increases with the effective water content (a). An exponential function fits the data quite well (R2 between 0.93 and 0.99 for different time intervals). The fit calculated at 6 min is shown in (As for filler mortars, fit parameters are used to estimate the amount of effective water transferred to initially dry CPS5 at various time steps. A statistical analysis shows that fit parameters are time independent. Water transfer kinetics from cement paste to initially dry CPS5 are found similar to those in the filler paste (). 6 min after casting, water content reaches 19% then remains fairly constant. Error bars are based on the 95% confidence level.Similar results are reported in reference In this section, existing theoretical models linking spread measurements to effective water content are considered. Our aim is to make sure that the relationship found between spread and effective water is consistent with both experimental results linking the yield stress of a fresh cement paste to its W/C ratio and theoretical results expressing the spread diameter of a yield stress fluid as a function of the yield stress. Spread has been shown to relate to yield stress where A is a constant depending on the sample volume and density. shows the density of our mortars made with a fixed saturated CPS and different effective water contents. For a fixed CPS, density appears reasonably independent of Weff/F ratio and may hence be considered constant.Previous studies show an exponential decrease of yield stress with the increase of W/C in the case of pure cement pastes where S stands for filler or cement mass, α is a parameter depending on the interactions between filler or cement grains in suspension, B depends on the interactions between filler or cement grains and the characteristics of the granular skeleton (concentration, size distribution, shape and surface rugosity). Using Eqs. , the variation of the spread diameter as a function of the effective water content becomes:The spread diameter logarithm scales as Weff/F in agreement with our experimental results. However, it is important to note that the conditions of applicability of Roussel’s model (3) are not always fulfilled in our experiments. Even if mortars exhibit relatively large spreads, the ratio of the final height to spread radius is in the range of 0.3 for the stiffest mortars which is larger than the maximum prescribed value of 0.1. shows the variations of yield stress calculated using Roussel’s model . Note however that the model fails to fit the data at the lowest W/S ratios for filler and cement mortars. This may be because of the fact that at such high volume concentrations of the CPS (caused by the decrease of effective water), the fit parameter B given in the Eq. can no longer be considered as constant and depends on the volume concentration of the CPS Water transfer between model fine RCA consisting of pure cement paste and fresh cement or filler paste have been investigated using spread measurements. The following conclusions can be drawn:An original experimental method to study water transfer between initially dry CPS and fresh filler or cement paste in contact with it is implemented. This method is based on the comparison of spread of mortars containing either initially dry CPS or saturated CPS and different amounts of effective water, while keeping all the other mixing parameters unchanged. An empirical exponential relationship is found between the spread diameter of mortars containing saturated CPS and the effective water content. This relationship is explained using a theoretical model based on the long wave approximation and an empirical model based on rheology measurements. The combination of the two models allows to express the spread of a mortar as a function of the effective water-to-solid ratio. This relationship is then used to estimate the effective water content in a mortar made with initially dry CPS knowing its spread. The amount of water transferred to the porosity of CPS is then deduced knowing the total water content.Using this method, we find that water content of initially dry CPS reaches a maximum during the first 6 min then remains fairly constant afterwards during the testing period of 90 min whatever the CPS porosity and the type of paste (filler or cement). The saturation degree increases with the CPS W/C ratio and varies between 49% and 87%. This increase can be explained by an increase of the permeability of CPS with the W/C ratio leading to faster water transfer from the paste to the porosity of CPS. Water transfer kinetics are found similar for CPS5 mixed with either filler or cement paste.It is interesting to note that even our most porous model RCA, namely CPS7 having a 0.7 W/C, remain unsaturated when mixed to a filler paste (saturation degree around 87%) at 90 min after the beginning of mixing. Given the lower W/C of the adhering cement paste of industrial RCA (usually around 0.4); assuming that these aggregates become saturated when mixed to a fresh cement paste during mixing is hardly relevant. Lower saturation degrees of industrial RCA are expected because of their finer porosity and the hydration reactions occurring in a cement paste, slowing down water transfer to the aggregates. This should be taken into account during mix design in order to reach the desired effective water content.Further investigation is needed to better capture the rheology of mortars made of such porous fine aggregates for the lowest W/S ratios. This work is underway and will be presented in a future paper.Using type III recombinant human collagen to construct a series of highly porous scaffolds for tissue regenerationAs an alternative biopolymer material without the risks of the use of animal-derived collagens in soft tissue engineering applications, recombinant human collagen polypeptide (RHC) was used to construct three-dimensional porous scaffolds. RHC and RHC-chitosan (RHC-CHI) porous scaffolds were fabricated using a freeze-drying method to create highly porous internal structures and then cross-linked with 1-ethyl-3-(3-dimethyl aminopropyl) carbodiimide (EDC). All scaffolds had interconnected porous structures with high porosity (90%), and pore size that ranged from 111 µm to 159 µm. The swelling ability and in vitro degradation of the prepared scaffolds were investigated. The mechanical properties could be tailored to meet the requirements of end-use application by adjusting the concentrations of the polymer or cross-linking agent, and the resulting mechanical strengths were comparable to those of biological soft tissues. The cytocompatibility of the fabricated porous scaffolds was investigated by seeding 3T3 fibroblasts into the porous structures, and then cell proliferation, distribution, morphology, and synthesis of extra cellular matrix-associated proteins were assessed. The results indicated that RHC-based porous scaffolds were non-cytotoxic and promoted the attachment and proliferation of the seeded cells. Finally, the in vivo study proved these porous scaffolds were able to accelerate the cell infiltration and collagen deposition that promoted the wound closure. Overall, the results indicate that RHC-based porous scaffolds show promise for use in soft tissue engineering due to their excellent in vitro cytocompatibility and adjustable mechanical properties.Soft tissue engineering is performed for the replacement and repair of skin tissue or loose connective tissues that are rich in fibroblast cells Collagens are widely used in tissue engineering studies and for tissue regeneration applications as the structural protein of the extra cellular matrix (ECM) in the human body, acting to maintain tissue structural integrity and biological function Although collagen scaffolds have excellent biological function for tissue engineering, current materials have crucial limitations due to poor mechanical properties and rapid degradation in vivo and in vitro. Approaches including chemical cross-linking of collagen and the use of blends of collagen with other copolymers have been tested in efforts to improve the mechanical properties of these materials and reduce degradation rates To date, very few studies have tested the use of recombinant human collagen to construct highly porous scaffolds or investigated the cell behaviors within such scaffolds To prepare RHC-CHI porous scaffolds, samples of RHC (GenBank Access Number: EF376007, kindly provided by the Bioengineering lab of Nanjing University of Science and Technology, Jiangsu, China) and chitosan powder (deacetylation degree > 90.0%, Shanghai Lanji Technology Development Co., Ltd.) were weighed, added to 0.2 mol/L acetic acid solution, and then stirred for 1 h to fully dissolve. The prepared RHC-CHI solutions were poured into then polytetrafluoroethylene (PTFE) molds and frozen at −20 °C overnight. Next, the frozen samples were lyophilized in a freeze-drier (Eyela. Fdu-1200. Japan) to obtain cylindrical porous scaffolds with 13 mm diameter and 5 mm thickness. A modified cross-linking method described previously was used to cross-link the porous scaffolds To characterize the internal morphology of the porous structures, dry scaffolds were carefully sectioned using a scalpel and then sputter-coated with platinum for 90 s. The coated surface samples were imaged by scanning electron microscopy (SEM, Philips XL30, Netherlands) at an accelerating voltage of 10 kV and working distance of 15 mm. Average pore sizes and porosities were determined using mercury intrusion porosimetry (Micromeritics Autopore IV, United States).FT-IR spectra of the samples were obtained from a Fourier transform infrared spectrophotometer (Bruker-EQUINOX55, Germany). Part of a dry scaffold was peeled off using tweezers and directly placed onto the testing stage. Spectra were recorded under transmittance mode at 2 cm-1 intervals for the wavelength range of 400–4000 cm-1.The RHC molecules (with and without cross-linking) were detected by HPLC (Agilent 1260 Infinity). Briefly, free RHC molecules remaining in the used cross-linking solutions and the used sample washing liquid were tested by HPLC. The weight of the uncross-linked RHC was then quantified relative to a predetermined RHC concentration standard curve (shown in ). Finally, the total detected amount of RHC was summed (Wd), and the cross-linking degree was calculated as the amount of detected RHC to the amount of total RHC powder (Wt) used to fabricate the porous scaffolds: (Wd/Wt)× 100%.The swelling ability of the samples was determined by measuring the change in mass of for dry and wet scaffolds. Dry scaffolds were first weighed and then fully immersed in PBS for 24 h. The scaffolds were then removed and wiped with filter paper to remove extra PBS on the surface before weighing the wet mass. The swelling degree (SD) of the scaffolds was calculated as the expression: SD = (Ww – Wd)/Wd× 100%, where Wd and Ww were the dry and wet weights of the scaffolds, respectively.To determine the biodegradation rate, each scaffold was immersed into 3 ml PBS and kept in an incubator at 37 °C. To ensure continuous biodegradation, the PBS was changed every 2 days. At each defined time point (days 3, 7, 10, 14, 21, and 28), scaffolds were removed and rinsed three times with distilled water before freezing in a freezer overnight and then freeze-drying. The degradation rate was calculated as: (Wo-Wt)/Wo× 100%, where Wo is the initial weight of the dry scaffold and Wt is the weight of the degraded scaffold at a specific time point.The compressive strength, compressive modulus, tensile strength, and tensile elastic modulus of the scaffolds were determined. Compression test was performed using a universal testing machine (Instron 5969) in uniaxial compression mode and equipped with a 50 N load cell. The 5 mm thickness samples were compressed up to 70% strain at a constant loading speed of 2 mm/min. The compressive modulus was obtained from the initial linear slope (10% strain) of the stress-strain curves and stresses at 70% strain were recorded as maximum compressive strengths. The tensile properties of the scaffolds were determined using a universal testing machine (Instron 5969) in uniaxial tensile mode, with crosshead speed of 2 mm/min, the maximum tensile strengths of the scaffolds were recorded at the break point and the elastic modulus were obtained from the gradient at the initial linear region of the stress-strain curve. Samples were cut into 13 mm × 5 mm rectangular strips with thickness of 3 mm and gauge length of 5 mm. All samples in the static mechanical tests were hydrated in PBS solution for 24 h before each test.NIH-3T3 mouse fibroblasts (European Collection of Cell Cultures) were used in cytocompatibility tests. Complete Dulbecco’s Modified Eagle Medium (DMEM) with 10% fetal calf serum, 2% HEPES buffer, 2% penicillin/ streptomycin, 1% -glutamine, 1% non-essential amino acids (Gibco Invitrogen), and 0.85 mM ascorbic acid (Sigma–Aldrich, UK) was used as cell culture medium throughout the tests.Cytotoxicity tests were carried out according to ISO 10993 by evaluating sample elutions. UV-sterilized samples were incubated in fresh medium for 24 h with a sample surface area/medium volume ratio of 3 cm2/ml. Separately, 3T3 cells were seeded at a density of 40 × 103 cells/cm2 in each well of a 48-well plates and incubated for 24 h until 90% confluent. The culture medium was then replaced with sample extraction medium and incubated for another 24 h. Cells cultured in complete DMEM were used as controls. Cells were washed with PBS and incubated in Alamar Blue solution (Bio-Rad) (1:10 Alamar Blue: Hank's Balanced Salt Solution (HBSS, Invitrogen)) for 80 min. The Alamar Blue solutions were then examined in an FLx800 plate reader (Bio-Tek Instruments Inc.) with excitation wavelength of 530 nm and emission wavelength of 590 nm. The morphology of cells cultured in different extracts was examined by calcein AM and ethidium homodimer-1 (Live/Dead™, Invitrogen) fluorescence staining in fluorescent microscopy (DMLB, Leica).For cell seeding, 150k 3T3 were carefully seeded on top of each scaffold. The seeded scaffolds were then immersed in culture medium and maintained at 37 °C in a 5% CO2 humidified incubator, and the medium was changed every 2 days. Samples were tested after culturing for 1, 3, 7, 10, and 14 days.Cell proliferation was determined by quantifying the total DNA content in scaffolds at each time point. At days 1, 3, 7, 10, and 14, scaffolds were washed with PBS twice and freeze-thawed three times to lyse the cells. Next, 100 μL samples from each scaffold were transferred into a 96 well-plate, and then 100 μL Hoechst stain (Hoechst 33258 DNA assay, Sigma-Aldrich) was added to each well. The plate was then placed on a plate shaker for 10 min before reading in a plate reader (FLX-800) using fluorescence excitation at 360 nm and emission at 460 nm. The results were calculated based on the pre-determined standard curve of series of known DNA concentrations.The proliferation and distribution of the cells in porous scaffolds were investigated by fluorescent microscopy on days 7 and 14. The scaffolds were washed with PBS three times, cut into half horizontally, stained in calcein AM solution (Live/Dead™, Invitrogen) for 15 min, and then examined by fluorescent microscopy (DMLB, Leica) at an excitation wavelength of 495 nm and emission of 530 nm. Cell distributions were determined at day 7 and 14, scaffolds were fixed with 4% paraformaldehyde fix solution for 30 min and cut into half vertically, then stained with 4’,6-diamidino-2-phenylindole (DAPI) and observed under fluorescent microscopy. To evaluate cell morphology, on day 14, scaffolds were fixed in 3% glutaraldehyde in 0.1 M cacodylate buffer for 30 min. The fixative was then replaced with 7% sucrose solution and stored at 4 °C overnight. Scaffolds were then washed in 0.1 M cacodylate buffer before post-fixing in 1% osmium. Next, samples were gradually dehydrated through a series of ethanol gradients and finally dried in hexamethyldisilazane (HMDS) before being sputter-coated with platinum for observation.The gene expression levels of integrin-α2, collagen I, and collagen III were measured using qRT-PCR. At selected time points, total RNA was extracted from fibroblast-seeded scaffolds by Trizol®, according to the instructions of the manufacturer. Reverse transcription was conducted with a OneScript Plus cDNA Synthesis Kit (Applied Biological Materials Inc., Canada) by incubation at 50 °C for 50 min and reactions were terminated by heating at 85 °C for 5 min (as described in the Applied Biosystems product manual). The polymerase chain reaction to amplify the cDNA was performed using a 10 μL reaction system, and real-time PCR was performed in a Real-Time PCR System (StepOne Plus, Applied Biosystems) with SYBR Green PCRMasterMix (Applied Biosystems). The 2-△△CT Method was applied to calculate the level of gene expression. Cells cultured in 35 mm culture dishes were used as control samples.SD rats (Beijing Vital River Laboratory Animal Technology Co., Ltd.) weighing 200–300 g were prepared in this study. All animal experiments were performed according to the protocols approved by the National Institutes of Health Guide for the Care and Use of Laboratory Animals, China. All experiments and procedures were approved by the Animal Experimentation Ethics Committee of Wenzhou Medical University. Rats were anesthetized with an intraperitoneal injection of 10% chloral hydrate (3.0 mg/kg). Biopsy punch was used to create four full-thickness excisional wounds with a diameter of 15 mm on the back of each rat. RHC-2.0, RHC-CHI-75 were conducted in this test. All samples were carefully applied to the trauma, then all samples including the wounds of control group were secured with Tegaderm™ dressing (3 M Health Care, Germany) immediately to protect them from dryness and self-grooming damage. At days 0, 3, 10 and 14 after treatment, photos of wound sites were taken, and the wound areas were measured with Image-Pro plus. For histological analyses, rats were sacrificed at days 14, and wound sites with surrounding skin were excised. Tissue specimens were 4% paraformaldehyde fixed and dehydrated in graded ethanol, then embedded in paraffin. Central wound sections with a thickness of 5 µm were then fixed on poly--lysine-coated glass slides and stained with hematoxylin and eosin (H&E) and Masson's trichrome (MT) (Beyotime Institute of Biotechnology, China). Images of granulation tissue formation of the regenerated tissue were taken with a Nikon ECLIPSE 80i (Nikon, Japan).The data are presented as mean ± standard deviation (SD), and at least five samples were measured for each group tested. Statistical analysis was carried out using Graphpad Prism 6.0 and statistical significance was assessed using One-way ANOVA (analysis of variance) was performed with Tukey test. Significance is indicated with *P < 0.05, * *P < 0.01, and * **P < 0.001, where P > 0.05 was considered not statistically significant.The cross-section images of the RHC and RHC-CHI scaffolds are shown in . Interconnected and porous structures were observed in all fabricated scaffolds, pore shapes and pore wall thicknesses varied with RHC concentrations (A,B and C). At low RHC concentration (1.5% w/v), pores were formed with thin sheet-like structures, and thicker pore wall structures were observed with increased RHC concentration. As shown in D, E and F, there were no significant differences in pore shape among RHC-CHI-based scaffolds, with homogenous pore structures observed in all samples. Average pore sizes and porosities of the RHC and RHC-CHI scaffolds are summarized in . The pore sizes of fabricated RHC porous scaffolds were between 111 µm and 131 µm, and average pore size of the RHC-CHI scaffolds ranged from 136 µm to 159 µm. The porosities of the RHC and RHC-CHI scaffolds were between 90% and 93%, indicating all fabricated scaffolds were highly porous.The molecule structures of RHC and RHC-CHI samples were analyzed by FT-IR and the results are shown in . Typical collagen band Amide I was found at 1640 cm-1, corresponding to stretching vibrations of CO and N-H. Amide II was observed at 1540 cm-1, corresponding to N-H deformation vibrations. Amide A was detected at 3290 cm-1, corresponding to O-H and N-H vibrations, and υC-H corresponding to Amide B was found at 3070 cm-1. There was no difference on wavenumber for RHC samples after cross-linking with EDC, compared to the uncross-linked RHC sample, but the intensities of N-H vibrations were found increased. For the RHC-CHI samples, the peaks for Amide I and II were found at 1655 cm-1 and 1565 cm-1, after sample cross-linked by EDC, the intensities of N-H and CTo determine the cross-linking degree of RHC molecules in the porous scaffolds, the amount of uncross-linked RHC was detected by HPLC to determine the weight loss compared to the total RHC used in fabrication. The HPLC results are shown in A. The RHC retention time was close to 11 min in the RHC standard solution, with no detected RHC peaks in the EDC cross-linked porous scaffolds. Thus, the cross-linking degrees were higher than 96% for all scaffolds, with no significant differences among these samples (The degradation degrees of the porous scaffolds were measured and are shown in C. All RHC scaffolds had similar degradation rates throughout the entire degradation test (P > 0.05), and degradation rates decreased with increasing EDC content in RHC-CHI samples. RHC-CHI-100 scaffolds showed the lowest mass loss, with only 2% weight loss on day 3% and 15.8% after 28 days, a significant lower degradation rate than those of the RHC-CHI-75 and RHC-CHI-50 scaffolds (P < 0.01).The swelling degrees of the porous scaffolds were determined by measuring the increase in mass after submerging in PBS and the results are shown in D. The swelling capabilities were proportional to the increase of RHC concentration as RHC-3.0 bound more PBS than RHC-1.5 and 2.0. The swelling degree decreased with increasing EDC content in RHC-CHI scaffolds. The highest swelling degree was achieved in the RHC-CHI-50 scaffold that could bind at least 88-fold of the PBS, and decreased to 34-fold in the RHC-CHI-100 scaffold (P < 0.001).The compressive strengths and modulus values were determined from compression tests by applying a constant strain rate (2 mm/min) to the pre-hydrated porous scaffolds. The obtained parameters are shown in . The RHC-3.0 scaffold has the highest compressive modulus (0.54 kPa), a value that is significantly higher than that of the RHC-1.5 and 2.0 (P < 0.05) scaffolds. The RHC-CHI scaffolds exhibited higher mechanical strengths compared to those of the RHC scaffolds fabricated using the same concentration. Both the tensile stress and elastic modulus of the RHC-CHI scaffolds were much higher than those of the pure RHC scaffolds. The tensile stress of RHC-CHI scaffolds was 50 kPa, significantly higher than the values of all RHC scaffolds. The mechanical strengths of the RHC-CHI scaffolds were largely influenced by the amount of EDC used in cross-linking, with the RHC-CHI-100 scaffold exhibiting the highest compression and tensile strengths. The representative compression and ultimate tensile stress-strain curves are shown in To determine the cytotoxicity of the samples, the Alamar Blue assay was used to assess the viability of the cells cultured in medium extractives, and cells morphology was examined by Live/Dead™ fluorescent staining. As shown in A, fibroblasts exhibited spindle-like shapes in all groups at 24 h of culturing and no dead cell were detected. The relative fluorescent values of all tested samples determined by Alamar Blue assay (B) were very similar, with no significant differences were observed between samples (P > 0.05), and with no significant difference between samples and control.The cell proliferation activities in the seeded scaffolds were evaluated by Hoechst DNA assay at defined culture times, and results are shown in C and D. DNA concentration increased with the culturing time and was proportional to the RHC concentrations from days 1–7, with significant differences in DNA concentrations found between RHC-1.5 and 3.0 scaffolds (P < 0.05). RHC-1.5 and 2.0 exhibited similar proliferation rates (P > 0.05). The DNA concentrations in the RHC-CHI scaffolds were lower than those of the RHC scaffolds. Additionally, the DNA contents were proportional to the amount of EDC, with the highest DNA concentration for the RHC-CHI-100 scaffold, with 7.5 µg/ml at day 14, significantly higher compared than the DNA concentrations of the RHC-CHI-50 (P < 0.001) and RHC-CHI-75 (P < 0.01) scaffolds.To investigate the proliferation status of 3T3 cells in different scaffolds, fluorescent images were taken at defined time points (day 7 and 14) and are shown in . At day 7, the numbers of live cells in RHC-1.5, 2.0 and 3.0 scaffold were similar, with homogenous distributions of the cells in each scaffold (A1, C1 and E1). At culturing day 14, higher cell densities were observed for each scaffold compared to those on day 7. The porous structures of all three types of RHC scaffolds were mostly covered by the proliferated 3T3 fibroblasts, and cells were also homogenously distributed (B1, D1, F1). No significant difference in cell density was found among RHC-1.5, 2.0 and 3.0 scaffolds at day 14. The RHC-CHI-75 and 100 scaffolds showed slightly higher cell densities compared to the RHC-CHI-50 scaffold (A2, C2, E2). On day 14, fibroblasts were homogenously distributed in the porous structures of all three samples and the cell densities were significantly increased as compared to those on day 7 (The distribution of the proliferated fibroblasts were determined by staining the cell nucleus with DAPI (). At culture day 7, fibroblasts were found distributed from the upper surface to the middle part of the porous scaffolds in all test samples; and large number of cells were found migrated to the bottom in all scaffolds on day 14. The morphology of 3T3 cells grown in RHC-1.5, 2.0, and 3.0 scaffolds were investigated by SEM at day 14 and the images are shown in . The wall structures of pores were covered with 3T3 cells for all three types of scaffolds, and the proliferated cells were well connected and firmly attached to the wall structures of the scaffolds. No significant difference of the cell morphology and density was observed among these three RHC scaffolds. Cells in RHC-CHI scaffolds also showed well-connected structures and were firmly attached to the wall of porous structures, similar to the cells grown on the RHC scaffolds. Additionally, there was no obvious difference in cell shape or orientation among all these three type of scaffolds.To measure the expression of genes encoding extracellular matrix-associated proteins, qRT-PCR was used. The expression levels of integrin-α2, collagen I, and collagen III were determined in RHC and RHC-CHI scaffolds, as shown in . The expression of integrin-α2 increased throughout the cell culturing period for both samples, and the highest expression was 80-fold higher than the control from the RHC scaffold (G). The expression of type I and III collagen also increased with culture time (H and I), but expression levels were much lower compared to the expression of integrin-α2. Generally, the mRNA expression levels of type I and III collagen were relatively low for the two types of scaffolds from day 1 to day 3, and then increased significantly on day 7. In addition, the RHC-CHI scaffolds exhibited higher expression on type III collagen at day 7 but lower expression at day 14 as compared to the RHC scaffolds.The wound closure rates and representative photos of rat surgery in vivo study are shown in . There was no significant difference between each group at first 10 days after surgery, while by day 14, the healing rate of RHC-based scaffold group reached to 95% approximately that showed significant healing progress compared to control (B). To confirm the feasibility of using RHC-based porous scaffolds for soft tissue regeneration, H&E staining was used to assess the epithelial regeneration and granulation tissue formation on day 14 post-surgery (Pore size and interconnected porosity are critical parameters that can provide appropriate mechanical properties to scaffolds. Previous study suggested an average pore size of fibroblast cells of 90–360 µm The molecular structure of RHC without cross-linking and EDC cross-linked RHC were analyzed by FTIR. shows that all typical wavenumbers of collagen retained their positions after cross-linking, suggesting that the EDC cross-linking process did not affect the secondary structure of the RHC Degradation rates are critical parameters of scaffolds, as a suitable rate of degradation could benefit overall mechanical and structural stability in applications. In this study, no significant differences in degradation rates were observed among three RHC scaffolds. This finding indicates the RHC molecules are well cross-linked within the porous structures, with similar cross-linking degrees for the three scaffolds. The degradation rates decreased with increasing EDC in RHC-CHI scaffolds. Previous work showed that an increased EDC concentration (10, 33, and 50 mM) increased the resistance of a collagen-based matrix to biodegradation The swelling ability of scaffolds can influence the mechanical and structural stability after implantation or during in vitro culturing. In this study, the swelling degrees of the RHC scaffolds increased gradually with increased RHC content (D), whereas the swelling degree of RHC-CHI scaffolds decreased with increased EDC content during cross-linking. Collagen is a hydrophilic biopolymer, and these different swelling degrees of RHC scaffolds may be due to greater stiffness of the scaffold with higher RHC concentration, since more biopolymers helped the scaffold maintain its microstructural stability and retain water molecules under hydration condition. Cross-linking is also known to reduce the swelling ability by reducing the number of hydrophilic groups (amino or carboxylic groups) of the material The designed scaffolds require enough tolerance to maintain their structural stability to provide a stable environment during culturing in vitro or implanting in vivo. An increasing collagen concentration (density) in the RHC scaffold was expected to improve the overall mechanical properties. Previous studies found that the compressive and elastic modulus values increased proportionally to increasing collagen concentration in the fabrication of porous scaffolds The mechanical properties of scaffolds for tissue engineering should closely match those of the healthy native tissue and provide enough mechanical support for implantation and tissue regeneration. The results show that our porous scaffolds are comparable in mechanical properties to native tissues such as skin, muscle, adipose, and brain tissue, containing adipocytes, fibroblasts, collagenous ECM, and blood vessels ) show three distinct regions, corresponding to the straightening, alignment, and disruption of the pore wall structures (struts) in the loading direction Water-soluble EDC is generally considered an efficient cross-linker that can covalently cross-link collagen-based materials and has low toxicity to the cells after removal by washing A, the fibroblasts exhibited spindle-like morphologies in all groups, indicating that cells were in an active growth state. The cell shape and density of all tested groups were consistent with the cellular metabolic levels determined by Alamar Blue assay, indicating no harmful cellular effects of the RHC and RHC-CHI scaffolds and further demonstrating EDC is an efficient and safe cross-linker for preparation of collagen-based biopolymers.To assess the viabilities and proliferations of the seeded fibroblasts within the porous scaffolds, the DNA contents were determined by Hoechst DNA assay and fibroblasts were examined by fluorescent microscopy at defined times. The cellular proliferation activities were sustained as DNA concentrations increased with the culture time (C and D). This finding is in agreement with the fluorescent results (shown in ), as cell densities on day 14 are higher day 7. Cell proliferation rates were proportional to RHC concentrations in RHC scaffolds and EDC in RHC-CHI samples. The mechanical strengths and degradation speed may regulate the cellular proliferation activities within the porous scaffolds, as fibroblasts show a higher proliferation rate in samples with stiffer mechanical properties or slower degradation rate. Cellular activities are substrate stiffness-dependent By comparing the cell distributions on day 7 and 14 (), it can be found the fibroblasts moved from the top to the bottom of the scaffolds, which indicated the porous structures of RHC and RHC-CHI scaffolds supported not only the proliferation but also migration of the seeded fibroblasts. The morphology of the proliferated fibroblasts was characterized by SEM (A-F) and showed fibroblasts were well-connected and firmly attached to the porous structures. The fabricated porous scaffolds not only supported the migration and the proliferation of the seeded fibroblasts, but also maintained their elongated shapes when attaching to materials. Thus, the RHC scaffolds show excellent morphology that is ideal for substrate interaction in biomaterials.The deposition of ECM-related proteins (integrin-α2, collagen I, and collagen III) was quantified by qRT-PCR. The induction of integrin expression indicated that the fabricated RHC scaffold can prompt the adhesion and migration of fibroblasts after seeding on the substrates, as integrin directly associates with the cell adhesive to materials To evaluate the possibility of using porous scaffolds for wound healing and tissue regeneration, a full thickness skin defect model in SD rats was used in the in vivo study. RHC-based porous scaffolds show a higher healing rate than the control (A and B), this result were in consistent to the results obtained from H&E and Masson's trichrome staining (C) as larger number of fibroblasts and denser collagen depositions were noticed in porous scaffolds that contained RHC. Specifically, extensive fibroblast infiltration with well-order structures on regenerated dermis suggests these porous scaffolds promoted the fibroblast proliferation and collagen formation, which further confirmed the results determined in the in vitro test. More importantly, mild localized immunoreactivity were found in RHC-based samples, which suggested RHC as biomaterials has no toxic effect to the wound area. Current results are also comparable to another study where a mussel-inspired agarose hydrogel scaffold constructed for skin regeneration In this study, highly porous (porosity > 90%) 3D scaffolds were successfully fabricated and our data demonstrated the pore size, swelling ability, stability, and mechanical property of the scaffolds can be tailored by increasing the RHC concentration or by introducing chitosan into the system. In vitro study showed our porous scaffolds exhibited no toxicity for seeded fibroblasts, with stimulation of the infiltration and proliferation of the seeded cells toward to their internal parts. Importantly, cellular activities depended on both scaffold stiffness and RHC fraction had been proved in the tests. Additionally, qRT-PCR analysis confirmed the expression of ECM-associated proteins, results from in vivo study indicated our RHC-based porous scaffolds were able to accelerate tissue regeneration by promoting fibroblasts proliferation and ECM deposition in the wounds. Overall, the RHC-based porous scaffolds demonstrate excellent potential for use in tissue regeneration and wound healing applications.Yang Yang: Conceptualization, Methodology, Testing, Writing – original draft, Writing – review & editing.Nicola M. Everitt: Supervision. Alastair Campbell Ritchie: Supervision.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Supplementary data associated with this article can be found in the online version at Effects of minimum quantity lubrication on turning AISI 9310 alloy steel using vegetable oil-based cutting fluidThis paper presents the effects of minimum quantity lubrication (MQL) by vegetable oil-based cutting fluid on the turning performance of low alloy steel AISI 9310 as compared to completely dry and wet machining in terms of chip–tool interface temperature, chip formation mode, tool wear and surface roughness. The minimum quantity lubrication was provided with a spray of air and vegetable oil. MQL machining was performed much superior compared to the dry and wet machining due to substantial reduction in cutting zone temperature enabling favorable chip formation and chip–tool interaction. It was also seen from the results that the substantial reduction in tool wears resulted in enhanced the tool life and surface finish. Furthermore, MQL provides environment friendliness (maintaining neat, clean and dry working area, avoiding inconvenience and health hazards due to heat, smoke, fumes, gases, etc. and preventing pollution of the surroundings) and improves the machinability characteristics.Currently, there is a wide-scale evaluation of the use of metalworking fluids (MWFs) in machining. Industries are looking for ways to reduce the amount of lubricants in metal removing operations due to the ecological, economical and most importantly occupational pressure. From a study, revealed that respiration and skin problems were the main side affects of MWF. However, studied the types of occupational risks associated with MWFs, which became airborne and formed aerosol during machining and showed that these risks were numerous and widespread. It is, therefore, important to find a way to manufacture products using the sustainable methods and processes that minimize the use of MWFs in machining operations. In addition, it is essential to determine the optimal cutting conditions and parameters, while maintaining long tool life, acceptable surface finish and good part accuracy to achieve ecological and coolantless objective. demonstrated successfully a method in the minimization of MWFs called near dry machining (NDM). NDM uses very small amounts of MWF in a flow of compressed air that can be approximately 10,000 times less than overhead conventional flood cooling. Besides, the costs of acquisition, care and disposal of MWFs are two times higher and have to be taken into account when the economics involved in machining operations are compared. The increasing cost associated with the use and disposal of MWFs can be up to 17% per part for automotive components. The total manufacturing cost has to be considered even if the costs associated with cutting tools increase with decrease in use of MWF. However, stated that the total manufacturing cost would be lower as compared to the cost of traditional overhead flood cooling using large amounts of water-miscible MWFs.Besides, according to the National Institute of Occupational, Safety and Health (), it is estimated that 1.2 million workers are potentially exposed to the hazardous/chronic toxicology effects of MWF. Workers can be exposed to MWF in a variety of ways. found that a source of significant exposure to MWF was inhalation of aerosols. NIOSH recommended no respiratory protection for MWF concentrations of 0.5 mg/m3 or less. However, showed that the chronic bronchitis, asthma, chest symptoms and airway irritation were linked to aerosol exposures of MWF as low as 0.41 mg/m3. Additionally, NIOSH (1997) reported that the effectiveness of OEM (original equipment manufacturer) mist enclosures was not built-in, which was a violation of the guidelines for exhaust ventilation of machining operations listed in technical report. Effectiveness of these enclosures was also reported to be less than 10% in eliminating unwanted mist during wet machining. Moreover, the goal of the new international global standard is to support environmental protection and prevention of pollution in balance with socio-economic needs. Organizations that consider the implementation of appropriate and economically viable technologies need only to achieve those environmental objectives incorporated in the standard. The international standard may affect all organizations that aim to supply or manufacture parts on a global or domestic scale. demonstrated the interest of dry machining and eventually met with success in the field of environmentally friendly manufacturing. However, these can be sometimes less effective when higher machining efficiency, better surface finish quality and severer cutting conditions are required. In these circumstances, semi-dry operations utilizing very small amounts of cutting lubricants are expected to become a powerful tool and, in fact, they already play a significant role in a number of practical applications. Minimum quantity lubrication (MQL) refers to the use of only a minute amount of cutting fluids typically at a flow rate of 50–500 ml/h. Sometimes this concept of minimum quantity lubrication is referred to as near dry lubrication or micro-lubrication. According to , the concept of MQL has also been suggested since a decade ago as a means of addressing the issues of environmental intrusiveness and occupational hazards associated with the airborne cutting fluid particles on factory shop floors. The minimization of cutting fluid also leads to economical benefits by way of saving lubricant costs and cycle time for cleaning workpiece, tool, and machine. However, there has been little investigation of the cutting fluids to be used in MQL machining. suggested the types of fluids not applicable for the minimum quantity lubrication were water mixed cooling lubricants and their concentrates, lubricants with organic chlorine or zinc containing additives, lubricants that have to be marked according to the decree on hazardous materials, and products basing on mineral base oils in the cooling lubricant 3 ppm (parts per million) benzpyrene. From performance, cost, health, safety and environment points of view, , therefore, considered vegetable oils as viable alternative to petroleum-based metalworking cutting fluids. The important factors for selecting the vegetable oils as a feasible choice are:molecules, being long, heavy, and dipolar in nature, create a dense homogeneous and strong lubricating film that gives the vegetable oil a greater capacity to absorb pressure.lubricating film layer provided by vegetable oils, being intrinsically strong and lubricious, improves workpiece quality and overall process productivity reducing friction and heat generation.higher boiling point and greater molecular weight of vegetable oil result in considerably less loss from vaporization and misting.vegetable oils are nontoxic to the environment and biologically inert and do not produce significant organic disease and toxic effect. reported no sign and symptom of acute and chronic exposure to vegetable oil mist in human.Significant progress has been made in dry and semi-dry machining recently and MQL machining in particular has been accepted as a successful semi-dry application due to its environmentally friendly characteristics. Some good results have also been obtained using this technique. employed MQL machining technique in turning AISI 4340 steel with uncoated carbide tool (SNMM 120408). During experimentation, process parameters such as cutting velocity, feed rate and depth of cut were kept constant at 110 m/min, 0.16 mm/rev and 1.5 mm respectively. Water-soluble cutting fluid was supplied at flow rate of 60 ml/h and mixed with compressed air prior to being impinged on the cutting zone at a high speed. Under same cutting conditions, MQL caused a significant reduction in tool wear and surface roughness as compared to dry and wet turning. used MQL machining technique in the reaming process of gray cast iron (GG25) and aluminum alloy (AISI 12) with coated carbide tools. The authors concluded that MQL caused a reduction in tool wear as compared to the completely dry process and, consequently, resulted in an improvement in surface quality of the holes. , on the other hand, describes the drilling of aluminum–silicon alloys as a process where dry cutting is impossible due to the high ductility of the workpiece material. Without cooling and lubrication, the chip sticks to the tool and breaks it in a very short time during cutting. conducted experiments on turning medium carbon steel (AISI 1040) using a venturi to mix compressed air (the air pressure was of 2.3 bar) with small quantities of a liquid lubricant, water or soluble oil (the mean flow rate was in between 3 and 5 ml/min). The mixture was directed onto the rake face of a carbide tool against the chip flow direction. The application of a mixture of air and soluble oil was able to reduce the consumption of cutting fluid, but it promoted a mist in the environment with problems of odors, bacteria and fungi growth of the overhead flooding system. For this reason, the mixture of air and water was preferred. However, even if the obtained results were encouraging, the system needed yet some development to achieve the required effects in terms of cutting forces, temperature, tool life and surface finish. developed alternative test equipment for injecting the fluid and used it with success in hard turning for which a large supply of cutting fluid is the normal practice. The test equipment consisted of a fuel pump generally used for diesel fuel injection in truck engines coupled to a variable electric drive. A high-speed electrical mixing chamber facilitated thorough emulsification. The test equipment permitted the independent variation of the injection pressure, the frequency of injection and the rate of injection. The investigations performed by the authors revealed that a coolant-rich (60%) lubricant fluid with minimal additives was the ideal formulation. During hard turning of an AISI 4340 hardened steel of 46HRC (460 HV), the optimum levels for the fluid delivery parameters were a flow rate of 2 ml/min, a pressure of 20 MPa and a high pulsing rate of 600 pulses/min. In comparison, for the same cutting conditions, with dry cutting and wet cutting, the minimum quantity of cutting fluid method led to lower cutting forces, temperatures, better surface finish, longer tool life. In addition, it was observed that tightly coiled chips were formed during wet turning and during minimal application, while long snarled chips were prevalent during dry turning. It must be noted that during minimal application, the rate of fluid was only 0.05% of that used during wet turning. The major part of the fluid used during minimal quantity application was evaporated; the remnant was carried out by work and chips and was too low in volume to cause contamination of the environment. dealt with the drilling tests using minimum cooling lubrication systems, which were based on atomizing the lubricant directly to the cutting zone. Small quantities of lubricant, in the order of 10–50 ml/h, were mixed with compressed air for an external feeding through a nozzle and for internal feeding through the spindle and tool. Internal feed systems with their ability to deliver the mixture very close to the drill–workpiece contact point may achieve very good results in terms of surface finish and tool life. presented the dry machining of synchronizing cones for automotive application. The work material was austenitic 22Mn6 steel. In the first step of their study, dry machining was compared to machining with coolant and minimal lubricant system. The used minimal lubricant system worked with special oil, which had food-grade quality. The volume flow rates of air and oil were about 50 l/min and 20 ml/h respectively and hence, the produced chips were dry after leaving the contact zone of the cutting process. At this oil volume flow, a single chip can carry a maximum of 1 ml. Therefore, the chips could be declared as being almost dry and passed for metallic recycling without further treatment. The results exhibited an advantage for the minimal lubricant technique and for the dry machining. , by model experiments, suggested that ester supplied onto a rake face of a tool decomposed to carboxylic acid and alcohol and its carboxylic acid formed a chemisorbed film with lubricity. , however, found that in actual conditions with high machining load, existence of this kind of boundary film was uncertain.The review of the literature suggests that the concept of MQL presents itself as a possible solution for machining in achieving slow tool wears while maintaining the cutting forces/power at reasonable levels, if the MQL parameters can be strategically tuned. The main objective of the present work was to experimentally investigate the roles of minimum quantity lubrication by vegetable oil-based cutting fluid on chip–tool interface temperature, chip color and shape, chip reduction coefficient, tool wear and surface roughness in turning alloy steel (AISI 9310) by the industrially used uncoated carbide tool (SNMG 120408 TTS) at different cutting velocities and feeds combinations as compared to wet and dry machining.Experiments were carried out by plain turning a 100 mm diameter and 710 mm long rod of AISI 9310 alloy steel of common use in a powerful and rigid lathe (France, 15hp) at different cutting velocities and feeds under dry, wet and MQL by vegetable oil conditions. These experimental investigations were conducted with a view to explore the role of MQL on the machinability characteristics of that work material mainly in terms of cutting temperature, chip formation, tool wear and surface roughness. The experimental conditions are listed in . The ranges of the cutting velocity (Vc) and feed rate (S0) were selected based on the tool manufacturer's recommendation and industrial practices. Depth of cut was kept fixed to only 1.0 mm, which would adequately serve the present purpose. Machining ferrous metals by carbides is a major activity in the machining industries. Machining of steels involves more heat generation for their ductility and production of continuous chips having more intimate and wide chip–tool contact. Again, the cutting temperature increases further with the increase in strength and hardness of the steels for more specific energy requirement. Keeping these facts in view, the commonly used alloy steel like AISI 9310 was considered in this experimental research.The MQL needs to be supplied at high pressure and impinged at high speed through the nozzle on the cutting zone. Considering the conditions required for the present research work and uninterrupted supply of MQL at a constant pressure of around 6 bar over a reasonably long cut, a MQL delivery system was designed, fabricated and used. The schematic view of the MQL set-up is shown in The effectiveness, efficiency and overall economy of machining of any work material by given tools depend largely on the machinability characteristics of the tool-work materials under the recommended condition. Machinability is usually judged by (i) cutting temperature, which affects product quality, and cutting tool performance (ii) pattern and mode of chip formation (iii) magnitude of the cutting forces, which affects power requirement, dimensional accuracy and vibration (iv) surface finish and (v) tool wear and tool life. In the present work, cutting temperature, chip pattern, chip formation mode, tool wear and surface roughness were considered for studying the role of minimum quantity lubrication.MQL by vegetable oil is expected to provide some favorable effects mainly through reduction in cutting temperature. As shown in , the simple but reliable tool-work thermocouple technique developed by The form, color and thickness of the chips also directly and indirectly indicate the nature of chip–tool interaction influenced by the machining environment. The chip samples were collected during short run and long run machining for Vc and S0 combinations under dry, wet and MQL conditions. The form and color of all those chips were watchfully examined and noted down. The thickness of the chips were repeatedly measured by a digital slide caliper to determine the value of chip reduction coefficient, ζ (ratio of chip thickness after and before cut), which is an important index of machinability. established the values in accordance with ISO Standard 3685 for tool life testing. A cutting tool was rejected and further machining was stopped based on one or a combination of rejection criteria given below:The machining temperature at the cutting zone is an important index of machinability and needs to be controlled as far as possible. Cutting temperature increases with the increase in specific energy consumption and MRR. During machining any ductile materials, heat is generated at the primary deformation zone due to shear and plastic deformation, whereas secondary deformation and sliding cause heat generation at chip–tool interface. Furthermore, rubbing produces heat at work–tool interfaces. All such heat sources produce maximum temperature at the chip–tool interface, which substantially influence the chip formation mode, cutting forces and tool life. That is why; attempts are made to reduce this detrimental cutting temperature. Conventional cutting fluid application may, to some extent, cool the tool and the job in bulk but cannot cool and lubricate expectedly and effectively at the chip–tool interface where the temperature is maximum. This is mainly because the flowing chips make mainly bulk contact with the tool rake surface and an elastic contact just before leaving the contact of the tool. Bulk contact does not allow the cutting fluid to penetrate into the interface. Elastic contact allows slight penetration of the cutting fluid only over a small region by capillary action. The cutting fluid action becomes more and more ineffective at the interface with the increase in Vc when the chip–tool contact becomes almost fully plastic or bulk. Therefore, the application of MQL at chip–tool interface is expected to improve on aforementioned machinability characteristics that play vital role on productivity, product quality and overall economy in addition to environment friendliness in machining particularly when the cutting temperature is very high.The average chip–tool interface temperature, θavg was measured using the tool-work thermocouple technique and plotted against cutting velocity for different feeds and environments undertaken. show the effect of minimum quantity lubrication on average chip–tool interface temperature under different cutting velocity and feed rate as compared to dry and wet conditions. However, it is clear from the aforementioned figures that with the increase in Vc and S0, average chip–tool interface temperature increased as usual, even under MQL condition, due to increase in energy input. The roles of variation of process parameters on percentage reduction of average interface temperature due to MQL have not been uniform. This may be attributed to variation in the chip forms particularly chip–tool contact length (CN) which for a given tool widely vary with the mechanical properties and behavior of the work material under the cutting conditions. This chip–tool contact length affects not only the cutting forces but also the cutting temperature. Post cooling of the chips by MQL jet is also likely to influence θavg to some extent depending on form of the chips and thermal conductivity of the work materials.Apparently, more reduction in average chip–tool interface temperature, θavg is expected by employing MQL but, in practice, reduction in temperature is found to be less because the MQL could not reach the intimate chip–tool contact zone. However, during machining at lower Vc when the chip–tool contact is partially elastic, where the chip leaves the tool, MQL is dragged in that elastic contact zone in small quantity by capillary effect and is likely to enable more effective cooling. With the increase in Vc the chip makes fully plastic or bulk contact with the tool rake surface and prevents any fluid from entering into the hot chip–tool interface. As shown in , effect of MQL cooling has improved to some extent with the decrease in feed and in particular at lower cutting velocity. Possibly, the thinner chips, especially at lower chip velocity, are slightly pushed up by the high-pressure MQL jet coming from opposite direction and enable it come closer to the hot chip–tool contact zone to remove heat more effectively. Further, at high cutting velocity, the coolant may not get enough time to remove the heat accumulated at the cutting zone resulting in less reduction in temperature under MQL condition.Besides, during minimal application, the cutting fluid is applied at the tool–work interface and there is a possibility of some tiny fluid particles penetrating the work surface near the cutting edge that forms the top of the chip in the next revolution. These particles, owing to their high velocity and smaller physical size can penetrate and firmly adhere to the work surface resulting in the promotion of plastic flow on the backside of the chip due to rebinder effect. This relieves a part of the compressive stress and promotes chip curl that reduces tool-chip contact length. This phenomenon, in turns, helps in reducing the chip–tool interface temperature further. The effectiveness of the MQL by vegetable oil was found to decrease with the increase in feed also for more intimate chip–tool contact. Nevertheless, still MQL was found to be more effective as compared to dry and flood cooling conditions. With the increase in feed rate, the chip–tool contact length generally increases but the close curvature of the grooves parallel and close to the cutting edges of the insert has reduced the chip–tool contact length. Thus, it possibly helped in reducing the chip–tool interface temperature further. However, it was observed that the MQL jet in its present way of application enabled reduction of the average cutting temperature by about 5–10% as compared to wet machining depending on the levels of the process parameters including Vc and S0. Even such apparently small reduction in the cutting temperature is expected to have some favorable influence on other machinability indices.The form (shape and color) and thickness of the chips directly and indirectly indicate the nature of chip–tool interaction influenced by the machining environment. The pattern of chips in machining ductile metals were found to depend on the mechanical properties of the work material, tool geometry particularly rakes angle, levels of Vc and S0, nature of chip–tool interaction and cutting environment. In absence of chip breaker, length and uniformity of chips increase with the increase in ductility and softness of the work material, tool rake angle and cutting velocity unless the chip–tool interaction is adverse causing intensive friction and built-up edge formation. shows that the low alloy steel when machined by the pattern type SNMG insert under both dry and we conditions produced ribbon type continuous chips at lower feed rates and more or less tubular type continuous chips at higher feed rates. When machined with MQL the form of these ductile chips did not change appreciably but their back surface appeared much brighter and smoother. This indicates that the amount of reduction of temperature and presence of MQL application enabled favorable chip–tool interaction and elimination of even trace of built-up edge formation.The color of the chips became much lighter i.e. blue or golden from burnt blue depending on Vc and S0 due to reduction in cutting temperature by minimum quantity lubrication. Chip reduction coefficient is also an important machinability index. For given cutting conditions, the value of ζ depends on the nature of chip–tool interaction, chip contact length and chip form all of which are expected to be influenced by MQL in addition to the levels of Vc and S0. The variation in value of ζ with Vc and S0 as well as machining environment are shown in . Almost all the parameters involved in machining have direct and indirect influence on the thickness of the chips during deformation. The degree of chip thickening is assessed by chip reduction coefficient that plays significant role on cutting forces and hence on cutting energy requirements and cutting temperature.The aforementioned figures clearly show that throughout the present experimental domain the value of ζ gradually decreased with the increase of Vc though in different degree under dry, wet and MQL by vegetable oil conditions. The value of ζ usually decreases with the increase in Vc particularly at its lower range due to plasticization and shrinkage of the shear zone for reduction in friction and built-up edge formation at the chip–tool interface due to increase in temperature and sliding velocity. In machining steel by carbide tool, usually, the possibility of built-up edge formation, and size and strength of the built-up edge if formed, gradually increases with the increase in temperature due to increase in Vc and S0. Then it decreases with the further increase in Vc due to too much softening of the chip material and its removal by high sliding speed. The aforementioned figures also show that MQL by vegetable oil has reduced the value of ζ particularly at lower values of Vc and S0. By MQL applications, ζ is reasonably expected to decrease due to reduction in friction at the chip–tool interface and reduction in deterioration of effective rake angle by built-up edge formation and wear at the cutting edges mainly due to reduction in cutting temperature.The cutting tools in conventional machining, particularly in continuous chip formation processes like turning, generally fail by gradual wear by abrasion, adhesion, diffusion, chemical erosion, galvanic action, etc. depending on the tool-work materials and machining conditions. Tool wear initially starts with a relatively faster rate due to what is called break-in wear caused by attrition and micro chipping at the sharp cutting edges.Cutting tools may often fail prematurely, randomly and catastrophically by mechanical breakage and plastic deformation under adverse machining conditions caused by intensive pressure and temperature and/or dynamic loading at the tool-tips particularly if the tool material lacks strength, hot-hardness and fracture toughness. However, in the present investigation with the tool, work material and the machining conditions undertaken, the tool failure modes were mostly gradual wear. The geometrical pattern of tool wear that is generally observed in turning by carbide insert is schematically shown in Surface finish is an another important index of machinability as the performance and service life of the machined component are often affected by its surface finish, nature and extent of residual stresses and presence of surface or subsurface micro-cracks, particularly when that component is to be used under dynamic loading or in conjugation with some other mating part(s). Generally, good surface finish is achieved by finishing processes like grinding but sometimes it is left to machining. Even if it is to be finally finished by grinding, machining prior to that needs to be done with surface roughness as low as possible to facilitate and economize the grinding operation and reduce initial surface defects as far as possible. The major causes behind development of surface roughness in continuous machining processes like turning ductile metals in particular are (i) regular feed marks left by the tool-tip on the finished surface, (ii) irregular deformation of the auxiliary cutting edge at the tool-tip due to chipping, fracturing and wear, (iii) vibration in the machining system, and (iv) built-up edge formation, if any.The variation in surface roughness observed during turning AISI 9310 low alloy steel by SNMG insert at a particular set of cutting velocity, feed rate and depth of cut under dry, wet and MQL conditions is shown in that surface roughness grows quite fast under dry machining due to temperature, which is more intensive and stresses at the tool-tips. MQL appeared to be effective in reducing surface roughness. Nevertheless, it is evident that MQL improves surface finish depending on the work-tool materials and mainly through controlling the deterioration of the auxiliary cutting edge by abrasion, chipping and built-up edge formation.Based on the results of the present experimental investigation, the following conclusions can be drawn:MQL provided significant improvements expectedly, though in varying degree, in respect of chip formation modes, tool wear and surface finish throughout the range of Vc and S0 undertaken mainly due to reduction in the average chip–tool interface temperature. Wet cooling by soluble oil could not control the cutting temperature appreciably and its effectiveness decreased further with the increase in cutting velocity and feed rate.The present MQL systems enabled reduction in average chip–tool interface temperature up to 10% as compared to wet machining depending upon the cutting conditions and even such apparently small reduction, unlike common belief, enabled significant improvement in the major machinability indices.The chips produced under both dry and wet condition are of ribbon type continuous chips at lower feed rates and more or less tubular type continuous chips at higher feed rates. When machined with MQL the form of these ductile chips did not change appreciably but their back surface appeared much brighter and smoother. This indicates that the amount of reduction of temperature and presence of MQL application enabled favorable chip–tool interaction and elimination of even trace of built-up edge formation.Surface finishes also improved mainly due to reduction of wear and damage at the tool-tip by the application of MQL.Dynamic rheological characterization of salep glucomannan/galactomannan-based milk beveragesThe steady flow and viscoelastic properties of glucomannan (salep) and galactomannans (locust bean gum, LBG and guar gum, GG) in milk beverages were investigated at 25 and 50 °C. The consistency index (K), flow behavior index (n), yield stress and thixotropic area were measured as functions of steady shear; elastic modulus (G′), loss modulus (G′′), tan δ and complex viscosity (η*) parameters were derived from oscillatory shear experiments. The steady flow behavior of mannan-based milk beverages was observed to be shear-thinning and thixotropic. Galactomannans exhibited greater shear-thinning and thixotropy than glucomannan in milk beverages. The synergistic effect was detected between salep and LBG with highest thixotropy. Increasing the temperature decreased Casson yield stresses of GG but not salep and LBG samples. Similar viscoelastic behavior was observed between salep and LBG, they could be classified as concentrated solutions but GG showed gel-like structure. At low frequencies, high tan δ values were observed for the salep and LBG samples indicating viscous character. On the other hand, GG sample had nearly the same tan δ values through the frequency sweep. Cox–Merz rule was tested to correlate the steady and dynamic viscosities of samples. It was found that Cox–Merz rule was applicable only to LBG–milk beverage among the studied samples.Mannan is a kind of hemicellulose, consisting of mannose chain with a monosaccharide. Glucomannans and galactomannans are polysaccharides composed of linear monomers of β--galactose linked β-1 → 4 bonds, respectively. Glucomannans can be extracted from various botanical sources and salep is one of the well-known glucomannans obtained from tubers of salep (from Orchidaceae family). Salep powder are obtained after inactivation of enzymes, drying and grinding of the tubers () and its mannose/glucose ratio is ranged in 2.0–3.0 (). Glucomannans are neutral water soluble fibers and many health-beneficial effects of salep are reported in literature (). Due to its health-promoting effects, hot salep–milk–sucrose solution is consumed as a beverage and long esteemed in Asia and Europe for boosting virility (For selection in the counterpart or supplementary hydrocolloid, the desired rheological characteristics should be compensated. However, it is not easy to determine exact rheological behavior due to complexity of food, inability of instruments and wide range of applied strain or stress during processing or consumption. Steady flow measurements are widely carried out to characterize the flow behavior of food products. The more sensitive method for rheological characterization is the dynamic rheological method (oscillatory test). In this test, the viscoelastic and gel characteristics of food could be determined by small amplitude oscillatory shear without alteration of the samples structure (). The parameters obtained from oscillatory tests are very sensitive to chemical and physical changes; therefore, they are useful for rheological evaluation in dairy systems (). The correlation between steady shear and oscillatory shear parameters could be observed for food systems. The Cox–Merz rule is used to predict steady shear viscosity from complex shear viscosity and vice versa (where η∗ is the complex viscosity (Pa s), η is the steady viscosity (Pa s), ω is the angular velocity (rad s−1) and γ˙ is the shear rate (s−1).The comparative study on steady and viscoelastic properties of mannan-based hydrocolloids in milk system may be helpful for preparation and processing of similar types of dairy beverages. Therefore, the main objective of this research is to investigate the rheological characteristics of healthy dairy beverage containing glucomannan (salep) and galactomannans (LBG and GG) with steady and oscillatory shear measurements.Milk was obtained from Çukurova University dairy house and the chemical composition of milk was given in . Guar gum (MP Biomedicals, Eschwege, Germany) and locust bean gum (Incom, Mersin, Turkey) studied were kindly donated by their respective companies. Salep (Mado, Kahramanmaras, Turkey), sugar (Mert, İstanbul Turkey), ginger and cinnamon (Arifoğlu, İstanbul, Turkey) were obtained from market.The preparation of milk beverages containing glucomannan and galactomannans was as illustrated in . The processed and standardized milk (pH: 6.79 ± 0.34, acidity (lactic acid): 0.128 ± 0.04% w/w, dry matter: 11.64 ± 0.34% w/w, fat: 3.20 ± 0.15% w/w, protein: 3.06 ± 0.09% w/w: density: 1.029 ± 0.02 kg m−3) were mixed and homogenized (Ultra Turrax blender, Janke & Kunkel KG, IKA, Werk, Germany) with other ingredients such as sugar (8.0% w/v), ginger (0.1% w/v), cinnamon (0.1% w/v) and hydrocolloids (0.7% w/v) after mixing, heating was carried out and held for 5 min at 85 °C. While hydrocolloid concentration was held constant as 0.7% (w/v) for all samples, the equal amounts (0.35% w/v) of hydrocolloids were used for combined samples. The ingredients, sample codes and results of chemical analyses of dairy beverages were shown in . Samples were cooled naturally to 25 °C at room conditions. Finally, samples were stored at 4 °C for further analysis.pH value of raw milk and beverages were measured by WTW digital pH meter at room temperature. The acidity values of raw milk and dairy beverages were calculated as percent lactic acid. Gravimetric method was used to determine dry solid content of samples. Fat content of samples were measured using Van Gulik methods. Kjeldahl method was used for determination of protein contents of samples (). Density of samples was measured using digital refractometer (Mettler Toledo RE50, Switzerland) at 25 °C.A controlled stress rheometer HAAKE RheoStress RS coupled with a Peltier/Plate TCP/P temperature control unit (HAAKE GmbH, Karlsruhe, Germany) was used to conduct rheological measurements using a cone and plate system (diameter: 35 mm, cone angle: 2°). The samples were allowed to rest for 5 min after loading. The flow curves were obtained by registering shear stress at shear rates from 0.08 to 300 s−1 (forward) in 150 s and down in 150 s from 300 to 0.08 s−1 (backward) at 25 and 50 °C. The Oswald-de Waele (Eq. ) models were used to describe the data of shear-induced behavior of viscous beverages:where τ is the shear stress (Pa), τy is the yield stress (Pa), K is the consistency index (Pa sn), and n is the flow behavior index.The hysteresis (thixotropic) areas, At, were obtained using a RheoWin Data Manager (RheoWin Pro V.2.64, HAAKE GmbH, Karlsruhe, Germany). The At values were calculated using Eq. where Aup and Adown are the areas under ascending and descending flow curves, respectively.Frequency sweep tests were conducted for all samples at 25 °C from 0.01 to 50 Hz at 1 Pa (in the linear viscoelastic range). In these test sinusoidal shear, the parameters G′, G′′, η* and tan δ (G′′/G′) were computed from raw data. The Cox–Merz rule (Eq. ) was used to predict steady shear viscosity from complex shear viscosity and vice versa. All measurements were performed in triplicate for each sample.The ANOVA tests were performed using SPSS 9.0 (SPSS Inc., Chicago, IL, USA). The means were compared LSD multiple range analysis (α |
≤ 0.05). The Pearson method was used for correlation between parameters. The rheological data were fitted to models using commercial software (SigmaPlot 6.0, Jandel Scientific, San Francisco, USA).The chemical compositions of all prepared beverages are given in . The values of acidity, dry matter, fat, and protein content parameters of the samples were found similar, statistically they were not significantly different (P |
> 0.05). The density values of GG samples (GG and LBG–GG) were higher than that of others.The typical steady flow curve of glucomannan/galactomannan in milk beverages was shown in . The apparent viscosities of all samples decreased at both 25 and 50 °C with increasing shear rate, this behavior is the evidence of shear-thinning properties. This type of behaviors was reported for many hydrocolloid solutions, due to formation of aggregated polymers in solutions and their high molecular weight. At low shear rate, the aggregates can be remained as strongly associated but they could be easily broken up with the effect of high shear. For the comparison of steady rheological characteristics of samples, the magnitudes of parameters (K and n) that obtained from Oswald-de Waele model were successfully used (R2 |
= 0.931–0.998). Galactomannans had lower n values than that of glucomannan; the lowest n value (0.26) at 25 °C was obtained for GG. Besides this, the consistency index values of galactomannans were also higher than that of glucomannan. reported that salep–milk samples had higher flow behavior index than salep–water system at 20 °C the shear rates between 0.33 and 33.3 rps. The shear-thinning behavior of salep solution was reported by several authors (). When the mixtures of galactomannan/glucomannan were used, the synergistic effects were observed (). For instance, Salep/LBG showed the higher shear-thinning behavior () than the others. Similarly, it was reported that salep had higher synergistic effect with guar gum than xanhtan and alginate (). On the other hand, the combination of galactomannan–galactomannan (LBG/GG) did not show any synergistic effect (n value of GG lower than that of LBG/GG). From these results, it could be suggested that the combination of galactomannan and glucomannan hydrocolloids could be used successfully for improving shear-thinning structure of milk beverages.Except salep and LBG, the flow behavior index of the samples increased at the high temperature (50 °C). Usually, flow behaviors of fluids tend to Newtonian behavior from non-Newtonian behavior at high the temperature due to the acceleration in the molecular movement with the effect of high thermal energy (). Whilst dairy beverages that contain salep or LBG showed similar behavior at both temperatures (P |
> 0.05), for GG samples, temperature had significant effect on the steady flow behavior. On the other hand, when the combination of hydrocolloids were used the temperature effect was more pronounced on the flow behavior, for instance, an increase in the temperature significantly decreased the consistency index of samples (Salep/LBG, Salep/GG and LBG/GG) (P |
< 0.05). The differences in the magnitude of the effect of temperature on the flow behavior of samples suggested that the formed network entanglements between salep and galactomannans were weak and unfolded with the effect of heating.As a result of steady flow tests, it was shown that the combination of salep and LBG had highly shear-thinning behavior in milk among studied samples. This synergistic relation could form the basis of designing a new gum mixture for dairy beverages. Presumably, the amount of galactose unit on the mannose chain could be responsible for the differences in the rheological behavior of galactomannan–glucomannan mixtures. Both guar and locust bean consist of a linear mannose chain substituted with galactose units, but LBG has less galactose residue than GG. The ratios of mannose to galactose are 2:1, 4:1 for GG and LBG, respectively (). The galactose-free regions and random distribution of galactose in LBG lead to unique synergistic properties to form a gel with polysaccharides which are found helical form in solution, e.g., carrageen (). Salep is a glucomannan with a level of substitution of one part of glucose to two or three parts of mannose. Probably due to the interactions between glucose residues of salep and galactose-free regions in LBG, the better synergy between salep and LBG was observed. Whilst, two fold helix structure of konjac glucomannan was reported in literature (), the precise structural details have not been reported for salep, and thus the studies on the structure of should be conducted to explain the exact mechanisms between salep and other hydrocolloids.Thixotropy is always to be expected from any shear-thinning mechanism. Due to the progressive breakdown of structures on shearing and slow rebuilding at rest, there are difficulties in mixing and handling of thixotropic materials. Thixotropic structure could be assumed from the area between the upward and downward flow curve (). All samples showed thixotropic behavior but galactomannans showed greater thixotropy than glucomannan. On the other hand, despite of low thixotropy of salep, Salep–LBG had highest thixotropy (). In fact, since the size of loops depend on many parameters, it is difficult to compare the thixotropy of samples quantitatively by the magnitude of area. Qualitative comparison showed that greater thixotropies were observed with the low n values for samples.The other important that parameter could be derived from the steady shear flow curves is the yield stress. It is the stress below which no flow is observed under the conditions of the experiment. Although the yield stress had practical importance for engineering purpose, the absolute yield stress is elusive property (). Thus, the concept of yield stress is under discussion with the questions by , but this is not the scope of this study. Yield stress has been currently used in engineering calculations, product quality and sensory assessment. For instance, a true value of the yield stress could be essential to proper design of tubular heating system where fluid velocity profiles are critical (), as in the case of production and sterilization of dairy beverages. Many models including yield stress are also accepted as standard models, e.g., Casson model for yield stress of chocolate by International Office of Cocoa and Chocolate. In this study two most common models, Herschel–Bulkley (Eq. ), were tested to determine the yield stress of the samples.Although the Herschel–Bulkley models gave good results for almost all samples (R2 |
> 0.98), the negative yield stress (not logical) values were obtained due to extrapolation. Therefore, the Casson model (R2 |
> 0.97) was used for the determination of yield stresses (). The highest yield stress value was obtained for Salep–LBG at 25 °C. Galactomannans had greater yield stress values than that of glucomannan. Increasing the temperature decreased the yield stress of GG but not those of salep and LBG. The negative Pearson correlation was detected (P |
< 0.05) between the magnitudes of yield stress and flow behavior index, n values. The lower n value gave higher yield stress for mannan-based hydrocolloids in the prepared milk beverages.Oscillatory (dynamic) rheological properties can be used along with steady shear flow parameters to provide insight on the structure of the sample (). The elastic modulus (G′), loss modulus (G′′) and complex shear viscosity (η∗) as a function of frequency (Hz) for salep, LBG and GG samples are shown in . Both G′ and G′′ of the salep and LBG were dependent on the frequency indicating viscoelastic structure. The magnitude of G′′ was greater than that of G′ up to nearly 1 Hz. This is a typical concentrated solution behavior (). On the other hand, for GG sample the G′ value is significantly higher than G′′ through all frequency, this pattern is the evidence of gel-like behavior (For comparison of the viscoelastic properties of samples, tan δ values were calculated. The values of the tan δ over the range of frequency varied with hydrocolloid type (). Salep and LBG samples showed similar pattern. At lower frequencies, higher tan δ value is the evidence of viscous character. As the frequency was increased, the viscous character decreased, solid-like character increased. The greater solid-like structure at higher frequencies could be explained by the Deborah number, and states that all materials tend to show higher solid-like characteristics over shorter experimental time scale (high frequency) (). On the other hand, GG had nearly the same low tan δ values through all frequencies. The analysis of oscillatory shear data from a pragmatic perspective could be made, i.e., the rheological behavior at low frequencies simulate swallowing of fluids by human subject, in contrast at higher frequencies that shows typical processing conditions. Hence, the comparison of viscoelastic properties of dairy beverages at low frequencies may provide relative assessment of their sensorial characteristics.Cox–Merz rule states that the complex shear viscosity becomes nearly equal to the steady shear viscosity when angular velocity is equal to shear rate (Eq. ). This rule has been studied for many polymers, solution, and complex food systems (). The results of application of Cox–Merz rule for salep, LBG and GG samples are shown in Salep sample did not obey Cox–Merz rule, it was observed that the magnitude of the η* values were lower than those of the η values at lower angular velocities or shear rates. At higher shear rate or angular velocity, η* became equals to η for salep. On the other hand, for LBG sample the Cox–Merz rule was satisfactorily applied (). The data set of η* vs. η was parallel for GG sample and thus the deviation is probably adjusted using shift factor (α) (Shift factor (α) was found as 0.18 for GG to correct angular velocity. found 0.26 and 0.65 for tomato juice with or without soy, respectively. The departures from the Cox–Merz rule were also reported for galactomannans at low shear rates or frequencies () due to the presence of high density of entanglements resultant from very specific polymer/polymer interaction (). On the other hand, in this study it was observed that Cox–Merz rule was found as applicable to LBG–milk beverage ( reported that for aqueous solution of LBG, η* and η had similar magnitudes at low shear rate and frequency, but η* became higher than η at higher shear rate and the departure increased with decreasing LBG concentration in aqueous solution.The departures from the Cox–Merz rule with the magnitudes of η* much greater than η values as in the case of GG sample could be explained with the structure decay due to effect of stress deformation applied to the system by oscillatory or steady shear (). The departures from this rule were reported for rice flour (). Salep/GG and LBG/GG samples showed similar departures from Cox–Merz rule (). For Salep/LBG, at low shear rate and frequency, η* are smaller than η; at higher shear rate and frequency, they become equals to each other. Similar behavior was reported by Hot milk beverages are popular in Asia and Europe due to health-promoting effects. This study determined the detailed rheological characteristics of milk beverages containing salep glucomannan and locust bean/guar galactomannans. Thus, the obtained rheological parameters could be used for in processing calculations and product development. Salep and locust bean showed similar viscoelastic behavior. Guar gum had completely different rheological characteristics in milk beverage as compared with salep and locust bean gum.Experimental investigation of roll-formed aluminium lipped channel beams subjected to combined bending and web cripplingRecently, the increasing popularity of aluminium members for use in roof and floor systems in the construction industry is attributable to their durability (because of corrosive resistance) and high strength-to-weight ratio compared to other structural materials a are fabricated members using a roll-forming method. ALC beams have played a significant role in structural applications such as purlins and rafters in roof systems and bearers in floor systems, as shown in The challenge with aluminium members is that their elastic modulus is only one third that of steel, and hence these ALC beams tend to buckle due to shear, web crippling, bending and combined actions. Different aspects of the structural behaviour of ALC beams have been investigated in the past. The shear behaviour of ALC beams was investigated by Rouholamin et al. The current American Iron and Steel Institute (AISI) standard . Among these load cases, the ALC beams under the IOF loading condition could be subjected to combined bending and web crippling actions when the span length was increased. To date, no study has been conducted to investigate the structural behaviour of ALC beams subjected to combined bending and web crippling actions. To fill this research gap, the purpose of this study is to investigate the strength and behaviour of ALC beams subjected to combined bending and web crippling actions, through an experimental program. The previous studies The ultimate bending moment capacities and the ultimate web crippling capacities of ALC beams play significant roles in non- dimensionalising the capacity results of ALC specimens subjected to combined bending and web crippling actions. Thus, the experimental program comprised three test series of pure bending, web crippling and combined actions, using ALC 5052-H36 beams supplied by Permalite Aluminium Building Solution Company summarises the details of the experimental tests in this study. A total of thirty-eight tests were conducted in the engineering laboratory at Griffith University, among which six pure bending tests, including one repeated test, were conducted by Nguyen et al. “BW” indicates the combined bending and web crippling test; “BD” and “WC” indicate the pure bending or the web crippling test, respectively;“10025” indicates an ALC with the nominal overall web depth of 100 mm and a nominal thickness of 2.5 mm;“N50” indicates a bearing length of 50 mm;“K1.0” indicates an interaction factor of 1.0;All the ALC test specimens in this study belonged to the same batch of specimens as the shear tests conducted by Rouholamin et al. presents the mechanical properties of all the ALC specimens in this study, in which E, fy, and fu are the average measured Young’s modulus of elasticity, yield stress, and ultimate stress, respectively. The calculated average values of E, fy, and fu are 66.7 GPa, 228.4 MPa, and 274.2 MPa, respectively. shows the measured stress versus strain curves obtained from the tensile coupon tests of five ALC beams in the study conducted by Rouholamin et al. . A total of six pure bending tests, including one repeated test, were performed in ). Details of the bending test set-up and procedure can be found in Nguyen at al. a and b present the front and side views of the typical four-point bending test set-up of the ALC BD-20025 section, whilst presents the applied load (in terms of bending moment) versus the mid-span vertical displacement of BD-20030, and shows the failure mode of the same specimen. The measured values of geometrical dimensions and test results of the ALC beams are given in b). It should be noted that the values of “MBD−Exp” are needed to non-dimensionalise the combined bending and web crippling test results, as described in this study. summarises the average measured geometric dimensions of web crippling specimens. According to AISI S909 . Thus, the length (LWC) of the web crippling test specimens in this study was calculated using Eq. (which is greater than 3(h+N)), as follows: a–c present the schematic diagram of the web crippling test set-up under unfastened IOF loading condition for the top, front and sectional views, respectively, and the typical web crippling test set-up is shown in a–c. This test set-up has been successfully used to experimentally investigate the web crippling behaviour under IOF loading conditions of cold-formed unlipped channel beams (Janarthanan et al. Two Linear Variable Differential Transformers (LVDTs) were used to measure the displacement of the specimens during testing, as shown in . LVTD-1 was positioned at the mid-span at one-third of the overall web depth from the loading plate to monitor the lateral deflection of the web elements. LVDT-2 was positioned at the loading plate to monitor the mid-span vertical displacement. The sampling rate of LVDTs was set to 1 Hz. At the commencement of testing, a small load was applied initially to allow the loading and end support system to settle evenly on the bearings. The MTS machine was then set-up to move the loading ram downwards at a constant rate of 1 mm/min during testing until failure. illustrates the curves of the applied load versus the lateral deflection (LVDT-1) and the mid-span vertical displacement (LVDT-2) of WC-20025-N100, whilst a–b present the failure modes observed from the tests for WC-10025-N50 and WC-20025-N100, respectively. The ultimate web crippling capacities (PWC−Exp) for each ALC beam given in were obtained from the experimental tests of the ALC beams under unfastened IOF loading condition. Two repeated tests (WC-10025-N50R and WC-20025-N100R) were conducted to confirm the accuracy and reliability of the test results. Minimal differences between the first and the repeated tests indicated that the test set-up and procedure were repeatable.A total of twenty-three tests including three repeated tests were conducted on the ALC beams to study their strengths and behaviour in combined actions of bending and web crippling. The test specimens had three different nominal overall web depths (100, 150 and 200 mm) and two different nominal thicknesses (2.5 to 3.0 mm). The measured geometrical properties of the test specimens are summarised in . In this table, the span length (LBW) of each ALC specimen of the combined bending and web crippling test is calculated using (2a+N), where “a” is the half span length of the test specimen, which is the distance between the centre of the support point and the loading point (see ). The half span lengths (a) of the ALC specimens subjected to combined bending and web crippling were varied in order to consider the effect of the lengths on the relationship between the bending moment and the applied concentrated load; the lengths were calculated using Eq. , “MBD−Exp” is the experimental ultimate bending moment capacity of an ALC beam obtained from the pure bending test, and “PWC−Exp” is the experimental ultimate web crippling capacity of an ALC beam obtained from the pure web crippling tests with similar section size and length of bearing plates. “K” is the interaction factor that is used to estimate the interaction level between the bending moment and the web crippling strength. “K” was chosen as 1.0, 2.0 and 3.0 for ALC beams having a 100 mm depth, 1.0, 1.5, 2.0, and 2.5 for ALC sections having a 150 mm depth, and 1.0 and 2.0 for ALC beams having a 200 mm depth (see The test arrangement of the ALC beams subjected to combined bending and web crippling is similar to that of the pure web crippling tests presented in Section . The only difference is the span length of the test specimens. The span length of the pure web crippling tests was calculated using Eq. , whilst that of the combined bending and web crippling tests was calculated using Eq. shows the schematic diagram of the combined bending and web crippling test of 20 030 section with K=1.0, whilst a–c present the two- and three-dimensional views of the test set-up for the combined actions tests.a) whilst 8 straps were applied for a test of BW-15025-N100-K1.0, as shown in The test results of the ALC beams subjected to combined bending and web crippling actions are given in . In this table, “PBW−Exp” is the ultimate applied load for each ALC beam subjected to combined bending and web crippling actions. “MBW−Exp” is the ultimate bending moment for each ALC beam, which is calculated by multiplying half of the ultimate applied load (PBW−Exp) by the corresponding half span length (a) of the respective ALC beam. shows the comparison of the applied load versus lateral deflection curves for BW-10030-N100 with three different interaction factors (K) of 1.0, 2.0, and 3.0, whilst presents the comparison of the applied load versus mid-span vertical displacement curves for the same specimens. As can be seen in , tests having the same section and bearing length, but with higher K values, resulted in a lower lateral deflection (LVDT-1) at the peak load compared to tests with smaller K. In contrast, shows that tests with higher K values resulted in a higher mid-span vertical displacement at the peak load compared to tests with smaller K. Additionally, it should be noted that tests with higher K values resulted in lower ultimate loads. The observed failure modes of the BW-10030-N50 section with different K values are shown in . In these figures, the failure mode of BW-10030-N50-K1.0 has less bending deformation (mid-span vertical displacement) than BW-10030-N50-K3.0. In contrast, BW-10030-N50-K1.0 has undergone more significant local deformation at the web underneath the bearing plate compared to BW-10030-N50-K3.0. Hence, it is evident that the interaction factors (K) have a noticeable effect on the failure modes of the ALC beams under combined bending and web crippling actions.The nominal section moment capacity (Mbl) in local buckling for beams without holes can be calculated using Eqs. which are recommended in Clause 7.2.2.3.2 of AS/NZS 4600:2018 Mbl=1−0.15MolMbe0.4MolMbe0.4Mbeforλl>0.776 where λl=MbeMol is the non-dimensional slenderness used to calculate Mbl, and “Mbe” is the nominal moment capacity for lateral–torsional buckling. In the absence of flexural buckling, Mbe was taken to be equal to the first yield moment at the extreme fibre, that is, Mbe=My=Zffy, in which “Zf” is the full section modulus of the extreme fibre at first yield. Additionally, “Mol=Zffol” is the elastic local buckling moment, in which “fol” is the elastic local buckling stress determined in accordance with a rational elastic buckling analysis or using CUFSM The nominal section moment capacities in local buckling (Mbl) of the ALC sections predicted by the current DSM, using Eqs. , were compared with the ultimate bending moment test capacities (MBD−Exp) of the ALC beams conducted by Nguyen et al. . The mean and coefficient of variation (COV) values of the experiment to the predicted bending moment ratio (MBD−Exp/Mbl) were 1.09 and 0.03, respectively. It was concluded in PAS/NZS1664.1=t2sinθ(0.46fy+0.02Efy)(N+140)10+ri(1−cosθ)where “θ” is the angle that is determined from the bearing surface plane to that of the web surface. Note that “θ” is taken as 90o for the ALC beams studied herein. The other parameters are as defined before.PAS/NZS4600=Ct2fysinθ1−CRrit1+CNNt×1−Chht, the following conditions must be satisfied: h/t≤ 200, N/t≤ 210, N/h≤ 2, θ=900, and ri/t≤ 5 for unfastened IOF loading conditions.) leading to accurate predictions as follows: PAS/NZS4600=Ct2Efysinθ1−CRrit1+CNNt×1−Chht, the parameter fy was replaced by Efy to consider the effects of elastic modulus and yield strength of the aluminium sections on the web crippling capacities of the ALC beams. The geometrical coefficients C, CR, CN and Ch proposed in show the design equations given in the Eurocode 3 PEC3=C1C2C3fyt2γM114.7−dw16.3t1+0.007NtforN/t≤60PEC3=C1C2C3fyt2γM114.7−dw16.3t1+0.007NtforN/t>60, the parameter fy was replaced by Efy to consider the effect of elastic modulus and yield strength of the aluminium sections on the web crippling capacities of the ALC beams. The factors C1, C2 and C3 were kept the same as above without any modifications. PEC3=C1C2C3k3k4k5Efyt2γM116−dw80t1+0.007NtThe experimental ultimate web crippling capacities (PWC−Exp) were compared in with the nominal web crippling capacity predicted by AS/NZS 1664.1 . In the table, the mean and corresponding COV values of the PWC−Exp/PAS/NZS1664.1 ratios are 1.02 and 0.05, respectively. The comparison indicates that Eq. is accurate in predicting the web crippling capacity of ALC beams under unfastened IOF loading conditions. The nominal web crippling strengths predicted by AS/NZS 4600 were compared with the test results as presented in are found to be unconservative with relatively low mean value PWC−Exp/PAS/NZS4600 of 0.83 and a corresponding COV value of 0.05. However, Eq. The comparison of the web crippling test results with the current design standard of the Eurocode 3 Part 1.3 . The mean value of 0.94 and a COV value of 0.14 indicate that the current design rules of Eurocode 3 The design rules for predicting the capacities of cold-formed steel sections under combined bending and web crippling actions are identical in AS/NZS 4600 shows a linear interaction between PExpPWC−Exp and MExpMBD−Exp, where “PExp” is the ultimate capacity obtained from the test series of pure bending, pure web crippling and combined actions, “PWC−Exp” is the ultimate web crippling strength obtained from the web crippling tests, “MExp” is the ultimate bending moment obtained from the test series of pure bending, web crippling, and combined actions, and “MBD−Exp” is the ultimate bending moment capacity obtained from the pure bending tests.The North American Specifications (AISI S100) to predict the capacities of cold-formed steel members having a single unreinforced web as follows: to predict the capacities of cold-formed steel members subjected to combined action of a bending moment and web crippling, as follows: shows the comparison of the section capacities predicted by the design rules in AS/NZS 4600 ) with the test strengths (ultimate applied load (PExp) and ultimate bending moment (MExp)) of the ALC beams under pure bending, pure web crippling and combined actions. As described earlier, the capacities of the combined tests need to be non-dimensionalised with respect to the ultimate web crippling capacity (PWC−Exp) for each ALC beam obtained from the pure web crippling tests and the ultimate bending moment capacity (MBD−Exp) for each ALC beam obtained from the pure bending tests. Thus, the PBW−ExpPWC−Exp and MBW−ExpMBD−Exp are presented in for combined bending and web crippling test strengths. The pure bending moment test capacity (bending (BD) presents a comparison of the combined bending and web crippling test results given in with the linear interaction equations predicted by AS/NZS 4600 . In this figure, the linear interaction curve predicted by AS/NZS 4600 demonstrates that the current design rules of AS/NZS 4600 The comparison of the experimental test results of the ALC beams in combined bending and web crippling actions with the current design strengths of AISI S100 . This linear interaction diagram is somewhat similar to that of AS/NZS 4600 also presents the comparison of the test results with the design strengths provided by Eurocode 3 . In the figure, the linear interaction curve shows that the combined bending and web crippling effect should be taken into account when the ultimate capacity of a combined bending and web crippling test (PBW−Exp) is larger than 25% of the pure web crippling strength (PWC−Exp) of the same section, and when the bending moment capacity of a combined bending and web crippling test (MBW−Exp) is larger than 25% of the pure bending moment capacity (MBD−Exp) of the same section. The design strengths provided by Eurocode 3 , it was concluded that the linear interaction equation provided in Eurocode 3 This paper presents the details and results of an experimental study that has been conducted to investigate the strengths and behaviour of unfastened ALC beams subjected to combined bending and web crippling actions under IOF loading conditions. The capacities of the ALC specimens under combined actions were non-dimensionalised with respect to the ultimate bending moment test capacities and the ultimate web crippling test capacities. The specimens under combined actions were also tested at various span lengths by applying different interaction factors to evaluate the interaction relationship between bending moment and web crippling capacities of the ALC beams. The combined bending and web crippling test capacities were then used to examine the appropriateness and consistency of the current design standards of AS/NZS 4600, AISI S100, and Eurocode 3, based upon their interaction equations. The following conclusions were drawn.The test specimens with lower interaction factors failed primarily due to web crippling, while those with higher interaction factors failed mainly due to bending.The ultimate capacities of the test specimens decreased with increased interaction factors, due to the bending effect.AS/NZS 4600 and AISI S100 are generally unconservative in predicting the capacities of ALC beams under combined actions of bending and web crippling, whilst Eurocode 3 is safe to be used.Anh-Vy Nguyen: Conceptualization, Methodology, Investigation, Experimental study, Writing – original draft. Shanmuganathan Gunalan: Conceptualization, Methodology, Supervision, Data curation, Project administration, Writing – review & editing. Poologanathan Keerthan: Methodology, Supervision, Writing – review & editing. Hong Guan: Supervision, Writing – review & editing. Sanam Aghdamy: Methodology, Writing – review & editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.The Mechanical Properties of Different alloys in friction stir processing: A ReviewThis review paper deals with the consequences of Friction Stir Processing on different alloys like Mg-4Y-3Nd(WE43), Mg-ZrSiO4-N2O3, Al-Si hypoeutectic A356 alloy, 5210 steel (WC-12% CO coated). These effects can be on mechanical properties like strength, hardness, machinability, tensile strength. FSP leads to grain growth and refinement of grains into fine structure. FSP is carried out by FSP tool at different speeds and angles which results in difference of properties in the friction stir processed alloy. FSP can be widely used in metals such as aluminium and magnesium that are lightweight and can be used extensively in various applications; but due to certain lack in strength and hardness they are not used in their original form and require certain processing to obtain desired properties.The dependence of fatigue crack growth on hydrogen in warm-rolled 316 austenitic stainless steelThe fatigue crack growth rate of warm-rolled AISI 316 austenitic stainless steel was investigated by controlling rolling strain and temperature in argon and hydrogen gas atmospheres. The fatigue crack growth rates of warm-rolled 316 specimens tested in hydrogen decreased with increasing rolling temperature, especially 400 °C. By controlling the deformation temperature and strain, the influences of microstructure (including dislocation structure, deformation twins and α′ martensite) and its evolution on hydrogen-induced degradation of mechanical properties were separately discussed. Deformation twins deceased and dislocations became more uniform with the increase in rolling temperature, inhibiting the formation of dynamic α′ martensite during the crack propagation. In the cold-rolled 316 specimens, deformation twins accelerated hydrogen-induced crack growth due to the α′ martensitic transformation at the crack tip. In the warm-rolled specimens, the formation of α′ martensite around the crack tip was completely inhibited, which greatly reduced the fatigue crack growth rate in hydrogen atmosphere.Most metallic alloys suffer a significant deterioration in mechanical properties when service in high pressure hydrogen environments, such as a marked increase in the fatigue-crack propagation and the susceptibility to hydrogen embrittlement []. Cr–Ni austenitic stainless steel (AUSS) is a good candidate for using in this circumstances because it has low susceptibility to hydrogen environment embrittlement (HEE) []. Unfortunately, solution-treated austenitic stainless steels have relatively lower yield strength compared to other types of stainless steels, which causing high wall thickness to ensure the safety of the vessels []. The mechanical properties can be ameliorated by plastic deformation at room temperature because of dislocation multiplication, twinning and strain-induced martensite transformation, while dislocation multiplication and twinning are the only two strengthening mechanisms in stable austenitic stainless steels [Many efforts have been made to clarify the effects of cold working on the HEE of austenitic stainless steel. Sezgin et al. [] found the dependence of hydrogen diffusivity on cold-rolled ratio. Tsong-pyng et al. [] reported that up to 80% cold deformation had little effect on the hydrogen diffusivity in AISI 310 stable austenitic stainless steel, while cold deformation increased the hydrogen diffusivity greatly due to pre-strain α′ martensitic provided pathways for hydrogen atoms (AISI301, AISI304). Han [] found that pre-strain at low temperatures resulted in a large amount of α′ martensite in metastable austenitic stainless steels. Moreover, the dynamic α′ martensite played a primary role in HEE of the pre-strained austenitic steels. Wang et al. [] elevate the level that the peak hydrogen concentration reaches. Except for α′ martensite, dislocation substructure was also considered as a key factor of the HEE of AUSS, as discussed in Ref. 10. The hydrogen effects on the static mechanical properties have been widely investigated [], but the hydrogen-induced loss of fatigue durability of metallic materials is more critical to industrial applications. Mine et al. [] investigated the fatigue crack growth rate (FCGR) of thermal hydrogen-charged specimens with different degrees of pre-strain, and found the coupled effect of α′ martensite and hydrogen-induced fatigue crack propagation. Kanezaki et al. [] found that more α′ martensite on the fatigue fractured surface formed in pre-strained 316 AUSS specimens than solution-treated AUSS 316 specimens, indicating that the α′ martensitic transformation was closely related to the deformation microstructure. The microstructure and texture caused by deformation dependent on the composition and deformation temperature in face-centered cubic materials []. Our recent studies had confirmed the temperature-dependence of warm-rolled AUSS304 specimens and discussed the effect of deformation structure on the HEE and hydrogen-enhanced FCGR []. However, the composition factor was not into account, which was a key point to HEE [The objective of this research was to provide a profound insight into the temperature-dependence of deformation microstructure of meta-stable AUS 316 with relatively high nickel equivalent. By the means of rolling condition regulation, the deformation structure was controlled, and it was possible to discuss the effect of each micro-structure (including dislocation structure, deformation twins and α′ martensite) on HEE and hydrogen-enhanced FGGR of 316 AUSS specimens separately. Finally, based on careful observation of fracture surface and phase structure around the crack pathway of warm/cold rolled specimens by Field-emission Scanning Electron Microscope (FeSEM) and Electron Back Scattered Diffraction (EBSD) method, the hydrogen-induced fatigue crack propagation process was studied from a dynamic perspective.The meta-stable AUSS used in this study was commercial type 316 (AISI 316) with weight percent (%): 0.02C, 0.56 Si, 1.17 Mn, 16.6 Cr, 10.2 Ni, 2.13 Mo. There was a study about δ-ferrite influence on fatigue growth rate and tensile properties in the hydrogen environment []. To address the uncertain introduced by δ-ferrite, all of 316 AUSS specimens were insulation-heated at 1100 °C for 30 min followed by quenching treatment to obtain single austenite phase, and named with the as-received specimen. reveals the microstructure of the specimen after solution-treat, it shows a microstructure of recrystallized austenitic single structure with the mean grain size approximately 100 μm, and no δ-ferrite was found.The type 316 AUSS plates after solution-treat were repeatedly rolled by a constant temperature rolling mill from 20 mm thickness to obtain a specific thickness reduction (−0.2, −0.4), this particular process is shown in . It was also necessary to avoid the sensitization effect which could increase the susceptible of austenitic stainless steels to intergranular corrosion [. The cylindrical surfaces of the SSRT specimens and the RD-TD surfaces of the CT specimen were mirror polished by abrasive paper (2000 meshes) before mechanical property test in the argon or hydrogen environment.The FCG and SSRT tests were performed using Instron 8801 universal strength testing machine which was outfitted with a good dynamic seal high-pressure gas environment vessel. The tensile test was conducted at a very low strain rate (5 × 10−5 s−1) in 5 MPa hydrogen or argon environment (99.999% gas purity). The vacuuming and aeration processes were alternated three times to completely replace the gas adsorbed on the inner wall of the chamber, ensuring that the gas purity in the chamber meets the standard (ANSI/CSA CHMC-1) []. The 30 min’ pressure stabilization process was performed before each tensile or fatigue test. The load was calibrated by an additional load cell to eliminate the influence of seal friction. The FCGR test was conducted with the compliance method, and the specific settings of the experimental parameters were arranged as follows: force range (ΔP = 5 kN), frequency (f = 1 Hz), and stress ratio (R = 0.1). All tests were performed at 25 ± 2 °C. And all experiments were repeated three times to avoid accidental errors.After the FCGR test, the CT specimens will continue to fatigue until total fracture for observation of the fracture surface by the FeSEM. Then the α′ martensite volume fractions on the fracture surface (near 40 MPa m0.5 ΔK) was measured by the ferrite method. The microstructure and phase structure of two representative specimens (T25-R20H2 and T400-R20H2) were studied by the SEM and the EBSD method. The specific sample preparation and operation process of the EBSD observation worked according to the following: a small specimen contained the complete crack was cut from the CT specimen by wire-electrode cutting; then, it was mechanical polished, ion etched with 6.5 kV voltage for 30 min by the Leica RES101 ion etching machine before EBSD observation test by using the OXFORD NordlysNano; all of the subsequent data was further analyzed in Channel5 software in the end.A large number of deformation twins were observed in T25-R20 and T200-R40 specimens after the rolling process as shown in , while the proportion of twins was smaller in the T200-R20 specimen, as shown in . However, no deformation twins were found in the T400-R20 sample. Olson et al. [] reported the temperature-dependence of the formation process of deformation twins, it was more likely to form twins when deforming at low temperatures. Tsakiris et al. [] also reported that the proportion of twins was determined by the strain degree. The deformation behavior was mainly twining at a low deformation temperature but shifts to dislocation slip at a high temperature. When dislocation slip was blocked due to piling up of dislocations with the increase of strain, twining happened again. By comparing , the elongation of grains was more severe and the deformation twins were gradually rotated parallel to the same direction of rolling with the increase of rolling strain.(a) and (b) illustrate the effects of rolling temperature and rolling strain on the stress-strain curves of warm-rolled 316 AUSS specimens in both atmospheres, the as-received curves were also plotted for comparison. All the specimens tested in a hydrogen atmosphere were named with TXX-RYY H2 and marked with solid symbols in (a) and (b), all the specimens tested in argon were named with TXX-RYY Ar and marked with hollow symbols. A slight decrease in elongation could be found when the testing environment changed from argon gas to hydrogen gas, and the difference in elongation diminished after warm rolling. The SSRT curve hardly changed with test atmosphere before necking. Static properties such as yield strength (YS) and ultimate tensile strength (UTS) of warm-rolled specimens seems not changed with the rolling temperature, and the elongation first increased then decreased with increasing rolling temperature. The UTS and YS increased, but the elongation decreased with increasing rolling strain as shown in . Nevertheless, the degree of variability in UTS, YS, and elongation decreased with increasing strain. shows the ΔK versus da/dN curves of 316 AUSS specimens with different rolling temperature in 5 MPa hydrogen or argon gases. All the samples tested in the argon environment showed a much lower fatigue growth rate than those tested in hydrogen gas, which indicated that hydrogen enhanced fatigue crack propagation. The FGGRs of warm-rolled specimens in both atmospheres decreased significantly by comparing with the as-received specimen, which implies that the deformation structure induced by warm-rolling decreased the FCGRs. In the argon atmosphere, the FGGRs of the specimens with different rolling temperatures presented a similar growth trend with ΔK. However, an interesting result was found by comparing the curves of T400-R20H2, T200-R20H2, and T25-R20H2 specimens:the slope of the above-mentioned curves presented an obviously decline with the rolling temperature rising. Namely, the T400-R20H2 specimen had a higher FCGR than the other two specimens in low ΔK regime, but the FGGR of T400-R20H2 gradually became lower than the other two specimens in high regime (ΔK>35 MPa m0.5). shows the FCGR curves of warm-rolled 316 AUSS specimens with different rolling strain in hydrogen or argon environment. The FCGRs of the hydrogen environment tested specimens showed different dependences on the rolling strain with those tested in argon gas. The rolling strain had little effect on the FCGRs of hydrogen environment tested specimens, while it influenced greatly on the FCGRs of those tested in argon. Namely, the FCGRs showed an obvious decline with increasing the rolling strain of specimens tested in argon gas. shows the SEM fractography images of as-received 316 CT specimens after FCGR tested in the argon or hydrogen atmosphere. The ΔK value which corresponded to the stress level near the crack tip had effects on the fracture surface morphologies []. Thus, all the SEM fractography images in this study were observed near 40 MPa m0.5 ΔK. The morphology of ductile fracture was found in the argon environment tested as-received 316 AUSS specimens, while the quasi-cleavage fracture surface with a secondary crack was observed in the as-received 316 AUSS specimens tested in hydrogen gas. Not only on the fracture surface of argon environment tested specimen but also in hydrogen, a considerable number of fatigue striations could be observed, which indicated that sufficient plastic deformation occurred during the crack propagation process. shows the difference of fracture surface morphologies of argon environment tested 316 specimens affected by different rolling strain or temperature. The ductile transgranular fracture surface with some stripes parallel to the crack propagation direction was seen in those argon environments tested specimens. The rolling temperature had little effects on the fracture surface morphologies. However, it was found that the spacing between the stripes gradually decreased with increasing rolling strain.As to the specimens tested in hydrogen gas, as shows, the step-like transgranular fracture surface was detected in the low temperature rolling specimens (T25-R20H2, T200-R20H2, and T200-R40H2), and the step-like features became more disorganized and multidirectional with increasing rolling strain. The step-like features which were indicated by the black arrow in , (b) and (d) were also found in the fracture surface of AISI 304 CT specimens, and it was caused by crack propagated along with the slip bands and deformation twins [, as emphasized by the yellow dotted box. There were two sets of slip bands inclined to one another at an angle of 60°through the whole plane. The similar fracture feature had been found in the AISI 304 tension specimen in a sub-ambient hydrogen atmosphere [ shows the α′ martensite volume fractions on the fracture surface (near 40 MPa m0.5 ΔK) tested in argon and hydrogen gas. The volume fractions were measured by a ferrite scope because of the ferromagnetic properties of α′ martensite []. The true α′ martensite content (CT) induced by cyclic deformation was calculated by the following formula:where CT – α′ martensite content induced by cyclic deformation, %; CF – α′ martensite content of fracture surface, %; CB – α′ martensite content of bulk, %.The CT value tested in argon gas was much higher than those in hydrogen to the specimens with the same rolling condition. It was noteworthy the CT value of the T400-R20H2 specimen was zero, which indicated that no α′ martensite formed in the plastic zone around the crack during the FCG process. In addition, the specimens rolled at lower temperatures (T25-R20H2, T200-R20H2, and T200-R40H2) had almost the same α′ martensite content in the vicinity of the crack, which implied that the strain level at lower rolling temperatures might have little effect on the content of α′ martensite in the vicinity of fatigue crack.. The formation of step-like features, as presented in . For the T400-R20H2 specimen, the most striking characteristic of crack was multi-directional, and a lot of secondary cracks could be observed. Another obvious difference between the crack pathways of above-mentioned two specimens were the slip-band: well-evolved slip bands even extended out of image could be found in T25-R20H2 specimen, while the slip bands concentrated around cracks for T400-R20H2 specimen.The FCGRs of warm-rolled 316 AUSS specimens were mainly affected by three factors: stress intensity at the crack tip, microstructure and testing environment []. There were inherent relations between the three. With the increase in the stress intensity at the crack tip, the dislocation density and the content of α′ martensite would increase to varying degrees, while the localized high-density dislocation and α′ martensite often led more serious hydrogen segregation. In order to understand why the FCGR curves of the 316 AUSS specimens tested in the above-mentioned 2 atm exhibited different temperature-dependence. Not only the microstructure of 316 AUSS specimens after warm rolling but also the later evolution of deformed structure in the fatigue crack propagation process in 2 atm should be carefully analyzed from a dynamic perspective. The deformation structure of austenitic stainless steel was closely related to the deformation temperature [], which made it possible to separately discuss the influence of deformation structures on the FCGRs. The most typical temperature-dependent deformation microstructure was α′ martensite. Md30 was a widely used index to assess the inclination of martensitic transformation in the austenitic steels. The Md30 values of 316 austenitic steel were calculated by the Angel's equation [Md30(K)=413−462([C]+[N])−9.2[Si]−8.1[Mn]−1.37[Cr]−9.5[Ni]−1.85[Mo]The calculated result was 265.5 K which was much lower than the rolling temperature, indicating that almost no α′ martensitic transformation occurred during warm rolling. This conclusion could also be confirmed by the metallographic photographs and the value of bulk α′ martensite content (CB) which was approximately 0.08% for all specimen. Therefore, dislocation multiplication and twinning were the only two deformation behaviors in the rolling process. In terms of low-temperature rolling, the resistance of dislocation motion was strong, which made it easy to achieve the stacking fault energy required by the twinning. For specimens rolled at 400 °C, the initiation and motion of dislocation were promoted, while twinning was completely inhibited. The deformation behavior was mainly twinning at low temperatures, but shifted to dislocation slip at high temperature in warm-rolled specimens with 20% thickness reduction (as mentioned in Section 3.1).It was only because of the variation on mechanical property caused by warm rolling that the FCGRs of the specimens experimentalized in the argon environment changed. The warm-rolled specimens showed the obvious reduction in the FCGRs compared to the as-received specimens, which can be attributed to the increase in yield strength caused by warm rolling. The plastic zone at the crack tip would shrink with the increase of YS []. However, the rolling temperature had little effect on the YS as illustrated in . The FGGR curves almost coincided with each other for the specimens tested in argon gas, while it declined obviously with increase of rolling strain. To the specimens experimentalized in hydrogen, the fatigue crack propagation became more complicated due to the coupling effect of high-pressure hydrogen, tri-axial stress and microstructure []. For example, the crack propagation in hydrogen environment was not completely limited by the plastic zone, secondary cracks were observed outside the plastic zone ahead of the crack tip []. In general, the accumulation of hydrogen promoted plastic deformation near the crack tip, which resulted in the higher FCGRs. In detail, the slope of the FCGR curve of those specimens showed a significant downward trend with the increase of rolling temperature, especially for the curve of the T400-R20H2 specimen in . However, the rolling strain had little effects on the FCGRs of the specimens experimentalized in the hydrogen atmosphere.The grain boundary map and misorientation angle distribution figure near the crack of two typical warm-rolled 316 specimens tested in hydrogen (T25-R20H2 and T400-R20H2) are shown in (a) and (b). A considerable quantity of low angle grain boundary (LAGB), as indicated by the green line, was found around the crack pathway of the T400-R20H2 specimen. But it decreased and concentrated on twin boundaries in T25-R20H2 specimen. There were two obvious angle peaks (around 3° and 60°) in the corresponding misorientation angle distribution figure, which represented dislocation structure and twin boundaries respectively []. The fraction of deformation twins dramatically decreased from 0.3 to 0.03, while the dislocation substructure fraction increased from 0.6 to 0.8 with the rolling temperature increased. (c) and (d) are the corresponding local misorientation map. The dislocation-induced misorientation indicated by the green line were discontinuities and concentrated near twin boundaries in T25-R20H2 specimen, while it was widely dispersed and cross-linked into nets in T400-R20H2 specimen.Both dislocation and deformation twins played important roles in HEE of the austenitic stainless steels []. As for dislocation, hydrogen was transported by dislocations [] and reduced the repulsion between dislocations []. Low-temperature deformation caused dislocation planar-slip and localized distribution of dislocation, but high-temperature deformation caused dislocation cross-slip and uniform distribution of dislocation. The high-density uniform distribution dislocation formed in T400R-20H2 transported considerable quantities of hydrogen atoms over sufficient distances at early stage of crack propagation then hydrogen segregation happened at crack tip, causing premature failure []. On the other hand, the twin boundaries formed in low temperature rolling acted as strong obstacles to the dislocation motion. Hydrogen promoted dislocation plane-slip but impeded cross-slip, which made that effect even more serious. The fracture mode changed because hydrogen increased the out-of-plane displacement []. This could be the reason why the T400-R20H2 specimen had a higher FCGR than the T25-R20H2 specimen when ΔK below 35 MPa m0.5.As for the deformation twin itself, it was less influential on HEE of austenitic steel compared with α′ martensite and dislocation. However, the volume fraction of twins greatly influenced the content of α′ martensite which induced by cyclic deformation near the crack tip. Nakada [] reported that twin boundary provided a preferential site for α′ martensite nucleation in 316 cold-rolled specimens because deformed twins and austenite grains together formed a double Kurdjumov–Sachs (K–S) relationship [] found α′ martensite preferentially nucleated on the intersection of twins. It was well discussed that the higher hydrogen diffusivity and the lower hydrogen solubility of the α′ martensite compared to the austenite phase made the hydrogen preferentially separated at the interfaces of the above two phases, which finally resulted in a high FGGR [. Almost no α′ martensite was detected in the plastic zone near the crack in the T400-R20H2 specimen, while the austenite phase was completely transformed into α′ martensite in the vicinity of the crack in the T25-R20H2 specimen. The crack of T400-R20H2 specimen was more multidirectional and accompanied by more secondary cracks, while the crack of T25-R20H2 specimen displayed a relatively straight feature. There was an obvious turning, as indicated by the yellow arrow in . The FCGR of the T400-R20H2 specimen was gradually lower than the T200-R20H2 specimen above 35 MPa m0.5 ΔK, which indicated the influence of deformation twins on the FCGR became more important with the increase of the ΔK value. And α′ martensite played an important role in this process.From experimental evidence and discussion mentioned above, we summarized the following ΔK-dependent mechanism about the fatigue crack propagation process of warm-rolled 316 specimens, as indicated in . The twins formed in the rolling process of T25-R20H2 caused crack tip blunting in the low ΔK regime [], but promoted α′ martensite nucleation in the high ΔK regime. The fatigue crack propagated preferentially along with the deformation twins and slip plane due to α′ martensite nucleation and hydrogen segregation [The effect of the crack-tip microstructural evolution on the hydrogen-induced fatigue crack growth in warm-rolled 316 stainless steel was investigated. The main conclusions were as follows:Warm rolling improved the strength, but did not increase the HEE susceptibility. The FCGRs of warm-rolled AISI 316 specimens tested in hydrogen decreased with the increase in rolling temperature.The deformation microstructure of type 316 steel showed a strong dependence on the pre-stain temperature. Deformation twins deceased and dislocations became more uniform with the increase in rolling temperature, inhibiting the formation of dynamic α′ martensite during the crack propagation.In the cold-rolled 316 AUSS specimen, deformation twins accelerated hydrogen-induced crack growth due to the α′ martensitic transformation at the crack tip. In the warm-rolled specimen, the formation of α′ martensite around the crack tip was completely inhibited, which greatly reduced the FCGRs in hydrogen atmosphere.The effects of thermo-mechanical load on the vibrational characteristics of ultrasonic vibration systemThe vibrational characteristics of ultrasonic vibration system play an important role in the stability and processing effect in ultrasonic machining. In this study, a theoretical analysis and experimental verification were employed to investigate the effect of the thermo-mechanical load on the vibrational characteristics of ultrasonic vibration system. Initially, a dynamic model was designed to analyze the influence of the thermo-mechanical load on the vibration characteristics. Based on the model, the single variable method was adopted to explore the effect of different mechanical loading and the rigidity coefficient of the tool on the vibrational characteristics. Then the experiment was conducted by imposing variable loads on the tool end face, and the amplitude, current, frequency and temperature of ultrasonic system were measured. Finally, the ultrasonic vibration drilling test was conducted to verify the experimental results. It was observed that the ultrasonic amplitude initially increased and later decreased with the increase in static load. In addition, with the increase in static load, the thermal effect was significant and the ultrasonic frequency presented a similar tendency, as the ultrasonic amplitude. Meanwhile, the variation of ultrasonic frequency was not significant under the thermo-mechanical load. The results of this study could provide a favorable reference in the design of an ultrasonic vibration system and selection the different tools in ultrasonic machining.Ultrasonic machining is a non-traditional mechanical processing method and widely utilized for the machining both conductive and non-metallic materials In general, during the ultrasonic machining, the whole vibration system is expected to run at an optimized performance, wherein the ultrasonic amplitude should reach a peak value at the resonant frequency. Since it is difficult to measure the ultrasonic amplitude during the processing, the ultrasonic vibration is supposed to be stable or unchangeable in the ultrasonic machining, without considering the influence of various processing parameters. Cong et al. using the theoretical and experimental results indicated that the cutting fore in the rotary ultrasonic machining (RUM) decreased with an increase in the ultrasonic amplitude Consequently, it is of great significance to explore the effect thermo-mechanical load on the vibrational characteristics on the ultrasonic vibration system. In this study, the vibrational characteristics of the ultrasonic system under thermo-mechanical load were investigated. Initially, the dynamic model of the vibration system was established. Subsequently, the relationship between the thermal-mechanical load and the ultrasonic vibrational characteristics was directly obtained by the experimental measurement, and the current was utilized to monitor the stability of the ultrasonic vibration. Finally, the effect of the thermo-mechanical load on the vibration system was verified using the ultrasonic vibration drilling test.The ultrasonic vibration system was composed of the transducer, front cover, horn and tool. In the ultrasonic machining, the load of the vibration system is usually variation with the tool wear. Meanwhile, the variation of the load brings nonlinearity to the vibration system, affects the vibrational characteristics of the ultrasonic vibration system, and causes instability in the process . The imposed load was equivalent to a linear spring with rigidity coefficient k and damping coefficient c.When the load was superimposed on the end face of tool, the dynamic equation of the system can be obtained as follows.m100m2x¨1x¨2+c1+c2-c2+c3-c2+c3c2-c3ẋ1ẋ2+k1+k2-k2+k-k2k2-kx1x2=(k1+jwc1)X0ejwt0, the transfer function under imposed load can be written as follows.G(s)=c1c2s2+(k1c2+k2c1)s +k1k2m1m2s4+[m2(c1+c2)+m1(c2-c3)]s3+[m2(k1+k2)+c1(c2-c3)+(k2-k)]s2+[k1(c2-c3)+c1(k2-k)]s+k1(k2-k)where m0 is the quality of the piezoelectric ceramic parts, m1 is the total mass of the preloaded bolt and front cover, m2 represents the total mass of booster and tool, c is the damping coefficient, c1 is the damping coefficient of the preloaded bolt and front cover, c2 is the damping coefficient of booster and tool, k is the spring rigidity coefficient, k1 is the rigidity coefficient of preloaded bolt and front cover, k2 is the rigidity coefficient of booster and tool, x0 is the displacement of the piezoelectric ceramics, x1 is the displacement of preloaded bolt and front cover, and x2 is the displacement of booster and tool. shows that the variation of the rigidity coefficient k and the damping coefficient c influences the transfer function of the vibration system. It is assumed that the imposed load F on the tool end face complies with the law of sinusoidal variation. In order to gain the relationship between the load and rigidity coefficient k and the damping coefficient c, the dynamic response model of load was introduced as follows.F=k3ix+cẋ=k3iAsin2πft+cA2πfcos2πft=Ak3i2+(c2πf)2sin(2πft+arccosk3ik3i2+(c2πf)2)where k3i denotes the rigidity coefficient of tool, and the subscript i represents the tool 1 and 2.where E is Young’s Modulus. It is well known that the Young’s Modulus E of a material is related to the temperature T. For tungsten steel, the Young’s Modulus E will decrease with an increase in temperature T. Moreover, ΔE can be defined as the change in E due to an increase in the temperature. When the temperature increases, the rigidity coefficient k3′ of the tool can be denoted as follows. indicates that the rigidity coefficient decreased with an increase in the temperature. Simultaneously, it can be seen from Eq. , when rigidity coefficient k and the damping coefficient c were constant, the variation load of the vibration system affected the amplitude and the frequency to a certain extent.The parameter of tools exhibits a significant influence on the load variation of the vibration system. Since the damping coefficient has a little influence on the temperature change and mechanical load On substituting the above parameters into Eq. , the Bode diagram of vibration system under different parameters can be plotted with the Mathematics software. presents variation in the frequency and amplitude under different rigidity coefficients. Compared with the frequency and amplitude under the rigidity coefficient k31, the frequency decreased by 13.8% and the amplitude increased by 8.4% respectively. Thus, the frequency decreased and the amplitude increased with the increase in rigidity coefficient.With the increase in temperature, according to Eq. , the rigidity coefficient is k31′=29.92×107N/m at the temperature T1 of 96 °C. The influence of the load on the amplitude and frequency at different temperatures was plotted. presents the effect of the mechanical load on the amplitude under different temperatures. Compared to the amplitude at the temperature T0, the amplitude at the temperature T1 decreased by 5.7%. In contrast, as presented in , the frequency at the temperature T1 decreased by 0.51%.The experiment was performed on X8130 universal tool milling machine. The test principle employed is shown in . The measurement device leadingly included the ultrasonic vibration system, the load measurement system and the amplitude measurement system. The ultrasonic vibration system was composed of the ultrasonic generator, transducer, horn and machining tool. The ultrasonic generator was primarily utilized to convert the alternating current into high-frequency electric oscillation for the ultrasonic vibration system. Then the transducer converted the electric oscillation into mechanical vibration at high-frequency. However, the amplitude of mechanical vibration generated by the transducer was generally too low to be used for mechanical machining. Consequently, the horn was added to amplify the ultrasonic vibrational amplitude to an applicable magnitude. The value of the imposed load was measured by a dynamometer (Kistler 9257B). The ultrasonic amplitude was measured by a laser displacement sensor (KEYENCE LK-G10). In order to measure the temperature during the experiment, the different loads were imposed on the end face of tool for at least 10 min. The temperature was measured with an infrared thermometer (BENETECH GM300)., the vibration system was fixed on the dynamometer and the machine table was adjusted to make the squeeze head contact with the tool end face. Then the laser displacement sensor was adjusted to produce the laser signal on the tool end face. The switch of ultrasonic generator was turned on, and a load was imposed on the tool end face through adjusting the workbench vertical movement. The value of load was displayed on computer 1, and the value of amplitude was displayed on computer 2. At the same time, the value of frequency and electric current was obtained from the control panel of the ultrasonic generator.In order to obtain the relationship between the resonant frequency and the ultrasonic amplitude, the tool 1 and tool 2 were utilized in experiment without any kind of load. Simultaneously, the relationship between the resonant frequency and the electric current was also gained. It was observed from that the amplitude and electric current initially increased, while later decreased with the frequency increasing for both tools. The resonant frequency of tool 1 was 35.14 kHz and that of tool 2 was 34.87 kHz, and the corresponding current was 0.21A and 0.23A, respectively.Experiments were conducted in two groups, in order to obtain the relationship between the ultrasonic amplitude, resonant frequency, temperature, current and the imposed load on the ultrasonic vibration system. The experimental variables are provided in . Firstly, the ultrasonic frequency was tuned at the resonant frequency of f1 = 35.14 kHz, and a load was imposed on the end face of tool 1. In order to monitor the temperature variation, the time for each load on the tool 1 lasted approximately 10 min. The next experiment was conducted when the temperature of tool was consistent with the ambient temperature. Secondly, the ultrasonic frequency was tuned at resonant frequency of f2 = 34.87 kHz, and a load was imposed on the end face of tool 2. The experiment of tool 2 was performed according to the above-mentioned method. In order to obtain credible data, each test was repeated three times and the measured results were averaged to get the final value., the variation tendencies of the ultrasonic amplitude and current for both tools 1 and 2 were identical with the increase in the imposed load. The ultrasonic amplitude initially increased and then decreased with the increase in load, as well as current. demonstrates the effect of load on the frequency and temperature of the vibration system. When the load was lower than 200 N, the variation of temperature was not significant, and the thermal effect on the vibration system was also negligible. In the stage, the mechanical load primarily acted on the vibration system and led to the resonant frequency increase. Consequently, the amplitude increased with the increased load in the stage. However, the thermal effect was distinct when the load was higher than 200 N, and with the load increasing, the ultrasonic amplitude exhibited a decreasing tendency. Simultaneously, the variation of current for the ultrasonic vibration system presented the same tendency as that of the ultrasonic amplitude. The change of current indirectly reflected the change of amplitude of the vibration system to some extent. presents the relationship between the current and the ultrasonic amplitude. It could be seen form that the ultrasonic amplitude increased with the increase in the current. In addition, the current of tool 2 increased by 15.7%, compared with that of the tool 1. Compared with the ultrasonic amplitude of tool 1 under the load 200 N, the amplitude of tool 2 increased by 9.4%. The experimental results were in good consistency with the theoretical analysis. presented the relationships between the frequency, temperature and imposed load for both tools 1 and 2. With the increase in the load, the frequency of both tools increased firstly and then decreased, while the temperature of the tool increased until reached thermal equilibrium. When the load was less than 250 N, the frequency increased, however, the frequency decreased when the values of the load were between 250 N and 400 N. The temperature of both the tools 1 and 2 increased when the load was lower than 300 N. When the load was higher than 300 N, the temperature reached a thermal equilibrium and result in the temperature stability. It is well known that the load is always coupled with the thermal effect for ultrasonic vibration system . The mechanical load increased the resonant frequency of the ultrasonic machining, while the thermal effect of ultrasonic vibration decreased the resonant frequency. Consequently, the resonant frequency did not monotonously increase with the increasing mechanical load, while due to the effect of thermo-mechanical load, the resonant frequency decreased at the higher temperature.It can be summarized that, according to the theoretical analysis, the frequency of the vibration system decreased with the increase in the rigidity coefficient, while the amplitude was increased. The experimentally analysis found that the frequency and amplitude of the vibration system tends to increase firstly and then decreased with the increase in load, when the temperature of the system increased.The ultrasonic vibration drilling test was performed on a modified CNC machine center (VMC850E) assisted with self-designed ultrasonic vibration devices. The experimental setup is shown in . The ultrasonic vibration system was fixed on the spindle of the machining using a clamp. The dynamometer (Kistler9257B) was mounted on the working table of the machine center to hold the workpiece with a jaw vice. The dynamometer was used to record the drilling force along the feed direction during the processing. In order to effectively verify the experimental measurement, both the tools 1 and 2 were used in the ultrasonic vibration drilling test. The test conditions are shown in . In order to obtain the different loads on the ultrasonic vibration system, the various feed rate were adopted in the test. Under each feed rate, the drilling time lasted for 2 min and the measured process was discrete. The load, temperature, current and ultrasonic frequency were discretely measured during the drilling time. These measurements were conducted in the next drilling time until the temperature of vibration system was consistent with the ambient temperature. The temperature of vibration system was measured by an infrared thermometer (BENETECH GM300). Simultaneously, the value of frequency and electric current was obtained from the control panel of the ultrasonic generator. In the test, the machine spindle was kept constant at the speed of 1500 r/min. In order to gain reliable data, each test was repeated three times and a final average value was obtained by averaging the measured results.In general, the ultrasonic frequency was dramatically higher than the natural frequency of dynamometer (Kistler 9257B), and the measured force was the maximum value of drilling force. Therefore, it was unreasonable to be regarded as an evaluation index of the machining performance. However, the average drilling force could be used as an index to depict the real-time vibration characteristics of the vibration system. As presented in , in the typical curve of the measured drilling force vs time, the average drilling force Fd was calculated by the following equation:where F was the time-varying measured drilling force, t0 and t1 denotes the time when the tool began and completed the drilling, respectively., the average drilling force and the temperature for both the tools of ultrasonic vibration system increased with the increase in the feed rate. Compared with the average drilling force and the temperature of tool 1 under the feed rate 15 mm/min, the force of tool 2 increased by 8.2%, and the temperature increased by 5.5%. The variation of feed rate of both tools was to be equivalent to impose different loads on the vibration system. Since the amplitude of the system cannot be directly measured in the ultrasonic vibration drilling test, as described in , the current change of the system indirectly reflected the change of amplitude of the system to some extent. It can be seen from that the resonant frequency of the vibration system presented a drift with the feed rate increase, and the current increased firstly and then decreased. When the feed rate was 15 mm/min, the current of tool 2 increased by 17.8% than that of the tool 1. The results indirectly verified that the amplitude increases with the increase of the rigidity coefficient. During the ultrasonic vibration drilling, it was also observed that the feed rate played an important role on the vibrational characteristic. When the feed rate was lower than 15 mm/min, the variation of temperature was not obvious and the thermal effect on the vibration system was also smaller. In the stage, the mechanical load was primarily acting on the vibration system and led to an increase in the resonant frequency and the amplitude with the feed rate increasing. However, the thermal effect was distinct when the feed rate was higher than 15 mm/min, and with the increasing feed rate, the resonant frequency and the ultrasonic amplitude appeared decrease tendency. This result was in good agreement with the experimental results. It also indicated that the mechanical load and the thermal effect were coupled in the ultrasonic machining, and the action of thermo-mechanical load exhibited a significant effect on the vibrational characteristics.The action of the thermo-mechanical load on the ultrasonic system in a certain range was responsible for an optimized performance of the whole ultrasonic system. In this study, the rigidity coefficient of the tool and the feed rate dramatically influenced the vibrational characteristics. Therefore, the tool with a higher rigidity coefficient and a reasonable feed rate should be selected during the ultrasonic vibration drilling.The effects of thermo-mechanical load on the vibrational characteristics were investigated in the present study by means of theoretical analysis and a subsequent experimental verification. A theoretical model was developed to reveal the influence of the rigidity coefficient on the frequency and amplitude of the ultrasonic vibration system, and also to demonstrate the effects of thermo-mechanical load. The main conclusions can be obtained as follows:It was observed that, during the machining of the ultrasonic vibration system, the ultrasonic amplitude and frequency were variable. Under the action of thermo-mechanical load, there was a critical load effect on the vibration system. Before the point of the critical load, the ultrasonic amplitude and the frequency increased with an increase in the static load, while after the critical load, the tendency of ultrasonic amplitude and frequency inversed.It was experimentally found that the variation in the current of the ultrasonic vibration system presented the same trend as the ultrasonic amplitude. Consequently, to a certain extent, the change of current indirectly reflected the change of amplitude of the vibration system.In ultrasonic vibration drilling test, the feed rate of the tools was to be equivalent to different load on the vibration system. The variations in the ultrasonic frequency and the current with the increase in feed rate in the test were in good agreement with the measurement experimental results.The authors declare that no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.Effect of free water on the flowability of cement paste with chemical or mineral admixturesThe particle packing state in cement paste and the characterization methods of free water were studied. The changes of free water in cement paste by adding mineral admixture and chemical admixture were measured, and the relationship between flowability and internal structure of cement paste was analyzed. The results showed that: water in cement paste can be classified by plastic limit test and liquid limit test. Excess water over the plastic limit which was the surplus water after filling the accumulate void of cement particles can only achieve the purpose of separating cement particles. When water exceeded the liquid limit, the free water caused the flow of paste under gravity. The improvement of flowability by adding superplasticizer was not only due to dispersion of flocculation structure, but mainly because of lower adsorption force field of cement particles to water. Superplasticizer reduced the thickness of water diffusion layer, and increased the flowability of the paste. The mineral admixture influenced the packing state and water adsorption capacity of particle materials.Water is the cheapest component of concrete, but it plays a pivotal role on concrete performance: water/cement ratio is one of the most important factors to control the mechanical properties of concrete, and unit water dosage plays a crucial role on regulating the performance of fresh concrete. Researches Water is the most fundamental factors that affect the concrete flowability. The effects of superplasticizer, mineral admixtures, sand ratio or some other parameters on concrete flowability are usually explained through quantitative analysis of the amount of free water. The flocculation of cement particles is the main factor to impede the flow of the paste, and superplasticizer can improve the flowability by dispersing the flocculation structure The specific objective of this study is to reveal the generation of “free water” and the mechanism of action. This study uses a correlation analysis approach to investigate the change process both macro performance of the cement paste and the internal structure of paste. Combined with the related concepts of plastic limit and plasticity index in soil mechanics, an attempt is made to establish a “free water” characterization method. Further, explain chemical admixtures and mineral admixtures on cement paste flowability change mechanism and lay a foundation for fine regulation of cement base material performance.Cement: PII52.5 Portland cement (PC) was complying with GB175-2007; its density was 3.14 kg/m3.Mineral admixtures: Fly ash (FA) and blast furnace slag (BFS); their densities were 2.18 kg/m3 and 2.6 kg/m3, respectively.Chemical admixture: Naphthalene-based superplasticizer (NSF); paste water reducing rate was 23% at the dosage of 0.75% of cement weight.The aim of this study was to determine how the characteristics of cement paste changed along with water–binder ratio (by volume). The test was separated into four systems: cement paste without superplasticizer and cement paste with 0.75% naphthalene superplasticizer, cement paste with fly ash replacing 15% Portland cement by mass and cement paste with blast furnace slag replacing 15% Portland cement by mass. The water–binder ratio was varied from 0.194 to 0.452.First step was to measure the density of the paste, and the paste volume equaled mass divided by density. A frustum-shaped cup was used to measure the density of cement paste. It was made from hard plastic, and its volume was 185 ml. Due to relatively large changes over the range of the water–binder ratio, the performance of pastes had significant fluctuations. To ensure the consistency of the filling state, fixed experimental rules were setting: the paste was filled into the cup over the edge of 3–5 mm. A knife was inserted into the pasted nine times along the inner circle at a distance of 10 mm to the edge, and then three times for each in two orthogonal directions. The surface was smoothed using a steel rule. After mixing, the above procedure should be completed quickly, and followed by measuring the weight. The entire process should be completed within ten minutes.The calculation formulas of the density of paste ρ0 and the total volume were shown below:In formulas: m0 was the mass of the paste in the cup, V0 was the volume of the cup; mc and mw were the mass of mixed cement and water respectively.The solid concentration of paste was defined as the ratio between the solid volume and the void volume of the paste. The void space contained water and air void. Therefore, the solid concentration of paste can be used to express the most tightly packed ability of solid particles in the paste. It can be calculated by the following formula:In the formula: e was the solid concentration; VTotal was the total volume including the void; Vc was the volume of cementitious binder, which can be calculated from the mix proportions.After the mixing process, the flowability was measured complying with GB/T8077-2000. The flowability was measured in terms of flow spread using the mini slump cone test. It concluded: (a) Pour the cement paste slowly into the slump cone until the slump cone is completely filled up; (b) Lift the slump cone gently and allow the cement paste to spread; (c) At the time of 30 s since lifting the cone, measure the diameters of the cement paste patty in two orthogonal directions, calculate the average diameter as the flow spread of the cement paste.The rheology parameter can be determined by NXS-11B rotary viscometer. The test samples were poured into a cylinder container, and then the spindle of the viscometer was introduced in the container for measurement. The viscometer measured the torque required to rotate the standard spindles in paste. Two shear stress–shear rate curves were obtained, one at increasing shear rate and the other at decreasing shear rate. The curve at decreasing shear rate, which is generally more consistent and repeatable, was used for evaluating the rheological properties of the cement paste sample. A linear regression analysis was carried out to determine the plastic viscosity (Pa s) and the yield stress (Pa) as slope and intercept of the regression line drawn through the data points in shear stress potted against shear rate plot.According to the knowledge of soil mechanics, with the gradual increase of moisture, the soil particles would be show different states, which were bulk powder, hardened solid, plastic state and the flow state, respectively. Plastic limit of the soil was defined as the critical moisture content of the transition from semi-solid to plastic state. And the liquid limit was defined as the critical moisture content from plastic state to flow state. Cement particles were similar to the soil particles at the initial process of combining with water. The plastic state of cement paste was a system which existed continuous force between the cement particles. Just after the water filled most of the void, uninterrupted system can form through Van de Waals forces, electrostatic force and liquid bridge. Referring to the soil mechanics, the plastic limit of cementitious particles can be defined as the smallest water–binder ratio to form an uninterrupted system. When the water–binder ratio was lower than this value, the system was just moist powder accumulation When cement particles were gradually filled with water, water firstly occupied the packing void of cement particles, during which the apparent volume of the entire system does not increase. Once the packing void was almost filled by the water, excess water will increase the particle spacing, and the apparent volume increased. Thus, by gradually changing the water–binder ratio, plastic limit can be determined by measuring the inflection point of volume change. When water content exceeded this value, the cement paste will have plasticity. shows the variation of the paste volume with the water–binder ratio. revealed that the volume of paste firstly has a gradual decline. When the cement came into contact with water, the first step was wetted also presented the change of plastic limit of cement by adding fly ash, blast furnace slag and NSF superplasticizer. The performance of cement paste can be significantly influenced by mineral admixture and chemical admixture. The figure showed that superplasticizer had the most obvious effect, followed by fly ash, and BFS had minimal effect. Adding admixtures reduced the plastic limit, and made the paste easier to achieve the plastic state. Tested points of different system in were fitted using the model of y |
= |
p1 |
∗ |
x |
^ |
p2 |
+ |
p3 |
∗ |
x |
^ |
p4, in which x, y were w/c and volume of the pate, respectively. And the plastic limits can be gained through calculating the extreme points of the math models. The results of fitting analysis were summarized in . The significance test results showed that P-value <0.01, so the fitting effect is satisfactory.The maximum solid concentration of paste reflected the accumulation of particles provided the solid concentration of different pastes. For each test curve, peak points were obtained by fitting the data points. And the maximum solid concentration values were listed in the last column of . It can be concluded that both mineral admixtures and chemical admixtures can improve the packing density of particles. And superplasticizer has the greatest significant effect.Two conditions were required to achieve higher solid concentration: lower air content and lower water content. The flocculation of particles had the most significant effect on it. More flocculation structure, more void space was formed. The decreasing packing density resulted in the reduction of solid concentration. However, by adding superplasticizer, the flocculation structure dispersed. The packing density was improved and solid concentration had the same trend. The effect of mineral admixtures was due to the changes in the distribution of particles. The improvement of binder particles increased the packing density, thereby increasing the solid concentration.Since the maximum solid concentration can be used to express the packing state, the relationship between particle packing and plastic state should be presented. presented the influence of maximum solid concentration on the plastic limit. With the maximum solid concentration increased, plastic limit decreased in a high correlation rule in which the R2 reached 0.91, and P-value of F-statistic was 0.001. Therefore, the particle packing state had the most significant effect on Type I free water. Increasing packing density was a basic way to reduce the plastic limit, and in this way it is easier to make a paste to be plastic.) was that the paste did not immediately become flowable even if water had exceeded the plastic limit. It illustrated that this type of free water was not the “free water” which can promote the paste to flow. In order to further study the effect of “free water” on paste, the rheological parameters of pastes were determined. showed the change of rheology parameters along with w/b ratio. When the w/b around the plastic limit, the yield stress of paste stated at a high level and did not change observably. Meanwhile, the plastic viscosity had the different trend with the yield stress, and it decreased gradually. In the Bingham model, yield stress showed the contribution of solid phase, and it expressed the friction dissipation. Plastic viscosity showed the contribution of the liquid phase, and it expressed the viscous dissipation.Before the plastic limit, yield stress did not change significantly, the same trend happened to the flowability of paste. The indistinctive change of the yield stress illustrated that this part of free water did not play the positive role in the paste flow, and this “free water” was still able to withstand the shear stress component. However, gradual change of plastic viscosity illustrated the ability of this water to reduce the viscous dissipation. When the paste changed from plastic state to flow state, a water film was gradually formed around the particles. And this water film was flexible but with mechanical transmission performance. Under shear stress, it will be plastically deformed. However, under gravity the paste did not flow freely. So it can decrease plastic viscosity but had no effect on the yield stress. It can be concluded that this film of water is impossible to facilitate relative movement of the cement particles.It can be concluded that: “Type I free water” was not the “free water” which was able to make the paste flow, but a type of water which separated the particles. The mechanism of Type I-free water is that: achieve the physical separation of closely packed cement particles, but remain an indirect interaction between the particles.Increasing the water content in the plastic paste can reach the flow state. The critical w/b ratio from plastic state to flow state was the liquid limit for cement. Water exceeded the liquid limit can be defined as “Type II free water”, and it can be calculated by subtracting liquid limits by the actual w/b ratio.Liquid limit of cement can be determined from the catastrophe point of flowability by continuously varying the w/b. showed the change of flowability along with w/b ratio. Water exceeding the plastic limit separated the particles, but the paste did not flow. When continue to increase water, paste started to flow, and this w/b was the liquid limit. For each curve, it can be divided into two parts: plastic state and flow state. According to the data point in , the liquid limit can be obtained by measuring the intersection of the two fitting line of two parts. The results were listed in . Mineral admixtures and chemical admixtures can influence the liquid limit. NSF significantly reduced the liquid limit. Fly ash also reduced the liquid limit, but the effect was weaker than NSF. BFS had no significant influences on the liquid limit. Different flow state suggested that different amount of free water was acting on the pastes.Typically, the water–binder ratio was briefly to characterize the composition of the cement paste. The flowability will increase along with the water–binder ratio because of the changes in the composition. However, in different system, the influence of water–cement ratio on flowability was not consistent. So, water–binder ratio was not a direct representation of flowability. By measuring the plastic limit and fluid limit, two types of free water can be calculated. Free water for different systems was listed in . Negative for free water implied no such free water formation.(a) showed that the flowability of cement paste increased with Type I free water. However, when the Type I free water was generated, paste may not flow. Moreover, the same volume of Type I free water for different paste caused discrepant flowability.Type II free water will generate when water exceeded the liquid limit. Type II free water makes the paste flow ((b), when Type II free water was generated, the paste became flowable. And all the four pastes had the similar influence trend for flowability. Therefore, compared with water–binder ratio and Type I free water, Type II free water can directly characterize the flowability of cement paste.Plastic limit and liquid limit together determined the free water. Adding admixtures will influence free water by changing the plastic limit and liquid limit. However, due to the introduction of admixtures, liquid limit and plastic limit usually varied in different degrees. It has been discussed that increasing packing density leads to the reduction of plastic limit. Therefore, at least one additional factor worked on the liquid limit. For example the action effect of superplasticizer, superplasticizer reduces the plastic limit by 0.1, but reduces the liquid limit by 0.3. This means that the increasing of packing density play a part role on increasing the amount of Type II free water. Another factor which works more effectively existed.Plasticity index was designated as value of liquid limit minus plastic limit. By adding superplasticizer, both packing density and plasticity index were varied. Liquid limit was more sensitive to superplasticizer than plastic limit. So the change of plasticity index was the most effective approach to change the Type II free water. The essence of reduction in plasticity index was the reduction of water content between plastic limit and liquid limit.In the above study, the different effect of Type I and Type II had been discussed. The fundamental reason for different type of water was the adsorption of water on the surface of cement particle. The mechanism of reduction of the absorbed water under function of superplasticizer can be explained that:Firstly, when the superplasticizer molecules were adsorbed by cement particles, cement particles were coated by a large number of organic polymers and enrichment of molecule was demonstrated in the form of micelles or lipid layer Adding mineral admixtures will also significantly affect the liquid limit. Due to different properties of mineral admixtures, each cementitious material should be discussed firstly. showed the plastic limit and liquid limit of Portland cement, fly ash and blast furnace slag. In the fly ash system, the lower liquid limit means that it is easy to form free water to make the paste flow. And it depends on the smooth surface and the lower surface energy of the fly ash. In the separate slag system, the highest liquid limit indicated that the formation of free water was hardest. Thus, the introduction of fly ash can reduce the absorption of water by replacing of cement, and reduce the liquid limit so as to improve the amount of free water. For the BFS, the BFS can improve the particle density and reduce the plastic limit, but on the other hand, the strong adsorption ability reduces the free water content. Under the balance of two factors, the introduction of BFS showed little effect.The effect of mineral admixtures on the flowability of the composite system should be further studied by the composite effect of the particle materials. The composite effect was discussed in the plastic state which different from the hardened state. If the parameters after composite are just the weighted average of the raw materials, it can be concluded that two components of the compound presented composite average effect. If not, there will be composite increasing effect of composite decreasing effect. For example, when the influence of cement–fly ash composite ratio on liquid limit was studied, firstly a line was obtain by connect the liquid limit of all cement and all fly ash samples. If the measured liquid limit of PC–FA composite was on the connected line, it means that two kinds of materials presented composite average effect. If the measured liquid limit was below the line, these mean two materials has superposition effect, so this situation can be defined as composite increasing effect.(a) showed that after adding fly ash, liquid limit point fall off. All the test point can be fitted as a liner, so fly ash and cement composite effect is just average effect according to the above analyses. Plasticity index of the composite effect is similar to the plastic limit, and did not present significant composite increasing effect ((b)). Therefore, liquid limit, controlled by the plastic limit and plasticity index, also fell on the composite line ((c)). Fly ash in cement composite application process, there was not composite increasing effect. So the structural features and basic performance of the composite system can be deduced through the study of the basic parameters of fly ash and cement.(a) that plastic limit curve of PC–BFS composites bend downward. It illustrated that PC–BFS composite has increasing effect. That may be caused by the complementary particle distribution to form a more closely accumulation. (b) shows plastic index of PC–BFS was just average effect after composited. Therefore the liquid limit of PC–BFS are only affected by the change of plastic limit, the results are shown in (c), and have a similar trend with the change of the (a). Despite their plastics limit and liquid limit were higher than the ordinary cement; BFS can improve the packing state of composite systems. The composite increasing effect on the plastic limit and the composite average effect in the liquid limit improve flow ability the PC–BFS system.Structural characteristics of composite paste in the plastic state can be included as that: compacted packing density and water adsorption effect of composite systems. In research of flowability of composite system: the liquid limit of compound system can be treated as the basic control indicators. If the liquid limit is lower, the higher flowability the paste can reach. And liquid limit is affected by two parameters of the plastic limit and plasticity index. Therefore, liquid limit can be regulated in two aspects of improving the total compactness of the system and reducing water absorption of particulate material to achieve the purpose of increasing liquidity.According to the above for the analysis of free water classification showed that: between the plastic state and flow state, there was a certain transition zone for water content. By adding admixtures can significantly change the water content in the transition zone. Compared to the packing density improvement of cement particles, change of water in the transition zone has a higher effect on increasing the flowability of water. According to this hypothesis of the transition zone, combined with the electric double layer adsorption principle in the solid–liquid system, water multilayer adsorption hypothesis was established as shown in In the solid–liquid system, the surface of the solid particles will form a double layer structure The cement particles were infiltrated firstly in contact with water. Since the role of static electricity and other effects, water molecules were adsorbed on the surface of cement particles. Liquid bridges were formed between the particles, and made the particles contact closely. Cement system presented dry and hard solid state. With increasing the water, the coating film around the particles increased and a diffusion layer gradually formed. The diffusion layer cannot pass the hydrostatic pressure and cannot flow freely. But when subjected to force, the water film can deform to move from thicker to thinner. This process makes the water filled most of the void between the cement particles, then, the paste has a plasticity. As water continues to increase, the water molecules can exceed the scope of the gravitational influence of the electric field and become free water. Free water can increase the distance between particles and lubricate the particles. Thus the paste can be exposed to any shear stress and presented flow state.The thickness of coating film depended on the mineral composition of the particles (chemical potentials), particle size and shape, the chemical composition of the absorbed ion and external conditions (pressure and temperature of the medium). Superplasticizer increased repulsion between particles and the packing density of the system. Thus less amount of water was required to form a diffusion layer needed by the plastic state. And cement system was easier in to the plastic state. Superplasticizer also reduced the effect of cement particles on the water. Thinner diffusion layer increased the amount of free water, and improved the flowability. In the past theories as the superplasticizer is added, flocculation become broken apart releasing the water from inside. When the flocculation structure of cement particles were broken, the water inside became the combined water film on the surface of particles. This process can increase the packing density of the system, but did not have the significant increasing of free water.Due to the different character of mineral or chemical admixtures, packing density of mixtures can be varied by the improvement of the particle state. Moreover, the admixtures will change the adsorbed capacity of the entire particle system.In this study, the correlation between macro performance of the cement paste and the internal structure of paste was explored. Combined with the related concepts of plastic limit and liquid limit in soil mechanics, the effect of chemical admixtures and mineral admixtures on cement paste flowability was analyzed. Test results allow the following conclusions:Liquid limit is the main parameters to characterize the flowability of granular material system mixed with water. Liquid limit was produced by plastic limit and plasticity index: plastic limit indicated the compacted packing density of particle material and plasticity index indicated the water adsorption capacity.Type I free water was not the “free water” which promotes the paste to flow. The mechanism of Type I free water is that: achieve the physical separation of closely packed cement particles, but remain an indirect interaction between the particles. Type II free water can directly characterize the flowability of cement paste.By adding chemical admixtures and mineral admixtures can increase the amount of free water. The increasing function can be divided into two parts: increasing the packing density and reducing the absorption of water. Chemical admixtures have both two functions and the latter is more significant. Composite reinforced effect between blast furnace slag powder and cement was existed in plastic stage by improving packing density and fly ash can reduce the adsorption capacity of composite system to improve the flowability which expressed as a composite average effect.The coating water film can be divided into the adsorbed layer and the diffusion layer. Water exceeded the coating film was identified as “free water”. The size of the adsorption layer is decided by the compacting state which was influenced by flocculation and particle distribution. The diffusion layer is determined by the water controlling ability. Based on this hypothesis, the effect of admixtures on flowability can be further discussed and some new materials which regulated the flowability can also be developed.Development and validation of a FRP-wrapped spiral corrugated tube for seismic performance of circular concrete columnsThis paper presents the cyclic behavior of circular concrete columns confined with a proposed FRP-wrapped spiral corrugated tube (FWSCT) that serves as a permanent ribbed surface between FRP and concrete. Five FWSCT column specimens with GFRP layers and axial load ratios as design parameters were tested for the flexural and shear performances. The FWSCT specimens that did not use transverse steel hoops in the entire column used longitudinal reinforcement for the flexural capacity and FWSCT for the shear capacity. Specimen FWSCT-0 was confined with only a spiral corrugated steel tube without GFRP wraps; Specimens FWSCT-1, FWSCT-3, FWSCT-5 and FWSCT-8 were confined with a spiral corrugated steel tube and additional 1, 3, 5 and 8 GFRP layers, respectively. Test results showed that Specimen FWSCT-0 experienced shear failure at about 1% drift; Specimen FWSCT-1 experienced flexural shear failure at about 4% drift, while Specimens FWSCT-3, FWSCT-5 and FWSCT-8 exhibited rupture of longitudinal reinforcement at drift ratios of 7% to 8%, without shear failure. A plastic hinge was developed in un-wrapped column ends, further extending into the footing. An analytical method that used the residual shear model and a proposed plastic hinge length reasonably predicts the flexural and shear capacities of FWSCT columns.An application of a steel tube to confine a concrete column has been demonstrated to be an effective way to improve structural performance, such as strength, ductility and stiffness Many works have confirmed that using FRP as confinement to concrete columns increases the flexural capacity, shear capacity and ductility of columns Cyclic tests were conducted on concrete columns using the FWSCT as shear and confinement mechanism. The objectives of the test program were to study (1) the flexural behavior of FWSCT concrete columns with different FRP layers and axial load ratios, and (2) the shear capacity of the FWSCT. Five circular reinforced concrete columns were designed with the same amount of longitudinal reinforcement; no transverse reinforcement was used in all specimens. One specimen that was confined by only a spiral corrugated tube served as a bench mark and others were confined by the FWSCT with different number of FRP layers. Since the effective strain of FRP in shear resistance is reduced by dilation of concrete in compression, the residual shear model The FWSCT is a spiral corrugated tube wrapped by FRP ((a)). The spiral corrugated tube is used as a permanent inner form for the fabrication of a FRP jacket; screw threads of the spiral corrugated tube considerably decrease the difficulty of manufacturing FRP ribs for bonding between concrete and FRP. The FWSCT provides not only confinement but also shear strength to concrete columns. A procedure of the FWSCT fabrication is summarized below:Clean the surface of a spiral corrugated steel tube by using Acetone (CH3COCH3).Brush a thin layer of ETERSET 2968P adhesive to improve bonding between steel and epoxy resin (Fill up the concave area of the tube with a mixture of resin [Eternal vinyl ester resin (Bisphenol A) and ETERSET 2960PT-S] and silica fume ((b) and (c)). Through few sample practices to achieve suitable viscosity for the best application, the mixing ratio of approximately equal weight is determined.Wrap FRP sheets around the tube with fibers aligned in the circumferential direction of the tube and 30 cm-overlap length (Repeat steps 4 and 5 until the required tube length. A 5 cm-overlap between two FRP sheets is used to ensure continuous confinement along the column length (For a multilayer FWSCT, repeat steps 4 to 6 up to the required number of FRP layers.A spiral corrugated steel tube that is 2500 mm long with 600 mm interior diameter is used as a mold for 1, 3, 5 and 8 FRP layers. Each FWSCT has five segments of FRP sheets in the tube longitudinal direction; both ends of the FWSCT are cut off with a designed length of 1940 mm. The FRP composites are made by impregnating unidirectional E-glass fiber sheets with epoxy adhesive; the impregnation process is conducted using a hand lay-up process. The fiber and epoxy are L 900-E (827 g/m2 in 0°; 45 g/m2 in 90°) and ETERSET 2960PT-S, respectively.A confined concrete model of Lee and Hegemier A spiral corrugated tube has a convex surface to produce interlock with concrete. The perfect bonding between the spiral corrugated tube and concrete is assumed for strain compatibility.The spiral corrugated tube is assumed as a smooth tube with an equivalent thickness ts and diameter D′, constantly along the column. The equivalent thickness ts (=0.54 mm) is calculated based on the same cross sectional area of the original corrugated tube and the assumed shape in one unit length (=28 mm), as shown in (b); the diameter D′ is the average of the interior and exterior diameters of the corrugated tube.The confining stress to concrete, fl, is the summation of confining pressures of the spiral corrugated tube, fl,s, and the FRP jacket, fl,frp:where Es is the elastic modulus of the spiral corrugated tube; Ef is the elastic modulus of the FRP jacket in hoop direction; tf is the thickness of the FRP jacket, and εl is the lateral strain of concrete:εl=-ν0εc-1-2ν02εc∗〈εc-εc,lim〉εc∗-εc,limCwhere the MacAulay bracket 〈〉 is zero when its inside value is positive; εc is the compression strain in the extreme fiber of the column section; ν0(=0.2) is the Poisson ratio of concrete; εc∗, εc,lim and C are parameters of concrete, function of concrete strength fc′. The confinement effectiveness fcc/fc and the axial strain εcc of confined concrete corresponding to a lateral strain εl are expressed aswhere fcc and fc are the axial stresses of confined and unconfined concrete corresponding to the same lateral strain εl, and Esec is the secant stiffness ((c)). Although both the extreme concrete fiber and FWSCT have the same axial strain based on the first assumption, the axial force provided by the FWSCT is still small and neglected in this work.A cross-sectional analysis with fiber strips is adopted to calculate the lateral force-displacement relationship of column specimens. The confined concrete, longitudinal reinforcement, spiral corrugated tube and GFRP are included in the analysis. An interactive procedure is used to calculate the neutral axis of the cross section, concrete and GFRP strains. Once the neutral axis and internal forces of the cross section are determined, the bending moment such as a crack moment, Mcr, first-yield moment, My′, idealized-yield moment, My, and ultimate moment, Mu, can be obtained. The first-yield displacement, Δy′, at M=My′ is calculated for double-bending columns where ϕy′ is the first-yield curvature; V is the column shear; EcIeff(=My′/ϕy′) is the effective flexural stiffness; Ec is the elastic modulus of concrete; Ieff is the effective moment of inertia; Ag is the gross sectional area of concrete; Ig is the moment of inertia of concrete; Leff is the effective column length; Lc is the clear column height; lt is the strain penetration length of longitudinal reinforcement into the footing (=0.022fsydb); db is the diameter of longitudinal reinforcement, and fsy is the yield strength of longitudinal reinforcement.The idealized-yield displacement, Δy, at M = My is calculated by multiplying the first-yield displacement, Δy′, and the ratio of My/My′. For the post-yield stage (ϕy<ϕ⩽ϕu), the plastic curvature, ϕp, is developed over a plastic hinge length, LpThe ultimate displacement of the column specimen, Δu, is determined based on the following conditions: (1) the concrete extreme fiber reaches the ultimate compression strain when the FRP jacket fails or (2) the longitudinal reinforcement reaches a strain value of 0.6 εsu, where εsu is the ultimate tensile strain of longitudinal reinforcement The shear strength of the FWSCT column is evaluated based on the ACI 440 where Vc is the concrete shear resistance; Vp is the shear component of the applied axial force due to a strut mechanism where θ(=30°) is the angle between the column longitudinal axis and shear crack; c is the depth of the neutral axis; εfe is the effective strain of the FRP jacket (0.004 or 50% of the rupture strain εfu based on the UCSD shear model); εsu,j is the ultimate strain of the spiral corrugated tube, taken as 60% of the rupture strain from material coupon tests The nominal shear strength of the FWSCT column based on ACI 440 where P is the axial force; b is taken as a column diameter,D, and the effective depth, d is taken as 0.8 D; ψf is 0.95 for a completely wrapped FRP member. The shear capacities of the FRP, Vfrp, and spiral corrugated tube, Vsct, are calculated based on Eqs. (10) and (11), respectively, with θ=45°. The effective strain of the FRP jacket, εfe, is limited to 0.004 for a completely wrapped member.Five circular column specimens were designed with 12 No. 8 longitudinal bars for flexural resistance (ρl=2.15%) and no transverse hoop along the entire column (). The height and diameter of specimens were 2000 mm and 600 mm, respectively. Five specimens were confined by a spiral corrugated tube (SCT) and zero, one, three, five and eight GFRP layers (). The thickness of a spiral corrugated tube was 0.4 mm, and the thickness of one GFRP layer was about 1 mm. Specimens FWSCT-0, FWSCT-1 and FWSCT-3 were expected to fail in shear based on Eq. ; the nominal shear capacities of these three specimens were 620, 690 and 897 kN (c)). Specimen FWSCT-8 was conducted to study its flexural behavior under a high axial load ratio (0.65Pn), and others were tested under a low axial load ratio (≈0.2Pn). All specimens were tested in a double-curvature bending mode using the MATS facility at NCREE ((a)). The top and bottom of specimens were fixed to the MATS facility, and the bottom platform was cyclically moved by two 1000 kN actuators.Columns were cast vertically from a single batch of concrete, specified to be 35 MPa. (a) shows material properties of longitudinal reinforcement and concrete cylinders at the day of test. (b) shows material properties of unidirectional GFRP (L900-E) coupons and a spiral corrugated tube. The matrix is composed of Eternal vinyl ester resin (Bisphenol A) and ETERSET 2960PT-S, having a nominal elastic modulus of 3.3–3.6 GPa. The spiral corrugated tube has 600 mm interior diameter and screw threads, which have the depth, width and spacing of 7, 16 and 28 mm, respectively (). The spiral corrugated tube is specified to be SPCC steel with the elastic modulus and yield strength of 163 GPa and 330 MPa, respectively (A motion capture system (Optotrak® Certus Motion Capture System) was used to capture the specimen deformation in tests. Each specimen had 20 markers along the column height to measure the lateral and axial displacement ((b)); additional four markers were located on top and bottom footings for reference. The curvature along the column height can be calculated based on these marker data. A linear variable displacement transducer (LVDT) was used to measure the relative displacement between the footing and loading platform. A dial gauge with accuracy of 0.01 mm was used to measure the slippage between the specimen and the loading platform. The lateral drift of specimens could be obtained by deducting the slippage from LVDT data. Strain gauges were used to measure strain of the longitudinal reinforcement and GFRP jacket (Five FWSCT circular columns under a constant axial load were tested laterally using a cyclic displacement protocol that has two cycles at drift ratios of ±0.25% and ±0.375%, followed by three cycles at drift ratios of ±0.5%, ±0.75%, ±1%, ±1.5%, ±2%, ±3%, ±4%, ±5%, ±6%, ±7% and ±8%. The ultimate displacement of specimen is defined as its strength below 80% of the peak lateral force. Specimens FWSCT-0, FWSCT-1, FWSCT-3 and FWSCT-5 are subjected to a low axial load of 1967 kN (≈0.2Pn), while Specimen FWSCT-8 is subjected to a high axial load of 6856 kN (=0.65Pn). The axial capacities of the GFRP jacket and spiral corrugated tube are relatively small compared to the axial capacity of concrete core because the fiber is mainly aligned along the circumference direction and the thickness of the spiral corrugated tube is 0.4 mm, providing one percent of Pn:where fc′ is the concrete strength at the day of test, fy is the yield strength of longitudinal reinforcement and As is the total area of longitudinal reinforcement.Specimen FWSCT-0 was confined by a 0.4 mm-thick spiral corrugated tube. Test results show that Specimen FWSCT-0 experienced shear failure at 1.4% drift (ductility of 1.1) due to inadequate shear strength. shows a diagonal shear crack through the spiral corrugated tube and concrete; the angle between the crack and the horizontal axis is 65°. (a) shows the load–displacement relationship of Specimen FWSCT-0 with the maximum lateral force of 911 kN. (a) shows the relationship between the axial displacement and lateral displacement. The maximum axial shortening of the column was 2.2 mm and the axial force remained unchanged during the entire test.Specimen FWSCT-1 that had one GFRP layer around the spiral corrugated tube failed at 4% drift, resulting in flexural shear failure of the column ((b)). Snapping of epoxy was noted throughout the test due to gradual cracking of epoxy in the GFRP jacket. shows that a distorted fiber area due to a poor fabrication had color change at 3% drift. A sign of GFRP rupture started at 4% drift (ductility of 5.9), resulting in strength degradation. Large rupture and delamination of GFRP jacket were observed at 6% drift ((a)) because these fibers that were distorted or discontinued along the circumference direction had stress concentration in the test. A FRP failure strain in the distorted fiber area was 0.9% (0.36 εfu) at 4% drift, but the maximum FRP strain in other locations reached 1.8% at 6% drift. Specimen FWSCT-1 under a constant axial load (0.19Pn) had axial expansion in an early loading stage because the bottom platform moved outwards to maintain the compression force in the column associated with the lateral deformation. When the specimen lost GFRP confinement, concrete crush caused shortening of the column in a later loading stage.Specimen FWSCT-3 that had three GFRP layers around the spiral corrugated tube had one longitudinal bar rupture at 7% drift (ductility of 10.4). Unlike Specimens FWSCT-0 and FWSCT-1 without sufficient shear strength, diagonal shear crack or fiber rupture was not found in the test. Concrete spalling that occurred within the top and bottom unwrapped column ends penetrated into the footing after 3% drift. Two additional longitudinal bars fractured in the second cycle of 8% drift, leading to significant strength degradation ((b)). Specimen FWSCT-3 had axial expansion throughout the test, which is similar to Specimen FWSCT-1 test before GFRP failure ((b)). This indicates that three GFRP layers provide good shear resistance and confinement to concrete core with acceptable seismic performance (Specimen FWSCT-5 that had five GFRP layers around the spiral corrugated tube experienced fracture of three longitudinal bars at 7% drift ((c)), resulting in strength below 80% of the peak strength. The overall behavior of Specimen FWSCT-5 was similar to that of Specimen FWSCT-3; no diagonal shear crack or fiber rupture was observed throughout the test. (c) shows the load–displacement relationship of Specimen FWSCT-5 with the maximum lateral force of 1174 kN, similar to 1131 kN of Specimen FWSCT-3. Moreover, Specimen FWSCT-5 had axial expansion throughout the test as observed in Specimen FWSCT-3 test (Specimen FWSCT-8 like Specimens FWSCT-3 and FWSCT-5 had no shear cracks or fiber rupture throughout the test. Concrete spalling that was observed at the column-to-footing face penetrated into the footing from 3% to 7% drift. A maximum strain of longitudinal reinforcement was 6.2% (0.56εsu) when bars fractured at 8% drift (ductility of 10.6). (d) shows lateral deformation of Specimen FWSCT-8 under a large axial load of 6856 kN (0.65Pn) and axial shortening ((d)). The column axial shortening with increasing drift is mainly due to concrete crushing and spalling in the unconfined region ( lists test results of Specimens FWSCT-0, FWSCT-1, FWSCT-3, FWSCT-5 and FWSCT-8. Concrete columns with a GFRP wrapped spiral corrugated tube show good strength and deformation capacities. Shear failure of Specimen FWSCT-0 that occurs at displacement ductility of 1.1 can be prevented by wrapping one GFRP layer around Specimen FWSCT-1 that reaches displacement ductility of 5.9. Specimens FWSCT-3 and FWSCT-5 under the same axial load of 1967 kN (=0.2Pn) reach displacement ductility of 10.4 and 8, respectively. Ductility of Specimen FWSCT-5 is less than that of Specimen FWSCT-3 because Specimen FWSCT-5 has more fractured longitudinal reinforcement, resulting in faster strength degradation. Specimen FWSCT-8 under the highest axial load of 6856 kN ((a)) has the highest peak strength among all specimens.(a) shows the normalized lateral force (V/Vyield) versus displacement ductility curves of five specimens, where Vyield is the shear force corresponding to the ideal flexural yield moment, My. All specimens have similar initial stiffness, but Specimen FWSCT-0 shows significant strength reduction after reaching the maximum peak force. Specimen FWSCT-8 has a lower normalized peak force than Specimens FWSCT-1, 3 and 5 due to the highest axial load ratio (0.65Pn). After removing the P-Delta effect from the response curve, Specimen FWSCT-8 has similar response with Specimens FWSCT3 and FWSCT-5 ((b)). The lateral strength of the FWSCT column is maintained in large drifts, but the increase of ductility is not proportional to the increasing number of fiber layers because Specimens FWSCT-3, FWSCT-5 and FWSCT-8 experience low-cycle fatigue failure of longitudinal reinforcement, not FRP fibers. shows curvature along the column height, which is significantly large at the top and bottom un-wrapped ends (30 mm from the footing face). The unwrapped height of 30 mm was used to prevent contact between the FWSCT and the bottom footing and top stub during lateral movement of the column so that dilatation of FRP caused by concrete compression was assured. The value of 30 mm was adopted based on the past construction practice for columns wrapped by the FRP or steel tube ). Therefore, a plastic hinge length is proposed based on lengths of the unconfined region and the strain penetration of longitudinal reinforcement inside the footing.(a) and (b) show strains of longitudinal reinforcement, measured 40 cm above the footing. A square symbolic line represents the average strain of gauge LS series from the test; a blue line and a red line represent predicted strains from the displacement analysis with a plastic hinge length, Lp, of 1818.5 mm The concave area of the spiral corrugated tube is filled up with a mixed material that is composed of a weight ratio 1:1 of silica fume to resin. With the high density of silica fume, the mechanical strength and elongation of the mixed material lower than pure resin is expected. During the test of specimen FWSCT-1, the mixed material became many small chunks and fell off from the spiral corrugated tube right after GFRP layer ruptured ((a)). Therefore, the contribution from the mixed material is ignored in analysis. shows analytical results of Specimens FWSCT-0, 1, 3 and 8, where the test envelopes were obtained after removing P-Delta effects. The analytical curves calculated based on the constant plastic hinge length of Lp (=299 mm) correlate well the test responses. The residual shear strength curves ((a) and (b)) intersect with the analytical curves at 1.3% drift (Specimen FWSCT-0) and 3% drift (Specimen FWSCT-1), respectively, indicating shear and flexural-shear failure as seen in the test. (c) and (d) show that the residual shear strength curves do not intersect with the analytical curves of Specimens FWSCT-3 and FWSCT-8, indicating no shear failure. However, the ACI 440 The shear strengths of the FRP and the spiral corrugated tube were calculated by using the residual shear model (Eqs. ). The strain for resisting shear was calculated by removing the dilatancy strain εl from the measured hoop strain. The dilatancy strain εl at each displacement level was calculated from Eq. , where the concrete strain, εc, and the neutral axis, c, were computed from measured strains in the longitudinal reinforcement (200 mm above footing). Assuming perfect bonding between the FRP and the spiral corrugated tube, shear forces provided from the FRP, spiral corrugated tube and axial load component were calculated at each drift. The concrete shear force was obtained by subtracting shears of the above components from the actuator force. plots shear force components for Specimens FWSCT-1 and FWSCT-3, which failed in flexural shear and flexural modes ((c)), respectively. In small drift levels, the shear force is mainly carried by the concrete aggregate, Vc, and axial force component of the strut mechanism, Vp. A significant shear increase in the FRP jacket, Vfrp, and the spiral corrugated tube, Vsct, is observed at 2% drift. Specimen FWSCT-1 fails at 4% drift, where a majority of shear is resisted by Vc and Vp, the shear resistance ratios of the FRP jacket and the spiral corrugated tube are 20% and 13%, respectively. For Specimen FWSCT-3, the shear resistance ratios of the FRP jacket and the spiral corrugated tube are 32% and 18%, respectively, at 7% drift, where half of the shear is resisted by the FWSCT.(a) shows the shear force of FRP in Specimens FWSCT-1 and FWSCT-3. The red color bar represents the shear force of one GFRP layer with a maximum force of 198 kN at 4% drift; the blue color bar represents the shear force of three GFRP layers with a maximum force of 361 kN at 7% drift. The solid line and the dashed line represent the shear strength of one and three GFRP layers, respectively, calculated based on Eqs. (10) and (12) with an effective strain, εfe of 0.9%, obtained from Specimen FWSCT-1 test. The shear strength decreases before 0.5% drift due to the dilatancy of concrete, where the dilatancy strain εl is obtained from Eq. . The dilatancy of concrete confined by the FWSCT remains unchanged because the curvature along the column except for both ends is small and constant, resulting in constant shear strength of the GFRP jacket and spiral corrugated tube (b) shows the shear force of concrete in Specimens FWSCT-1 and FWSCT-3. The concrete shear strength based on ACI 440 A FRP-wrapped spiral corrugated tube (FWSCT) was developed to simplify the fabrication of a ribbed interface between concrete and FRP. Five large-scale specimens were tested to study the flexural and shear behaviors of columns with the FWSCT and longitudinal reinforcement ratio of 2.15%; no transverse reinforcement was used in all columns. Specimen FWSCT-0 was confined by only a 0.4 mm-thick spiral corrugated tube; Specimens FWSCT-1, 3, 5 and 8 were confined by additional one, three, five and eight layers of GFRP around a spiral corrugated tube. Test results showed that Specimen FWSCT-0 experienced shear failure at 1.4% drift and Specimen FWSCT-1 experienced flexural shear failure at 4% drift. Specimens FWSCT-3, FWSCT-5 and FWSCT-8 failed at 6 ∼ 8% drift due to rupture of longitudinal reinforcement. The following conclusions are drawn based on this study.The FWSCT that replaces the transverse reinforcement improves the seismic performance of concrete columns, increasing ductility, shear strength and energy dissipation. Although Specimen FWSCT-8 under a high axial load of 6856 kN (=0.65Pn) shows axial shortening throughout the test, its seismic performance is acceptable with rupture of longitudinal reinforcement at displacement ductility of 10.6. The measured maximum strain is 6.2%, around 0.5εsu from reinforcement tests.The FWSCT restraints the development of concrete flexural and shear cracks inside the tube confinement, so the plastic hinge is formed within the unwrapped region (30 mm between the FWSCT end and the footing) and the yield penetration region of longitudinal reinforcement inside the footing. The proposed plastic hinge length can be used to predict the lateral force versus displacement response of the FWSCT columns in this work. Note that since the test program was focused on the behavior of FWSCT specimens with one aspect ratio and different fiber wraps, more tests should be conducted to verify if the proposed plastic hinge length is applied to FWSCT columns with other aspect ratios.The failure strain, εfu, of GFRP is 1.9 ∼ 2.5% from material coupon tests. Although Specimen FWSCT-1 has distorted fibers around the tube during the hand lay-up process, the maximum failure strain is 0.9%, exceeding a design value of 0.4% based on ACI 440 Note that the application of FWSCT reduces the height of the region where the plastic deformation occurs and concentrates near the base and top of the column (unwrapped region). This behavior leads to a rapid deterioration of column stiffness because the material at the “toe” (critical section) is degrading at a high rate, similar to what was observed in the self-centering or rocking columns with unbonded post-tensioned tendons ). Incorporated with load–displacement analysis, the plastic hinge length that is developed into the top stub and bottom footing as well as the unconfined column region (30 mm in these specimens) gives a best description for the test results of specimens (Fabrication and characterization of a microelectromechanical tunable capacitorA micromechanical tunable capacitor fabricated using the commercial 0.35 μm complementary metal oxide semiconductor (CMOS) process and the post-process has been investigated in this study. The structure of the tunable capacitor consists of a membrane, supported beams, driving and sensing electrodes. The membrane is sustained by the supported beams. The tunable capacitor requires only one wet etching post-process to release the suspended structures. The post-process has the advantages of easy execution and low cost. The tunable capacitor contains a driving part and a sensing part. The sensing part generates a change in capacitance when applying a driving voltage to the driving part. Experimental results show that the tunable capacitor has a capacitance of 1.38 pF, a tuning range of 85% and a Q-factor of 40 at 100 MHz.Tunable capacitors are important components in communication circuits. Recently, microelectromechanical systems (MEMS) technology has been employed to fabricate various microstructures, microactuators and microsensors, such as electromagnetic microrelays The complementary metal oxide semiconductor (CMOS)–MEMS illustrates the structure of the micromechanical tunable capacitor, which consists of a membrane, supported beams, anchors, driving and sensing electrodes. The membrane is sustained by the supported beams. The area of the membrane is 154×154 μm2, and the thickness of the membrane is about 1 μm. All supported beams are 94 μm long, 2 μm wide and about 1 μm thick. The fixed electrodes under the membrane are taken as the driving and sensing electrodes as shown in . The sensing electrode locates under the center of the membrane, and the driving electrode situates under the sides of the membrane. The dimensions of the sensing and driving electrodes are shown in . The height of the sensing electrode is larger than that of the driving electrode. The gap between the membrane and the driving electrode is about 4 μm, and the gap between the membrane and the sensing electrode is about 1 μm. The micromechanical capacitor contains a driving part and a sensing part. The sensing part is constructed by membrane and sensing electrode and the driving part is comprised of membrane and driving electrode. illustrates the schematic cross-section of the tunable capacitor. As shown in , the membrane is held by the stiffness of the supported beams when there is no driving voltage. When applying a driving voltage to the driving part of the tunable capacitor, the driving part produces an electrostatic force. As shown in , the membrane is actuated by the electrostatic driving force, so that the gap between the membrane and the sensing electrode changes, resulting in the sensing part generates a change in capacitance.The finite element method (FEM) software, CoventorWare, is used to simulate the behaviors of the micromechanical tunable capacitor. The simulated procedure of the micromechanical tunable capacitor includes establishing model, selecting element type, meshing the model, defining material properties, setting boundary conditions, applying loads and executing calculations. The model of the tunable capacitor is established in accordance with the dimensions in , and then the model is meshed using triangular element. The material of the tunable capacitor is aluminum. The mass density of 2679 kg/m3, Young's modulus of 70 GPa and Poisson's ratio of 0.3 are adopted depicts the displacement distribution of the tunable capacitor. shows the relationship between the membrane displacement and the applied voltage. The simulated results show that the membrane has a displacement of 0.38 μm with a driving voltage of 23 V. presents the stress distribution of the tunable capacitor when a driving voltage of 23 V is applied. The maximum stress of 14 MPa located at the end of the supported beams is below the yield strength of aluminum (124 MPa). Therefore, the motion of the tunable capacitor can be operated in the elastic range under the driving voltage of 23 V.The micromechanical tunable capacitor is fabricated using the 0.35 μm CMOS process from Taiwan Semiconductor Manufacturing Company (TSMC). demonstrates the fabrication flow of the micromechanical tunable capacitor. illustrates the cross-sectional view of the micromechanical tunable capacitor after completion of the CMOS process. The sacrificial and structure layers of the tunable capacitor are the silicon dioxide and metal layers of the CMOS process, respectively. As shown in , the sacrificial layer is under the membrane and beams. In order to obtain the suspended membrane and beams, the sacrificial layer must to be removed. A post-process displays that the use of wet etching with silox vapox III at room temperature etches the sacrificial layer and releases the suspended structures. The silox vapox III (from Transene Company, Inc.) is composed of ammonium fluoride, glacial acetic acid, aluminum corrosion inhibitor, surfactant and DI water. The etch rate for the silicon dioxide is 960 Å/min. shows the scanning electron microscope (SEM) image of the micromechanical tunable capacitor after completion of the post-process. The micromechanical tunable capacitor is fabricated using the CMOS–MEMS technique, and its fabrication is compatible with the CMOS process, so the micromechanical tunable capacitor has a potential to be integrated with IC on a chip.The capacitance and Q-factor of the tunable capacitor depend on its impedance. The impedance Z of the tunable capacitor can be expressed as where Z0 denotes the characteristic impedance and S11 is the return loss of the tunable capacitor. The capacitance C of the tunable capacitor is given by where f represents the frequency and Z is the impedance of the tunable capacitor. The Q-factor of the tunable capacitor is given by , the capacitance and Q-factor of the tunable capacitor can be yielded if the parameter S11 is known. The Agilent 8510C network analyzer and a Cascade probe station were employed to measure the parameter S11 of the tunable capacitor. The tunable capacitor was mounted on the probe station. The power supply applied dc voltage to the driving part of the tunable capacitor. The parameter S11 of the tunable capacitor at different driving voltages was measured by the network analyzer, and the Agilent ADS software was utilized to evaluate the capacitance and Q-factor of the tunable capacitor in accordance with Eqs. depicts the capacitance changes of the tunable capacitor with different driving voltages after all parasitic capacitances are extracted. shows the relation between the capacitance and driving voltage for the tunable capacitor at different frequencies, which the data are constructed from . The results revealed that the capacitance of the tunable capacitor changed from 1.38 to 2.56 pF at 100 MHz and from 1.33 to 1.82 pF at 300 MHz as the driving voltage from 0 to 21 V. Thereby, the tunable capacitor had a capacitance of 1.38 pF at 100 MHz and a tuning range of 85%, and it had a capacitance of 1.33 pF at 300 MHz and a tuning range of 37%. displays the Q-factor of the tunable capacitor. The results showed that the tunable capacitor had a Q-factor of 40 at 100 GHz. The Q-factor of the tunable capacitor decreased as the frequency increased.The tunable capacitor proposed by Dec and Suyama A micromechanical tunable capacitor has been fabricated using the CMOS–MEMS technique. The fabrication of the micromechanical tunable capacitor was compatible with the CMOS process, so the tunable capacitor had a potential to be integrated with IC on a chip. The maximum stress of the tunable capacitor simulated by the CoventerWare was 14 MPa, which the value was below the yield strength of aluminum (124 MPa). Therefore, the motion of the tunable capacitor could be operated in the elastic range. The tunable capacitor required only one wet etching post-process to release the suspended structures. The post-process had the advantages of low cost and easy execution. Experimental results showed that the tunable capacitor had a capacitance of 1.38 pF, a tuning range of 85% and a Q-factor of 40 at 100 MHz.Anatomy of nanomaterial deformation: Grain boundary sliding, plasticity and cavitation in nanocrystalline NiThe deformation of nanocrystalline metals is a complex process that involves a cascade of plastic events, including dislocation motion, grain boundary activity and cavitation. These mechanisms act simultaneously and synergistically during fracture, masking their individual roles and often resulting in a wide range of failure modes in the same material. Using large-scale molecular dynamics simulations, we dissect the size-dependent deformation of nanocrystalline Ni nanowires for a range of diameters spanning a few nanometers to the bulk. By analyzing the localization of von Mises shear strain and stress triaxiality, we identify the key nanostructural features, the role of each elementary process and the dominant deformation mechanism as a function of sample diameter. Our atomic level analysis not only provides a fundamental understanding of the deformation of nanocrystalline Ni, but also demonstrates that large-scale simulations can be an essential complement for modern in situ electron microscopy/atom-probe tomography.Decades of experimental studies have demonstrated that nanocrystalline (NC) metals The deformation of NC materials is complex, involving disparate plasticity mechanisms operating either sequentially or simultaneously, including dislocation plasticity, grain boundary mediated plasticity In view of these experimental and computational challenges, we focus on very large scale MD simulations to investigate the deformation of NC Ni nanowires and bulk. By systematically varying sample diameters with controlled nanostructure, we are able to identify the role of the same microstructural features in different systems at different sample scales and compare the deformation in these nanowires with that in a periodic cell (pc) resembling bulk NC metals. This also allows us to dissect each deformation mechanism and reveal its role during deformation, and how it interplays and competes with all the other deformation mechanisms. Through these simulations, we provide unprecedented atomic-level details of the entire process of deformation, from initiation of plasticity to macroscopic failure.We simulated tensile deformation of a set of nanocrystalline Ni nanowires with identical nanostructures but with diameters ranging from 8 ⩽ |
D |
⩽ 57 nm and a periodic cell (see a) at a constant true strain rate of 0.1 ns−1. During tensile loading, constant temperature and zero lateral normal stresses (in the periodic sample) were maintained using a Nosé–Hoover thermostat a shows the engineering stress–engineering strain (σyy-εyy) curves for uniaxial tensile tests of nanowires and bulk NC Ni. The stress–strain curves exhibit nearly identical linear behavior in the early stages of tensile loading, but become non-linear and diverge starting at strains less than εyy |
= 2.5% (see c shows that a residual strain of ∼0.5% is present upon unloading the 20 and 57 nm nanowires from 2.5% applied strain, indicating that the non-linearity in the stress–strain curves below εyy |
= 2.5% is a result of plastic deformation, not non-linear elasticity (this is confirmed by the linearity in the stress–strain behavior of the perfect crystal at this strain; see a). The ultimate tensile stress (UTS) is achieved between 4 and 5% strain in all of the samples (the UTS slowly increases with increasing nanowire diameter and approaches the bulk nanocrystalline value for the same grain size a also shows the true stress–true strain curve for the periodic cell. This curve confirms that the strain softening/lack of strain hardening seen in the engineering stress–strain curves is real.The stress–strain curves show that the yield strength and ductility are strong functions of nanowire diameter. The mechanistic origin of these differences can be deduced by visualizing the deformation at early stages. To this end, we focus on an applied strain of 2.5%, where the non-linearities in the stress–strain curves become clear. Following the evolution of the atomic structure to this point shows that, up to and including this strain, no dislocation plasticity occurs. To characterize the deformation features, we focus on four quantitative measures of the deformation, two of which are sensitive to the orientation of the sample relative to the applied strain axis (i.e. the nanowire axis) and two of which are invariant measures of the deformation. These are: (i) the tensile strain parallel to the nanowire axis εyy; (ii) the component of the displacement perpendicular to this axis uz; (iii) the von Mises local shear strain invariant εvM show the spatial and probability density distributions of these four quantities. In each of the figures, lattice atoms are in grain interiors and non-lattice atoms are at grain boundaries and the free surfaces (in the nanowire cases).We first examine the atom-level tensile strain εyy, as shown in . The spatial distribution of εyy is qualitatively similar for all of the cases. εyy tends to be large along grain boundaries but is never large within grain interiors or at the free surface. This indicates significant deformation along the grain boundaries even at this small applied strain. These strains are largest along the grain boundaries oriented for maximum shear (i.e. ∼45° relative to the stress axis). b and c shows the probability density of this strain component P(εyy) for lattice and non-lattice atoms. While P(εyy) for lattice atoms is narrow and centered at ∼1.5%, the values of εyy for non-lattice atoms (mainly at grain boundaries) are commonly an order of magnitude larger than those for lattice atoms. This, together with the spatial distribution of εyy, confirm that strain is strongly localized at grain boundaries. In addition, P(εyy) for lattice atoms is insensitive to the nanowire diameter, while the width of this distribution for non-lattice atoms broadens with increasing nanowire diameter.While the spatial distributions of strain suggest that strain is strongly localized at grain boundaries, we can quantify this by focusing on atoms subject to at least twice the applied strain (i.e. >5%; see a). This analysis shows that, while there is a significant number of atoms showing strain levels twice that of the applied strain within both grain interiors and at grain boundaries, approximately four times as many atoms exhibiting such large strains are at grain boundaries relative to the grain interiors. This is particularly significant since the total number of atoms in grain interiors far exceeds that at grain boundaries. Since the stress–strain behavior for the single-crystal nanowire is nearly linear for strains exceeding 5% (see a), the non-linearity observed earlier in the stress–strain behavior for the nanocrystalline nanowires at a must be attributable to the deformation localized at grain boundaries. Further, since this non-linearity is not the result of elastic non-linearity (again, see the single-crystal results in c), the strain along the grain boundaries is plastic (i.e. non-recoverable deformation is localized at grain boundaries). We return to this point below.The measurement of εyy alone does not suffice to characterize the mechanism of deformation at grain boundaries. Deformation at grain boundaries can occur through strains normal to the boundary planes, grain boundary shear, or mass diffusion to or along grain boundaries. To distinguish these mechanisms, we consider alternative strain metrics. We note that the grain boundaries in each case exhibit less localization of volumetric (hydrostatic) strain than tensile strain (not shown). This suggests that, for Ni nanocrystalline nanowires, simple grain boundary expansion is not a key characteristic of grain boundary deformation. Next, we consider displacements perpendicular to the loading direction uz, as seen in . The spatial distribution of this displacement shows that there are discontinuities in uz along many grain boundaries (see a). This implies that neighboring grains slide relative to each other along grain boundaries, consistent with earlier NC simulations a illustrates that shear strain εyz is in the 10–20% range at many grain boundaries. Compared with an applied strain of only 2.5%, this is nearly an order of magnitude higher, but at the same order of magnitude as that of the tensile strain εyy identified previously.b and c shows the probability distributions of uz for lattice and non-lattice/grain boundary atoms, respectively. b quantifies the percentage of atoms with uz |
> 0.85 a0. As the sample size increases, both distributions become significantly narrower, indicating the increased kinematic constraint associated with increasing nanowire diameter. Furthermore, the less apparent discontinuities in uz across grain boundaries and the sharp decrease in the percentage of atoms with large displacement (see b) with increasing nanowire diameter suggest that sliding occurs more readily where the constraint of surrounding grains is less.In order to characterize the deformation associated with grain boundary shear, we calculate the von Mises local shear strain invariant. As shown in , the spatial distribution of εvM is qualitatively similar in the cross-sections of the nanowires of different diameters. The positions where the shear strain invariant is large correlate perfectly with grain boundaries and never with grain interiors or the free surfaces; this indicates that (i) significant grain boundary shear occurs during the early stages of deformation in these samples and (ii) there is no slip in the grain interiors (i.e. no dislocation glide). The density distributions P(εvM) in b and c show that εvM for grain boundary atoms spans an order of magnitude larger shear strain than that for lattice atoms. c shows that ∼13% of atoms have εvM |
> 5% and the majority of them are at grain boundaries (∼10.5% at grain boundaries vs. ∼2.5% at lattice positions). Comparisons of the percentages of grain boundary atoms with volumetric strain and von Mises local shear strain exceeding 5% (∼2.5% vs. ∼11%) suggest that the deformation at grain boundaries is dominated by shear.Similar to the tensile strain εyy, the magnitude of εvM at grain boundaries varies significantly, with some grain boundaries exhibiting strains an order of magnitude larger than others. This is, in large part, associated with the orientation of the boundary planes relative to the loading axis. The shear deformation at grain boundaries with large εvM could be in the regimes of plastic deformation and hence contribute strongly to the overall plastic deformation of the system identified earlier in the stress–strain curves (see c). We verify this conjecture by examining the residual εvM (i.e. after the applied tensile stress is removed). shows the spatial and probability distributions of εvM of two nanowires at 2.5% applied strain and subsequent unloading from that strain. For lattice atoms, nearly complete recovery of εvM is seen, indicating that the grain interiors deform elastically. However, the majority of grain boundary atoms show only mild recovery of the shear strain induced by the tensile loading. Operationally, we define the non-recoverable shear strain along the grain boundary as grain boundary sliding.The analysis of εvM illustrates that the initial deformation of all samples is qualitatively similar and is strongly influenced by grain boundary sliding. Grain boundary sliding must satisfy geometric constraints and thus may cause additional stresses to build-up, especially at grain boundary triple junctions, where sliding is discontinuous. The nature of these stresses can determine the subsequent plastic deformation modes. Continuum plasticity theory suggests that the plastic deformation mode may be governed by the stress triaxiality η; shear deformation occurs where η is small and void nucleation/growth occurs where η is large. We now examine the distribution of stress triaxiality η (see a and b shows that the majority of atoms in grain interiors exhibit triaxiality between 0 and 0.5, with a peak at ∼0.2, which is qualitatively consistent with the overall uniaxial tensile state (0.33 corresponds to a homogeneous uniaxial tensile stress state). However, η in the vicinity of and/or at grain boundaries can substantially deviate from these values. Close examination of a shows that the triaxiality near triple junctions is particularly large in magnitude (both positive (in red) and negative (in blue)). In addition, in large size samples, higher stress triaxiality values (η |
> 0.9) are seen when two triple junctions are connected by a grain boundary oriented perpendicular to the loading direction (see also d). Such grain boundary structures can serve as void nucleation sites in subsequent deformation. c shows P(η) for non-lattice/grain boundary atoms, where a peak in the vicinity of 0.2 is seen for all the cases. In the case of nanowires, two additional peaks are observed, at approximately 0.7 and −0.2. These two peaks are due to the surface stress, which places atoms in the outermost surface layer under tension and atoms in the inner surface layer under compression, respectively (see the inset of c). This effect is very strong very close to the surface, as many atoms in the inner surface layer are in compression even with the current applied tensile strain of 2.5%. show the percentage of lattice and non-lattice/grain boundary atoms with η |
< 0,0 < |
η |
< 0.66 and η |
> 0.66, respectively. As the sample diameters increase, the percentages of both lattice and non-lattice/grain boundary atoms with η |
< 0 decrease. In contrast, the percentage of atoms with 0 < |
η |
< 0.66 changes substantially, from ∼66 to ∼ 73% for lattice atoms and from ∼9 to ∼6% for non-lattice atoms. A similar trend is found for η |
> 0.66, where a moderate increase in the percentage of lattice atoms and decrease in the non-lattice atoms are seen. In d2 and d3, the decrease of η in non-lattice atoms with increasing sample size is accompanied by an increase of η in lattice atoms.Because each nanowire contains exactly the same grain microstructure at its central axis, we can perform a quantitative comparison of εyy, uz, εvM and η for a specific feature in the center of the samples, as shown in . The plots of εyy, uz and εvM, as seen in a–c, show a strong correlation between them; the locations of large uz jumps match with the locations of high εyy and εvM. Quantitative comparison of εvM within the identical microstructures of all cases shows that grain boundaries in the smaller diameter nanowires undergo larger shear deformation than the corresponding boundaries in the larger diameter nanowires (see c). Meanwhile, the distributions of εyy, uz, εvM and η in the largest diameter nanowire are practically identical to those of the bulk. The trend of decreasing εyy, uz and εvM and increasing η at the central region with increasing sample diameters arises from geometric constraint: i.e. when a grain boundary slides/expands in the interior of a nanowire, the other grains resist its motion. In larger diameter nanowires there is increased constraint, limiting the amount of grain boundary deformation. In smaller diameter nanowires, the proximity of free surfaces decreases constraint, allowing easy grain boundary sliding.The above analysis suggests that the macroscopic failure mode may likewise be a strong function of the nanowire diameter. Deformation at grain boundaries clearly has different consequences when the system size (i.e. nanowire diameter) is larger than the nanostructural length scale (i.e. grain size). Even if the initial deformation mechanisms are similar in all nanowires (boundary sliding), there are remarkable differences in the corresponding stress states that result from it, leading to significant differences in the ensuing deformation mechanisms. This is evident in the subsequent plastic deformation after reaching the UTS. shows the atomistic fracture process following yield. The small diameter nanowires (8 and 10 nm) fracture in a single plastic event that corresponds to the abrupt stress drop seen in . Close examination of the fracture shows that the process is dominated by grains sliding along a single boundary, as evident in The deformation of the 20 nm nanowire is likewise dominated by grain boundary sliding. However, the first grain boundary sliding event does not immediately precipitate fracture. Instead, stick–slip dynamics are observed, corresponding to the two serrations in its stress–strain curve. The number and magnitude of these serrations are nanowire length dependent for movies of the fracture process of all nanowires). This grain boundary migration eventually creates a continuous path for grain boundary sliding to reinitiate and continue. As further evidence of the dominance of grain boundary sliding for these three nanowires, we note that no appreciable necking is present at their fracture locations.In the larger diameter nanowires (30 and 57 nm) and the bulk NC, dislocations nucleate and propagate through entire grains, resulting in gradual strain softening. As we further load these samples, grain boundary sliding and dislocation plasticity continue, resulting in local necking (in the nanowire cases) beyond the ultimate stress. In addition, voids nucleate close to grain boundary triple junctions in both nanowires at the later stages of deformation (see d and e). In addition to dislocation plasticity and grain boundary sliding, void nucleation, growth and grain boundary migration are also active in these nanowires, especially during the later stages of fracture.d), a single void is nucleated at a grain boundary triple junction as a result of the sliding of grains close to the free surface. This single void later joins with the free surface, resulting in a necked single-crystal region connecting the upper and lower parts of the nanowire. The void nucleation, growth and coalescence occur at strains between 9 and 11%, which correspond to a relatively sharp drop in the stress–strain curve of this nanowire (see d). The subsequent deformation of this nanowire is localized to this single-crystal region and the deformation resembles the elastic–perfectly plastic deformation governed by dislocation nucleation and propagation In the 57 nm nanowire, multiple voids are nucleated, as shown in e. Some of these voids grow and coalesce along grain boundaries, resulting in intergranular fracture. In addition, some transgranular fracture features are also observed following the initial intergranular fracture (see for movie of the fracture process). The rapid growth and coalescence of voids also correspond to the sharp drop in the stress–strain curve of the nanowire. In this nanowire, grain boundary migration is particularly active during the voiding process. Some of the grain boundaries migrate for a distance of 5–10 nm, i.e. on the same order of grain size. As a result, grain growth is observed near the fracture surface.a shows the initial plastic deformation process of the NC bulk, where dislocation nucleation and propagation (green lines) are observed. At ∼4% applied strain, most grain boundaries coincide with their original locations, with the exception of a small number of grain boundaries that migrate a few lattice spacings close to their triple junctions. With increasing strains, multiple voids are formed in this NC bulk, similarly to those observed in the 57 nm nanowire. However, strain localization through necking is inhibited due to the bulk geometry. The high density of grain boundaries effectively stops void growth as they meet at grain boundary triple junctions. Close examination of the deformation mechanisms reveals competitive and cooperative plasticity, where grain boundary sliding, migration, dislocation plasticity and cavitation are all operating simultaneously and synergistically, as evident in b–d. This results in ductile plastic deformation in this sample.The plastic deformation mechanisms and nanostructure evolution in the larger diameter nanowires and the bulk can be understood as follows. The fact that grain boundary sliding is the dominant failure mode in small diameter nanowires confirms that grain boundaries have a lower resistance to shear deformation compared to shear along crystallographic slip planes via a dislocation nucleation mechanism. Conversely, in larger diameter nanowires (30 and 57 nm), grain boundary sliding is mechanically constrained by grain boundary triple junctions. As a result, stress concentrations build up at those triple junctions and allow alternative mechanisms to operate. This is in addition to the stress concentration arising from material elastic anisotropy. a shows the von Mises stress σvM at 2.5% strain for the 57 nm nanowire. We note that large values of σvM occur close to many grain boundary triple and quadruple junctions. Close examination of the nanostructures in the larger diameter nanowires (30 and 57 nm) at a later stage (5% applied strain) shows that dislocations are primarily nucleated close to grain boundary triple junctions with high σvM. a shows such examples. The locations of initial dislocation nucleation correlate well with the locations of high σvM. Nevertheless, we also note that not all triple junctions with high σvM nucleate dislocations. This is presumably associated with the slip system orientation within the grains with the large stress concentration.Dislocation nucleation and propagation relieve stress in high stress concentration regions. This leads to shifting the load to lower stress regions and making catastrophic failure less likely. As a consequence, other regions including those with high stress triaxiality η, must share more load. This is evident by noting the marked increase in stress triaxiality η in b at 5% applied strain, as compared with that in at 2.5% strain. High triaxiality makes void nucleation more probable, especially with subsequent deformation, which can further increase the triaxiality. Indeed, close examination confirms that there is a strong correlation between the locations of void nucleation (at a later stage) and high stress triaxiality (prior to void nucleation), as seen in The above results show that, by merely tuning the nanowire diameter (at fixed nanostructural scale), we can dissect the deformation mechanisms of Ni nanowires and observe a transition in the operative mechanisms from simple single grain boundary shear into the more complex bulk-like void nucleation and growth mechanism. This provides a simple approach to understanding the complex deformation pathways as a function of sample size. In this manner, we are able to characterize the anatomy of NC nanomaterial failure as a function of the sample to grain size ratio. is a visual summary of the deformation mechanisms observed in this study. The richness of this failure anatomy comes from the strong competition and cooperation of different deformation mechanisms dictated by the dearth of dislocation sources within NC metals. Not only are there few initial sources, but Ni has a relatively high barrier to dislocation nucleation due to its high stacking fault energy (the stable and unstable stacking fault energy are 125 and 366 mJ m−2 using this interatomic potential). It is important to note that the lack of stress relief via the operation of conventional dislocation sources leads to the operation of alternative plasticity mechanisms, especially grain boundary sliding and voiding.The abundance of grain boundaries in NC materials makes grain boundary sliding the first operative stress relief mechanism in all of the cases studied. However, the subsequent deformation varies considerably with nanowire diameter. If the nanowire diameter is of the same order as the grain size, the system easily locates a single grain boundary that percolates throughout the entire sample and is oriented for sliding. Such through-thickness grain boundaries provide easy paths for localized shear/sliding, as demonstrated by the small diameter nanowire cases (8 and 10 nm). For thicker nanowires, grain boundary sliding is inhibited due to the kinematic constraints imposed by neighboring grains (grain boundary triple- and quad-junctions). For slightly thicker nanowires (20 nm), stress-driven grain boundary migration For larger nanowires, the grains are too constrained for either stress-driven grain boundary migration or grain boundary sliding to be effective at reducing stresses. In such cases, grain boundary triple junctions act as stress concentrators, both because of grain boundary sliding and material elastic anisotropy. Two possible deformation mechanisms exist as a result of the stress concentration at grain boundary triple junctions: dislocation nucleation and void nucleation. Both are potent stress relief mechanisms. Which will be activated depends on both the intrinsic material properties (such as the unstable stacking fault energy, grain boundary toughness) and the actual stress conditions (e.g. von Mises stress, stress triaxiality and their relation to the lattice crystallographic orientation). Dislocation nucleation will be favored over void nucleation at triple junction regions with: (i) high von Mises stress; (ii) crystallographic orientation favorable for dislocation nucleation; and (iii) a relatively low barrier to dislocation nucleation.For the Ni nanowires, strain localization follows void nucleation, leading to void growth and coalescence. Interestingly, our 30 nm diameter NC nanowire simulations show examples where, following void coalescence, only a single grain spans the sample neck. In fact, this was exploited previously in an experimental study on single-crystal deformation In this work, we have studied the tensile deformation and failure behavior of NC Ni using very large scale MD simulations. By controlling the nanowire diameter and nanostructure, our simulations lead to a clear picture of the strongly size-dependent anatomy of deformation of NC Ni. Although all samples are constructed from the same polycrystal, the same nanostructural feature acts differently in nanowires of different diameters and in NC bulk. The mechanical constraints in thicker nanowires reduce the effectiveness of grain boundary sliding to shed load and instead induce alternative plastic deformation mechanisms. Our simulation clearly demonstrates that the properties of the nanomaterial cannot be separated from those of the nanosystem. By slowly increasing the amount of constraint (or increasing nanowire diameter), we can effectively interpret the increasingly complex deformation mechanisms of thicker and thicker nanowires. By dissecting the elements of the deformation in this way, we are able to identify the most important nanostructure features and atomic level mechanisms of deformation in NC Ni. Such atomistic details can provide important guidance and complement current in situ atom probe tomography of nanomaterials.Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.actamat.2013.06.026Foreign object damage on the leading edge of gas turbine bladesThe severe damages to the leading edge of aircraft blades occur when millimeter-sized particles such as sands, gravels or even the pieces of the engine components impact those of blades, which is called hard body impact or foreign object damage. This damage produces the geometry discontinuity such as the notch on the blades which becomes the site for fatigue crack initiation.FOD on the leading edge of the turbine blade is done by using the finite element method in this paper. Experimental stress analysis is performed for investigating the stress concentration factor at the crater base and is compared with the data from the finite element and the analytical method. The comparison shows that the finite element method results agree well with the experimental and analytical data at the crater base. Then the residual stress along the largest blade length is obtained for the potential crack initiating regions, and at the end, the analysis focuses on the comparison between the quasi-static indentation and fully dynamic impact for three critical locations where the tensile residual stresses cause crack initiation.dimensionless residual stress in x-direction of the plateForeign object damage (FOD), taking the form of small hard particle ingestion during takeoff and landing of aircraft, can cause significant damage to airfoils in the fan, compressor and turbine stages of aero-engines. The size of these objects such as gravel or sand is typically in the millimeter regime, with impact velocities determined primarily by the blade speed and in the range of 100–350 m/s, depending on the specific engine The history FOD phenomenon can be divided into two categories:(i) Foreign object damage occurs on the leading edge of compressor blades or low-temperature turbine stages which are both made of titanium alloy (ii) Sometimes this type of damage happened to the high-temperature turbine stages which are made of Ni-based superalloy. Papers have published in this field are about blades with TBC coating (b), while the undamaged gas turbine blade is shown in The high-temperature turbine engine blades, which are typically made of Ni-based superalloy, experience low-cycle fatigue (LCF) loading due to normal start-flight-landing cycles, and high-cycle fatigue (HCF) loading due to vibration and resonant airflow dynamics, often superimposed with a high mean stress. Under such cyclic loads, smaller indentation craters created by FOD can become sites for fatigue crack initiation and thus severely decrease the lifetime of the blade, often by several orders of magnitude Perhaps one of the biggest challenges in the prevention of FOD-related failures lies in understanding the nature of the damage caused by the FOD impact. A better understanding of this damage would provide valuable insight into the formation and propagation of FOD-initiated fatigue cracks allowing a more realistic lifetime estimate A number of different approaches have been tried in order to simulate FOD in the laboratory. Early approaches often employed a quasi-static chisel indenter to introduce a notch on the leading edge of a blade or specimen For modeling foreign object damage on the leading edge of a gas turbine blade, the following items are done:The piece of the turbine engine is impacted on the leading edge of the turbine blade. The impacted piece is considered nickel based superalloy (In617) at 300°C. The mechanical properties of it at 300°C are: Young's modulus E=190MPa, Poisson's coefficient υ=0.3 and density ρ=8360kg/m3The turbine blade is considered nickel based superalloy René 80. The temperature of the turbine blade is assumed 871°C that agrees with the impacted place. The impacted place is at 13 of the end of the turbine blade compatible with real cases. The stress–strain curve of René 80 superalloy is given in . The mechanical properties of René 80 superalloy are: Young's modulus E=130MPa, density ρ=8160kg/m3 and Poisson's coefficient υ=0.3The spherical particle is impacted on the leading edge with three different diameters D1=3.2mm, D2=2mm, D3=1.27mm and different velocities are in the range of 100–350m/s.For simplifying the modeling, the turbine blade is modeled rectangular cross-sectional features with the plate length L1≫t, the plate width L2≫t (L1=3.5L2 which is not very important) and thickness t<1.3mm (for 13 of end of the turbine blades leading edge).The In617 spherical particle with diameter D is impacted normal to 13 end of the leading edge of René 80 superalloy plate as the blade which its left side is clamped. This model is sketched in (a). Deformed specimen after impact is shown in (b). Potential crack initiation regions are also depicted in (c) which are at the bottom of the indent (A), outside the crater rim (B), one crater radius away from the crater (C), and at the bulge tip (E). The depth of penetration, δ, the crater width, w, measured in the central plane of the 3D model is sketched in (d), and the maximum bulge width, b, are also illustrated. Although the bulge tip seems to be the fatigue crack initiation site, cracks are not observed in this region in real FOD which will be explained by the FEM results.The plastic pile-up height at the crater rim, h in , is small compared with δ and w. By neglecting the pile-up effects, cf. 2δ=D−D2−w2→2δ−D=D2−w2→(2δ−D)2=D2−w2→4δ2+D̸2−4δD=D̸2−w2→w2=4δD−4δ2 is used for examination in verifying the impacted region profile obtained from the quasi-static chisel indenter.The kinetic energy of the impacted particle is KE=12mv02=π12D3ρPv02 where ρP is the particle density and v0 is the impact speed. Dimensionless impact energy can be obtained with defining σYD3 as the normalization factor:A uniaxial loading applying to the blades radically is cyclic according to the real condition in turbine engines. For simulating this condition, the cyclic stress σapplied varies with the time variable, τ, cf. , at load ratio of σapplied=0.1 with a maximum nominal stress σmax of 300 MPa, which is about 12 of the yield stress of René 80 applied to the specimen along x-axis (cf. The main factor for initiation cracks on the impacted site is the combination of the residual stress component in the same direction of applied load, σxx, and the elastic stress concentration factor, kt, that is equal to ktσxx.For simulating this issue, using the ABAQUS (ABAQUS Inc., 2006) is considered. Explicit method is preferable than implicit one because the speed, accuracy, and trustworthy of solving are more acceptable. Using the velocities, displacements, and accelerations of the beginning state in each increment duration is the basis of this method. Also, time increments are considered very small. A small fraction of time for this issue is on the order of 10−10 traversing the smallest element. The heat differential along the blade is considered adiabatic because the temperature at 13 of the end of the leading edge (impacted region) is always constant value (871°C) in flight duration. The Coulomb friction coefficient is taken to be 0.1 because it has a minor effect. The substrate is meshed by 20 000 4-node linear tetrahedron elements where the mesh density near the impact site is 8000 of the elements mentioned above. The spherical particle is assumed rigid which is impacted specimen with initial speed and earth gravity acceleration but the distance away from top side of the specimen (impacted site) is not important, and the existing of the same indent profile with real FOD (the same depth of the penetration and crater width) is only necessary. The noticeable point is that the histories of residual stresses and final residual geometry are recorded with the simulation, and after impact the cyclic load is applied to one side of the plate while another side of that is clamped. For superalloys, the yield stress does not increase with increasing strain rate and the strain rate (ε.) for René 80 superalloy has a minor effect and is taken to be constant form 1.167×10−4/S at 871°CNormalized penetration, δ/D, as a function of the dimensionless impact energy, Ω1/2, for three different particle diameters D1, D2 and D3 is plotted in . As seen, the crater caused by FOD is deep when the kinetic energy of the particle is high, and the relationship between δ/D and Ω is the tertiary order. The third order polynomial (3) can be obtained by fitting the data in c1, c2 and c3 have constant values and their magnitude depend on particle diameter. It means that the bigger diameter particle has, the deeper the penetration produces.The bulge width, b/t, as a function of normalized penetration, δ/D, is plotted in for three different particle diameters D1, D2, and D3. The bulge width increases linearly with normalized penetration. It can be seen that the deeper penetration produces in the specimen, the more bulge width is.There are experimental methods for measuring stress concentration factor including photoelastic stress analysis, brittle coatings or strain gauges. Although all these approaches have been successful, all have environmental and accuracy disadvantages. During the design phase, there are multiple approaches to estimating stress concentration factors. Several catalogs of stress concentration factors have been published. Theoretical approaches, using elasticity or strength of material considerations, can lead to equations. There may be small differences between the catalog, FEM and theoretical values calculated. Each method has advantages and disadvantages. Many catalog curves were derived from the experimental data. FEM calculates the peak stresses directly and nominal stresses may be easily found by integrating stresses in the surrounding material. The result is that engineering judgment may have to be used when selecting which data applies to making a design decision. Many theoretical stress concentration factors have been derived for infinite or semi-infinite geometries which may not be analyzable and are not testable in a stress lab, but tackling a problem using two or more of these approaches will allow an engineer to achieve an accurate conclusion.(c)) from three different methods (finite element method, analytical method, and photoelasticity method) is obtained, while just FEM applies to the site E.The elastic stress concentration is applied after impact. This factor is defined as the proportion of the stress at the region, local stress, to one away from the geometry discontinuity, namely, kt=σlocal/σ, where σ is the remote stress. It is obtained for crater base (A) and bulge tip (E) (cf. Whereas three dimensional nature of the problem only has a minor effect on the stress concentration behavior, we can simplify that into two dimensional problems for finding stress concentration factor at the bottom of the notch. Also in this simulation, the spherical notch fits in the shallow notch. Therefore, the center plane of the specimen included maximum depth of the notch is considered. In this case, the circular curve with a radius of D, the depth of the shallow notch, fits on the semicircular curve of the shallow notch. Because of this procedure, the 2D Peterson method Peterson's stress concentration factors establishe and maintain a system of data classification for most applications of stress analysis in both catalog and equation cases. Stress concentration factor is calculated by Peterson for each element with an elliptical hole by uniaxial stress σ as indicated in . This equation can be shown as considered in Eq. Consider the curvature, r, for the elliptical hole as mentioned in Eq. , stress concentration factor for elliptical hole can be obtained as indicated in Eq. By cutting the first element with the symmetrical axis A–A′ as it is shown in , elliptical hole is changed into an element with a notch for which stress concentration factor should be calculated. The normal stresses on section A–A′ are small and can be neglected. It can be taken as an approximate solution for an element with a shallow notch. According to this approximation, the stress concentration factor for a notch is only a function of the depth, δ, and radius of curvature of the notch. The reverse case is correct too which means that modeling the notch with an elliptical hole as indicated in can be used for calculating stress concentration factor of the notch. So, stress concentration factor of the notch is the same as one for an elliptical hole as mentioned in Eq. The elastic stress concentration factor as a function of normalized penetration for three different particle diameters D1, D2, and D3 is plotted in respectively. In these figures, kt at the crater base is obtained from three different methods, but kt at the bulge tip is gained from finite element method only. At the crater base, comparison shows that the elastic stress concentration factor obtained from analytical method is about 10% more than Kt from photoelastic method and the one obtained from finite element method is about 5% more than Kt from photoelasticity. Also at the bulge tip, the elastic stress concentration factor obtained smaller than unity which can be interpreted, namely, its z and y positions rise after impact which causes to increase the cross-sectional area at the bulge tip, with the constant applied force, becomes the stress decreasing factor It is obtained equations which are embedded into for stress concentration factor at the crater base. These equations are shown in formulas for (δ/D1, D1/t), (δ/D2, D2/t), (δ/D3, D3/t) respectively:Kt≅40.93(δD1)3−31.24(δD1)2+10.1(δD1)+1.063Kt≅66.79(δD2)3−42.96(δD2)2+11.46(δD2)+1.04Kt≅161.5(δD3)3−72.89(δD3)2+13.7(δD3)+1.017 shows that the equations above are equivalent with good accuracy which specifies that kt is independent of δ/D.In the next section, the two dimensional photoelasticity applied in this paper is described, but the question is that why three dimensional photoelasticity did not use. First of all, the applied stress which is along the longest length of the blade is first main stress, σ1, and the stress coming from the blade weight is second main stress, σ2, thus Mohr's circle for this problem will be two dimensional. Second, the length and width of the blade are much larger than its thickness, t, namely, t/L1<1/20 and t/L2<1/20, so three dimensional issue turns into the 2D.Photoelasticity is an experimental method to determine the stress distribution in a material. The method is mostly used in cases where mathematical methods become quite cumbersome. Unlike the analytical methods of stress determination, photoelasticity gives a fairly accurate picture of stress distribution even around abrupt discontinuities in a material. The method serves as an important tool for determining the critical stress points in a material and is often used for determining stress concentration factors in irregular geometries.Before discussing about photoelastic method, the review of the nature of light must be presented because this method is based on the light property. The light propagating in the positive x direction away from the source at a velocity v can be expressed asThe scope of the spectrum of visible light is a narrow band, ranging approximately 15.7 to 27.5μin. (400 to 700 nm) in wavelength. Within this range, different wavelengths are interpreted as different colors by the human eye. The wavelengths of typical colors are given in . In other words, the color the eye observes depends on the frequency or orientation of frequencies, since the velocity v is a constant.For familiarization with the principle of photoelasticity, the wave plate and the plane polariscope must be described. The wave plate, also known as a retarder or phase shifter, is an optical element, which can resolve a light vector into two mutually perpendicular component waves and transmit both waves at different velocities, as shown in . Such a material with two different indices of refraction in the two perpendicular directions is known as a birefringent or doubly refracting material. In , axis f is referred to as the fast axis and axis s is referred to as the slow axis, since vf is assumed to be greater than vs. The angle θp is defined as the angle formed by the light vector and the fast axis. Since there is a difference in velocities, both Lf and Ls component will emerge from the birefringent material at different times, or there will be a phase difference between these two component waves. The distance Δf, by which the component wave Lf in the plate trails the wave in a vacuum, is given by: where if=v0/vf is the index of refraction along the fast axis direction. Similarly, the distance Δs, by which the component wave L, in the plate trails the wave in a vacuum, given by: Thus the relative linear phase shift can be expressed asThis serves as the basis for designing optical retarders. The relative angular phase shift Δ between these two components emerging from the plate can be proved to be:It may be observed that certain noncrystalline transparent material, which are optically isotropic under normal conditions, behave like wave plates when loaded (i.e., they temporarily become birefringent and have the ability to resolve a light vector into two orthogonal components transmitted with a different velocity). This phenomenon disappears when the applied load is removed, so it is called temporary birefringent. This physical characteristic is the basis of photoelasticity. In a material exhibiting temporary birefringent, the changes in the indices of refraction are linearly proportional to the applied load or to the stresses if the material is linearly elastic. This observation was first reported by Maxwell i1−i2=k(σ1−σ2),i2−i3=k(σ2−σ3),i3−i1=k(σ3−σ1) where i1, i2, and i3 are principal indices of refraction for waves vibrating parallel to the directions (1, 2, and 3) of principal stresses; k is the relative stress–optic coefficient, usually assumed to be a material constant (it actually varies with the wavelength); and σ1, σ2, and σ3 are the principal stresses at a point, respectively.Consider a two-dimensional case, where the stressed model is a plate with its normal parallel to the direction of the propagation of the light. Assume that the in-plane principal stresses σ1 and σ2 do not vary through the thickness of the plate and σ3 is zero (plane stress case). Since the stressed model behaves like a wave or retardation plate, the light vector will be resolved into two perpendicular components emerging from the plate with a relative retardation. By using Eqs. where d is the thickness of the stressed plate. The relative angular retardation, Δ, is given by is the expression of the stress–optic law in a plane stress case. In engineering practice, the stress–optic law is more commonly expressed as where N=ϕ/2π is the relative retardation in terms of a complete cycle of retardation and is also called the isochromatic fringe order. Mf=λ/k (lb/in. or N/m) is known as the material fringe value, which is a material property for a given wavelength of light and is usually calibrated at the time of the test. The stress difference σ1−σ2 in a two-dimensional model can therefore be determined if the material fringe value Mf can be determined by calibration and if the isochromatic fringe order can be measured experimentally at each point. This is actually achieved using a polariscope. A plane polariscope is an optical instrument that can produce a plane-polarized light and can measure the resulting phase difference when the polarized light passes through a stressed photoelastic model. The plane polariscope consists of a light source and two linear polarizers. The linear or plane polarizer is an optical element, which can resolve a light vector into two orthogonal components: one is transmitted and the other is absorbed, as shown in . The axis parallel with the transmitted component is called the axis of polarization. For illustration, let the light vector striking a plane polarizer be expressed as where the initial phase is taken as zero for simplicity, it is unimportant in photoelasticity. When the light enters the plane polarizer, it is resolved into two orthogonal components, one (Lt) parallel to the axis of polarization and transmitted; the other (La) perpendicular to the axis of polarization and absorbed. These components are given, respectively, byLt=AL′cosθpeiwt=ALeiωt,La=AL′sinθpeiωt=AL⁎eiωt where θp is the angle between the axis of polarization and the incident light vector, as shown in A commonly used plane polariscope is shown in . The plane polarizer near the light source is called the polarizer and its axis of polarization is called the axis of the polarizer. The other one is known as the analyzer and its axis of polarization is called the axis of the analyzer. Since the two axes are perpendicular to each other, no light will be transmitted through the analyzer when the transparent model is stress-free, and a dark field will result. For example, when the plate model, shown in , is subjected to an in-plane loading (σ3=0), the principal stress σ1 makes an angle α with the axis of the polarizer. As described earlier, the polarizer resolves an incident light vector into two orthogonal components, but only the one parallel to the axis of polarization will be transmitted. Using Eq. , the plane-polarized light vector L emerging from the polarizer will beThis light vector enters the stressed plate, which behaves like a wave plate. The vector is decomposed into two orthogonal components in the directions of principal stress and are given byLet d be the thickness of the plate. Then the two-component waves will travel with different velocities v1 and v2 through the thickness and emerge asL1′=ALcosβei(ωt−ϕ1)andL2′=ALsinβei(ωt−ϕ2) where ϕ1 and ϕ2 are the phases shift with respect to a wave in the air (note that the velocity in a vacuum is about 1.0003 times the velocity in the air). The two components will then center the analyzer, but only the components of the two waves that are parallel to the axis of the analyzer will be transmitted, as shown in . Consequently, the final transmitted light vector La is given byLa=ALsinβcosβ[ei(ωt−ϕ2)−ei(ωt−ϕ1)]=ALsin2βsin2ϕ2−ϕ12ei[ωt−(ϕ2−ϕ1)2−π2]Because the intensity of the light I is proportional to the square of the amplitude (the coefficient of the time-dependent term), it becomes where ϕ is the relative retardation and is given byϕ=ϕ1−ϕ2=2πd(i1−i2)λ=2πdk(σ1−σ2)λ=2πd(σ1−σ2)λ indicates that the isochromatic fringe position depends on the wavelength (λ) of the light being used and the difference (σ1−σ2) of the principal stresses. It is independent of the relative position (α) of the perpendicular polarizer and analyzer. If a white light (consisting of all wavelengths of the visible spectrum) is used, the isochromatic fringe patterns appear as a series of colored bands, since the difference of principal stresses in general produces extinction only for a particular wavelength. Only when (σ1−σ2)=0 (at isotropic points), black isochromatic fringe will be observed under white light.After familiarization with the basis of photoelastic method, the test which was done for obtaining the elastic stress factor must be explained. In this experiment, the used plane polariscope for producing the isochromatic fringe order is shown in . This device has the polarizer, the analyzer, two legs for exerting the force P, and the location for placing the specimen which becomes fixed with two pins setting into two holes are existed at two ends of the specimen. For setting up the instrument, the specimen must be placed first in its location, and then the analyzer must be rotated with respect to the polarizer in order to be seen the specimen in dark color totally indicating that it is stress-free. By applying the force P=49N to the legs, this force exerting in tension to the specimen produced the isochromatic fringe order, and in the next step, the photo was taken in the best quality, with 5 mega-Pixel resolution and 10X-digital zoom, in order to process and interpret the fringes. As mentioned before, kt=σlocal/σremote and also σ=NMf/d, so the elastic stress concentration turns into following form indicates that the elastic stress concentration factor at each point is the order of the inchromatic fringe at that point divided to the order of one at the remote region where the stress is uniform, away from the geometry discontinuity (cf. , the kt=5/3 is computed for the crater base, with the normalized penetration δD1=0.09375.It is assumed that a rigid In617 superalloy sphere particle with diameter 3.2 mm and incident speed of 300 m/s is impacted normal to René 80 superalloy thin plate with t=1mm in order to find the residual stress field. show the plot of the residual stress field σxx/σY obtained from finite element analysis. that there are three primary zones of tension which are the potential sites for initiation fatigue cracks. These regions of residual tension are: outside the crater rim, denoted by B, one crater radius away from the crater, at C, and at the bulge tip, E. It can be observed from that there is a region at the bottom of the crater with compressive stresses denoted by A, counterbalancing the residual tensile stresses in deep indents.ktσxx, which is the main factor for crack initiation as mentioned before, is smaller than 0.45σY at the bulge tip E, with reference to for gaining the elastic stress concentration and for σxx, which is why the crack initiation has not been observed in real FOD at this site. So, the comparison between static indent and dynamic impact stresses is done just for three regions out of four potential crack initiation sites in the next section.For comparison, the profile of indentation due to dynamic impact must be the same with one existing by quasi-static analysis. In this case, there is a crucial condition: the diameter of the particle in two methods must be the same. There is a question that must residual stresses values due to both methods be same related to the same indentation profiles. In the next paragraph, this question and the quasi-static analysis is explained concisely.The normal impression of an In617 superalloy spherical particle into a thick René 80 superalloy substrate is considered as the quasi-static method. As sketched in , a rigid sphere of three different diameters D1, D2, and D3 is pushed into a half-space by a static load P. The indentation load is then removed so that the contact diameter is w and the indent depth is δ, both measured after unloading. The half-space is taken to be initially stress-free and infinitely deep, consistent with the assumption that the foreign object is small compared to the substrate thickness. The functional form introduces the experimental relationship between the static load P and the indent depth, δ:The relationship between δ and w is, as mentioned before:Here, σu is ultimate tensile stress. For René 80 superalloy substrate, σu=650MPa is considered. The necessary force P to produce the certain w and δ in the quasi-static chisel indenter is presented in Eq. . To find the dynamic residual stresses, a rigid In617 superalloy sphere with three different diameters and several incident speeds impacting normal the René 80 superalloy thin sheet with t<1.3mm is considered. The comparison between the static indent and the dynamic impact stresses, with the same indent profile, at regions A, B and C as a function of normalized penetration δ/D1, δ/D2, and δ/D3 is plotted in , at crater base A, there is the difference of 30% between the static indent and dynamic impact stresses at δD1=0.26 becoming 50% at δD1=0.34, and at regions B and C, stresses are in the range of 0.95σY–1.38σY. It can be observed from that at the crater base A, the difference between the static indent and dynamic impact stresses is 27% at δD2=0.3, and which becomes 40% at δD2=0.424, and stresses existing by the two methods are in the range of 0.86σY−1.21σY at B and C, also as seen from , there is the difference of 26% at δD3=0.33 getting 36% at δD3=0.39 at A, and at B and C, stresses are in the range of 0.6σY–0.96σY. By the way, the stresses difference between the two methods at regions B and C is negligible as seen from three figures above.Based on the numerical, finite element method, evaluation of a spherical hard-body impact on a thin plate of a René 80 superalloy and experimental stress analysis for finding the elastic stress concentration factor, the following conclusions have been obtained:The FEM results showing ktσxx is more than the yield stress of the substrate at three critical out of potential regions is responsible for crack initiation, and compatible with the several available damaged blades.The more δ/D in deep indents, the more intense compressive stresses at the crater base causes to prevent from crack propagation, consistent with the observed damaged blades in real cases.The comparison between static indent and dynamic impact shows that stresses are quite close, except at the crater base of deep indents.Stress concentration factor at the crater base, which is independent of particle diameter, D, increases with δ/D increments.Although photoelastic method is usually used for calculating stress concentration factor, using it for very shallow notch has some difficulties such as taking a high quality picture and then interpreting the image of it. If possible, it is suggested that analytical and finite element methods are used for calculating stress concentration factor; however, the results obtained from photoelastic method are more reliable.The elastic stress concentration factor results show that three dimensional FEM results at the crater base agree well with two dimensional photoelastic and analytical methods clearing that the logical assumption, two dimensional applied stresses to the blade, was correct.(c)), the more the diameter of the impacted particle, the less δ/D the difference between static indent and dynamic stresses starts to exist in, and the more δ/D, the more stresses difference, and also in the same δ/D, the more the diameter of the impacted particle, the more stresses difference too.The start point of turning tensile stresses, both static and dynamic, into compressive is about δD=0.26 which is independent of the spherical hard body diameter.(c)), the more the diameter of the impacted particle, the more intense tensile stresses values, from both methods.Microstructural evolution of strain rate related tensile elastic prestrain on the high-cycle fatigue in medium-carbon steelWhen engineered structures undergo regular cyclic loading processes, they would often be affected by extensional strain. To highlight the effect of tensile strain rate on subsequent fatigue damage in medium-carbon steel, predeformation was entirely controlled in the elastic regime with strain rates ranging from 10−5s−1 to 10−2s−1. Evolutionary response of sample temperature and peak cyclic strain, microstructures, internal fatigue initiation, fatigue propagation in samples fractured during tensile elastic prestrain (TEP)-HCF tests were studied. Our results revealed that compared with non-prestrained, the effect of TEP rate on fatigue life was non-monotonic and beneficial. Strain rate related TEP had fundamentally realized lattice structure reconstruction and transform in sliding mode, and overall slipping of lattice structure and free consumption of interface dislocations that resist fatigue crack propagation was key for the observed leap in fatigue strength.Medium-carbon steel typically has carbon content in the range of 0.3–0.6 wt%, and it can possess a good balance between ductility and strength. Medium-carbon steels are typically used in large-sized components, forgings, and machined components. Besides, these components that bear cyclic loading will often be subjected to instantaneous and violent loading during normal operation, such as large strain, instantaneous impact, etc. It is foreseeable that the study of prestrain loading is important for a wide array of uses in safety evaluation on fatigue performance of structural steels and vehicle components. Scholars first made materials strain to a certain degree, and then carried out fatigue cyclic loading to study the prestrain fatigue properties of the materials, which has made great progress in the last few decades. In 1959, Dugdale [] was among the first scientists to highlight that the response of a material to cyclic loading may in some cases depend on its previous strain history. To date, the effect of prestrain deformation on fatigue behavior has been studied by researchers in this field for decades. More and more studies have shown that the “memory effect” of prestrain has important influence on fatigue properties of metallic materials [] highlighted that effect of prestrain on 304L type stainless steel is mainly due to back stress. It is considered that the prestrain memory effect of fcc lattice metal materials is more reflected in the internal stress response, while little effect on grain boundaries []. When the prestress was low, the fatigue notch sensitivity reduction of two-phase steel DP600 helped to increase the fatigue strength [] et al. pointed out that the prestrain greater than 15% has a positive effect on the fatigue resistance of low carbon steel, and the fatigue strength has increased by nearly 50%. From studies of low alloy high strength steel and double phase steel, it was found that the effect of prestrain on fatigue strength not only depends on the prestrain level [], but also depends on cyclic plastic strain accumulation caused by the degree of stress ratio [In additions to the reasons mentioned above, tensile prestrain memory effect on subsequent cyclic behavior is consistent with the fact that it may be related with the stability of the dislocations structures inherited from the prestrain []. Prestrain induces a high dislocation density with large stored energy in medium-carbon steels, and during fatigue the stored energy will help in rearranging the tangled dislocations and accelerating the crack growth process [The different observed effects during monotonic and cyclic deformations of metals are mainly influenced by the nature of the material (the stacking fault energy), physical-metallurgical factors (grain size, impurities, particles, precipitation, etc.), and the deformation conditions (loading type, strain rate, and temperature) []. Although the effect of quasi-static plastic prestrain on the high-cycle fatigue (HCF) effect of metallic materials was well studied, the mechanisms and microstructure evolution of tensile elastic prestrain (TEP) on the HCF remain unclear enough. Zhu et al. studied the effect of rate related TEP on HCF process of SAE 1050 steel and found that the elastic prestrain rate had a clear effect on the subsequent HCF, the impact of which was non-monotonic. Furthermore, it is necessary to understand the microstructure and local stress/deformation distribution on crack initiation and propagation during the rate related TEP on HCF process.Therefore, medium-carbon steel SAE 1050, a material usually used in wheels, axles, gears, and components that are required to possess higher cyclic fatigue resistance [], was used in this paper. In the elastic prestrained stage, constant prestrain deformation was maintained at 0.16%, which was close to the low yield point, and elastic predeformation strained at different strain rates ranging from 10−5s−1 to 10−2s−1. Subsequently, stress-controlled HCF tests were performed in air at room temperature with a constant stress amplitude of 402 MPa that was determined by the strain rate related yield stress, and sinusoidal wave loading with a stress ratio of 0.1.In the current study, medium-carbon steel SAE 1050 was used in this work. The material as received was hot rolled, and heat treatment was carried out at 860 °C for 1.5 h and after quenching at 840 °C, the steel sample was tempered at 460 °C for 2 h to achieve a homogeneous microstructure. Steel sample having a typical dual-phase metallurgical structure with the ferritic-pearlitic microstructure, as seen in The geometry and dimensions of the specimens are illustrated in . The gage length and diameter are 44 and 8 mm, respectively. All the analyses, including the tensile and fatigue tests, were carried out on specimens with geometry that satisfied the requirements of ISO 6892-1: 2009 and ISO 1099: 2006(E) international standards for both tensile and fatigue testing.Specimens prestrained under tensile loading were analyzed using a CMT 5305 servo-hydraulic testing machine equipped with an electro-mechanic extensometer under constant total strain amplitude (0.16%) control, with different strain rates between 10−5s−1 and 10−2s−1. The prestrain deformation was completed within the elastic regime.Subsequently, the cyclic deformation behavior of the prestrained specimens was investigated in the HCF regime by using a GPS 100 resonant testing device, an electromagnetic shaker based HCF test machine, at a frequency of 115 Hz determined by resonance with the specimen and the device that was within abnormal vibration frequency range of high-speed railway wheels []. The strain rate has a clear effect on the yield stress of metallic materials [] that is also sensitive to ambient temperature, as shown in . Therefore, the entire HCF monitoring experiment was carried out under a constant of maximum tensile stress amplitude of 402 MPa, which was below the estimated low yield stress that could reach 406 MPa on the condition that the frequency of the specimen is consistent with the high-frequency testing machine in air at 20 °C [], and sinusoidal wave loading with a tensile stress ratio of 0.1. During the process of HCF, the specimen temperature was continuously measured with both the help of thermocouples and strain foil on the area of the sample gage up to the point where the specimen experienced fatigue failure, which was helpful to characterize the thermodynamic response of specimens under the same fatigue test prestrained at different elastic tensile strain rates. And, the continuous acquisition of cyclic strain depends on the NI-9235 module of National Instruments.Microstructures of both prestrained and prestrain-fatigued specimens were characterized by transmission electron microscopy (TEM; FEI Tecnai F20 instrument) operated at 200 kV to study the influence of the prestraining rate on the microstructural evolution and the fundamental fatigue micro mechanisms in operation. In addition, fracture morphologies of the fatigue failed specimens were observed by scanning electron microscopy (SEM) (JEOL JSM-7001F). EBSD samples prepared as longitudinal sections were cut near the fatigue crack initiation sites along the radial cross-section from the fracture surface. Afterwards, careful grinding and mechanical polishing, as well as an electropolishing finish were applied.Prior to HCF testing, specimens were chosen to be prestrained at 0.16% with different straining rates ranging from 10−5s−1 to 10−2s−1. The variation of the lifetime of the specimens as a function of the prestrain rate during HCF is shown in . First, it should be pointed out the fatigue life of materials without prestrained was all below 300000, and the prestrained with different strain rates would improve the fatigue life in varying degrees. Besides, the influence of TEP rate on fatigue life was nonlinear and nonmonotonic, interestingly, which indicated that at least two conflicting mechanisms governed the process of HCF behind. It is clearly seen that HCF lifetime increases initially with increasing pre-straining rate but reduces subsequently, and the maximum durability of the non-monotonous curve is in the internal of 10−4.5s−1 to 10−3.5s−1 of TEP rate. Reasons for nonmonotonicity of lifetime changes with pre-straining rate are discussed in section During HCF, 5 representative samples were selected for continuous collection of temperature and cyclic strain responses, as shown in Although strain rate related prestrain was completed within the elastic regime, it had a very significant response to the temperature and cyclic strain during subsequent fatigue. When the prestrain rate was low, temperature response of the sample reached the maximum value at the beginning of fatigue, and peak cyclic strain also reached the maximum, which was close to 0.2%. In the residual fatigue process, the temperature and cyclic strain response were relatively stable until fatigue fracture. Besides, it was worth noting that those of strain rate 10−4s−1 under elastic prestrain were the lowest in all experiments. Conversely, when the prestrain rate was high, the temperature of the specimen remained relatively stable before the fracture, and the cyclic strain presented a slow cumulative trend of evolution until the maximum peak response that was reached at fracture. In aggregate the peak response of cyclic strain had a higher increased uptrend than that of low prestrain rates.Compared with the prestrained, the fatigue life of the original specimen was the least. The responses of temperature and peak cyclic strain both reached their maximum value in the very beginning of fatigue.The characteristics of the fracture surface were investigated to study the areas where potential microscopic plastic strain could occur, which would help to determine the driving force for crack initiation and propagation.When the prestrain rate was relative lower (-I, II), fatigue source fracture was dominated by cleavage-like facets and microcracks, which indicated the existence of enhancement units with several microns and had larger free volume resistance to the initiation of fatigue source. On the contrary, striations along the direction of crack propagation and tiny secondary cracks were the main observed features for that the prestrain rate was higher (-III, IV). Analogously, finer fatigue striations and more secondary cracks were found in In the fatigue stable crack propagation stage of prestrained, a large number of fatigue striations, facets and secondary cracks were the main fracture characteristics. The difference was that the surface was relatively coarse at lower prestrain rates (-I, II), whereas it was smooth when the prestrain rates were higher (-V with non-prestrained, more facets and cracks were found, but no significant striations appeared. Those showed different degrees of resistance to fatigue crack propagation just by prestrained with different strain rates and non-prestrained.The microstructures characteristic of pre-fatigued samples is shown in . Following TEP with a lower pre-straining rate, there were few dislocations within the original structure, most of which were confined to the grain or phase boundaries. However, interestingly, with the increase in prestrain rate, more dislocation multiplications and greater dislocation density existed in the interior of grains other than at boundaries. However, the dislocations hadn't already formed walls or cells during the process of TEP., dislocation microstructures on the cross-sectional area near the fracture surface of the specimens have been imaged. It was interesting that the evolution of dislocations seemed to have continued and maintained special genetic heredity that preexisted in the interior of prestrained samples with different prestrain rates. For example, in the sample that was prestrained at the lowest rate of 10−5s−1, dislocations were still limited to the boundaries, and only a small amount could spread into grains. In (II) with prestrain rate of 10−4s−1, it shows a TEM image in which most local nearly parallel arranged free dislocation lines extended evenly on activated slip bands within grains, however, only a few dislocations were gathered at boundaries. With increase in prestrain rate, an increasing number of dislocations were accessed, wound, and pinned even further within structures ((III, IV)). When the sample with non-prestrained, the structure had formed a clear system of dislocation lines, cells and walls, similarly, most of which were also pinned within grains ((V)). It could be concluded that with increasing prestrain rate, a higher local microscopic plastic strain was produced in the internal structure of grains.For EBSD measurements, longitudinal sections beneath the fatigue source were prepared. Inverse pole figures on equator plane of cubic crystal system (001) plane are shown in . Some differences and features became obvious regarding the EBSD mappings with TEP rates ranging from 10−5s−1 to 10−2s−1 and non-prestrained:The prestrained specimens showed a higher point-to-point misorientation in grains beneath the fatigue fracture surface, compared to lower prestrain rates, demonstrated by increased areas of multi-colored individual grains in the images. The evolution of the microstructure orientation of the specimens cyclically loaded was generally classified into four stages: inconsistent microstructure orientation (-I), uniform microstructure orientation within individual original grains (-II), fine subgrains with high-angle grain boundaries inhomogeneous distribution (-III, IV) and fine grains with higher angle grain boundaries uniform distribution away from the fracture surface layer within individual original grains (With increasing prestrained rates, subgrains aggregation gradually emerged and moved toward the grain interior. It can be judged that prestrain rates affected the distribution and dissipation of microstrain.High-magnification of EBSD orientation mappings revealed that most microstructure orientations within grains or sub-grains just beneath the fatigue source were approximately inclined to slip planes of {110} and {112}, primary slip planes in BCC crystal structure, demonstrated by areas colored green and purple respectively.However, it was not all cases that the primary and easy slip planes appeared in the position near the critical surface of fatigue source. Thus, it can be seen that the responses of lattice reconstruction to cyclic deformation were distinctly different: (I) no sufficient digestion or absorption fatigue cyclic strain energy through lattice slipping, (II) homogeneous lattice deformation. From this view point, a certain amount of strain rate could result in a positive effect in lattice strengthening. However, when the prestrain rate was higher than 10−3s−1, sub-grains with smaller grain size generated at the high-angle boundary were dendritic, extending into the interior and spreading. Besides, only microstructure orientations on fracture surfaces within small sub-grains were approximately uniform and inclined to the primary slip plane. Accordingly, the contribution of homogeneous lattice deformation within sub-grains to lattice strengthening was weakness. It was thus clear that homogeneous slipping and unified volume of lattice were the two keys to fatigue strengthening., evolution features of grains and lattices beneath the fatigue propagation interface were correspondingly similar but weakened to some extent. Before the crack propagation, the microstructure had undergone evolution to various degrees. There were more high-angle grain boundaries near the fatigue propagation interface, and the effect on the grain boundary to hinder the crack propagation was bound to be more significant. No matter what stage of fatigue fracture process, it was along the interface position of uncoordinated strain, depending on gradient difference in degree of reinforcement on both interface sides.From the experimental results of TEP-fatigue, it was found that the strain rate had a significant effect on the subsequent fatigue behavior, even if the prestrain was completely controlled in the tensile elastic strain zone. For homogeneous materials, the fatigue source was closely related to the heterogeneous microstructure formed by local microplastic deformation. Whereafter, the movement and deflection of slip bands would easily occur at the interface between both sides in non-uniform deformation, which was beneficial to counteract or accumulate cyclic strain energy. It was found that different dislocation structures appeared in the specimen of SAE 1050 steel just after the process of tensile elastic predeformation, which would help to provide different sites and locations for the occurrence of heterogeneous microscopic strain during the subsequent fatigue tests []. Elastic prestrain rate had various influences on fatigue initiation and propagation, lattice deformation and microstructural remodeling in subsequent fatigue process, which would lead to fatigue life increasement in varying degrees by prestrained with different rates.Through the collection of continuous temperature and cyclic strain during the fatigue process, it was found that the temperature all increases rapidly at the beginning of fatigue, but the response of peak cyclic strain increasing rate before stability was not the same.Under a low strain rate of predeformation at 10−5s−1, slip dislocations were fewer and inclined to pile up at the grain boundary during fatigue ((I)). Accumulation of plastic strain produced by fatigue was concentrated on the original existing surface defects, grain boundaries and phase interfaces. The dislocation accumulation at boundaries was easy to form shear effect through dislocation climbing, and it was responsible for fatigue damage []. TEM characterization helps to master the main law, but it is difficult to analyze the distinct structural response on fatigue source region. In the EBSD investigation, it was observed that microstructure orientations within original grains beneath the fracture surface were most inclined to slip planes of {110} and {112}, the primary slip planes in BCC crystal structure, but other than that lattice orientations on fatigue source were chaotic. Besides, during cyclic deformation, the planar slip tends to assemble in certain dislocation bands, which would provide a much convenient channel for vacancies diffusing to the GBs and give rise to deformation localization []. For the localized deformation case, strain concentrated in narrow areas, causing great fatigue damage []. Therefore, the peak cyclic strain increasing rate was faster before reaching stable stage, which reflected a weaker cyclic hardening ability. Dislocation gathering at original grain boundary was initially attributed to the sliding or torsion of lattice plane within local individual grains on the fatigue interface. However, a lower prestrain did not form an integral and uniform lattice strengthening within the whole original grain. As the cyclic strain progressing, the mismatch between two different lattice structures in the grains began to increase, leading to both an increase in uncoordinated cyclic strain and a decline in the mobility of free dislocations. Accordingly, cyclic strain response was stable and had a trend of slow cyclic hardening during most time of fatigue initiation. And, more concentrated and obvious signs of brittle fracture, wider secondary cracks and smaller facets of 2–5 μm diameter were appeared in the fatigue source surface. Therefore, the fatigue initiation mechanism under low prestrain rate of 10−5s−1 was similar to dislocation oscillations of lattice structures within local original grains and dislocation cross-slipping at grain boundaries.With the increase of the prestrain rate, it was interesting to find that there were more homogeneous large-area and low-angle interfaces in the grains beneath the critical surface of fatigue source. As a result, more uniform interfacial strengthening occurred within the original grains. As seen from II and II’, in the crack source region, for 10−4s−1 prestrain rate, it was exhibited that microstructure orientations within original grains on the fracture surface were favorably parallel to one of the primary slip planes, which reflected uniform lattice deformation in the original grain as a unit. It had been found that, prestrained by appropriate strain rate of 10−4s−1, slipping dislocations may be released during the fatigue process, which improved the intracrystalline deformation homogeneity [] and delayed the nucleation of the micro-scale cracks []. Meanwhile, for the prestrained specimen, many gliding dislocations may firstly be formed in the “soft orientation” grains, though the prestrained by appropriate strain rate, and the gap between the applied stress for dislocation slipping in “soft orientation” and other grains became small []. So, it can be concluded that the both intracrystalline and intergranular deformation homogeneity would enhance with appropriate strain rate of 10−4s−1. The uniform strengthening by sub-interfaces and weakening at original grain boundaries consumed the excess cyclic strain energy with larger deformation volume. Therefore, as the cyclic strain progressing, cyclic strain response had a trend of aggrandizement hardening effect during most time of fatigue initiation, and the fatigue source fracture was characterized by typical brittle fracture features of smaller secondary cracks and larger facets. As a result, it had the longest fatigue life. Therefore, the fatigue initiation mechanism under appropriate prestrain rate of 10−4s−1 was similar to slow lattice dislocation oscillations within the whole original grains and inhibition of dislocation cross-slipping at grain boundaries.With further increase in prestrain rate, slip dislocations were accessed, wound, and pinned within organizational structures to form new dislocation structures within different organizational phases whether soft (ferrite) or hard phase (pearlite) resulting from accumulation of micro plastic strains ((III, IV)). In a short time before free dislocations forming complex interfaces structure in the grain, it was positive enhancement by dislocations multiplication in short range order. So it was different from lower prestrain rates, when the prestrain rate was faster than that of 10−3s−1, that cyclic strain response had a faster trend of hardening just at the fatigue beginning. However, cyclic strain softening during most time of fatigue initiation was largely due to interfaces formation and easy cross-slipping of dislocation []. In fact, cell boundary activities can be readily activated by the stress field built up by the high density of extrinsic dislocations in the non-equilibrium cell boundary []. In turn, the dislocations lodged in cell boundaries can easily facilitate cell sliding and rotations across the cells []. In the EBSD investigation, it was clearly noticed that heterogeneity of sub-grain size with medium or high-angle boundaries on the fatigue source was the typical microstructure as the prestrain rate was faster than that of 10−3s−1. Fine micron sub-grains had already been formed before fatigue initiation, and all microstructure orientations on fracture surfaces within sub-grains were approximately uniform and inclined to the primary slip planes. So that obvious degrees of lattice strengthening formed between the sub-grains on the fatigue interface. However, the threshold of uncoordinated strain in the sub-grains on both sides of the interface caused by the difference in the size of the sub-grains was much lower than those where the prestrain rate was lower. Under the restriction of these special micro-structure, lower incompatible strain energy threshold and mobility of free dislocation resulted in a large number of near parallel fatigue striations appeared near the source location reminiscent of the occurrence and dominance of “locally” brittle failure mechanisms at the fine microscopic level, leading to a sharper reduction in fatigue life. Therefore, the fatigue initiation mechanism under higher prestrain rate than that of 10−3s−1 was similar to rapid dislocation oscillations within new sub-crystalline structures and dislocation cross-slipping at medium-angle boundaries of sub-grains.Compared with prestrained, non-prestrained was different in fatigue initiation process and mechanism under the identical fatigue condition. Incorporating with the analysis of EBSD characterization of micro-structure on fatigue source, homogeneity and high-density of sub-grain size with high-angle boundaries on the fatigue source had been formed before fatigue initiation. At the initial stage of fatigue, it could help to increase the response of peak cyclic strain by nucleation and propagation of massive free dislocations. Due to high frequency loading characteristics of HCF, finer and more uniform sub-grains with 1~3 μm diameter were generated (-V’). A large number of dislocation multiplication and lackness of prestrain strengthening led to stronger cyclic softening in the initial stage than those of prestrained. Then it entered a stable and slow cyclic hardening during long-term fatigue source initiation process, which was mainly result from the short-range order and the planar slipping in sub-grains with smallest scales (-V). Most lattice distortions within sub-grains and surface defects on the sub-grain boundaries led to the shortest fatigue life. Accordingly, the fatigue initiation mechanism under non-prestrained was similar to rapid dislocation oscillations within fine sub-grains and dislocation cross-slipping at high-angle boundaries of sub-grains.Fatigue initiation is defined as short and mixed-mode crystallographic cracks, while fatigue propagation stage is long cracks growing via a plastic blunting or a ductility exhaustion mechanism []. Through EBSD analysis, it was found that the interface distribution with random boundary angles and microstructure had evolved in different degrees before crack propagation. Compared with the fatigue source, the accumulation of cyclic strain was all controlled by the sub-grain multiplication and lattice reconstruction in the original grain, and the strength of the barrier also depended on the relative orientations of the microstructure at the boundary. However, the degree of lattice reconstruction in grains or sub-grains was relatively lower than that on fatigue source, which presented more randomness. Therefore, the fatigue crack had expanded before primary slip planes formed within grains or sub-grains, leading to a lower degree of cyclic strain energy consumed by lattice reconstruction and sub-grain nucleation. In addition, the grain boundaries with much surface defects played an important role in the fatigue propagation stage. Accordingly, no matter prestrained or non-prestrained, facets and secondary cracks were prevalent on the fracture surface.Fatigue damage mechanisms of SAE 1050 steel under elastic prestrained with different rates and non-prestrained are refer to . For the prestrain or non-prestrain-fatigue process in this paper, the fatigue interface was mainly in the region where the non-equilibrium plastic strain locally generated. It was assumed that only the stress normal to the critical interface was responsible for fatigue damage []. In addition, strain rate related TEP had fundamentally realized lattice structure reconstruction and transform in sliding mode. Both dislocations impingement on the interface and a significant increase in the grain boundary interfaces were not favorable for improving the fatigue properties.In this study, we carried out HCF tests on the TEP-ed with rates ranging from 10−5s−1 to 10−2s−1 and non-prestrained to reveal the effect of microstructure and lattice slip modes on the fatigue machanisms. Following conclusions can be drawn:Compared with non-prestrained, the effect of TEP rate on fatigue life was non-monotonic and beneficial. It will help to provide a scientific support for the research on elastic fatigue damage and physical enhancement fatigue mechanisms.When the prestrain rate was at low strain rate between 10−5s−1 and 10−4s−1, the fatigue initiation mechanism was similar to dislocation oscillations of lattice structures within local original grains or dislocation cross-slipping at grain boundaries. Cyclic strain response was first softened and then slowly hardened. In this section of prestrain rates, with the enhancement of both intracrystalline and intergranular deformation homogeneity at an appropriate strain rate of 10−4s−1, microstructure orientations on fracture source surface within original grains were approximately uniform and inclined to primary slip planes {110} and {112} in BCC crystal structure, which contributed to delay the fatigue initiation.When the prestrain rate was at high strain rate between 10−3s−1 and 10−2s−1, the fatigue initiation mechanism was similar to rapid dislocation oscillations within new sub-crystalline structures and dislocation cross-slipping at medium-angle boundaries of sub-grains. Cyclic strain response was first hardened and then slowly softened. High prestrain rate was helpful for the grain refinement and reconstruction of lattice structure in the original grains in the initial stage, but fewer incompatible strain energy threshold and lower mobility of free dislocation and more surface defect on the sub-grain boundaries resulted in a sharper reduction in fatigue life.The fatigue initiation mechanism under non-prestrained was similar to that of prestrained with high strain rates. Cyclic strain response was characterized by rapid softening followed by slow hardening. Without prestrain hardening, due to high frequency loading of HCF, lattice distortions within sub-grains and surface defects on the sub-grain boundaries led to the shortest fatigue life.On fatigue propagation interface, the degree of lattice reconstruction in grains or sub-grains was lower than that on fatigue source interface, and the grain boundaries with much surface defects played more important role in fatigue propagation stage.For the prestrain or non-prestrain-fatigue process in this paper, the fatigue interface was mainly in the region where the non-equilibrium plastic strain locally generated. Strain rate related TEP had fundamentally realized lattice structure reconstruction and transform in sliding mode. Overall slipping of lattice structure and free consumption of interface dislocations that would help to consume the incompatible strain energy and enhance the fatigue strengthening mechanisms.Asymptotic fields of stress and damage of a mode I creep crack in steady-state growthAsymptotic fields of stress, strain rate and damage of a mode I creep crack in steady-state growth are analyzed on the basis of Continuum Damage Mechanics by employing a semi-inverse method. A damage field for steady-state crack growth represented by an undetermined power function rl of radius r from the crack tip is assumed first, and the corresponding asymptotic stress field of a mode I crack in a non-linear creep damage material is analyzed by solving a two-point boundary value problem of non-linear differential equations. Then, the exponent l of undetermined damage field is determined so that the assumed damage field may be consistent with the resulting asymptotic stress field and the damage evolution equation. Finally, the relations between exponent p of the asymptotic stress distribution and exponents n and m of power creep constitutive law and the power creep damage law are elucidated. The effects of material damage on the crack-tip stress field in non-linear materials are discussed in detail. Comparison between the results of the present analysis and those of earlier papers of fracture mechanics on the creep-crack growth analyses based on grain-boundary cavitation is also made.) has been obtained for an ideal discrete crack in intact non-linear hardening materials, the fracture process in usual ductile materials is brought about by nucleation, growth and coalescence of distributed microscopic cavities in front of the crack-tip, and this damage field gives significant influence on stress field near the crack-tip. Therefore, analyses of effects of material damage on the stress and strain fields near crack-tip in non-linear materials provide very important problems not only for evaluation of crack behaviour in materials but also for discussion of stability and convergency of numerical analyses. In this context, these problems have been discussed in a number of papers, especially for elastic–plastic-brittle cracks (In the case of creep cracks, in particular, the asymptotic stress fields at the crack-tips in materials subject to damage were analyzed by for mode I and mode III creep cracks in steady-state growth, and by for a mode I stationary crack. However, because of difficulties of stress-damage coupled analysis, they could not derive complete and consistent results. Namely, could not satisfy the boundary conditions of a sharp crack in their numerical analysis, and obtained an approximate solution by replacing the boundary conditions by those of a V-notch; this replacement may lead to a significant error in stress singularity at the crack-tip (, on the other hand, made a priori assumption of vanishing stress components at the crack tip, this assumption may give too much constraints to the analysis; i.e., these analyses may need further refinement.One of the major causes in difficulty in the analyses of crack tip fields in damaged or strain softening materials is concurrence of the elliptic and hyperbolic regimes of the governing field equations together with related discontinuity in deformation gradient and stress (). Moreover, the mathematical structure of governing equations may be affected largely by the modeling of damage., furthermore, analysed the influence of creep damage on crack-tip fields under small-scale-creep conditions by the use of finite element method. However, because their analysis is numerical and is concerned with a blunt crack, systematic information on the effect of material damage on the asymptotic crack-tip field is not available from the analysis.Because of the engineering importance, a number of papers discussed the problems of creep-crack growth also from the view point of fracture mechanics and micromechanics (). However, most of these analyses are not only one-dimensional and are focused on a plane in front of the crack-tips, but also disregard the effect of damage on the stress fields. Therefore, systematic and three-dimensional analyses of the crack-tip field in materials undergoing creep damage are hardly available in these papers of fracture mechanics.The present paper is concerned with an elaborate continuum damage mechanics analysis of the asymptotic fields near a mode I creep crack in steady-state growth; damage field and its effects on the asymptotic stress- and strain-rate fields at the crack are solved by the semi-inverse method. Namely, a damage field for steady-state crack growth represented by an undetermined power function rl of radius r from the crack tip is assumed first, and the corresponding asymptotic fields of stress and strain-rate of a mode I creep crack are analyzed by employing power-law creep damage theory (). Then, the exponent l of the undetermined damage field is determined so that the assumed damage field may be consistent with the resulting stress field and the damage evolution equation. Finally, the relations between exponent p of the asymptotic stress field at the crack tip and exponents n and m of power creep constitutive law and the power creep damage equation are elucidated. The effects of material damage on the crack-tip stress field for non-linear materials are discussed in some detail. Comparison between the results of present analysis and those of earlier papers of fracture mechanics on creep-crack growth analyses based on grain-boundary cavitation is also discussed.Let us take a mode I creep crack extending at a constant rate v in a stationary cartesian coordinate system O−X1X2X3 as shown in , and assume that the material in the vicinity of the crack is in the state of plane strain or of plane stress. Then, we further move cartesian coordinates o−x1x2x3 and polar coordinates o−rθz with origins o at the tip of moving cracks, where the direction x1 and that of θ=0 are in the direction of crack extension. By denoting the components of stress and strain with respect to moving coordinates by σij and εij, the governing equations for a mode I creep crack in steady-state extension are given as follows: denotes the material time derivative with respect to time t.If we represent the damage state of material by an isotropic damage variable , and employ the hypothesis of strain equivalence in damage mechanics, the creep constitutive equation of a damaged material can be given as follows ( are the deviatoric stress and the equivalent stress, respectively. The symbols n and A are the creep exponent and material constant, respectively.By assuming that the creep damage is governed by the equivalent stress, the damage evolution equation in multi-axial state of stress may be given as follows ( denote material constants. In the particular case of steady-state crack growth, we haveSince the present paper aims to elucidate the effect of material damage on the asymptotic fields near the creep-crack tip, we will assume the following asymptotic solution for the crack-tip stress: where K and s are undetermined constants, while is an unknown function of θ. By substituting , we have the components of the asymptotic stress field as follows: where p=s−2 represents the exponent of stress field, and are given by expressions in the corresponding brackets [ ] in , the undetermined constant K corresponds to the stress intensity factor of a non-linear material and depends on exponent n of the creep constitutive equation In order to determine the asymptotic stress field at the crack-tip, we will have to determine first the damage field were determined, then by substituting the creep rate obtained from the resulting D and stresses of , a set of non-linear ordinary differential equations for the unknown function could be derived. However, it is difficult in general to derive a rigorous solution of throughout the whole region of analysis.Thus, in the present analysis, we will determine by semi-inverse method an asymptotic damage field which satisfies the evolution equation in the region in front of the crack-tip. Namely, by referring to experimentally observed damage field (), we first postulate an elliptic damage distribution represented by a power function . Then, the asymptotic stress field can be obtained by the use of resulting damage field and , and finally the exponent l of the undetermined damage field can be determined so that the postulated damage field together with the relevant stress field may satisfy the damage evolution equation According to the experimental observation on the damage distribution around a mode I creep crack in OFHC copper at 250°C in steady-state growth (), contour of the damage field can be represented by a semi-ellipse in front of the crack and by a wake parallel to the crack plane behind the crack.In view of this observation, we will now assume the damage distribution of where l and r0 are parameters characterizing the damage distribution, while and k denote the θ-distribution of the damage field and its aspect ratio. The locus , in particular, represents the boundary of the damage field where D=0, and hence is the boundary between the damaged and the undamaged region.As described already, by substituting the stress and damage fields of , and then by substituting the resulting creep rate , we can readily obtain the differential equations governing unknown function . The differential equations can be written for the states of plane strain and plane stress as follows:Because of the symmetry of the stress components σrr and σθθ at θ=0 and of the vanishing condition of the stress components σrθ and σθθ at the crack plane θ=π, we have the following two boundary conditions for the differential equations ) as an initial value problem. For this purpose, the initial values of should be specified besides the initial conditions of are homogeneous with respect to function can be specified arbitrarily. As regards , on the other hand, we will specify a proper undetermined constant β. Then, besides the condition are prescribed for the differential equations In order to calculate the differential equations by a shooting method for a given damage field (i.e., for given l and can be readily integrated numerically if the values of the exponent s in are given properly. Thus, the values of s and β can be determined as the eigen values of the differential equations such that the numerical solution can be determined as an eigen function of the eigen values The numerical integration of differential equations are performed by the fourth-order Runge–Kutta method, while the solution of non-linear simultaneous equations for are obtained by the Gauss–Newton least-square method so that they satisfy the condition are not unique in general. Thus, we will obtain only the solution which corresponds to the lowest exponent s, and this lowest exponent s is subjected to the following condition of the bounded stress work done in a material element including crack tip: In the above analysis, the two-point boundary value problem of differential equations was calculated for the prescribed damage field of , and gave the relation among the exponent of the damage distribution l, the creep exponent n and exponent s (or p) of the stress distribution. However, the damage field is not consistent with the damage evolution equation and the resulting asymptotic stress field.Since the determination of the damage field which satisfies the damage evolution equation for the entire region of the problem is difficult, we will satisfy this condition approximately by specifying the damage field of so that it may be consistent with the evolution equation only in the region in front of the crack because this region gives largest influence on the asymptotic fields.On the crack plane θ=0 in front of the crack, the evolution equation In order that this condition could be satisfied always, we have the following relations:which specifies the exponent l of the damage distribution implies that the crack rate v is proportional to the coefficient B of the damage evolution equation , exponent of damage distribution has the value 0≤l<1, and hence predicts the infinite crack rate v=∞ in the case of uniform damage l=0.The stress and the damage field in front of an extending crack together with the ensuing creep-crack growth rate depends significantly on the level of applied load (). The creep-crack growth rate v under HRR field has been reported to be characterized by the non-linear fracture mechanics parameter implies that creep-crack rate v is related to the exponent m of the creep damage evolution equation in addition to the creep exponent n of , and shows clear contrast with the results of earlier papers because is characterized by the creep exponent n., the eigen value s (and hence the exponent of the stress field p=s−2) has been obtained for given sets of the damage exponent l and the creep exponent n as parameters; i.e., we have p−l−n relation among the exponents of p, l and n. The detailed numerical procedure to obtain p−l−n relation and its explicit result have been reported in the previous paper of the authors (, on the other hand, specifies the consistent values of l as a function of the exponent p of stress distribution and exponent m of the damage evolution equation; i.e. p−l−m relation. By the use of these two relations of p−l−n and p−l−m, we can readily calculate the value of exponent p as a function of the creep exponent n and damage exponent m. show the numerical results for the exponent p of the asymptotic stress field of mode I creep crack in steady-state growth, for the case of k=1 in . The dotted lines, on the other hand, represent the exponent p of the HRR stress field for undamaged non-linear materials: Since the exponent p<0 implies the stress singularity at the crack-tip r=0, the HRR field has always stress singularity for any finite value of the stress exponent n. However, as observed in , the presence of material damage increases significantly the value of the exponent p, and may give non-singular stress field even for finite values of n. Namely, shows that the stress singularity of the asymptotic field is determined by the relative values of n and m, and this is a very important result as the effect of the material damage on the asymptotic field at a crack-tip., it will be observed that, for a given set of n and m, the case of plane strain has larger stress singularity than that of the plane stress, which is different from the cases of undamaged non-linear materials (In the fracture tests of ductile materials, the fracture toughness of cracked thick specimens is known to be lower than that of thin specimens. This is usually attributed to the triaxial stress at the crack tip induced in the state of plane strain. shows that, when a damage field exists at the crack tip, besides the triaxial stress, plane strain state has larger stress singularity. Thus, it should be noted that, in view of material damage, the fracture toughness of ductile materials in the state of plane strain may be further decreased from that of plane stress state. represent the approximate expression to the corresponding numerical results, and are given by the following relations: coincides with the numerical results within the error of 0.01 (plane strain state) and 0.02 (plane stress state) except for a few results of m=1.According to the previous paper of the authors () (where symbol m was used instead of l) in the state of plane strain, the p−l−n relation described in can be expressed by the following approximate relation: we have l , and thus substitution of this l into give the approximate relations among the creep exponent n, the damage exponent m, the exponent of stress distribution p and exponent l of the damage distribution consistent to the stress distribution of Since the damage variable has the range 0≤D≤1, specifies the exponent l to be l≥0. Then, which is usually satisfied because the relation is ascertained for most metallic materials (, the value of the exponent of stress distribution p is Namely, this result implies that the asymptotic stress field at a crack tip may be singular or non-singular when the set of exponents n and m is in the range of . It should be noted once more that the condition is subject to the limitation of a physical requirement furnishes very important information not only for the evaluation and understanding of creep crack behavior in structural component, but also for the discussion of the stability and the convergency of its numerical analyses. Namely, the problem of mesh-dependence of numerical results is usually one of the most crucial problems in the local approach of fracture based on the finite element method and damage mechanics; besides the hyperbolicity of the governing equations, the singularity at the crack tip may be one of the major causes of the mesh dependence. Then, by dashed lines. As observed in the figure, as regards the value of n corresponding to the bound of singularity p=0, coincides with the corresponding numerical results within the error of 5%.In the case of the plane stress, on the other hand, it is difficult to do a similar argument as above, because we could not obtain a simple expression for p as show the effects of a damage field on the radial distribution of the asymptotic stress field at the creep-crack tip in the case of a typical creep exponent n=5. The solid and dashed lines were calculated by the stress field of together with different values of the exponent p shown in . The dotted lines, on the other hand, represent the asymptotic stresses of the undamaged HRR fields. Though the lines of m=6 coincides with that of the HRR field because the case of m=n+1 corresponds to the undamaged materials, they have been eliminated in because of the physical requirement of , all the stress components σij as well as the equivalent stress σEQ have an identical radial distribution, and these radial distributions are also same in all θ-directions.Since the radius r=r0 represents the boundary between the damaged and undamaged zone and implies D=0, all the lines in corresponding to the undamaged material (i.e., the value corresponding to HRR field) at r/r0=1. When r/r0 tends to 0, on the other hand, the stresses σij for m=5 tend to ∞ since the stress exponent p is negative in this case.Hitherto a number of models have been reported to analyze the process of creep-crack growth from the view point of damage mechanics () and of fracture mechanics and micromechanics (). Besides that most of these analyses are one-dimensional, the effects of damage on the stress field have been hardly elucidated systematically. However, , among them, analysed damage and stress field at a mode I blunted creep-crack in plane strain state by finite element method by employing Kachanov-type creep damage constitutive equations. They demonstrated variation of the stress distribution from the elastic crack-tip field at the instant of loading through the stage of creep-crack growth. Their analysis show that after the crack starts to grow, the crack tip stress decreases towards zero due to damage. Since the creep and the damage exponent in their analysis are n=5 and m=3, their results conform to the results of , on the other hand, show the θ-variation of the three stress components for the states of plane strain and plane stress, respectively. The HRR field has been entered by dotted lines for the sake of comparison. The cases of (a) and (b) in these figures correspond to the non-singular stress fields (), respectively. Because the magnitude of the coefficient K of have been normalized by the use of the equivalent stress In the case of the plane strain state of , though the stress components show smooth distribution, every component vanishes at θ=π because of damage. This is in contrast to HRR field shown by dotted lines. The stress components have larger values at θ=0 than those of , and this may be accounted for by the singular stress field in , on the other hand, dominant singularity is observed in θ-distribution, and it is more salient in the case of singular stress field of . In both cases, all the stress components at θ=π vanish because of its complete damage.By substituting the asymptotic stress of , we have the expression of the creep rate is always infinite at the crack tip r=0 irrespective of the nature of the asymptotic stress field. This may correspond exactly to the steady-state crack growth.By referring to the experimental observations (), the semi-inverse analysis of Chapter 3 was performed by postulating the damage distribution of has been performed for the special case of the shape factor k=1; i.e., semi-circular damage field in front of the crack combined with a wake parallel to the crack plane.In order to discuss the effect of shape of the damage region in some detail, we will now perform the calculation for five cases of shape factor k=1.0–3.0. shows the relations between the damage shape factor k and exponent of stress distribution p for a stress exponent n=5, for the states of plane strain and plane stress. The results of shows that the effects of damage shape factor k is insignificant for each case of the damage exponent m. This implies that the factor which governs singularity of the asymptotic stress field is local character of the damage field rather than the global geometry of the damage distribution.The effects of material damage on the asymptotic stress field of a mode I creep crack in steady-state growth were analysed on the basis of continuum damage mechanics by postulating power law creep damage theory. The resulting governing differential equations were solved by semi-inverse method. The relations between exponent p of the asymptotic stress field and exponents n and m of the power law creep constitutive law and the power creep damage law were elucidated in detail. The results of the present analysis are summarized as follows: While the HRR-field of non-linear fracture mechanics always shows the stress singularity at the crack-tip for any finite value of the creep exponent n, the preceding material damage in front of the crack tip decreases the singularity, and may give non-singular stress field.In the particular case of mode I creep crack in the state of plane strain, by representing the asymptotic stress field at the crack-tip and the preceding damage field by the expressions approximate expressions for p and l were derived as follows: where n and m are exponents of the power creep law and the power creep damage law. For a uniform damage distribution l=0, this relation leads to The above relations imply that the conditions m−1≤n<m+1 and m+1≤n give the relations p<0 and p≥0; i.e., singular and non-singular stress fields, respectively. This results furnishes very important information not only for evaluation and understanding of creep crack behavior, but also for discussion of stability and convergency in its numerical analyses.While the asymptotic stress fields in the states of plane strain and plane stress have the identical stress singularity in undamaged materials, the state of plane strain has more significant stress singularity than that of plane stress in the case of preceding damage.Temperature dependence of the elastic moduli of the nickel-base superalloy CMSX-4 and its isolated phasesElastic constants of anisotropic cubic materials were determined by acoustic resonance measurements at temperatures ranging from RT to 1300 K. The temperature dependence of Young's modulus E, shear modulus G, and Poisson's ratio ν of superalloy CMSX-4 and its isolated γ′ and matrix phases were measured and compared with room temperature ultrasonic speed measurements. The orientation dependence of the engineering constants E, G and ν was determined. A comparison to models in literature predicting γ′ morphology changes during creep is presented and agreement is found with the experimental data measured in this work.For modeling the morphology changes of superalloys, it is important to know the difference in the elastic moduli of their single phases. As first calculated by Pineau For an anisotropic crystal, elastic moduli depend on the crystal orientation. Characteristic of materials with cubic symmetry are the elastic constants c11, c12 and c44. Due to practical engineering reasons, the elastic moduli are often used with reference to a specific crystal orientation, mostly [001].Any orientation dependence of the engineering constants E, G, and ν may be defined by: direction on a plane with normal vector The orientation dependence of E with a uniaxial stress state in are commutable. With the direction of shear stress in direction in a plane with normal direction parallel to the stress axis and a perpendicular vector indicating the direction of contraction. In the case of the Poisson's ratio ν, To show the strong anisotropic behavior of E, G, and ν (), the orientation dependencies of these moduli are calculated from the elastic constants of the matrix material measured by ultrasonic speed measurements at room temperature, c11=262, c12=161 and c44=144 GPa. show the orientation dependence of Young's modulus. It can be seen that the maximum elastic modulus is in 〈111〉 direction, the minimum in 〈001〉 direction. For a more precise view () the same orientation dependence is plotted as contour lines in the standard orientation triangle. The elastic modulus in [111] direction is about three times higher than in [001], reflecting the high anisotropy factorYoung's modulus E depends only on the direction of stress axis, whereas, G and ν depend on two directions. For a given stress direction G and ν do not have rotational symmetry. In polar diagrams are used in order to illustrate this. The center of the ‘ellipse’ represents the direction of the stress axis and the distance from the center to the outer line gives the value of G or ν in direction. As evident, [001] and [111] are the only orientations that are rotationally symmetric, so that a single value of G and ν can be used for these orientations. In is shown as a polar plot for various planes with normal around some orientations of the stress direction in the standard orientation triangle. Again the anisotropy factor is reflected, since the shear modulus varies up to a factor of 2.85 for a [101] stress axis direction on the (010) plane as compared with the (10 the orientation dependent Poisson ratio is shown. Again, the center of the curve is the orientation of stress axis in the standard stereographic projection as the distance to the curve. Negative values of the Poisson's ratio ν, as well as ν>0.5, are possible. In the case of [101] tension stress the material does not contract but even expands in [10] direction by an amount of about 12% of the expansion in stress direction, =0.123 ε[101]. Whereas in the perpendicular direction [010], the contraction is high and amounts to ε[010]=−0.69 ε[101].As evident, E, G, and ν have strong anisotropic behavior. Slight deviations from [001] or [111] orientations causes a relatively large change in E, G, and ν and destroy the rotational symmetry of [001] and [111] orientations. For the exact [001] and [111] orientations =[111], the second vector of G and ν can be chosen arbitrarily from all vectors perpendicular to The resonance method allows the determination of elastic constants of materials with high precision over a wide temperature range, since the piezocrystal can stay outside the furnace. The elastic constants can be calculated from a partial spectrum of measured longitudinal and torsional resonance frequencies of cylindrical specimens. The basis are the frequency equations which are determined by the tree-dimensional equation of motion in cylindrical coordinates (r, ϕ, z), the displacement vector of For the {[100], [010], [001]} basis, the stiffness matrix for cubic material is given by:Denoting the cij, respectively, c′ij of the elastic matrix C as aij, the system of partial differential equations are obtained:With rotational symmetry, which is the case for the z-direction parallel to [001] or [111]:resulting in a set of differential equations: and is the equation for torsional vibration with the tangential displacement V(r).Using V(r)=V0eαrJ1(βr), with Jn as the nth order Bessel function yields:From the boundary conditions τrϕ(r=a, z, t)=0 and τϕz(r, z=0, t)=τϕz(r, z=1, t)=0 the frequency equation for torsion resonance is:The frequencies are calculated as follows:For crystal orientation [001] with a15=c15=0:for crystal orientation [111] with a15=c15′≠0G001, respectively, G111 can be calculated from the measured torsional resonant frequencies. The longitudinal vibrations are coupled with radial vibrations and are described by . A solution has been found only for a15=0. Using U(r)=U0J1(pr) and W(r)=W0J0(pr).with the solutions p12=h2 and p22=k2 and the displacements U(r) and W(r)From the boundary conditions of cylindrical specimensThese lead to the equations for the eigenvalues:As well as in the isotropic case, the boundary conditions τrz(r, z=0, t)=τrz(r, z=1, t)=0 are not fulfilled. The approximation is valid if l≫r0, in our case l≥50 mm and l/r0>8.It is possible to calculate the Young's modulus and the Poisson's ratio in both [001] and [111] orientation by inserting the geometric data, the density, and the determined longitudinal and torsional resonance frequencies, fLn and fTn, respectively. Using one is able to determine c44 by a single torsion resonance frequency for both [001] and [111] oriented slabs. Further torsion resonance frequencies increase the accuracy in determining c44., allows to determine the remaining coefficients of the stiffness matrix. Using ωn=2πfLn and γn=nπ/l, we obtain for each longitudinal resonance frequency fLn one . In case of cubic symmetry two elastic constants are remaining to be determined (c11 and c12). They can be obtained by at least two longitudinal resonance frequencies. More than two measurements increase the accuracy of the elastic parameters.An advantage of the resonance method is that the elastic constants can be obtained over a wide temperature range, up to melting temperature. Disadvantage is the strong restriction to exact cylindrical geometry, with length l>50 mm and high aspect ratio length/diameter about 10. This is especially difficult for single crystal samples since the cylindrical axis should be parallel to either [001] or [111] crystallographic direction.The elastic moduli of CMSX-4 and its single phases have been determined from room temperature up to 1273 K in air. In order to achieve high-temperature stability, the compositions of the single phases have been slightly changed from the compositions that were measured by local measurements in CMSX-4 Cylindrical specimens of 18 mm diameter and 110 mm length of the three alloys have been used to get the elastic moduli by resonance measurements. CMSX-4 and γ′ phases were tested in near [001] and [111] directions. For the matrix alloy only one near [111] oriented sample was available. The exact specimen orientations were determined by Laue X-ray measurements. As the crystals have deviations of 2–9° from the [001] and [111] orientations, as indicated in , Eqs. (5)–(7) were used to get the corrected cij parameters. Despite the small deviations, G and ν are assumed to be rotationally symmetric for these orientations. The average of all perpendicular directions in the misorientation was used. The equations have been used in a variation form because the terms can only be analytically inverted for the exact [001] and [111] orientations. With the given cij the elastic moduli for [001] orientation were calculated using Ultrasonic speed measurements were performed on cylinders with parallel surfaces, thickness and diameter of about 20 mm, and [101] plane normal, as outlined in . The longitudinal speed c1[101] may be obtained with a probe for longitudinal waves. By turning a probe producing transversal waves around the specimen axis one can get two ultrasonic waves that are polarized perpendicular to each other and that have the speeds . Depending on azimuthal angle, one of the transversal waves dominates.By measuring the time difference of two consecutive echoes the transit time from the transducer into the material is cancelled out. With the three speeds and the specimen density ρ, the elastic constants can be calculated by:The direction of ultrasound propagation in Advantage of the ultrasonic speed method is that the sample size can be fairly small and therefore the orientation accuracy is only determined by the cutting tools and is therefore <1°. Disadvantage is that temperature dependence can be determined only in a very narrow temperature range (up to 400°C). shows the temperature dependence of Young's modulus of CMSX-4 and its isolated phases. It can be seen that below 1023 K Young's modulus of the matrix is larger than that of the γ′ phase. This ratio changes for temperatures above 1023 K. The temperature dependence of CMSX-4 is not linear. Its decrease is highest for high temperatures. This is caused by a partial dissolution of the precipitates.A rule of mixture (infinetely long γ′ slabs surrounded by matrix), as well as finite element calculations The higher elastic modulus of the superalloy CMSX-4 as compared with its constituents might be due to two reasons, (a) the compositions of the matrix and γ′ phase were adjusted in order to ensure single phase material, which could lead to a slight change in elastic behavior, and (b) the explanation given in the paragraph before by the availability of only one matrix single crystal with a small deviation from [111]. This will be discussed in detail at the end of this chapter.Temperature dependence of the shear modulus is shown in . It can be seen that the difference between the different materials is smaller than that for Young's modulus. Similar to the Young's modulus the shear modulus of γ′ is larger than that of the matrix for temperatures above 1023 K and vice versa for lower temperatures. The shear modulus of CMSX-4 has values between the separated phases as expected by the rule of mixtures. shows the temperature dependence of Poisson's ratio for the three observed alloys. It can be seen that the scatter is much higher than that for E and G. In contrast to E and G, the temperature dependencies of Poisson's ratios of matrix and γ′ are nearly parallel.The transformation from the [111] measurements to [001] increases the error if some deviation from the exact [111] orientations is given. For the matrix phase only one [111] sample was available. In case of the matrix the error bars in indicate the deviation between two measurements with the same sample. For the γ′ phase and the superalloy the error bars in show the difference between data form [001] oriented specimens and data which has been transformed from measurements of [111] oriented specimens to the [001] orientation.Motivation for these measurements is given by different models predicting γ′ morphologies during high temperature deformation. The Pineau model the calculations of Pineau predict a morphology change to plates or rafts with an applied tensile stress. Compression stress should result in needles parallel to the stress axis. This behavior at elevated temperatures is in good agreement with many experimental observations and measurements of the temperature dependence of the misfit of CMSX-4 , Mγ′−Mmatrix is positive for all temperatures above room temperature.the external stress σ(>0 for tensile stress) and the misfit δ give the sign of the rafting process. shows the temperature dependence of m. A positive sign leads to the growth of needles, a negative to the development of rafts. Therefore this model predicts rafts at all temperatures above room temperature.With the given experimental data all models correctly predict the morphology changes.The change in composition, which is necessary to stabilize the separated phases give a change in the elastic constants, compared with the two phases in the superalloy. At temperatures where both separated phases have equal Young's modulus or shear modulus, the superalloy that is the mixture of the two phases, should show the same values. This is not the case due to the slight changes in composition.With the resonance method it is possible to determine the elastic constants of anisotropic cubic materials. The temperature dependence of the Young's modulus, shear modulus, and Poisson's ratio of the superalloy CMSX-4 and its isolated γ′ and matrix phases have been presented and compared with the elastic constants measured by ultrasonic speed measurements at room temperature. The orientation dependence of the elastic moduli E, G, and ν is shown as an example. The Pineau model Understanding of adiabatic shear band evolution during high-strain-rate deformation in high-strength armor steelThe microstructural evolution and formation mechanism of adiabatic shear band (ASB) in a high-strength armor steel were investigated using a laboratory-scale split Hopkinson pressure bar, and the results were correlated with the actual ballistic impact behavior. The interrupted dynamic compressive test results reveal that a deformed ASB (dASB) starts to form right after the stress collapse and it develops into a transformed ASB (tASB). In the ballistic impact, wide tASBs form mostly at the perforated surface, and narrower tASBs are branched from the tASB. Very fine equiaxed grains of ∼190 nm in the tASB developed during the dynamic compression indicates that the dynamic recrystallization occurs even in 86.5 μs, and then the grains grow up to 260 nm in 9.5 μs. Rotational dynamic recrystallization mechanism and grain-growth rate model were proposed based on the calculation of temperature rise from a thermo-elasto-plastic finite element method, which provide a reasonable explanation for the formation and growth of fine equiaxed grains during both the dynamic compression and ballistic impact. A linkage of equiaxed subgrains and elongated parent subgrains demonstrates that the equiaxed subgrains did not evolve from nucleation and growth processes but from the sub-boundary rotation. Based on the underlying formation mechanisms and kinetics of ASBs, this study would suggest a reliable method to interpret the ASB formation and associated fracture mechanism during the ballistic impact.Excellent protection-capability, transportability, maneuverability, and maintenance have been required in armored vehicles and tanks to achieve an ensured combat-crews’ survival []. The primary characteristic needed for designing armor materials among the various requirements is the protection-capability, especially under a ballistic impact. When the armor materials are subjected to the ballistic impact under extremely high dynamic loading environments, adiabatic shear bands (ASBs) are usually formed within a very localized area. The ASBs form by a thermo-mechanical instability induced from the heavy plastic flow and abrupt temperature rise [], thereby often resulting in the cracking and consequently catastrophic failure. Although many studies have been conducted to understand the formation mechanism and microstructural evolution of ASBs [], there still exist many debates on potential mechanisms controlling the ASB formation. These mechanisms include the melting and amorphization, dynamic and/or static recrystallization, dynamic and/or static recovery, and phase transformation []. One of the challenges for revealing the mechanism is how to understand the microstructural evolution within ASBs.The ASB is defined as an extremely localized region in a material subjected to the high-strain-rate deformation. If the strain rate is sufficiently high, there is not enough time for heat to diffuse away from the locally deformed region, which readily causes a local temperature rise. When the thermal softening effect due to this adiabatic heat surpasses the strain-hardening effect, the plastic instability occurs and consequently develops the local region into the ASB []. In general, two types of ASBs have been reported in the literature [], i.e., deformed ASB (dASB) and transformed ASB (tASB), depending on their microstructural appearance. dASBs form as many grains are severely elongated along the shear direction []. On the other hand, tASBs form commonly in various metals, and appear as white-etched bands in optical micrographs []. There have been many studies on revealing dominant formation mechanisms of tASBs by controlling the microstructural evolution. Meyer et al. [] reported the crystalline-to-amorphous transition at the ASB in a stainless steel for the first time. Amorphous structures have been observed in the pure copper []. In addition to the amorphous structures, phase transformation such as martensite to austenite transformation has also been reported in duplex steels, 301 stainless steels, and Ti alloys []. As well as the phase transformation, Mataya et al. [] observed a significant grain refinement within ASBs, which was attributed to a dynamic recrystallization or recovery. The dynamic recrystallization within ASBs of Ti alloys, Cu alloys, and steels was also suggested by Meyers et al. [], respectively. The white-etched ASBs in steels, thus, are associated the increased resistance to chemical etching for fine recrystallized structures []. Despite these extensive studies, the grain-growth kinetics within the ASB is still unclear []. A few studies on the grain-growth kinetics are available [], but there are no observations and interpretations directly confirmed in terms of detailed microstructural evolutions.The formation of tASB seriously deteriorates a load-carrying capacity [], thereby leading to a catastrophic failure. Thus, it should be carefully examined to enhance overall dynamic properties as well as ballistic performance of armor materials. Ballistic impact tests are generally used for the accurate evaluation of armor materials, but are time-consuming and costly as they contain many complex experiments of large target specimens and fast projectiles. For detailed analyses of ASB formation, they also show limitations of samples collected from fragmented or perforated target specimens. Thus, the laboratory-scale dynamic tests are essentially required for the basic understanding of ASBs and for the correlation with the ballistic impact test results. For example, a split Hopkinson pressure bar (SHPB) has been used for the laboratory-scale dynamic compressive test. This is because the deformation mode is similar to that of the ballistic impact test, and the test method is much simpler and more economical. Furthermore, controlling of experimental parameters as well as obtaining the dynamic-property data including stress-strain curves are enabled to investigate the ASB formation and fracture behavior []. However, it is still very challenging to trace the evolution of microstructures during the ballistic-impact deformation. Studies on the microstructural evolution within the ASB formed by the SHPB and the correlation with the ballistic impact data have not been reported yet.In the present study, the microstructural evolution of ASBs formed in a high-strength armor steel was investigated by using the SHPB technique. An interrupted dynamic compressive test was performed to investigate the microstructural evolution by stages and to characterize detailed microstructures of ASBs. A ballistic impact test was also conducted to study the fracture behavior and microstructures of ASBs and to correlate them with the dynamic deformation behavior obtained from the laboratory-scale SHPB. These results show that the formation mechanisms and kinetics of ASBs formed in the ballistic impact can be entirely explained by the dynamic-compression results. In particular, the microstructural analysis reveals the growth of fine equiaxed grains within the ASB in a very short time during the dynamic compression and the existence of a gradient structure formed during the ballistic impact. This significant finding confirms that the growth of equiaxed grains can occur during the high-strain-rate deformation. Furthermore, the present study would suggest a reliable method based on high-strain-rate deformation behavior to interpret the ASB formation and fracture mechanism by the ballistic impact.The armor steel used in this study was a high-strength one (thickness; 6 mm), whose commercial brand names is ‘ARMOX 500T’ [] manufactured at Swedish Steel Oxelösund AB, and its chemical composition is Fe-0.28C-0.27Si-0.87Mn-0.009P-0.001S-0.5Cr-0.9Ni-0.36Mo-0.002B (wt.%). This is referred to as ‘500T’ for convenience. This steel consists of a tempered martensite structure.1%-nital-etched microstructures of longitudinal-short-transverse (L-S) plane were observed by an optical or a scanning electron microscope (SEM). Electron back-scatter diffraction (EBSD) analysis (step size; 50 nm) was performed to characterize the ASB microstructure by a field emission scanning electron microscope (FE-SEM, Quanta 3D FEG, FEI Company, USA). Thin foils prepared by a focused ion beam (FIB, Quanta 3D FEG, FEI Company, USA) were observed by a transmission electron microscope (TEM, 2100, Jeol, Japan) at 200 kV.Plate-type specimens (width; 6 mm, thickness; 1.5 mm, gage length; 25 mm, longitudinal orientation) were tensioned at room temperature at a strain rate of 10−3/s by a universal testing machine (8801, Instron, USA, capacity; 100 kN). Microhardness was measured across the ASB by a dynamic ultra-microhardness tester (DUH-211S, Shimadzu, Japan) under 10 g load. Dynamic compressive tests were performed by an SHPB. 5ϕ × 4-mm cylindrical bar was prepared in perpendicular to the rolling direction so that the projectile-traveling direction might match to the compressive-loading direction. The specimen was installed between incident and transmission bars, and was compressed by a striker bar controlling a firing air pressure of 0.34 MPa, which resulted in an impact momentum of 16.3 kg∙ms−1. During the dynamic compression, incident, reflective, and transmitted waves were detected by strain gages, and recorded in an oscilloscope. The recorded waves were used for obtaining the data of engineering stress, strain, and strain rate by the following equations [where AB, AS, EB, CB, and LS are the cross sectional area of bar, cross sectional area of the specimen, elastic modulus of bar material, velocity of elastic wave in the bar, and specimen length, respectively. εT, εR, and t are the transmitted strain pulse, reflected strain pulse, and deformation time, respectively.Target specimens (size; 300 × 400 × 6 mm) were ballistically impacted by a 12.7 mm APM2 projectile (speed; about 600 m/s) at normal obliquity. After the ballistic test, the perforated target specimen was half-sectioned, polished, and etched in a 1%-nital solution for the microstructural observation.a–c shows optical, SEM, and EBSD inverse pole figure (IPF) images of the L-S plane of the 500T steel. The steel consists of tempered martensite (a and b), while band structures are well developed, and the prior austenite grain size (PAGS) is about 20 μm (c). The formation of band structures is attributed to the segregation of C and Mn during the casting procedure, like in conventional high-alloyed steels [The room-temperature hardness and tensile test data are listed in . The Vickers hardness is very high above 500 HV. The yield and tensile strengths are also quite high above 1.3 and 1.7 GPa, respectively, while the elongation is moderate at 10%.a shows engineering stress-strain curves obtained at various sequential strains from the interrupted dynamic compressive test. The specimens were dynamically compressed after a stopper ring was inserted between incident and transmitter bars to obtain the sequential dynamic strains of 2–3% interval, as previously described in Refs. []. For example, the strain of 25% could be obtained by using a stopper ring of 3 mm in height in comparison to the 5ϕ × 4-mm cylindrical bar specimen. The compressive strain rate resultantly obtained from the impact momentum of 16.3 kg∙ms−1 was about 3900 s−1. The engineering stress-strain curves exhibit a fluctuation phenomenon because stress and strain values were obtained from several waves detected by strain gages during the dynamic compression. All the curves obtained at the sequential strains are almost same within a small error range, which indicates the reliable dynamic curve shape. The yield strength, maximum compressive strength, and total strain (strain up to the controlled strain) were measured from the curves, and the results are shown in . The yield and maximum compressive strengths are very high above 1.9 and 2.9 GPa, respectively, while the total strain is good at 35.8%. Low-magnification photographs of the dynamically compressed cylindrical specimens are shown in b. Cracks start to appear at the 33% strain in the about-45-degree direction.In order to examine the critical strain for starting the ASB formation, the interrupted dynamic compressive test was conducted by using stopper rings []. ASBs do not form until the strain of 25%, and start to form at the strain of 28%. a–d shows low-magnification optical micrographs of the half-sectioned area of the specimen edge. A deformed ASB (dASB) start to form diagonally inside the 28%-strained specimen (a) as band structures are severely bent along the shear direction. White-etched transformed ASB (tASB) appears along the shear direction at the 30% strain (b). This ASB forms very narrow within about 3 μm in width. At 33%, a crack initiates and propagates along the extended ASB of about 10 μm in width (c). At 35%, the crack propagated along the ASB is opened, while some other cracks initiate laterally from the ASB (d), and a complete separation occurs at 36% (Detailed microstructures of ASBs, i.e., dASB and tABS formed at 28% and 30%, respectively, were examined by the EBSD analysis. a shows an EBSD IPF map of the dASB of a red-boxed area of a. Grains were elongated along the shear direction, and their width is about 0.8 μm. Fine grains are also mixed with the elongated grains. b shows an EBSD IPF map of the tASB of a red-boxed area of b. Very fine equiaxed grains form within the tASB, adjacent which more elongated grains are observed. The width of the tASB is about 3 μm, which matches to the ASB width of c shows a size distribution of fine equiaxed grains of a yellow-boxed area of b. The average size of equiaxed grains is about 190 nm.a shows an EBSD IPF map of the tASB and crack of a red-boxed area of c. Very fine equiaxed grains are observed in the center of the ASB, along which a crack propagates. The width of the ASB is about 10 μm, which matches to the ASB width of b–d shows the IPF map, phase map, and grain-size distribution, respectively, of a yellow-boxed area of a. The interior ASB microstructure consists of a single BCC phase (b and c), which indicates no retained austenite inside the ASB. The average size of equiaxed grains is about 260 nm (d), which is smaller by about two orders of magnitude than the prior austenite grain size (about 20 μm, The microhardness was measured at a 15-μm interval across the ASBs, and its profile is shown in . The hardness is very high in the center of the ASBs. The peak hardness of the dASB at the 28% strain is about 731 HV, which is higher by about 100 HV than that of the adjacent matrix. The peak hardness increases to 871 HV at the 30% strain as the dASB develops into the tASB composed of fine grains of 190 nm in size (b and c). This hardness increase is attributed to the work-hardening effect due to dynamic deformation and grain refinement at the 30% strain, it decreases slightly to 848 HV as equiaxed grains are coarsened to 260 nm (d). The matrix hardness around the ASB is higher (by about 80 HV) than that of the non-deformed specimen (548 HV, ) because the overall matrix is hardened by the dynamic compressive deformation. There are hardness-reduced areas between the ASB center and adjacent matrix. These are heat-affected zones (HAZs) formed by a softening induced from an adiabatic heating []. The heat-affected zones are placed at the 15-μm distance from the ASB center. It is also noted that the hardness reduction in the HAZ is larger near the tASB formed at the 30 or 33% strain than near the dASB formed at the 28% strain. This is because the adiabatic heating was larger in the more highly-strained tASB than in the dASB according to the actual measurement of adiabatically-heated zone of the ASB center during the torsional split Hopkinson bar test of ultra-high-strength steels [a is a low-magnification photograph showing a target specimen perforated after the ballistic impact test. b shows an optical micrograph of a red-boxed area of a. Since the perforated area and its vicinity were subjected to the severe ballistic impact, plastic-flow lines (viewed from band structures) are bent toward the projectile-traveling direction, as indicated by dotted lines. The perforated surface is mostly covered with relatively wide tASBs (width; 30–70 μm, yellow-arrow marks in b). This implies that the main crack propagates along the tASB formed on the perforated surface (surface-ASB) while the projectile penetrates through the target specimen. Some narrower tABSs (width; 5–25 μm) are branched from the wide surface-ASB.a shows an EBSD IPF map of the tASB of a red-boxed area of b. Very fine equiaxed grains and heavily elongated grains are observed at the tASB of about 10 μm in width. b–d shows the IPF map, phase map, and grain-size distribution of a yellow-boxed area of a. All fine grains have a single BCC phase, and their size is about 220 nm, which is similar to that of tASB formed in the dynamically compressed specimen (b–d). There exist some black-colored areas in b and c, which indicate the areas having a very low confidence index (CI) which provides a measure of indexing reliability in the EBSD analyses []. In order to achieve the data reliability in EBSD images, these areas are generally uncounted. e shows the microhardness profile of the ASB. The peak hardness of the tASB center is 861 HV, which is higher by about 200 HV than that of adjacent matrix. This value is similar to that of the tASB formed in the dynamically compressed specimen (848–871 HV, ). There are also heat-affected zones near the ASB. These overall microstructural and hardness results are similar to those of the dynamic compression case, although ASBs form under the more severe loading conditions.a shows an EBSD IPF map of the surface-ASB (width; about 35 μm) of an orange-boxed area of b. This ASB is divided into two regions, i.e., ‘coarse-grained ASB (CG-ASB)’ and ‘fine-grained ASB (FG-ASB)’, based on the grain size. b and c shows the grain-size distribution of the CG-ASB and FG-ASB regions, whose average grain sizes are 480 and 360 nm, respectively. These sizes are larger than that of the narrow ASB (220 nm, d) branched from the surface-ASB. This difference in grain size is attributed to the grain growth induced from the frictional heat generated by a fast-traveling projectile. d shows the microhardness profile of the wide surface-ASB. The peak hardness appears in the FG-ASB region (789 HV), and there exists a heat-affected zone between the FG-ASB region and adjacent matrix. This peak hardness is lower than that of the narrow ASB (861 HV, Since various cracking phenomena occurring during the ballistic impact of high-strength armor steels are associated with the formation of ASBs [], dynamic compressive characteristics need to be analyzed in relation with the intensity of ASBs. In this study, microstructural evolutions of ASBs formed by the interrupted dynamic compression and ballistic impact are comparatively investigated. From this understanding, detailed formation mechanisms of ASBs are verified.According to the microstructural analyses of ASBs, very fine equiaxed grains of 190–260 nm in size are found within ASBs (b–d). This structure is similar to those observed in previous high-strain-rate deformation studies [], and known to be caused by the dynamic recrystallization. During the dynamic compression, the deformation occurs at a very rapid rate, and plastic flows are heavily localized within a narrow region in an extremely short time so that the temperature rises abruptly before the emission of thermal energy [Since the experimental measurement of temperature rise during the dynamic compression is very difficult, the following equation is generally used for estimating the temperature rise [where β, σ, ε, ρ, and Cv stand for the fraction of plastic work converted into heat (Taylor-Quinney parameter), true stress, true strain, density, and specific heat capacity, respectively. This temperature rise is caused by the interior thermal energy converted from the deformation energy. Thus, the temperature rise estimated from this equation explains the rise of the whole gage section of specimen, which cannot be applied to the localized region like the ASB. Thus, the more accurate temperature calculation is required in consideration of the localized inhomogeneous deformation.The temperature distribution inside the dynamically compressed specimen was calculated by thermo-elasto-plastic finite element method (FEM) simulations using an ABAQUS version 6.9 and explicit schemes of dynamic solutions. Cylindrical-bar-sample configuration and specimen geometry were same to the experimental ones. The specimen had a surface to surface contact with both the incident and transmission bars having a friction coefficient of 0.1. Initial velocity of a striker bar was measured to be 26.1 m/s by using a high-speed camera during the experiment. A 4-node thermally coupled axisymmetric quadrilateral (CAX4RT) was selected as an element type of every mesh. Mesh sizes were biased from 0.05 to 0.005 mm towards the compressive specimen edge to focus on the thermal concentration at the edge. The mesh size of 0.005 mm is small enough to detect the thermal concentration in consideration of the specimen dimensions (5ϕ × 4 mm). In terms of mesh sensitivity, it was noted that the temperature peaks at the edge could be underestimated when the mesh size was not small enough. Intrinsic properties of the 500T steel were measured experimentally, and the results are shown in . Thermal conductivity, specific heat, and inelastic heat fraction were set to be 32.73 W/m∙K, 0.46 J/g∙K, and 0.9, respectively. Johnson-Cook (JC) constitutive model [] suitable to simulate the high-strain-rate and high-temperature deformation of metals and alloys was used. The JC model is given by:where A, B, n, C, and m are the yield stress at the reference temperature and reference strain rate, coefficient of strain hardening, strain hardening exponent, strain-rate-hardening coefficient, and thermal softening exponent, respectively. ε¯, ε¯˙, ε˙0, and T∗ are the plastic strain, plastic strain rate, reference strain rate, and homologous temperature, respectively. The homologous temperature is defined as:where T, Tr, and Tm are the temperature of the steel, reference temperature (normally room temperature), and melting temperature, respectively. The dynamic compressive results and quasi-static tensile test results at 25, 400, 500, and 600 °C were used for the calculation of A, B, n, C, and m values, which are calculated to be 1210 MPa, 1060 MPa, 0.18, 0.0125, and 0.547, respectively. These values are slightly different from the previous results of the ARMOX 500T steel []. This difference might come from the high-temperature testing conditions and methods. In particular, the calculation of temperature rise within the ASB might be slightly varied with the m value, which receives an interesting attention in the ASB examination, although detailed parametric analyses on temperature rise were not carried out. It is expected that the temperature rise would be reduced by the decrease in shear localization within the ASB due to the decreased thermal softening with increasing m value.a shows the FEM-simulated temperature distribution of the dynamically compressed specimens under the impact momentum of 16.3 kg∙ms−1, which is the same condition as the experiment. The temperature rise is intensively converted from the deformation energy at the specimen edges along the shear direction. When the strain rate is sufficiently high, there is not enough time for the heat to diffuse out, and thus the heat concentrates at the specimen edges. b shows the temperature distribution as a function of distance along the shear direction from the specimen edge corner (black-arrow mark in a). The peak temperature reaches 965.7 and 1058.3 K at the 28% and 35% strains, respectively, and the temperature decreases gradually with increasing distance from the corner. These peak temperatures might not be enough to reach the austenite range within a very short time of several tens of microseconds. According to Rajasekhara et al. [], furthermore, the martensite to austenite transformation was estimated within a wide annealing temperature range in an AISI 301LN stainless steel, and the time required for austenite formation at the annealing temperature of 800 °C was about 10–100 ms, which was reasonably agreed with the experimental data. During the dynamic compressive deformation, the time for the ASB formation and complete separation is within 103 μs (c), which is several orders of magnitude shorter than the time required for the austenite formation. Thus, the abrupt rise of temperature in such ASB during the dynamic compressive deformation does not make the original martensite structure transform into the austenite.An extremely localized band region, i.e., ASB, forms with a plastic instability when the thermal softening effect due to adiabatic heating surpasses the strain-hardening effect. The adiabatic heat effect accelerates the softening and strain concentration, thereby resulting in the microstructural changes and the formation of fine equiaxed grains within the ASB (a and b). The dASB displays an elongated structure which is aligned along the shear flow direction (] observed a transition from dASB to tASB due to a heavily shear flow in tempered martensitic structure. Meyer et al. [] revealed bands of martensite laths highly elongated and extended along the shear direction during the deformation at ∼103 s−1 of a quenched and tempered HY-100 steel. According to Cho et al. [], dASBs of about 20 μm in width were initially observed at a strain rate of 103 s−1 in a tempered martensitic steel, but the narrower tASBs were observed in the center of the dASBs at the higher strains. They explained this phenomenon by the highly concentrated local strain and temperature rise, which confirms our microstructural evolution related to the transition from dASB to tASB (a–d). The tASB consists of equiaxed grains which are known to form by the dynamic recrystallization in previous studies [], and the typical dynamic recrystallization takes place above the half of melting temperature (in Kelvin) of metals []. The peak temperatures calculated above the 28% strain are greater than 0.5 Tm (900 K) of the steel, indicating that the dynamic recrystallization can occur within this ASB.In order to confirm the formation of ASB by the dynamic recrystallization, the EBSD grain orientation spread (GOS) analysis representing the orientation difference between every point in a specific grain and average grain orientation was conducted. a, respectively, formed by the dynamic compression or ballistic impact. The GOS data are mathematically expressed as [GOS=1N∑A=1N{min[cos−1(trace[gave(higA)−1]−12)]}where A is the Ath point in the grain, N is the overall number of point in the definite grain, gA is the orientation of the Ath point, gave is the average orientation of the grain, and hi is the symmetrical component. The GOS data can be used to distinguish the deformed and dynamically recrystallized grains. In general, GOS values of 1–1.5° are used as a threshold, and grains having the threshold GOS or lower are regarded as dynamically recrystallized ones []. Here, the GOS analysis is used for differentiating whether grains located within the ASB are recrystallized or not, instead of quantitatively analyzing the recrystallized grains. Thus, an average GOS value of 1.3 is used as a threshold GOS value of dynamic recrystallization in this study.The dASB starts to form at the 28% strain, and consists mostly of elongated grains of about 0.8 μm in width, together with some small equiaxed grains (expressed by blue-colored areas in a). These equiaxed grains result from the dynamic recrystallization occurred at 965.7 K (a) above the recrystallization temperature. Unlike the dASB, the tASB of dynamically-compressed or ballistically-impacted specimens consist of blue-colored grains (i.e., GOS values of 1.3° or smaller, b–e). This result confirms that tASBs form primarily by the dynamic recrystallization. The tASB of 3 μm in width starts to form at the 30% strain, and extends to 10 μm at the 33% strain, where the temperature rises to 993.4 and 1040.3 K, respectively (a). As a result, the dynamic recrystallization occurs sufficiently at 993.4 K, and the dynamically recrystallized region extends to the width of 10 μm at 1040.3 K. From this understanding of the calculated temperature and microstructural analyses, kinetics of ASB formation can be discussed further in the next section.The dynamic recrystallization is classified into a migrational type which principally involves a grain-boundary migration and a rotational type that involves a sub-boundary rotation forming high-angle grain boundaries []. Since the time required for developing a grain of 0.1 μm in size by the grain-boundary migration is much longer by several orders of magnitude than the deformation time [], it is hard to accept that the grain-boundary migration can be a primary mechanism for the dynamic recrystallization within ASBs. Instead, the sub-boundary rotation can be a feasible mechanism to form equiaxed micro-grains in a very short time. Many recent studies [] have shown that very small equiaxed grains inside ASBs form by the sub-boundary rotation.According to the rotational dynamic recrystallization (RDR) mechanism, initial grains are elongated along the shear direction, and then split into subgrains. This grain subdivision continues as the deformation proceeds, and consequently an equiaxed nanocrystalline structure is constructed by the sub-boundary rotation of about 30° []. The process of sub-boundary rotation forming high-angle boundaries works for minimizing the interfacial energy. The time required for rotation process is described by the following equation [t=L1kTf(θ)4δγDb=L1kTf(θ)4δηDb0exp(−Qb/RT)where t is the time, L1 is the average subgrain diameter, θ is the subgrain misorientation angle, δ is the grain-boundary thickness, η is the grain boundary energy density, Db0 is a constant related to grain boundary diffusion, Qb is the activation energy for grain boundary diffusion, and f(θ) is expressed by:f(θ)=3tan(θ)−2cos(θ)3−6sin(θ)+23−439ln2+32−3+439lntan(θ/2)−2−3tan(θ/2)−2+3where the parameters of η, δ, δDb0, Qb, k, and R are 0.985 J/m2 for pure iron [], 0.5 nm, 1.1×10−12 m3/s for α−iron, 174 kJ/mol for bcc metal [], Boltzmann constant of 1.38×10−23 J/K, and gas constant of 8.314 J/mol∙K, respectively. The subgrains need to rotate about 30° to form recrystallized grains.The variation of angle (θ) as a function of time obtained from Eq. a and b. The temperature (T) varies from 0.40 to 0.55 Tm for the subgrain size (L1) of 190 nm (a), and the L1 varies from 100 to 1000 nm at 0.50 Tm (b). This result implies that the higher T and the smaller L1 require the shorter time for the sub-boundary rotation of 30°. Particularly when the temperature is higher than 0.50 Tm, the RDR occurs possibly in a very short time, while it requires a relatively longer time below the temperature of 0.45 Tm. In c, the average size of recrystallized equiaxed grains within the initial tASBs at the 28% strain is about 190 nm. It can be seen from a that the time required for the sub-boundary rotation of 30° is longer than 20 μs and 8 μs at 0.50 Tm and 0.55 Tm, respectively, for the L1 of 190 nm.c shows the compressive strain as a function of time during the dynamic compression at the strain rate of 3900 s−1. The strain-time data can be obtained from the reflected wave and time data recorded in the oscilloscope. The compressive strain increases linearly with increasing time, the stress collapse occurs at 74 μs, and the time for initiation of dASB and tASB are 81 and 86.5 μs, respectively. The ASB starts to form in 7 μs after the stress collapse, and it propagates progressively. Cracks initiate at 96 μs and propagate at 99.5 μs along the already-formed ASBs to reach the complete separation at 103 μs. Since the temperature rises to 993.4 K (much higher temperature than 0.5 Tm) at 86.5 μs where the tASB forms for the first time (c), fine equiaxed grains can form sufficiently. In the ballistic impact, tASBs can form more easily because the ballistic impact results in the higher temperature rise and the smaller L1 under the much higher strain rates. Thus, the proposed RDR mechanism provides a reasonable explanation for the occurrence of dynamic recrystallization within the tASB during both the dynamic compression and ballistic impact in the 500T steel.Equiaxed grains of 190 nm in average size form (c) and then grow up to 260 nm for 9.5 μs (c). This grain growth within the ASB is also observed in the ballistically impacted specimen (], the grain-growth rate under high strain rates was be expressed by the following differential equation:dDdt=(Db+k1γ˙Dbt)(ηD+τi2E)2ΩδkT+αμb2ηD22ρm3γ˙where D, t, Db, k1, and α are the grain size, time, grain boundary diffusion coefficient, constant 0.0041 [], respectively. The Db is expressed by Dboexp (-Qb/RT), where Dbo, Qb, R, and T are the constant related to grain boundary diffusion, activation energy for grain boundary diffusion, gas constant, and temperature, respectively. The Db increases with increasing temperature, which raises the grain growth rate. γ˙, E, b, Ω, ρm, μ, and τi are the strain rate, elastic modulus, burgers vector, atomic volume (= b3), mobile dislocation density, shear modulus, and applied shear stress, respectively. They are estimated to be 3900 s−1 measured in this study, 201 GPa for ARMOX 500T steel [], 1.53×10−29 m3, 4.6×1013 m-2 for lath martensitic steel [], and 1464 MPa for ASB formed along the shear direction (45 deg from the compressive loading direction), respectively. The present grain-growth-rate model expressed by Eq. reflects well effects of strain rate and temperature on grain-growth rate under the high-speed deformation, and explains the experimental results on grain growth within the ASB in consideration of high-speed deformation and high adiabatic heating.The calculated grain sizes are plotted as a function of time, as shown in d. For the dynamic compression at the strain rate (γ˙) of 3900 s−1, the initial grain size and temperature at t = 0 s are 190 nm and 993.4 K, respectively. For the ballistic impact, the γ˙ of 105 s−1 [] was used, and the temperature rise within the ASB was estimated to be 1673 K which was experimentally measured in the C-300 steel []. Since the ballistically impacted specimen does not contain any amorphous structure, the temperature rise is expected to be below the melting point (1800 K). In the dynamic compression, the grain size starts to increase almost linearly with increasing time, and then exponentially increases after a few microseconds, as drawn by a black line in d. It takes about 7 μs for the initial growth of equiaxed grains from 190 to 260 nm. This corresponds approximately to the experimentally measured time, 9.5 μs (c). In the ballistic impact, the grain size increases exponentially from the beginning, as drawn by a red line in d. It takes less than 1 μs for the initial equiaxed grain to grow to 480 nm corresponding to the experimental one (a–c). Since the strain rate during the ballistic impact is known as about 105–3 × 105 s−1 [], the deformation time is much shorter by two orders of magnitude than that of dynamic compression. The great increase in strain rate in the ballistic impact induces the temperature rise due to the adiabatic heating, and motivates the mobility of grain boundaries [], which can lead to the rapid rate of grain growth. Therefore, these results are reasonably accepted, and confirm that the growth of equiaxed grains can occur at both strain rates of 3900 s−1 and ∼105 s−1 in the dynamic compression and ballistic impact, respectively.The grain growth might occur after the deformation followed by the subsequent cooling. The cooling rate within the ASB after the deformation was measured to be about 107 K∙s−1 [], which was quite rapid, while the density of mobile dislocations reduced rapidly. According to Hines et al. [], once the deformation has ceased, the dislocation density within the grain boundary can decrease substantially from 1012–1013 to 108–109 cm−2 in a very short time (about several tens of microsecond). During the cooling, thus, the grain growth rate decreases, but the growth can occur, although its amount is not large.a and b shows TEM bright-field (BF) images and selected area diffraction (SAD) patterns of the central area of tASBs collected from red-boxed areas of b of the dynamically-compressed and ballistically-impacted specimens, respectively. Extremely fine equiaxed grains of 200–300 nm in size are observed, which matches well with the EBSD data (d). A number of dislocations are present throughout the equiaxed grains. This is attributed to the extremely large generation of dislocations due to the heavy deformation during the dynamic compression and ballistic impact. The dislocation density of the equiaxed grains is still high, although it reduces considerably by the dynamic recrystallization. The diffraction patterns of the ASB display ring-like patterns (insets of a and b). These ring-like patterns indicate that multiple crystalline orientations obtained from very fine grains exist clearly even inside such a narrow ASB area. Traces of splitting of elongated grains are also observed within the ASB as shown in a dashed box of d shows a schematic view of an elongated grain inside the dashed box of c. Such a linkage of equiaxed subgrains and elongated parent subgrains suggests that the equiaxed subgrains did not evolve from nucleation and growth processes.e and f shows BF images and SAD patterns of the exterior areas near the tASBs. Parallel subgrains are elongated along the shear direction. The width and aspect ratio of subgrains are 60–140 μm and 6–14, respectively. The SAD patterns ([111] zone axis, insets of e and f) shows slightly dispersed spot patterns, which are different from ring patterns of the center of ASBs (a and b). This implies that the substructure contains some low-angle boundaries or that a significant amount of misorientation exists in local lattices. With respect to the microstructural evolution, the elongated subgrains form before the formation of tASB (a) or exist in the exterior area of tASB (b). The severe deformation induces the elongation and subdivision of grains; however, it can be deduced that the temperature rise is insufficient to rotate the sub-boundary by 30°.Based on the temperature rise calculation and systematic microstructural characterization, the microstructure evolutions during the dynamic compression (γ˙; 3900 s−1) are schematically illustrated in a shows initial equiaxed tempered martensite with PAGS of 20 μm. These grains are elongated along the shear direction, and dislocations are accumulated in sub-boundaries inside the elongated grains (b). The elongated grains are split into subgrains, and a dASB forms at the time of 81 μs. As the deformation proceeds, the grain subdivision continues, and fine equiaxed subgrains of 190 nm in size form by the rotation of sub-boundaries, thereby leading to the formation of tASB at 86.5 μs (c). Finally, the peak temperature rises to 1040.3 K at 96 μs, and a crack initiates and propagates along the tASB composed of very fine equiaxed grains to reach the failure (In the ballistic impact, most of cracks readily initiate and propagate along the already-embrittled ASB areas. Although the strain rate of actual ballistic impact is much higher than that of dynamic compression, the ASB formation behavior obtained from the laboratory-scale dynamic compressive test can be adapted to understand the ballistic behavior.In the dynamic compressive test, the ASB starts to form as a relatively wide dASB (width; 30–40 μm) along the shear direction at the 28% strain (a). The dASB develops into the very narrow tASB (width; about 3 μm) at the 30% strain (b). The tASB width tends to increase to 10 μm as the strain increases to 33% (c), and cracks initiate and propagate along the tASB (d). It is interesting to note that this ASB formation and cracking behavior is observed similarly in the ballistically impacted specimen. Most of ASBs of the ballistically-impacted specimen are wider (10–55 μm, b) than those of the dynamically compressed specimens (3–10 μm, b and c), while cracks initiate and propagate along ASBs located near the perforated surface, whose shape is similar to that of the dynamically compressed specimens. The reason for the wider ASBs in the ballistically impacted specimen can be interpreted by the more severe deformation inducing the wider region of the smaller subgrains and the higher temperature rise, which enables for sub-boundaries to rotate about 30° easily.According to the EBSD and TEM analysis results, the interior of ASBs consists of very fine equiaxed grains, and their sizes are 190–260 nm in the dynamically compressed specimens (d) and 220–480 nm in the ballistic impact specimen (b,c). The main formation mechanism of these grains is the RDR caused by the adiabatic heat generated during the high-strain-rate deformation, and the subsequent grain growth occurs within a very short time. When the grain growth rate is different, the gradient structure composed of different-sized grains forms in the areas such as the surface-ASB of the ballistically impacted specimen (a–c). The formation of fine equiaxed grains and their growth can occur in less than 1 μs (d), and ASBs containing these grains have very high hardness values depending on the grain size. shows the variation in hardness of ASBs (d) as a function of average size of equiaxed grains formed during the dynamic compressive or ballistic impact tests (b,c). The hardness is much higher than that of the steel matrix, and decreases as the average grain size increases. This result indicates that the inverse correlation between the hardness and grain size is well observed in both the dynamic compression and ballistic impact. This hardness trend as well as the formation behavior of ASB and cracking works for plausibly interpreting the microstructure evolution and fracture behavior during both the dynamic compression and ballistic impact. The present dynamic compressive test effectively evaluates the ASB formation and cracking, and it would provide an important insight on whether ASBs or cracks form or not during the ballistic impact.In this study, the evolution of ASB during high-strain-rate deformation in the high-strength armor steel was investigated by using the SHPB technique. An interrupted dynamic compressive test was performed to investigate microstructural evolutions by stages and to characterize detailed microstructures of ASBs. These results were correlated with those of the actual ballistic impact behavior. The main conclusions can be drawn as follows:The 500T steel consisted of tempered martensite (PAGS; ∼20 μm), and exhibited high strength and hardness above 1.7 GPa and 500 HV, respectively. According to the interrupted dynamic compressive test, the dASB started to form diagonally at the 28% strain right after the stress collapse, and developed into tASB with ∼3 μm in width at the 30% strain. At the 33% strain, a crack initiated and propagated along the extended ASB of ∼10 μm in width to reach the final failure at the 36% strain.For the dynamic compression, the dASB consisted of elongated grains of ∼0.8 μm in width and some fine grains. The further-developed tASB was composed of very fine equiaxed grains of ∼190 nm in size, and the equiaxed grains grew up to 260 nm during the time of 9.5 μs. The interior tASB consisted of a single BCC phase, which indicated the phase transformation did not occur.For the ballistic impact, relatively wide tASBs (width; 30–70 μm) mostly formed at the perforated surface, while some narrower tASBs (width; 5–25 μm) were branched from the wide surface-ASB. Very fine equiaxed grains and heavily elongated grains were observed at the narrow tASB. All fine grains had a single BCC phase, and their size was ∼220 nm, which was comparable to that of tASB formed in the dynamically compressed specimen. The average grain sizes varied from 360 nm to 480 nm, thereby forming the gradient structure at the surface-ASB, which was attributed to the grain growth induced from the frictional heat generated by a fast-traveling projectile.The proposed RDR mechanism provided a reasonable explanation for the formation of fine equiaxed grains within the tASBs during both the dynamic compression and ballistic impact. The temperature rose to 993.4 K at 86.5 μs where the tASB formed initially in the dynamic compression. Under these temperature and time conditions, the sub-boundary rotation of 30° occurred, which indicated that the dynamic recrystallization led to the formation of fine equiaxed grains. In the ballistic impact, tASBs could form more easily because of the higher temperature rise and the smaller L1 under the much higher strain rates.The proposed grain-growth-rate model provided a reasonable explanation for the grain growth within the ASB. It confirmed that the growth of equiaxed grains could occur at both strain rates of 3900 s−1 and ∼105 s−1 in the dynamic compression and ballistic impact, respectively. ASBs containing fine equiaxed grains had very high hardness values above 681 HV depending on the grain size, and the inverse correlation between the hardness and grain size was well observed in both the dynamic compressive and ballistic impact specimens.The formation behavior of ASBs as well as the cracking in the ballistic impact was correlated well with the dynamic compression in terms of microstructural evolution, formation mechanisms and kinetics of ASB, and hardness. Based on the reasonable correlation of the formation mechanisms and kinetics of ASBs, this study would suggest a reliable method to interpret the ASB formation and fracture mechanism by the ballistic impact based on the high-strain-rate deformation behavior.Min Cheol Jo: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Data curation, Writing - original draft, Visualization. Selim Kim: Methodology, Data curation, Validation. Dae Woong Kim: Methodology, Investigation. Hyung Keun Park: Methodology, Investigation. Sung Suk Hong: Resources, Funding acquisition. Hong Kyu Kim: Resources, Funding acquisition. Hyoung Seop Kim: Writing - review & editing. Seok Su Sohn: Conceptualization, Visualization, Funding acquisition, Writing - review & editing, Supervision. Sunghak Lee: Conceptualization, Project administration, Writing - review & editing, Supervision.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Study on flexible large-area Poly(vinylidene fluoride)-based piezoelectric films prepared by extrusion-casting process for sensors and microactuatorsPoly(vinylidene fluoride) (PVDF)-based film is a typical kind of piezoelectric films with wide applications, which is mainly prepared by the casting process. It is difficult to obtain large-area film and realize continuous fabrication. In this paper, Firstly, PVDF/PZT@105(lead zirconate titanate)/GO(graphene oxide) composite films with various GO contents were prepared via the casting process, and through comparison among the dielectric and mechanical properties, the optimum GO addition amount was determined. Subsequently, PVDF-based piezoelectric film(PVDF/PZT@105/GO)was prepared via the extrusion-casting process. Comparison between the composite films prepared by two different processes were taken. Note that the extrusion-casting process is favorable for obtaining superior properties such as higher density, dielectric constant, breakdown strength, and piezoelectric coefficient. Besides, during the exploration of the polarization technology it is found that the improvement of polarization field intensity tends to be is the most important factor affecting the piezoelectric properties of the film. The piezoelectric coefficient (d33) of PVDF/PZT@105/GO film prepared by the extrusion-casting process can reach 26 pC/N. Finally, the electrodeformation effect of the composite film was studied, obtaining the electromechanical strain up to 2%, which is much bigger than the piezoelectric ceramics ever been reported and can be used in the microfluidic field.Poly(vinylidene fluoride) (PVDF) films are widely applied as flexible piezoelectric sensors, soft robotics, energy harvesters, and actuators [] for they have lightweight, flexibility, superior mechanical properties, electrical breakdown strength, ferroelectricity, and piezoelectricity []. Also, it exists many limitations such as low dielectric permittivity (ε) and nonpolar phase in normal condition. To overcome these shortcomings, ceramics with high ε are thought of comprising them with PVDF, leading to a combination of flexibility, high dielectric breakdown, and high dielectric constant []. Generally, the improved dielectric permittivity (ε) always obtains at the expense of breakdown strength (Eb) in polymer dielectrics due to the following factors: (1) Electric field distortion at the interface between inorganic fillers and organic matrix. (2) Agglomeration or voids induced by the poor compatibility of inorganic fillers with an organic matrix. To overcome these shortcomings, conductive fillers, including carbon nanotubes [], and carbon fibers are recently been employed to prepare high-εr composite materials. GO-based composites are an important research direction as they have shown excellent performance []. At present, the research of GO composites mainly focuses on GO polymer composites and GO-based inorganic nanocomposites. At the same time, GO can improve the mechanical properties of Polymer-based material [Eb is one of the key parameters determining flexible films with good piezoelectric properties. Firstly, the composite piezoelectric film can only show excellent piezoelectric properties after an appropriate polarization process. Secondly, good electrodeformation effect of polymer matrix composites can only be achieved under a large electric field. At present, researches on composite piezoelectric films are mainly focused on composition, structural design, and related applications. There are few studies on polarization technology, especially in the field of flexible film with less ceramic filling. Therefore, it is very important to study the polarization technology of flexible composite piezoelectric film for the preparation of composite piezoelectric film with high piezoelectric coefficient. Moreover, There has been many researches on the electrodeformation effect of piezoelectric ceramics and pure polymers. Whereas there are few studies on the electrodeformation effect of composite piezoelectric materials. It is of great significance to study the electrodeformation effect of composite piezoelectric materials and grasp the action law for the application of composite piezoelectric materials in the field of micro-drive.Currently, the method of casting is generally adopted in lab to prepare PVDF-based films [], which possesses the following disadvantages: (1) It is hard to obtain high density as a large number of solvent is used in the preparation process. (2) The preparation efficiency is quite low to realize mass production. (3) Large-area films are difficult to be prepared. The extrusion-casting process [] can produce large-area, high-density polymer films, which has been widely used in the preparation of PE, TPU, an son on. While it is rarely reported in the preparation of PVDF/PZT composite piezoelectric film. In this work, we prepared PVDF/PZT@105/GO film by the extrusion-casting process with 15 wt% PZT addition(the reason for adding 15 wt% PZT is to maintain the flexibility of the films and improve the electrical properties as much as possible, because when the addition amount is too large, the films are difficult to densification, and exist larger brittleness). The performance is systematically compared with that obtained via the casting process. It is found that the films prepared by the extrusion process shows better properties. The d33 of PVDF/PZT@105/GO film prepared by the extrusion-casting process can reach 26 pC/N and the electromechanical strain up to 2%.Poly(vinylidene fluoride) (PVDF) powders were purchased from Shandong huaxia shenzhou new materials Co., Ltd.. Commercially available PZT-5H powders (Jude Electronic Technology Co., Ltd., China, Shandong, China, d33 = 590 pC/N, density = 7.6 g/cm3) were used as fillers. Commercial GO powders were obtained from Chengdu Zhongke Times Nano Energy Tech Co., Ltd.. Titanate coupling agent(UP-105) was obtained from Nanjing youpu chemical Co. Ltd. N,N-dimethylformamide (DMF) was supplied by Aladdin Biochemical Technology Co., Ltd.Firstly, PVDF/PZT@105/GO (PVDF/PZT = 85:15 wt) films with various GO contents were prepared by the casting process. All powders were proportionally dispersed in DMF (powders: DMF = 1:10, mass ratio) by magnetic stirring for 3 h at 25 °C, followed by stirring at 70°Cfor 30 min to form a stable suspension. The suspension was then cast into a glass pane, and drying at 60 °C, composite films with thicknesses of 30–120 μm were obtained.Then, PVDF/PZT@105/GO film was prepared by extrusion-casting-drawing-line equipment (PVDF:PZT@105:GO=85:15:0.1(mass ratio), PZT@105 represents that PZT is modified by a coupling agent(UP-105) with a mass fraction of 0.8%). All powders were first added to a ball-milling pot containing a certain amount of alcohol, then mixed in a ball mill for 6 h, and finally dried in a blast dryer. The composite powders were first granulated and then extruded at 250 °C via an extrusion–casting–drawing line device. The relevant photos were taken by a digital camera. The morphology was characterized by scanning electron microscopy (FESEM, S-4800, Hitachi, Tokyo, Japan). The crystal structure was measured by X-ray diffraction(XRD, Bruker D8 Advanced, Germany). The mechanical properties test response of samples were tested by a dynamic mechanical analyzer(DMA)(RSA-G2 Solids Analyzer, TA Instruments, USA). For electric measurement, the films were coated on the two surfaces with silver electrodes (Φ6 mm) using a coating method. The frequency dependencies of dielectric properties were measured with a NOVOCONTROL test system (Concept 80, Germany). Electric breakdown tests were carried out with a Withstand Voltage Test System (7474, EXTECH ELECTRONICS CO., LTD.), the samples were immersed in silicon oil. The piezoelectric coefficients(absolute value) were measured using a static tester(Piezo Test; Acoustic, Chinese Academy of Sciences). The electric displacement-electric field (D-E) loops and electromechanical strain were measured with a Premier II ferroelectric test system (RTI-Multiferroic, Radiant Technologies Inc.) at 100 Hz. shows the photo and schematic diagram of PVDF/PZT@105/GO film in our work. To enhance the dispersion and combinability of PVDF and PZT in the film, a coupling agent (UP-105) is used to modify the surface of PZT with a mass fraction of 0.8%, labeled as PZT@105 []. To ensure the flexibility of the film, the addition amount of PZT@105 of 15 wt% is chosen and GO is added to improve the electrical properties. As can be seen, PZT is filled into PVDF matrix and GO is dispersed between PZT particles and PVDF matrix.At first, the composite piezoelectric films with various GO contents were prepared by the casting process (PVDF/PZT@105 = 85:15 wt%) with GO contents of 0 wt%, 0.05 wt%, 0.1 wt %, 0.15 wt %, 0.25 wt%, 0.5 wt%, 1 wt%, 1.5 wt%, 2 wt%, 2.5 wt%, respectively. shows the photographs of the composite films prepared by the casting process. shows the SEM images of the composite piezoelectric films with various GO contents. As can be seen, when the content of GO is lower than 0.15%, the film possesses good densification. When the content of GO reaches 0.25%, obvious pores appear in the films, and with the increase of GO content, the number of pores increases. As referred due to the existence of π-π coupling, Van Der Waals forces, and high specific surface area, GO will irreversibly agglomerate and even rearrange itself back into the graphite structure, which makes it difficult to obtain the stable dispersion of GO. shows dielectric properties of all the PZT/PVDF@105/GO composite films with various GO contents. By comparing the dielectric constant of all the samples at 1 KHz, it can be seen that the dielectric constant of the films has been improved after the addition of GO. While in the low frequency (1 Hz), it can be seen that film without GO has a greater dielectric constant than those with a small amount of GO(0.05%,0.1%,0.15%), which is mainly due to the fact that the interface polarization is important in low frequency. As film without addition of GO possesses poorer density with a lot of gaps, which resulted in increased interface effect. By adding a small amount of GO, the density of the films increases, the gap decreases, interfacial polarization effect is abate. As the GO content is increased to a certain range, dielectric constant is significantly improved both in low frequency and high frequency ranges. This can be ascribed to the fact that GO is a zero-distance semiconductor, its conduction and valence bands meet at the Dirac point. GO has a two-dimensional sheet structure with high conductivity and a large aspect ratio, which can be used to obtain polymer matrix composites with high dielectric constant at very low content. GO with the ultrahigh specific surface area can form more micro capacitor structures in the organic matrix to improve the dielectric properties of the composite system.As can be seen from the dielectric loss diagram, the film without GO has a strong interface effect due to its poor compactness with a dielectric loss higher than that of the film with a small amount of GO. When the GO content reaches 0.25%, the dielectric loss is increased significantly. Combined with the dielectric constant curve, it can be concluded that by adding an appropriate amount of GO, density of the film can be greatly improved with the a higher dielectric constant and lower dielectric loss.The PVDF/PZT@105 composite film exhibits low elongation at the elasticity range and high yield stress [(a). However, with the addition of GO (0.05–0.15%), the elongation at break is increased to some degree. This result indicates the addition of GO can improve the interface associative property between PZT and PVDF matrix. And a well-dispersed GO can effectively enhance the mechanical properties of the PVDF/PZT@105/GO composite films. When the content of GO reaches 0.25%, the mechanical properties show a downward trend. This is because when the content of GO is relatively small, it can be well dispersed in the matrix material and form a certain bond strength compound with the matrix. The high-strength GO can transfer stress and prevent the rapid growth of cracks, thus strengthening and toughening the matrix and improving the strength and toughness of the composite material. With the increase of GO addition, the dispersion uniformity and bond saturation of GO in the matrix becomes worse, and some of the GO is agglomerated, bringing in the formation of internal microcrack defects, resulting in the decrease of tensile strength and elongation at break.Through the previous analysis, it can be seen that the addition of an appropriate amount of GO can promote the densification of the films, improving the dielectric constant, with a low dielectric loss. In this part, PVDF/PZT@105/GO composite film with 0.1% GO content is prepared by the extrusion-casting process, and the related properties of PVDF/PZT@105/GO composite films are compared with those composite films with the same component prepared by casting.The microcosmic morphology can be observed from , showing that the PVDF/PZT@105/GO film prepared by casting has a poor density with many defects and voids around the interface (). However, this phenomenon largely disappeared in the film prepared by the extrusion-casting process(). The film prepared by casting process can not get good density because a large number of solvent is used in the preparation process. In the drying process, as the solvent evaporates, leaving many holes. The extrusion-casting process does not use solvent to ensure the density of the films. XRD spectra() shows the film prepared by the extrusion-casting process exists mainly an α crystal. While β-phase dominates prepared by casting. It shows a distinct peak at 2θ = 17.66°, 18.3° and 19.90°, representing the(100), (020), and (110)diffraction plane of the α-phase []. The β-phase shows characteristic peaks at 2θ = 20.26°, which is partial overlapped with the peaks of α-phase in 2θ = 19.90°. The corresponding XRD curves are shown in , the diffraction results show that diffraction degrees of 2θ = 17.6, 18.3, 19.9, and 26.5 related to the α-phase are disappearing and new peaks at 2θ = 20.26 and 2θ = 36.3 are appearing as a characteristic of the β-phase.The main reason is that when the film is prepared by the extrusion-casting process, the temperature is as high as 250 °C. When the polymer melt is extruded, the molten state of PVDF is changed sharply from high temperature to low temperature. α phases is easy to be formed in PVDF after cooling in a high temperature melting state. When the casting process is used, the temperature is relatively low and β phase is easy to be formed.The mechanical properties of PVDF/PZT@105/GO composite films prepared by different processes are shown in . As can be seen that the films prepared by the extrusion-casting process are superior to the casting process. Films prepared by the extrusion-casting process have excellent tensile properties and dynamic modulus, this is mainly due to the fact that the film prepared by casting process can not get high density, which has been discussed above. shows the stress-strain curve and strain-modulus curve of the film measured under compression mode(the sample diameter is 15 mm). By comparing with , we can see that the film exhibits different mechanical properties in different modes. In the tensile mode, the stress-strain curves of the film show linear correlation at the beginning of the stretching, and then the yield point is reached, following the stress begins to decline, indicating that it has exceeded the elastic range of the film. While the modulus shows a trend of increase firstly and then decrease, without any no linear relationship between them. In the compression mode, it can be seen that the film is always in the elastic region within a large range of relative deformation, and its stress curve and modulus curve show a similar linear relationship with the compression deformation. The phenomenon is mainly related to the molecular structure of the PVDF which is a kind of chain molecules. In the tensile state, elongation can be realized by the movement of the molecular chain extension. However, under the condition of compression, as a result of the existence of repulsive force between the molecules, it is difficult to achieve volume contraction, leading to a stress increase sharply (In practical applications, when used as a sensor (including the piezoelectric nanogenerator), it is mainly to collect the electrical signals generated by pressure. While when being used as a strain-gauge, it is mainly to detect the electrical signals under tensile deformation. Therefore, it is of great significance to clarify the mechanical laws in different modes for the practical application of composite piezoelectric films.Temperature is an important factor to be considered in the application of elastomers. Changes of temperature often lead to varying in mechanical and electrical properties. Generally speaking, the temperature variation is mainly influenced by two factors: the ambient temperature and energy conversion such as dielectric loss. The mechanical properties of PVDF-based films at different modes are shown in (storage modulus curve depended on temperature. In stretch mode, the ratio of length to width of the film is 5:2, the amplitude deformation is 0.2%, the oscillation frequency is 2 Hz. In the compression mode, the sample diameter is 15 mm, the amplitude deformation is 0.5%, the oscillation frequency is 2 Hz). It can be seen that the storage modulus of PVDF/PZT@105/GO composite film decreasing with temperature increasing, especially in stretch mode. Generally speaking, the applying temperature of PVDF-based films as actuators and sensing materials is between 25 and 40 °C. By comparing the storage modulus of different PVDF-based films in this interval, we found that PVDF is very sensitive to temperature. As temperature increases, the storage modulus decreasing sharply in stretch mode, with only 1.76% surplus at 40 °C compared with 25 °C. PVDF-based composite films show enhanced temperature stability in compression mode, the decline magnitude of the storage-modulus has been greatly reduced, with 44.4% surplus when the temperature is 40 °C compared to 25 °C, It is probably associable with the molecular structure of the PVDF which has been discussed above. The change of modulus can seriously affect the force-electric conversion effect, so PVDF-based composite films have advantages in compression mode application than tensile under various temperatures.The dielectric properties, mainly contain dielectric constant (ε) and dielectric loss (tanδ), breakdown strength, ferroelectric and piezoelectric are very important parameters. gives comparisons of dielectric behavior of PVDF/PZT@105/GO films depends on the frequency (25 °C) prepared by the extrusion-casting process and casting. In all the films, the dielectric constant decreases with the increases in frequency because the space charge polarization disappears replaced by the dipolar polarization. The PVDF/PZT@105/GO film prepared by the extrusion-casting process has a larger dielectric constant and lower dielectric constant due to its good density and uniformity.Breakdown strength (Eb) is a crucial factor of composite films. We use Weibull statistic to analyze Eb as described in Equ.116.In this equation, F(E) is the cumulative probability of electric failure, β evaluates the scatter of data, E represents the breakdown electric field, and α is the electric field strength for the sample to breakdown at a 63% probability. The results are presented in (b). In principle, the breakdown process is defined as the growth of the breakdown path []. In this process, regions with many defects and voids will break down first, as breakdown path grows through the film, the overall breakdown happens when connecting two electrodes. So, for enhancing the breakdown strength, it is plausible to eliminate interface defects and hinder the growth of electro-tree. For PVDF-based composite films, interfaces between ceramic fillers and polymeric matrices are the most likely weak points. By comparing the breakdown strength at different temperatures, we can see that PVDF/PZT@105/GO films prepared by the extrusion-casting process have higher breakdown strength than the casting process, these results due to the good compactness. The Eb of PVDF/PZT@105/GO films decreases with the temperature increases from 25 °C to 80 °C. This is because with the increase of temperature, the molecular activity of PVDF increases, and the number of free electrons increases, which will lead to the growth of electro-tree easily.The dielectric response under low electric field could not reflect the overall polarization mechanism of PVDF-based composite films due to the dipoles movement under a high electric field is the critical factor to determine the dielectric performance. So, we provide the displacement versus electrical field loops (D–E loops) of PVDF-based composite films. The displacement versus electrical field loops (D–E loops) is shown in (c) As could be seen that, the maximum displacement prepared by the extrusion-casting process is bigger than the casting process at the same electric field due to its higher density which is similar to the excellent dielectric properties.(d) shows the piezoelectric coefficient(d33) of different films polarized at various temperatures. The PVDF/PZT@105/GO film prepared by extrusion-casting process shows the d33 value as 26 pC/N when polarized at 25 °C, higher than the casting process because this type of film has a higher breakdown field, it can be polarized under larger electric field intensity. The piezoelectric coefficient is decreased with an increase in the polarize temperature due to the decrease of breakdown strength. From this, we can also see that the polarization field intensity lays a greater influence on the polarization performance than the temperature.Through the comparison, it can be seen that the properties of composite films prepared by the extrusion casting process are better than the casting. These experimental results confirm the feasibility of this process, which is of great significance for realizing industrial production. At the same time, we can also see from the results that the films polarized at low temperature have a larger piezoelectric coefficient. In general, piezoelectric materials need polarization under high temperature and high electric field intensity, such as piezoelectric ceramic materials. At high temperature, the activity of dipole enhancement, is advantageous to the dipole flip, realizing the orientation arrange. However, in the PVDF/PZT@105/GO composite films, PZT and PVDF exist contrary piezoelectric coefficient after polarization under the same electric field, leading to the piezoelectric performance partially offset. So the polarization process appears especially important. In the early, neat PVDF film was prepared using extrusion casting process, the crystallinity is about 30%, after polarization under the different temperature and electric field intensity, the piezoelectric coefficients are less than 10 pC/N, the piezoelectric coefficient of PVDF/PZT@105/GO composite films in this experiment can achieve 26 pC/N, which is mainly due to the fact that PZT getting better polarization, playing an obvious piezoelectric effect.Three conclusions can be drawn from the above analysis: (1)With the increases in temperature, the breakdown strength of the film decreases; (2) PVDF/PZT@105/GO composite films can achieve good piezoelectric performance at low-temperature polarization, mainly because the polarization field strength is relatively large; (3) The polarization field intensity lays an important influence on the polarization process.To further prove that the piezoelectric effect of the film is mainly caused by the polarized PZT ceramic particles, the crystallinity and phase structure of PVDF in the PVDF/PZT@105/GO composite films are characterized.(a). The degree of crystallinity(ΔXc) is calculated according to Equ.2[Where ΔHm represents the melting enthalpy and ΔH100 is the melting enthalpy for a 100% crystalline sample. With ΔH100 = 103.40 J/g being the melting enthalpy for pure PVDF[37][]. The calculated result shows that the crystallinity of PVDF/PZT@105/GO composite films is around 22%, which is mainly related to the raw material and the process method.The FT-IR data of the samples is shown in (b). The α-phase of PVDF has the absorption bands at 614, 763, 795, 855, 976, 1150, 1210, and 1383 cm−1, and the β-phase is located at 840 and 1279 cm−1. The relative amount of the β-phase in the PVDF film can be evaluated using the following Eqn. where Fβ represents the β-phase content, Aα and Aβ correspond to absorption bands at 763 and 840 cm−1, respectively. The result shows that the β phase is about 28.4%. This is mainly because the extrusion temperature is more than 250 °C, after being extruded from the die head, it is cooled by the casting roll to form a solid film, PVDF is easy to form α-phase when it cools down sharply in the high-temperature molten state.It can be seen that the crystallinity and β-phase content of PVDF are very small in the PVDF/PZT@105/GO composite films. In this experiment, when the extrusion-casting process is used to prepare the film, a large amount of raw material is needed, so the relatively cheap PVDF is used, and its piezoelectric coefficient is not more than 10 after repeated tests. Therefore, we believe that PZT mainly plays a piezoelectric role. Subsequently, we will further analyze the reasons for PZT particles to achieve good polarization.According to Furukawa's theory of effective electric field for the spherical PZT ceramic particles wrapped in the PVDF matrix, the electric field strength applied to each ceramic particle is given by Equ.4[Where, ε1 and ε2 are the dielectric constants of the polymer matrix PVDF and the ceramic PZT, E0 refers to the applied electric field, Φ is the volume fraction of the PZT. When the composite material is polarized, if the applied electric field is small, as the PZT particles are wrapped in the PVDF matrix, the effective electric field acting on the PZT particles is relatively small, so that the PZT particles can't be polarized effectively. It can be seen from the formula that only the dielectric constant of the polymer matrix is close to the piezoelectric phase, Ec is close to E0, so that PZT can be fully polarized.In our experiments, the addition amount of PZT@105 is 15 wt%, which is converted to a volume fraction of about 4 vol%. The dielectric constant of PVDF and PZT is about 15 and 1700, respectively. According to Eqn. , about 2.7% of the applied electric field will act on PZT particles, so only under a high applied electric field PZT can be fully polarized.Weibull distribution is used to calculate the breakdown strength of the PVDF/PZT@105/GO composite films at 40 °C and 60 °C ( shows that the breakdown strength and the largest actual electric field intensity can be acted on the PZT particles of PVDF/PZT@105/GO composite films prepared by the extrusion-casting process with various temperatures. It can be seen that as the temperature increases, the breakdown strength decreases obviously, the breakdown strength reaches 197 kV/mm at 25 °C with the actual effect electric field intensity of 5.32 kV/mm on PZT. While with the temperature increasing to 80 °C, the breakdown strength is reduced to 91 kV/mm, and the actual electric field intensity acting on the PZT is reduced to 2.43 kV/mm.There are many mechanisms accounting for the decrease of the breakdown strength with the increase of temperature.The dielectric properties of materials are often measured in a relatively high-frequency range. Therefore, it is difficult to reveal their dielectric properties of polymer composites with fillers at ultra-low frequencies. shows the frequency dependence of the dielectric properties of the PVDF/PZT@105/GO composite films. It has been observed that the dielectric constant decreases with the increase in frequency and the PVDF/PZT@105/GO composite films have the lowest dielectric constant at low temperature compared with high temperature ((a)). This may be due to space charge polarization in the boundary interface. At higher frequencies, the dielectric constant is slightly decreasing due to the poor polarization response, which requires a large relaxation time. It is evident that the dielectric constant increases with the raise of temperature. This is because at high temperature, the thermal motion of the polar molecules is high and dipoles are aligned which leads to the higher orientation polarization and hence high dielectric constant.(b) that the dielectric loss increases with the raise of temperature, especially under the low frequency. This is mainly due to the fact that there exists interface polarization effect under low frequency. The raise of temperature is favorable for the increase of activity of dipole and the increase in the number of free electrons, resulting in the increase of dielectric loss. During the polarization process, direct current field is taken, according to the variation law of dielectric loss with the temperature at low frequency, it can be analyzed that when the film is polarized at high temperature, there is a large dielectric loss, which leads to a easy breakdown of the film.The frequency variation of AC conductivity of PVDF/PZT@105/GO composite films at vatious temperatures as a function of frequency is shown in (c). It is observed that conductivity increases with the increase in temperatures. The conductivity steadily increased with the increase in frequency. The frequency-independent contribution to the conductivity at low frequency (which corresponds to the dc conductivity), and a contribution which increased with frequency at higher frequencies can be noted.At present, some scholars have studied the relationship between breakdown strength and mechanical properties of polymer-based materials. The breakdown strengths of these materials are estimated based on the electromechanical breakdown model [where Eb represents electromechanical breakdown strength, Y is the Young's modulus, ε0 is the permittivity of vacuum, and εr is the dielectric constant.The PVDF/PZT@105/GO composite films prepared by the extrusion-casting process are stretched at various temperatures and their mechanical properties are characterized by dynamic mechanics analyzer. The ratio of length to width of the films is 5:1 and the stretching rate is set to be 0.5 mm/s. Stress-strain curves of films at various temperatures are shown in (a). From the curves, it is evident that with the increase of temperature, the stress is decreased. The same results can be seen in (b), which shows the strain-modulus curves at various tensile temperatures. According to Eqn. , the decrease of modulus may be one of the reasons for the reduced breakdown strength at high temperatures.The breakdown of dielectrics under an electric field is a complicated process synthetically affected by a field-induced electromechanical breakdown and current-induced thermal breakdown. The increased Eb of the gradient-structured nanocomposites is mainly ascribed to the improved mechanical properties. Usually, Young's modulus is decreased continuously with the increase of the temperature, which is accordant with the variation trend of the breakdown strength. For instance, as the temperature rising from 25 °C to 80 °C, Young's modulus is notably decreased. The electromechanical breakdown occurs when the field-induced electrostatic stress reaches the critical value overcoming the mechanical stress. Therefore, a higher modulus of elasticity usually indicates stronger electrostatic forces endurance which finally gives rise to higher breakdown strength. Besides, leakage current also plays important role in determining the breakdown behaviors of dielectrics, since the current-induced Joule heating eventually leads to thermal breakdown of materials.The leakage current densities of the PVDF/PZT@105/GO composite films prepared by the extrusion-casting process are thus characterized as given in , showing that the leakage current densities increase with temperature. The leakage current reveals the amount and migration behaviors of mobile charges in polymer composites, which are mainly injected from the electrode.Thus, it can be concluded that, the dielectric loss, conductivity and leakage current is proportional to the temperature, meanwhile, the modulus to be opposite, which leads to a sharp decline in the breakdown strength at high temperature.In order to confirm the polarization field strength on the properties of the piezoelectric effect, we carried out polarization of the PVDF/PZT@105/GO composite films prepared by the extrusion-casting process under different applied electric field at the fixed temperature of 25 °C. The results are shown in . With the increase of the electric field strength, the electric field strength applied to each ceramic particle increases obviously and the d33 simultaneously increases. When the applied electric field intensity reaches 120 kV/mm, the field intensity acting on the PZT reaches 3.24 kV/mm, and the d33 is significantly increased to nearly 15 pC/N. Finally, the piezoelectric coefficient reaches 26 pC/N with the applied electric field of 180 kV/mm.The dielectric response under high electric field could reflect the polarization mechanism of PVDF-based composite films as the dipole movement under high electric field is the critical factor determining the dielectric performance. Thus, we provide the displacement versus electrical field loops (D–E loops) of PVDF-based composite films at various temperatures, frequencies, and electric field intensities, the results are shown in (a) shows the P-E hysteresis loop of the PVDF/PZT@105/GO composite films prepared by the extrusion-casting process under various frequencies at room temperature. It can be seen that as the frequency decreaseing the residual polarization increases which can be due to larger polarization nature with enough polarization time. (b) shows the hysteresis loops at different temperatures. It can be seen that with the increase of temperature, the residual polarization obtained at the same field strength becomes larger, highly relevant to the activity of the dipole increases with the increases of temperature, which is more conducive to the dipole turnover. Generally, the increase of temperature is conducive to the directional arrangement of dipoles to achieve a good polarization effect. In comparison with (c), it can be seen that increasing the electric field intensity can also increase the residual polarization. This is mainly because more dipoles (ferroelectric domains) can be aligned directionally under a large electric field intensity, thus increasing the residual polarization. that the increase of the polarization time, polarization temperature, and the applied electric field can improve the residual polarization. In the process of polarization, increasing the polarization temperature and electric field intensity is generally adopted for achieving good polarization in ferroelectric materials to achieve excellent piezoelectric performance. In this article, conclusion proves that the applied electric field enhancement is the most important factor for the piezoelectric performance improvement in the PVDF/PZT@105/GO composite films with low content of PZT, this is mainly because with temperature increases, the breakdown strength decline sharply, the polarization field strength is low, the electric field strength applied to each PZT particle is very low, it is difficult to realize the domain switching which restricts the improvement of piezoelectric properties.We prepare electrodes of different structures in the PVDF/PZT@105/GO film prepared by the extrusion-casting process. The results are shown in . The electrodes are prepared by screen printing (When a piezoelectric material is placed under a mechanical stress (△σ), a charge is generated across its opposite faces. The energy (E) generated as a result of the applied stress is given by Eqn. where d is the piezoelectric charge coefficient, ε is the dielectric constant, A is the electrode area and h is the thickness of the piezoelectric material. With the development of the 5G era, most of the deep-sea monitoring and positioning identification systems that have been put into use while often highly dependent on the "active" power supply due to technical limitations, which greatly limits their application in the deep sea. Therefore, it is urgent to develop a device that can integrate self-power supply [], monitoring, and sensing. The key materials for devices have become the top priority. Piezoelectric materials can not only transform the force to electricity through deformation, achieving energy collection, but also can sense pressure, generate electrical signals. The extrusion-casting process can be used to continuously prepare large-area films, which can be applied to special fields such as deep-sea. shows the application example of composite piezoelectric films in the deep sea.Although giant electrostriction has been observed in relaxor ferroelectric (RFE) poly(vinylidene fluoride) (PVDF)-based polymers, however, the exact origin for electrostriction has not been fully understood []. The piezoelectric strain coefficient(d33*) of the PVDF/PZT@105/GO film prepared by the casting process cannot be obtained in the experiment as its breakdown strength is too small. (a) shows the strain ratio of the PVDF/PZT@105/GO film prepared extrusion-casting process with different electric field strength. As can be see that the electromechanical strain increases as the electric field strength increasing. When the electric field strength is 220 kV/mm, the electromechanical strain can reach 0.8 μm. This trend is understandable because electromechanical strain is proportional to the square of the electric field, that is consistent with the electromechanical mechanisms involving electrostatic and electrostrictive strains. The thickness of the film used in the piezoelectric deformation coefficient experiment is 35 μm. Thus, its strain ratio is about 2.3%, and the d33* is 104 pm/V. (b) presents the relevant results reported in the current literature []compared with our experiment. The enhanced electromechanical performance in the composites can be explained by two key factors in the aspect of electrostatic and electrostrictive strain mechanisms, the electrical and mechanical properties represented as dielectric constant (K) and elastic modulus (Y), respectively []. In this experiment, PVDF in the composite film prepared by extrusion casting molding technology has low crystallinity and low modulus. Moreover, the addition of PZT improves the dielectric constant of the film. At the same time, due to the obvious interface effect, a large amount of charge is accumulated at the interface between PZT and PVDF, forming small capacitors in PVDF (). From the perspective of electric field distribution (Equ.4), the lower the dielectric constant is, the greater the electric field intensity is distributed. Thus the electric field intensity re-applied to PVDF is increased, realizing the enhancement of electrodeformation effect.Electrostriction occurs by controlling the frequency and magnitude of the applying voltage, realizing the function of micro pump and microvalve, which can be applied in microfluidic chips [The electromechanical strain is measured with a Premier II ferroelectric test system at 100 Hz. When this method is used for measurement, the displacement obtained is the maximum displacement of the film in the longitudinal direction, as shown in However, the deformation of the film in different areas is not uniform. We used the finite element simulation method to simulate the deformation and stress distribution of neat PVDF film in different locations in the electrode covered area (applying electric field is 20 kV/mm) and the relevant results are shown in We can see that the central region exhibits a small deformation and larger stress. This is mainly due to the fact that under the applying electric field, the film does not only contain the volume deformation of longitudinal effect, as the film is in the bound state, the stress is relatively concentrated in the edges of the electrodes, exhibiting large deformation. However, the region covered by the electrode will also generate a deflection effect on the whole, and the maximum position of the overall displacement is in the central region. So the stress generated in the central region is relatively large.In the practical application process, the shape of the micro-pump and micro-valve can be designed according to the deformation law of the film under the electric field to achieve the best effect.This study has demonstrated a technique for processing large-area of PVDF-based composite films meanwhile significantly increasing the d33 and d33* by the melt blending extrusion-casting process. The d33 of PVDF/PZT@105/GO film can reach 26 pC/N due to it can be polarized under larger electric field intensity. The d33* reaches 104 pm/V, it's a big enhancement with related articles currently reported.Chao Zhang: Data curation, Writing – original draft. Huajun Sun: Supervision. Quanyao Zhu: Validation, Writing – review & editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.The following is the supplementary data related to this article:Supplementary data related to this article can be found at Simulation of the hydration kinetics and elastic moduli of cement mortars by microstructural modellingThe ability of the VCCTL microstructural model to predict the hydration kinetics and elastic moduli of cement materials was tested by coupling a series of computer simulations and laboratory experiments, using different cements. The novel aspects of this study included the fact that the simulated hydration kinetics were benchmarked using real-time measurements of the early-age phase composition during hydration by in situ X-ray diffraction. Elastic moduli are measured both by strain gauges (static approach) and by P-wave propagation (dynamic approach). Compressive strengths were measured by loading mortar prisms until rupture. Virtual samples were generated by VCCTL, using particle size distribution and phase composition as input. The hydration kinetics and elastic moduli were simulated and the numerical results were compared with the experimental observations. The compressive strength of the virtual mortars were obtained from the elastic moduli, using a power-law relation. Experimentally measured and simulated time-dependence of the major cement clinker phases and hydration product phases typically agreed to within 5%. Also, refinement of the input values of the intrinsic elastic moduli of the various phases enabled predictions of effective moduli, at different ages and different water-to-cement mass ratios, that are within the 10% uncertainty in the measured values. These results suggest that the VCCTL model can be successfully used as a predictive tool, which can reproduce the early age hydration kinetics, elastic moduli and mechanical strength of cement-based materials, using different mix designs.In recent years, ever-improving computational resources have facilitated the study of the 3D microstructure of cementitious materials and its relationship with the physical properties, based on computer models that generate virtual materials and accurately simulate the mechanisms of microstructural development. An integrated approach that encompasses both measurement and modeling is fundamental to understanding experimental observations and to developing an advanced design of cement-based materials.In this study, we test the capabilities of the Virtual Cement and Concrete Testing Laboratory (VCCTL) models The accuracy of the simulated kinetics is benchmarked using in situ X-ray diffraction experiments coupled with Rietveld refinement, which returns the actual time-dependent phase composition of the hydrating cement paste. Both simulation and experiments were performed on three different cements, prepared at a different water-to-cement mass ratios (w/c) and cured at different temperatures.A detailed evaluation of the intrinsic elastic properties relative to the individual phases is performed, based on a review of recent literature data. Particular focus is given to the elastic moduli of the C–S–H phase, whose values are extrapolated by a quantitative method.Both static and dynamic elastic moduli, in addition to compressive strength, are measured for mortars with different composition and w/c, to establish the most appropriate method of measurement to be used for comparing actual and predicted properties.A general working relationship between elastic moduli and strength is defined, based on different cements and w/c.The starting materials used in this work were an ordinary CEM I 52.5R Portland cement and a limestone CEM II/A-LL 42.5R Portland cement (hereafter C1 and C2). A third mix was obtained from a CEM I 52.5R cement blended with 5% and 10% by mass of silica fume (hereafter C3), and used to validate the relationship between elastic moduli and compressive strength. The solid oxide composition and mineralogical phase composition, as measured by X-ray fluorescence and X-ray diffraction, respectively, are shown in . The particle size distributions, measured by laser scattering, are displayed in . The aggregate used for the mortar samples is a CEN normalized siliceous sand, having a mean solid density of 2620 kg/m3, a bulk modulus of 33.2 GPa and a shear modulus of 24.5 GPa.Mortar samples were used as reference test materials to study the accuracy of the computer model in predicting compressive strength and elastic moduli. The mortars were prepared by mixing 0.9 kg of cement with 2.7 kg of sand. The adopted mixing procedure and curing conditions were based on the EN 196-1 standard Measurements of the mechanical and elastic properties were performed on mortar prisms with standard dimensions 40 mm × 40 mm × 160 mm. Compressive strength and elastic moduli measurements were performed at 1 d, 7 d, and 28 d of hydration for C1 and C2. For C3, compressive strengths were measured at 28 d 60 d of hydration, for additions of 5% and 10% by mass of silica fume.The axial compressive strengths were measured by loading the mortar prisms between plates with dimensions 40 mm × 40 mm until rupture, as prescribed by the EN 196-1 standard The Young’s modulus of each mortar prism was measured both by a dynamic and a static method. The dynamic measurements were made by a non-invasive method using the propagation of compressional waves (P-waves) through the sample. The dynamic Young’s modulus Ed is calculated from the measured P-wave velocity according towhere ν and ρ are the measured Poisson’s ratio and density of the material, respectively. The Poisson’s ratio of each mortar prism was measured by equipping the prisms with three strain gauges. Two gauges were placed on opposite faces in order to measure the extent of the compression, parallel to the direction of the applied load, whereas the third gauge was placed at right angles, in order to measure the transverse extension. Values of the Poisson ratio of 0.20 and 0.18 were obtained at 7 d and 28 d, respectively, and a value of 0.20 was assumed at 1 day. Static measurements of Young’s modulus, performed following the UNI 6556 standard Early age hydration kinetics were studied by in situ X-ray diffraction (XRD) performed on cement pastes obtained by mixing C1 and C2 with deionised water at w/c |
= 0.5 and 0.6, respectively. The samples were prepared using an orbital shaker, with a mixing time of 1 min, placed in a sample holder having a diameter of 35 mm and covered with an X-ray transparent foil. XRD patterns were acquired using a diffractometer in Bragg–Brentano geometry, equipped with a Cu-anode X-ray tube. The measurements were performed in situ, at time intervals of 20 min, up to about 20 h after the beginning of hydration. Isothermal conditions of 25 °C and 23 °C were used for C1 and C2, respectively.The volume fraction of each crystalline phase was determined by Rietveld full-profile fitting analysis. The fundamental parameters approach was applied to simulate the instrumental contribution to line broadening and asymmetry VCCTL was used to simulate the development of mechanical properties for virtual models of the materials described in Section . VCCTL is a suite of integrated, microstructure-based computer models for creating virtual 3D cement paste microstructures, for simulating the hydration of those microstructures under a variety of curing conditions, and for calculating the time-dependent mechanical and transport properties of concrete materials made using the paste as the binder. The phase composition, w/c ratio and particle size distribution of the cement, as well as the amount, grading and physical properties of the aggregate (i.e., density, bulk and shear moduli) are supplied as input by the user. Spherical harmonics are used to describe the shape of the clinker particles VCCTL simulates microstructure development during cement paste hydration using an agent-based model that is based on a set of probabilistic rules to mimic the dissolution, diffusion, and precipitation of the phases present in the system The simulated microstructure is used as input for the calculation of the linear elastic moduli of the material. This is achieved by a multi-scale approach. At the smaller length scale, the linear elastic moduli of the cement paste are calculated by a finite element (FE) model that assigns a trilinear cubic mesh element to each voxel of the digital microstructure and enforces periodic boundary conditions to the computational domain. The phases assigned to each voxel are assumed to be elastically isotropic. The effective elastic moduli of the paste are then calculated by minimizing the total elastic energy in response to an applied displacement At the scale of the mortar, the effective elastic moduli of the composite material are computed from differential effective medium theory, which treats the cement paste as an elastically homogeneous matrix. The calculation proceeds iteratively; in each iteration a small number of aggregate particles are embedded in the matrix and the dilute limit is used to calculate the composite moduli. This composite is then homogenized into a new matrix with those properties in the next iteration. The process is repeated until the target volume fraction of aggregate particles is reached. Full details of the procedure are available elsewhere Elastic moduli are rarely measured for industrial samples, but the compressive strength is frequently measured as an indicator of mechanical integrity and of anticipated structural performance. However, fundamental calculation of compressive strength of a random composite material is an especially difficult task because it depends on subcritical crack formation, growth, and coalescence. As an empirical alternative, we use a power-law relation between compressive strength and Young’s modulus of the concrete or mortar similar to that proposed by Neville Given the elastically anisotropic nature of the individual cement phases, the elastic moduli of the multi-phase cement materials should ideally be computed from the full elastic tensors of the single phases. However, full elastic tensors have been calculated only for a few of the phases found in cement materials. Moreover, the use of full elastic tensors requires assumptions on the orientation of the phases present in the microstructure, and is computationally intensive, so VCCTL accepts isotropic averages of the full elastic tensors as input for the FE computation. However, such isotropic averages cannot be unequivocally defined and depend on the way the phases mechanically interact with each other. Lower and upper bounds for polycrystals, known as Reuss and Voigt bounds The values of the elastic moduli for the main clinker phases alite (C3S), belite (C2S), and aluminate (C3A) were inferred from a combination of measurements obtained by resonant ultrasonic spectroscopy, nano-indentation Published experimental data on the elasticity of C–S–H are scarce, due to the absence of long range order in this phase. This is unfortunate in terms of modelling the elastic and mechanical properties of cement materials, since C–S–H is the dominant phase for the development of such properties in hydrated cement binder materials. Therefore, any error associated with the intrinsic properties of C–S–H will have a significant impact on the computed effective properties of the material. Constantinides and Ulm In the absence of experimental measurements or calculations on saturated C–S–H gel, we estimate the elastic properties of water-saturated C–S–H using a two-phase system that consists of two end members, namely C1.65SH1.75 (“dry” C–S–H) and H2O. The dry C–S–H end member is assigned the above elastic properties calculated by Shahsavari The unknown x is determined by enforcing the same linear relation on the density of water-saturated C–S–H, which is assumed in advance to be 1900 kg/m3 based on values reported for saturated pastes gives Ksat |
= 29 GPa. Using the same procedure, the estimated shear modulus of water-saturated C–S–H is Gsat=13 |
GPa. The remaining elastic moduli can then be calculated from (Ksat,Gsat), resulting in an estimated Young’s modulus Esat=34 |
GPa (equal to the value previously reported in A set of virtual microstructures was created, based on the material properties and mixture proportions described in Section . Input to VCCTL consisted of (a) the dry cement clinker phase volume fractions and surface area fractions obtained by quantitative XRD and microscopy, (b) the cement particle size distribution measured by laser scattering, (c) the density, elastic moduli and grading of the fine aggregate, and (d) heat release curves obtained by isothermal calorimetry.Two cement paste microstructures were created: (1) C2 with w/c |
= 0.6 and (2) C1 with w/c |
= 0.5. Hydration of both microstructures was simulated by VCCTL, using a constant temperature of 23 °C and 25 °C respectively, corresponding to the hydration conditions used for the in situ XRD analyses. This represents a first level of validation, by which the consistency of the simulated hydration kinetics is checked against the experimental measurements, by comparing the time evolution of the fraction of cement phases present in the system during the first 24 h of hydration. A set of seven virtual mortars were then created, with proportions sand:cement:water being those of the samples used for the experimental determination of the elastic and mechanical properties (see Section and 4 vol% of entrained air. The simulated volume is a region of interest at the scale of the cement paste (100×100×100 voxels with a resolution of 1 |
μm per voxel) consisting of bulk paste and interfacial transition zone (ITZ). The latter is simulated by inserting an imaginary yz-planar boundary within the microstructure that no cement particle is allowed to cross when being randomly placed. This boundary therefore acts as a physical wall constraining the local packing of cement particles, much as a physical aggregate surface does . Finally, the calculated elastic moduli of bulk paste and ITZ are passed to the differential effective medium theory algorithm, which computes the elastic moduli and mechanical strength of the mortars, based on the amount, grading and intrinsic elastic properties of the sand aggregate. compares the simulated and measured time-dependent volume fractions of the phases present in C1 and C2 pastes, hydrated at 25 °C and 23 °C respectively. The volume fractions are scaled to the total volume of the system (i.e., phases and pore solution). Alite is the most abundant clinker phase, and C–S–H portlandite and ettringite are the main hydration products. Also, capillary porosity represents a fundamental microstructural feature in terms of development of mechanical properties. The experimentally measured values of the other clinker phases do not vary monotonically in time and have relatively large associated uncertainty show that the predicted volume fractions of alite, C–S–H, portlandite and capillary porosity generally agree with experimental measurement to within about 5% for both cement pastes. The exception is ettringite, for which the simulations tend to underestimate the experimentally measured amounts. In particular, the experimentally determined ettringite phase fraction for C2 displays a somewhat scattered trend, which is still increasing at the end of the experiment (∼20 h) whereas a steady state concentration of approximately 2 vol% is reached after about 10 h of simulated hydration. C1 displays a higher amount of ettringite and in this case, both the experimental and predicted volume fractions reach a steady state, although in the simulation this occurs ∼5 h prior to what observed experimentally, with the amount of ettringite present in the system at steady state being about 20% smaller. The lack of a steady state, as experimentally observed for C2, is likely due to the presence of a significant amount of calcite in the system, which tends to stabilize ettringite with respect to monosulfoaluminate, due to precipitation of monocarboaluminate The experimental measurements of the elastic moduli and compressive strengths are reported in A linear relation is observed between the “dynamic” and “static” elastic moduli, with the value of the latter always being smaller compared to the dynamic modulus (see ). This behavior is commonly observed and attributed to the non-linear nature of the stress–strain curve for cement materials, due to inelastic contributions.Since the FE method for the computation of the elastic properties, as implemented in VCCTL, simulates the elastic response of the material, the calculated Young’s modulus is compared to the dynamic Young’s modulus. In addition, it is important to compare the experimentally determined compressive strength with that estimated by VCCTL using the empirical power-law relation, since this property is important in practical applications. As already explained in Section , an empirical power law curve is used to estimate the mortar compressive strength from the dynamic Young’s modulus. Experimental data relating the elastic moduli and compressive strength of different concrete materials typically have a high amount of scatter. Therefore, using an empirical equation to represent a correlation between elastic moduli and strength therefore may adequately reflect the average correlations among such data but will have significant uncertainty when applied to a given mortar , the best two-parameter power law fit, with a coefficient of determination R2=0.9945, isWe wish to emphasize the empirical nature of this equation; one should be cautious about applying the same power law to a mortar that is much different in nature from the ones used in the regression. Here, in order to give an estimate of the error associated to the use of this relation, compressive strengths are calculated for the mix C3, which is not included in the dataset displayed in Measured and calculated values of Young’s moduli and compressive strength at different ages and w/c, for C1, C2 and C3, are displayed in . Again, very good agreement between simulation and experiment is observed both for the moduli and the compressive strengths, for all mixes, at the different hydration times, w/c and silica fume additions considered. In fact, the predicted moduli and strengths generally lie within the 10% coefficient of variation in the measured values.In this study, we have shown the ability of the microstructural model VCCTL as a tool for the design of cementitious materials. VCCTL takes as input the following experimental data:aggregate grading, density and elastic moduli.The output returned by VCCTL consists of the virtual 3D microstructure, time-dependent phase composition and elastic moduli of the simulated material. The elastic moduli of the mortars are calculated by the model from the simulated 3D microstructure. Since there is no physical theory that directly links the elastic moduli to mechanical properties such as compressive strength, the latter has to be estimated using experimental calibration curves that relate the two physical quantities.One of the novel aspects of this study, compared to previous applications of microstructural models, is that the simulated early age hydration kinetics of the individual phases is compared to the real kinetics obtained by in situ XRD experimental measurements. The results () show that VCCTL captures, to a very good approximation, the time variation of the volume fraction of C–S–H, portlandite and capillary porosity, which are the main constituents that determine the final elastic and mechanical properties of the material. The time variation of the volume fraction of alite, the main clinker phase, is also appropriately reproduced by the model, with the differences between experimental observations and simulations mostly lying within the extent of the experimental uncertainties. On the contrary, more significant differences are observed for the curves describing the time evolution of ettringite. However, given the relatively small amounts of ettringite present in the system, the observed differences, of less than 3% of the total volume of the system, are not likely to have a significant effect on the physical properties of the material as a whole. show a very good agreement between the measured and predicted dynamic Young’s moduli and compressive strengths. The results also show that the Young’s moduli can be converted to compressive strength, by using the power law relation displayed in Eq. , with very accurate results for both the cements used for the calibration of the “compressive strength vs. Young’s modulus” and the cement blended with different amounts of silica fume, which had not been used for the calibration.In conclusion, VCCTL proved to adequately predict both the early age hydration kinetics and the elastic properties of mortars obtained from different cements. Empirical relations can be used to estimate the compressive strength of the virtual materials with good accuracy.The mechanism for the high dependence of the Hall-Petch slope for twinning/slip on texture in Mg alloysA Hall-Petch slope (k) that is highly changeable with texture, as extensively reported in Mg alloys, is ultimately related to the variation of deformation modes. In this paper, the influence of different (0002) distributions on k for twinning and slip was systematically studied using an AZ31 rolled plate ([0002]//ND) and extruded rod ([0002]⊥ED together with a random distribution around the ED). The ND and ED refer to the normal direction of the plate and extrusion direction of the rod, respectively. A high dependency of k on the (0002) distribution is found, namely, a much lower k for {101¯2} twinning in the plate (219 MPa μm1/2) than that in the rod (435 MPa μm1/2), but a much higher k for slip in the plate (437 MPa μm1/2) than that in the rod (235 MPa μm1/2). Compound use of the difference in Schmid factor (ΔSF) and geometric compatibility factor (m′) quantitatively explains this orientation effect on k. ΔSF relates to the extra stress needed for the activation of slip/twinning in a neighboring grain, and m′ reflects the efficiency of the stress concentration at the onset of slip/twinning in an adjacent grain. The lower m′ for twinning in the rod versus the plate primarily accounts for the higher k for twinning in the rod. A much larger inclination of basal poles away from the ideal texture exists in the plate than in the rod, which induces a higher activity of basal slip during tension. The resultant high fraction of slip transfer from basal slip in one grain to prismatic slip in the neighboring grain largely amplifies ΔSF and reduces m′, both of which yield a higher k for slip in the plate than in the rod. The relationship between the crystallographic orientation and m′ was also calculated for different types of deformation transfer, and the main factor that determines m′ was revealed.Grain refinement has proven to be an effective approach for enhancing the strength of metals, according to the classic Hall-Petch (H-P) relationship where σy is the yield stress, σ0 is the friction stress when dislocations glide on the slip plane, d is the average grain size, and k is the stress concentration factor representing grain boundaries (GBs) as an obstacle to slip. Similar to slip, the stress for twinning was also reported to follow the H-P relationship For Mg alloys with a hcp structure, basal slip is often the easiest deformation mode. However, in highly textured Mg products, prismatic slip or {101¯2} twinning can become the predominant mode under certain specific loading paths. For example, prismatic slip dominates the tension deformation along the ED of an AZ31 rod and {101¯2} twinning during compression. Different slip systems or twinning have been reported to display different values of k. It is often considered that slip with a higher critical resolved shear stress (CRSS) possesses a higher k than that with a lower CRSS . The variation of k with the loading path is well illustrated in the variation of k from 158 to 411 MPa μm1/2 in an AZ31 plate by changing the tensile direction away from 0 to 90° with respect to the normal direction (ND) It is apparent that most previous studies on the highly changeable k in Mg alloys are ultimately related to the variation of deformation modes. For a given deformation mode, it is found that if the slip planes in two neighboring grains have a common line of intersection in GB and are collinear with the Burgers vectors of dislocations, then the dislocation in one grain can pass unimpeded through the GB into the adjacent grain Two typical texture components are found in Mg products: the basal texture in a rolled plate and the fiber texture in an extruded rod. The distribution of (0002) poles in a plate ([0002]//ND) is different from that in a rod ([0002]⊥ED together with a random distribution around the ED). Although the k in the Mg plate and rod has been extensively studied, the measured k for twinning or slip was not reported in a similar grain size range. As discussed previously, the k is changeable with grain size, and it is therefore difficult to accurately determine how this different (0002) distribution affects the k for a given deformation mode. In the current study, a comparative study of the k for twinning and slip in a Mg AZ31 plate and rod was performed in the same grain size range. A high dependence of k on texture was revealed, namely, a much lower k for {101¯2} twinning in the plate (219 MPa μm1/2) than in the rod (435 MPa μm1/2) but a much higher k for slip in the plate (437 MPa μm1/2) than in the rod (235 MPa μm1/2). This work placed great emphasis on the effect of different (0002) distributions on the twinning/slip transfer and the relationship between slip/twinning transfer and k.A Mg AZ31 extruded rod (16 mm in diameter) and hot-rolled plate (10 mm in thickness) were used in the current study. The extruded rod and hot-rolled plate were subjected to different annealing treatments to prepare samples with different grain sizes. The details of the annealing processes and the designations of samples are given in . Tension and compression tests along the transverse direction (TD) of the plate and the ED of the rod at room temperature were performed on a Shimadzu AG-X (50 kN) machine using a strain rate of 10−3 s−1. The specimens for compression tests of the plate were blocks of dimensions 9 mm × 9 mm × 12 mm and specimens of the rod were cylinders of 16 mm in diameter and 20 mm in height. The specimens for tensile tests were dog-bone shaped with a gauge length of 13 mm and a cross-section of 4 × 2.5 mm. An extensometer was used to correct the strain during tension tests. At least three samples were tested for each condition.Specimens for optical observation were mechanically ground followed by etching with acetic picral (1 g of picric acid, 2 ml of acetic acid, 2 ml of water, and 16 ml of ethanol). Pole figures were measured using X-ray diffraction (XRD, Rigaku D/max-2500PC). The measured incomplete pole figures were analyzed to determine the orientation distribution function (ODF), and complete pole figures were reconstructed. Electron backscatter diffraction (EBSD) mapping was conducted on a scanning electron microscope (SEM, TESCAN MIRA3) equipped with a HKL-EBSD system using a step size of 0.25 μm. The samples for EBSD mapping were mechanically ground and electro-chemically polished in an AC2 electrolyte at 20 V for 90 s. All EBSD data were analyzed using the Channel 5 software.The optical micrographs of the plates and rods are shown in . The grain sizes in both the plate and rod vary within 13–56 μm. The samples for the tensile tests have a grain size of 13–36 μm to enhance the activity of prismatic slip, and those for compression have grain sizes of 23–56 μm to increase the {101¯2} twinning propensity. The as-used grain size ranges used to initiate {101¯2} twinning/slip in the plate are similar to those in the rod, which can eliminate the grain size effect on k. presents the pole figures of samples. All of the plates have a strong basal texture with basal poles largely parallel to the ND and a random distribution of the prismatic planes (a–e), whereas the rods possess a typical texture with the (0002) poles largely perpendicular to the ED and randomly distributed around the ED (f–j). A preferred distribution of prismatic planes is noted in the rod. Different annealing treatments minimally alter the texture in both the rods and plates.It has been extensively reported that prismatic slip dominates during tension along the TD of the plate or the ED of the rod, whereas {101¯2} twinning occurs during compression shows the SFs as a function of the relative spatial position in EBSD micrographs in one plate and rod. Note that {101¯2} twinning with a negative SF would lead to contraction along the c-axis and would not be activated. Therefore, a negative SF for twinning is equivalent to zero and is treated as zero during calculation of the distribution and the average of SFs in this study. Obviously, the SFs for prismatic slip are high and similar in the plate and rod, similar to those for {101¯2} twinning.The true stress-strain curves under tension and compression are given in with the relevant yield stresses listed in . The compressive curves of both the plates and the rods exhibit a sigmoidal shape, the typical feature of a {101¯2} twinning predominant deformation. A large difference in the increment of yield stress between the rod and plate is observed with refined grain size. The yield stresses against grain size−1/2 are given in , the k for {101¯2} twinning (ktwinning) in the rod (435 MPa μm1/2) is much higher than that in the plate (219 MPa μm1/2), whereas that for slip (kslip) in the rod (235 MPa μm1/2) is much lower than that in the plate (437 MPa μm1/2). Obviously, the crystallographic orientation distribution has a great influence on both the ktwinning and kslip.The most commonly discussed mechanism for the GBs effect on the H-P relationship is the dislocation pile-up theory a, where k expresses the magnitude of the GB obstacle effect against slip propagation. A higher GB obstacle effect corresponds to a higher kwhere τc is the CRSS required for the operation of a dislocation source, r denotes the distance from the dislocation pile-up to the nearest dislocation source in the adjacent grain, and M is the Taylor orientation factor. In hcp polycrystals, the determination of M is complicated by plastic anisotropy. For example, M is suggested to be 6.5 where basal slip occurs at a low stress that k is primarily determined by M for a given deformation mode. When M is taken as the reciprocal of the averaged SFs, the ktwinning or kslip in the plate should be similar to that in the rod, according to . Obviously, with this condition, the use of could not explain the great difference in either ktwinning or kslip between the rod and plate in this work. The propagation of slip from one grain to its neighbor depends on both the externally applied stress and the stress concentration created by dislocation pile-up at the GBs. Wyrzykowshi et al. The geometric compatibility factor for slip (m′slip) has been widely used to study the slip transfer behavior between neighboring grains where α/β is the angle between the slip planes/slip directions of two neighboring grains, and m′slip generally represents the extent of local strain due to slip in a grain being resolved onto slip systems in an adjacent grain. Because the local strain is related to the number of piled dislocations, its value and direction determine the magnitude and distribution of the local stress field Up to now, the boundary effect on ktwinning has not been well understood. Recently, Barnett et al. reported that twin nucleation, propagation, and transfer to neighboring grains dominates the initial yielding of a Mg AZ31 plate b. This type of twinning transfer is frequently observed and forms paired twins c, many twin pairs (T1-T2) exist in a 0.5% compressed AZ31 plate along the TD. In other words, the boundary obstacle effect on twinning can be described by how the boundary affects the twinning transfer. Intensive studies also show that twinning often follows the rule that a higher SF facilitates easy twinning activation where ϕ/φ is the angle between the twinning plane normals/twinning shear directions of two neighboring grains. Similar to m′slip, m′twinning can also reflect the “efficiency” of stress concentration in the onset of twinning in neighboring grains, and in this work, it is used to evaluate how the crystallographic orientation affects ktwinning.According to the above discussions, ΔSF and m′ are two effective parameters for evaluating the crystallographic orientation effect on k. ΔSF can represent the extra stress needed for the activation of slip/twinning in an adjacent grain, and m′ expresses the efficiency of stress concentration in the initiation of slip/twinning in the next grain. ΔSF corresponds to the effect from externally applied stress, and m′ corresponds to the influence from internal stress concentration. A higher ΔSF or a lower m′ contributes to more difficult deformation propagation and the resultant higher k.In this work, the ΔSF and m′ for prismatic slip (mP−P′) and {101¯2} twinning (mT−T′) calculated from more than 800 pairs of neighboring grains in a plate and rod are shown in , respectively. The activated slip system/twinning variant between neighboring grain is determined by both the SF and m′. However, the slip system/twinning variant with the highest SF might not be the one with the highest m′ and vice versa, it is therefore hard to judge which slip system/twinning variant could be activated. In this work, the slip system with the highest SF is considered to be activated during the calculation of ΔSF, and the one with the highest m′ activated during the calculation of m′. The details about the method to calculate m′ could be found in Refs. a and b that no obvious difference occurs in the averaged ΔSF for twinning in the plate (0.084) and in the rod (0.04), as is the case for prismatic slip in the plate (0.05) and in the rod (0.026). As shown in a and b, the majority of mT−T′ in the plate (average = 0.827) are greater than 0.7, whereas those in the rod (average = 0.605) have a broad distribution from 0.2 to 1. A similar trend is observed for mP−P′. The above results show that the orientations in the rod create a lower mP−P′ and mT−T′, an indication of a higher boundary obstacle effect for both slip and twinning in the rod. This trend agrees well with that for ktwinning, with values of 435 MPa μm1/2 in the rod and 219 MPa μm1/2 in the plate, but contradicts with that for kslip, with values of 235 MPa μm1/2 in the rod and 437 MPa μm1/2 in the plate. These results imply that other factors might affect the kslip in this study.In fact, a portion of the basal poles in a highly textured AZ31 plate or rod incline away from the ideal texture (basal poles parallel to the ND in the plate and perpendicular to the ED in the rod), which leads to activation of basal slip during tension along the TD or ED. The activation of basal slip might generate different types of slip transfer and eventually influence the k. Therefore, the tilt angles of the basal poles (Φ) from the ideal orientation in a plate and rod were measured and are shown in . A striking difference can be found in the much broader distribution of Φ between 1° and 45° in the plate compared with that for 0°–15° in the rod.In this work, we calculated the CRSS/SF for basal slip and {101¯2} twinning and prismatic slip to determine the predominant modes as a function of Φ during tension along the TD and ED. The mode that gives the minimum value is the dominant mode. For the plate, only the basal poles in the TD-ND plane were considered for this calculation. For both the plate and rod, only one fixed orientation at a given Φ was calculated. The input CRSS ratio in polycrystalline Mg alloy is an complex issue . In both the plate and rod, the dominant mode is prismatic slip with Φ below 13°, and basal slip with Φ = 13–68° and {101¯2} twinning with Φ over 68°. Combined with the results in , a much higher activity of basal slip should be observed during tension of the plate than that of the rod. In fact, the activation of a large number of basal slip after 5–6% tension on a pure Mg plate was confirmed by Cepeda-Jiménez et al. using slip trace analysis The grain fractions favorable for basal slip, prismatic slip, and {101¯2} twinning during tension and compression of a plate and rod were calculated using the same CRSS ratio, and the results are listed in . For both the plate and rod, more than 300 grains were used in this calculation. The fraction favoring basal slip during tension reaches 33% in the plate but only approximately 7% in rod. A much lower fraction is noted in favor of basal slip during compression of both the rod and plate. The grains favoring basal slip (labeled as B) during tension of the plate and rod are marked in the inverse pole figure maps in . In this case, basal-prismatic slip (B-P) transfer and basal-basal slip (B-B) transfer exist in addition to prismatic-prismatic slip (P-P) transfer. The fraction of B-P transfer accounts for 43% in the plate but only 13% in the rod. In addition, approximately 10% B-B transfer occurs in the plate. To further confirm the high activity of basal slip and the occurrence of B-P, B-B and P-P transfers during tension of the plate, slip trace analysis was conducted on a 3% tensioned plate. The initiated slip was selected based on the best match of the slip traces. Whenever more than one slip could be chosen, the one with the greatest SF was chosen. Examples showing the prismatic slip (grain 1) and basal slip (grain 2) are presented in a. Approximately 130 grains in 6 different maps were analyzed. Basal slip takes place in approximately 28% grains, which agrees well with the results in . This further confirms that the selection of CRSS ratio in this work is reasonable. The occurrence of B-P, P-P and B-B transfers can be confirmed in The geometric compatibility factors for B-B transfer (mB-B′), B-P transfer (mB-P′) and P-P transfer (mP−P′) in plate and rod were calculated and are shown in . In the plate, B-P transfer shows a quite low m′ (average = 0.423) compared with P-P transfer (average = 0.846). Therefore, the m′ drops to 0.654 considering the P-P, B-B and B-P transfer, much lower than that with only consideration of P-P transfer (approximately 0.800 in ). In this case, the m′ for slip transfer in the plate is close to that in the rod (0.626). In addition, as shown in , compared with P-P transfer, B-P transfer increases the activation stress difference (ΔStress) between two neighboring grains. For example, assuming a maximum ΔStress condition for P-P transfer such as a grain with a Φ of 0° and an adjacent one with 13°, the ΔStress is only 2 MPa. In contrast, for one grain with a Φ of 0° and a neighboring one with 20°, B-P transfer takes place, and the ΔStress increases to 15 MPa. A static measurement of ΔStress in the plate and rod from approximately 900 paired grains is shown in . In both the rod and plate, a much lower ΔStress occurs for P-P transfer, and a quite high ΔStress occurs for B-P and B-B transfer. The ΔStress of 94% slip transfers in the rod is below 6 MPa, but the ΔStress of 33% slip transfers exceeds 6 MPa in the plate. Finally, the average ΔStress in the plate (5.9 MPa) is more than two times that in the rod (2.4 MPa), which is equivalent to amplifying the ΔSF. It can be observed that the activation of B-P transfer not only reduces the geometric compatibility factor but also increases ΔSF, both of which contribute to increasing the k. Previously, certain researchers considered that the inclusion of basal slip in a prismatic slip predominant deformation decreases the kThe above discussions show that the reasons for different ktwinning and kslip in the rod and plate can be well explained. A high activity of basal slip occurs in the plate, but it is limited in the rod under tension (see ). The main slip transfer in the rod is P-P transfer, whereas a high fraction of B-P transfer exists in the plate in addition to P-P transfer. Although the geometrical compatibility factor for P-P transfer in the rod is much lower than that in the plate, the high fraction of B-P transfer greatly amplifies the ΔSF and greatly reduces the geometrical compatibility factor, both of which contribute to increasing kslip in the plate. Therefore, the higher kslip in the plate than in the rod is a result of the higher activity of basal slip in the plate than in the rod. During compression, {101¯2} twinning dominates. Armstrong et al. , the fraction of grains favoring basal slip/prismatic slip in both the plate and rod is limited under compression. Therefore, the effect of slip on ktwinning is quite limited. Because a similar ΔSF occurs for twinning in the plate and rod (a and b), the lower ktwinning in the plate than in the rod is mainly a result of the higher m’twinning in the plate.It can be observed that crystallographic orientation distributions can pose a great influence on both kslip and ktwinning in Mg alloys. In fact, the Taylor orientation factor M in also reflects the orientation effect on k. In this sense, the ΔSF and m′ play a role similar to that of M. Previously, the reciprocal of averaged SFs was frequently used to substitute M. The results in present study strongly show that the averaged SF cannot accurately express the influence of the crystallographic orientation on the boundary obstacle. This effect could be understood in the following manner: two neighboring grains possess the same SF of 0.4, whereas another two neighboring grains have SF values of 0.3 and 0.5, respectively. Although a similar averaged SF is present in the two cases, deformation transfer in the latter case is more difficult. In addition, the averaged SF does not include the role of stress concentration efficiency in deformation prorogation. Therefore, in Mg alloys, the determination of a suitable value for M is complicated. Further work is needed to build the quantified relationship between M and ΔSF/m′.Although the mechanism for twinning is different from that for slip, the value of ktwinning is also determined by the orientation distribution. Twinning was often observed to have a greater k than slip, as evidenced from Ti It can be observed that m′ is an important parameter used to evaluate the crystallographic orientation effect on k. Moreover,m′ has a close relationship with crystallographic orientation, and this relationship is analyzed in a, the orientation relationship of two neighboring grains can be described as an angle between their c-axes (θ) and a rotation around the c-axis (ω). Due to the symmetry of the hcp structure, ω varies within 0°–30° and θ within 0°–90°. It can be observed that m′ for B-B (mB-B′), B-P (mB-P′), P-P (mP−P′), and twinning-twinning transfers (mT−T′) varies to a large extent with the variation of θ, whereas varying ω in the range of 0°–30° at a given θ only slightly changes mB-P′mT−T′, mP−P′ and mB-B′ (a–c). For example, when ω varies from 0° to 30°, mT−T′ drops from 1 to 0.7. In stark contrast, when θ varies from 0° to 90°, mT−T′ drops from 1 to 0.23. Therefore, the values of mT−T′, mP−P′, mB-B′, and mB-P′ are primarily dependent on the angle between the c-axes of two grains, and mT−T′, mP−P′ and mB-B′ generally drop with increasing θ, but mB-P′ shows a reverse trend. This result implies that to achieve a higher k, increasing the θ between neighboring grains is an effective approach.To reveal why mT−T′ and mP−P′ are much lower in the rod than in the plate (), the distribution of θ measured from 300 pairs of neighboring grains in the plate and rod is shown in . Obviously, θ in rod has a broad distribution of 0°–90°, whereas the majority of θ in plate are within 0°–40°. Therefore, the relatively higher angle between the c-axes of two adjacent grains in the rod is the main reason for the much lower mT−T′ and mP−P′ than that in the plate.As demonstrated in many publications, the measured σ0 in the H-P relationship in Mg rods is often higher than that in Mg plates during tension tests Therefore, σ0 is mainly determined by the CRSS of activated slip. Under tension along the TD of the Mg plate or the ED of the Mg rod, prismatic slip is often the predominant mechanism. Nevertheless, as discussed previously, a much higher activity of basal slip occurs during tension of the plate than in the rod. The CRSS of basal slip is much lower than that of prismatic slip, and a lower σ0 in the plate than in the rod is the result. Under compression, the main mode is {101¯2} twinning, and the activity of basal slip is limited, as shown in . As a result, similar σ0 exists in the rod (approximately 10 MPa) and plate (approximately 19 MPa).It is often observed that for both the tension and compression tests, an AZ31 rod displays a higher yield strength than the AZ31 plate despite their similar grain sizes . The findings in this work can offer some new insights into this problem. As discussed above, the much larger deviation of basal poles away from the ideal texture in the plate than in the rod leads to the much higher activity of basal slip in the plate under tension. The lower activation stress of basal slip than prismatic slip will lead to the lower tensile yield strength in plate than in rod. However, during compression, the predominant deformation mode is {101¯2} twinning and basal slip is limited in both the plate and rod. As seen in , the (0002) distribution in the rod results in a harder twinning transfer behavior than that in plate, which contributes to enhancing the compressive yield strength in rod. Therefore, The difference in mechanical properties between the plate and rod is a result of texture difference.The current study systemically studies the influence of different (0002) distributions in an AZ31 hot-rolled plate ([0002]//ND) and extruded rod ([0002]⊥ED together with a random distribution around the ED) on k for twinning and slip. The mechanism of the high dependence of k for twinning and slip on the (0002) distribution was addressed, and the key findings are summarized as follows:A high dependence of k on the (0002) distribution is observed for both slip and {101¯2} twinning, i.e., a much lower k for twinning in the plate (219 MPa μm1/2) than that in the rod (435 MPa μm1/2) and a much lower k for slip in the plate (437 MPa μm1/2) than that in the rod (235 MPa μm1/2).Compound use of ΔSF and m′ between two neighboring grains can clearly decipher this orientation effect on kslip/ktwinning. The lower m’twinning in the rod than in the plate primarily accounts for the higher ktwinning in rod. A much higher activity of basal slip occurs during tension of the plate than of the rod due to the larger deviation of the basal poles away from the ideal orientation in the plate than in the rod. The highly activated basal slip amplifies the ΔSF and reduces the m′ in the plate, which eventually leads to the higher k for slip in the plate than in the rod.The m′ for B-B transfer, P-P transfer, B-P transfer and T-T transfer is mainly determined by the angle (θ) between the c-axes of two adjacent grains. A larger θ leads to a lower m′ for B-B, P-P and T-T transfers but a higher m′ for B-P transfer. It is found that the θ in the rod has a broad distribution in the range of 0°–90°, whereas the majority of that in the plate is within 0°–40°. This difference generates a different m′ for both slip and twinning transfer between the rod and plate.Strain rate effect on the mechanical behavior of polyamide composites under compression loadingThis paper presents an experimental study on the effect of strain rate on the compressive behavior of polyamide composites. Contrary to thermoset woven reinforced composites, thermoplastic woven reinforced composites have always received less interest despite its excellent damage and impact resistances. In this context, this work aims to study the behavior of fiber reinforced thermoplastic composites submitted to high strain rate in compression. The tested material is a thermoplastic composite made of armor tissue of equilibrate glass fiber and the matrix is composed of Polyamide 6 (PA6/Glass). The material is prepared with the fibers woven in 0/90 direction.The compressive mechanical response of PA6/Glass composite was determined in the transverse and longitudinal fibers directions at quasi-static and high strain rates. The hydraulic machine and Split Hopkinson Pressure Bar experiments were conducted to determine the dynamic and quasi static compressive deformation and fracture of the PA6/Glass at strain rates from 10−5 s−1 to 1 s−1 and 100 s−1 to 2500 s−1, respectively.In this work, the main goals were to determine the strain rate effect on: elastic modulus, failure stress and failure energy as a function of the loading direction. The strain rate sensitivity of the failure stress level and failure energy were observed. In addition, the failure mechanism was characterized by examining the fracture surfaces using the scanning electron microscopy (SEM) method.In quasi-static conditions of loading, the material reached its capacity due to the formation of shear bands, that concerned all three tested compression directions. In dynamics, the failure took place by shearing followed by delamination. In case of dynamic loading in the direction perpendicular to fibers, the observations made by SEM showed that the failure of the composite had a fragile nature.Mechanical properties of a polymer composite subjected to dynamic loading strongly depend on mechanical properties of its components (fibers, matrix, interface) as well as components dimensions and their 3D distribution in the volume The matrix constitutes the continuum phase of the composite and its role is to link fibers together, then to transfer the mechanical loads to fibers and finally to protect fibers against any external aggression such as chemicals or moisture. The effect of the strain rate on composite matrixes was widely studied in Fibers improve mechanical characteristics of the composite: rigidity, resistance at failure, hardness. The most popular reinforcements used for high strain rates are: glass, carbon and Kevlar®. Ayax The fibers surface is often treated chemically to improve adherence with the matrix. The works of Bless The same specimen shape was tested in compression by Harding et al. In case of compression, dynamic tests were carried out for the matrixes with different layer stacking sentences, many authors The failure in compression is generally related to micro-buckling induced by a local misalignment of fibers. Jumahat et al. A detailed study of the process of kink bands formation was carried out by Nowadays, thermoplastic composite have experienced strong growth in industries such as aerospace or automotive and this is held in many contexts. On the one hand, they are light materials which can be easily used for element production using moulding by injection method. It enables the production of complex shapes in large series and the mould has good durability. Contrary to thermosetting composites, they are recyclable. What is more, they propose remarkable mechanical and physical properties: high Young’s modulus, good shock resistance and good resistance/density ratio. However, their heterogeneous and anisotropic structure make more difficulty in understanding and characterizing their damage under dynamic loading.Among thermoplastic composite materials, those with glass fibers and Polyamide (PA) demonstrate a large potential in engineering applications. Major applications of PA6s are in automotive parts where they are used as electrical connectors and light-duty gears. Glass reinforced resins are used for engine fans, radiator heaters, brake-fluid reservoir, valve covers and hydraulic hoses. They are also used as hammer handles, gears and sprockets, bushing and cams. Electrical applications include wiring devices, plugs, connectors, power-tool housing, washers and small appliances. They are also used in ski boards, roller skater, bicycle wheels and fishing lines. Biaxially oriented PA film is extremely tough and is used for meat and cheese packaging, cook-in-bags and vacuum-fill pouches.However, the understanding of the mechanical behaviour of these materials under dynamic loading conditions is limited due to the associated technical hitches at high strain rates. This can be improved by using Split Hopkinson Pressure Bar (SHPB) Most of the high strain-rate characterization studies are focused towards the thermosetting composites such as epoxy and polyester matrices which are reinforced mainly with carbon and glass fibers As mentioned, the effect of strain rate on the mechanical properties of composite materials has been studied since several years. However, there is still a need to get more reliable data for engineering design. Additionally, the failure mechanism under different strain rates needs to be clarified. The objective of this study is to determine the effect of strain rate on the mechanical behaviour of the woven glass-fiber-reinforced Polyamide PA6 composite. The dynamic test results are compared to the quasi-static values. The procedure proposed in The material used is a thermoplastic composite made of armour tissue of equilibrate glass fiber and a matrix composed of Polyamide 6 (PA6/Glass composite). It is fabricated using a double belt press (). The glass fibers have an average diameter of 10 μm and define 50% of the total volume. The weave pattern is shown, The tests were carried out on cylindrical specimens, loaded in compression along the three directions: L1, L2 (L being the longitudinal direction to the fiber) and T (transversal direction to the fiber), see . In order to minimize errors related to friction or those due to radial inertia, the specimens were relatively short with a ratio length over diameter close to 1.0.In order to explain the strain rate influence on the tested material, the effect of the loading velocity on the mechanical response of the PA6/Glass composite in different compression directions will be presented in the next part. Then, the analysis of the surfaces on which the impact was applied will help to explain the failure mechanism in static and dynamic loading conditions.A complete study for a wide range of strain rates was performed under compression using a hydraulic machine (Zwick) which is available to deliver a maximum force of 100 kN and a displacement of 300 mm. Using this device, the strain rate varies between 10−5 s−1 to 1 s−1.In order to perform dynamic compression, Split Hopkinson Pressure Bar (SHPB) system is used. A short specimen is placed between two long elastic bars. The loading is performed thanks to a projectile impacting the input part, . The well known SHPB technique is discussed for example in Using SHPB, the maximum strain rate is close to 5⋅103 1/sDynamic compression tests are frequently used to characterize material behaviour at high strain rates, mainly for metals or some polymers. However, problems arise when the material used is composed of a thermoplastic matrix. Some disadvantages can be listed, one example is the wave reflection at the interface fiber-matrix which induces a phenomenon of the wave dispersion in the material.For a complete definition of the mechanical properties of the composite during compression tests a procedure developed and described in The force-displacement recorded allow to calculate the stress-strain curves. The curves are presented in for three compression directions: L1, L2 (L is the longitudinal direction of the fibers) and T (T is the transversal direction to the fiber). It can be deducted from the curves that for the three compression directions the material behaves in a semi-fragile way. On the one hand for small strains, these curves present elastic linear behaviour. This linear behaviour strongly varies as a function of strain rate in the T compression direction. On the other hand, the linear part is followed by a non-linear one and this is when the strain rate sensibility is remarkable for the L compression direction. This observation can be explained by the beginning of the material deformation.This fragile behaviour is more important for the cases when compression is applied along the direction of fibers which is due to the poor resistance at failure.The problem of dispersion could be corrected by a factor from the solution of the equation of frequencies related to an infinite cylinder When the incident wave εI(t), reflected waveεR(t)and transmitted wave εT(t) are measured along the bar, it is possible to describe the strain, stress curves on time. However, before using the elastic waves εwave, a FFT treatment is performed to consider the Pochammer-Chree effect where εwave(t) is the elastic wave measured along the bars on time.The results are reported in the following picture, . It is observed that the correction allows to reduce some frequency inducing a smooth of the original signal.Using the previous measurements, the following equality corresponding to a force equilibrium may be used, Eq. Moreover, the stress, strain and strain rate may be defined thank to the elastic waves and assuming a one-dimensional stress wave theory where l0 is the initial length of the specimen and c0 is the celerity of the elastic wave in a bar. and integrating it over time, the strain may be calculated, Eq. Finally, the average stress applied to the specimen is defined, Eq. where As is the initial cross-section of the specimen, Eb is the Young's modulus of bars, Ab is the cross-section of the bars. The stress defined Eq. The difficulty in the SHPB system consists essentially in the elastic waves transport. Deformations are measured experimentally at the surface of the bar. Theoretically, they should correspond to the axial displacement of the complete cross-section of the bar. This could only be possible if the propagation of the wave inside the bar is unidimensional, i.e. the displacements of all points of a given cross-section are uniform. However, during the impact of the projectile into the incident bar, the generated wave is of a certain irregularity in its beginning phase, this is principally due to geometric irregularities at the interface bar-projectile.In order to provide a more reliable description of the material behaviour in dynamic conditions, it is essential to take account of errors related to phenomena which occur systematically during the tests. One of the main artefacts changing the material behaviour in terms of stress level is related to the friction effect on the bars-specimen interface. In addition, inertia is also acting on the measurement but this effect is smaller in comparison with the friction effect Therefore, the stress defined for the material behaviour σ(t) using Split Hopkinson Pressure Bar (SHPB) is defined as follows, Eq. The term corresponding to the overstress state related to friction without inertia effect may be calculated using the model proposed by Klepaczko-Malinowski where μ is the friction coefficient, ls is the length of the specimen and ϕs is the diameter of the specimen. Therefore, if a lubricant is used to reduce the friction effect, the stress calculated σ(t) and based on the waves corresponds to the stress level imposed on the specimen Δσ∼μt→0. In order to understand more precisely the PA6/Glass composite behaviour in dynamic compression, and in particular the failure mechanism, a series of tests have been carried out. The main interest was paid to the evolution of the resistance in compression and the energy at failure as a function of the strain rate. The large range of strain rates was studied, namely from 100 s−1 to 2500 s−1.For each test condition, three specimens were tested. represents a summary of the stress-strain curves of the PA6/Glass composite, loaded parallel and perpendicularly to fibers.The shape of stress-strain curves depends essentially on the strain rate and fibers direction. It is deduced from these curves that the elastic modulus of the composite in L compression direction is superior to that in T compression direction. The sensibility to strain rate of the maximum stresses is more important for T direction than for L direction. Many authors In the configuration L, the fibers work directly in compression what explains small deformations in this direction, mostly because of the elevated elastic modulus value. The resistance at failure of the material is higher in T direction than in L direction. Once the failure level is reached, the stress level drops dramatically. The material failure is of the fragile nature in both directions of loading.During the dynamic tests, the absence of plastic deformation of the PA6/glass composite is found. The thermomechanical coupling is then neglected, because the rise of the temperature within the composite material during the deformation is very slow.The exploitation of the quasi-static tests results allowed to determine a value of the failure stress in compression for the PA6/Glass composite. In parallel, for the dynamic regime, the strain rate effect on the failure stress value was revealed. present the influence of the strain rate on the failure stress level for the three compression directions L1, L2 and T. These results demonstrate a positive sensibility of failure stresses to strain rates in compression.In the compression directions L1 and L2, the failure stresses remain insensible to strain rates in quasi-static domain. On the contrary, in the dynamic domain, the strain rate effect takes a predominant role in changing the failure stress for PA6/Glass composite. The results obtained for the compression directions L1 and L2 are different from those recorded for the compression direction T. In the latter case, the failure stress represents an almost linear function of the strain rate. A considerable strain rate sensitivity is reported in both domains: quasi-static and dynamic.In the T direction where the matrix is acting more than the fibres, the material behaviour is reporting a viscous behaviour. The viscous behaviour is related to the strain rate sensitivity of the polyamide matrix. It is typically observed for semi-crystalline polymers The modelling of the curve presented in is made using the least squares method which permits to calculate the sensitivity coefficients of the failure stress to strain rate (quasi-static and dynamic). The coefficients are calculated in the way to minimize differences with experimental results.The stresses evolve according to the following equation:For ε̇=1s-1, it corresponds to the failure stress in quasi-static conditions along the T compression direction: σr0=435MPa. This is close to the experimental value, , with σr0exp≈442MPa. The parameter β represents the strain rate sensibility coefficient of the failure stress value, β = 25 MPa. illustrates the sensibility of stresses to the strain rate effect of the PA6/Glass composite for a given deformation level of 0,01 and for three compression directions (L1, L2 et T). The same algorithm of the least squares method is used to generate the curves. The linear correlation of this curve is given by the following equation:For ε̇=1s-1, it represents the stress level for a strain level of 0.01 under quasi-static conditions, α is the strain rate sensitivity coefficient at deformation level of 0.01, α = 6 MPa. For the T compression direction σ0 = 82 MPa, the stress value is higher for the L directions, σ0 = 115 MPa. Comparing α to β, Eq. , it can be noticed that the strain rate sensibility is more important for the stress level close to failure.In case of the T compression direction, the strain rate sensitivity is moderated in the whole range of strain rates. In case of the L compression directions, the strain rate sensibility is more important, but only above the strain rate level of 102 s−1. reveals the existence of three ranges of the strain rate effect, two of them being for L direction and one for T direction. The first one corresponds to quasi-static loadings, the failure stress being little affected by this parameter, rather non-sensitive at all. The second range corresponds to high speed loading for which a strong strain rate effect is observed. In this last zone, the mechanism of the viscous drag is predominant, and the composite behaves in a quasi-viscous manner. Both concern the L1 and L2 directions. The third range is described by a quasi-logarithmic impact of the strain rates on the failure stresses – such behaviour is recorded for the T direction.The failure test is also intended to measure a ratio of the restitution energy which is defined as the energy absorbed by the specimen during shock. The total energy at failure Wfailure is defined as follow:where S0 and l0 are respectively the cross-section and initial length of the specimen and εr is the deformation at failure.The variation of the energy at failure value of the PA6/Glass composite is a function of the strain rate for all three compression directions L1, L2 and T as it is reported in . This energy at failure value increases with the impact velocity. This increase is more important for the direction T than for directions parallel to fibers distribution (L1 and L2).During the dynamic test, the absence of the plastic deformation was observed. It may lead to conclusion that for the PA6/Glass composite thermomechanical coupling can be neglected, i.e. the increase of temperature in the material as well as material deformation are very low.In quasi-static compression and to describe qualitatively the damage and failure mechanisms, the post-test observations of specimen faces were made. For three compression directions, the material perishes due to shearing. illustrate the state of the specimens smashed in quasi-statics. The failure mode is the shearing for both longitudinal and transversal compression directions. The shearing makes the specimen separate into several parts. The failure surface is oriented at ≈54° and starts at the corner of the specimen (The shearing mechanism of composites has not been well explained yet. Some authors, for example R. Effendi When the dynamic compression in the transversal direction T is considered, a failure appears after the shearing zone is created. On the contrary, for the compression longitudinal directions L, the failure is produced through the shearing of fibers followed by the delamination and finally to decomposition into several tranches. Sometimes the state of failure is quasi-general, this is due to the peeling off of fibers and to the crack propagation in the matrix. The observations made by using the scanning electron microscope of the failure surfaces confirmed the described aspects of the fragile failure of the material tested under dynamic conditions (In the direction T, this is due to the fragilization of the matrix related to the diminution of the mobility of molecular chains. presents the SEM micrograph obtained for the directions L. Pictures of the surface of fragile failure with transversal cracking is shown, the phenomenon is related to poor adherence between matrix and fibers. This poor adherence depends on the fiber-matrix interface, fibers length and thickness. If improved, it can considerably enhance fiber protection against shock. -c clearly shows the fiber pull-out with a considerable length encountered during the dynamic compression.The use of different experimental techniques to cover quasi-static and dynamic behaviour allowed to determine composite characteristics of the composite in the large range of strain rates from 10−5 s−1 to 2500 s−1. Experimental data revealed an important strain rate sensibility on: the elastic modulus, failure stress and failure energy. This was observed especially for the strain rates superior to 1 s−1. This strain rate sensibility is also dependent on the compression direction (longitudinal or transversal).A relevant observation was the fact that the material presented low resistance to shock, being fragile in all three directions in which it was solicited. Concerning a thermomechanical coupling, a very small temperature increase in specimens was registered. This was due to a brittle material behaviour which did not attribute enough time for heating before failure.The experimental results also provided data about deformation at failure conditions as well as failure mode for PA6/Glass composite. In regime quasi-statique, it is shown that the composite failed by shear banding along the diagonal axis. The microscopic observations on the failed samples have proved that the composite failed by the decohesion between fibers and matrix and fibers pull out mechanisms. These observations confirmed the fragile failure of the polyamide composite under dynamic conditions. It was also confirmed that the failure is a direct consequence of the damage which precedes it. This damage phase is particularly interesting in order to understand failure mechanisms of PA6/Glass composites.Supplementary data to this article can be found online at The following are the Supplementary data to this article:Physics of direct bonding: Applications to 3D heterogeneous or monolithic integrationDirect wafer bonding and thinning technologies are now extensively used in combination to produce SOI wafers (silicon-on-insulators) or innovative engineered substrates. Emerging demands of new functionalities at the material or device level for 3D integration have allowed increasing the level of maturity of these technologies. This paper will review the physics of wafer direct bonding and its implementation for vertical integration devices of processed strata with vertical interconnects.3D (three-dimensional) integration technology has been identified as a possible solution to some of the challenges presented by continued scaling of IC devices according to Moore’s Law. In parallel, 3D technology has also been identified as an enabling technology for improved integration of heterogeneous devices. Use of the 3rd dimension introduces the possibility of shorter wiring and the associated potential benefits to resistivity, power consumption, delay, etc., not least as a response to the challenges of ‘More Moore’ scaling. It also introduces the possibility of ‘packaging’ or stacking heterogeneous devices offering form-factor improvement to the pursuers of ‘More than Moore’ heterogeneous integration. However, the term ‘3D technology’ represents not just one generic technology, but rather a range of technologies and processes that can be adapted or developed in order to allow micro- or nano-electronic wiring to benefit of the 3rd dimension to efficiently connect different chips and functionalities. In the absence of a clear convergence of standards, integration of devices for diverse applications and of differing critical dimensions will require different technological approaches. These include but are not limited to the following basic elements: wafer and chip bonding and alignment, inter-strata connections, intra-strata connections (including through silicon via’s), thinning and handling of wafers, chip on wafer planarization, thermal management and design/simulation/testing. CEA-Leti Minatec is working on developing processes in all of the above mentioned technologies with a view to develop a complete ‘3D technology tool box’ (Direct wafer bonding refers to a process by which two mirror-polished wafers are put into contact and held together at room temperature by adhesive forces, without any additional materials Clearly, bonding conditions are a common key point to succeed in a 3D staking by direct bonding. Wafer surfaces have to be contamination free (particle and organic) and smooth enough to adhere to each other, whatever the material nature. In the case of particle contamination, wafers are deformed around particles inducing quasi circular unbonded areas located at the bonding interfaces. Bonding defect sizes are strongly related to particle sizes. Assuming that the particles are incompressible and if the particle size is smaller than the wafer thickness, it is worth noting that the unbonded circular area radius, r, can be larger than the wafer thickness (r |
> 2tw).where γ is the wafer surface energy, E′ the reduced Young’s modulus and tw the wafer thickness, and it is assume that both wafers of the bonding structure are similar. The reduced Young’s modulus corresponds to the ratio of the Young’s modulus and (1 − |
ν) in which ν is the Poisson coefficient. For instance in the case of two 525 μm thick Si bonded wafers, Tong and Gosele A critical case is put in evidence when the non-bonded area radius, rcrit, is about the total thickness of the two wafers, 2tw. It corresponds to a critical particle size, hcrit. When particle size is smaller than hcrit, it induces an unbonded area size which is much smaller (several orders of magnitude) than in the previous cases. In case of die-to-wafer bonding, the presence of particle can impede the bonding and drastically decrease the bonding yield, so for pick-and-place tools have to be adapted to direct bonding (particle contamination reduction). The variation of unbonded area radii versus particle sizes is shown in The surface microroughness plays a key role in the understanding of physical and chemical phenomenon at the bonding interface. Indeed, to establish bonding mechanisms at nanometer scale in the silicon and silicon oxide structures, a rough surface model has been considered in both hydrophobic and hydrophilic bonding cases shows the surface energy variation versus annealing temperature for the bonding of (a) two hydrophobic silicon wafers and (b) a hydrophilic Si wafer to a hydrophilic thermally oxidized Si wafer.During thermal annealing, bonding interface closes up, and there are chemical species evacuations out of the structure. It worth noting that the bonding mechanisms are really different in the hydrophobic case (e.g. Si–Si bonding) and hydrophilic case (e.g. Si–Si, Si–SiO2, SiO2–SiO2). In the latter case, hydrophilic Si surface means that a native oxide is present at the surface, most of the case generated by the wet or dry chemical surface cleaning step. We focused on the hydrophilic case which is the most current structure used because of its higher bonding energy at low temperature, and it also concerns the 3D integration technology.To obtain an oxide film buried in a stack via a bonding process, two ways are possible: either a Si–SiO2 or a SiO2–SiO2 bonding. For thick oxide film (>150 nm), these two types of bonding seems to behave similarly during anneals, for instance used to strengthen the stack. This can be assumed through bonding strength measurements and scanning acoustic microscopy observations, i.e. thanks to macroscopic scale characterizations.However, at a nanometer scale, bonding mechanisms of interface closure and water diffusion are different. These results have been put in evidence with thinner oxide films (<20 nm thick) using two complementary characterization techniques: X-ray reflectivity (XRR) In the case of Si–SiO2 bonding, during annealing at low temperatures (T |
< 250 °C), bonding interface closes up via siloxane bonds formation (Eq. ) explains the increase in bonding energy since low-temperature annealing. It strongly impacts the interface water diffusion.Interface water diffuses to silicon side through native oxide film and reacts with silicon bulk to form additional thin oxide film (Eq. ). The second by-product of the reaction is hydrogen which is the main source of bonding defects.After annealing in the [250–700 °C] temperature range, the bonding interface remains quasi unchanged and then between 700 °C and 1100 °C, bonding interface closes up definitely. The surface energy reaches around 2 J/m2.In the case of thin SiO2–SiO2 bonding, the bonding interface closes up also at low annealing temperature (T |
< 250 °C), but water cannot diffuse through oxide films and stays at the bonding interface. As for Si–SiO2 bonding, SiO2–SiO2 bonding energies are also increased, thanks to these thermal anneals which are applied subsequently to the bonding. For instance, surface energies around 400 mJ/m2 are obtained after 200 °C annealing (). Annealing at higher temperature (T |
> 250 °C) enables water to diffuse into the oxide films and to form silanol groups via the reaction (Eq. ). For T |
< 700 °C, silanol groups are immobile in the oxide volume which does not enable water to diffuse until bulk silicon. So, no oxidation can occur. It means that there is no hydrogen production, and consequently absence of bonding defects in this temperature range. This study has revealed the interest of the SiO2–SiO2 bonding compared to Si–SiO2 bonding.The use of SiO2–SiO2 bonding process can be to either obtain a targeted buried SiO2 layer or the mean to stack specific engineered structures. 3D level integration is one of the fields of applications where SiO2–SiO2 bonding can be applied Processed wafers exhibit various surface topologies. To fulfil direct bonding specifications in terms of smoothness, a silicon oxide layer is usually deposited on top of the processed wafer. Deposited SiO2 layer thickness depends on the amplitude and spatial distribution of surface topology. A chemical–mechanical planarization process, CMP, can be performed to smooth the surface until reaching bonding specifications. The surface microroughness after CMP has to be smoothed (lower than 0.5 nm RMS) all over the wafer. High-bonding energies even after low-temperature treatments can be then obtained. presents a comparison between surface energies after 200 °C annealing during various times for two different oxide types: thermal SiO2 and deposited SiO2. Whatever the oxide type, 2 h appears as a reasonable time to get more than 90% of the surface energy maximum Thermal SiO2 to thermal SiO2 bonding serves as a reference for which no CMP was performed on surface before bonding. Because of their roughness, deposited SiO2 layers need to be smoothed by CMP. It is worth noting that deposited SiO2 to deposited SiO2 bonding in which surface is smoothed by CMP exhibits very higher mechanical strength than the reference. It is worth noting that deposited SiO2 surface energies are fully compatible with subsequent thinning down techniques.More generally approaches other than CMP have also been deeply investigated to obtain high surface energies which can be applied to Si–Si bonding, Si–SiO2 bonding or SiO2–SiO2 bonding. The most well-known approaches consist in the use of surface plasma activation processes carried out before surface contacting. Most of them enable over 1 J/m2 surface energies after < 400 °C annealings The direct bonding was also successfully applied to die-to-wafer bonding in pick-and-place tools. This allows the stacks of die of different technologies nodes, different sizes or from different materials, e.g. III–V on CMOS Wafer-to-wafer or die-to-wafer alignment accuracy is a key parameter to realize high density inter-strata or intra-strata connections. Furthermore, speed and accuracy are two requirements for an industrialized solution to alignment for 3D integration purposes. With wafer-to-wafer stacking, ±1 μm misalignment and even less can be achieved with optical alignment and direct bonding technique. Alignment equipments are currently available for such applications ). A first feasibility of this technique has been demonstrated in laboratory environment at CEA-Léti, the wettability contrast was obtained using hydrophilic–hydrophobic surface activation for direct bonding. A microelectronic compatible process is only at early phase and will be first used after a coarse positioning with existing pick-and-place tool; anyway alignments of few microns were already obtained on 5 × 5 mm dies To validate the direct bonding as a key step for 3D integration, a wafer with one Cu damascene level was bonded face down on a Si bulk carrier using SiO2 direct bonding and thinned down to 12 μm prior to via processing. Copper TSVs are performed to connect Cu pads. To complete the integration, a last Cu damascene level is processed in order to interconnect the TSVs. shows a FIB-SEM cross-section of the TSV chain with a diameter of 3 μm and a pitch of 9 μm. Typical static resistances measured with Kelvin structures are given in . As expected, this value decreases with the increase in the TSV diameter and is close to 120 mΩ for the 3 μm TSV. The yield of TSV chains were measured on 53 dice within a 200 mm wafer. Less than 50 mΩ of resistance dispersion was obtained for around 95% of chains with 3248 via per chain.Using metal as the bonding layer in 3D ICs is an attractive choice since the metal will act as a mechanical bond to hold the active layers together and an electrical bond to establish a conductive path between active layers in a 3D IC’s stack. Mixed oxide/metal bonding will enable a vertical interconnect during wafer bonding. Furthermore, a patterned metal interface will allow the rerouting of interconnect if necessary. With this technology, heat dissipation problems may be overcome in 3D ICs, heat generated in the upper layers can be conducted through the metallic bonding paths down to the heat sink. Thermo compression bonding has been investigated for metal to metal bonding Copper wafer direct bonding is demonstrated and characterized first on blanket surface. This technique enables the bonding at room temperature, atmospheric pressure and at air. Samples used for the experiments were 200 mm Si wafers with a stack of 500 nm thermal oxide, 10 nm TiN and 1 μm Cu deposited by physical vapor deposition followed by electroplating. TiN acts as a copper diffusion barrier. All wafers were annealed after copper deposition in N2 ambient at 400 °C. Atomic force microscopy (AFM) was performed on as-deposited copper layers. The root mean square (RMS) roughness measured with a 20 × 20 μm2 scan was about 15 nm. An appropriate chemical mechanical polishing (CMP) step was then used to lower the roughness down to 0.4 nm RMS, this roughness is mandatory to ensure a good bonding. Surface hydrophilicity was characterized by measuring the contact angle between a deionised water droplet and the surface. For as deposited copper, the measured value was 49°, after a chemical preparation, a 5° contact angle was obtained allowing though a hydrophilic bonding. After surface preparation, wafers were put into contact face to face at room temperature, atmospheric pressure and ambient air.Scanning acoustic microscopy (SAM) was used to evaluate the Cu–Cu bonding quality and its behaviour with annealing. shows a SAM on a manually bonded pair, and few non-bonded zones (mainly due to particle contamination) are seen. After an annealing step of 400 °C during 30 min, no degradation of the bonding quality is recorded.Depending on the mechanical stress applied (shear or traction force), the behaviour of a bonding interface will not be the same. Since copper is a ductile material, the measured copper to copper bonding energy will then depend strongly on the solicitation mode and though on the characterization technique. When there is a shear contribution in the bonding interface opening method, the measured energy is increased due to the bonding layer ductility. We then characterized the bonding energy with a pure mode I Double Cantilever Beam (DCB) Maszara’s Blade Technique This technique consists in measuring the debonded length induced by the insertion of a blade at the bonding interface. When the characterized stack is symmetrical, the mechanical opening with this Maszara’s Blade Technique occurs without shear contribution, and though the ductile work component is minimized At room temperature, high-bonding energy in the range of 2.8 J/m2 is obtained. This high-bonding energy value (compared to oxide bonding energy) can be explained by the fact that even the ductile work is minimized, there is still a small component of ductility in this energy measurement method. When an annealing step is applied to the bonded pair, copper self-diffusion through the bonding interface happens. Above 200 °C, the bonding interface gets strong enough so that the fracture initiated by Maszara’s Blade Technique cannot propagate through it. A bonded pair was thinned down to 10 μm to validate the ability of this bonding technology to handle 3D post processes. One can see that no delamination occurred even at the edge of the bonding (, mixed surface (copper, oxide) is to be prepared for bonding. Since the copper bonding energy is higher at low temperature than the oxide bonding, copper pad surface preparation is of importance.Standard damascene CMP process is the most used process to planarize metal levels in microelectronics. However, to avoid leakage, the process induces a dishing of the copper pads on patterned surfaces (). This surface topology is prohibitive for direct bonding application. If two patterned wafers are bonded together using a standard CMP process, dishing on copper pads will prevents metal contact even after a 200 °C annealing step during 30 min ( compares SAM characterization of two patterned bonded pair prepared with and without optimized CMP process. When this special CMP process is used, almost all the wafers are bonded; just small voids were induced by particles contamination.Some experiments have been carried out on patterned wafers with a copper surface density around 20%; patterned wafers mixed surface Cu/SiO2 has been planarized by CMP with a dishing depth in the range of 20 nm on silicon oxide lines. The direct bonding was manually initiated. Bonded pairs were then diced to carry out samples for scanning electron microscopy (SEM) and bonding toughness analyses. By performing a Maszara’s adhesion measurement as explained for full sheet bonding approach, two different behaviours have been recorded. If the patterned sample is bonded on full copper blanket, the bonding is monitored by the copper interdiffusion, though the bonding energy increases with temperature (). Since only 20% of the bonded surface is copper bonding, the bonding energy at room temperature is in the order of magnitude with the measured bonding energy for full copper blanket to full copper blanket bonding.For blanket copper sample bonded to blanket oxide layer, the bonding energy does not increase with temperature (). In this case, no copper interdiffusion is possible.In the case of direct pattern copper bonding, energy evolution is mainly driven by copper interdiffusion and not by the oxide bonding.In order to verify the feasibility of localized electrical interconnect at the bonding level, wafers with electrical test pattern in an SiO2-oxidized silicon were prepared with the surface preparation described earlier and bonded face to face in an EVG Smart View alignment tool. The alignment marks were done at the copper level. After successive a 200 °C annealing step, alignment was characterized by infra-red microscopy (Misalignments characterization was performed on die all along vertical and horizontal diameter of the bonded pair. Alignment marks on the patterned wafer enable a misalignment measurements accuracy in the range of 0.5 μm on x and y axis. records the obtained X/Y misalignment. For all measurements, the misalignment was below 1 μm/1 μm. Misalignment stayed constant even after grinding down to 15 μm.). The bonding contact area Ac is 10 μm × 10 μm. After an annealing at 200 °C for 2 h, one of the silicon wafers was completely removed down to the oxide. Then, the oxide was etched away to access the copper pads with tips. The contact resistance Rc and the specific resistance ρc are calculated from experiment as explained in Eqs. where VMH and VML are the top and bottom branch electrical potential respectively, and I is the current passing through the bonding interface.The contact resistance Rc and the specific resistance ρc were, respectively, equal to 9.8 mΩ and 0.98 Ω μm2 (). Rc is one order of magnitude smaller than the resistance of a 3 μm diameter via and is also in accordance with Rc values obtained on daisy chain by thermo compression on Cu/Sn interdiffusion bonding, anyway with higher bonding temperature Direct oxide and copper bonding are powerful techniques to address 3D integration for wafer-to-wafer or die-to-wafer stacks. High-bonding energies and alignment of 1 μm are achievable in both cases with no degradation with post processes. For mixed oxide/copper bonding, the electrical behaviour of the copper to copper bonding was demonstrated.Performance of practical beam-to-SHS column connections against progressive collapseHollow sections are widely considered for structural column members due to their inherent architectural and structural advantages. The commonly used types of hollow sections include square, rectangular, and circular hollow sections (abbreviated as SHS, RHS, and CHS, respectively), whilst elliptical hollow sections (EHS) have also recently emerged as a structurally and aesthetically appealing solution From the load transfer point of view, these beam-to-column connections are mainly subjected to bending and shear under normal conditions. When appropriately designed and fabricated, all the three solutions shown in can be readily employed in practice and it seems that they have been serving the construction industry reasonably well over the past decade. However, there is sparse investigation into their performance when subjected to more complex loading states (e.g. combined axial force, bending, and shear) in conjunction with high ductility demand, and the lack of information may pose risk of unexpected failure when extreme loads occur. In particular, progressive collapse has been recognised as an essential design consideration, following several major accidents in the last century (e.g. Ronan Point apartment block and Murrah Federal building) However, most of the existing studies on structural progressive collapse have focused on steel frames with open section beam-to-open section column connections, whereas the robustness performance of those with practical beam-to-tubular column connections is still not well understood. Compared with the case of open section columns where bolted beam-to-column connections can be readily used, the behaviour of beam-to-hollow section column connections may be less easily predictable due to more complex connection detailing. With increasing popularity of the application of hollow section columns in modern construction , are reported. The test results, including failure modes/sequences, load–deformation responses and stress conditions, are presented, and the load transfer mechanism along the entire loading process is thoroughly discussed. Comprehensive finite element (FE) models are then established to enable further interpretation of the test results, and design comments are finally outlined based on both experimental and FE results.Three test specimens, corresponding to the three typical connection configurations shown in (a). The overall length l0 of the double-span sub-frame was 4.5 m, leading to a span-to-depth ratio of l0/H |
= 15.0. The two ends of the system were vertically and horizontally constrained but were free to rotate (i.e. pin-supported). This boundary condition was considered to reasonably reflect the points of contra-flexures in real moment frames, as illustrated in . Each set of results in the table was based on the average values of three coupons for each part.The test setup, consisting of a servo actuator (capacity = 2000 kN), a column base sliding support, and self-balanced horizontal and vertical support frames, is schematically shown in (b). A quasi-static point load was applied by the actuator to the top of the centre column with displacement control. During the loading process, the upper part of the column was fixed to the loading head, and the lower part was guided to move vertically through the sliding support, such that no rotational movement of the column was allowed. This led to a generally symmetrical performance of the system at the two sides of the column (i.e. ‘east’ and ‘west’ sides for ease of discussion), which is true when the column immediately above the affected floor can offer sufficient rotational restraints. In fact, minor gaps existed between the column and the sliding support, and therefore slight rotation can still be induced. The tests were terminated when either complete fracture of the connection occurred or the limiting displacement Δmax of the test frame was reached (Δmax was approximately 400 mm, corresponding to a beam chord rotation of 0.178 rad). For specimen I-W, however, malfunction of the column base sliding support occurred during the test, and a certain level of column rotation was induced. In order to prevent damage to the actuator, the test stopped at a relatively early stage for this specimen when the displacement reached 200 mm. The two ends of the system were pin-supported via two hinges such that a full axial restraint was maintained. This was used to reflect the condition of relatively strong/rigid neighbouring sub-structures providing a sufficient level of axial restraints, which can be true for most typical steel frames due to the strong axial restraints offered by the adjacent beams in conjunction with the ‘diaphragm effect’ of the floor system The applied point load was automatically recorded by the actuator system, and the deflection of the double-span system was monitored through placing a series of displacement transducers along the beam length with certain intervals, as shown in (a). Strain gauges were employed to monitor the strain distributions over critical beam sections, as generally shown in (b). For each specimen, the strains over the E1 and W1 sections (615 mm from the east and west beam end hinges respectively) were recorded to deduce the axial force development within the sub-frame, as discussed in detail in Section . The strains over the critical sections, i.e. sections E2/W2 and E3/W3, as illustrated in (b), were also recorded to examine the strain development conditions near the joint fractural zone.In general, all the specimens exhibited satisfactory load resisting capacity and ductility supply. No weld failure was observed, which indicated good weld quality for the specimens. The load–deflection responses of the three specimens, with the associated key failure stages identified during the loading process, are shown in . It should be noted that both the applied load F and the normalised load F/FP are given in the figures, where FP is the theoretical vertical resisting load corresponding to the formation of full plastic hinges of the beam at the critical sections W3/E3, under a flexural bending mechanism. In addition, both the displacement Δ and the beam chord rotation θ are given in the figures.When the weld along the beam web was replaced by a shear tab bolted connection, as was the case for specimen I-WB, the failure behaviour could be evidently changed. As shown in The load–deflection response of the specimens can be further depicted through the deflection profiles obtained from the displacement transducers placed along the length of the beams, as shown in (a). For specimens I-WB and ST-WB, because of the presence of the column base sliding support, the performance at the two sides of the column was generally symmetrical. For specimen I-W, however, the malfunction of the sliding support caused column rotation, and thus larger deflection was observed at the west side of the column due to localised development of cracking. Importantly, it can be seen that at initial loading stages, i.e. Δ |
< 30 mm, a typical curved deformation shape was exhibited, which indicated that the resisting mechanism was mainly governed by flexural bending. With increasing deformations, the deformed configuration was gradually changed to that exhibiting two straight lines intersecting at the location of centre column, indicating that plastic hinges were developed near the connection zone. This reveals that the ductility demand of the specimen subjected to column removal was mainly accommodated by the connection zone, and the progressive collapse resistance of the system was mainly dependent on the performance of these connections under complex internal forces.Typical strain gauge readings of the specimens are shown in The test results generally showed a similar level of ultimate load resistance (as listed in The load transfer mechanism of the specimens can be further interpreted through the internal forces developed within the sub-frame. As mentioned previously, the strain gauge readings in section E1/W1 can be employed to calculate the internal forces at the section, as given by:where N1, M1 and V1 are the axial force, bending moment and shear force at section E1/W1, respectively; E, A and I are the Young’s modulus, cross-sectional area and second moment of area of the beam, respectively; Σε/n is the average strain over the section; Δε/Δh represents the curvature of the section; l1 is the horizontal distance between section E1/W1 to the pin-support; and δ1 is the vertical deflection of the beam at section E1/W1 (according to the readings from the displacement transducers), as illustrated in (a). Based on the internal forces at section E1/W1, the vertical and horizontal reactions (VR and HR, respectively) of the pin support can be obtained:where tan |
θ1 |
= |
δ1/l1. Considering the equilibrium of the beam segment, as shown in (a), the internal forces at any section can be obtained using the following expressions:Ni=HRcosθi+VRsinθi,Vi=VRcosθi-HRsinθi,Mi=VRli-HRδiwhere i indicates the corresponding values (i.e. axial force, shear force or bending moment) at any section Ei/Wi. It should be noted that the calculation of Mi is based on the assumption of non-fractured section, where the centroid is at the mid-depth of the beam. When fracture occurs, this calculated moment is inaccurate over the fractured section, and thus the result can only be considered as an indicative (or ‘virtual’) moment.Based on the above equilibrium equations, The load resistance mechanism can be further elaborated by illustrating the contributions from flexural bending action and catenary action to the overall resisting load. Based on the free body diagram shown in (b), the portion of the resisting load contributed to by the catenary action FR-C can be expressed as:and that contributed to by the flexural bending action FR-F can be easily obtained by deducting FR-C from the overall resisting load. (c) shows the contributions of the two actions to the resisting load, and the responses were in line with the previously discussed evolutions of the axial force and bending moment. The results confirmed that the load resistance of the specimens significantly relied on catenary action at large deflections, especially when Δ exceeded 200 mm.In practical design of building structures against progressive collapse, it is normally considered that the progressive collapse potential of a structure is governed by the ductility supply of the connections. The major design guidelines (e.g. DoD) stipulated a series of acceptable plastic rotation angles (Acceptance Criteria) for various connection types for nonlinear modelling of steel connections, and failure may be considered to occur if the plastic rotation angles of the connection exceeds the acceptable ones. In particular, if a connection exhibits an idealised multi-linear curve type as shown in (a) (which is the case for the current specimens), detailed acceptable plastic rotation angles (i.e. limiting values of ‘a’ and ‘b’) are listed (a). The plastic rotations can be obtained by deducting the yield rotation θy from the overall beam chord rotation. In general, all the three specimens showed sound ductility when subjected to mid-column removal. The plastic rotation angle a (i.e. that prior to initial fracture) ranged from 0.031 to 0.065 rad, which significantly exceeded the acceptance criterion proposed by DoD The focus of the current experimental study was given to the static performance of the double-span systems subjected to centre column loss, but when actual extreme events occur (e.g. blast), sudden column removal, which is associated with dynamic response, can be a more rational assumption that realistically reflects the consequence of an extreme event. Sudden removal of a column is in effect close to suddenly applying the gravity load on the same structure in the absence of the column at the beginning, especially when significant displacements can be sustained by the structure as a result (b), if the static load–deformation response is known, the allowable dynamic (i.e. sudden column loss) load resistance at any ductility demand can be obtained by achieving an equivalence between external work and internal energy, i.e. when the two hatched areas become identical. By considering different levels of ductility demand and employing the energy balance principle, a dynamic (pseudo-static) curve, which represents the relationship between the sudden applied load and the associated dynamic deformation, can be constructed.As the early finish of the test for specimen I-W prohibited a complete understanding of its load resistance mechanism, the development of numerical modelling can offer an efficient complementary insight into its progressive collapse performance at later loading stages. The numerical study can also effectively reveal the complex stress distributions within the structural components, which may help explain the fracture initiation and propagation phenomena of the three specimens. The general nonlinear finite element (FE) analysis package ABAQUS The C3D8R elements, which are 8-node linear brick elements with reduced integration and hourglass control, were employed for all the structural components, including the SHS column, H beam, diaphragm plates, shear tab, and high-strength bolts. The general meshing size for the column and beams was approximately 5 mm, but a refined meshing size of around 1 mm was employed for the areas adjacent to the connection zone, as typically shown in . ‘Hard contact’ with no penetration in the normal direction was considered for all contact pairs, and a coefficient of friction of 0.45 was used corresponding to the actual treatment of the steel surface. As no weld failure was observed during the tests, the ‘tie’ interactions were employed to simulate all the complete penetration groove welds. The boundary conditions of the models were applied to reflect the actual conditions of the test setup, where idealised pin-supports were considered at the two external ends of the beam and the centre column was only allowed to move vertically with no in-plane rotation. For specimen I-W, however, two boundary conditions for the centre column were considered: (1) the column was laterally restrained along the length, which is consistent with the boundary condition for the other two specimens, and (2) the constraints at the lower part of the column was removed, which was used to consider the actual case where the column base sliding guide did not work properly for this specimen. For the latter case, the material fractural strain (as discussed below) of the beam at one side of the column (east side) was slightly increased in order to trigger non-symmetrical performance (e.g. fractural development) of the symmetrical FE model.The basic nonlinear material property of steel was simulated using the isotropic hardening model with the von Mises yield criterion. The fundamental material properties, including the modulus of elasticity, yield strength, and ultimate strength, were obtained from the tensile coupon test results. The engineering stress σEng and strain εEng were then converted to true stress σT and strain εT in ABAQUS, as expressed by:and the true plastic strain εp for ABAQUS input can be obtained by:To simulate fracture of steel, the progressive ductile damage model offered by ABAQUS was employed. The damage model allows for ductile fracture of steel that experiences extensive plastic deformation in the necking phase prior to fracture, and after the initiation of fracture, a user-defined degradation response of the material stiffness is enabled, where the fully damaged elements will be deleted from the mesh. Therefore, in order to capture the progress of material damage, two sets of parameters need to be incorporated, namely, a damage initiation criterion and a damage evolution response. The damage initiation criterion describes the maximum equivalent plastic strain which initiates damage. The damage evolution law describes the condition of degradation of the material stiffness once the corresponding initiation criterion has been reached, and a linear damage evolution law was considered in the current study.To simulate the fracture of steel under a uniaxial state, the failure true stress σf and strain εf (at which fracture is triggered) can be obtained from the coupon test results and by using the following equations:where Ffracture and Afracture are the tensile load and the necked (reduced) cross-sectional area of the coupons where fracture occurred, and A0 is the original cross-sectional area of the coupons. When the material is subjected to multi-axial stress states, the influence of stress triaxiality on the material fractural behaviour may need to be considered. However, as detailed triaxial material testing is normally not considered as a standard procedure in common experimental programmes, and metal fracture itself is a complicated issue, inconsistent approaches were normally employed in various investigations where PEEQ is the equivalent plastic strain, T is the stress triaxiality which is the ratio of the hydrostatic stress over the von Mises stress. Rupture Index is an indicator reflecting the potential for ductile fracture (i.e. the higher the PEEQ, the higher the potential for fracture), and the value at fracture for a specific material may be obtained by using Eq. with the uniaxial coupon test results, where T |
= 0.33 for the uniaxial loading state. Employing a consistent Rupture Index for the same material, the plastic fracture strain (the PEEQ value that causes fracture) at various stress triaxiality conditions (i.e. various T values) can be obtained. These plastic fracture strain and stress triaxiality (T) pairs were then directly input into ABAQUS for simulation of steel fracture at various stress states. It should be noted that this is only a convenient and simplified way of simulating the fractural phenomenon of steel with the consideration of stress triaxiality, whereas the actual triaxial performance also depends on other factors such initial material imperfections and the direction of rolling The load–deflection responses and fractural phenomena of the specimens predicted by the FE models are compared with the test results as shown in . Good agreements are generally observed between the FE predictions and test results, especially in terms of the trend of load dropping and regaining responses as well as the fractural patterns. The minor discrepancy may be caused by some test uncertainties which are difficult to be fully reflected by the FE model. For instance, in the actual test, it was difficult to fully fix the pin-supports in the axial direction due to slight unavoidable gaps in the hinges as well as in the adjacent connectors; however, the beam ends of the FE model were considered as pin-supported in an idealised manner with no movement allowed in the axial direction. This idealised pin support condition in the FE model can cause more significant compressive arching effect in the initial stage, which may explain the slightly higher initial resisting load of the FE predictions compared with the test results for some specimens. Possible variations of material properties could also lead to the discrepancy. Nevertheless, the proposed FE modelling strategy can well capture all the key stages of the specimens from initial column removal until final collapse. Importantly, the late-stage load resisting mechanism of specimen I-W, which was not recorded by the test, is revealed by the FE predictions.Generally speaking, the rationality and effectiveness the FE modelling strategy, especially the way of addressing the complex issue of fracture simulation of the steel components, is verified. Whilst parametric studies are not within the scope of the current paper, the validated numerical model can form an important basis for the future studies towards more detailed design regulations of such beam-to-SHS column connections (or similar connections types).Harmonic balance method magnetorheological elastomerDynamic stability of magnetorheological elastomer based adaptive sandwich beam with conductive skins using FEM and the harmonic balance methodThe dynamic stability of a partially treated magnetorheological elastomer (MRE) cored sandwich beam with conductive skins subjected to time varying axial load has been studied. The finite element method (FEM) and Guyan reduction method are used to derive the governing equation of motion which is similar to that of Mathieu's equation. The instability regions of the sandwich beam for the principal parametric resonance case are calculated by using the harmonic balance method. Effects of applied magnetic field, static load, dynamic load, the length and the location of the MRE patch on the stability of the sandwich beam are investigated. The results suggest that the stability of the MRE embedded sandwich beams are strongly influenced by the strength of the applied magnetic field, static load, dynamic load, the location and the length of the MRE patch.Harmonic balance method magnetorheological elastomerMagnetorheological elastomers (MRE) have great potential in developing stiffness variable devices which can find applications in many intelligent structures. These materials are increasingly being used as semi-active/active vibration devices in various applications For past few decades various MREs are being developed based on natural and synthetic rubbers by many researchers Nowadays the magnetorheological elatomers have been implemented in sandwich structures as core material to achieve controllable properties of sandwich structures with suitable magnetic field. Sandwich beams are increasingly being used in the design of high performance load carrying structures when high specific strength and stiffness to weight ratios are desired. Many works have been reported on free and forced vibration of sandwich beams using various approaches and different methods When a beam is subjected to a time varying axial load the system behaves as that of a parametrically excited system The dynamic instability of sandwich structures induced by parametric excitation has been investigated by many researchers. Kar and Sujata In all most all the above literature simple classical or higher order theory have been used to find the governing equation of motion of sandwich beams which are suitable for only simple structures with classical boundary conditions. Using this formulation it is very difficult to predict the response and instability regions for complicated and real life systems. Hence in this present work an attempt has been made to develop a finite element based method which can later be used to study complicated MRE embedded viscoelastic cored sandwich beam. Here Guyana reduction method is used to reduce the size of the mass and stiffness matrices by writing the equation of motion which is in the form of Mathieu–Hill's equation in terms of master degrees of freedom. The natural frequencies obtained using this method, have been compared with the published results. The instability regions are determined by solving the obtained Mathieu–Hill's equation using Harmonic balance method. The effects of static and dynamic loads, magnetic field strength and location and length of MRE segment on the instability regions are determined.(a) shows the schematic diagram of a three layered MRE cored sandwich beam of length L, top, bottom and core layers thickness ht, hb and hc, respectively. (b) shows the same sandwich beam when the core layer contains both the viscoelastic patches of lengths L1 and L3 and a MRE layer segment of length L2. This system is subjected to a time varying axial force, P(t)=Ps+Pdcos(Ωt). Here Ps and Pd are the static and dynamic load respectively. t is the time and Ω is the excitation frequency.In this formulation the longitudinal displacements of the mid-planes of the top bottom and core layers in the x-direction are u0t,u0bandu0c. w is the transverse displacement of the beam. The following assumptions have been considered for the modeling of the sandwich beam using FEM. It is assumed that the deformation of top and bottom skins obeys Euler Bernoulli beam theory. The three layers have the same transverse displacement w. The MRE embedded viscolelastic core of the sandwich beam deforms due to shear only. While the non-MRE parts of the core are not affected by magnetic field, only the MRE part of the core is affected by the magnetic field. The zero field Young's modulus and shear modulus are same for both MRE and non-MRE parts in the core. There is no slippage and delamination between the layers during deformation.The strain in top and bottom skins can be expressed in terms of axial displacement in the neutral axis of the respective layer and the transverse displacement as follows.where subscript j=t and b for top and bottom faces, respectively, u0j is the axial displacement of the mid-plane of skin j, and zj is the distance of the mid-height of skin j from the neutral axis.The total kinetic energy of the sandwich beam can be obtained by adding the kinetic energy due to the transverse displacement of all the layers, axial displacements of top and bottom skins and the rotation due to shear strain of the MRE embedded viscoelastic core.T=12∫0L(m(∂w∂t)2+mt(∂ut∂t)2+mb(∂ub∂t)2+ρcIc(Hhc∂2w∂x∂t+(∂u0t/∂t)−(∂u0b/∂t)hc)2)dxwhere m=mt+mc+mb. mt,mc and mb are the mass per unit length of the top, middle and bottom layers respectively, ρc and Ic are the density and the moment of inertia about centroid of the core, respectively.The expression for potential energy of the system U can be obtained by adding the potential energy due to extension and bending of the skins, shear deformation of the core and work done due to the magnetoelastic loads in the skins which is given as follows.Uebs=12∫0L(EtAt(∂ut∂x)2+EbAb(∂ub∂x)2)dx+12∫0L(EtIt+EbIb)(∂2w∂x2)2dx+12∫0LGc⁎Ac[Hhc∂w∂x+u0t−u0bhc]2dx+∫0L[ntut+nbub+mtmw,x+mbmw,x]dx.Here the complex shear modulus Gc⁎=Gc(1+iηc), where Gc is the storage shear modulus, Ac is the cross sectional area of core, i=−1 and ηc is the core loss factor. nj and mjm are the magnetoelastic loads and moments due to conductive skins which are expressed in terms of the longitudinal displacement (uj) and transverse displacement (w) as (Zhou and Wang mjm=B02bhjμ0(π2lnxL−xuj,x−hj2πwj,xxlnxL−x+wj,x)−B02bhj312μejwj,xxx.Here μ0andμe are respectively the permeability of the free space and the face materials. B0 is the static magnetic field which is perpendicular to the skins and parallel to the chain like structures of iron particles in MRE.The non-conservative work done due to periodic axial load isThe above equations are applicable for MRE embedded sandwich beam with either a fully or partially treated MRE core.A standard beam element with two end nodes () with four degrees of freedom (DOF) at each node is considered for modeling of the sandwich beam using FEM. The DOF include the transverse displacement w, axial displacement of top skin ut, axial displacement of bottom skin ub and the rotational displacement θ of the beam. The elemental displacement vector isThe elemental displacements can be determined in terms of displacements of two nodes aswhere [Nw],[Nut]and[Nub] are commonly used linear and cubic polynomial beam shape functions. The shape functions are [Nw]={1−3x2le2+2x3le3x−3x2le+x3le2003x2le2+2x3le3−x2le+x3le200}[Nut]={001−xle000x2le0}[Nub]={0001−xle000x2le}}The potential energy term can be rewritten in nodal displacement variables for one element with length le as follows:The expressions for the matrices [K1],[K2],[K3],[K4]and[K5] are given in Similarly, the kinetic energy term can be rewritten as[Me]=∫0le(m[Nw]T[Nw]+mt[Nut]T[Nut]+mb[Nub]T[Nub]+ρcIc[Hhc[dNwdx]+Nut−Nubhc]T×[Hhc[dNwdx]+Nut−Nubhc])dxand the external work done term can be rewritten asUpon substituting the expressions for kinetic energy T and potential energy U into Hamilton's principle, described asThe governing equations of motion for the un-damped partially or fully treated MRE sandwich beam element in the finite element form can be obtained as[Me]and[Ke] are the elemental mass and stiffness matrices. Assembling the all elemental matrices for all the elements, the global governing equation of motion of MRE embedded sandwich beam as follows:For the MRE embedded sandwich beam, the matrices [M],[K]and[Kf] are formulated by imposing compatibility conditions which are identical transverse displacements, w1|x=L1=w2|x=L1, w2|x=L1+L2=w3|x=L1+L2 and axial displacements, uj1|x=L1=uj2|x=L1, uj2|x=L1+L2=uj3|x=L1+L2 and the slopes θ1|x=L1=θ2|x=L1, θ2|x=L1+L2=θ3|x=L1+L2 at the interfaces of the viscoelastic material and MRE patches within the core of the sandwich beam ((b)). Each MRE patch is modeled independently and then coupled with the adjacent non-MRE segments.Considering the damping effect of MRE on the sandwich beam the equation of motion can be rewritten as[M]{q¨}+[K]{q}+[C]{q}−(Ps+PdcosΩt)[Kf]{q}=0where [C]=iηc[K], here ηc is the loss factor of the MRE.To reduce the size of the matrix the Guyana reduction method is used. In this method, DOF of the FE model are designated as either slaves or masters without force term can be partitioned according to master DOF {q¯m} and slave DOF {q¯s} as follows([KmmKmsKmsTKss]−ω2[MmmMmsMmsTMss]){q¯mq¯s}={00}Solving the lower partition and substituting into upper partition and following the procedure given in The entire set of DOF is expressed in terms of masters DOF by the equation,[Mr]{q¨m}+[Kr]{qm}+[Cr]{qm}−(Ps+PdcosΩt)[Kfr]{qm}=0where[Mr]=[T]T[M][T],[Kr]=[T]T[K][T],[Cr]=[T]T[C][T]and[Kfr]=[T]T[Kf][T].For the analysis of stability of sandwich beams the method developed by Bolotin [Mr]{q¨m}+[Kr]{qm}+[Cr]{qm}−(Ps+PdcosΩt)[Kfr]{qm}=0The static and dynamic loads PsandPd can be represented in terms of the static buckling load Pcr as, P(t)=αPcr+βPcrcosΩt, where αandβ are the static load factor and dynamic load factor, respectively. Now Eq. [Mr]{q¨m}+[Kr]{qm}+[Cr]{qm}−(αPcr+βPcrcosΩt)[Kfr]{qm}=0The above equation is a Mathieu–Hill equation with a periodic coefficient. The periodic motion of the system is usually the boundary case of vibrations with unboundedly increasing amplitudes. Therefore it is important to study the dynamic instability of the system and determination of the boundaries of the dynamic instability regions. The first-order trivial solution of the Eq. with period of 2T, where T=2π/Ω are expressed as,Here {A} and {B} are vectors independent of time, t. Substituting the Eqs. leads to the eigenvalue equations in matrix form:|[Kr]−(αPcr−βPcr)[Kfr]−Ω24[Mr]−Ω2[Cr]Ω2[Cr][Kr]−(αPcr+βPcr)[Kfr]−Ω24[Mr]|=0Hereafter, this equation is referred as the equation of boundary frequencies. The above equation is used to find the boundaries of principal instability regions of the system.Using the expressions of the developed finite element model a MATLAB code has been developed to obtain the natural frequency, loss factor, parametric instability and dynamic response of a simply supported MRE embedded sandwich beams for different configurations. Performing the convergence study it has been decided to use 32 elements in FE analysis. Initially the developed code is validated by finding the natural frequencies without considering the axial load for different sandwich beam available in literature.First a symmetric sandwich beam is considered taking the material and geometric properties as in the work of Howson and Zare which are found to be in good agreement with the results of Howson and Zare shows a comparison of natural frequencies obtained from the present model and the results of Banerjee et al. In the present numerical analysis a symmetric sandwich beam with MRE embedded core has been considered for simply supported end conditions. The geometric and material properties of the sandwich beam are as follows. The span of the beam, L=416 mm; width, 30 mm; the top and bottom skins thickness, ht=hb=1mm, the core thickness, hc=3 mm. The top and bottom aluminum skins have Young's modulus 72 GPa and density 2700 kg/m3. The permeability of air gap and aluminum skin are μ0=4π×10−7 and μe=1.2566650×10−6, respectively. Following expressions for the shear storage modulus and loss factor of natural rubber based MRE (containing 80% of iron particles) have been used which are obtained by curve fitting () the experimentally obtained data of Chen et al. Gc=(−6.9395B06−9.1077B05+71.797B04−93.422B03+38.778B02+2.43B0+2.7006)MPaηc=5.3485B06−17.787B05+22.148B04−12.185B03+2.3522B02+0.1526B0+0.228In this work along with the full length MRE core sandwich beam as shown in (a), seven other different types of MRE embedded sandwich beam structures have been considered for numerical analysis. shows three different configurations (CI, CII and CIII) of the sandwich beam having the same total MRE patch length but with different individual patch length and locations. Similarly, shows four different sandwich beam configurations LI, LII, LIII and LIV having the same MRE patch length but with different MRE patch locations.The variation of modal frequencies and loss factors of a fully MRE cored sandwich beam with different magnetic field is shown in , where the static load factor α is zero. It is noted that the modal frequencies of first three modes increase with the strength of the applied magnetic field ((b) shows the effect of magnetic field strength on the loss factor. In all the three modes, the loss factor initially increases and then decreases with increase in magnetic field strength. It is because that the stiffness of the sandwich beam increases with the magnetic field strength due to the increase in complex shear modulus of MRE (), where as its damping decrease with increase in magnetic field strength ((a) shows the variation of the modal frequencies with the static load factor α. The modal frequencies in all the three modes decrease with the increase in static load factor.(b) shows the influence of α on the loss factor where one may observe that in all the modes the loss factor increases with increase in the static load factor. It may be noted that initially the loss factor of the sandwich beam is less than that of the MRE and with increase in α this value increases significantly. For example with B0=0.6T, loss factor for MRE is equal to 0.26 (Fig. B2) and with α=0 the loss factor of the sandwich beam is 0.19, 0.14 and 0.1 for first, second and third mode respectively. The corresponding values for α=1 are 0.37, 0.21 and 0.135.The effect of variation of magnetic field strength on the fundamental frequency and loss factor for the different configurations of a MRE embedded viscoelastic cored sandwich beam is shown in (a) that the fundamental frequency increases with increase in magnetic field. Also it can be observed that at higher magnetic field the fundamental frequency of CII is more than CI. Similarly the fundamental frequency of CIII is more than CI and CII. For full length MRE core sandwich beam the fundamental frequency at higher magnetic field is larger than the other configurations. The increase in the frequency with increase in magnetic field can be attributed to the increase in the complex shear modulus of the MRE patch which increases the stiffness of the sandwich beam. Also the distribution of MRE patches in the core increases the stiffness of the beam.(b) shows the influence of magnetic field strength on the loss factor for the different configurations of a sandwich beam. In all the configurations, the loss factor initially increases and then decreases as the magnetic field strength increases. This trend is much obvious for the configurations CIII and fully MRE core of sandwich beam and less evident for the configurations CI and CII. As the loss factor is merely the ratio of dissipated energy to the total strain energy which initially increases and then decreases as shown in , so the dissipated energy and hence the loss factor of the system as shown in (b) initially increases and then decreases with increase in magnetic field.The influence of static load factor on the fundamental frequency and loss factor for the different configurations of a MRE embedded viscoelastic cored sandwich beam is shown in (a) the fundamental frequency in all the configurations decreases with the increase in static load factor. The influence of static load factor α on the loss factor is shown in (b). It can be observed that in all configurations the loss factor increases with static load factor. This can be attributed to the fact that for the same dissipated energy the total strain energy decreases with increase in static load factor α. shows the effect of variation of magnetic field strength on the fundamental frequency and loss factor for the different configurations of the sandwich beam shown in . Also the results have been compared with those of the configuration CI and the fully treated MRE core of sandwich beam. Here similar trend has been observed as in . One may observe that due to symmetry, the fundamental frequencies and loss factors for location LI and LIV and also for LII and LIII are same as shown in (a) and (b) respectively. Also it can be observed that at higher magnetic field the fundamental frequencies and loss factors of LI and LIV in which the MRE patches are located at the support ends are more than those of LII and LIII.The influence of static load factor on the fundamental frequency and loss factor for the same configurations discussed in previous is shown in . It is observed that in all configurations fundamental frequency decreases and loss factor increases with increase in static load factor. Here also due to symmetry the fundamental frequencies and loss factors for location LI and LIV and also for LII and LIII are same.In this subsection, the stability of a MRE embedded viscoelastic cored sandwich beam subjected to periodic axial load has been investigated considering various system parameters and different configurations based on the length and location of the MRE patch in the core for the simply supported end condition. shows the instability regions of the system with configurations CI and CIII for α=0,B0=0.2T. Here while the regions bounded by the curves are unstable (marked U), the regions outside the curves are stable (marked S). To validate these instability regions the time response corresponding to the three points A, B and C which lie in the stable, unstable and stable regions respectively have been plotted as shown in (a) and (c) show that the response corresponding to the point A and C are stable and that corresponding to point B is unstable as the response increases with time. It may be noted that the response amplitude and settling time corresponding to point C is found to be more than that of the point A. Further in (a) the time response corresponding to configuration CIII is also plotted which shows the response amplitude and settling time for configuration CIII is less than that of CI. Hence in this way by properly locating the MRE patch one may passively reduce the vibration of the system.The effect of magnetic field B0 and static load factor α on the first principal instability regions for different configurations of a sandwich beam for the simply supported end condition have been determined and are shown in . Considering the instability boundary line of configuration CI ((a)), it can be observed that with decrease in dynamic load factor β the unstable region decreases and the system can operate for a wide frequency range for lower value of β. Further, there exists a critical value of β (βcr) below which the system has stable region and hence can operate at any frequency without vibration. shows the variation of instability regions for different configurations, CI, CII, CIII and fully MRE cored sandwich beam with different values of magnetic field strength and static load factor. It is observed that for the same value of α and B0 while the fully MRE cored sandwich beam has the least instability region the instability region of configuration CIII is less than that of the configurations CII which is less than that of CI. It can be attributed to the fact that the instability region in the first case is least as the length of the MRE patch is more in this case. Also, though the total length of the MRE patch is same in configurations CI, CII and CIII, due to their relative location, in case of CIII the stiffness is higher in comparison to CII which is more than that of CI. Further one can actively increase the stiffness of the sandwich beam by applying magnetic field.For constant value of static load factor α, from (a) and (b) it is observed that with increase in magnetic field strength the instability regions decreases and moves upward. Hence in this case the system remains stable for a higher value of dynamic load factor β. This is because that the stiffness of the beam changes as the shear modulus of MRE increases with the application of magnetic field.(a) and (c) for same value of magnetic field with increase in static load factor α, it is observed that the stability of the system deteriorates as the width and βcr of the instability regions increases. One may get similar observation by comparing (b) and (d) which have been plotted for higher amplitude of magnetic field and static load factor.The critical values of dynamic load factor βcr for different configurations with different system parameters are presented in the . Considering the case α=0andB0=0.2T the value of βcr=0.375 for the configuration CI but for the same system parameter the value of βcr is 0.456 for the configuration CIII. So the configuration CIII of sandwich beam can be operated at a higher value of dynamic load for a wide range of frequency. Similarly considering the case α=0.6andB0=0.6T the value of βcr is 0.203 for the configuration CI but for the same system parameter the value of βcr is 0.246 for the configuration CIII. In case of configuration CIII the operating range of dynamic load decreases with increase in static load factor α. shows the influence of location of the MRE patch on the stability of the sandwich beam which has been obtained for four different configurations, LI, LII, LIII and LIV (). Also these results are compared with those obtained for the configuration CI and fully MRE cored sandwich beam. Comparing the (a) and (b), the instability regions decrease with increase in magnetic field for all the locations of the sandwich beam. From (c) and (d) one may observe that with increase in static load factor α, while the width of the instability regions increases the value of βcr decreases making the system more unstable. One may observe that due to symmetry the instability regions of simply supported end condition are same for location LI and LIV and also for LII and LIII. For the same system parameters the instability regions of locations LI and LIV are less than that of the locations LII and LIII. This is because that stiffness and damping capacity of the locations LI and LIV increase due to the location of MRE patches at the boundary edges of the simply supported sandwich beam as presented in The variation of critical dynamic load factors βcr for different locations with different system parameters are shown in the . Considering the case α=0andB0=0.2T the value of βcr=0.485 for the configurations LI and LIV but for the same system parameter the value of βcr is 0.444 for the l configurations LII and LIII. So for the configurations LI and LIV the system can be operated for a higher value of dynamic load for a wide range of frequency. Similarly considering the case α=0.6andB0=0.6T the value of βcr is 0.257 for the configurations LI and LIV but for the same system parameter the value of βcr is 0.224 for the configurations LII and LIII. In case of configurations LII and LIII the operating range of dynamic load decreases as compare to configurations LI and LIV with increase in static load factor α.In this paper, the stability of a sandwich beam with conductive skins has been investigated for the principal parametric resonance condition. Using finite element method the mathematical modeling of the MRE embedded sandwich beam has been carried out. The Guyana reduction method is used to present the equation of motion in terms of the nodal transverse displacement. The harmonic balance method is used to determine the instability regions of the sandwich beam for different system parameters. The comparison of the results obtained herein with those in the previous literatures indicated that the natural frequencies and loss factors can be predicted with considerable accuracy using the method presented.Analysis has been made for eight different configurations of the sandwich beam by varying the location and length of MRE patch. It has been observed that the stability of the sandwich beam can be changed by varying the length and position of the MRE patches in a viscoelastic core. Also for same length of MRE patch it can be altered by changing the location of the MRE patch. So the system stability can be achieved passively by changing the length and location of the MRE patches in the core and actively achieved by applying magnetic field of suitable amplitude. One may use this formulation for developing stiffness variable devices for vibration attenuation and for the sandwich structures with complicated geometry.[K1]=∫0leEtAt[dNutdx]T[dNutdx]dx[K2]=∫0leEbAb[dNubdx]T[dNubdx]dx[K3]=∫0le(EtIt+EbIb)[d2Nwdx2]T[d2Nwdx2]dx[K4]=∫0leGc⁎Ac[Hhc[dNwdx]+Nut−Nubhc]T[Hhc[dNwdx]+Nut−Nubhc]dx[K5]=(B02bhtμet)∫0le[dNutdx]T[dNutdx]dx+(B02bhbμeb)∫0le[dNubdx]T[dNubdx]dx+(πB02bht2μ0)∫0le(1ln(1/(le−x)))[dNutdx]T[dNwdx]dx+(πB02bhb2μ0)∫0le(1ln(1/(le−x)))[dNubdx]T[dNwdx]dx−(B02b(ht2+hb2)2πμ0)∫0leln(1le−x)[d2Nwdx2]T[dNwdx]dx+(B02b(ht+hb)μ0)∫0le[dNwdx]T[dNwdx]dx−(B02b12(ht3μet+hb3μeb))∫0le[d3Nwdx3]T[dNwdx]dxEffect of CFRP properties, on the bond characteristics between steel and CFRP laminate under quasi-static loadingCarbon fibre reinforced polymers (CFRPs) have been widely used in the last few decades. The bond between steel members and CFRP is the main issue in rehabilitation. Rehabilitation is considered when structures have cracks or damage. The CFRP section that needs to be used in rehabilitation depends on the damage amount or crack thickness. This paper reports the experimental and numerical effects of CFRP properties and sections on the bond between CFRP laminate and steel members under quasi-static loading. Three CFRP moduli (low CFRP modulus, normal CFRP modulus and ultra-high CFRP modulus) and two CFRP sections (20 × 1.4 mm and 10 × 1.4 mm) were used in this research. The results show that small CFRP sections are very sensitive to evaluate the bond properties between CFRP and steel, and the ultra-high CFRP modulus with low tensile strength has significant effects on the bond between CFRP and steel.The use of carbon fibre reinforced polymers (CFRPs) in structural strengthening has grown in the last few decades. CFRP is attractive to structural engineers due to its unique properties, including its high strength compared to its light weight, good resistance to corrosion, ease of installation and its ability to adhere to different structural sections. Different types of CFRP are available sheets, laminates, rods etc.); all these types can be used in the strengthening of concrete and metallic structures in different applications. A number of researchers have studied the bond characteristics between CFRP and concrete members under static and dynamic loadings As many steel structures have deteriorated due to ageing, changes in their use, and environmental corrosion, they need to be strengthened to resist the new loads to which they are subjected. Static tensile loading is one of the applied loads on structures such as steel bridges and buildings. The main issue for CFRP strengthening is the bond; the use of an appropriate type of adhesive results in good bond enhancement. In this paper the bond characteristics between CFRP laminate and steel members under quasi-static loading are investigated experimentally in a series of double-strap specimens. Low, normal and ultra-high moduli of CFRP (CFK150/2000, 200/2000 and MBrace laminate 450/1500, respectively) were used in this testing program. Two CFRP sections were used (20 × 1.4 mm and 10 × 1.4 mm) to investigate the effect of CFRP section size on the bond properties. Araldite 420 epoxy was used to bond the CFRP to the steel members. The outcomes were focussed on the maximum failure strength, strain distribution along the bond length, failure mode and the effective bond length.The materials used in this experiment were mild steel, Araldite 420 epoxy, low modulus CFRP CFK 150/2000 laminate, normal modulus CFRP CFK 200/2000 laminate and ultra-high CFRP modulus MBrace laminate 450/1500. As mentioned in previous research, the actual properties of these materials are a little different from those claimed by the manufacturer In this study, low modulus CFRP laminate specimens were prepared according to ASTM 3039-08 In this research, three types of CFRP were used to study the joint behaviour. Specimens of normal CFRP modulus were prepared according to ASTM 3039-08 to find their tensile mechanical properties, these mechanical properties are necessary for use in finite element simulations and to compare the results with those reported by the manufacturers. The ultimate tensile strength, ultimate strain and elastic modulus were: 2861 MPa, 1.4% and 203.0 GPa, respectively.Ultra-high modulus CFRP laminate was used in the double strap joint specimens to have a good understanding of the effect of various CFRP moduli on the bond properties between CFRP and steel in the double strap joints. MBrace laminate 450/1500 with thickness of 1.2 mm was used in this research, the actual modulus of elasticity and tensile strength was close to the manufacturer ones. The modulus of elasticity, ultimate strain and tensile strength were 457.8 GPa, 0.35% and 1602 MPa respectively, whereas the manufacturer properties are 450.0 GPa and 1500 MPa, respectively.Araldite 420 epoxy is a two-part epoxy, its curing time is 7 days under 25 °C. The ultimate tensile strength, ultimate strain and modulus of elasticity are 32.0 MPa, 4% and 1900 MPa respectively, as claimed by manufacturer technical sheet.As this research focuses on the bond properties between steel and CFRP laminate, mild steel plates with grade A36 were used to form the double strap joint. The mechanical properties were tested in this study under quasi-static loading, as it was necessary to find the actual yield and ultimate stresses to be used in simulation using finite element analysis. The measured yield and ultimate stresses were 361.0 and 525.0 MPa, respectively.This project studies the effect of quasi-static loading on the bond between steel and CFRP laminate. Three types of CFRP modulus were used in this testing program. Two different CFRP sections were used to study the effect of specimen size on the bond properties. Mild steel of grade A36, Araldite 420 adhesive, low CFRP modulus, normal CFRP modulus and ultra-high CFRP modulus were used to configure the CFRP/steel double-strap joint. The joint was manufactured by gluing two steel plates on their cross sections using Araldite 420 epoxy, and the two steel members were aligned during bonding to avoid eccentricity when loading (see ). They were then cured for 24 h to obtain the adhesive set.After adhesive setting, the steel surface was sandblasted along the bond area to remove dust, paint, oil and any other suspended materials on the surfaces and to ensure good contact between the epoxy and steel along the bond area. The sandblasted surface was then cleaned with acetone before adhesive application to provide a chemically active surface. According to the manufacturer’s requirements, the adhesive layer was added after the steel surface was fully dry. As Araldite 420 has two parts, the mixing percentages and procedure were carried out according to the manufacturer’s specifications. CFRP laminates were cut into the required lengths and wiped with alcohol to ensure they were free from any dust. CFRP laminates were then attached to the sandblasted steel surface using the Araldite 420 epoxy. The adhesive was uniformly applied on the bond area with an approximately triangular cross-section to help the epoxy to be distributed uniformly along the bond area.Finally, CFRP laminates were attached on the joints immediately after adding the adhesive layer to ensure that the resin was still workable. Uniform squeezing was applied when attaching the CFRP laminate to expel the air bubbles, using a steel plate supported by two washers at the ends to create a uniform adhesive thickness along the bond length. The specimens were then cured for 24 h prior to preparing the other sides of the joints to ensure no slippage or damage occurred. The same preparation procedure was used for the other side of the specimens. The bond length from one side of the joint (L1) was smaller than (L2) to ensure that the failure occurred in the shorter side (L1). The specimens were cured for more than 7 days according to the manufacturer’s recommendation for the adhesive.In this study, three CFRP types (low, normal and ultra-high CFRP modulus) and two CFRP sections (10 × 1.4 mm and 20 × 1.4 mm) were used to study their effect on the ultimate joint capacity, strain distribution along the bond and failure mode under quasi-static loading. A schematic of a double-strap specimen is shown in In this research, an MTS testing machine (see ) with a maximum capacity of 250 kN in tension with hydraulic grips was used to test the double-strap joint specimens under static tensile loads, with a loading rate of 2 mm/min.As mentioned earlier, three types of specimens were used in this static testing, with different CFRP cross-sectional areas and different moduli of elasticity. Low, normal and ultra-high moduli CFRP were used in this test to find the effect of CFRP’s elastic modulus on the bond between steel and CFRP laminate. The two different CFRP cross-sections (20 × 1.4 mm and 10 × 1.4 mm) were used to find the effect of their size on the ultimate strength of the joint. A total of 165 specimens with CFRP/steel double-strap joints using Araldite 420 epoxy were tested to determine the ultimate load-carrying capacity, the effective bond length (the bond length beyond which the load stays constant) and failure modes with the above different parameters. These 165 specimens included 66 specimens with low CFRP modulus and cross-sectional areas of 10 × 1.4 mm, 33 specimens with low CFRP modulus and cross-sectional areas of 20 × 1.4 mm, 33 specimens with normal CFRP modulus and cross-sectional area of 20 × 1.4 mm and 33 specimens with ultra-high CFRP modulus and CFRP cross sectional areas of 20 × 1.2 mm. As one of the findings is the strain distribution along the bond, two methods of capturing strain were used; the conventional foil strain gauge technique and the 3-D correlated solution camera. The foil strain gauges were mounted on the top of CFRP surface and the centre of each joint on one side and connected to a data acquisition system, and the photogrammetry camera captured the strain along the bond area of the other side of the specimens. The correlated solution camera system has high strain resolution 0.005% (50 microstrain), strain measurement of 1000% or higher.All specimens were painted with white paint along the bond area, and then each specimen was painted with black dots using a fine marker, as recommended in the 3-D correlated camera manual. Each dot on the specimen represents one foil strain gauge; the camera captured the strain that developed on the double strap joint during the loading. A number of images were taken using the same 3-D correlated camera with high resolution to monitor the propagation of failure, as shown in Three different series were carried out in this testing program; the differences in these series are related to CFRP modulus and cross-sectional area. All specimens were tested under tensile quasi-static loading with a load rate of 2 mm/min. summarises the specifications of the three scenarios of this testing program. The adhesive thickness was constant for all specimens; all specimens were tested in the same environment and had the same curing time, and an MTS machine with a capacity of 250 kN in tension was used for testing all specimens.The adhesive layer was calculated using the following formula:The total specimen thickness was measured using a digital vernier. The thickness was measured at three different points on specimens, and the average of these three readings was considered to be the total joint thickness. By knowing the thickness of the whole specimen, the CFRP laminate and the steel plate, the thickness of the adhesive can be calculated from the above equation.In this research program, three-dimensional modelling was used to simulate the CFRP–steel double-strap joint specimens loaded under quasi-static loading using ABAQUS software 6.13. However, three-dimensional modelling has some disadvantages, For example, a powerful computer is required and the process is time-consuming. However, but it gives more accurate results than two-dimensional modelling. A desktop computer was provided to run the simulation of the specimens (3.20 GHz 4 CPUs processor, 12.0 GB RAM and hard drive capacity of 1 TB), and the small-size scale of the specimens eliminates the disadvantage of the time required. Moreover, the choice of 3-D modelling in this research was necessary to enable good comparisons between the actual testing and FE analysis by obtaining accurate results in terms of failure modes and strain distribution from the FE simulation. The three-dimensional models were simulated using non-linear finite element analysis using ABAQUS implicit code to investigate the effect of CFRP properties on the strain distribution, ultimate joint strength and failure criteria of the CFRP laminate-steel double-strap joints.As the double-strap joint specimens are symmetric in the X, Y and Z axes, this feature has advantages in using FE analysis; only one eighth of the double-strap specimens was simulated by applying symmetric boundary conditions to all nodes corresponding to YZ, XZ and XY Cartesian planes, as shown in The figure above shows the geometry and boundary conditions that applied in FE modelling. To perform the experimental test accurately in the FE analysis and to make FE models match real specimens, a displacement boundary condition was applied at the end of the steel plate model in X-direction to perform the same displacement mode in the actual experimental test. As is known, in this type of joint, the load transfers from steel to CFRP via the adhesive layer, and for this reason a finer mesh was applied to the adhesive layer compared to the steel and CFRP layers in order to study the failure mode of this joint. After meshing all layers of the model, pure master–slave contact was applied to the adhesive layer with steel and CFRP, the adhesive layer being used as the slave surface and the two other adjacent surfaces being used as the master surface due to the fact that the adhesive layer is a soft material compared to the other two. The same adhesive thickness was modelled as measured from the actual specimens.ABAQUS 6.13 has a large range of element types. The CFRP–steel double strap joints consist of three different layers: steel, adhesive and CFRP laminate. Each layer was modelled using the appropriate element, the steel plate by 8-node linear brick, reduced integration, hourglass control (C3D8R) and it was modelled as elastic–plastic material to obtain accurate results for the adhesively-bonded joints, as reported by The material properties used in FE modelling are described in details in , the tensile properties of steel, adhesive and CFRP are included in these tables which were used in defining the material properties in all models.In this research, three sets of results were obtained from the three different series of CFRP–steel double-strap joint specimens tested under tensile quasi-static loading: ultimate joint capacity, strain distribution along the bond length, and failure mode. These findings were found with different parameters.The ultimate joint capacities for both the experimental tests and the analytical models of CFRP–steel double-strap joints are summarised in .The same parameters used in the experimental tests were used in the finite element analysis with quasi-static loading (2 mm/min) and various bond lengths starting from 30 to 130 mm for all series, show the comparisons between the experimental tests and the analytical models for all different parameters. show the ratio of (PFEPEX) has an average start value of 0.77 for the first two bond lengths, then it starts to increase and ranges between 0.85 and 0.94 for the remaining bond lengths. This range of the ultimate joint capacity ratio is considered to be acceptable. As shown in , for specimens with low CFRP modulus and 10 mm CFRP section, there is inconsistency in the maximum joint strength for each bond length. In the previous series, in which CFRP laminate had a cross-sectional area of 20 × 1.4 mm, the joint capacity increased with the increment of the bond length, but in this series the values of the joint capacity fluctuated with the increment of the bond length (L1). The larger bond lengths cause higher degrees of fluctuation. The joints with small sections are assumed to have more accurate results when there is a perfect bond, but practically it is hard to achieve the 100% perfect bond as it needs special and precise instruments for CFRP applications. Applying larger cross section of CFRP to the joint would decrease the percentage of error.The authors attribute this variation in load to the adhesive sensitivity; this sensitivity is due to:The small width of the CFRP laminate (10 mm), which can cause eccentricity in testing due to any slight movement of the laminate before the adhesive set.The larger bond length causes higher sensitivity as the chance of CFRP and adhesive movement is higher.The impact of CFRP properties on the effective bond length of the CFRP–steel double-strap joint specimens was investigated numerically and experimentally, and then compared with other test results from other researchers. show a comparison between the experimental investigation and the numerical modelling results for the three types of CFRP modulus. It is evident that changing from low modulus to normal modulus CFRP has no effect on the effective bond length; the effective bond length is 110 mm as obtained from the experimental investigation, which is comparable to the finite element analysis results. The current low CFRP–steel double strap joints’ results were compared with those of Xia and Teng 2005 . The average bond strength and effective bond length values for specimens with normal CFRP modulus were close to those for specimens with low CFRP modulus, shows the ultimate bond force versus bond length for specimens with normal CFRP modulus. However for specimens with ultra-high CFRP modulus, the effective bond length was found to be 70 mm (see ). This significant change is mainly due to the lower tensile strength of the ultra-high modulus CFRP laminate compared to the low and normal CFRP moduli. The finite element analysis for models with ultra-high CFRP modulus showed very close results that agreed very well with the experimental ones. The same effective bond length value for both experimental and analytical tests means that finite element models are modelled reasonably well.For joints with small size CFRP laminate, as shown in , it was hard to obtain the effective bond length for this type of joints as the small size of CFRP had negative effects on the results, which showed some fluctuation in the maximum joint capacity for the same bond length. This fluctuation increased with the increment of the bond length. The reason for this fluctuation in results is that joint resistance, which mainly depends on the bond between CFRP and steel, was affected by the adhesive size. No effective bond length result for this series was observed, as the results of maximum joint capacity were not reliable.Based on the two methods of capturing strain, which were the correlated solution camera (VIC3D) and foil strain gauges, which were used to capture the strain along the bond length, the results of these two methods are compared and plotted in . The figure shows that the strain gauge reading of maximum strain at a joint is very close to that captured by the correlated solution camera; therefore, all ultimate and distributed strain readings have been taken from the correlated solution camera, as it gives the strain at different locations along the CFRP laminate within the double-strap joint specimen.In the case of strain distribution along the bond length between low CFRP modulus and steel plate, the results show that maximum strain occurs at the joint, and then it decreases linearly away from the joint. The strain values at the far end of the joint and for all load levels are close to each other, as shown in . The same curve trend was obtained from specimens with normal CFRP modulus, but with a little difference in strain values, as shown in . However, significant effect on the strain distribution was shown for specimens with ultra-high CFRP modulus, shows the strain distribution along the bond length of ultra-high CFRP modulus. The ultimate strain at the joint shows significant decrease comparing to the specimens with low and normal CFRP modulus. The reason of obtaining less strain values in specimens with ultra-high modulus is due to high modulus of elasticity which is 450 GPa as the ultimate strain is very low comparing to the other two types of CFRP. A comparison of ultimate joint capacity against ultimate strain for the two types of CFRP modulus within the CFRP–steel double-strap specimens is shown in One of the most important outcomes in the current test program is the failure pattern of the CFRP–steel double-strap specimens, which gives more understanding of load transfer and the material that resists more in the composite joint. In 2007, Zhao and Zhang summarised six expected failure modes for adhesively-bonded joints between steel and CFRP. These six failure modes are shown in The six failure modes in the figure above can be defined as follows: (a) steel and the cohesive layer interface failure, (b) cohesive layer failure, (c) FRP and adhesive debonding failure, (d) CFRP delamination, (e) CFRP rupture and (f) steel yielding failure. Depending on these proposed failure modes, there are some differences in failure mechanism in the four different series. For the current test program, the failure modes were different for the four series as the CFRP properties were different. For Series one, which had low CFRP modulus and 20 mm CFRP width, the failure mode was found to be mixed between steel–adhesive debonding (a) and adhesive layer failure (b) for bond lengths less than the effective bond length, as shown in . The failure mode is different when the bond length reaches close to the effective bond length and becomes completely steel–adhesive debonding, as shown in . This changing in failure mode when the bond length is close to the effective bond length or beyond gives an indication of the range of effective bond length, which is another way to prove the effective bond length in addition to the maximum failure capacity. The outcomes from finite element analysis were shown to be very close to the experimental results, and de-bonding failure was very clear. However, adhesive failure was not shown clearly, as adhesive failure occurs at a certain distance from the joint.The failure mode in Series two which had 10 mm width of CFRP and low CFRP modulus was FRP delamination (d) for all bond lengths, as shown in For specimens in Series three with normal CFRP modulus and 20 mm CFRP width the failure mode for all bond lengths was debonding between steel and adhesive (failure mode a). The failure modes of this series of tests are shown in For specimens with ultra-high CFRP modulus, the failure modes were completely different from the other joints (series 1, 2 and 3). The failure mode for the last series (ultra-high CFRP–steel double strap joints) was shown to be FRP delamination (failure a) for specimens with bond length below the effective bond length and FRP rupture (failure e) for specimens beyond the effective bond length. show the failure modes of this type of joins.Very close failure patterns were observed from finite element analysis for all types of joints with different CFRPs (low, normal and ultra-high CFRP modulus) and 20 mm CFRP width, whereas steel–adhesive debonding failure was numerically observed for models with low CFRP modulus and 10 mm CFRP width, which is CFRP delamination in the experimental tests. show the failure patterns for all types of joint in FE analysis.In order to study the impact of failure mode on the bond stress of the specimens along the bond line, the current results of normal CFRP specimens were compared with those of Al-Zubaidy, Zhao et al. 2011 shows the average bond stress versus bond length for their test and the current one. Evidently, the laminates of the current tests have higher bond strength for the same bond lengths. This is attributed to the type of failure modes observed in the two systems. Joints with CFRP laminates exhibited steel–adhesive debonding, while the failure mode observed in the joints bonded by CFRP sheets was delamination within the CFRP sheet.This paper presents the effect of CFRP properties (section size and elastic modulus) on the bond characteristics between CFRP and steel plates in double-strap joints under quasi-static loading. Comprehensive experimental testing was carried out in this program by testing 165 CFRP–steel double-strap specimens with low, normal and ultra-high CFRP modulus and two CFRP sections (20 × 1.4 mm and 10 × 1.4 mm). The results were compared with numerical analysis. The following conclusions can be drawn:Using small size CFRP laminate with a width of 10 mm does not give accurate results as the adhesive size is small and its capacity to resist the load is very sensitive to any movement.For 20 mm CFRP width, changing from low to normal CFRP modulus has no effect on the effective bond length, which is found to be 110 mm for both types of CFRP in the double-strap joint specimens, whereas significant change in the effective bond length for specimens with ultra-high CFRP modulus was observed, the value of effective bond length for the specimens with ultra-high CFRP modulus is 70 mm.CFRP width has influence on the effective bond length, for specimens with low CFRP modulus and 20 mm CFRP width the effective bond length was 110 mm whereas it was found to be 135 mm for specimens with low CFRP modulus and 50 mm CFRP width. For specimens with ultra-high CFRP modulus and 20 mm CFRP width, the effective bond length was 70 mm whereas it was found to be 110 mm for 50 mm bond width.Changing from low to normal CFRP modulus has insignificant effects on the maximum failure strain and strain distribution, and lower strain values were observed for specimens with normal CFRP modulus compared to those with low CFRP modulus. However significant decrease was observed in the ultimate strain and strain distribution along the bond length for specimens with ultra-high CFRP modulus, this decrement is due to the modulus of elasticity of CFRP which is 450 GPa.Little increment in the maximum joint capacity was found when using normal CFRP modulus in the double-strap joint specimens compared to the low CFRP modulus specimens. However significant decrease was observed in the maximum failure capacity for specimens with ultra-high CFRP modulus, this was due to the low CFRP tensile strength which is 1500 MPa and thickness of 1.2 mm.Failure modes for both specimens with low and normal CFRP moduli were quite similar; the failure mode was debonding between steel and adhesive, in addition to some adhesive failure which occurs for both types of specimens. Whereas different failure mode was observed for specimens with ultra-high CFRP modulus, FRP delamination for specimens with bond length below the effective bond length, and FRP rupture for specimens with bond length equal and beyond the effective bond length.The CFRP modulus has major effect on the strain distribution along the joint, while the CFRP tensile strength has the major effect on joint capacity.The numerical analysis results are close to those from the experimental test program which confirms that the specimens were modelled reasonably well.Finally, all those findings are limited to the current ranges and types of parameters/materials. These findings may not be valid in case of different types of loading or materials.Mobility and solubility of antioxidants and oxygen in glassy polymers II. Influence of physical ageing on antioxidant and oxygen mobilityThe mobility of small molecules in a glassy polymer is largely determined by the amount of free volume present in the material. The amount of free volume can be altered by changing the physical state of the polymer. Physical ageing reduces this amount, whereas the thermal rejuvenation increases it. The change in free volume was monitored by oxygen permeation and antioxidant sorption experiments. A clear correlation was found between the physical ageing on the one hand and oxygen permeability on the other. Since the mobility of antioxidants and oxygen are important parameters for the stabilisation of a polymer against oxidation, the physical state of the polymer can have a significant influence on the service life of the product.The efficiency of the stabilisation of a polymer product by antioxidants against oxidation depends on the consumption and loss (evaporation) of the antioxidants from the material. Experimental work showed a direct relationship between the physical parameters, solubility and mobility of the antioxidant, and the service life of a polymer product. Furthermore, the service life of a polymer product is affected by the concentration and transport of oxygen in the polymer. This means that polymers that are highly permeable to oxygen can show a lower stability against oxidation. The permeability of oxygen is determined by its solubility and mobility in the polymer. The solubility is determined by the chemical composition, whereas the mobility by the morphology of the polymer. The later is demonstrated by a similar solubility of oxygen in liquid hydrocarbons and polyolefins, but a significant lower mobility in polyolefins than in liquid hydrocarbons Generally at moderate temperatures, the permeability of oxygen is sufficient to reach almost the equilibrium solubility over the whole thickness Thermo- and photo-oxidation can be suppressed by the use of appropriate antioxidants. The efficiency of suppressing chemical degradation reactions depends on certain physical properties of the antioxidant molecules. In order to obtain a good efficiency of the stabiliser against oxidation in the polymer, antioxidant molecules must be able to inactivate the radicals and/or decompose the hydroperoxide groups as soon as they are formed. The availability of the antioxidants at the oxidation site is determined by the solubility and mobility of the antioxidant in the polymer, and the availability of oxygen by its permeability in the polymer.For polyolefins, an empirical relation was found between the protection time (τ), the diffusion coefficient (D) and the solubility (S) of antioxidants according to: τ∼f(S2/D). It was found that a very high mobility of the antioxidant does not guarantee a high stabilisation efficiency From the research on the efficiency of antioxidants it becomes clear that the mobility and solubility of the antioxidant are very important parameters in polymer stabilisation, as well as the permeability of oxygen in the polymer. The magnitude of these parameters is governed by the polymer–antioxidant and polymer–oxygen interactions. The physical state of the polymer has an influence on the mobility and solubility of the antioxidant and/or oxygen. This physical state can be changed by, for example, ageing, rejuvenation, deformation, orientation and stress. Most of these phenomena change the free volume in the polymer, which is responsible for changes in diffusion and possibly in solubility. Ito et al. A study on the influence of ageing and rejuvenation on the mobility of an antioxidant and the permeability of oxygen is presented in this paper. In a forthcoming paper, the influence of deformation, orientation and stress will be discussed.The free volume present in an amorphous polymer is a very significant parameter determining the mobility of any additives present in the polymer. The diffusion coefficient of an additive can be correlated to the free volume by a model developed by Vrentas et al. The free volume in a polymer can be changed by several pretreatments, such as physical ageing, orientation, rejuvenation and the application of a tensile stress. In this paper, changes in free volume due to ageing and rejuvenation will be modelled and incorporated in the model describing the diffusion coefficient. In this way, the significance will be elucidated of the physical state of the polymer in relation to the mobility of a stabiliser and oxygen.The diffusion transport of small molecules in amorphous polymers is related to the frozen in “free volume” D0 is a pre-exponential factor, E the critical energy that a molecule must possess to overcome the attractive force holding it to its neighbours, R the universal gas constant and T the temperature. γ Is an overlap factor that is introduced because the same free volume is available to more than one molecule (this parameter should be between half and one). 2* are the specific critical hole-free volume of the additive and the polymer segment required for a diffusion jump. FH is the free volume in the polymer. ξ is the ratio of molar volume of the jumping unit of the additive to that of the polymer (=2*M2j). M1j andM2j are the molecular weight of the jumping unit of the additive and polymer respectively. For higher concentrations of additives in glassy polymers, the mutual diffusion coefficient, Dm1, can be calculated using the following equation M1 is the molecular weight of the additive, φ1 the volume fraction additive A a constant derived from and χ the polymer solvent interaction parameter. The second term on the right hand side incorporates the Flory–Huggins theory for rubbery systems and the first term on the right hand side is a modification for the diffusion behaviour in glassy polymers.The glass transition temperature for an additive–polymer mixture, Tgm, can be calculated by an expression derived by Couchman and Karasz Tg1 and Tg2 are the glass transition temperatures (K), w1 and w2 the weight fractions, and ΔCp1 and ΔCp2 the change in heat capacity (J/g/K) at Tg1, and Tg2 of the additive and polymer, respectively.FH1 is the free volume of the additive and FH2 the free volume of the polymer. The latter depends on the physical state of the polymer: glassy or rubbery. The free volumes can be calculated by the following equations:K11, K21, K12, K22 and K12g are the free volume parameter of the additive (K11, K21), liquid polymer (K12, K22) and glassy polymer (K12g). The values of the free volume parameters of the additive can be derived from viscosity measurements When a polymer is cooled from the melt to temperatures below the glass transition temperature, the molecular mobility decreases and the polymer becomes a glass. In the glassy state, thermodynamic equilibrium has not been reached and parameters like specific volume continue to decrease. This volume reduction in time is called physical ageing. The decrease in volume of the polymer glass can be attributed to a decrease in free volume in the polymer Some authors made a distinction between the physical ageing and annealing of a polymer sample. For example, Bauwens The change in free volume is best measured using positron annihilation. Two free volume parameters can be obtained from positron annihilation measurements. The first is the lifetime (τ3) of the ortho-positronium, which is a measure for the average hole size in the polymer. The second is the intensity (I3) and is directly coupled to the concentration of free volume voids in the sample. It was found that physical ageing of polycarbonate changes the amount of voids significantly, but the lifetime, τ3, remained practically the same and thus the sizes of the free volume holes does not change much The reduction in free volume upon physical ageing or annealing is very difficult to predict, since it depends, for example, on the type of polymer, ageing temperature and thermodynamic state of the starting material. Chan et al. FH2e is the free volume of the polymer at equilibrium, FH2o that at time zero after rejuvenation, τ the relaxation time of ageing in the polymer and β accounts for a distribution in relaxation times. At lower temperatures the difference in free volume at equilibrium and time zero is larger than at higher temperatures. However, the relaxation time is also longer, resulting in a slower decrease in the free volume.The effect of physical ageing in a polymer can be reduced by rejuvenating the sample. For thermal rejuvenation this means that the polymer is heated above its glass transition and quenched afterwards. Positron annihilation experiments showed that the free volume increases when a polymer is heated above its Tg. After quenching, the excess free volume is frozen in. The cooling rate determines the amount of excess free volume that will remain in the polymer.The direct measurement of the free volume, a crucial parameter in the ageing process, is probably the most attractive technique to study ageing The probability of o-Ps formation is called the intensity o-Ps, Io-Ps, and is proportional to the number of cavities in the system. In this manner, the total free volume fraction (Ff (%)) can be evaluated from the following equation:in which C is an empirical constant (0.0018 Å−3 for polycarbonate ρ Is the density of the polymer. It has to be remarked that Io-Ps can be affected by effect of prolonged positron irradiation. In the past, several studies concerning aging of PC and other amorphous polymers through PALS have been presented (Petrick Six polymer materials were used for the experiments on antioxidant sorption and oxygen permeability. A selection of these polymers were physically aged, annealed or thermally rejuvenated and the change in sorption behaviour was determined.Additive free polycarbonate (Lexan 105) was received from General Electric Plastics. 20 wt.% solutions were made by dissolving the appropriate amount in methylene chloride (Fluka). After 2 h stirring at room temperature a homogeneous solution was obtained. This solution was cast on a glass plate and after evaporation of the solvent polycarbonate films were obtained, having thicknesses between 55 and 65 μm. The films were dried at room temperature for at least 2 days, before further experiments were conducted (=PC–G).Polycarbonate K1 film was produced by Kodak Eastman Chemicals. The 25 μm film was kept at room temperature for 31 years (PC–K).Polystyrene (N5000) was supplied by Shell. A film was cast from a 20 wt.% solution in methylene chloride. After drying at room temperature the resulting film thickness ranged between 35 and 45 μm (PS–S).A Window film 6003 produced by DOW (25 μm) was kept at room temperature for 16 years (PS–D).An additive free PMMA sample was supplied by Röhm and Haas. A film was cast from a 20 wt.% solution in methylene chloride. After drying at room temperature the resulting film thickness ranged between 35 and 45 μm (PMMA).Polysulphone film (25 μm), obtained from Union Carbide was kept at room temperature for 33 years (PSU).LDPE film (36 μm), obtained from ESSO was kept at room temperature for 30 years (LDPE).The poly (ester–ether) block copolymer was received as a 25 μm film from DSM. The polyester phase is PBT (65%) and the polyether phase is polytetrahydrofuran (35%) (PebE).Unfortunately, the exact composition of the old samples (PC–K, PS–D, PSU and LDPE) is not known. Especially, the amount of stabiliser for the protection of the polymers against degradation will have changed in time and it is not inconceivable that some degradation has taken place. However, these aged polymers will only be used to obtain information about the difference in the amount of free volume of the aged material and after rejuvenation. So, if it is assumed that the chemical composition does not change upon rejuvenation, the small amount of chemical degradation that may have taken place in the previous 30 years will not influence the outcome of the experiments.Physical ageing was accomplished by keeping the polymer at ambient conditions for a period of time. The polymers PC–K, PS–D, PSU and LDPE are already physically aged for a number of years. The polymers PC–G, PS–S and PMMA were physically aged after casting the polymer from a solution.Annealing of polycarbonate was done at 110 °C in an oven for periods up to 150 days. Annealing of PMMA was done at 80 °C. Oxygen availability during annealing has been reduced by placing the films between two polyimide layers and wrapping this package in aluminium foil.Cast and/or aged samples were thermally rejuvenated. Thermal rejuvenation was performed by heating the polymer above the glass transition temperature for 2 h. This means 180 °C for polycarbonate; 130 °C for polystyrene and 220 °C for polysulphone. For polyethylene, the glass transition temperature is below storage temperature. This means that the free volume in this polymer is in equilibrium and will not change upon rejuvenation. In order to verify this, the film was heated to 120 °C and quenched afterwards.PC from General Electric (Lexan 161) was used for all the experiments (PC–G2). The polymer was first dried at about 120 °C under vacuum and compression moulded to obtain sheets of 4 mm thickness. Specimens of about 1 mm2 area were obtained from the sheet. Before starting ageing experiment, PC samples were thermally rejuvenated at about 170 °C and cooled down in ice. A convenient number of samples was subjected to ageing at two different temperatures: 25 and 128 °C; and were used for PALS experiments at different ageing times.PALS measurements were performed on all the above mentioned samples, by exposing them to the radioactive isotope 22NaCl with an activity of 6 μCi. A fast–fast coincidence circuit PALS spectrometer with a lifetime resolution of 240 ps as monitored by using 60Co source was used to record all PALS spectra. The counting rate was about 70 cps. Each spectrum was collected to a fixed total count of 2 × 106, high enough to get a good analysis but low enough to avoid any substantial radiation effects. The spectrum is analysed using POSITRONFIT, which describes the spectrum as a convolution of the instrument resolution function and a finite number of negative exponential plus the background as shown by where R(t) is the resolution function of the system, λl is the inverse of the annihilation time (annihilation rate), and B is the background. All spectra were resolved in three lifetime components: a short one related to p-Ps annihilation, an intermediate one related to free positron annihilation, and a long one component related to o-Ps annihilation.The oxygen permeability was measured at room temperature using the setup depicted in . An oxygen pressure of 8 bar was applied to one side of the polymer film. The increase in pressure at the other side of the polymer film is monitored in time as can be seen in . From the slope of the pressure evolution in time (Δp/Δt) the permeability can be calculated, according to P=C d Δp/Δt. C is a constant in which the dimensions of the apparatus and oxygen pressure are accounted for, and d is the thickness of the polymer film. The permeability, P, is expressed in cm3 mm atm−1 day−1 m−2. The time tL in is the time lag, which can be used to estimate the diffusion coefficient. This time lag can be obtained from ordinary diffusion equations The sorption of the small antioxidant butylated hydroxy toluene (BHT, Sigma) was measured in several pretreated polymer films. A 20 vol.% solution was made of the antioxidant in decane. The solutions were placed in an oven at 80 °C. Small polymer films were placed in the antioxidant solution. After certain times, a sample was removed from the solution and rinsed twice with iso-octane and once with ethanol. After drying, the total amount of antioxidant that diffused into the sample at was measured using UV spectroscopy as was described in the previous paper The sorption of the antioxidants into the polymer film is modelled by simple Fickian diffusion. The total amount of antioxidant in the polymer films at time t (Mt) was measured. This can be described by the following diffusion equationM∞ is the total amount of antioxidant in the film at equilibrium and d the thickness of the film. For the initial part of the diffusion process (Mt/M∞ <0.6) this equation can be rewritten into:so, when plotting the total amount absorbed by the film versus the square root of the time, a straight line should be obtained for small times. Its slope can be recalculated into the diffusion coefficient, when the thickness and equilibrium solubility is known. A list of all experiments performed is given in In order to evaluate the physical state of the polymer, stress–strain curves are obtained. Using a home built (TNO) tensile tester, a small film is strained at 1 mm/min at 23 °C and the force is monitored. From these measurements the Young's modulus and stress–strain behaviour of the polymers were determined.For modelling the diffusion coefficients of antioxidants and oxygen a number of parameters are needed. Most of the parameters for polycarbonate are given in the previous paper . Parameters for other polymers studied in this paper are also listed in this table. The values for the free volume of unaged material at room temperature,FH20(RT), were obtained from positron annihilation measurements found in the literature. The molar masses of the jumping units are also found in the literature, except for PSU. This value is assumed equal to that of polycarbonate, because it contains the same bis-phenol group.The results of the oxygen permeability measurements on the various polymers are listed in . The influence of physical ageing, and thermal rejuvenation is clearly visible. The permeability is a function of the diffusion coefficient and the solubility of oxygen (P=D1S). When measuring the change in permeability after a certain physical treatment, this can be caused by a change in mobility or solubility of oxygen. Since the solubility depends on the chemical interactions between polymer and oxygen, it is not to be expected that this parameter changes when a polymer is aged. In order to verify this, the time lag as described in was measured for aged and rejuvenated polycarbonate samples. It was found that the solubility was a constant and independent of physical ageing and equal to 0.23±0.02 cm3/cm3/atm for PC–G and to 0.41±0.02 cm3/cm3/atm for PC–K. The difference in oxygen solubility between PC–G and PC–K is most likely caused by differences in composition due to the production process of the polymer, the molecular weight or the presence of additives.The sorption of butylated hydroxy toluene in polycarbonate for the aged and rejuvenated films is shown in . From this figure it is clear that annealing of a polycarbonate film hardly influences the sorption behaviour.The diffusion coefficients and the equilibrium concentration at infinite time (Ceq (mg/g)) derived from the BHT sorption experiments are listed in . Sorption experiments of BHT in polycarbonate show a small increment of the mobility with annealing time of the small molecules in polycarbonate, as can be seen in . The concentration of dissolved antioxidant at equilibrium is practically constant at 57±3 mg/g (). However, the changes upon annealing are very small and all fall within the error margins of the measured points, and a firm conclusion cannot be drawn. A decrease in permeability does not occur.An increase of the mobility of small molecules in polycarbonate upon annealing at 135 °C was found by Pekarski et al. , the influence of physical ageing on the oxygen permeability in polycarbonate, polystyrene, polymethylmethacrylate, polysulphone and polyethylene is clearly visible. Upon physical ageing of the cast films for more than 100 days, the oxygen permeability decreases slightly for polycarbonate, but significantly for polystyrene and even more for polymethylmethacrylate. The oxygen permeability of the physically aged commercial films of polycarbonate, polystyrene and polysulphone increases drastically when the films are thermally rejuvenated. However, the permeability of low density polyethylene does not change at all, even after 30 years of ageing. This is caused by the fact that the free volume is always in equilibrium and no volume recovery takes place. If a more intensive thermal treatment is applied, then recrystallisation may cause a change in the permeability.In the case of polycarbonate there was difference found between physical ageing at room temperature and annealing at 110 °C. In the decrease in oxygen permeability is shown upon ageing of the polycarbonate film. A significant decrease was found that is in agreement with the predictions concerning physical ageing. However, when the same film is annealed at a higher temperature (=110 °C), only a very small decrease can be seen. This small decrease in the permeability is visible in . The decreases in oxygen permeability due to ageing and annealing in . The solubility of oxygen in polycarbonate at a pressure of 8 atm is roughly 2 mg/ml Since the oxygen permeability measurements are performed at room temperature, the exp(−E/RT) term is incorporated in the prefactor, D01. The permeability, P, is obtained by multiplying the mobility and the solubility:In contrast to the strong dependence of the permeability of, for example, CO2 on the concentration or pressure in glassy polymers to the data points. The value of β was assumed to be 1. This means no distribution in relaxation times. The value for the free volume at the start of the experiment was calculated from the free volume parameters in FH2o=0.0583 ml/g). The equilibrium free volume, FH2e, was calculated from the fit and found to be 0.0524 ml/g for 23 °C and 0.0570 ml/g for 110 °C. This results in a decrease in free volume of 0.0059 ml/g for ageing at 23 °C and only 0.0013 ml/g for annealing at 110 °C. The relaxation time for ageing at room temperature, τ, was found to be 126 days (≈107 s). This is two orders of magnitude lower than the relaxation times found by Wimberger-Friedl et al. For the aged polymers the shift in free volume upon ageing can be calculated using the following equation under the assumption that the solubility hardly changes with ageing:Po is the permeability of the rejuvenated polymer and Pe that of the polymer at equilibrium. The value of γ is assumed to be equal to 1. In , the calculated values for the free volumes are listed for the polymers studied. From , it can be concluded that the change in free volume upon ageing is comparable for the polymers PC–K and PS. The free volume decrease of PC–G, PMMA and PSU is slightly higher. It is also clear from this table that the volume recovery of PS due to ageing for 110 days is equal to the volume recovery after 25 years of ageing. The decrease in free volume for PC after 400 days is larger than after 31 years. This can be explained by the difference in PC compound or additives present in the polymer. did already show that at 400 days an equilibrium oxygen permeability was almost reached. The change in free volume of LDPE after ageing is negligible, due to the absence of volume changes above the glass transition temperature.Some authors have also measured the free volume of aged PMMA The change in free volume due to physical ageing, can be obtained directly from the PALS measurements. In the free volume is given for a polycarbonate sample aged at 25 °C. The solid line is a fit of to the data points. The relaxation time was set on 126 days, which is similar to the relaxation time from the oxygen permeability measurements. The value for the free volume before ageing, FH2o was equal to 0.0594 ml/g, and the ultimate equilibrium free volume, FH2e, was found to be 0.0528 ml/g. The decrease in free volume upon ageing is comparable to the oxygen permeability results (0.0059 versus 0.0066). This means that an excellent correlation was found between the PALS data and the oxygen permeability experiments.) results in a significantly smaller reduction in free volume of 0.0012 ml/g (0.0595–0.0583), which has been reached already after ca. 20 days. This corresponds well with the change in free volume of 0.0013 ml/g as obtained from oxygen permeability measurements for annealing at 110 °C. Also the relaxation time of 10 days corresponds well with the relaxation time of 9 days found by oxygen permeability measurements. This small change in free volume is also corroborated by the positron annihilation measurements of Higuchi et al. The difference between annealing and ageing for polycarbonate can also be seen in the stress–strain curves of the pre-treated polymer as depicted in that there is a significant difference between the annealed and aged polycarbonate samples (curves 3 and 4). This difference was also found by Bauwens it is obvious that thermal rejuvenation also changes the stress–strain behaviour of a cast film. Rejuvenation decreases the Young's modulus of polycarbonate, and shows an onset of a yield point. As was shown in , the thermal rejuvenation does not have an influence on the oxygen permeability in a polycarbonate film. Furthermore, from it is clear that the mobility and solubility of the small antioxidant, BHT, also hardly changes upon thermal rejuvenation (=5.7×10−16 m2/s and 51 mg/g). This means that a cast film can be regarded as a rejuvenated film when mobility and solubility of small molecules is concerned.The service life of a polymer product depends on several parameters. Important are the presence of oxygen and antioxidants at the oxidation site. In the previous paper The mobility of small molecules in a glassy polymer is largely determined by the amount of free volume present in the material. In the previous paper Physical ageing at room temperature and annealing at temperatures just below Tg are different processes. The oxygen permeability in polycarbonate decreased significantly upon ageing, but only slightly when annealed at 110 °C. The stress–strain behaviour of aged samples deviated from annealed samples indicating a different polymer morphology. The effect of physical ageing on permeability can be described using an exponential decay function of the free volume with only one relaxation time. The loss of free volume with ageing is comparable for the glassy polymers studied, namely polycarbonate, polystyrene, polymethylmethacrylate and polysulphone.With respect to the service life of polymer products under thermal stress, it is concluded from the results presented that the lifetime can depend on the pre-treatment and service conditions of the product. Since physical ageing decreases the free volume and therefore the mobility of oxygen, the service life can increase. This is because of the reduced availability of oxygen at the oxidation site. Annealing only has a minor effect on both oxygen permeability and antioxidant mobility and will therefore not have a major influence on the service life.Mechanical and vibrational responses of gate-tunable graphene resonatorThe vibrational mechanical properties of gate-tunable graphene resonator were investigated in detail using finite element analysis (FEA) and simulation. Treating the graphene resonator as a two-dimensional (2D) thin plate, the relationship between resonance frequency and driving force was explored. The effects of built-in tension, adsorbates and graphene size on the performance of resonator including resonance frequency and tunability were also studied. It was shown that resonance frequency could be tuned by the electrostatically induced average tension due to driving force, and exponentially increased with increasing driving force. When the single-layer graphene resonator without any adsorbates had no or very small built-in tension, the tunability of resonator was greater. However, for a high-frequency-range resonator, the resonator with high built-in tension should be used. The simulation results suggested potential applications of graphene resonators tuned by a driving force, such as widely tunable or ultrahigh frequency nanoelectromechanical systems (NEMS) devices.Graphene, an interesting 2D nano material, possesses exceptional mechanical, electrical, optical and thermal properties On the other hand, some theoretical studies have been made on the mechanical vibration behavior of graphene resonators. Chowdhury et al. However, existing models only analyze specific or single graphene resonator such as one boundary condition, one shape, and have limitations in considering enough influence factors. MD simulations are time-consuming and limited to graphene resonator at the nanoscale, which cannot model the graphene resonators in the practical experiments. Thus, a common model with more practical applications and accuracy is needed.In this paper, the mechanical properties and resonance frequency of gate-tunable graphene resonator were performed by FEA and simulation. Treating the graphene as a linearly elastic 2D thin plate in the model used in our previous work The gate-tunable carbon-nanotube resonators shows simple schematic of a gate-tunable graphene resonator, which is similar with carbon-nanotube resonators. Both sides of the graphene are clamped due to the Van der Wals forces between graphene and substrate. At first, the graphene resonator is initially relaxed without an external force. After that, the dc gate voltage (VG) and bias voltage (VSD) are applied to the gate and graphene suspended above the gate at a distance (d), respectively. The surfaces of both gate and suspended graphene will produce equal number of positive charge and opposite charge, which generates external driving force (Fd) induced by an electrostatic capacitive force downward on the graphene. The deflection of suspended graphene under the driving force will result in the change of the capacitance (C) between the gate and the graphene according to C≈ε0LW/d, where ε0 is the vacuum permittivity, and L and W are the length and width of the graphene, respectively. If C′=dC/dz is the derivative of the capacitance with respect to the distance, the total electrostatic force on the graphene is given byThen the resonance frequency of its oscillations is calculated by FEA simulation using COMSOL multiphysics. In this work, it is assumed that the driving force is uniformly distributed over the graphene. The deflection of the graphene due to the driving force induces tension and strain in the graphene on both sides. Therefore, the relationships between the gate voltage, driving force, deflection, tension and resonance frequency are studied. shows an FEA model for the graphene resonator. The model consists of linearly elastic 2D thin plate elements with isotropic material parameters clamped along the sides of the graphene. The dimensions of graphene are width of 20 nm, length of 500 nm and thickness (t) of 0.35 nm. A unique advantage of the model is that the thickness of graphene is given in the plate interface, instead of directly in the geometry. The simulation of resonance frequency includes two steps. The first step is statics analysis to calculate the average tension induced by the deflection of graphene due to the driving force. Geometric nonlinearity considered in the study setting is indispensable due to the nonlinear deflection of graphene. In the second step of the simulation, modal analysis is performed to determine the resonance frequency. The calculated average tension above is input as initial built-in tension and doubly clamped on the graphene sides is the boundary condition. Geometric nonlinearity is also considered. The proposed model is also suitable for all clamped graphene resonator.The dynamics analysis of a linear resonator with a uniform cross-section has been described with elastic beam theory where the thickness t=0.35 nm, the density ρ=2200 kg/m3, and the Young's Modulus E=1 TPa. The bending moment of a rigid beam is I=Wt3/12.For high tension (T ⪢ EI/L2) the frequency can be expressed as For the verification of the proposed model, resonance frequencies of graphene under different built-in tensions are firstly simulated, and the simulation results are compared with analytical expressions and experiments. The exact value of the Poisson ratio has little effect on the output of the resonance frequency and then 0.17 is chosen shows the resonance frequency as a function of built-in tension using the FEA model and the above expressions. The resonance frequency under weak tension is almost unchangeable, while increases sharply under high tension. Moreover, the simulation results using the FEA model agree well with that calculated by the elastic beam theory. Recently, many groups In this section, we focus on the relationship between the resonance frequency and driving force, and corresponding mechanism. As can be seen from , the influence of tension on the resonance frequency of graphene resonator is significant. The tension in the graphene, which is electrostatically induced by the driving force, varies depending on how much stretching is imposed by the driving force. To illustrate it, we analyzed and discussed the mechanical response of the graphene resonator under driving force.To describe in detail, the relationships of gate voltage, driving force, average tension, center deflection and maximum tension are plotted in (a), the induced driving force symmetrically increases with the increasing |VG|, assuming the distance d=200 nm. For a doubly clamped membrane, the average tension in the membrane is fundamentally induced by the gate voltage and the relationship between them can be described as (b) shows the average tension as a function of the gate voltage using the above analytical expression and FEA simulation. There is a good agreement between the two methods.The relationship between the center deflection and the driving force can be fitted by the power function dM=9.555 Fd0.3447, as shown in (c). This fitting function is in excellent agreement with previous work by Altalay et al. For graphene with pretension, small deflections induced by driving force do not substantially change the built-in tension and the graphene resonator behaves as a linear tensile elastic membrane. However, when the deflections are large enough, the tensions change significantly (d), the average tension is almost linearly proportional to the driving force, which is a natural result since an externally applied force along the lateral direction on the string induces linearly increasing tensions on both sides on the string. The inset in (d) shows the average tension versus the log10(Fd). Note that for small Fd the average tension is almost constant and approximately equal to 0, while the constant value is 1.2 N/m in the previous work (e), smaller than the adhesion energy. Therefore, all driving force considered in current work is well below the maximum driving force, and the graphene will not be seperated from the substrate.For a membrane under tension, the resonance frequency is enhanced by the strengthened rigidity. The simulated results of fundamental resonance frequencies under different driving force are shown in (a). Here, the resonance frequency is 307 MHz for Fd=0.1 nN. The resonance frequency increases with the increasing driving force, and then can be regressed by the power function f=649.5 Fd0.3262, which is in good agreement with f~Fd0.333 derived from previous experiments For gate-tunable mechanical resonators, the tunable range is very important for them to achieve high sensitivity and low power consumption. (b) shows the increasing rate of the resonance frequency as a function of the driving force, which is obtained from the deviation of the data in (a). The increasing rate decreases rapidly when the driving force is less than 0.02 nN and finally reaches a stable value. Since the driving force is almost linearly proportional to the potential difference between the graphene resonator and the gate, it indicates that sensing can be achieved with low power consumption; i.e. at low gate voltage, and the applied force perturbation induces a considerable change in the resonance frequency.where μ is the linear mass density of the string, n is the harmonic order number and T is the average tension. The average tension in the graphene induced by driving force is calculated to investigate the relationship between them and resonance frequency in (c). The fitting equation for the average tension is f=1070 T0.467, which is in good agreement with classical continuum mechanics in Eq. (d) shows the resonance frequency as a function of the center deflection. As can be seen from (d), the resonance frequency linearly increases with increasing center deflection, which is compatible with the Eq. To further explore the performance of the graphene resonators, we studied the effects of built-in tension, adsorbates and graphene size on the resonance frequency and tunability. Previous experiments show that the built-in tension is induced by the fabrication process or decrease in temperature . The resonance frequency increases with increasing the gate voltage away from a minimum at VG=0 due to the tension induced by the gate voltage. As the built-in tension increases, the resonance frequency increases and its tunability using gate voltage is remarkably reduced, an undesirable feature.(a) shows the resonance frequency as a function of the driving force for different built-in tensions. It can be seen that the resonance frequency increases as the built-in tension increases, similar to . For the high built-in tension of 0.5 N/m, the resonance frequency remains constant regardless of the driving force, while change in resonance frequency is obvious for small tension. Furthermore, the ranges of resonance frequency tuned by built-in tension (i.e. tunability of resonators) at a driving force are changed. To describe in detail, we calculated the range of resonance frequency as a function of the driving force, the relation of which is shown in (b). As the driving force increases, the tunability of graphene resonators decreases. Kwon et al. (a) shows the resonance frequency as a function of the built-in tension for different driving force. It is explicit that the resonance frequency increases with increasing built-in tension and driving force. The resonance frequency for the small built-in tension of 0.001 N/m is the same as or slightly less than that without built-in tension. Such results show that the performance of resonators tuned by driving force (i.e. gate voltage) can be clearly affected by the built-in tension, mainly by changing the controlled temperature (b), the resonance frequency tuned by the built-in tension is higher than that tuned by the driving force. A reasonable explanation is that the maximum built-in tension in the simulations is 0.5 N/m, which is higher than the maximum tension induced by driving force (0.086 N/m), increasing the resonance frequency higher.It should be noted that the mass density of graphene resonators is larger than the theoretical value. One possibility for the extra density is adsorbates such as electron-beam resist residue from the fabrication process (a). The extra mass density affects the resonance frequency significantly. As the coefficient increases, the resonance frequency decreases and the curve becomes more and more gentle. (b) depicts the range of resonance frequency as a function of the adsorbed mass coefficient. The tunability of graphene resonator is reduced due to the adsorbates. So the adsorbates should be removed due to its negative influence on both the resonance frequency and tunability.In fact, the influences of graphene size on the resonance frequency are illustrated in the previous work illustrate the effects of length and thickness on the performance of graphene resonator, respectively. As the length or thickness increases, the range of resonance frequency decreases. In addition, for Fd=0, the resonance frequency linearly increases with the number of graphene layers, which is confirmed by Eq. under no tension. This is a new interesting finding in our work. While the resonance frequency first decreases with the number of graphene layers and then it increases at a driving force. As the driving force increases, the critical number of layers increases. The resonance frequency is determined by both the tension and graphene thickness, and the tension induced by driving force decreases with increasing thickness, resulting in a critical thickness.For the gate-tunable mechanical resonators, the tunable range is very important for them to be utilized with high sensitivity and low power consumption. The effects of built-in tension, adsorbates and graphene size on the resonance frequency and tunability are investigated in this section. The results show that the tunability of single-layer graphene resonator without any adsorbates and built-in tension or has very small built-in tension is greater. However, the resonator with high built-in tension is more suitable for a high-frequency-range resonator.To conclude, we performed the vibrational mechanical properties of gate-tunable graphene resonator using FEA simulation. We found that the effect of driving force on the resonance frequency could be equivalently considered as tension effect. The resonance frequency as a function of built-in tension testified the accuracy of the proposed model by reaching an excellent agreement with previous theoretical and experimental works. The relationship between resonance frequency and average tension induced electrostatically by the driving force could be almost regressed by a square root function. The resonance frequency tuned by the built-in tension was higher than that tuned by the driving force. Furthermore, the tunability of resonators could be strengthened by decreasing the built-in tension, adsorbates and graphene thickness. However, for a high-frequency-range resonator, the higher built-in tension was helpful. The proposed model is also suitable for all clamped graphene resonators.Rapid viscoelastic changes are a hallmark of early leukocyte activationTo accomplish their critical task of removing infected cells and fighting pathogens, leukocytes activate by forming specialized interfaces with other cells. The physics of this key immunological process are poorly understood, but it is important to understand them because leukocytes have been shown to react to their mechanical environment. Using an innovative micropipette rheometer, we show in three different types of leukocytes that, when stimulated by microbeads mimicking target cells, leukocytes become up to 10 times stiffer and more viscous. These mechanical changes start within seconds after contact and evolve rapidly over minutes. Remarkably, leukocyte elastic and viscous properties evolve in parallel, preserving a well-defined ratio that constitutes a mechanical signature specific to each cell type. Our results indicate that simultaneously tracking both elastic and viscous properties during an active cell process provides a new, to our knowledge, way to investigate cell mechanical processes. Our findings also suggest that dynamic immunomechanical measurements can help discriminate between leukocyte subtypes during activation.The mammalian immune response is largely based on direct interactions between white blood cells (leukocytes) and pathogens, inert particles, or other host cells. Mechanical properties of leukocytes regulate their migration in the microcirculation to reach their targets, and their interaction with these targets. Yet these mechanical properties and their evolution upon leukocyte activation remain poorly studied. We developed a micropipette-based rheometer to track cell viscous and elastic properties. We show that leukocytes become up to 10 times stiffer and more viscous during their activation. Elastic and viscous properties evolve in parallel, preserving a ratio characteristic of the leukocyte subtype. These mechanical measurements set up a complete picture of the mechanics of leukocyte activation and provide a signature of cell function.The understanding of cell mechanics has progressed with the development of micromanipulation techniques such as micropipette aspiration (). Microfluidics-based approaches such as real-time deformability cytometry now allow high-throughput mechanical measurements (). Yet these techniques make it difficult to track mechanical changes in cells stimulated by soluble molecules () and even more difficult when cells are stimulated by activating surfaces or partner cells (Tracking these changes can bring a wealth of information on cell function in healthy conditions and diseases. Here, we illustrate this by focusing on white blood cells (leukocytes). These cells, among other functions, fight infected cells or pathogens, remove dead cells, and identify antigens at the surface of other cells and eventually build an immune response against a detected threat. To do so, leukocytes activate by forming with other cells specialized interfaces called immunological synapses. Different leukocytes form different types of synapses, which share several molecular () but also mechanical features. One of these mechanical features is force generation, which is now well documented in different types of leukocytes. For instance, we have shown that a T lymphocyte generates forces when forming a synapse (). Others recently showed that B cells generate traction forces during activation (), and Evans et al. quantified decades ago contractile forces generated during phagocytosis (). The role of these forces is still an open question. Their suggested functions, such as allowing a tight cell-cell contact or probing the mechanical properties of the opposing surface, place these forces at the core of leukocyte activation (). In this study, we focus on another mechanical feature: changes in leukocyte viscoelasticity during their activation. These changes have been shown to exist in T cells, phagocytes, and B cells. We have shown that during activation, T cells stiffen (). Pioneering observations showed that during phagocytosis, the cortical tension of a phagocyte increases dramatically while this cell engulfs its prey (), and more recent observations confirmed mechanical stiffening of leukocytes during phagocytosis (). We also recently quantified elastic changes in B cells during activation (As for force generation, the function of the mechanical properties of leukocytes during activation is not yet understood and open to speculation (see ). Yet it is important to quantify and describe them for two reasons. First, we need a complete picture of the mechanics of leukocyte activation to properly incorporate mechanics into currently proposed models of the activation of the different types of leukocytes. Second, beside the fundamental interest of understanding these mechanical changes, they can have very important consequences in the context of disease. Indeed, mechanical properties of leukocyte dictate how easily leukocytes migrate in or out of tissue or flow in small blood vessels (), which contributes to their trapping in pulmonary vasculature in lung diseases such as acute respiratory distress syndrome (). Being trapped or slowed down while traveling in a capillary can be due to an increased cell stiffness, but also to an increased cell viscosity. Understanding cell viscous properties is thus also important, although viscous properties are much less explored than elastic ones because of inherent difficulties in quantifying them.Most measurements of leukocyte mechanics, including the ones mentioned above, were focused on elastic and not viscous properties. However, it was recognized decades ago that leukocytes are viscoelastic and not only elastic (), so in many situations we miss an important aspect of leukocyte mechanics. Fabry et al. () and others have shown that one can expect the viscous properties of leukocytes to be linked to their elastic properties. It was recognized that resting leukocytes such as neutrophils () conserve a ratio of cortical tension/cell viscosity of ∼0.2–0.3 μm/s, even though macrophages can be 10 times more tensed than neutrophils. The ratio of viscous to elastic properties seems to be constrained within a rather narrow range of values, and many studies showed this peculiar aspect of biological matter in various cell types (). Here, we asked whether for a given cell type, elastic and viscous properties of leukocytes respected a relationship while they were both evolving over time. To do so, we quantified the evolution of both elastic and viscous properties during the activation of three types of leukocytes. We used a micropipette rheometer to activate leukocytes with standardized activating antibody-covered microbeads (), and we further probed early mechanical changes occurring in leukocyte-target cell contacts by using atomic force microscopy in single-cell force spectroscopy mode (The rheometer was build based on the evolution of our profile microindentation setup (). Micropipettes were prepared as described previously () by pulling borosilicate glass capillaries (Harvard Apparatus, Holliston, MA) with a P-97 micropipette puller (Sutter Instruments, Novato, CA), cutting them with an MF-200 microforge (World Precision Instruments, Sarasota, FL), and bending them at a 45° angle with an MF-900 microforge (Narishige, Tokyo, Japan). Micropipettes were held by micropipette holders (IM-H1; Narishige) placed at a 45° angle relative to a horizontal plane, so that their tips were in the focal plane of an inverted microscope under brightfield or DIC illumination (T cells: TiE; PLB cells: Ti2; Nikon Instruments, Tokyo, Japan) equipped with a 100× oil immersion, 1.3 NA objective (Nikon Instruments), and placed on an air suspension table (Newport, Irvine, CA). The flexible micropipette was linked to a nonmotorized micropositioner (Thorlabs, Newton, NJ) placed on top of a single-axis stage controlled with a closed-loop piezo actuator (TPZ001; Thorlabs). The bending stiffness k of the flexible micropipette (∼0.2 nN/μm) was measured against a standard microindenter previously calibrated with a commercial force probe (model 406A; Aurora Scientific, Aurora, Canada). Once the activating microbead was aspirated by the flexible micropipette, the cell held by the stiff micropipette was brought into an adequate position using a motorized micromanipulator (MP-285; Sutter Instruments). Experiments were performed in glass-bottom petri dishes (Fluorodish; World Precision Instruments). Images were acquired using a Flash 4.0 CMOS camera (for T cells) or a SPARK camera (PLB cells), both from Hamamatsu Photonics, Hamamatsu City, Japan. To perform rheological experiments, the setup automatically detects the position of the bead at the tip of the force probe at a rate of 400–500 Hz and imposes the position of the base of the flexible micropipette by controlling the position of the piezo stage. The deflection of the force probe is the difference between the position of the bead and the position of the piezo stage. Thus, the force applied to the cell is the product of this deflection by the bending stiffness k. A retroaction implemented in MATLAB (The MathWorks, Natick, MA) controlling both the camera via the Micro-Manager software () and the piezo stage moves the latter in reaction to the measurement of the bead position to keep the desired deflection of the cantilever; a controlled force is applied to the cell at any given time. Experiments were performed at room temperature to avoid thermal drift. Qualitative behavior of T cell and PLB cells is unchanged at 37°C (data not shown). We quantified the fluid drag due to micropipette translation (, Section 1) and the potential effect of fast cell deformation on our rheological measurements (, Section S2). The accuracy when measuring the phase shift depends on the acquisition frequency of both force and cell deformation (xtip), which is 400–500 Hz depending on the size of the region of interest chosen for the acquisition. This leads to a time resolution of 2–2.5 ms. The measured loss tangent had a typical value of η = (K″/K′) = tan(φ) ≈ 0.3–0.5, i.e., φ ≈ 0.3–0.5. When expressed in seconds instead of radians, this phase lag represents a delay Δt = φ/2πT, where T = 1 s is the period of the oscillatory force modulation, which leads to Δt = 46–74 ms. This is reasonably long when compared with our time resolution so as to be accurately measured. Note that the uncertainty on the phase lag influenced more K″ than K′ because K″ is proportional to sin(φ), whereas K′ is proportional to cos(φ).Rheological measurements were analyzed by postprocessing using a custom-made Python code. During force modulation, the sinusoidal xtip signal was fitted every 0.5–1 period interval over a window that was 1.5–2.5 periods long (i.e., every 0.5–1 s with a window of 1.5–2.5 s for a frequency of force modulation f = 1 Hz) using a function corresponding to a linear trend with an added sinusoidal signal (two free parameters for the linear trend, two for the sinusoidal signal when imposing the frequency f = 1 Hz). Best fit was determined using classical squared error minimization algorithm in Python.Mononuclear cells were isolated from peripheral blood of healthy donors on a Ficoll density gradient. Buffy coats from healthy donors (both male and female donors) were obtained from Etablissement Français du Sang (Paris, France) in accordance with INSERM ethical guidelines. Human total CD4+ isolation kit (130-096-533; Miltenyi Biotec, Bergisch Gladbach, Germany) was used for the purification of T cells. Isolated T cells were suspended in FBS:dimethyl sulfoxide (90%:10% vol/vol) and kept frozen in liquid nitrogen. 1–7 days before the experiment, the cells were thawed. Experiments were performed in RPMI 1640 1× with GlutaMax, supplemented with 10% heat-inactivated fetal bovine serum (FBS) and 1% penicillin-streptomycin (all from Life Technologies Thermo Fisher Scientific, Waltham, MA), and filtered with 0.22 μm diameter pores (Merck Millipore, Burlington, MA).Dynabeads Human T-Activator CD3/CD28 for T Cell Expansion and Activation from Gibco were purchased from Thermo Fisher Scientific (ref. 11131D; Carlsbad, CA). These 4.5 μm superparamagnetic polymer beads, coated with an optimized mixture of mouse anti-human monoclonal IgG antibodies against the CD3 and CD28 cell-surface molecules of human T cells, mimic stimulation by an antigen presenting cell (APC). The CD3 antibody is specific for the ε chain of human CD3. The CD28 antibody is specific for the human CD28 costimulatory molecule, which is the receptor for CD80 (B7-1) and CD86 (B7-2). These beads induce the phosphorylation of several signaling proteins (). Control beads were noncoated 4.5 μm polystyrene beads.Primary B lymphocytes were isolated from spleens of adult C57BL/6J mice (10 to 20 weeks old) and purified by negative selection using the MACS kit (130-090-862) in the total splenocytes. Animal procedures were approved by the CNB-CSIC Bioethics Committee and conform to institutional, national, and EU regulations. Cells were cultured in complete RPMI 1640-GlutaMax-I supplemented with 10% FCS, 1% penicillin-streptomycin, 0.1% β-mercaptoethanol, and 2% sodium pyruvate (denominated hereafter as complete RPMI).Silica beads (5 × 106; 5 μm diameter; Bangs Laboratories, Fishers, IN) were washed in distilled water (5000 rpm, 1 min, RT), incubated with 20 μL 1,2-dioleoyl-PC (DOPC) liposomes containing GPI-linked mouse ICAM-1 (200 molecules/μm2) and biotinylated lipids (1000 molecules/μm2) (10 min, RT), and washed twice with beads buffer (PBS supplemented with 0.5% FCS, 2 mM MgCl2, 0.5 mM CaCl2, and 0.5 g/L D-Glucose). Then, lipid-coated beads were incubated with AF647-streptavidin (Molecular Probes, Eugene, OR) (20 min, RT) followed by biotinylated rat anti-κ light chain antibody (clone 187.1; BD Biosciences, Franklin Lakes, NJ) (20 min, RT), used as surrogate antigen (su-Ag) to stimulate the B cell receptor. Control beads were coated with ICAM-1-containing lipids only (no su-Ag was added). The number of molecules/μm2 of ICAM-1 and su-Ag/biotin-lipids was estimated by immunofluorometric assay using anti-ICAM-1 or anti-rat-IgG antibodies, respectively; the standard values were obtained from microbeads with different calibrated IgG-binding capacities (Bang Laboratories). The lipid-coated silica beads were finally resuspended in complete RPMI before use. Such a use of lipid-coated silica beads as pseudo-APCs to study immune synapse formation, cell activation, proliferation, and antigen extraction by B cells has been previously set up and reported by us (). They provide the adhesion ligand ICAM-1 for the integrin LFA-1 expressed at the B cell surface and tethered BCR-stimulatory signal (su-Ag) in a fluid phospholipid environment.The human acute myeloid leukemia cell line PLB-985 is a subline of HL-60 cells based on STR fingerprinting (). Gene expression in the two lines is similar but not identical (). PLB-985 cells were cultured in RPMI 1640 1× GlutaMax (Gibco, Gaithersburg, MD) supplemented with 10% sterile heat-inactivated FBS and 1% sterile penicillin/streptomycin. Cells were passaged twice a week and differentiated into a neutrophil-like phenotype by adding 1.25% (v/v) of dimethyl sulfoxide (Sigma-Aldrich, St. Louis, MO) to the cell suspension the first day after passage and a second time 3 days after changing the culture media (20 and 8 μm diameter polystyrene microbeads at 106 beads/mL (Sigma-Aldrich) were washed three times by centrifugation at 16,000 × g for 3 min and resuspended in Dulbecco’s PBS (DPBS; Gibco) filtered with 0.22 μm diameter pores (Merck Millipore). Beads were then incubated overnight at room temperature with 5% (w/v) bovine serum albumin (Sigma-Aldrich) in DPBS. Beads were washed again three times by centrifugation at 16,000 × g during 3 min, resuspended in DPBS, and incubated with 1:500 anti-bovine serum albumin rabbit antibody (ref. B1520; Sigma-Aldrich) in DPBS for an hour at room temperature. These IgG-coated beads were washed three times by centrifugation at 16,000 × g for 3 min with DPBS and resuspended in DPBS at 106 beads/mL before use. Control beads were uncoated polystyrene beads, inducing very rare cases of adhesion with the cell but no phagocytosis. PLB cells tried almost systematically to internalize 20 μm activating beads by performing frustrated phagocytosis and phagocyted 8 μm activating beads.3A9m T cells were obtained from D. Vignali () and cultured in RPMI completed with 5% FBS, 10 mM Hepes, 10 mM sodium pyruvate in 5% CO2 atmosphere. COS-7 APCs were generated as previously described () by stably coexpressing the α and β chains of the mouse MHC class II I-Ak, cultured in Dulbecco’s modified Eagle’s medium (DMEM; 5% FBS, 1 mM sodium pyruvate, 10 mM Hepes, and geneticin 10 μg/mL). Cells were passaged up to three times a week by treating them with either trypsin/EDTA or PBS 1× (w/o Ca2+/Mg2+), 0.53 mM EDTA at 37°C for up to 5 min.The anti CD45 antibodies used for this study were produced from the hybridoma collection of CIML, Marseille, France (namely H193.16.3) (). Briefly, cells were routinely grown in complete culture medium (DMEM, 10% FBS, 1 mM sodium pyruvate) before switching to the expansion and production phase. Hybridoma were then cultured in DMEM with decreasing concentrations of low-immunoglobulin FBS down to 0.5%. Cells were then maintained in culture for five additional days, enabling immunoglobulin secretion before supernatant collection and antibody purification according to standard procedures.The expression of TCR and CD45 molecules on T cells and MHC II molecules on COS-7 APC was assessed once a week by flow cytometry (anti-TCR PE clone H57.597 and anti-CD45 Alexa Fluor 647 clone 30F11 were purchased from BD Pharmingen). The count and the viability, with trypan blue, were assessed automatically twice by using Luna automated cell counter (Biozym Scientific, Vienna, Austria). Mycoplasma test was assessed once a month. Culture media and PBS were purchased from Gibco (Life Technologies). PP2 (Lck inhibitor) was purchased from Calbiochem (San Diego, CA).Culture-treated, sterile glass-bottom petri dishes (Fluorodish FD35-100; World Precision Instruments) were incubated with 50 μg/mL anti-CD45 antibody for 1 h at room temperature. The surfaces were extensively washed with PBS 1× before a last wash with HBSS 1× 10 mM Hepes. The surfaces were kept wet with HBSS 1× 10 mM Hepes before seeding T cells.T cells were counted, centrifuged, and resuspended in HBSS 1× 10 mM Hepes and were kept for 1 h at 37°C 5% CO2 for recovery before seeding. The cells were seeded at room temperature, and after 30 min, a gentle wash was done by using two 1 mL micropipettes to maintain as much as possible a constant volume in the petri dish and hence avoid perturbations by important flows. After 1 h incubation, the petri dish was mounted in a petri dish heater system (JPK Instruments, Berlin, Germany) to maintain the temperature of the sample at ∼37°C. 10 min before experiments, 10 μM (final concentration) of Lck kinase inhibitor (PP2 drug) was added and homogenized in the sample. We kept this drug present along all the experiments.The day before the experiment, COS-7-expressing MHCII cells were incubated with the peptide of interest with a final concentration of 10 μM, allowing 100% occupation of MHC II molecules. Before the experiment, the cells were detached from the cell culture plates by removing the cell medium and washing once with PBS 1× and then by a 0.53 mM EDTA treatment for 5 min at 37°C 10% CO2. The cells were resuspended in HBSS 1× 10 mM Hepes and were allowed to recover before to be seeded into the sample. The peptide p46.61 (which is CD4 dependent) was purchased from Genosphere (Paris, France) with a purity >95%.The setup has been described in great detail elsewhere (). Measurements were conducted with an AFM (Nanowizard I; JPK Instruments) mounted on an inverted microscope (Axiovert 200; Zeiss, Oberkochen, Germany). The AFM head is equipped with a 15 μm z-range linearized piezoelectric scanner and an infrared laser. The setup was used in closed-loop, constant height feedback mode (). MLCT gold-less cantilevers (MLCT-UC or MLCT-Bio DC; Bruker, Billerica, MA) were used in this study. The sensitivity of the optical lever system was calibrated on the glass substrate and the cantilever spring constant by using the thermal noise method. Spring constant were determined using JPK SPM software routines in situ at the start of each experiment. The calibration procedure for each cantilever was repeated three times to rule out possible errors. Spring constants were found to be consistently close to the manufacturer’s nominal values and the calibration was stable over the experiment duration. The inverted microscope was equipped with 10× and 20× NA 0.8 and 40× NA 0.75 lenses and a CoolSnap HQ2 camera (Photometrics, Tucson, AZ). Brightfield images were used to select cells and monitor their morphology during force measurements through either Zen software (Zeiss) or Micro-Manager (Lever decoration. To make the cantilevers strongly adhesive, we used a modified version of our previous protocols (). Briefly, cantilevers were activated using a 10 min residual air plasma exposure, then dipped in a solution of 0.25 mg/mL of wheat germ agglutinin or 0.5 mg/mL of concanavalin A in PBS 1× for at least 1 h. They were extensively rinsed by shaking in 0.2-μm-filtered PBS 1× and stored in PBS 1× at 4°C. Before being mounted on the glass block lever holder, they were briefly dipped in MilliQ-H2O to avoid the formation of salt crystals in case of drying and hence alteration of the reflection of the laser signal.APC capture. In separate experiments, we used side view and micropipette techniques, and we observed that 1) this allows the presented cell to be larger than the lever tip, excluding any unwanted contact of T cell with lectins and 2) the binding is resistant enough to ensure that any rupture event recorded is coming from the cell-cell interface (). After calibration, a lectin-decorated lever is pressed on a given COS7 cell for 20–60 s with a moderate force (typically 1–2 nN), under continuous transmission observation. Then, the lever is retracted far from the surface and the cell is allowed to recover and adhere or spread for at least 5 min before starting the experiments (Single-cell force spectroscopy experiment. The surrogate APC is then positioned over a desired T cell. Because the lever is not coated with gold and hence almost transparent, one can finely position the probe over the target. Force curves are then recorded using the following parameters: maximal contact force 1 nN, speeds 2 μm/s, acquisition frequency 2048 Hz, curve length 10 μm, and contact time 60 s. At the end of the retraction, lateral motion of the cells is made by hand by moving the AFM head in the (x, y) plane, relative to the petri dish substrate until no more force is recorded by the lever, signaling that full separation was achieved (). One APC cell was used to obtain one force curve on at least three different T cells, and three APCs at least were used for each condition. No apparent bias was detected in the data when carefully observing the succession of the measures for a given APC, for a given lever, and for a set of T cells.Data processing and statistics. Force curves were analyzed using JPK Data Processing software on a Linux 64 bit machine. Each curve was evaluated manually, except for calculation and plotting of mean ± standard deviation (SD) for relaxation curves, for which ad hoc Python scripts were used. Data were processed using GraphPad Prism (v7) on a Windows 7 machine. On graphs, data are presented as scatter dot plots with median and interquartile range. A data point corresponds to a force curve obtained for a given coupled T cell-APC except for the small detachment events, for which one data point corresponds to one such event (all events were pooled). Significance was assessed using Mann-Whitney tests in GraphPad Prism v7 with ∗p < 0.05,∗∗p < 0.01,∗∗∗p < 0.001, and ∗∗∗∗p < 0.0001 below; not significant otherwise.We implemented a real-time feedback loop in our micropipette force probe setup ()) allowing us to impose a controlled small oscillatory force modulation ΔFcos(ωt) (angular frequency ω = 2πf, frequency f = 1 Hz) superimposed onto a constant force (F). A total force F(t) = (F) + ΔFcos(ωt) is thus applied to the leukocyte during its activation after the contact with an activating microbead coated with cell-specific antibodies. The contact is ensured by pressing the bead against the cell with a force Fcomp (0.12–0.36 nN). This initial compression, from which we extract the cell's effective Young’s modulus EYoung ()), is followed by an imposed force modulation regime, in which we measure oscillations in the position of the tip of the flexible micropipette xtip(t) = <xtip> + Δxtipcos(ωt − φ) of average value xtip, amplitude <xtip> (typically 100 nm, with accuracy within a few nanometers), and phase lag φ. Changes in xtip(t) reflect changes in cell length (b). Because the cell is shorter when the force is higher, xtip(t) decreases when F(t) increases and corresponds to the lag between a maximum of the force and the following minimum of xtip(t) (b, inset, bottom right). From xtip(t) and F(t), we deduce the complex cell stiffness K∗ = K′ + iK″, of elastic part K′ = (ΔF/Δxtip)cosφ and viscous part K″ = (ΔF/Δxtip)sinφ (). We validated our setup by quantifying K∗ of red blood cells (). We obtained values of K′ very consistent with values predicted by existing models, and also obtained, as expected, very low values of K″ (Video S1. Activation of three types of leukocytes studied with the micropipette rheometer(top: T cell, middle: B cell, bottom: PLB cells). All bars represent 5 μm. Time is in minutes:seconds.Video S2. Validation of the micropipette rheometer by performing microindentation measurements on a red blood cellThe bar represents 5 μm. Time is in minutes:seconds.We probed three different types of leukocytes during their specific activation and observed qualitatively similar behavior: both K′ and K″ increase and reach a maximum that is three- to eightfold larger than their initial value within few minutes (∼2 min for T and B cells, ∼5 min for neutrophil-like PLB985 cells) after the contact between the leukocyte and the relevant activating microbead (). The increase of K′ and K″ is in clear contrast with the constant values obtained using control nonactivating beads (black lines in ). Yet it is worth mentioning that the initial value of K′ and K″ is higher for activating beads than for control beads for T and B cells. We explain this by the fact that the initial time point for K′ and K″ is actually already ∼10 s after initial cell-bead contact, leaving some time for early mechanical changes to occur (see later regarding mechanical changes). We evaluated the effect of temperature in the case of T cells by performing experiments at 37°C. T cells behaved qualitatively the same at 37°C but reacted faster and reached higher levels in K′ and K″ (Both K′ and K″ depend on cell geometry, so to exclude the possibility that changes in K′ and K″ only reflect geometrical changes, cell-intrinsic mechanical properties such as Young’s modulus and viscosity have to be extracted from K′ and K″. To do so, we first convert K′ and K″ into a storage modulus E′ and a loss modulus E″, respectively. In the case of T cells and B cells, we do so by modeling cell geometry (For PLB cells, we use a modified setup in which a nonadherent and nonactivating glass bead indents the cell on its “back” () while the cell phagocytoses an activating bead at its “front” ()). This alternative setup leads to the same increase in K′ and K″ as measured using the original setup with front indentation with an activating bead (b). Having a sphere-against-sphere geometry, we can use a linearized Hertz model to extract E′ and E″ moduli (, Section S8). Lastly, we performed cyclic indentation experiments to measure directly the Young’s modulus over time (with a limited time resolution of ∼30 s; dotted curves in l); indentation occurs only for a short time at the beginning of each cycle, after which the indenter retracts from the cell, marking the end of a cycle, immediately followed by a new cycle (). In the case of PLB cells, we tested the influence of bead size by performing indentation in the “back” of cells phagocytosing either 20 or 8 μm beads. For both bead sizes, the cells’ Young’s modulus increased significantly during phagocytosis when comparing early (t = 52 s) versus late (t = 286 s) times (l, EYoung (t = 286 s) > EYoung (t = 52 s), at least 14 cells from at least three independent experiments for each condition, p < 0.0001 for 20 and 8 μm beads, Mann-Whitney test).Video S3. Modified setup to indent the “back” of a PLB cell while the cell phagocytoses an activating bead on its “front”The bar represents 10 μm. Time is in minutes:seconds.Video S4. Cyclic indentation experiments to directly measure the Young’s modulus over time of a PLB cell phagocytozing an activating beadThe bar represents 10 μm. Time is in minutes:seconds.To allow a simple interpretation of E′ and E″, which were obtained in a regime of oscillatory forces, we convert them into an effective Young’s modulus EYoungeq and an effective viscosity ν, respectively. To calculate EYoungeq, we compare the Young’s modulus measured by initial compression and E′ measured right after, when force modulation begins (). For PLB cells, we used cyclic back indentation again as described above to measure both Young’s modulus and E′ not only at initial time but during the whole activation. This showed that E′ and EYoung are proportional, with a phenomenological coefficient C such that E′ = CEYoung. C is measured to be constant over time for PLB cells, and so for T and B cells, we assume that C is also constant over time (Using this approach, we measured the effective Young’s modulus of the three cell types over time (, j–l). To calculate the effective cell viscosity, we consider a simple model consistent with a Newtonian liquid and cortical tension model of a cell (), in which a Newtonian viscosity is introduced as ν = E″/ω. The resulting Young’s modulus and viscosity increase until reaching a maximal value that is two- to threefold higher than the baseline value for T and B cells, and ∼11-fold higher for PLB cells (We asked whether mechanical changes were localized close to the activation area in the leukocyte. In the case of T cells, we used a modified setup similar to the one allowing to indent PLB cells on their back (a). In that case, an auxiliary pipette brought the activating microbead in contact with the T cell on its “side”: at the equatorial plane (distance between the activating and indenting beads smaller than 5 μm) or close to the tip of the holding pipette, at the farthest possible location from the activating bead (distance between the activating and indenting beads larger than 5 μm, ). This allowed us to quantify mechanical changes during activation depending on the distance to the cell-bead contact area. We computed an equivalent Young’s modulus EeqYoung as described in , Section S9, which led to a good agreement with EYoung measured at the initial time. T cells exhibited a different behavior depending on the location of the activating microbead; the closer the indenter was to the activating bead, the larger the maximal value of EeqYoung measured during activation. Cell stiffening thus occurs with a different amplitude depending on the location on the cell relative to the contact zone with an activating surface.Video S5. Modified setup using an auxiliary pipette to bring an activating microbead in contact with a T cell on its “side”The bar represents 5 μm. Time is in minutes:seconds.In T cells, mechanical changes precede morphological ones; K′ increases slowly within seconds after cell-bead contact, before cell morphology starts changing (i.e., before the T cell produces a large protrusion (). The onset of this growth is followed by a short period during which K′ stays relatively constant. This phase ends by a faster increase of K′ during protrusion growth (). The start of the faster increase in K′ starts when the tail of the cell in the holding pipette starts retracting (a sign that K′ and cell tension are two equivalent ways to describe cell stiffness; , Section S11). Of note, T cells have large membrane surface stores (), so it is unlikely that the acceleration in K′ increase could be explained by reaching the limits of membrane stores (To confirm with an independent technique that T cell mechanics may be modulated within seconds when it encounters an APC before any large morphological change occurs, we used AFM and performed single-cell force spectroscopy (SCFS) experiments ()). As a model APC, we used COS-7 cells expressing MHCII molecules that can be loaded with peptides of desired affinity as previously shown (). We used murine 3A9m T cells and immobilized them on a coverslip by adhering them using anti-CD45 antibodies (). To measure rapid mechanical changes using this technique, we prevented potential large active cell deformations by using the pan-Src kinase inhibitor PP2 (). Although PP2 inhibits TCR-mediated Lck- or Fyn-dependent intracellular phosphorylation events and downstream signaling cascades (), it does not inhibit all molecular events such as migration arrest, kinapse, or microcluster formation upon T cell activation (). The washout experiment showed that PP2 in fact enables to pause signalization without abrogating the antigen dependence of early T cell activation (The SCFS experiments provide for each cell doublet the force-tip sample separation curve, which is the AFM equivalent of the force-indentation curve shown in b (inset, bottom left), with three parts: 1) pushing the cells together, 2) maintaining the contact, and 3) detaching the cells by pulling them apart. The contact mechanics at initial time was quantified by measuring the slope of the force-tip sample separation curve (called contact slope herein), which reflects the stiffness of the cell doublet. This contact slope was not modified by the presence or absence on the APC of the hen egg lysozyme (peptide p46.61)-derived peptide recognized by the murine 3A9m T cells (d). However, in the separation part of the force curves, the presence of the peptide induced an increase in the force needed to fully detach the two cells in parallel with an increase of the number of discrete separation events, indicating that the interaction was indeed peptide specific (The measurement of the contact slope corresponds to the very first instant of cell-cell contact (a, bottom). To measure cell mechanical changes after this contact, we quantified the force relaxation when the AFM lever motion was stopped and piezo position was kept constant after reaching a contact force of 1 nN (, b and c). We observed a striking difference in this force relaxation depending on the presence versus absence of a saturating concentration of the antigenic peptide (b); the force relaxation was much slower in presence of the antigenic peptide, as quantified by the lower value of the ratio ΔF/F0 at different times after the start of the relaxation (c). This measurement reflects global viscoelastic properties of the cell-cell doublet but does not disentangle elastic and viscous properties. Furthermore, having the two cells pressed against each other in series does not allow simply excluding a contribution of a mechanical change in the APC. However, mechanical properties of APC COS-7 cells were not modified by the presence of the peptide (). As a consequence, we expect that the major contribution to the difference in force relaxation is indeed due to the T cell. Our SCFS experiments are thus consistent with our micropipette force probe experiments and show that specific recognition during T cell-APC contact may induce mechanical changes within a few seconds and without any TCR signaling.We then asked whether variations in elastic and viscous properties were related to each other. Prior works show that in several cell types, the loss modulus E″ and storage modulus E′ of a cell are related to each other. In fact, their ratio η = (E″/E′), the loss tangent, lies within a narrow range of 0.1–0.3 (). For a material such as a purely viscous liquid, the storage modulus vanishes so that η is arbitrarily large, whereas for a purely elastic material, the loss modulus vanishes and so does η. A finite and constant value of η for a cell implies that the stiffer the cell, the more viscous it is. This narrow range of loss tangent is consistent with the conserved ratio of cortical tension to cell viscosity in leukocytes (see ). In biological matter, similar to soft glassy materials (), stress relaxation over time often follows a power-law (with an exponent that we shall call α) (). The loss tangent η is frequency dependent and is expected to be approximately equal to tan(π/2α) at low frequencies (, Section S13). Therefore, by measuring the power-law exponent α independently, we should recover the value of η = (E″/E′) (which should also be equal to (K″/K′) because the contribution from geometry is eliminated in this ratio ()). To test this prediction, we performed stress relaxation experiment on resting PLB cells (c) and obtained values for α that were very consistent with the predicted value of (2/π)arctan(K″/K′) (which is equivalent to comparing tan(π/2α) and (K″/K′); gray circle in b). We then compared K″ vs. K′ curves obtained during activation of T cells, B cells, and PLB cells (b, we plot the corresponding value of α = (2/π)arctanη=(2/π)arctan(K″/K′); these curves are remarkably consistent for T and B cells, and for PLB cells, K″-K′ curves obtained by indentation in the front and in the back of the cell are very similar and differ from the T and B cell common curve. Interestingly, Bufi et al. (d), but their measurements were made at a single time point. Maksym et al. () tracked over time both the loss and storage moduli of human airway smooth muscle cells contracting because of the administration of histamine (d, inset, top left). Their data are again very consistent with our measurements. Roca-Cusachs et al. () used AFM on neutrophils and found a loss tangent very consistent with our measurements on PLB cells obtained with 20 and 8 μm beads (Based on our results, we propose a simple model of leukocyte mechanical changes during activation (e): mechanical changes begin seconds after receptor engagement at the leukocyte surface. Cell morphological changes start a few tens of seconds later, concomitant with stiffening and increase in viscosity. Viscous and elastic properties of the leukocyte evolve following a characteristic relationship defined by the loss tangent.We showed that during activation, various types of leukocytes see their stiffness and viscosity increase significantly within few minutes. The initiation of mechanical changes upon contact with an activating surface starts within seconds and these changes precede morphological changes. By using the same technique—avoiding potential differences due to different techniques ()—we show for the first time, to our knowledge, with ∼1 s time resolution how both viscous and elastic properties evolve during immune cell activation. We further show that elastic and viscous properties follow a relationship that is cell-type dependent; T and B cells keep the same ratio between viscous and elastic properties, whereas neutrophils follow a different ratio, independently of the size of their target.Most published measurements of cell viscosity were performed on leukocytes in a resting state. Some micropipette aspiration studies led to leukocyte viscosity in the range of 100–200 Pa.s () and are consistent with values obtained in fibroblasts (). These values are higher than the viscosities of ∼5–20 Pa ⋅ s that we measured in resting leukocytes. This discrepancy might be explained by model dependence and by differences in the shear rate applied to cells. Our measurements are much closer to results by other groups; Sung et al. () obtained a cytotoxic T cell viscosity of ∼30 Pa ⋅ s, Schmid-Schönbein et al. () measured a leukocyte viscosity of ∼13 Pa ⋅ s, and Hochmuth et al. () extrapolated a value for neutrophil viscosity of ∼60 Pa ⋅ s. Interestingly, Lipowsky et al. () did not restrict to baseline viscosity and studied neutrophils stimulated by the chemoattractant FMLP. The authors reported a neutrophil viscosity increasing from ∼5 Pa ⋅ s at resting state to ∼70 Pa ⋅ s upon stimulation.Mechanical changes might not have a function per se but might be concomitant to force generation by cells. Indeed, cell contractility and cell stiffness are correlated in muscle cells (), and single cells mirror mechanical and energetic features of muscle contraction; single myoblasts follow a single-cell equivalent of a Hill relationship between force generation and rate of contraction (). Furthermore, it also appears that single muscle cells become stiffer when they contract; Shroff et al. () observed a roughly twofold increase in the stiffness of a cardiomyocyte during its contraction. Although leukocytes have a different organization of their actomyosin cytoskeleton, it is tempting to speculate that all leukocytes share generic cytoskeletal-based properties requiring that cells stiffen to generate force. This could explain the apparent contradiction that in leukocytes, the stiffening that we have quantified occurs in situations requiring an efficient spreading. Indeed, phagocytes need to increase their surface by spreading on their prey to engulf it, whereas T and B cells need to spread widely on the cell they encounter to quickly scan a surface that is as large as possible on the cell they interact with (). Alternatively, forming a stiff synapse might allow its stabilization (Although the molecular details leading to changes in viscoelastic properties are yet to be understood, cell-scale physical considerations allowed Evans et al. () to conclude that viscous properties of cells are conferred by bulk components of the cell, as opposed to surface viscosity due to the actin cortex. As a result, we expect that the large increase in the viscous properties of leukocytes that we observed are largely due to intracellular reorganization, not only cortical reorganization. Interestingly, Tsopoulidis et al. recently showed that T cell receptor engagement triggers the formation of a nuclear actin network in T cells (), which could contribute to these bulk mechanical changes. Fritzsche et al. observed submembrane actin pattern reorganization that influenced the membrane architecture of HeLa cells, but not their mechanical properties (). These observations may lift an apparent contradiction in T cells, in which the formation of an immunological synapse requires actin to depolymerize at the center of the synapse, including in cytotoxic T cells where actin gets actually depleted across the synapse within 1 min (). Other contributors must then explain the stiffening that we observe, and in addition to the nuclear actin network (), another possible contributor may be a secondary actin network. Indeed, Fritzsche et al. () found in T cells that besides the dense cortical network forming a rosette-shaped structure in the basal lamellipodium and devoid of actin at its center up to 3 min after initial contact, another actin network assembles 150–300 nm above the cell-substrate contact.We expect inner reorganizations causing mechanical changes to impact inner cell dynamics, such as organelle trafficking. This includes mitochondrial relocation that is known to happen in several types of leukocytes upon activation (). Regarding the cell surface, although we dismissed surface effects as key contributors to cell viscosity, surface receptors are transmembraneous, so the formation of diffusional barriers with slowed diffusion at the cell surface as observed during leukocyte activation could be one manifestation of the increase in cell viscosity (). As an alternative to the above considerations that mechanical changes might not have a specific function, these changes in viscosity might help confining molecules of interest in the vicinity of the synapse. By sequestering these molecules because of higher stiffness and viscosity (implicating an increased energetical cost to move away from this zone), early mechanical changes might help integrate at the cellular scale the information input incoming from the single-receptor scale at the synapse. Considering this efficient processing from nano- to microscale is also worth integrating in mechanistic description of early immunological signaling, including models considering a frictional coupling of the TCR to the cytoskeleton (Our study highlights that variations of both elastic and viscous properties are relevant to understand immune cell mechanics during activation, as well as their relationship in the form of the loss tangent η, and how the latter evolves over time. All the leukocytes that we tested show very large changes in both elastic and viscous properties, but monitoring the time evolution of the loss tangent exhibits a mechanical fingerprint specific to cell types. It is tempting to speculate that the evolution of the loss tangent during activation can become a valuable tool to discriminate between healthy and pathological leukocytes, as already suggested by considering static values of η (Finally, our observations suggest a possible generalization to cells other than leukocytes. In line with what was observed by Thoumine et al. () in fibroblasts or Abidine et al. in epithelial cancer cells (), we propose that getting stiffer and more viscous while spreading is a common behavior across cell types. The time evolution of the loss tangent during cell spreading remains to be explored.P.-H.P., Y.H., and J.H. designed experiments. A.Z., S.V.M.-C., A.S., F.M., Y.H., P.-H.P., and J.H. performed experiments. A.Z., A.S., Y.H., P.-H.P., and J.H. analyzed the data. A.B., S.D., E.H., S.D.-C., H.-T.H., A.I.B., Y.R.C., Y.H., C.H., and O.N. contributed material. P.-H.P. and J.H. wrote the manuscript with helpful critical reading by the other authors.Supporting material can be found online at Document S1. Supporting materials and methods and Figs. S1–S10Document S2. Article plus supporting materialLateral resistance capacity of stiffened steel plate shear wallsThe steel plate shear wall system has been used in a number of buildings as an innovative lateral force resistance system. Stiffened steel plate shear walls possess greater stability and energy absorption during dynamic loading, such as during seismic loading, when compared with unstiffened steel plate shear walls. Openings, however, often exist in the steel plate shear walls due to various functional requirements of the structure. These openings may negatively impact the overall capacity of the shear wall, necessitating additional stiffening. Therefore, an experimental research program was instituted to investigate the seismic behavior of stiffened steel plate shear walls, with and without openings. Strength, stiffness, ductility and energy absorption were evaluated based on the results of reversed cyclic loading tests on three specimens. Two of the test walls had openings, while one wall was constructed without any openings. The test program results showed that stiffened steel plate shear walls exhibit satisfactory seismic behavior, and, as expected, the strength and stiffness characteristics of the walls were reduced in walls with openings. In addition to the test program, an analytical study utilizing a beam–shell mixed Finite Element (FE) model of a single-story wall panel with boundary columns is made to determine the critical factors influencing the shear strength reduction of stiffened wall panels with the opening. Furthermore, extensive numerical calculation and parametric analysis are conducted to derive a simplified formula for the determination of the shear strength reduction coefficient. In addition, complex elasto–plastic FE models of the three specimens are developed to investigate in detail the lateral force resistance behavior of stiffened steel plate shear walls. Good agreement is observed between the experimental and numerical results. Finally, a design method for calculating the lateral resistance capacity, based on the test program and the FE model analysis, is recommended to be used for the routine design practice of stiffened steel plate shear walls.► Experimental research program on seismic behavior of stiffened steel plate shear walls was instituted. ► Formula for determination of shear strength reduction coefficient of stiffened wall panels with opening is derived. ► Design method for calculating lateral resistance capacity of stiffened steel plate shear walls is recommended.The steel plate shear wall (SPSW) system has been used in a number of buildings in North America and Japan as an innovative lateral force resistance system. SPSW systems, in early stages of development, were treated for design and analysis purposes like vertically oriented plate girders Due to the excessive volume of steel consumed and the associated increase in cost, thick SPSW systems have been gradually replaced by thin SPSW systems. Thin SPSW systems have been studied by many researchers In addition to this research, a “Strip Model” was proposed However, the design codes mentioned require that SPSW only resists the horizontal loads, while the boundary columns of the SPSW system resist the vertical loads. In order to comply with this requirement, the field construction sequence has the main frame columns and beam elements erected first, and steel shear wall panels are then installed or attached to the main frame elements. However, this sequence may lead to the insufficient lateral stiffness of the main frame and a significantly longer duration of construction. As a result, SPSW stiffeners could be utilized, in the proper sequence, to prevent early buckling of steel plates subjected to the vertical load. Further, the load–displacement hysteretic loops show a significant pinch effect due to the early buckling of unstiffened steel plates with an attendant reduction in energy-consuming capacity, whereas stiffened SPSWs exhibit better seismic resistance characteristics. In the early 1970s, Takanashi et al. In addition to solid SPSWs, systems with openings, necessitated by the functional requirements of the structures, have gradually received attention in recent years. Three kinds of opening formats for steel plate shear walls have been reported in literature, as shown in (a)–(c), respectively. Perforated steel plate shear walls were first proposed and experimentally studied by Roberts and Sabouri-Ghomi (b) shows unstiffend SPSWs with full openings, in which an interior column connects the main steel frame to the SPSW system along on edge of the opening. Li (c) to determine the failure mechanism. They then proposed a methodology of analysis for lateral resistance capacity of unstiffened SPSWs.(d) represents SPSWs with partial openings, as studied in this paper. These walls are similar to those utilized in the Tianjin International Financial Conference Hotel in Tianjin in China. Vertical and horizontal stiffeners are provided to prevent premature buckling of steel plates and to reinforce the openings.Because of the lack of experimental and theoretical research on SPSWs with openings in the literature, with or without stiffeners, an integrated research program was developed. This program includes an experimental program, detailed finite element simulations and theoretical parametric studies for design recommendation purposes. The main object of this research is to develop a calculation method to determine the lateral resistance capacity of SPSWs for routine design practice, utilizing a shear strength reduction coefficient of stiffened wall panels with openings.The prototypes of the experimental program test units are located on three floors of the Tianjin International Financial Conference Hotel in Tianjin in China. Three representative steel plate shear walls were selected for the 1/5 scale model tests based on their overall configurations. The first test specimen is configured with an SPSW with openings and is designated as SPSW-1. The second test specimen, an SPSW without any openings, is designated as SPSW-2. The third test specimen is an SPSW with both openings and an interior column and is designated as SPSW-3.The overall dimension of each of the three test panels are similar as shown in . The thickness of the SPSW panels, in each case, is 4 mm. The boundary columns are concrete filled steel tube (CFST) columns. A heavy steel I-shaped beam, 300×180×20×20, was placed on the top of the top panel to avoid local buckling of the end where the ram applied the horizontal load and provided uniform transfer of the load to wall panels and columns. The bottoms of the test specimens were connected to a rigid steel I-shaped beam, 990×800×30×40, which was anchored on the ground. The bottom half-panel and the top panel were designed to simulate the boundary conditions found in routine design practice. The position and dimension of openings are as shown in . U-shaped section 24×12×3 stiffeners were welded on both sides of the wall panels to prevent premature buckling of wall panels under the service load and to provide additional stiffening at the openings. Rectangular sections, 30×14, were welded on one side of the wall panels at the bottom of each opening in order to simulate the lateral constraint action provided by the concrete slabs of the actual structure. Photographs of portions of the actual test specimens are shown in The material properties of steel and concrete are shown in shows the initial measured out-of-plane deformation for the bottom half-panel, and the first and second level SPSW wall panels and the beams of the three test specimens, where the northward out-of-plane deformation is positive, while the southward out-of-plane deformation is negative. The maximum initial out-of-plane deformation of the wall panels is 16 mm, 12 mm and 9 mm for the three specimens respectively, while the maximum of the steel beams is 18 mm, 9 mm and 11 mm, respectively. The dimensionless parameter β is employed for investigating the influence of initial out-of-plane deformation where δimp is the magnitude of initial out-of-plane deformation, b is the plate width, and h is the plate height. Thus, the maximum β of three specimens can be calculated as 0.018, 0.012 and 0.011, respectively. The study conducted by Behbahanifard Each test specimen was situated with the panel parallel to the east–west axis, standing on the north side of the panel and facing south. The vertical loads were firstly applied at the top of the CFST columns by two vertical hydraulic jacks for three units, representing the action of gravity loads. For SPSW-1 and SPSW-2, both of the values of two vertical loads were 500 kN, whereas for SPSW-3, the loads provided by the western and eastern hydraulic jacks were 400 kN and 800 kN, respectively, and a girder of large stiffness was placed at the top of the interior column and the eastern column in order to make the vertical load provided by the eastern hydraulic jack equally applied to the interior column the eastern column. Horizontal loads representing the action of an idealized earthquake were then applied by two actuators that were connected to the top beam on one hand and to the reaction wall on the other hand. Two triangular supports were designed as lateral support devices to prevent the global out-of-plane deformation of specimens. The specimens were anchored to the laboratory base through a rigid beam. The typical test setup is shown in The horizontal loads were imposed using load-control scheme and then displacement-control scheme. The detailed loading procedure is as follows: (1) the horizontal loads were applied in three levels using a load-control scheme before the yielding of specimens and repeated only once at each control point; and (2) the horizontal loads were imposed using a displacement-control scheme after the yielding of specimens that could be known when an inflection appeared and repeated twice at each control point. When the lateral load dropped below 85% of the maximum load, the test could be stopped. illustrates the arrangement of various instrumentations utilized to measure displacements as well as strain. The instrumentation utilized as well as the configuration for SPSW-1, SPSW-2, and SPSW-3 were similar. S1 and S2 are MTS Company digital load cells with a working range of −250 mm to 250 mm, and were used to monitor the horizontal input loads, while S3 and S4 are Chengdu Servo Hydraulic Equipment Company digital load cells with an upper working range 600 kN, and were used for vertical loads. Five LVDTs, D1–D5, arranged horizontally, were used to obtain the lateral displacements of each level. Two LVDTs D6 and D7 were used to eliminate error induced by any bottom plate and rigid beam slip. Two pairs of LVDTs were arranged diagonally to measure the shear deformation of the first and third level panels. Four LVDTs were placed perpendicular to the wall panels to measure out-of-plane deformations. Moreover, a number of strain rosettes were arranged to measure the steel plate shear strains, and strain gauges were placed at various locations to measure the plastic development level of the columns, beams and stiffeners.(a)–(c) shows global failure modes of the three specimens. It can be observed that for SPSW-2, the buckling extended diagonally over the entire height of the specimen. The SPSW-1 openings, enhanced by stiffeners, inhibited the propagation of global buckling and the buckling was less significant than for SPSW-2. The interior column in test specimen SPSW-3 prevented the development of global buckling more effectively than the stiffened openings in test specimen SPSW-1 and the local buckling only appeared locally in each story panel. illustrates typical failure patterns observed in the three test specimens. Fracturing of the steel plates occurred at the opening in Level 1 on both SPSW-1 and SPSW-3. Out-of-plane deflection of the western column and tension field fracture were observed in the later phase of loading for SPSW-2.Little out-of-plane deformation was observed before yielding in any of the three specimens, demonstrating that the design principles of stiffened steel plate shear walls were achieved for each of the three specimens.Applied lateral load versus measured test specimen top displacement response is shown in for each of the three test specimens. It can be observed that the expected satisfactory seismic behavior of the SPSW systems was confirmed by test results. The lateral resistance capacity and the lateral stiffness of SPSW-1 were smaller to those of SPSW-2 and SPSW-3 respectively, indicating that the lateral resistance capacity and lateral stiffness may be reduced by wall openings and increased by the addition of interior columns. Moreover, the pinch effect of the hysteretic loops of SPSW-3 was significantly less than that of SPSW-1, demonstrating that the use of an interior column may improve the overall wall stability resulting in increased energy-consuming capacities of the system.It should be noted however, that some voids were present in the base area of the CFST column with compression buckling observed for the eastern column of SPSW-1. This may account, in the latter phase of loading, for the rapid decrease of the system strength.According to the research work conducted by Park to reflect the shear deformation of wall panels, where the representation of αi (i=1,2) and di (i=1,2,3,4) are shown in shows shear load versus shear angle responses of third level wall panels of specimens. Several significant observations can be made from . First, it can be observed that the shear stiffness of SPSW-1 was smaller than that of SPSW-2, demonstrating that the opening had a negative influence on the shear stiffness of the wall panel. Second, since the compressive buckling behavior of the steel plate of SPSW-1 far from the opening was more significant than that of the steel plate reinforced by stiffeners near the opening, the shear deformation of the wall panel was much smaller when load was applied from the west rather than from the east, with the wall panel shear deformation developing continuously when the load was applied from the east. Third, the shear deformation of the SPSW-2 wall panel without the opening, when load was applied from the west or east, was similar due to the geometric symmetry of the specimen. Last, the shear deformation of the SPSW-3 wall panel with the opening was larger than that of the wall panel without the opening. This demonstrated that the reduction effect on the shear stiffness of the wall panel due to opening was not completely compensated for by reinforcing the openings with stiffeners., the yield and ultimate points are determined from the lateral load versus top displacement skeleton curves shown in lists the measured characteristic loads and displacements for each of the test specimens. The ductility factor μ is expressed as the ratio of the ultimate displacement Δu to yield displacement ΔY and is also shown in According to the discussion mentioned above, the opening imposes a significant and adverse influence on the shear strength of wall panels. A single-story wall panel with boundary columns is selected as the basic numerical example, as shown in . Based on this basic example, the parametric analysis can be carried out to investigate the influence of different parameters on the reduced strength of stiffened wall panels with the opening so that the simplified formula can be finally derived. also illustrates the nonlinear beam–shell FE model of the basic numerical example using the general FE package ANSYS 12.0 Compared with boundary columns, the axial stiffness of wall panels is small, thus only carrying a small portion of vertical loads, based on which it is assumed that the boundary columns carry the whole vertical loads and the wall panels are under a pure shear state. shows the influence of boundary columns on the shear strength of the wall panel with the opening. The results given in (a) and (b) are based on the FE model of an single-story wall panel with the opening and boundary columns shown in , and that of a wall panel with the opening simply supported on four sides under a pure shear state, respectively. It can be observed that the confinement effect of boundary columns has a remarkable influence on the shear strength of wall panel with the opening. For the wall panel with the opening but without boundary columns, the shear loading capacity may be reached when the steel plate near the opening yields so that the strength of the steel plate cannot be fully developed. However, for wall panels with the opening and boundary columns, the shear loading capacity can increase continuously until almost the entire steel plate yields under shear, which indicates the boundary columns could enhance the shear loading capacity of wall panel under the lateral loads as shown in In addition, on one hand, the flexural stiffness of the steel beam is much larger than that of the wall panel for the actual SPSW system and the concrete slabs between stories provide a strong constraint for the wall panel, and on the other hand, the confinement effect of boundary columns already makes the shear strength of the wall panel with the opening fully developed. That is why the steel beam is not modeled, the influence of which is only simulated by constraining the rotation of wall top and wall bottom, different from the boundary column, which has no constrained rotational degree of freedom in order to make sure the boundary column does not carry any shear load, working only as constraints to wall panels. The boundary condition and load mode of the FE model are also shown in For the convenience of discussion, two significant concepts are defined here.How to achieve the design principle of stiffened steel plate shear walls for the numerical analysis is discussed first. The initial disturbance must be imported in the nonlinear buckling analysis of the wall panels. If the buckling strength is larger than the yield strength, the buckling will not occur before the ultimate loading capacity is reached. However, if the initial disturbance is not imported, the buckling will not occur even if the buckling strength is much smaller than the yield strength. Obviously, the yield rather than the buckling will occur if the initial disturbance is not considered in the model; that is, the ultimate loading capacity is equivalent to the yield strength for such a case. Therefore, the design principle of stiffened steel plate shear wall that requires the buckling does not occur before yield can be achieved through the FE model into which the initial disturbance is not imported.The shear strength reduction coefficient of stiffened wall panels with the opening should be further defined. The shear strength reduction coefficient of stiffened wall panels with the opening is defined aswhere Vsp,o is the shear strength of stiffened wall panels with the opening, which can be obtained from the numerical analysis, and Vsp is the shear strength of stiffened wall panels without the opening by the Von Mises yield criterion for pure shear throughout the entire panel. However, for unstiffened wall panels without opening, the yield may not occur throughout the panel, even if the constraint of boundary column is big enough to make the post-buckling strength of wall panel developed fully. The “Strip Model” has been employed to predict the shear strength by some researchers. Obviously, the shear strength of the stiffened wall panels is larger than that of the unstiffened wall panels.The factors reflecting the influence of the opening include opening area, panel width to height ratio, opening width to height ratio, opening horizontal and vertical position and flexural stiffness ratio of boundary column to wall panel. The opening area is apparently the most important factor that affects the shear strength reduction coefficient, the influence of which can be reflected using opening ratio χ aswhere A is the wall panel area, and Ao is the opening area. Then, the influence of other five factors except the opening area on the shear strength reduction coefficient is shown in It can be concluded from the discussion above that the main factors influencing the shear strength reduction coefficient include opening area, wall panel height to width ratio and opening width to height ratio (opening height to width ratio), based on which a simplified formula for calculating the shear strength reduction coefficient of stiffened wall panels with opening is derived.The simplified formula should have the following characteristics, that (1) opening ratio χ is the main factor, while the influence of other factors are relatively small; and (2) wf should approach 1 as χ approaches 0, and wf should approach 0 when χ approaches 1. Thus, the following formula is proposed to calculate the shear strength reduction coefficient wf:β={0.005(boho)2−0.094(boho)+1.089boho≥11.04−0.04(hobo)boho<1 gives the variation of wf with the change of opening ratio χ for different values of h/b, and give the variation of wf with the change of opening ratio χ for different values of bo/ho and ho/bo, respectively. It can be observed that (1) wf decreases with increasing of h/b; and (2) maximum of wf can be reached when bo/ho=1, and wf decreases when bo/ho changes to both sides of 1.In order to sufficiently verify the accuracy of proposed formula, large amounts of numerical results are obtained by the full combinations of various values of the three critical parameters χ, b/h and bo/ho (ho/bo) within the selected parameter range. Comparison between these numerical results and the formula predictions are carried out for each item of Eqs. , respectively. Good correlations can be observed between numerical results and formula predictions.In order to investigate the seismic behavior of stiffened steel plate shear walls intensively and propose the design method for calculating the lateral resistance capacity further, a numerical study is conducted using the general FE package MSC.Marc (2005r2) compares the failure patterns between experimental and numerical results. Global buckling modes of SPSW-1 and SPSW-2 with the buckles extending through the steel beams between stories are shown in (a) and (b), and a local buckling mode of SPSW-3 with the buckles occurring in stories is shown in (c), which illustrates the interior column provides a strong confinement to the wall panel. (d) and (e) show typical failure patterns of steel plates near the openings. It can be found that a good agreement is achieved between failure patterns predicted by using numerical models and observed in the test.Lateral load versus top displacement responses by numerical models are compared with the measured curves in . The experimental and numerical ultimate strengths for three specimens are shown in . Some voids in the base area of the eastern CFST column have a negative influence on the lateral force resistance behavior of SPSW-1, thus, the lateral resistance capacity of SPSW-1 predicted by the FE model is about 10% larger than that obtained by the test, whereas good correlations can be observed between the numerical and test results for SPSW-1 and SPSW-2. Conclusively, FE models of specimens are proved to be reasonable and accurate and can be used to conduct the parametric analysis further.A method to calculate the lateral resistance capacity of unstiffened steel plate shear walls has been proposed by Park et al. The overall shear loading capacity Vs is defined as the sum of the lateral loading capacity of the frame Vsf and the shear loading capacity of the wall panel Vsp (Vsp,o):(a), the lateral loading capacity of the moment frame action is developed by the plastic moments of frame members considering P–Δ effects of the axial force N aswhere Mpc is the ultimate moment of columns subjected to compression and beading, Mpb is the ultimate moment of steel beams subjected to bending The overall flexure loading capacity Vf is determined by the section bearing capacity of the system base on the basis of the cantilever beam action from Eqs. . The position of the plastic neutral axis can be obtained from Eq. (b). The prism compressive strength fc of the concrete material should be modified Tsc(b+bc)+Tc(x+bc2)+Tspx2+Tsp′(b−x)2=Nx−N(b−x)+MThe lateral resistance capacity of stiffened steel plate shear walls Vpred is determined as the minimum of Vs and Vf, and the corresponding action represents the failure mechanism of stiffened steel plate shear walls. compares the lateral resistance capacity between modified numerical results and formula predictions. The calculated values are in good agreement with the numerical results.The lateral resistance capacity of stiffened steel plate shear walls with openings and without openings is investigated in this paper, and the main research work is summarized as follows:Three stiffened steel plate shear wall specimens were tested to investigate preliminarily the seismic behavior. The test results showed that stiffened steel plate shear walls possess high strength, good ductility and satisfactory energy-consuming capacity, and the strength and stiffness were obviously reduced due to openings. Stiffeners can be used to reinforce the openings so that the stiffness and stability of steel plate shear walls with openings can be significantly enhanced.A beam–shell mixed FE model of a single-story wall panel with boundary columns is presented. Parametric studies based the FE model reveal that the critical factors dominating the shear strength reduction coefficient of stiffened wall panels with the opening are opening ratio, wall panel height to width ratio and opening width to height ratio (opening height to width ratio). A simplified formula is proposed and verified by large amounts of numerical results.Elasto–plastic elaborate FE models on stiffened steel plate shear wall specimens is developed to study the complicated behavior of stiffened steel plate shear walls. Good agreements can be achieved between the experimental and numerical results. Finally, a simplified design method for calculating the lateral resistance capacity is proposed based on the failure mechanism of stiffened steel plate shear walls with consideration of the moment frame action and the cantilever action.Study on the degradation of mechanical properties of corroded steel plates based on surface topographyDegradation laws of mechanical properties of corroded steel plates were studied by experimental method and numerical simulation method based on surface topography in this paper. First, Q235 steel plate was subject to accelerated corrosion with artificial salt spray, and the characteristics of the surface of corroded steel plate were measured by three-dimensional morphology observation instrument to obtain the values related to corrosion damage parameters, and the relationship between the surface characteristic parameters and the corrosion rate was established. Then the stress-strain curves and mechanical properties of the corroded steel plates were obtained by monotonic tensile test. Finally, the mechanical properties of steel plates with real corroded surfaces were studied by numerical simulation method with reverse engineering software Geomagic Studio and finite element software ANSYS, and the stress concentration phenomenon caused by corrosion pit was discussed. The results showed that: (a) the corrosion rate is within 15%, the stress-strain curves have obvious yield plateaus; (b) and with the increase of corrosion rate, yield plateaus, yield strength, ultimate strength, and fracture strength of corroded steel plates does not decrease much, but ductility significantly decreases; (c) when the corrosion rate is over 15%, all the mechanical property index significantly decreases; (d) the constitutive model was established, and the law of the variations of the parameters of the model was summarized; (e) the numerical simulation method is feasible compared with the experimental results.Steel structure has the phenomenon of corrosion damage if being exposed in the corrosive environment such as soil, air, acid rain, marine climate etc. for a long time The corroded surface of the material is rough and irregular In this paper, the damage parameters of the corrosion steel and their effects on the macro mechanical properties of the steel were studied from the angle of the surface feature, and the constitutive model of corrosion steel was established and the variation of parameters was analyzed.In addition to the experimental method, the numerical simulation analysis based on real surface topography is necessary. Because of the huge amount of 3D data points, it is very complicated and difficult to exchange data with ANSYS and import the data into ANSYS directly. Therefore, in order to use computer technology to reflect effectively the degradation of the mechanical properties of the corroded steel plate based on real surface topography, the Geomagic Studio There were nine sets of specimens named A0i–A8i (280 mm × 50 mm × 8 mm) Neutral salt spray accelerated corrosion test was conducted to obtain the corroded specimens, based on the standard of GB/T 10125–2012 . They were sprayed for 30 min with NaCl solution 4 times a day and rotated every day to provide uniform exposure to the salt spray. After exposed for several months, respectively, the specimens were retrieved and cleared away the corrosion products with dilute hydrochloric acid and distilled water, and then kept in CaO desiccator until the scanning test and tensile test. In order to achieve the mass-loss rates of the corroded specimens, they were weighed on an analytical balance before and after the accelerated corrosion test, and expressed in ρw (the weight loss rate or corrosion rate). The sampling time were the first group: 30 days, the second group: 110 days, the third group: 150 days, the fourth group: 250 days, the fifth group: 310 days, the sixth group: 370 days, the seventh group: 440 days, and the total experiment period was 440 days.The corroded specimens were subject to rust removal, and processed into the test pieces shown in , drawled a vertical line every 5 mm along the length direction, selected three points on each vertical line and measured residual thickness of the steel by vernier caliper (see The middle areas of both sides were measured by three-dimensional non-contacting surface topography (PS50 see ), and the size of the areas was 40 mm × 20 mm (40 mm along the length, and step size was 50 μm; 200 mm along the width, and step size was 50 μm), and a and b were used to name different sides. 3D data of each measurement area were obtained by professional 3D software, then the void volume ratio Vw, the average corrosion depth Dmean, the maximum corrosion depth Dmax and the related evaluation parameters Sa, Sq etc. were obtained.The continuous definition of Sa is given in Eq. And the void volume ratio Vw is the ratio of the void volume of the test area after corrosion to the volume of the smallest cube that can be encapsulated in the test area.Monotonic tension instrument model is DNS300, as showed in . The extensometer was positioned in the middle part of the test pieces with the gauge, the length of which was 50 mm. Test pieces would be loaded until fracture happened, and extensometer would be removed.The changes of the surface of the test pieces in the salt spray environment can be seen from the surface topography. The 3D surface topography is composed of three parts: True picture, color chart and color height. Only one-sided samples of part of the test pieces are listed due to the large amount of samples (see Observation and analysis of surface topography shows that: (a) in the initial stage of corrosion, only part of the test piece was severely corroded with many pinholes on the surface, and corrosion occurred in a vertical direction, which was shown clearly on the topography as well as seen with naked eye after dust removal; (b) as the corrosion time increased, the corrosion spread to the whole surface, and deeper and bigger holes appeared due to pinholes joined together slowly, and U - shaped etch pits, elliptical shaped etch pits, conical pits, etc. appeared; (c) at the late stage of the corrosion, pits continued to develop and spread, part of the which produced secondary pits, and part of the surface of the plate peeled off with the corrosion developing to uniform corrosion, however, the morphology became more complex.According to the experimental results, the corrosion damage parameters of the specimens A01–A81 are shown in that with the increase of the corrosion time t, average thickness hmean, corrosion damage parameters, such as corrosion rate ρw, void ratio Vw, average corrosion depth Dmean, maximum corrosion depth Dmax, Sa, Sq etc. increased, and conformed to BidoseResp model. For example, the relationship of corrosion rate with time is shown in . It can be seen that the curves are highly consistent with the model proposed by R.E. Melchers There are many methods to characterize the damage degree of the materials, but they have less contact with each other at present. Therefore, it is very necessary to establish the evaluation of different characterization methods, and to evaluate the development degree of corrosion steel in a more comprehensive way. The relationship between the corrosion rate and the surface characteristic parameters was established (see Eq. Dmax=593.356–593.356×exp−45.800ρw,ρw≤7%,R2=0.99156Dmax=119.947+6495.400ρw,ρw＞7%,R2=0.94479Dmean=278.491–278.491×exp−66.200ρw,ρw≤7%,R2=0.9964Dmean=−127.039+5245.300ρw,ρw＞7%,R2=0.98842Vw=5.429–5.428×exp−105.300ρw,ρw≤7%,R2=0.9915Damage morphology of the non-corroded steel and the steel under accelerated corrosion by the neutral salt spray are shown in . It can be seen from the experiment that (a) necking phenomenon still existed after loading to fracture of all the test pieces; (b) the surfaces of the steel plates were roughened due to corrosion and the fracture position changed with the non-corroded steel plate being in the middle and the corroded ones being shifted to the most vulnerable position or near the most vulnerable position. And observation and contrast Fracture morphology showed in : the fracture morphology of specimen with no corrosion or no obvious corrosion is basically groove type, and the edge is regular arc, which is the cup cone fracture, and consistent with the characteristics of ductile fracture ( (a), (b)). Fracture morphology of corrosion specimen that the surface has obvious corrosion pits is shear type or edge irregular type. Shear fracture is due to serious general corrosion, such as the A82 specimens ( (b)). And the specimens that corrosion morphology is obviously, stress concentration caused by the etch pits makes the irregular fracture path, such as the A73 specimens ( (d)); (c) Because of the damage and the uniformity of the surface caused by corrosion, and the influences of weak cross section and the stress concentration of the corrosion pits, large pits were detected where fracture happened. It is likely that the corrosion pits on the surface of specimens develop faster initiation and propagation of cracks in a material at high-stress levels.The nominal stress was calculated by initial cross-sectional area in the previous study. And it is much smaller than the real value in this way, which can affect the degradation of the mechanical property caused by the local pitting. Reasonable nominal stress was calculated by minimum cross-sectional area of the steel plate to get more close to it in this paper.According to the experimental results, the mechanical properties of the specimens A03–A83 and A02–A82 are shown in has shown that average thickness hmean, minimum thickness hmin and minimum section area Amin, and mechanical properties, such as the yield strength fy, ultimate strength fu, elastic modulus Es, elongation at break εbr etc. decreased with the increase of corrosion time. that, the corrosion rate is within 15%, with the degree of corrosion increasing, yield strength, ultimate strength, fracture strength, and elastic modulus of corroded steel plates does not decrease much, but ductility significantly decreases. When the corrosion rate is over 15%, all mechanical property indexes significantly decrease.The decline of the mechanical properties of the material is mainly due to the damage of the material surface caused by corrosion. On the one hand, the cross section decreases; on the other hand, it is the stress concentration of corrosion pits. The stress concentration increases the local stress level, which lead to the yield in advance and then accelerate surface to appear the plastic zone, resulted in inhomogeneous plastic deformation of the material center and surface layer, and the bigger the stress concentration coefficient, the weaker plastic deformation ability. Therefore, reduction of plasticity is likely due to the corrosion pits on the surface of specimens develop faster initiation and propagation of cracks in a material at high-stress levels.The relationship of fracture strain with corrosion rate is shown in where, εbr is fracture strain; ρw is corrosion rate(weight loss rate)., the four-stage model is applied in the monotonic loading curve of the steel plate: the first stage is the elastic section (O-Y); the second one is the yield section (Y-H); the third one is the reinforcement section (H-U); the fourth one is the ultimate load until the fracture phase (U-F), and the mathematical expressions are shown in Eq. σ=Esεε<εyfyεy≤ε<εshfu+fy−fuεu−εεu−εshP1εsh≤ε<εufu−fu−fbrε−εuεbr−εuP2εu≤ε<εbrwhere,Es is modulus of elasticity;fy is yield stress;fu is limit stress;fbr is fracture stress;εy is yield strain;εu is ultimate strain;εsh is strain for the hardening point;εbr |
is Fracture strain;P1 is shape parameter for the rising segment;P2 is the parameter for falling section.The comparison between the experimental model and the constitutive model curve is shown in that the results of model analysis are consistent with experimental study quite well. The corrosion rate is within 15%, the stress strain curves have obvious yield plateaus, and the degree of corrosion increasing, the yield plateaus shortened, yield strain and ultimate strain of corroded steel plates do not decrease much. When the corrosion rate is over 15%, the yield plateaus significantly shortened, and ultimate strain significantly decreases. The stress concentration caused by corrosion pits increases the local stress level, which lead to the yield in advance and then accelerate surface to appear the plastic zone, resulted in accelerating inhomogeneous plastic deformation of the material center and surface layer, shortened the yield platform, and the bigger the stress concentration coefficient, the shorter the yield platform.All the experimental data were fitted with the formula, and the values of the parameters of the model of each group were obtained, and the parameters of the constitutive model of the non-corroded and corroded steel plates are shown in Within the range of 40 mm × 20 mm, the data of about 320,000 3D coordinates were obtained from 3D surface of corroded steel by PS50 and the data can be used by Geomagic Studio to restore the physical model and the physical model which are transformed to the surface geometry model.A21 is taken as an example in this paper to display the steps of reverse reconstruction as follows:(1) Processing and application of point cloud data.The measurement area of surface topography is 40 mm × 20 mm, mainly at the stress area, where the distance between the two corrosion surfaces is the average thickness. After data alignment, removal of noise points, data reduction and other steps, the final results are shown in (2) Fast reconstructions of polygonal phase and corrosion surface.(a)). Then the surface patches will be created after the completion of the curvature line. The more the surface patches, the more accurate the curved surface will be in principle, but the maximum amount of patches that Goemagic Studio 2013 can combine is 999. Therefore, the 8 × 2 sets of data were studied in this paper, which makes the long edge data 48, and the short edge data 20, and multiple NURBS were obtained (see After the completion of the curved surface, the grid will be constructed, which will be used to fit the curved surface. The model of corrosion surface reconstruction will be obtained by combining NURBS surface (see ). Geometric reconstruction of the corrosion surface will be completed by Goemagic Studio, which paves the way for creating a three-dimensional solid model with ANSYS. Among the many formats of files conducted by Goemagic Studio, the IGS format can be received by ANSYS, thus, corrosion surface model of IGS format is stored to complete the whole process of the corrosion surface reconstruction model. Three dimensional solid model of strain gauge region (50 mm × 25 × maximum residual thickness-A21) is created by CATIA (see ) are created by the above method. And the stress distribution in the elastic stage by10 MPa is drawn in , the stress concentration phenomenon is obviously due to the complexity of the surface topography, and the maximum stress concentration factor appears in the surface position (3.176). The surface of the corrosion steel is formed by the uneven corrosion pits, and it makes the material itself is not continuous. The main stress line is curved at the edge of the rust hole under the action of axial tension, which improves the local stress level and affects uniformly distribution of the stress of the specimen section. Then the stress concentration caused by the rust pits not only resulted in the unequal tensile stress of three directions, but also increased the local strain rate at the same time, which lead to the yield in advance and then accelerate surface to appear the plastic zone, accelerate inhomogeneous plastic deformation of the material center and surface layer, result in micro cracks formed easily around the rust pit and gradually developed. Therefore, reduction of cross section and the stress concentration eventually leads to a decline in the strength and ductility of steel, particularly the ductility.Stress concentration factor of specimens is shown in The relationship between Kt and Sq/hmean is shown in , where, Kt is the stress concentration factor, Sq is given in Eq. , and hmean is the average residual thickness. It can be seen that the curve of Kt and Sq/hmean is found to fit the BidoseResp function model (see Eq. ), the curve of εbr and Kt is found to fit the exponential model (see Eq. ), therefore, the more rough the surface and the greater the loss of cross section, the greater the stress concentration factor, and the greater impact on the degradation of the mechanical properties. Eq. are all linked, which is to get the elongation at break through the surface damage.Kt=1.591+1.9160.7611+100.882−58.472Sqhmean+0.2391+1010.917−674.919Sqhmean are interconnectedness, which is to get the approximate elongation at break through the damage parameter obtained in different ways. It has a good reference value for the estimation of the life of the material and of the degradation of the mechanical properties in the external corrosive environment in the engineering practice.The docking of Data between Geomagic Studio and ANSYS is very good, and the two corrosion surface models imported in ANSYS were used as the two dimensions of the 3D model, and Boolean operations was applied to achieve the three-dimensional model after the creation of the cube. The size of the model was 50 mm × 25 mm.20 nodes and solid187 were applied in the 3D model in this paper, and the size of the mesh, obtained by free meshing, was 0.003, which was tetrahedral mesh (see ). In order to improve precision and reduce the computational cost, the length of mesh we divided on the corroded surface is 0.2 times as long as that on the area away from the corroded surface. Every model was divided into approximately 300 thousand units.According to the results of the test, the elastic modulus of the non-corroded steel plates E |
= 2.1 × 105 |
MPa, and the Poisson's ratio v |
= 0.3. It should be found the yielding point, hardening point, and ultimate point from experimental nominal stress-strain curves of A0, then several average points between the nodes should be found yet. Real stress and strain relationship should be inputted in ANSYS. Real stress = nominal stress × (1 + nominal strain), real strain = ln(1 + Nominal strain) (see The multi-linear kinematic hardening model and displacement loading method were adopted. The fixed end restraint was applied at − 25 mm at the end of one side of the model, which could simplify the calculation and was conducive to convergence. The displacement loading was applied at 25 mm at the end of the other side.In the case of A81, by analyzing some stress diagrams after time step loading, as showed in , the stress distribution of the surface is uneven because of the irregular surface. The area where the stress is maximum is located in some corrosion pits on the corroded surface. The damage of the steel surface caused by corrosion, on the one hand, is the reduction of the section caused by erosion; on the other hand, is the stress concentration caused by pitting corrosion. The generation of stress concentration improves the local stress level, makes the steel surface to advance into the yield stage, and causes the surface to accelerate into the plastic zone, causes core and outer surface of the steel material to produce uneven plastic deformation. The greater the degree of corrosion, the more obvious the decrease of the yield load, the ultimate load, and plastic performance under the load.By extracting the support reaction on every step, the load corresponding to the displacement was obtained, resulting in the load-displacement curve, then stress was obtained by loading divided by minimum plate thickness, and the strain was obtained by displacement divided by the primary scale. The nominal stress-strain curves of specimens under different corrosion degrees are shown in . Where mi represents simulated specimen., the simulated and experimental load-displacement curves are basically consistent. All of the elastic modulus, the yield load, and the text data of the ultimate load and the error of the simulated value are within a reasonable range. And the linear degradation law obtained from the numerical simulation and that obtained from the experiment were similar, and the values of strength degradation obtained from the numerical simulation were more obvious than those of the experiment. The simulation method presented in this paper can accurately predict the response of steel under monotonic loading, and it can be reducible to 3 zigzags, and can lay the foundation for the nonlinear analysis of the following components.(1) In the initial stage of corrosion, pinholes with small corrosion depth were mostly observed on the surface topography, and corrosion occurred in a vertical direction. With the increase of corrosion time, the pinhole corrosion pits gradually grew larger in a horizontal direction, and U - shaped etch pits, elliptical shaped etch pits, conical pits, etc. appeared. At the late stage of the corrosion, pits continued to develop and spread, part of which produced secondary pits, and part of the surface of the plate peeled off.(2) The regularities of damage parameter are highly consistent with the model for the natural marine climate. The relationship between the corrosion rate and the surface characteristic parameters in this paper was established.(3) It can be seen from the experiment date that the corrosion rate is within 15%, the stress strain curves have obvious yield plateaus, and with the degree of corrosion increasing, the yield plateaus shortened, and yield strength, ultimate strength, fracture strength of corroded steel plates does not decrease much, but ductility significantly decreases. When the corrosion rate is over 15%, the yield plateaus significantly shortened, and all mechanical property index significantly decreases. And the relationship of the fracture strain with corrosion rate was established.(4) It can be seen from the simulation analysis that the stress concentration phenomenon is obviously due to the complexity of the surface topography, and the maximum stress concentration factor appears in the surface position. The surface of the corrosion steel is formed by the uneven corrosion pits, and it makes the material itself is not continuous. The main stress line is curved at the edge of the rust hole under the action of axial tension, which improves the local stress level and affects uniformly distribution of the stress of the specimen section. Then the stress concentration caused by rust pits not only resulted in the unequal tensile stress of three directions, but also increased the local strain rate at the same time, which lead to the yield in advance and then accelerate surface to appear the plastic zone, accelerate inhomogeneous plastic deformation of the material center and surface layer, result in micro cracks formed easily around the rust pit and gradually developed. Therefore, reduction of cross section and the stress concentration eventually leads to a decline in the strength and ductility of steel, particularly the ductility.(5) The constitutive model of steel plates with different corrosion degrees was established, and the law of the changing of parameters with different corrosion degrees was summarized. Geomagic Studio and ANSYS were used to simulate and study the monotonic tensile mechanical properties of real corroded surfaces. The results show that the numerical simulation method is feasible. An experimental and numerical study is devoted to investigate the degradation laws of mechanical properties of corroded steel plates. It will further improve the theory to evaluate seismic performance of existing steel structure. And provide the technical basis for the civil engineering disaster prevention and reduction.Viscoelastic parameters of invasive breast cancer in correlation with porous structure and elemental analysis dataInvasive ductal carcinoma (IDC) is the most common and aggressive type of breast cancer. As many clinical diagnoses are concerned with the tumor behavior at the compression, the IDC characterization using a compression test is performed in the present study. In the field of tissue characterization, most of the previous studies have focused on healthy and cancerous breast tissues at the cellular level; however, characterization of cancerous tissue at the tissue level has been under-represented, which is the target of the present study.Throughout this article, 18 IDC samples are tested using a ramp-relaxation test. The strain rate in the ramp phase is similar for all samples, whereas the strain level is set at 2,4 and 6%. The experimental stress-time data is interpolated by a viscoelastic model. Two relaxation times, as well as the instantaneous and long-term shear moduli, are calculated for each specimen.The results show that the long-term and instantaneous shear moduli vary in the range of 0.31–17.03 kPa and 6.03–55.13 kPa, respectively. Our assessment of the viscoelastic parameters is accompanied by observing structural images of the IDCs and inspecting their elemental composition. It is concluded that IDCs with lower Magnesium to Calcium ratio (Mg:Ca) have smaller shear modulus and longer relaxation time, with a p-value of 0.001 and 0.01 for the correlation between Mg:Ca and long-term shear modulus, and Mg:Ca and early relaxation time.Our identification of the IDC viscoelastic parameters can contribute to the IDC inspection at the tissue level. The results also provide useful information for modeling of breast cancer.environmental Scanning Electron MicroscopeInvasive Ductal Carcinoma (IDC) is the most aggressive type of breast cancer, representing 80 percent of all breast cancer diagnoses. IDC starts in the milk duct and spreads to the surrounding tissues. The national cancer institute estimated that the probability of IDC development in the following ten years of life for 20-year-old women is 0.1%, whereas this value increases to 1.4 and 2.3% for 40 and 50-year-old women, respectively There are several modalities for non-invasive measurement of mechanical properties of tissues. Elastography is a method in which a stimulus is imposed onto the tissue, and the tissue response is studied using imaging techniques ]. This method can be used as a diagnostic tool for clinical examinations with the advantage of high sensitivity, quantitative measurements, and low costs Biological tissues show nonlinear and the time-dependent behaviors. The time dependency can be addressed by the viscoelastic material models. Zhang et al. This paper offers a number of viscoelastic parameters for identifying the mechanical behavior of invasive ductal carcinoma in a ramp-relaxation test. Of particular interest and novelty is testing the IDC at the tissue level, which is suitable for extracted samples during surgical biopsies. Using the mechanical test data at the tissue level, viscoelasticity of samples is quantified by two relaxation times and two shear moduli. In addition, there is considerable interest to correlate the macrostructural features with the microstructure of IDC. In this regard, the micropore structure of IDC and the elemental composition are provided. This study has the novelty of correlating the mechanical viscoelastic parameters to the tissue porosity and Mg:Ca ratio as an indicator of tissue malignancy. The strength of this correlation is justified and significant relation is observed between macro- and micro-structural features.Eighteen IDC samples from 18 female cases are provided from Besat medical center (Hamedan, Iran). The samples belong to cases within the age of 40–50. The pathology reports confirmed the invasive ductal carcinoma for all tissue specimens. presents five samples with their approximate dimensions in the Cartesian coordinate system. All of the followed procedures were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) complying with the Helsinki Declaration of 1975 as revised in 2013.Informed consent was obtained from all patients for being included in the study. The specifications of tumor samples, including the geometrical dimensions along with the physiological age of the donor, are listed in . Regarding the irregular shape of each sample, each sample is in initially converted into a cylindrical shape with diameter and thickness of 10 mm. The samples are preserved by placing them in 0.9% of saline solution at 25 °C and kept away from direct sunlight An unconfined compression test has been commonly used for the tissue characterization ). The device is equipped with a load cell of 1 kgf capacity (BONGSHIN, Korea). This load cell provides a sensitivity of 3 mV/V equal to 0.03 N and an accuracy of 0.5%. The indentor is equipped with a cylindrically shaped probe with a diameter of 5 mm for the measurement. An algorithm is provided to detect the contact point between the sample and the load cell. The samples are preloaded in terms of the strain from 2 to 6% during the ramp phase.During the loading process, the lateral surface of the cuboid-shaped specimen is free, whereas the top surface is loaded, and the bottom surface is located on the base plate of device. A Teflon tape is attached to the base plate to minimize friction effects shows the loading diagram during the compression test. Each IDC sample is compressed at three strain levels of 2, 4 and 6% and a strain rate of 0.1 s−1 in the ramp phase. The compressive load is calculated from the contact point. Subsequently, in the relaxation procedure, the samples remain in the hold phase for 180 s. Each sample is allowed to relax after each test in 0.9% saline solution for at least 20 min For the viscoelastic characterization of IDC, the generalized Maxwell model consisting of two Maxwell arms is selected. In a previous study by the author of the present study For this configuration, a relationship between the total stress σtotal(s) and the total strain εtotal(s) in the Laplace domain is described as:σtotal(s)={Ke+K1ss+1τ1+…+Kjss+1τj}εtotal(s)where, Ke is the isolated spring constant and Kjs are constants of the springs located in the Maxwell arms, j is the number of the Maxwell arms, and τjs are the relaxation times and the relaxation time is obtained using the following equation:, for the generalized Maxwell model with two Maxwell arms, two relaxation times would be attained. In the stress-relaxation test, the strain level is constant:leading to the following equation in the Laplace domain:Thus, for the stress-relaxation test, combining σtotal(s)={Ke+K1ss+1τ1+…+Kjss+1τj}ε0s(s)An inverse Laplace transformation then leads to the stress-strain relation in the time domain as:where, σtotal(t) is the total stress of the viscoelastic model in the time domain. According to , a new material property is defined by where, Erel is Young's modulus in the relaxation phase. By assuming the tumor samples as incompressible materials [], with Poisson's ratio of 0.5, the relationship between Young's modulus in the relaxation and the shear modulus takes the following form:where, G is the shear modulus. By substituting , the long-term shear modulus (G∞), and the instantaneous-shear modulus (G0) [The instantaneous modulus denotes the initial elastic response and the long-term modulus refers to the material behavior at the equilibrium state. In the relaxation test, with recording force and time during the hold phase, where, F is the recorded force at the hold phase, and A is the cross-sectional area of the IDC sample. By considering j = 2, for the proposed viscoelastic model, the final form of the force-strain equation reads:where, τ1 and τ2 are relaxation times. The relaxation time with a higher value is called the late relaxation time and is indicated by τ1 whereas, the smaller one is referred to as the early relaxation time and is denoted byτ2.The mechanical response of biological tissues depends on the tissue structure. Environmental Scanning Electron Microscope (ESEM) is used to determine the topography of the porous structure of the IDC samples after the compression test. Throughout scanning, the elemental composition of samples is determined. Structural images are obtained by Quanta 200, vacuum mode of ESEM (FEI Company, USA), and the elemental composition is evaluated by Energy-Dispersive X-ray Spectroscopy (EDS) in Quanta 200, vacuum mode of ESEM with SDD detector. ESEM is suitable for the observation of hydrated and wet tissue samples. When equipped with an EDS, a quantitative analysis of chemical elements would become available for the tissue specimens. In the present study, Mg:Ca ratio is measured for all tissue specimens using EDS.The force versus time data is collected for the IDC samples during the relaxation period at three strain levels of 2, 4 and 6%. The raw data is provided for one IDC sample in b presents related experimental errors for the same sample at 4% strain. According to the error plots, the uncertainty of force measurement is less than 0.03 N for all IDC samples.Repeatability is checked at three strain levels for each IDC sample to note less than 1% deviation in the force measurements. Moreover, a sensitivity analysis is conducted by increasing the strain level and studying its effect on the measured force. To this end, the strain level is increased by 200 and 300%, and the minimum and maximum force variations are recorded. It is observed that by 200% increase in the strain, the minimum increase in force is 17.14% for IDC #3, whereas the maximum increase in force figures out at 33.02% for IDC #9. Meanwhile, when the strain is increased by 300%, the minimum force is increased by 10.3% pertinent to IDC #16 and the maximum force increases by 35.13% for IDC #11.The recorded force-time data at the hold phase is interpolated using . The optimization task depends on the selection of suitable initial parameters of this equation. Since the trend of RMSE variation as the objective function of the optimization procedure is unknown, the selection of initial values is difficult; meanwhile the initial values are very important in finding the global minimum of the function rather than finding the local minima. To reduce this problem, the function optimization is performed using different initial values, manually. In particular, each of the parameters is given a range and the result is evaluated. The range of initial values is spanning orders of magnitude from 0.1 to 10, where the fitting quality is reasonable. This interval is divided by 18 points. As a result, 20 optimization results are obtained for each case. The evaluation of results shows that there is small difference between the obtained parameters. Accordingly, result with the minimum RMSE is selected for further analysis. However, according to the nonconvex shape of the fitting function, it is not guaranteed that the global minimum is obtained, although the obtained values are considered as the optimized values. The obtained parameters are used to calculate the shear moduli, as well as the relaxation times. In , the fitted curves to the experimental data is plotted for four samples. The goodness of fit is evaluated in terms of R-squared (R2) and the root mean squared error (RMSE) in table S1 of supplementary material. According and table S1, R-squared values are very close to 1 and RMSE values are close to zero; both indicate excellent performance of the proposed model during the relaxation period.In the present analysis, it is assumed that effect of nonlinear viscoelastic behavior is negligible. However, according to the experimental results in this is not the case, i.e., the tissue response does not linearly vary with the loading, which is the strain. As a result, the stress-strain relationship is nonlinear. For some materials, the strain level at which the material becomes nonlinear changes with increasing time. Therefore, extremely long-time predictions may require the use of nonlinear viscoelastic constitutive equations, even for very low strain levels. Consequently, nonlinear stress-strain relations must be established in such a way that the magnitude of the applied strain is taken into account. Nevertheless, a deeper analysis of the impact of non-linear viscoelastic behavior on the stress relaxation predictions should be performed to include the dependence of results on the loading history. It is worth mentioning that when notifying the nonlinearity effects, it is necessary to establish the degree of non-linearity. In addition to the linear assumption, the results of the present study belong to a constant strain level during the relaxation period. Although in the experiments the value of the maximum force depends on the strain level by the end the ramp phase, it is better to include the data of varying strain, which is not considered in the present study. Therefore, the model parameters depend on the strain level through the maximum measured force. To be more inclusive, experiments should be conducted for different types of loading, in which the model parameters can be estimated versus the strain and time., five parameters are extracted for each tissue sample, Ke, K1, K2, τ1 and τ2. Other parameters are calculated using these parameters and by implementing . Based on different microstructure of each specimen, the value of these parameters varies between the specimens. Additionally, regarding the viscoelasticity of IDCs, the model parameters change with the strain and the strain rate. Consequently, the procedure of determining the viscoelastic parameters should be performed separately for each sample and for each strain. To avoid overfitting, the number of data is increased for each IDC at a specified strain; as for each specimen, data is collected every 0.015 s during 180 s of the test duration.The instantaneous and long-term shear moduli, as well as the early and late relaxation times are determined using the experimental stress-time data. Table S2 of supplementary material reports the exact values for the mentioned viscoelastic parameters. present a bar plot of the relaxation parameters for IDC samples. According to this figure, the instantaneous shear modulus is significantly greater than the long-term modulus during 180 s of the relaxation period. For some IDC samples, e.g. case #5 at 4% strain, the instantaneous shear modulus is about ten times greater than the long-term shear modulus. In this regard, the average ratio of instantaneous modulus to long-term modulus is 6.0, 3.4, and 2.6 at three strain levels of 2%, 4%, and 6%, respectively.a and b, the highest and the lowest values of the long-term shear modulus are attributed to sample #5 at 6% strain and sample #3 at 2% strain, respectively. In addition, the highest and the lowest values of the instantaneous shear modulus are linked to samples #5 and #4, respectively, both at 4% strain. One also notes that by increasing the strain level, G0 is reduced from 2 to 4% strain, though the converse is true for samples #5, #9 and #15.Since the shear modulus is obtained from the spring constants using , it represents the elastic behavior of the tissue. Table S2 of supplementary material reports two dashpot constants located in the Maxwell arms for the IDC samples at three strain levels. An analysis of the dashpot constants indicates that the numerical values of η1 and η2 are significantly different as the ratio η1η2 varies from 0.4 to 40. Moreover, both damping coefficients decrease with the strain level; therefore, the tissue relaxation could be delayed at higher strain levels. Furthermore, as can be seen in c and d, for most of the presented cases, both early and late relaxation times follow a decreasing trend when the strain level increases from 2 to 4 and 6%. Samples #2, #3 at 4% strain (τ1), samples #3, #4, #8 at 4% strain (τ2), and samples #4, #11 at 6% strain (τ2) do not follow the same trend. This can be attributed to the issues related to the IDCs microstructure, selection of the material model and the experimental errors. The IDC has anisotropic properties due to irregular arrangement of micropore structure within the tissue, therefore, the mechanical response depend on the loading direction on the sample. This may result in variation between the mechanical response of different samples and at different strain levels. Additionally, anisotropic behavior of the biological specimens has effects on the outputs of the selected material model. Another source of difference for the mentioned cases may originate from the stress relaxation procedure between successive experiments. Due to differences in the microstructure of IDCs, the extent of stress relaxation and recovery could be different. Eventually, experimental errors in data collection and calculation of the relaxation times may affect the accuracy of results. The above-mentioned issues not only have effects on the trends of relaxation times variation with the strain level, but also may be a source of uncertainty and scatter of the results among other samples. All in all, 7 cases among all 108 cases (at all strain levels and for both relaxation times) show a different trend. Therefore, about 93% of cases show a reduction in the relaxation time with the strain.Curve fitting of the results for the IDC samples, as presented by a for IDC #1, shows that the maximum force is recorded at the beginning of the relaxation period. Subsequently, the required time for 60 and 40% reductions of the maximum force is calculated for the IDC samples at three strain levels. a provides a zoomed view of the force versus time for IDC #1 during the first 20 s. The arrows in a indicate the occurrence of 60 and 40% of stress relaxation process. The force data are normalized by the maximum force (b) and the required times for 60 and 40% reductions of the maximum force for 18 specimens are reported in , at higher strain levels, more time is required for mechanical stress relaxation. In this regard, for some IDC samples, stress relaxation to 40 and 60% of the initial value does not occur during the specified relaxation period. The blank data in means that for some IDC sample, stress relaxation by 40% from the maximum value does not occur during the period of experiment. Additionally, the required time for stress relaxation increases with the strain level. The average time for 60% stress reduction is 4.7, 6.2 and 14.2 s at the strain levels of 2, 4 and 6%, respectively. Numerical values of the required time for stress relaxation by 40 at 6% strain and stress relaxation by 60 at 2% strain both for IDC #2, are not consistent with other reported values. As previously mentioned for IDC #2, the anisotropic structure of the specimen and direction of the applied load with regard to the fibers’ orientation within the specimen, as well as the experimental errors could be the reason for the abrupt values reported for this specimen. It should be mentioned that the value of relaxation times is sensitive to small variation in the measured force, as an increase of about 0.3 N in the measured force for IDC #3 (presented in c) results in 2.7-fold variation in the calculated relaxation time. Performing the mechanical tests by considering the anisotropic properties of tissue may reduce the possible errors.ESEM images of IDC samples at a magnification level of 200× are shown in . By employing image-processing, the porosity of IDC samples is extracted from ESEM images. K-means clustering algorithm is implemented for image-processing in order to calculate the porosity of samples. In this regard, pixels of RGB color image are clustered in an optimized number, in a way that variations between clusters converge to zero. By identifying the desired cluster with the minimum variation, the number of blackest pixels (pores) is obtained. Finally, to calculate the porosity based on the clustered pixels, porosity=numberofblackestpixelstotalnumberofpixelsintheimage, porosity values equal to 0.29 and 0.33 are obtained for IDC #1 and IDC #3, respectively. According to the data provided in table S2, the instantaneous and long-term shear moduli of samples #1 and #3 are plotted in a and b indicates that the numerical values of the instantaneous and long-term shear moduli of IDC #1 are higher than those of IDC #3 at all strain levels. Considering the definition of shear moduli, which represents the elastic behavior of tissue, IDC #1 is identified as stiffer than IDC #3. This finding is in agreement with the topology of the porous structure of IDC samples, i.e., the volume fraction of the solid matrix is higher in IDC #3 compared to that of IDC #1. A comparison between the tissue stiffness through the long-term shear moduli at 2% strain and the volume fraction of solid matrix (1-porosity) is presented for IDC samples in c. According to this figure, the IDC stiffness increases with the volume fraction of the solid matrix.Through EDS analysis, the elemental composition of the IDC samples is deduced with listing the Mg:Ca ratio. There is considerable interest to correlate the macrostructural features (viscoelastic parameters) with the elemental composition of IDCs. However, there is very little detail known about the chemical composition of the cancer cells.To evaluate the Mg:Ca ratio for the IDC samples, result of a research by Scott et al. Statistical analysis is performed to show the relationship between Mg:Ca ratio and the viscoelastic parameters derived for each IDC sample. According to the sample size, Spearman correlation is used with rs being an indicator of the strength of correlation and p-values are calculated using IBM SPSS Statistics 26.0.0.0. P-values more than 0.1 and between 0.1–0.05 indicate very weak and weak evidences for the proposed hypothesis, whereas, p-values between 0.05–0.01 and less than 0.01 indicate strong and very strong evidences, respectively. The results show that at 2% strain rs = 0.99, and a very strong and positive monotonic correlation exists between Mg:Ca ratio and G∞. Also, a strong and negative correlation is observed for Mg:Ca ratio and τ2, where rs = −0.7. A strong and negative correlation is found between Mg:Ca ratio and η1 where rs = −0.9. Finally, a moderate and negative correlation exists between Mg:Ca ratio and τ1 where rs = −0.5. presents the correlation coefficient for other strain levels. The p-values indicate that there are significant differences between the Mg:Ca ratio and G∞ with a p-value of 0.001 and also between Mg:Ca and τ2 with p-values of 0.01 at 4% strain and 0.01 at 6% strain, and between Mg:Ca ratio and η1 with a p-value of 0.005 at 4% strain. A difference could be observed between Mg:Ca ratio and η1 with a p-value of 0.005 at 6% strain. However, the strength of the correlation is deteriorated for the correlation between Mg:Ca and τ1, where the p-value is equal to 0.1., the ratio of Mg:Ca is plotted together with the long-term shear modulus, and η1 for the IDC samples at the strain level of 2%. According to , IDC #3 has the minimum G∞ and Mg:Ca ratio and the maximum η1, whereas the maximum of G∞ and Mg:Ca ratio and the minimum of η1 could be observed for IDC #4. It could be inferred that the stiffness increases with Mg:Ca ratio, whereas, the viscosity is reduced.In the present study a new approach is carried out for the identification of invasive ductal carcinoma. Through this approach, some parameters are introduced which can suitably capture the IDC viscoelasticity. Of particular interest and novelty is testing the IDC at the tissue level. The instantaneous and long-term shear moduli, as well as the early and late relaxation times are determined using the experimental stress-time data. According to findings (), the instantaneous shear modulus is significantly greater than the long-term modulus during the relaxation period. The decrease in shear modulus during the relaxation period is due to the viscous behavior of the tissue. In the hold phase, springs located in the Maxwell arms have a minor load-bearing contribution compared to the dashpots. Over time, the contribution of Maxwell springs diminishes, leading to a reduction in the long-term shear modulus. Additionally, the study of the relaxation times indicates that there is a considerable difference between the early and late relaxation times. Distinct values of two shear moduli and two relaxation times indicate that the implemented viscoelastic model is suitable for IDC characterization particularly at the tissue level.Additionally, it is of particular interest to assess the potential of the proposed parameters in distinguishing normal tissue from breast tumors. According to data published in There is no published data on the relaxation behavior of IDC through viscoelastic modeling at the tissue level. However, to prove the reliability of this study, comparisons are provided between the results of the present study and those of the most relevant studies. Due to scatter of results among IDCs, the closest data to the reported values by relevant studies are selected. compares the relaxation times of the present study and those reported in In another interesting study, Carmichael et al. There is considerable interest to correlate the extracted macrostructural features with the microstructure of IDCs. This study has the novelty of correlating the mechanical viscoelastic parameters to the tissue porosity and Mg:Ca ratio as an indicator of tissue malignancy. The strength of this correlation is justified and significant relation is observed between macro- and micro-structural features (). According to the results, an IDC sample with a rather compact structure and a small porosity has a higher Mg:Ca ratio demonstrating a more elastic response.It is worth mentioning that there are some concerns on the model parameters. Soft tissue tumors are not isotropic and exhibit directional anisotropy in three-dimensional space. The material anisotropy is mainly attributed to the variations in the direction of collagen fibers. The mechanical response of tumoral tissue depends on the collagen fibers content and alignment, which is not considered in the present study, because of the complexity in modeling. Instead, the overall effect of collagens network is considered on the mechanical behavior. Additionally, the fibers orientation has variation among the specimens, which could be attributed to the stage of tumor growth. This variation is neglected in the mechanical characterization of IDCs. Therefore, although the model parameters are useful for the assessment of the IDC specimen, it cannot provide detailed information on the microstructure of tissue, including the fibers orientation, tissue anisotropy and stage of tissue malignancy. Eventually, experimental errors in data collection and calculation of the relaxation parameters may affect the accuracy of results. This issue could be a source of uncertainty and scatter of the results among tissue specimens.IDC viscoelastic response is identified using a ramp-relaxation test. To this end, 18 IDC samples undergo a compression test with force versus time being recorded. During the test, the strain rate is constant, whereas the strain level is set at 2, 4 and 6% during the ramp phase. The recorded data are fitted to the generalized Maxwell model with five elements allowing for the determination of the model parameters. By employing these parameters, two relaxation times, which are referred to as the early and late relaxation times, are obtained. Additionally, the numerical values of the instantaneous and long-term shear moduli are obtained. The results show that the relaxation times and the shear moduli have distinct values. Moreover, the goodness of fit of our viscoelastic model to the experimental data is evaluated through the use of two measures being R-squared (R2) and the root mean squared error (RMSE). The average values of R2 and RMSE are evaluated as 0.98 and 0.006, respectively. Study of the viscoelastic parameters at three different strain levels indicates that:➢ Both early and late relaxation times decrease with the strain level for the IDCs.➢ At higher strain levels, more time is required for the relaxation of IDC samples from the mechanical stress.➢ According to the IDC sample properties, the relaxation procedure may not thoroughly happen during the specified period.In order to find the correlation between the IDC tissue structure and the viscoelastic parameters, ESEM images and the elemental composition of the IDCs are carefully investigated to note that:➢ Based on the investigation of the elemental composition, the average Mg:Ca ratio is rather high for IDC tissue.➢ A higher value of Mg:Ca ratio corresponds to a higher long-term shear modulus with a p-value of 0.001, which indicates a very strong relationship.➢ A higher value of Mg:Ca ratio corresponds to smaller damping constant with an average p-value of 0.005, which indicates a strong relationship.➢ A higher value of Mg:Ca ratio corresponds to smaller early relaxation time with a p-value of 0.01, which indicates a very strong relationship.Results of the present study indicate that the viscoelastic parameters could provide valuable information to shed light on the IDC behavior. This will assist the diagnosis. Furthermore, recording the transient variation of the IDC mechanical properties will make the proposed method suitable for a follow-up procedure.All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2013. Informed consent was obtained from all patients for being included in the study.This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.The authors declare that they have no conflict of interest.Supplementary material associated with this article can be found, in the online version, at doi:A high-strength, ductile Al-0.35Sc-0.2Zr alloy with good electrical conductivity strengthened by coherent nanosized-precipitatesDuctility and electrical conductivity of metallic materials are inversely correlated with their strength, resulting in a difficulty of optimizing all three simultaneously. We design an Al-Sc-Zr-based alloy using semisolid extrusion to yield a good trade-off between strength and ductility along with excellent electrical conductivity. The Al-0.35Sc-0.2Zr wire with a diameter of 3 mm exhibited the best combined properties: a tensile strength of 210 ± 2 MPa, elongation of 7.6% ± 0.5%, and an electrical conductivity of 34.9 ± 0.05 MS/m. The average particle size of nanosized Al3(Sc, Zr) precipitates increased from 6.5 ± 0.5 nm to 25.0 ± 0.5 nm as the aging time increased from 1 h to 96 h at 380 °C, accompanied by the corresponding volume fraction variation from (6.2 ± 0.1) × 10−4 to (3.7 ± 0.1) × 10−3. As proved by transmission electron microscopy observation, the high strength originates from the effective blockage of dislocation motion by numerous nanosized Al3(Sc, Zr) precipitates whilst both electrical conductivity and ductility remain at a high level due to the coherent precipitates possessing an extremely low electrical resistivity.The demand for electric power increases rapidly with the fast development of economic activities, leading to an increasing requirement for aluminium (Al) alloy wires bearing a good combination of mechanical properties and electrical conductivity. The current-carrying capability of wires has been established to be directly proportional to the square root of the increase in the wire temperature, i.e., the increasing current-carrying capability leads to an increase in wire temperature. Currently, the Al-Mg-Si alloys system is widely used for wires, which can be divided into two types according to tensile strength, i.e., high strength and moderate strength. Among them, tensile strength of high strength Al-Mg-Si alloy is 295–315 MPa, with corresponding elongation of 3.0%-3.5% and conductivity of 30.5–30.7 MS/m, whilst those of moderate strength Al-Mg-Si alloy wire are 240 MPa, 3.5% and 33.9–34.2 MS/m, respectively Al-Sc-Zr alloys are key metallic material with a great practical potential given their unique combination of high-temperature creep resistance Concerning alloy composition engineering in designing the next generation of Al alloys, scandium (Sc) contributes significantly to strength through coherent nanoscale Al3Sc precipitates Pure Al (≥99.7 wt%), Al-2.12Sc (wt%) and Al-4.6Zr (wt%) were heated with specific ratios at 720 °C for 1200 s in a medium-frequency induction furnace (50 kW, KGPS50-2, China), under a protective atmosphere of argon gas. shows the weight percentages of impurities in pure Al (99.7%). Electrical conductivity decreases with increasing impurities, which increase electrical resistivity by intensifying electron scattering. Subsequently, Al-xSc-0.2Zr alloy wires were prepared by a continuous semisolid extrusion process After the semisolid extrusion processing, Al-xSc-0.2Zr rods were divided into several parts, kept at 630 °C for various duration of 6, 12, 24, 36, and 72 h (solid solution processing), quenched in water at 15 °C, and then further aged at 380 °C for 1–96 h to obtain Al3(Sc, Zr) precipitates with different Fv/d values. Furthermore, Al-0.35Sc-0.2Zr rods were cold-drawn into wires with various diameters (D = 10.2, 8.5, 7.6, 6.3, 5.5, 4.5, 3.6, 3.0, 2.0, and 1.0 mm) using a drawing machine at a speed of 0.05 m/s.Tensile specimens were cut from the middle parts of the obtained wires with various diameters (D = 10.2, 8.5, 7.6, 6.3, 5.5, 4.5, 3.6, 3.0, 2.0, and 1.0 mm) using electron discharge machining. The tensile tests were conducted at room temperature on a CMT 5105 PC-controlled mechanical testing system (MTS Co. Ltd, USA) at a constant crosshead speed of 5 × 10−3 mm/s, corresponding to an initial strain rate of 1 × 10−4/s. Three parallel tests were performed on specimens with the same diameter to assure the reliability of the testing.Electrical resistance of the studied wires was measured at room temperature, using a digital DC resistance tester (PC36C, China) with a current range from 100 μA to 10 A and a resistance range from 200 μΩ to 1999.9 Ω. Each mean resistance value was obtained from five replicates of the specimens with a length of 800 mm. The measured resistance value can be adjusted to the standard one (20 °C) according to the following equation:where R20 and RT are resistance value at 20 °C and T °C, respectively, and α is temperature coefficient of resistance (TCR), with:where K20 is the conductivity rate (20 °C) in units of %IACS (International annealed copper standard, 100%IACS = 58 MS/m), ρ20 is resistance rate, Ω mm2/m, S is the intersection area (mm2) and L is the length (m) of the conductor.To study the microstructure of the Al-0.35Sc-0.2Zr alloy, specimens were collected from the central area of the cylindrical wires parallel to the extrusion direction and mechanical polishing from both sides to a final thickness of 50 μm. Subsequently, foils of 3-mm diameter were punched and thinned using an ion beam thinner (Gatan, Inc., Pleasanton, USA). Transmission electron microscopy (TEM) observation was performed under a field-emission-gun (FEG) Tecnai G2 20 microscope (FEI, Oregon, USA) operating at an accelerating voltage of 200 kV. The dislocation density was estimated by counting individual dislocations crossing the thin foil surface shows the effect of aging time on tensile strength and electrical conductivity of Al-Sc-Zr alloys aged at 380 °C. For each alloy, tensile strength increased with increasing aging time from 0 to 36 h and then remained constant after 36 h of aging. One can clearly see that the addition of Sc element led to an increase in tensile strength. Of the four alloys, Al-0.4Sc-0.2Zr alloy revealed the highest tensile strength during the whole duration of the aging treatment, which can be attributed to its high Sc content because the Zr content was maintained for the four alloys. As the aging time reached 36 h, the tensile strength of the Al-0.4Sc-0.2Zr alloy increased to 182 MPa, which was approximately 45 MPa higher than that of the Al-0.25Sc-0.2Zr alloy. For applications of Al-Sc-Zr alloys, this increment is very large and encouraging because high strength can improve the security and service life of this type of alloy wire. Obviously, the effect of aging time on tensile strength is trivial when the aging time exceeded 36 h.Regarding electrical conductivity, the increase in aging time from 0 to 48 h led to increasing electrical conductivity in the four alloys heated at 380 °C. The change in electrical conductivity was very similar to that of tensile strength, and it remained constant after 48 h. The addition of Sc resulted in lower electrical conductivity for the series of Al-Sc-Zr alloys. For example, Al-0.25Sc-0.2Zr alloy revealed the highest value of 36 MS/m after aging for 48 h at 380 °C. In contrast, as the Sc content increased to 0.4 wt%, electrical conductivity of Al-0.4Sc-0.2Zr alloy showed the lowest value of 34 MS/m after aging for 48 h at 380 °CWe conclude that 48 h is the cost-efficient aging time to obtain a wire with high strength and good electrical conductivity. As mentioned above, a trade-off between strength and electrical conductivity in the studied alloys is inevitable. Considering the factors of cost, strength and electrical conductivity, Al-0.35Sc-0.2Zr alloy was therefore selected as an optimal candidate in this study, and the corresponding microstructure and properties after aging, mechanical and hot-resistance tests were investigated in detail in the following sections.Bright-field TEM micrographs and selected-area-electron-diffraction (SAED) patterns of the Al-0.35Sc-0.2Zr alloy after different heat treatments are presented in is the presence of a number of spherical precipitates, which are dispersed throughout the matrix. With the increasing aging time, the average diameter and volume fraction of the precipitates gradually increased (). For example, the average particle size of the precipitates was 6.5 ± 0.5 nm after aging at 380 °C for 1 h. ((a)). However, this size increased to 25.0 ± 0.5 nm after aging at 380 °C for 96 h ((d)). The corresponding volume fraction increased from (6.2 ± 0.1) × 10−4 to (3.7 ± 0.2) × 10−3 (). Energy dispersive X-ray spectroscopy (EDX) analysis suggested that the precipitates mainly contained Al, Sc, and Zr with a chemical composition in wt% of approximately ∼97.22 Al, 2.11 Sc, and 0.77 Zr at position A, along with 96.02 Al, 2.55 Sc, and 1.43 Zr at position B. The atomic ratio of Sc to Zr decreased from 2.74 to 1.78, suggesting that Zr content increased at the expense of Sc in the precipitates as the aging time increased from 1 h to 48 h. It should be pointed out that EDX analysis provides qualitatively chemical composition with a wide error range of 2%-20% associated with the surface status of specimen as well as the selected correction factor. Hence, we used EDX to determine the chemical nature (i.e. qualitative analysis) in the precipitates. The quantitative analysis was determined the results of X-ray diffraction (XRD) and TEM analysis.The precipitates of these compositions were referred as Al3(Sc, Zr) with a L12 structure similar to Al3Sc (e, f), respectively. The average particle size of the precipitates increased from 10 nm to 15 nm with increasing aging time. One can see that the particle size increased not only with increasing temperature but also with the increasing aging time.In addition, the corresponding SAED patterns at positions A and B are shown as (g, h). Two systems of periodic spots can be seen in (g). One set of spots were observed, as indicated by a rectangle, showing R11 = 6.75, R12 = 9.54, along with an angle of 90° between R11 and R12. Therefore, these spots are indexed as the Al3(Sc, Zr) phase (simple cubic (L12), a = b = c = 0.4089 nm) according to the [110]β zone axis. Another set of spots indicated by a rhombus were indexed as α-Al (face-centred cubic (FCC), a = b = c = 0.4049 nm) matrix according to the [110]α zone axis. In (h), one set of spots indicated by small rectangle reveal R11 = 6.89, R12 = 6.90, and an angle of 90° between R11 and R12. These spots were indexed as Al3(Sc, Zr) phase (simple cubic (L12), a = b = c = 0.4089 nm) according to the [001]β zone axis. The other set of spots connected by a large square were indexed as α-Al (face-centred cubic, FCC, a = b = c = 0.4049 nm) matrix according to the [001]α zone axis. Thus, the spherical precipitates were confirmed to be Al3(Sc, Zr) phase with a L12 structure similar to Al3Sc To explore the effect of aging time on mechanical properties, tensile tests were conducted on the Al-0.35Sc-0.2Zr alloys aged at 380 °C for different durations (). After solution treatment, the obtained alloy wire exhibited a very low tensile strength of 76 MPa and a much higher elongation of 58%. As the aging time increased to 36 h, the tensile strength increased to 163 MPa, twice as high as that of the alloy without aging treatment. With the further increasing aging time from 36 h to 96 h, the tensile strength remained constant. However, the elongation varied in a totally different way from how the tensile strength varied, decreasing to 34% after aging for 36 h at 380 °C, then further decreasing to as low as 25% as the aging time increased to 96 h.A series of cold drawing was conducted on Al-0.35Sc-0.2Zr alloy after aging for different durations at 380 °C to obtain wires with various diameters. (a) shows the variation in tensile strength and elongation for Al-0.35Sc-0.2Zr alloy aged for different time durations with various diameters. As mentioned above, with the increasing aging time, tensile strength increased but elongation decreased. In contrast, the decreasing nominal diameter of wires led to an increase in tensile strength and a decrease in elongation. For example, after aging for 60 h at 380 °C, the tensile strength and elongation were 162 MPa and 25% for the Al-0.35Sc-0.2Zr wire with a diameter of 10.2 mm. However, as the wire diameter decreased to 1.0 mm, tensile strength increased to 210 MPa and elongation significantly decreased to 4%. An optimized combination of tensile strength and elongation was achieved by a wire with a diameter of 3.6 mm aged at 380 °C for 60 h, revealing a tensile strength of 210 MPa and elongation of 7.2%, which were 32% and 260% higher, respectively, than the values of 159 MPa and 2.0% from the international classification for standards (ICS) (b) shows the effect of both aging time and diameter of the wires on electrical conductivity of Al-0.35Sc-0.2Zr alloy. For Al-0.35Sc-0.2Zr alloy with a specific diameter, the electrical conductivity increased as the aging time increased, although the trend was significantly different. With aging time increasing from 24 h to 48 h, electrical conductivity increased from 34.2–35.1 MS/m for the wires with a diameter of 10.2 mm. However, as aging time further increased from 48 h to 60 h, electrical conductivity increased slightly from 35.1 to 35.2 MS/m. Electrical conductivity slightly decreased with the decreasing diameter of the wire aged for a specific time. For example, the diameter of Al-0.35Sc-0.2Zr wires decreased from 10.2 mm to 1.0 mm with increasing strain of the cold drawing, resulting in a slight decrease in electrical conductivity from 35.2–34.6 MS/m at the same aging conditions (380 °C/60 h).After aging at 380 °C for 60 h, Al-0.35Sc-0.2Zr wires with various diameters were maintained at 230 °C and 400 °C for 1 h. Subsequently, tensile tests were conducted to investigate the variation in strength resulting from different temperatures, as shown in (c), compared to the results tested at room temperature ((a)). At the three test temperatures, tensile strength of Al-0.35Sc-0.2Zr wires with a specific diameter decreased with increasing temperature, although the effect of temperature on tensile strength was weak, especially between 230 °C and 400 °C. However, the variation was dramatically different for various diameters, i.e., the thermal stability was closely related to the diameter of the Al-0.35Sc-0.2Zr wires, and that of the thick wires was higher than thin wires. The decrease in tensile strength was only ∼5 MPa for the Al-0.35Sc-0.2Zr wire with a diameter of 10.2 mm as temperature increased from room temperature to 400 °C. However, over the same temperature region, tensile strength decreased from 210 MPa to 195 MPa for Al-0.35Sc-0.2Zr wire with a diameter of 1.0 mm.In Al-xSc-0.2Zr alloys, dimension, size, and distribution of the Al3(Sc, Zr) precipitates all played an important role in the ultimate mechanical properties supporting the conclusion that Al3(Sc, Zr) precipitates can still serve as effective obstacles to the movement of dislocations in Al-0.35Sc-0.2Zr alloy aged for different durations. Some dislocations were terminated by several nanosized precipitates ((a, b)). As dislocations were pinned by precipitates, higher stress is required for the dislocations to escape the blockage of the precipitates to proceed moving. During the deformation of Al-0.35Sc-0.2Zr alloy, numerous dislocations stopped and tangled around the nanosized Al3(Sc, Zr) precipitates ((a, b)). Several studies have shown that rare earth atoms can effectively impede dislocation movement (c, d) shows high-resolution transmission electron microscopy (HRTEM) images of Al3(Sc, Zr) phase and α-Al matrix after tensile deformation, and by referring to the SAED patterns in (e, f), the Al3(Sc, Zr) precipitates were coherent with α-Al matrix along [001]Al direction, with an interplanar spacing of 0.2025 nm for (0-20)Al plane of the α-Al matrix and 0.4089 nm for (010)Al3(Sc,Zr) plane of the Al3(Sc, Zr) particles. The lattice mismatch between the Al3(Sc, Zr) precipitates and the α-Al matrix along with the resulting stress field can influence the deformation of the alloys by restricting their dislocation movement (c, g)). This observation is much interesting because deformation twins have not been experimentally confirmed in single or polycrystalline pure Al, even when shock-loaded at low temperatures It is conceivable that as deformation proceeded, more dislocations stopped and tangled around Al3(Sc, Zr) precipitates. Consequently, stress should have increased rapidly to a level that induced localized plastic flow. Dislocations in a material can interact with the precipitates in either of the following two ways. If precipitate particles are small, dislocations would cut through them. For larger precipitate particles, looping or bowing of the dislocations would occur and result in longer dislocations. Hence, dislocations will preferably cut across the obstacle if they are coherent precipitates or will bypass if they are incoherent where M is Taylor factor, fv is volume fraction of the precipitates, b is Burgers vector (2.85 × 10−10 m), and d is precipitate diameter. G is the shear modulus (∼35 GPa). Volume fraction of the precipitates was estimated as fv = 3.7 × 10−3 = 0.37% by TEM observation (), owing to the precipitates preserving a phase totally different from that of the matrix. Consequently, the increase in yield strength from precipitates was determined using Eq. as 400 MPa. Obviously, the high strength in current sample originates significantly from the strengthening effect of the high density of nanoparticles. Nevertheless, here the estimated value is much higher than the strength tested by tension. The obvious difference should be associated with early failure in the specimens resulted from localized stress concentrations. Another reason of discrepancy is that the Al3(Sc, Zr) are coherent precipitates whist Eq. A decrease in both particle size and spacing of adjacent precipitates increases not only the stress required for dislocation movement but also dislocation density, leading to the increased strength of the studied alloys. The increasing volume fraction of the spherical Al3(Sc, Zr) phase formed in Al-xSc-0.2Zr alloys with increasing Sc concentration resulted in an increase in tensile strength (). For the specific Sc content of 0.35 wt%, as the aging time increased from 1 h to 96 h, despite the average diameter increased from 6.5 ± 0.5 nm to 25.0 ± 1.0 nm, the volume fraction of the spherical Al3(Sc, Zr) particles increased from (6.2 ± 0.1) × 10−4 to (3.7 ± 0.2) × 10−3. Following Eq. , the strength associated with precipitation strengthening should have increased due to the reduced spacings between the spherical Al3(Sc, Zr) particles. As the dislocations moved into the vicinity of the spherical Al3(Sc, Zr) particles, they piled up because of impeding effect of the precipitates (), leading to an increase in the strength of the alloy. This conclusion was supported by tensile tests (During deformation of the Al-0.35Sc-0.2Zr alloy, numerous tangled dislocations were present around the Al3(Sc, Zr) precipitates (), suggesting that the nanosized particles in the Al-0.35Sc-0.2Zr alloy were useful for retaining a high dislocation density. Our results show that the ratio of volume fraction to diameter of the Al3(Sc, Zr) precipitate, fv/d, remarkably increased from 9.0 × 10−5 to 1.5 × 10−4 nm−1 with an increase in aging time from 1 h to 96 h. Obviously, the nanoscale precipitates facilitated the retention of high density of dislocations in Al-xSc-0.2Zr alloys, thereby preventing slip and increasing strength. Furthermore, nanosized Al3(Sc, Zr) precipitates modified the plastic deformation in their vicinity and promoted the formation of deformation bands, leading to an increase in strength.The extending extrusion technique was utilized here to result in a large effective strain after one pass, as high as that of ECAP processing after 5 passes. Thus, the new technique is cost-effective and energy-efficient. Most importantly, dendrite segregation was avoided, resulting in more uniformly distributed spherical grains which are beneficial for homogeneous deformation to improve ductility. Parallel studies show that superplastic behaviour of Al alloy 7075 should be related to the similar preparing process (accumulative roll bonding) Aging treatment can promote precipitation. As shown in , the volume fraction of nanosized precipitates increase with increasing aging temperature and time. The interactions between dislocations as well as dislocations and precipitates can impede dislocation motion. The increased volume fraction of precipitates can facilitate the dislocation storage during deformation, thus increasing work hardening. Recently, a novel Al-Cu-Li alloy exhibits a strong aging response in different aging processes due to different strengthening phases Electrical conductivity of Al-0.35Sc-0.2Zr alloy decreased with decreasing aging time durations along with the decreasing diameter of wires (where ρ˜M is electrical resistivity of pure Al, ∑iρiciis that of solute atoms (ρi is specific resistivity of the ith solute and Ci is concentration of this solute such as Sc and Zr atoms), a/λp1/2 is contribution of precipitates to resistivity (a is a constant and λ is the spacing of the precipitates with unit in nm). According to Eq. , electrical resistivity is positively proportional to the concentration of solute atoms and negatively proportional to the spacing of precipitates. Thus, it is possible to improve conductivity by aging to obtain an increase in the spacing of precipitates and a decrease in the concentrations of solute atoms. The addition of Sc, Zr led to a decrease in the electrical conductivity due to the increasing electron scattering, which could be attributed to the increasing lattice distortion, concentration of point defects and solute atoms. The increasing temperature and duration of the aging treatment can effectively decrease the concentration of solute atoms, defects and the related lattice distortion in matrix, thereby increasing conductivity ((b)). That is to say, a trade-off between good conductivity and high strength can be made using proper aging treatment. For example, although the spacing of the precipitates decreased from 130 nm to 110 nm with increasing time from 48 h to 96 h for the Al-0.35Sc-0.2Zr wire aged at 380 °C, the volume fraction of the precipitates increased from (3.1 ± 0.1) × 10−3 to (3.7 ± 0.1) × 10−3, which was responsible for the decreasing solute atoms in matrix. Consequently, a good conductivity of 39.2 MS/m and high strength of 162 MPa can be maintained at the whole duration of aging treatment (Electrical conductivity and ductility are inversely related with strength. Nevertheless, our present results reveal that a good trade-off between strength and ductility as well as electrical conductivity can be achieved using coherent nanosized Al3(Sc, Zr) precipitates. The strength can be improved precipitation strengthening and whilst electrical conductivity and ductility remain at a high level due to the low level of defects associated with the good coherency between the nanosized Al3(Sc, Zr) precipitates and the Al matrix. Using chemical composition design, a continuous rheo-extrusion process, heat treatment and cold drawing, an Al-0.35Sc-0.2Zr conductor with a diameter of 3 mm has combined properties including a tensile strength of 210 ± 2 MPa, an elongation of 7.6 ± 0.5%, and a conductivity of 34.9 ± 0.05 MS/m that are better than those of IEC 62004-2007 with tensile strength of 162 MPa, elongation of 1.7% and a conductivity of 30.8 MS/m The fact that tensile strength decreased but electrical conductivity increased with the increasing solution time is believed to be related to the precipitated phase dissolved into the Al matrix and the decreased dislocation density. As the aging time increased, tensile strength increased initially and then remained constant because of the increasing size and content of the Al3(Sc, Zr) precipitates. The small, dispersed Al3(Sc, Zr) precipitates can be effective obstacles to the movements of dislocations and sub-grains, leading to an increase in the tensile strength. However, the electrical conductivity decreased due to the increasing electron scattering effect. During cold drawing, the tensile strength increased and the elongation decreased with the decreasing diameter of the studied wires. The electrical conductivity of alloy wires decreased with an increase in the number of drawing passes. The declining scope of electrical conductivity was maintained at less than 0.58 MS/m. This is because the equiaxed grains were elongated with the increase in the number of drawing passes, forming deformation bands in the drawing direction. With the increase in the dislocation and vacancy densities, the electronic scattering effect was enhanced, resulting in a decreasing conductivity of the alloy wires.In this work, Al-xSc-0.2Zr (x = 0.2, 0.25, 0.30, 0.35, 0.40) alloys were successfully processed via semisolid extrusion, solution treatment, aging treatment, and cold drawing. Al-0.4Sc-0.2Zr alloy revealed the highest tensile strength during the whole duration of the aging treatment, which is ascribed to the maximum addition of Sc of all the four alloys. After aging at 380 °C for 36 h, tensile strength of Al-0.4Sc-0.2Zr alloy was 182 MPa and approximately 45 MPa higher than that of Al-0.25Sc-0.2Zr alloy, indicating an increase in materials quality and service life. The average particle size of nanosized Al3(Sc, Zr) precipitates increased from 6.5 ± 0.5 nm to 25.0 ± 0.5 nm as the aging time increased from 1 h to 96 h at 380 °C, accompanied by the corresponding volume fraction variation from (6.2 ± 0.1) × 10−4 to (3.7 ± 0.1) × 10−3. The small and dispersed Al3(Sc, Zr) precipitates can effectively suppress the movements of dislocations, leading to an increase in tensile strength. Electrical conductivity increased with increasing aging time and increasing wire diameter, due to the decreasing solute atoms, defects and lattice distortion in the matrix. Al-0.35Sc-0.2Zr wire with a diameter of 3 mm exhibited the best combined properties: a tensile strength of 210 ± 2 MPa, elongation of 7.6% ± 0.5%, and an electrical conductivity of 34.9 ± 0.05nMS/m, compared with those of the IEC standard 62004-2007 (tensile strength of 162 MPa, elongation of 1.7%, and electrical conductivity of 34.8 MS/m).Professor Guan’s research interests focus on short metal forming process and microstructure and property tailoring of light alloys. His group invented a novel short metal-forming process, continuous rheo-extrusion process, which enables one-step metal forming from liquid metal to the final products. Compared to conventional metal extrusion process, energy consumption and cost of this new technique is significantly reduced. His group also developed a new method of preparing ultra-fine grain alloys, ACEF-accumulative continuous extrusion. By virtue of this novel processing method, ultra-fine grain alloys with changing cross-sections and infinite length can be continuously prepared, and the preparation route is obviously shorter than traditional methods. The relevant equipment was independently developed and has been applied to industry. The invention of combined process of continuous rheo-extrusion and accumulative continuous extrusion was awarded gold prize in the 44th International Exhibition of Inventions of Geneva. As the project leader, Prof. Guan has undertaken six projects of the National Natural Science Foundation of China including one State Key Project and one Outstanding Young Scientist Foundation Project. His scientific achievements were published on Acta Mater., Scientific Reports, Acta Biomater., etc., and his eighty-one literature is indexed by SCI, whose citation exceeds one thousand times. As the first contributor, he obtained nine authorized national invention patents and has been granted Liaoning Second Prize of Technological Progress, Liaoning Youth Science and Technology Award and the first prize of China Scientific Papers on Nonferrous Metals etc. Three graduate students directed by him obtained Excellent Master Degree Papers of Liaoning Province. He has been grantedsix talent projects above provincial or ministerial level, including the first session of China National Funds for Outstanding Young Scientists. Prof. Guan also won the honorary title of Top Ten Science Talents of Liaoning Province.Yongfeng Shen is currently Professor and Ph.D. Supervisor at School of Materials Science and Engineering, Northeastern University. He received his Ph.D. degree from Institute of Metal Research, Chinese Academy of Sciences in 2006. He has worked as the visiting scientist at Pacific Northwest National Lab (PNNL) of USA (2009–2010). He is also the degree thesis evaluation experts of Department of Education for Materials Science and Engineering, and the member of Liaoning provincial science and technology experts. Shen’s research interests include the design and development of nanostructured metallic materials; advanced high strength steels including thin strip and thin slab casting of high strength steels; thin film and coatings related preparation and characterization methods. Abovementioned areas of interest involve the use of a broad spectrum of materials characterization techniques including X-ray diffraction including high-energy neutron diffraction, transmission and scanning electron microscopy, electron back scattered diffraction (EBSD), Transmission electron microscopy (TEM), and mechanical testing including nanoindentation and tensile/compressive tests. In particular, Shen has made scientific contributions to the separation and purification of nonferrous metals during enterprise work experience. In the past ten years, as a chief investigator, he has succeeded in winning many competitive research grants including two programs from the National Natural Science Foundation of China, one General Armament Department Project, etc. Prof. Shen has contributed more than 80 original journal publications (including top ranking journals such as Science, Acta Materialia, Scientific Reports, Bioresource Technology, Scripta Materialia, Materials Science and Engineering A, etc.), 12 patents including 2 international patents and delivered more than 10 plenary/keynote/invited talk at conferences/symposia, which have attracted over 3000 citations (Scopus). Prof. Shen has won some prestigious awards including 44th International Exhibition of Inventions Geneva- Gold medal (2016), 44th International Exhibition of Inventions Geneva- Silver medals (2016), The First Prize of Liaoning Province Natural Science, Provincial Science and Technology Department, Liaoning (2014), The First Prize of National Scientific and Technological Progress, State Council, China (2012).Molecular dynamics simulations study of nano particle migration by cluster impactMolecular dynamics (MD) simulations are performed in order to investigate the radiation effects of a huge and slow gas cluster for the surface cleaning process. When a large argon cluster with the size ranging from 20,000 to 300,000 is accelerated with a total of 30 keV, each constituent atom carries very low energy ranging from 1.5 eV/atom to 0.1 eV/atom. In many cases, the cluster does not penetrate the solid target surface but is deflected in a lateral direction. This collisional process results in a high density particle flow spreading along the surface plane due to cohesion of the cluster, which suggests the capability to modify the irregular surface structure, without damage in the target. The MD simulations demonstrate that such a huge cluster sweeps a nano particle (NP, 3 nm in radius) attached on a planar silicon target's surface. From the investigation of various conditions of cluster impact, it is found that the migration distance is correlated with the kinetic energy applied on the NP by the impact of cluster atoms. Additionally, the MD results suggest the existence of optimized parameters for the maximum migration distance for the offset distance between the cluster and the NP, and the cluster size for constant total energy (equivalent to energy per atom or kinetic energy density). The optimized offset distance was estimated as the summation of radii of the incident cluster and the NP. The optimized energy per atom was suggested around 0.6 eV/atom, where the cluster efficiently spreads in lateral direction keeping higher kinetic energy density of particle flow.The gas cluster ion beam (GCIB) is a unique ion beam technique where a gas cluster, a large aggregation of source atoms/molecules, is generated as a cluster, and then ionized, accelerated, and radiated on the target. Several experiments In the previous works performed in both experiments For the cluster ion beam process, the incident energy per atom is an important parameter to cause surface damage, and it can be controlled by changing the cluster size. For example, when the total incident energy is 10 keV, the X1000 and X10000 clusters carry 10 eV/atom and 1 eV/atom, respectively. However, it is not clear whether such low-damage irradiation conditions have enough capability to remove surface contamination. In this paper, we demonstrate several molecular dynamics simulations of large and slow cluster impact on a solid target with solid nano particles attached. The motion and energy transfer process were investigated and the mechanisms of surface cleaning were discussed.Molecular dynamics (MD) simulations were performed in order to examine the collisional process of a large cluster impacting on a solid surface and its cleaning effect. In this simulation, three different types of atom are prepared to represent an incident Ar cluster, Si(100) target and a nano particle. The interaction between the Si atoms is described by the Stillinger-Weber model in {Si, NP}, are governed by the Lennard-Jones 12-6 model described in , in which the parameters are taken from Additionally, the mass of the NP atom is defined as 12 amu. From these definitions, the bulk properties of the NP areThese properties imply that the NP is hard enough so that it does not collapse as a result of the cluster impact with all conditions in this study. This fact may simplify the problem to discuss the dynamics among cluster, surface and NP. However, on the other hand, it is noted that the parameter set in is artificially designed by the authors so it does not match with real materials. The NP consists of 10,000 NP atoms, and has a spherical structure with 3 nm radius. After the preliminary simulation of the structural optimization of the NP attached on the Si(100) surface, the binding energy between the NP and surface is calculated as about 70 eV.The target Si(100) surface includes more than 2 million atoms and has 69.5 × 69.5 nm of surface area and 8.6 nm of depth. The atoms in the region 1 unit cell length forming the edge and bottom of the target are fixed to keep a diamond structure, and several layers inside it act as a thermal bath by Langevin dynamics to absorb excess impact energy and keep the target temperature at 300 K. Various sizes of Ar clusters from 20,000 to 300,000 were prepared as the projectiles. In this work, the total kinetic energy of projectile is fixed as 30 keV, so the incident energy per atom of projectiles varies from 1.5 eV/atom to 0.1 eV/atom. These projectiles were radiated on the target along the surface normal, aimed at several points on the target away from the NP center. The incident angle for the projectile to impact on surface was not varied.Firstly, the dynamics of incident cluster atoms to a planar target surface is examined. shows the map particle and kinetic energy density of the argon atoms during the impact of Ar100000 30 keV on a planar Si(100) target. The size of the mesh point is 0.5 nm × 0.5 nm.When the incident cluster makes contact with the target surface, the bottom of the cluster is compressed and the particle density increases at the impact center. On the other hand, the cluster atoms around the impact point do not move anymore or penetrate the target surface, so the kinetic energy density for these atoms decreases and the kinetic energy is transferred to the edge of the contact region, where the atoms can move outside ((b) and (c)). Through the multiple collisions inside the cluster, the initial momentum of the incident cluster along the surface cluster is deflected to the parallel to the surface. As shown in (c) and (d), the most energetic part can be found at the edge of the cluster, and this area also moves outside, spreading and gradually decreasing in value. Meanwhile, the particle density map indicates that the densest area continues to reside around the impact center for long time, but the atoms in this area carry less kinetic energy.The trajectory and time evolution of the most energetic point are shown in (a) shows the trajectory of the mesh point in cylindrical coordinate (z: height, r: radius) which gives the maximum kinetic energy density at each moment, whereas (b) represents the time and the value of the corresponding point in it can be concluded that the highest energy density can be realized at (t, r, z) = (10 ps, 10.75 nm, 0.75 nm) with the value of 18 eV/nm3, as indicated by the arrow symbols. Considering the discussion in , it is supposed that this point is related with the radius of the incident cluster. Additionally, it is interesting that the value at the energetic point may surpass the initial kinetic energy density (11 eV/nm3), and this effect is expected to contribute to the surface smoothing and cleaning.As the time proceeds, the energetic point moves outside and its value also diminishes. (a) shows that the most energetic mesh point jumps randomly between the outside and impact center after a long time has passed, which means that the characteristic collective motion due to the cluster impact does not occur. shows the MD simulation results of the Ar cluster impacting on the Si(100) target with the attached NP. The snapshots represent the cross-sectional view, which are cut along the center line of the cluster, the target and the NP. The incident cluster consists of 100,000 atoms and is accelerated with a total of 30 keV (namely 0.3 eV/atom). For all conditions, the clusters are radiated along the surface normal of the Si targets, with a varying offset distance from the NP. The offset distance is chosen between 0 and 24 nm. Here, it is noted that the radii of the incident cluster and NP are about 9.5 nm and 3 nm, respectively. Additionally, the time transition of the position and the kinetic energy of the NP are shown in (a) shows the trajectories of the center of mass of the NPs. The circles in the figure indicate the final position of the NPs at 77 ps, which are equivalent to the bottom snapshots in (b) represents the time transition of the kinetic energy of NPs. suggest that the motion of the NP differs according to the offset distance. Identically, when the offset distance is 0, the incident cluster atoms hit the both sides of the NP symmetry. Thus, the lateral migration of NP is suppressed and the NP moves only along the surface normal. In this case, from the detailed motion shown as blue line and circle in , the center of mass of the NP first moves downward to reach 2.5 nm from the surface, and is then reflected and remains 2.8 nm, which corresponds that the bottom edge of the NP (with 3 nm radius) moves once to 0.5 nm and remains at 0.2 nm under the surface level, respectively. Additionally, it can be found in (a) that the target surface atoms around the contact point are disordered, which means that damage may be caused with a specific collisional process.(b), (c) and (d), the flow of cluster atoms becomes asymmetric and hits the NP on one side, which contributes to the NP motion in a lateral direction. When the offset distance is 6 nm ((b)), a part of the incident cluster atom collides with the NP directly. The NP gains large kinetic energy and moves rapidly. In this case, it is noted that the NP moves to more than 34 nm after 60 ps, which means that the NP is out of range of the target area, making it difficult to discuss the migration distance and energy profile.For the larger offset distance (cases of (c) and (d)), most of the cluster atoms collide with Si target atoms first, rather than NP atoms, and are then deflected in parallel to the surface plane. Even in such case, the collective flow of deflected atoms shows the capability to apply enough kinetic energy for NP migration. The kinetic energy transfer diminishes as the offset distance increases.(b), when the offset distance is 6, 12 or 18 nm, the kinetic energy of the NP rises rapidly and then decreases gradually. This means that the NP gains a large amount of kinetic energy by the impact-like collision and loses it by friction with the target surface. Additionally, it is suggested that there seems to be a threshold energy where the NP starts to migrate and that it is related with the binding energy between the target and the NP.For further discussion, the relationships among the impact offset distance, maximum gain of NP kinetic energy and migration distance on the x-axis for various offset distances are shown in (c), it is suggested that the migration distance is generally correlated with the maximum kinetic energy gain. However, if one looks carefully, when the offset distance is small, the migration distance is small, even if the same kinetic energy is given. This seems to be due to the implantation of the NP or the effect that some cluster atoms override the NP, as shown in (a) and (b). In this simulation condition, the highest kinetic energy gain is observed around 7.5 nm of offset distance, and these offset distance values lead to a larger NP migration, as in (b). This result agrees well with the results and discussion in , but includes the results for different cluster sizes ranging from Ar20000 to Ar300000. The total incident energy is constant at 30 keV, but the incident energy per atom and the cluster radius are different. For example, Ar20000 has a 5.45 nm radius and carries 1.5 eV/atom, while Ar300000 has 13.6 nm and 0.1 eV/atom. As shown in (c), when the offset distance is large enough, the offset distance and migration distance show good correlation. However, explicit divergence from the correlation can be found when both the cluster size and offset distance are small.(a) and (b), it is supposed that the optimized offset distance which gives the maximum kinetic energy and migration distance depends on the cluster size and is related with the radius of the incident cluster. Moreover, there is an optimized condition of Ar50000 (0.6 eV/atom) to realize the maximum migration distance. If the cluster size is as small as 20,000 and the incident energy per atom is as large as 1.5 eV/atom, the NP penetrates deeper than in other conditions because of the larger energy transform by the direct impact at a small offset distance, which may interfere with the lateral migration. Additionally, when the offset distance is larger than 10 nm (which corresponds to the sum of the radii of the cluster and NP), the incident cluster impinges itself to create a small dimple on the silicon target surface. After impinging, the cluster atoms are reflected from the target. The direction of the reflected atoms contains a vertical component and does not tend to flow in parallel to the surface. This motion of incident atoms results in the reduction of kinetic energy transfer to the NP.On the other hand, if the total incident energy is constant, increasing the cluster size means decreasing the incident energy per atom as well as the kinetic energy density. When the offset distance is small and the cluster and NP collide directly, the kinetic energy gain of the NP by impact is simply estimated by multiplying the kinetic energy density and the area of the NP. This means that the kinetic energy gain is reduced as the cluster size increases. When the offset distance is large enough, it is estimated that the cluster atoms included in the projection area from the NP to the cluster contribute to the motion of the NP. Under this estimation, the sum of the kinetic energy of the atoms to be projected to the NP is constant. This may be one of the reasons that the kinetic energy gain and migration distance become universal for various cluster sizes.The impact of a huge and slow cluster on a solid target has been investigated by molecular dynamics (MD) simulation from the viewpoint of surface cleaning. By utilizing a huge cluster such as Ar100000, a very slow but high density particle flux can be realized. The initial stage of the impact between a cluster and a solid target is mainly dominated by the incident energy per atom rather than the total kinetic energy. Therefore, if the incident energy per atom or the incident energy density is less than the surface binding energy, the incident cluster atoms cannot penetrate the target surface, but are compressed at the interface. As a result of the multiple collision effect at the interface, the cluster atoms spread in parallel to the surface as a corrective flow of dense energetic particles, which may contribute to the characteristic surface modification process, such as nano particle (NP) migration.The MD results of cluster impacts with various parameters revealed that the NP starts to move when it gains sufficiently large kinetic energy from a collision impact to overcome the binding energy with the target. After migration, the NP loses its kinetic energy and stops by friction with the target. This kinetics means that the kinetic energy gain and migration distance have good correlation with each other. The investigation of the impact offset's dependence on the kinetic energy gain (and migration distance) showed that there is an optimized offset distance to cause the longest migration distance, and it is nearly equal to the summation of the radii of the cluster and the NP. These results are also explained by the investigation that the point of highest energy density can be realized at the edge of the incident cluster in the radial axis and at the near surface level. Additionally, the magnitude of the kinetic energy density may exceed that which the cluster carries initially.In this paper, the dynamics of the cluster impact were described in only qualitative terms. Formulation of the migration process depending on the cluster and NP size, the incident cluster energy and the binding energy of the NP will be studied by further MD simulation and detailed discussion.Available onlineat www.sciencedirect.com ...-" ....;- ScienceDirect JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 2011, 18(12): 65-70 Effect of Heat Treatment Process on Mechanical Properties and Microstructure of Modified CNS-n F1M Steel YANG Ying, YAN Qing-zhi, MA Rang, GE Chang-chun (School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China) Abstract: Ferritic/martensitic (F/M) steels have been recommended as one of the candidate materials for supercriti› cal water cooled reactor (SCWR) in-core components use for its high thermal conductivity, low thermal expansion coefficient and inherently good dimensional stability under -irradiation condition in comparison to austenitic steel. CNS- IT F/M steel which has good mechanical properties was one of the 9-12Cr F/M steels designed for SCWR in the previous work. In this study a modified CNS- IT F/M steel was used and it’s ultimate tensile strength was 925 MPa at room temperature and 483 MPa at 600 ’C after optimizing heat treatment parameter. The ductile to brittle transi› tion temperature of modified CNS-IT F/M steel is -55 •C. Those are at the same level or even higher than that of CNS-IT and some commercial F/M steels nominated for SCWR in-core component use. The transmission electron microscope (TEM) results showed that the mechanical properties of the tempered martensite was closely related to the decompo› sition stage of the martensite. Key words: supercritical water reactor; ferritic/martensitic steel; cladding material Supercritical water cooled reactor (SCWR) has been selected as one of the candidate concepts for Generation IV nuclear energy systems for its im› proved economics, safety, sustainability and prolif› eration resistancei’". As the only water cooled reac› tor in Generation IV nuclear system SCWR is more suitable for China nuclear energy industry, most of our design and construction experiences are on water cooled reactor. But harsh operation parameter posed significant challenge to in-core materials[Z-3J. Nowadays, numerous investigations have been carried out on survey of the materials for SCWR in› core components but none of the existing materials can fulfill good mechanical properties, excellent cor› rosion resistance in supercritical water (SCW) and acceptable dimensional stability under irradiation at the same time as SCWR in-core components de› mand. So developing new materials for the use of SCWR in-core components is of great importance. The authors’ team has focused the research on 9-12Cr F1M steels for SCWR in-core components use for several years. CNS- II F1M steel is one of our de› signed 12Cr F1M steels. Preliminary test results showed that CNS- II F1M steel is good in some of the mechanical properties, but it still needs to be improved in corrosion resistance and ductile to brit› tle transition temperature (DBTT). In this work, modified CNS- II F1M steel was prepared through adjusting components and optimizing process indexes on the bases of CNS- II F1M steel. Current results showed that the mechanical properties of modified CNS- II F1M steel have surpassed that of CNS- II and even surpassed or equal to those similar kinds of steels which were recommended for SCWR in-core component use and have shown an excellent match of strength and toughness. In this study the relationship of heat treatment parameter, mechanical properties and microstructure of modified CNS- II F1M steel will be discussed. 1 Experimental Procedure The chemical composition (in mass percent, %) of modified CNS- II F1M steel used in this work is Cr 12.00, CO. 10, Mn 1. 00, Ni 1. 00, Mo 1. 00, W 1. 10, N O. 06, Ta O. 15, B 0.001, Al 0.02, Si O. 17, V 0.2, S/P<O. 005 and Fe Balance. A 50 kg Foudation Item: Item Sponsored by National Basic Research Program of China (2007CB209800) Biography: YANG Ying(l983-). Female. Doctor Candidate; E-mail: [email protected]; Received Date: June 21. 2010 66 Journal of Iron and Steel Research, International Vol. 18 1209060 Time/min 30 ------------ ___ 700’t ~._----..._---- __-- SOO’t -- 300 ’--__...J.... ~__......... .J..J o ~ §l 400 ]’ ~ 350 450 Fig. 2 Brinell hardness of modified CNS- n F1M steel as a function of tempering time dispersive spectrum (EDS) system at 200 kV. Small disks were cut out of the samples tempered at differ› ent temperatures; these were mechanically polished down to a thickness of 50 nm and then thinned using a standard electrolytic double jet technique. As an elec› trolyte, a mixture of 95 % ethanol and 5 % perchloric acid was used at -20 ’C, 40 V. 2 Results and Discussion 2.2 Thnsile properties of the modified CNS-n F/M steel All tensile and impact testing specimens were taken along the rolling direction. Three specimens were prepared for every testing condition, and two of them were tested to remove the chance element from the testing results, another was used as a sub› stitute. As the testing results showed well reproduc› ibility, no substitute specimens were used. Fig. 3 shows the room temperature ultimate tensile strength and yield strength of modified CNS- IT F1M steel tem› pered in different conditions. The ultimate tensile strength and yield strength of modified CNS- IT F1M steel did not show notable reduction when the sam› ples were tempered at 700 ’C from 20 to 120 min. When tempering temperature rose to 800 ’C they re› duced dramatically in the first 50 min and then the rate of the strength reduce decreased. After tempe› ring at 800 ’C for 120 min the yield ratio of modified CNS- IT F1M steel could reach O. 75. 2. 1 Hardness change of modified CNS- n F1M steel during tempering The Brinell hardness of modified CNS-IT F1M steel after tempering was measured using a 2. 5 mm in› denter under 187.5 kgf load with a loading duration of lOs in a Brinell hardness testing machine. There was a dramatic hardness reduce in the first 20 min during the tempering process, as shown in Fig. 2. The critical temperature of modified CNS-IT F/M steel was measured by thermal expansion method on Gleeble 1500 thermal-mechanical simulator. The crit› ical points of modified CNS- IT F1M steel were as follows: M s 290 ’C, M f 209 ’C, Ad 860 ’C and A c3 910 ’C. The 9-12Cr F/M steels used for high tem› perature applicants, such as boiler and turbine com› ponents in power plant, were always used in quenched-and-tempered conditions for its excellent combination of mechanical, oxidization-resistance properties and high creep resistance[4-6]. As the an› ticipated operating temperature of SCWR was up to 600 ’C, there was a small temperature range left for tempering. The modified CNS-IT F1M steel was tem› pered at 700 and 800 ’C for 20, 50, 90 and 120 min respectively, in order to find the suitable condition under which the steel can gain the best match of strength and toughness. The mechanical properties of modified CNS- IT F1M steel after tempering were evaluated according to GB. The microstructure of modified CNS- IT F1M steel after tempering was examined by lEOL lEM› 2100 transmission electron microscopy with an energy Fig. 1 SEM morphology of modified CNS- n F1M steel after rolling ingot was fabricated by vacuum induction melting method and then forged and hot rolled into plate with the final size of 15 mm X 100 mm X 2 500 mm. The hot rolling was performed at the temperature range of 1100 to 900 ’C followed by water spray cooling. Fig. 1 shows the microstructure of modified CNS- IT F1M steel after rolling. The microstructure consists of lath martensite and a small amount of ferrite elongating along the rolling direction. The volume fraction of the ferrite was measured with im› age analysis software (Image J), and statistics from more than ten different images, the average result was 4.5%. Issue 12 Effect of Heat Treatment Process on Modified CNS- II F1M Steel 67 Fig.3 Ultimate tensile strength (a) and yield strength (b) of modified CNS- I F1M steel as a function of tempering time 2. 3 Impact properties of modified CNS-n F1M steel It is well known that irradiation can cause F1M steels produce microstructure defects and cause an increase in yield stress[IO]. This irradiation harden› ing caused embrittlement can be measured by the in› crease in DBTT of the steel[ll]. The DBTT of the steel was determined as the middle of the energy lev› el between the upper and lower shelf energies[12]. In this study the impact properties of modified CNS- II F1M steel was measured using the Charpy-V shape samples. The impact energy of modified CNS-II F1M steel tempered in different conditions was tested at room temperature and - 40 •C, and the results are in Fig. 4. As tensile strength, the samples tempered . at 700 •C for different time did not show much difference in impact energy. When the temperature rose to 800 •C the impact energy increased with the tempering time extended at both temperatures. The impact energy of the samples tempered at 800 •C was considerably higher than their counterpart tempered at 700 •C. .. ... 120100 .___700 ’t: I <, 700 ’t: 60 80 Time/min lh)1000 ~ 900 i 800 Q,) .., "ii5 ~ 700 600 20 40 <II 1200 (a) ~ 11100 +-1-~f----+--_ tl Q,) ] 21000 ~ .~ ,;:: ..... 900~~=========~==:::=:::: 120100 + <, 800’t: + 700 t; -- 40 60 80 Time/min 20 OL..-...L...-_--’-__.L.-_--L..__.L.-_-’----l 20 100 80 ~ ~ J ~ 60 = Q,) 100 I (b) 60 120r-------------__--, (a) Fig. 4 Impact energy of modified CNS- I F1M steel tested at room temperature (a) and -40 ’C (b) as a function of tempering temperature As discussed above the samples tempered at 800 •C for 120 min show the best match of strength, ductility and have the highest impact energy at both test temperatures simultaneously. The samples were tested from room temperature to -120 •C, in order to determine the DBTT of modified CNS-II F1M steel after tempering at 800 •C for 120 min, the results are in Fig. 5. According to the definition of DBTT, the DBTT of the steel is about - 55 •C which is higher than that of CNS- II F1M steel and in the same level 25 200 400 600 Modified CNS- n 917–7 891–9 873–23 482. 5–12.5 CNS-n 840 750 655 443 EUROFER97[7] 690 550 500 300 T91[8] 680 570 ll F82H[8] 640 450 ll HT9[9] 900 780 690 EP832[9] 790 690 610 Test temperature/"C For high temperature used structure material excellent high temperature strength is as important as room temperature strength. The samples tem› pered at 800 •C for 120 min were tested at 200, 400 and 600 •C, in order to determine the high tempera› ture strength of modified CNS- II F1M steel. The test results in Table 1 show that as the testing tem› perature rose, the steel also performed very good strength. The room temperature and high tempera› ture strength of modified CNS- II F1M steel have surpassed CNS- II and even surpassed or in the same level with some of the commercial F/M steel contai› ning Cr of 9%-12%, proposed for SCWR in-core com› ponents use. Excellent strength of modified CNS-II F/M steel at both room temperature and high temperature display advantages for SCWR in-core material use. Table 1 Strength of modified CNS- I F1M steel, CNS- I F/M steel and some of candidate 9-12Cr F/M steels tested at different temperatures Rm/MPa Note: 1) The data are tested at 350 •C. 68 Journal of Iron and Steel Research. International Vol. 18 this work modified CNS- IT F1M steel was water spray cooled just after hot deformation so the dislo› cation density in the martensite was even higher. Martensite decompose process consists of two ad› verse sides, one is the reduction of dislocation densi› ty and disappearence of the lath structure which re› duce strength of the tempered martensite, mean› while, increase toughness; the other is the forma› tion of the carbide which increases the strength of tempered martensite through precipitation strength. During the early stages of the tempering process the dislocation density decreases fast and then gradually gets more slowly[l4], this is coincide with the hard› ness change of modified CNS- IT F1M steel, as shown in Fig. 2. Fig. 6 shows the microstructure of the samples tempered at 700 and 800 ’C for different times. Fig. 6 (a) and (b) show that samples tem› pered at 700 ’C have similar kind of microstructure, characterized by very high dislocation density and lath structure in some areas. This explains why the sam› ples tempered at 700 ’C for different times all have -,very high strength and relatively low impact energy. .While the tempering temperature rises to 800 ’C, the decomposition rate of the martensite speeds up remarkably. Fig. 6 (c) shows that after the first 20 min the lath structure almost disappeared, the dislocation rearranged, and lots of subgrain formed. The micro- 30-60 -30 0 Temperaturez C -90 () L......J’--_.......__...L-__.L..-_---L__-’--’ -120 120,..--------------::--, Fig. 5 DBTI of modified CNS-n F1M steel with 9Cr F1M steel T91 used in supercritical fossil plants[13] . !:::? ~ ’" 60 i .E - 30 90 2. 4 Transition electron microscopy of modified CNS- n F1M steel It is known to all that when martensite forms during cooling from austenite the dislocations are al› so created together with the lath structure which are all provide for the high strength of martensite. And tempering gives us a chance to reduce strength and increase toughness at the same time. This makes change of mechanical properties through different tempering regime possible and makes the tempered martensite a very useful material in many situations. In (a) 700 •C. 20 min; (b) 700 •C. 120 min; (c) 800 •C. 20 min; (d) 800 •C. 120 min. Fig. 6 Microstructure of modified CNS-n F1M steel tempered at different temperatures Issue 12 Effect of Heat Treatment Process on Modified eNS- II F1M Steel 69 structure of the sample tempered at 800 ’C for 120 min was made up of small equiaxed grains so it had high› est impact energy. The formation of carbide is another important process during tempering and it can compensate for the strength loss due to the lath structure decompo› sition. Fig. 7 shows the morphology of the carbide formed during tempering under different conditions. The carbide formed in the first 20 min when the samples was tempered at 700 and 800 ’C and became coarsening with the temperature raised and time ex› panded. The newly formed carbide is characterized by a lamellar morphology as shown in Fig. 7 (a) then it becomes coarsening. Fig. 7 (e) and (f) are the morphologies of the precipitate in the sample tern- pered at 800 ’C for 120 min and the micro-diffraction pattern records from it. The micro-diffraction pat› tern shown in Fig. 7 (e) has been indexed in terms of a fcc crystal structure, which completely coin› cides with the diffraction pattern from Cr15. 58 Fe7.42 C 6 in the zone axis of [110]. The result from the energy dispersive spectrum confirmed it, as the atomic ratio of Cr and Fe in the precipitation is about 2 : 1. There are tiny of Mn, Mo and W in the precipitation. The precipitations in other samples show the same morphology with the precipitate detected in Fig. 7 (e) and the energy spectrum results are also same with it. So the main precipitation in modified CNS-II F1M steel is Cr15. 58 Fe7.42 C 6 and the Cr and Fe atomic ratio in the precipitate change within a small range. (a) 700 ’C, 20 min; (b) 700 ’C, 120 min; (c) 800 ’C, 20 min;" (d) 800 ’C, 120 min; (e), (f) Diffraction pattern recording from it. Fig. 7 Morphology of precipitate in modified eNS- n F1M steel tempered at different temperatures 3 Conclusions The mechanical priorities of modified CNS- II F1M steel, after tempering at 800 ’C for 120 min, are in the same level with the similar kinds of com› mercial 9-12Cr F1M steel candidated for SCWR in› core component use. Under this tempering condi› tion, the ultimate tensile strength of modified CNS› II F 1M steel at room temperature and 600 ’C are 925 and 483 MPa respectively. The upper shelf en› ergy of modified CNS- II F1M steel is about 110 J and DBTT is - 55 ’C, which show best match of strength and toughness. The mechanical properties of martensite can be modified within a very large range through tempe› ring. In this study the best tempering parameter for modified CNS- II F1M steel is 800 ’C, 120 min. In this condition the microstructure of modified CNS› II F1M steel is composed of equiaxed ferrite and carbide precipitated at intra-grain and inter-grain. The carbide precipitate in modified CNS- II F1M steel during tempering is Cr15.58 Fe7.4 2C6 with a crys› tal structure of fcc. References: [lJ Abram T, Ion S. Generation-TV Nuclear Power: A Review of the State of the Science [1]. Energy Policy, 2008, 36(2): 4323. [2J Murty K L, Chrtit I. Structural Materials for Gen-IV Nuclear Reactors: Challenges and Opportunities [JJ. Journal of Nuclear Materials, 2008, 3830/2): 189. [3J Yvon P, Carre F. Structural Materials Challenges for Ad› vanced Reactor Systems [JJ. Journal of Nuclear Materials, 2009,385(2): 217. [4J Klueh R L. Reduced-Activation Steels: Future Development for Improved Creep Strength [JJ. Journal of Nuclear Materi› als, 2009, 375(2): 159. 70 Journal of Iron and Steel Research, International Vol.18 [5J Ghassemi-Armaki H, Chen R P, Maruyama K et al. Static Re› covery of Tempered Lath Martensite Microstructures During Long-Term Aging in 9-12%Cr Heat Resistant Steels’ [1]. Ma› terials Letters, 2009, 63(28): 2423. [6J Schneider A, Inden G. Simulation of the Kinetics of Precipitati› on Reactions in Ferritic Steels [1]. Acta Materialia , 2005, 53 (2): 519. [7J Lindau R, Moslang A, Schirra M. Thermal and Mechanical Behavior of the Reduced-Activation-Ferritic-Martensitic Steel EUROFER [1]. Fusion Engineering and Design, 2002, 61-62 (2): 659. [8J Tong Z, Dai Y. The Microstructure and Tensile Properties of Ferritic/Martensitic Steels T91, EUROFER-97 AND F82H Ir› radiated up to 20dpa in STIP-m[1]. Journal of Nuclear Mate› rials, 2010, 3980/2/3): 43. [9J Maloy Stuart A, Romero T, James M R et al. Tensile Testing of EP-823 and HT-9 After Irradiation in STIP II [1]. Journal of Nuclear Materials, 2006, 3560/2/3): 56. [10J Maloy Stuart A, Romero T, James M R et al. Embrittlement [l1J [12J [13J [14J of Irradiated Ferritic/Martensitic Steels in the Absence of Irra› diation Hardening [1]. Journal of Nuclear Materials, 2008, 377(3): 427. Rieth M, Dafferner B, Rohrig H-D. Embrittlement Behavior of Different International Low Activation Alloys After Neu› tron Irradiation [1]. Journal of Nuclear Materials, 1998, 258› 263: 1147. Klueh R L, Soolov M A, Hashimoto N. Mechanical Proper› ties of Unirradiated and Irradiated Reduced-Activation Mar› tensitic Steels With and Without Nickel Compared to Proper› ties of Commercial Steels [1]. Journal of Nuclear Materials, 2008,374(1/2): 220. Dai Y, Marmy P. Charpy Impact Tests on Martensitic/Ferrit› ic Steels After Irradiation in SINQ Target-3 [1]. Journal of Nuclear Materials, 2005, 3430/2/3): 247. Pesicka J, Kuze I R, Dronhofer A, et al. The Evolution of Dislocation Density During Heat Treatment and Creep of Tempered Martensite Ferritic Steels [1]. Acta Materialia , 2003, 51(6): 4847. and the energy spectrum results are also same with it. So the main precipitation in modified CNS-II F1M steel is Cr15. 58 Fe7.42 C 6 and the Cr and Fe atomic ratio in the precipitate change within a small range. (a) 700 ’C, 20 min; (b) 700 ’C, 120 min; (c) 800 ’C, 20 min;" (d) 800 ’C, 120 min; (e), (f) Diffraction pattern recording from it. Fig. 7 Morphology of precipitate in modified eNS- n F1M steel tempered at different temperatures 3 Conclusions The mechanical priorities of modified CNS- II F1M steel, after tempering at 800 ’C for 120 min, are in the same level with the similar kinds of com› mercial 9-12Cr F1M steel candidated for SCWR in› core component use. Under this tempering condi› tion, the ultimate tensile strength of modified CNS› II F 1M steel at room temperature and 600 ’C are 925 and 483 MPa respectively. The upper shelf en› ergy of modified CNS- II F1M steel is about 110 J and DBTT is - 55 ’C, which show best match of strength and toughness. The mechanical properties of martensite can be modified within a very large range through tempe› ring. In this study the best temperinEffect of Heat Treatment Process on Mechanical Properties and Microstructure of Modified CNS-II F/M SteelFerritic/martensitic (F/M) steels have been recommended as one of the candidate materials for supercritical water cooled reactor (SCWR) in-core components use for its high thermal conductivity, low thermal expansion coefficient and inherently good dimensional stability under irradiation condition in comparison to austenitic steel. CNS-II F/M steel which has good mechanical properties was one of the 9-12Cr F/M steels designed for SCWR in the previous work. In this study a modified CNS-II F/M steel was used and it's ultimate tensile strength was 925 MPa at room temperature and 483 MPa at 600 °C after optimizing heat treatment parameter. The ductile to brittle transition temperature of modified CNS-II F/M steel is −55 °C. Those are at the same level or even higher than that of CNS-II and some commercial F/M steels nominated for SCWR in-core component use. The transmission electron microscope (TEM) results showed that the mechanical properties of the tempered martensite was closely related to the decomposition stage of the martensite.Biography: YANG Ying(1983-), Female, Doctor CandidateInfluence of the stiffness of bone defect implants on the mechanical conditions at the interface—a finite element analysis with contactThe study focused on the influence of the implant material stiffness on stress distribution and micromotion at the interface of bone defect implants. We hypothesized that a low-stiffness implant with a modulus closer to that of the surrounding trabecular bone would yield a more homogeneous stress distribution and less micromotion at the interface with the bony bed. To prove this hypothesis we generated a three-dimensional, non-linear, anisotropic finite element (FE) model. The FE model corresponded to a previously developed animal model in sheep. A prismatic implant filled a standardized defect in the load-bearing area of the trabecular bone beneath the tibial plateau. The interface was described by face-to-face contact elements, which allow press fits, friction, sliding, and gapping. We assumed a physiological load condition and calculated contact pressures, shear stresses, and shear movements at the interface for two implants of different stiffness (titanium: E=110 GPa; composite: E=2.2 GPa). The FE model showed that the stress distribution was more homogeneous for the low-stiffness implant. The maximum pressure for the composite implant (2.1 MPa) was lower than for the titanium implant (5.6 MPa). Contrary to our hypothesis, we found more micromotion for the composite (up to 6 μm) than for the titanium implant (up to 4.5 μm). However, for both implants peak stresses and micromotion were in a range that predicts adequate conditions for the osseointegration. This was confirmed by the histological results from the animal studies.Bone substitute materials are used as an alternative to autogenous bone grafts to fill large defects in bone (). The successful osseointegration depends not only on the material of the implants and their surface quality but also on the mechanical conditions at the interface. In addition to possible problems related to micromotion (), critical contact stresses can inhibit the bony incorporation of an implant. Overloading the bony bed leads to creep or fatigue, whereas underloading (stress protection) induces bone resorption (Recently, in vivo experiments have been performed to study the osseointegration of bone substitute materials into epiphyseal bone (). In a previous work, we developed an animal model to study the osseointegration of newly developed implant materials within load-bearing regions of trabecular bone (). Prismatic specimens were implanted into the ovine tibia, underneath the medial plateau () so that part of the compressive load in the knee went through the implant. The mechanical conditions at the bone–implant interfaces, however, were unknown in these experiments. In particular, the influence of the implant stiffness on the mechanical environment was unclear. Previous studies of osseointegration in hip implants indicated that less stiff implants yield better osseointegration (We hypothesized that a low-stiffness implant results in a more homogeneous stress distribution and less micromotion because it has similar strains with the adjacent bone tissue. The aim of the present study was to determine if a bone defect implant with a modulus closer to that of trabecular bone yields mechanical conditions at the interface that are known to be better for osseointegration. Specifically, we asked whether a low-stiffness implant results in a more homogeneous stress distribution and less shear movement at the interface to the bony bed than a high-stiffness implant.Using the finite element (FE) program ANSYS (ANSYS, Inc., Canonsburg, PA, USA), a three-dimensional, non-linear, anisotropic FE model of the proximal ovine tibia was developed. The geometry of the FE model was based on 60 contiguous computer tomography slices from a right ovine tibia (slice distance=1 mm; pixel size=0.59 mm×0.59 mm). Segmentation of trabecular and cortical bone was done using the image processing software SURFdriver (S. Lozanoff, University of Hawaii, and D. Moody, University of Alberta). A preprocessor module developed with the ANSYS Parametric Design Language (APDL) reconstructed the bone geometry using a bottom up procedure () and resulted in a tibia model with approximately 45,000 hexahedron elements. The simple prismatic implant was created, meshed independently with approximately 2000 hexahedrons, and inserted into the bone defect. The mesh was finer around the implant where higher stress gradients were expected (The interaction between implant and bone was described with 774 face-to-face contact elements on the implant surface and 252 target elements on the bony bed. The contact elements took into account press fit, gapping, and interfacial friction in order to simulate shear movements (). We used the Newton integration scheme in order to avoid extensive penetration at the sharp edges of the implant. The contact was described with Coulomb's friction law. Both implants had smooth surfaces (roughness, RA=0.3–0.6 μm). Measured values of the coefficient of friction between bone and smooth metal plates were in the range of 0.28–0.44 (). We assumed a lower coefficient of friction (μ=0.2), to take into account the in vivo environment (blood, marrow). A small press fit of 1 μm in the axial direction was modeled using a thermal expansion of the implant elements only in the axial direction. The amount of the initial press fit at surgery was difficult to quantify and probably larger. However, it is known that creeping of bone reduces press fit to such small values in a few hours. Furthermore, we included an initial gap of 10 μm at both vertical interfaces, because direct contact or press fitting cannot be obtained at these sites. Physical and non-physical contact parameters are shown in The material properties of cortical bone in the diaphysis and epiphysis () were assumed to be transverse isotropic (). The subchondral plate was assumed isotropic and stiffer than the cortical bone (). Homogeneous, orthotropic material properties were chosen for the trabecular bone (). The implant materials used were a composite material (polyurethane and glass ceramic) and titanium that served as control material in the animal model (). Both implant materials were described as being isotropic with linear elastic properties (The load acting on the tibial condyles was determined from a musculoskeletal model () assuming a slowly walking sheep. The total load of 400 N (components: 390 N in distal and 90 N in anterior direction) was divided between the medial and lateral condyles in a ratio of 60–40, respectively. We assumed a non-uniform pressure distribution with a peak pressure of 1.6 MPa on the medial condyle (). The positions of the loaded areas and pressure peaks were derived from the thickness and the structure of the subchondral plate (). The load was applied in six load steps (0, 100, 200, 300, 400, 0 N) in order to obtain results for the whole simulated load cycle. The first load step (0 N) contained only the initial press fit. The last load step simulated the relaxation from 400 to 0 N. Nodes at the distal end of the model were fixed in all degrees of freedom.The FE model fulfilled the following minimal requirements. The strains in the loaded intact tibia were less than 0.07%, which is within the range of physiological strains (). Peak penetrations at solution convergence were less than 0.1 μm for the composite implant and 0.5 μm for the titanium implant. Using a refined mesh (236,000 DOF instead of 156,000) the peak contact pressure increased about 10% and the peak shear movement increased about 2% for the composite implant. In addition, we determined the sensitivity of the results to variations in the material properties of bone. An increase of 10% in the bone moduli, which also increased the absolute contact stiffness, resulted in an increase of about 13% in the peak contact pressure and a decrease of about 9% in the maximum shear movement.For a further evaluation of the model, the axial displacements of the loaded tibia with an empty defect were computed and compared to results of an in vitro experiment. A right ovine tibia with an empty defect was attached to a material testing machine and loaded with a compressive force of 400 N through the intact knee (flexion angle 15°). The reduction Δh in the defect height (h=6 mm) was measured with a dial gauge at six different positions inside the defect. The model predicted the reductions in height Δh with an average (RMS) error of 14 μm and a peak error of 23 μm (The non-linear problem was solved iteratively with automatic step size control. One analysis needed a total of 28 equilibrium iterations for all applied load steps. The ANSYS contact result CONTSLID did not yield correct kinematical shear movements if contact opened during the simulation. We therefore developed a post-processor macro in APDL to determine the shear movement from the absolute positions of the associated contact surfaces. We calculated the patterns of contact pressure, shear stress, contact status, and shear movement at the implant surface.The peak pressures for both implants were higher than the compressive stresses in the intact tibia. For the intact tibia, the peak axial compressive stress was 1.11 MPa at a transverse section where the proximal interface would be located and was 0.53 MPa at the location of the distal interface. There was high pressure on the proximal interface close to the dorsal edge (, region A), whereas the vertical interfaces of both implants were nearly unloaded (region C). The region of high pressure is directly underneath the location of the highest pressure on the medial condyle. Similar to the contact pressure, peak shear stresses (titanium: 0.22 MPa; composite: 0.16 MPa) were on the proximal interface close to the dorsal edge (Distributions of normal and shear stress at the interface were more homogeneous for the low-stiffness implant () than for the high-stiffness implant. For the composite implant, the peak compressive stresses were 2 times higher at the proximal (2.1 MPa/1.11 MPa) and distal (1.0 MPa/0.53 MPa) surface compared to the intact tibia. For the stiffer titanium implant, the peak compressive stresses were 5 times higher (5.6 MPa/1.11 MPa) at the proximal surface and 3 times higher (1.5 MPa/0.53 MPa) at the distal surface. The patterns of the shear stresses on both implants () were similar to those of the contact pressure () and were more homogeneous for the softer implant.Micromotion had larger magnitude and covered larger areas for the composite implant than for the stiffer titanium implant (). Nearly the whole distal surface of the composite implant was in sliding contact at the load maximum (400 N), whereas the stiff implant showed more sticking- and gapping-type contact (). The vertical surfaces of both implants showed large areas of gapping contact. The patterns of contact status changed during the simulation of the load cycle. Sticking areas became smaller with increasing load for both implants. The peak shear movement of 6.0 μm appeared at the outer edge of the distal surface of the composite implant (, region D). For the stiffer titanium implant, the peak shear movement was 4.5 μm on the distal surface. At these areas, the implant surface moved anteriorly relative to the bony bed.Using a model with finite contact elements, we quantitatively determined the mechanical environment at the contact between implant and bone.The model was limited by the use of homogeneous material properties for the trabecular bone. We used a single load case to represent the dominant loading environment of slowly walking or standing sheep. Ligaments and muscles were not considered in the load and boundary conditions. In contrast to our assumption, the in vivo direction and distribution of the loads do not remain constant during a loading cycle. In order to minimize computation time, we represented the load cycle with the single load distribution.The tibia model was validated by an in vitro experiment in which the tibia defect was unfilled. This experiment was designed to test the most critical part of the model, which was the mechanical behavior of the tibial plateau above the defect under axial load. Variations of geometry or material properties in this part showed a strong influence on the carrying capacity of this plate-like structure and therefore resulted in large variations in the contact variables. An overestimation of the carrying capacity would lead to an underestimation of the contact pressure and vice versa. The calculated and measured deformations correlated well validating this part of our model. Unfortunately, the quantitative results of the contact variables could not be verified directly.This model predicts only the initial contact conditions between the implant and the bone. In vivo, these conditions change over time as osseointegration and bone remodeling occur. Normal stresses would change only slightly as a result of changing bone density. However, the magnitude of micromotion would change significantly, as osseointegration occurs. In future models, it would be interesting to investigate the effects of these biological processes on the contact conditions.The stiffness of the implant material had a marked influence on the local mechanical conditions at the interface. The results of this study indicated that a low-stiffness implant has similar deformations to that of the surrounding trabecular bone. This reduces the peak pressures and leads to more homogeneous pressure distributions. However, the softer implant had a smaller load-carrying capacity, therefore, increased the load in the cortical shell next to the defect. The implants where placed fully within trabecular bone while the defect in the cortical shell remained unfilled. In addition, both implant materials were stiffer than the surrounding trabecular bone. Therefore, in both cases, the vertical force through the implant was intensified compared to the intact tibia, leading to increased stresses at the horizontal interfaces. However, stresses in trabecular bone remained below compressive yield stress of 10–20 MPa (, region A and B) where we calculated higher contact pressures corresponded generally with locations of increased bone density in our animal experiments (). These changes in bone morphology may result from bone remodeling adapted to altered loading conditions (The patterns of the shear stresses on both implants were similar to those of the contact pressures. In areas with a sliding contact, the ratio of shear stresses to contact pressures was given by a constant factor, the coefficient of friction. Areas with a gapping contact were free of any surface stresses. Peak shear stresses on both implants (titanium: 0.22 MPa; composite: 0.16 MPa) were lower than the ultimate shear stress (1.0–2.0 MPa) of ovine trabecular bone (The patterns of contact status changed during a load cycle and areas of sticking, sliding or gapping contact changed their sizes and moved. However, there were particular points on both implants (e.g. the dorsal edge on the proximal interface, , region A) where sticking contact always occurred. Therefore, the implant did not change positions between load cycles.In this model, the compliant implant had more shear movement between implant and bone, particularly at the distal interface, than the stiff implant. This observation was in contrast to our hypothesis. In this model, the proximal interface of the loaded bone was displaced anteriorly. This movement was transferred through the sticking contact area at the proximal interface (region A in ) to the implant. Therefore, shear movements of the implant at the distal interface were anteriorly directed. The shear movement for the softer composite implant was greater than for the titanium implant because the normal stresses were lower, and therefore frictional stresses were also lower. However, even the highest amount of shear movement (6 μm with the composite implant) seems not to be critical for osseointegration (The largest relative movement normal to the surface (gapping) of approximately 6 μm was observed with the composite implant at the lower edge of the dorsal surface. This movement was coupled with the shear movement of the distal surface of the implant in ventral direction. Comparing this to our histological results, this amount of movement does not hinder osseointegration. In the histological and microradiographical sections, the horizontal interfaces were always well integrated after 6 month. In some animals, there was a decrease in bone density 6 months after surgery in that region (, region C). This remodeling probably occurred because the bone in this region was nearly unloaded. Further work is needed to analyze the bone remodeling processes in relation to the mechanical environment including the strain energy density in the bone adjacent to the implant.In conclusion, we found that the characteristic distributions of the mechanical contact variables (normal and tangential stresses, contact status, shear movement) were influenced significantly by the implant material stiffness. The low-stiffness implant was characterized by a more homogeneous stress distribution with stress values in a more physiological range than the stiff implant. This enhances osseointegration compared to the stiffer implant. Even though the low-stiffness implant had greater micromotion in both cases, peak stresses as well as micromotion were in a range acceptable for the osseointegration of the bone defect implants. Using FE models to determine the contact conditions and mechanical environment at the bone–implant interface will aid not only in understanding the biological response of the bone around the implant, but also aid in designing more effective bone defect implants.A finite element analysis of the retinal hemorrhages accompanied by shaken baby syndrome/abusive head traumaWe aimed to elucidate the mechanism of the retinal hemorrhage (RH) accompanied by shaken baby syndrome or abusive head trauma (SBS/AHT) by analyses using a computational model. We focused on a hypothesis that the vitreoretinal traction due to acceleration and deceleration caused by abusive shaking leads to retinal hemorrhage. A finite element (FE) mechanical model with simple spherical geometry was constructed. When the FE mechanical model was virtually shaken, the intensity of the stress applied to the retinal plane agreed well with the results from an analysis using a physical model made of agar gel. Impacts due to falling events induced more intensive tensile stresses, but with shorter duration, than the shake did. By applying a mathematical theory on tackiness, we propose a hypothesis that the time integration of the stress, in the unit of Pa·s, would be a good predictor of the RH accompanied by SBS/AHT. A single cycle of abusive shake amounted to 101 Pa·s of time integration of inflicted stress, while a single impact event amounted to 36 Pa·s. This would explain the paradoxical observation that shaking induces RH while RH due to impact events is only seen in a major event such as a fatal motor vehicle accident.Shaken baby syndrome or abusive head trauma (SBS/AHT) is caused by violently shaking an infant with or without impacting on the head, and is characterized by serious brain and nerve damages including death. Along with damages such as subdural hematomas or diffuse axonal injuries, SBS/AHT is often accompanied by retinal hemorrhages (RHs). RHs are empirically regarded as an important symptom to distinguish abuse from accident because it is seen in approximately 85% of the victims of SBS/AHT whereas it is observed under accidental context only with decisive external injuries such as those in fatal motor vehicle accidents (). In contrast to the term SBS, the term AHT does not require shaking as a necessary factor, but shaking is still considered as a very major factor. It is important to elucidate the mechanism of the specificity of RH to SBS/AHT to establish a firm scientific basis for the recognition of abuse, which will hence contribute to its prevention.A major volume inside the eyeball is filled with a tissue called vitreous body, a transparent and gel-like tissue placed behind the lens. The inner surface of the retina, the sensual tissue connected to the optic nerve, is directly attached to the vitreous body. The soft and delicate structure of the retina is supported by the sclera, a tough tissue maintaining the spherical shape of the eyeball. The sclera is also known as the white of the eye and forms the outermost layer of the eyeball together with the cornea. There lies a layer of tissue called choroid between the retina and the sclera, which supplies the retina with oxygen and nourishment through capillary network and also shuts out stray light with its pigmentation.When an infant is subjected to violent shaking, several factors are hypothesized to be included in the occurrence of RHs, e.g. increased intracranial pressure, increased intrathoracic pressure and orbital injury. Among them, we focused on a hypothesis that the vitreoretinal traction due to acceleration and deceleration caused by the shaking leads to the damage of the retinal tissues because this factor is most feasible and attracting most attention (Because detailed description of abusive events based on witnessing is very scarce, simulation analysis is necessary to verify clinical or autopsy findings. Animal experiments reproducing abusive settings are an important option to consider, but are with several inevitable problems, e.g. the difference in morphology and physical properties of animal models from human infants, the complexity and individual variability of animal models that may hinder the analytical process and the serious ethical concerns.Computer simulation is a powerful tool to analyze the mechanism of this phenomenon because it is able to compensate for the limitations of the animal experiments. We have developed a finite element (FE) mechanical model to tackle this problem. This model is made by dividing the subject into numerous but finite solid and plate elements. Then the equations describing the elasticity of each element are computed simultaneously.Two preceding papers have employed the FE method to analyze this problem (), which concluded that the shaking could be responsible for the RHs in SBS/AHT. The models used in these studies contained parts based on medical images, and were elaborate and realistic. However, these studies suffered from an unexplained phenomenon termed as stress buildup (). This is partly because these models were somewhat too complex, and thus ironically concealed the relation of cause and effect.Therefore, we generated our model from scratch, assuming a simple spherical geometry. By giving up some extent of reality, we attempted to remove inessential factors for a clearer analysis. We examined the stress tensor in our analysis, instead of considering the von Mises stress, as in one of the preceding papers (). The von Mises stress is often used to describe the yield strength of hard materials used in machines or architectures, and is not necessarily applicable to the detachment between soft tissues as vitreous body and retina. On the other hand, tensile, compressive and shearing components of the stress with respect to the retinal plane can be extracted from the stress tensor, and their relevances to RH can be discussed separately. pointed out the importance of the time integral of stress in understanding the mechanism of RH in SBS/AHT, through a study using a dummy doll equipped with an eyeball model. We reconstructed this eyeball model as an FE mechanical model to further examine this idea. While only the normal component of the stress was obtained from the measurements in , the whole stress tensor is available from the computational analysis.We constructed a simple computational model of an eyeball for FE mechanical analysis that included the vitreous body, the cornea, the sclera, the fatty tissue and the orbit (). Our model is with controllable numerical precision and is easily modified because it is fully automatically generated by a Fortran95 program (Supplementary material 1). This FE mechanical model was analyzed using a computer-aided engineering platform (HyperWorks Version 11.0, Altair Engineering, Inc., Troy, MI, USA). The spherical shape of the vitreous body had a cubic core, surrounded by six peripheral shapes attached on each side of the cube. This sphere was covered with the sclerocorneal membrane. This eyeball was further wrapped with a layer of fatty tissue. The anterior part of the fatty tissue was absent to reproduce eye opening. The layer of the fatty tissue is then covered with a cortical bony layer representing the orbit. All of the adjacent elements shared common nodes. The vitreous body and the fatty tissue were modeled with hexahedral solid elements; the cornea, the sclera and the orbit were modeled with tetragonal plate elements.The radius of the eyeball and the orbit were set to 10 mm and 16 mm, respectively, and the thickness of the cornea, the sclera and the orbit were all set to 1 mm (). Mass densities of all materials were set to 1 g/mL. Poisson׳s ratios of all materials were set to 0.5, which means all materials were incompressive. Young׳s moduli of each material were cited from the literature: the cornea, ca. 10 MPa (). The orbit was considered as a rigid body. Young׳s modulus of the fatty tissue was set within the average range of soft-tissue properties of humans, 47 kPa, as in . Young׳s modulus of 1.9 kPa, that of 0.5% agar, was employed to simulate the mechanical property of the vitreous body of infants, and Young׳s modulus of 30.3 kPa, that of 1.0% agar, was also used for comparison (). All of the elastic materials used in the FE mechanical model were isotropic and assumed linear relation between stress and strain, i.e. Hooke׳s law.The very thin membranous structures of the retina and the choroid were not explicitly reproduced in our model. Alternatively, we considered the outermost elements of the vitreous body as representing the mechanical state in the vicinity of the retina. The components of stress tensors were retrieved from the simulation results using a Tcl/Tk script (Supplementary material 2), while the coordinate system of the stress tensor was transformed to one tangential to the retinal plane and orthogonal to the local latitudinal and longitudinal axes.The data were cited from a previous study (). A doll simulating a one-month-old infant was shook by an imitate perpetrator to obtain data of violent shaking and its effect on the fundus of the eyeball. This doll was also subjected to a free falling of 50-cm high to a hard floor. This doll was equipped with an eyeball model, which had a plastic shell filled with agar gel simulating the vitreous body. The neck of the doll only tethered the head to the body, similarly as a newborn infant. Shaking was monitored with an accelerometer set on the head of the doll parallel to the sagittal axis, whose positive direction corresponded to the posterior direction of the doll, and was used as the input to virtually move the computational FE model, which was initially at rest. The reproduced shaking movement was one-dimensional, straight along the z-axis, since only one accelerometer was used. The stress invoked by the shake at the fundus of the eyeball model was recorded by a pressure sensor, and used to verify the computational results.The eyeball model was sinusoidally shook in the computer simulation framework with a frequency of 2.5 Hz and a stroke of 30 cm along the sagittal axis, as a rough simulation of an abusive shake event. Two Young׳s moduli of the vitreous body were tested, i.e. 1.9 kPa and 30.3 kPa, corresponding to that of 0.5% and 1.0% agar gel model, respectively (). In a microscopic point of view, the retinal tissue may be exposed to either tensile, compressive or shear stresses. The tensile and compressive stresses are described by the component of the stress tensor normal to the retinal plane, while the shear stresses are denoted by the shear components parallel to the retinal plane. These components of the stress tensor are separately discussed in the following paragraphs.The anteroposterior axis of the eyeball model coincided with the axis of simulated abusive shaking. The anterior side of the model was assumed to be facing the perpetrator shaking horizontally. shows an instantaneous snapshot of latitudinal distribution of the components of the stress tensor in an eyeball subjected to this sinusoidal shake. This snapshot was taken at the moment when the eyeball was just beginning to be pushed away from the imitate perpetrator during a cycle of shake, when the intensity of the stress components came to a climax. The inconsistency between the forced movement of the surrounding sclerocorneal membrane and the inertia of the vitreous body was maximal at this moment. As mentioned in the Methods section, we focus on the stress tensor of the outermost elements of the vitreous body in our model, as they represent the mechanical state in the vicinity of the retina., tensile stresses were applied to the retinal plane in the posterior hemisphere, while the compressive stresses were applied in the anterior hemisphere. The shearing stress peaked in the equatorial area; the odd-shaped shoulders at ±45° seem to be artifacts probably due to the discontinuity of the model mesh. The intensity of the shearing stress was about two orders of magnitude minor than those of tensile or compressive stresses. Therefore, we suspect the tensile stress as the main cause that leads to major deformation of the tissue near the vitreoretinal attachment that leads to destruction of the capillary network and hence RH. This broadness of the stress application, together with the unpredictably wobbling nature of abusive shaking, will account for the broad and non-localized nature of RH in SBS/AHT, extending even to the ora serrata (As a consequent outcome of that the axis of the simulated shake was strictly along the sagittal axis, which will probably never be the case in actual abuse events, the most intensive tensile stress appeared precisely at the posterior pole when the eyeball is just pushed back during a cycle of a shake. By considering a simple shake of a simple model, we are able to locate the point exposed to the harshest stress and discuss the worst case. Thus, hereafter, we focus on the posterior pole, where the stress was most intensive.The change of the component of the stress tensor normal to the retinal plane at the posterior pole along time is plotted in . The subtle difference in the response curves in spite of the 16-times difference in Young׳s moduli indicates that this physical property, difficult to measure (), fortunately did not affect much of the results. shows the simulated stress change due to an experimentally measured acceleration of the head of a shaken dummy doll cited from . The eyeball model was filled with 0.5% agar gel as a model of the vitreous body. Simulated and measured stress change at the posterior pole showed acceptable agreement to support the discussion below. shows the acceleration and stress change when this doll was subjected to an impact by falling from a 50-cm high to a hard floor, hitting in the front. As is intuitive, an intensive acceleration and stress change appeared in a very short time range, which is paradoxical to the experience of not causing RH in this kind of mechanical stress.We admit that we do not have any feasibility data to discuss the effect of vitreoretinal traction directly, which is the main target of criticism to FE studies of this kind (). Neither we reproduced detachment phenomenon in our model; all of the adjacent elements shared common nodes, which actually means that no detachment occurs in our simulation. However, comparing effects due to shaking and impact, apparently very different phenomena, in the same measure may give us an important insight described in the following paragraph.A formula describing the tackiness based on a setting with a simple geometry has been provided (). When two discs with a radius of a are bound with a layer of liquid adhesive of viscosity of η with a thickness of h1, the applied tensile stress denoted by F, the time duration of stress application denoted by t and the resultant thickness of the adhesive layer h2 are related as follows:This formulation is based on that when a given region of a layer of adhesive thickens due to a tensile force, there must be a flow of adhesive material towards this region, parallel to the plane of the layer of adhesive material, to fill the extra volume required for the thickening. Since the left-hand side of Eq. is proportional to time, this can be a good mechanical explanation of the term stress buildup, often used in this field without clear definition. That this formula includes a factor of viscosity, a property universal to liquid, supports the feasibility of this theory. Thus, according to this theory, time integration of the normal stress to the retina may be a good predictor of RH.If we calculate this value for the shake shown in , 101 Pa·s per cycle of shake is obtained. On the other hand, 36 Pa·s per impact is calculated for the impact shown in . When the above values based on a mathematical model on the mechanism of adhesion were calculated from the areas of the graphs of the stress changes, it was shown that the value of multiple round of shaking might readily surpass that of single impact. This may clearly explain why RH is characteristic to the shaking injury. Similar values are reported in the study using a dummy doll equipped with an eyeball model, which reported 107 Pa·s for a single cycle of abusive shaking and 60–73 Pa·s for a single event of fall, and reached the same conclusion (The classical theory on tackiness assumes the major origin of tackiness being the lateral flow of viscous fluid of adhesive material. This lateral flow of adhesive fluid between the vitreous body and the retina might be a more reasonable explanation for the pleated retinal folding than to attribute this to the effect of shear stress, which was shown to be about two orders of magnitude minor (). The counterpart compressive stress that appears in the opposite side of the cycle of shake will not contribute to the repair of the detachment of the adhesion because compressing by a soft matter such as the vitreous body itself will not be able to turn the unevenness of the viscous fluid layer back to the initial uniform distribution.The strength of the vitreoretinal attachment is known to depend on the location; it is stronger in the surroundings of the macula and in the area approaching the ora serrata. We were not able to evaluate the effect of this factor since our model cannot reproduce detachment. That the shear stress is minor in the observed stress field in the eyeball implies that the effect of the strength of the attachment in a given region is restricted to a narrow vicinity in terms of longitude and latitude. Thus, the distribution of vitreoretinal attachment strength and the distribution of RH are not likely to be directly correlated. This coincides with the non-specific nature of the RH distribution.As a rough estimation, we calculated thickening ratio (h2/h1) as a function of the initial thickness of the layer of liquid adhesive from Eq. ). We compared the effect of a single event of impact (Ft=36Pa·s) and 10 cycles of shake (Ft=1010Pa·s). We assumed η=0.7mPa·s, simulating water under physiological temperature, and a=10 mm. shows that the thickening ratio as a result of 10 cycles of shake can be far greater than that as a result of single impact, when the initial thickness is above ca. 5 μm. Although we are not able to specify the actual identity of the layer of liquid adhesive hypothesized in Eq. , the assumption of this layer with a thickness in the order of cell size at the vitreoretinal boundary may be not too far from reality, especially in the area without stronger vitreoretinal binding.The FE mechanical model used in this study is simple yet retains essential features of real eyeballs adequate for the analysis. In this study, we have succeeded to develop a reasonable explanation for the paradoxical finding of RH in abusive context by keeping our model simple enough to clearly analyze the phenomenon based on a sound mechanical theory following a reliable chain of cause and effect. Our study may be too primitive in some aspects, but surely provides a firm basis for further analyses.Supplementary data associated with this article can be found in the online version at Combined `heat flow and strength' optimization of geometry: mechanical structures most resistant to thermal attackThis paper outlines a new direction for fundamental heat transfer: a multidisciplinary approach (combined heat transfer and strength of materials) in the conceptual design of structures that have two functions, mechanical strength and resistance (survival) in the presence of sudden thermal attack. The two functions are considered simultaneously, from the start of conceptual design. This is unlike traditional approaches, where structures are optimized for mechanical strength alone, or for thermal resistance alone. In the first part of the paper, the profile of a beam loaded in bending is optimized by maximizing the lifetime in the presence of sudden heating. The propagation of the heat wave through the beam causes softening, because of the gradual transition from elastic behavior to thermoplastic behavior. In the second part of the paper, the subject is a beam of concrete reinforced with steel bars. It is shown that the clash between the mechanical and thermal objectives of the beam generates the shape of the beam cross-section, and the position of the steel bars in the beam cross-section. The generation of optimal architecture for maximal global performance under global constraints in freely morphing systems is constructal design. On the background of the constructal architectures that have been developed so far, the present paper outlines the first steps toward the constructal design of multiobjective (multidisciplinary) architectures.distance between two consecutive bars, mThe earliest work was devoted to the simplest type of geometry generation: systems the development of which is driven by a single objective. For example, in the tree-shaped constructs generated for cooling a volume the single objective is the minimization of the global thermal resistance (e.g., The great diversity and apparent lack of `correlation' of the structures that emerge in nature and engineering can be attributed to the fact that even the simplest element of a complex system has more than one objective. This is why a systematic extension of the constructal approach to multi-objective systems is necessary and timely. A first step in this direction was described in Ref. The combined `flow and strength' geometry proposed in Ref. In this paper we take the combined `flow and strength' constructal method in a new direction: systems that must be mechanically strong and, at the same time, must retain their strength and integrity during thermal attack. Mechanical structures become weaker and may collapse if they are exposed to intense heating. The collapse of the World Trade Center is a reminder of how dangerous the effect of sudden intense heating can be. Large buildings, highway overpasses and industrial installations are vulnerable.The classical approach to providing a structure with thermal resistance against intense heating is by coating the structure with a protective layer after the structure has been designed ), and beams of concrete reinforced with steel (). In both classes the solid structure is penetrated by time-dependent conduction heating. We show that the mechanical and thermal objectives compete, and that this competition generates the optimal geometry of the system.Consider a beam simply supported at each end (). The beam geometry is two-dimensional, with the length L and symmetric profile H(x). The total load F [N m−1] is distributed uniformly over the beam length L. The force F is expressed per unit length in the direction perpendicular to the plane of . The weight of the beam is assumed to be negligible in comparison with the load. The beam profile is sufficiently slender so that its deformation in the y-direction is due mainly to pure bending.The beam is initially isothermal at the ambient temperature T∞, where it behaves elastically throughout its volume. The modulus of elasticity is E, which for simplicity is assumed constant. Thermal attack means that at the time t=0 the beam is exposed on both surfaces to the uniform heat flux q″. Temperatures rise throughout, but they rise faster in the subskin regions (). These are the first regions where the material behavior changes from elastic to plastic. The last to undergo this change is the core region of thickness Z(x), in which the material behaves elastically.The total bending moment in a constant-x cross-section is (e.g., Refs. where W is the beam length in the z-direction, which is perpendicular to the plane of . This moment is balanced by the moment due to the tensile and compressive stresses (σ) that are present in the cross-section. When σ is less than the yield stress σy, the material behaves elastically. The yield stress decreases as the local temperature increases. For simplicity, we assume a linear model for the effect of T on σy,where the β coefficient is a property of the material, and Tref is a reference temperature, such that σy,ref=σy(Tref). For the sake of convenience, the reference temperature was set equal to the ambient temperature, Tref=T∞ and σy,ref=σy,∞. In the elastic core the stresses vary linearly (e.g., Ref. In this expression σy is the yield stress at y=±Z/2, which is associated with the instantaneous temperature at that location, T, cf. Eq. . We assume that in the peripheral regions outside y=±Z/2 the material is perfectly plastic, so that σ is equal to σy(T), where T is the local temperature. summarizes qualitatively the distribution of stresses in the cross-section, at a time when plastic regions are present, Z<H. In this model we accounted for the fact that in the beginning there is a time interval when the entire beam is elastic, and the maximum stress (σmax, at y=±H/2) is still below the yield stress. During this initial time interval the beam deflection is constant in time. The moment formed by the stresses in the beam cross-section,leads to a two-term expression that accounts for the elastic and plastic regions, can be combined to pinpoint the location of the elastic–plastic interface, Z(t,x), for a specified beam profile H(x), and temperature distribution T(t,x,y).Consider next the beam deflection in the y-direction. The local radius of curvature ρ of the deformed beam is (e.g., Refs. As a first approximation, for small deflections the position of the neutral line [y=δ(x)] can be written asIn the absence of a plastic zone, the stress in the outer fibers (y=±H/2) is. On the other hand, when a plastic zone is present, the maximum stress is reached at the plastic–elastic interface, σmax=σy[T(Z/2)]. Eq. can be integrated twice to obtain the position of the neutral line. The boundary conditions areThe maximal deflection occurs in the midplane,The amount of beam material is fixed, and, in view of the two-dimensional geometry of We considered many profile shapes, e.g., Eq. in the next section. For every assumed shape, we calculated numerically the time evolution of the maximal deflection, δm(t). The objective is to identify the shape for which δm is the smallest at a given t. This shape is the most resistant to thermal attack.The numerical work was conducted in dimensionless terms by using the dimensionless variables:The local beam temperature is known from Fourier analysis The infinite sum in the square brackets is important only in the beginning, and vanishes rapidly for To start with, we considered a family of beam shapes that are smooth and thicker in the middle, e.g., The shape parameters C and m are related through the size constraint The geometry is characterized by one shape parameter (m), which plays the role of degree of freedom, and by three construction parameters: until the elastic core disappears at a location x̃. The model constructed in the preceding section is not valid when the elastic core is absent. shows that the deflection increases in accelerated fashion in time, and that can be minimized by selecting the shape parameter m. This is the key result: the beam geometry can be selected in such a way that the beam as a whole is most resistant to thermal attack. This is a result for how the whole beam performs––a global result––because is a global feature. All the strained fibers contribute to The influence of shape on performance is described further in has been plotted for three m values. Because the objective is to achieve the smallest , we conclude that the best shape (m) changes as the time increases. The intersecting curves mean that mopt decreases as t̃ increases. This decrease accelerates in time, as shown in . The same figure shows that the minimal mid-plane deflection , which corresponds to the optimally changing shape mopt (t̃), also accelerates in time. If t̃ denotes the prescribed life-time of the beam––the time in which it must withstand the thermal attack––then for every t̃ there exists an optimal beam shape. are the short times, where deflections are small and comparable with deflections based on the assumption that thermal attack is absent. In this limit there is a definite beam shape that is optimal. This is also the limit in which the model constructed in The optimization of the beam profile for maximal resistance to thermal attack is instructive in a fundamental sense, because it proves that an optimal beam profile exists. A beam profile that is easier to manufacture than the smoothly-varying profile assumed in . The beam is thickest in the middle (Hmax) and thinnest at the ends (Hmin). The area of the profile continues to be constrained,. This profile has one degree of freedom, the role of which is played by the dimension . This dimension was optimized so that the mid-length deflection is minimal for a specified life-time t̃. The optimization results presented in The minimized deflection is also reported in accounts for the influence of the temperature on the yield point. A larger with increasing temperature. The decrease of The sensitivity of the optimized geometry to changes in system size (. The amount of material used to build the beam is proportional to the parameter . Thicker beams are stiffer, i.e. they experience smaller deflections for a given load.In this section we illustrate the opportunity for optimizing the internal structure of a beam of concrete reinforced with steel bars. Once again, the objective is maximal survivability to thermal attack. The beam is in pure bending, and its cross-section is shown in . The steel bars run in the direction perpendicular to the figure, and are modeled as a slab with cross-section hs×b. The beam is loaded such as the steel slab is in tension, while the concrete situated above the neutral line is in compression.Thermal attack is modeled as a uniform heat flux (q″), which is imposed suddenly on the periphery of the beam cross-section. The most critical part that is vulnerable under thermal attack is the steel, therefore in the simplest model we focus on the q″-heating that is applied on the bottom of the cross-section, which is the closest to the steel. A layer of concrete of thickness λ protects the steel against the thermal wave driven by q″. The thickness λ plays an important role. In order for the beam to support a large load, λ must be small: the steel must be positioned as far as possible from the top of the beam cross section. On the other hand, a high resistance to thermal attack requires a large λ. The competition between these two requirements represents an optimization opportunity.A competition exists because the beam design must meet two objectives, mechanical strength and thermal resistances. There are two constraints, the area of the beam cross-sectionand the cross-sectional area of the steel, As=hsb. Alternatively, the steel constraint can be expressed as the area fraction occupied by steel in the cross-section,Because steel is expensive, it is reasonable to assume that hs≪h, or φ≪1. The distance from the top of the beam to the mid-line of the steel cross-section isIn accordance with the classical model of a reinforced beam where hn denotes the position of the neutral line, which is given byThe heating of the beam from the bottom is a process of unidirectional time-dependent conduction in a heterogeneous medium containing two materials, concrete of thermal conductivity k, and steel. The assumption that the amount of steel is small (φ≪1) justifies the use of a conduction model in which the steel is represented by a line drawn at The analytical solution for the temperature field is The elastic modulus of steel decreases monotonically as the temperature increases. Consequently, the heating process has the effect of decreasing the beam stiffness, Eq. . We account for the coupling between the changing temperature field and the global stiffness of the beam by using the relative (dimensionless) elastic modulus The reference elastic modulus was set at Es (20 °C) = 200 GPa, which is representative of both low and high carbon steel. The relative modulus for steel is where T is expressed in °C. The elastic modulus of concrete was assumed insensitive to temperature changes, and was set at Ec=20 GPa. The thermal properties of concrete are k=1.44 W m−1 |
K−1 and α=6.92×10−7 m2 |
s−1. Numerical simulations were performed for a beam with these material properties and A=0.3 m2, φ=0.03 and q″=2×104 W m−2.The cross-section geometry has two degrees of freedom, the aspect ratio h/b and the protective thickness λ. In the first phase of numerical simulations we fixed h/b and varied λ. shows the evolution of the global stiffness in time, as the heat wave expands into the beam. Most resistant to this softening effect are beams with thicker protective layers. Such beams are also the weakest when not under thermal attack.If the life-time (t) for the survival of the beam under the effect of q″ is specified, then the reading of at constant t shows that there exists an optimal λopt(t) where the beam stiffness is maximal . In other words, for a beam to support its load with maximal stiffness at the end of its life under thermal attack, it must be designed with an optimal thickness for its protective layer: λopt is the trade-off between the mechanical and thermal objectives recognized at the start of . The optimal thickness of the protective layer is shown in An alternative way to exploit the mechanical and thermal trade-off is by relaxing the assumption that the aspect ratio of the cross-section is fixed. In this case λ and h/b may vary. If the global stiffness of the beam (before heating) is specified by design, , then λ is a function of h/b. This function is illustrated in : λ is almost proportional to h/b, and almost inversely proportional to is constrained the geometry of the beam cross-section has only one degree of freedom, λ or h/b (e.g., ). The global stiffness decreases monotonically as the q″-heating process persists. The decrease in is slower when h/b is larger. This makes sense, because taller cross-sections have thicker protective layers. At a specified lifetime t, increases monotonically as h/b increases. This behavior is unlike in There are at least three reasons that limit the push toward larger h/b and λ values. First, during a real thermal attack scenario q″ acts all around the beam cross-section. When h/b is large, the h-tall side surfaces play a significant role in the heating of the steel bars, and because of this the unidirectional conduction model no longer applies. The second reason is that tall beam cross-sections (large h/b) require large heading room. The rooms and buildings in which such beams are used must be tall. Finally, if the beam width b is too small then, contrary to the model of , it may be impossible to place the steel bars with enough spacing between them in one single row––impossible to embed them securely so that they would cling to the surrounding concrete. has the merit that it shed light on the opportunity to optimize the reinforced beam geometry. A more realistic model of the beam cross-section is presented in . The beam height and width are h and b. The total cross-sectional area A is constrained, Eq. . There are n round steel bars of diameter D. The spacing between two adjacent bars is d. The area fraction occupied by steel in the cross-section isThe slab-shaped region occupied by the n bars is surrounded by a protective layer of concrete. It is assumed that the distance from this region to the nearest heated surface is the same (λ) in each of the three directions from which heating is threatening: from below and from the sides.As noted in the preceding section, an important construction requirement is that each steel bar must continue to cling to concrete when it is in tension. This requirement calls for positioning the bars sufficiently far from each other. Design rules have been developed for meeting this requirement we require that the bar-to bar distance d must be greater than or equal to D. If the required bars (required by the specified φ) do not fit in a single row, then they must be placed equidistantly in two rows.The description of the temperature history in the beam cross-section is available analytically in the limit φ≪1, when the only conductive material that matters is concrete. The temperature history due to q″-heating imposed at t=0 on all four boundaries is The origin of the x–y coordinates is placed in the center of the beam cross-section: see . The temperature of each bar cross-section is assumed uniform and equal to the concrete temperature at the x–y location of the bar center.It is possible to combine this bidirectional time-dependent conduction model with the elasticity-temperature model of Eqs. , and to calculate the position of the neutral line and the time-evolution of the global stiffness of the beam. This approach would limit the results to beams and lifetimes (under attack) when every element of the beam is still stressed in the elastic domain.In this section, we chose a more realistic and general strength model, to take advantage of the refinements contributed by the heat transfer model. To calculate the maximal deflection of a beam in a general way, i.e., without assuming that the elastic regime prevails throughout, it is necessary to calculate the stresses at every point in the three-dimensional reinforced beam. Then the deflection differential equation has to be solved. A simpler version of this approach is available. To characterize the strength of the beam in a global sense, one can use (instead of deflection, or , fc′ and h̄ represent the strength of steel, the strength of concrete, and the y-position of the bars measured from the top of the beam,The overbar indicates an average made over all the steel bars that are present. The strength of the concrete fc′ has been evaluated at the average temperature of the beam cross-section,The effect of the local temperature on the strength of steel and concrete is taken into account by using the dimensionless factors where the reference strengths for steel and concrete are fs (20 °C) = 500 MPa and fc′ (20 °C) = 35 MPa. The influence of temperature on , the beam cross-section has three geometrical degrees of freedom: h/b, λ and n. For each assumed geometry (h/b, λ, n), we monitor the evolution of the nominal moment strength in the presence of heating from all sides, Mn(t). The constrained parameters are A, φ and q″. We also fixed the initial nominal moment, leaving only two degrees of freedom, h/b and n. shows the relation between the aspect ratio h/b and the protective layer thickness λ for a specified initial strength and number of bars. The curves for n>1 exhibit jumps as the aspect ratio increases. These jumps are due to discrete changes in the internal structure––the way the bars are positioned in the beam cross-section. For instance, when the aspect ratio is high, in order to satisfy the condition d=D (see ) the designer is forced to place many bars in a single row.In the absence of thermal attack, all the beam designs described by the curves of are equivalent. They provide the same nominal moment at t=0. However, they behave differently in case of thermal attack. For example, shows the time evolution of Mn for a one-bar beam. At a given time, it appears that there is an optimal aspect ratio h/b for maximal strength. Similar calculations have been performed for n=2 and 3. The results are shown in . The existences of an optimal design for a given time is again confirmed.Finally, all the optimal shapes and structures are reported in . Even though the optimal beam shape (h/b) varies depending on how many bars are embedded in the beam, the beam performance under thermal attack does not appear to be significantly affected by the number of bars.Multiobjective systems are numerous and manifold, and to address simultaneously their objectives calls for truly interdisciplinary research. In this paper, we illustrated the interdisciplinary approach by showing that shapes and structures of beams can be optimized to face thermal attack. Examples of optimized shapes were the beam profile and cross-sectional aspect ratio. Optimized internal structure was the position of the steel bars in concrete.The optimal architecture of the multiobjective system is a consequence of the competition between objectives. For the beams treated in this paper, the competition is between the requirement of high strength in the absence of thermal attack, and the call for thermally insulated structures that resist thermal attack. The beam geometry is generated by conflict. For example, the steel bars in a beam of reinforced concrete must be placed as far as possible from the top of the beam cross-section, in order to support the largest bending moment. On the other hand, the steel bars must be positioned far from all the exposed surfaces (including the bottom of the beam cross-section) in order to maximize the resistance to the heat wave that penetrates the beam.The work presented in this paper is fundamental and exploratory. Its principal objective is to show that the “combined heat flow and strength” method of Ref. More realistic models can be combined with the method outlined in this paper, in the pursuit of optimal architectures that serve more than one objective. Structures of greater complexity (e.g., buildings) promise to benefit from the multidisciplinary approach advocated in this paper.One of the reviewers of this paper commented on the availability of all-powerful CFD optimization codes in the structural community. It is important not to confuse the method of constructal design with the blind optimization of every possible feature in a design that, if free, has an infinity of such features.The reviewer also noted that real design consists of flights of imagination, and with this we agree wholeheartedly. The difficulty is that flights of imagination translate into shorter and shorter leaps as structures become more complex. The challenge is to inspire flights of imagination early in the evolution of configuration, when the design is still nakedly simple. Problems such as the configurations of are significant leaps forward from the amorphous black box with which an all-powerful CFD code might start. To sense where the optimization opportunities lie requires intuition. One of the objectives of good research is to improve intuition. Constructal design efforts are oriented in that direction.In constructal design, we see the development of high-performance complex flow structures as the optimized assembly of optimized elements and optimized simpler constructs. This route from the elemental to the complex, from small to large, from single-scale to multi-scale, and from single-objective to multi-objective represents the strategy of constructal design. The better the strategy, the larger the leaps. The better the teaching of strategy, the stronger the intuition in the still unbiased minds of the audience.It is `good strategy' to know like an alphabet the elemental systems that have had their shapes and structures optimized, e.g., the round cross-section for the duct with least flow resistance, the tree network for maximal access between a point and an area, and the tapered cantilever beam of equal strength Another reviewer commented on the strong interdisciplinary character of this paper. Combined heat transfer and strength of materials should be brought to the attention of both fields. This means publishing not only in structural mechanics, as the post-September 11 literature is showing, but also in heat transfer. The present paper is a case of interdisciplinary research at its best––a fundamental problem that is pursued with interest by a team of researchers from both thermal engineering and civil engineering.For the continued vigor of heat transfer as a research arena with purpose, it is crucial that each of us brings to the attention of the heat transfer community the important questions––the new opportunities––that lie at the interfaces with neighboring or distant fields.Effects of Metalloid B Addition on the Glass Formation, Magnetic and Mechanical Properties of FePCB Bulk Metallic GlassesLow-cost Fe80P12−xC8Bx (x = 0, 1, 2, 3 and 4 at.%) bulk metallic glasses (BMGs) with good soft magnetic and mechanical properties were prepared, and effects of metalloid B addition on the glass-forming ability (GFA) as well as thermal, magnetic, and mechanical properties of the BMGs were investigated. It was found that the proper B substitution for P improves the GFA of the Fe–P–C BMGs. The alloy with 2 at.% B addition manifests the highest GFA with critical diameter for glass formation of 2 mm. Besides, these BMGs exhibit good soft magnetic properties featured by high saturation magnetization of 1.35–1.57 T and low coercivity of 2.2–7.7 A/m as well as unique mechanical properties of high fracture strength of ∼3.3 GPa and visible plastic strain of 0.4%–2.5%. The combination of high GFA, good soft magnetic and mechanical properties as well as low cost makes the present Fe–P–C–B BMGs promising as soft magnetic materials for industrial applications.Fe-based ferromagnetic metallic glasses (MGs) have attracted tremendous attention due to their excellent soft magnetic properties, e.g. high saturation magnetization Ms and permeability as well as low coercivity and core loss, and good mechanical properties. These BMGs exhibit both good soft magnetic and unique mechanical properties, which make them promising as soft magnetic materials in potential applications. However, in general various metallic elements, such as Al, Ga, Zr, Nb, Mo and Y, are always involved in these BMGs to improve their GFA. Nevertheless, the introduction of these non-ferromagnetic elements invariably decreases the Fe concentration and hence leads to the decrease in Ms and also the increase in the material cost. Therefore, it is necessary to develop Fe-based BMGs with both high GFA and high Ms using low cost constituent elements.Recently, a series of Fe–P–C alloys, which exhibit good soft magnetic properties and low cost and can be fabricated into the bulk form, have been developedAlloy ingots with nominal compositions of Fe80P12−xC8Bx (x = 0, 1, 2, 3 and 4 at.%) were prepared by induction melting mixtures of pure elements of Fe (99.5 mass%), C (99.9 mass%) and industry-grade pre-alloys of Fe–P (25.12 mass% P) and Fe–B (17.73 mass% B), in an argon atmosphere. Cylindrical rods of 1–2 mm in diameter and 30–50 mm in length and ribbons with a dimension of ∼30 μm in thickness and 5 mm in width were fabricated by copper mold casting and single-roller melt-spinning, respectively.Phase structures of the specimens were identified by X-ray diffraction (XRD) with Cu Kα radiation and transmission electron microscopy (TEM). Crystallization behaviours of the as-prepared bulk samples were characterized by differential scanning calorimetry (DSC) at a heating rate of 0.33 K/s. Hysteresis loops and coercivity of all the samples were measured at ambient temperature using a vibrating sample magnetometer (VSM) under an applied magnetic field of up to 800 kA m−1 and a dc B–H loop tracer under a field of 1 kA m−1, respectively. All the samples for the magnetic measurements were annealed at 50 K below the glass transition temperature Tg for 600 s. The density ρ was measured by Archimedes' method. Uniaxial compression was conducted using a mechanical testing machine at a strain rate of 1 × 10−4 s−1 at ambient temperature. Test samples with a gauge aspect ratio of 2:1 were cut from the as-cast 1-mm-diameter cylindrical rods. The elastic properties were determined by ultrasonic pulse-echo techniques using as-cast glassy rods with diameter of 1 mm and length of 2 mm. The elastic constants including Young's modulus E, shear modulus G, bulk modulus K and Poisson's ratio ν were calculated according to the measured data of longitudinal and transverse sound velocities vl and vt. At least five samples were tested for each composition to ensure the reproducibility. shows the XRD patterns of the as-cast rods with the critical diameters of glass formation dc for Fe80P12−xC8Bx (x = 0, 1, 2, 3 and 4 at.%) alloys. All the patterns manifest only broad diffraction humps without any crystalline peaks, which identify the amorphous nature of them. The formation of glassy phase is further confirmed by TEM. The high-resolution TEM micrograph and selected-area electron diffraction (SAED) pattern of the as-cast alloy (x = 2) with a diameter of 2 mm are shown in . The SAED pattern consists of only halo rings with no lattice fringe detectable from the high-resolution TEM image, revealing no evidence of any crystallization as well. As listed in , the dc of the Fe–P–C–B alloys increases from 1.5 to 2 mm with the increase in the B content from 0 to 2 at.%. Yet further B substitution for P would deteriorate the GFA. The enhanced GFA by proper addition of B can be explained by the “confusion principle”: the more the elements involved, the lower the chance that the alloy can select viable crystal structures, and the stronger tendency of glass formation. Also, the atom radius of B lies between those of P and C. The addition of B causes more complicated size mismatch and leads to more efficient atom packing, thus improves the GFA shows the DSC curves of the glassy Fe80P12−xC8Bx (x = 0, 1, 2, 3 and 4 at.%) alloys in their critical diameters. All the samples display a glass transition, followed by a supercooled liquid region and crystallization process. With the increase in B content from 0 to 4%, the Curie temperature Tc monotonically increases from 578 to 613 K, and the glass transition temperature Tg and onset crystallization temperature Tx increase from 699 to 712 K and 722–742 K, respectively. It is supposed that the increases in Tg and Tx are caused by the reinforcement of the atomic bonding strength among the constituent elements caused by the B substitution for PThe saturation magnetization Ms and coercivity Hc of the Fe80P12−xC8Bx (x = 0, 1, 2, 3 and 4 at.%) alloys were obtained according to the measured hysteresis M–H loops, as shown in . It is seen that all the loops show typical soft magnetic behaviors. The dependences of Ms and Hc on the B content are depicted in (b). With increasing B content from 0 to 4%, the Ms gradually increases from 1.35 to 1.57 T. In comparison, Hc deceases with the increase in B content and reaches the lowest value of 2.2 A/m at the B concentration of 2%. The increase in Ms can be explained by the different electron configurations of B and P atoms. For the Fe-metalloid type amorphous alloys, the magnetization varies with the alloying metalloid elements because of the transfer of charge between two species of atoms (e.g. from B to Fe). The valence electrons of metalloid elements would transfer to the d band of Fe atoms, which deceases the Ms of the alloy. The Ms of Fe–P–C–B BMGs is improved because the sp electrons of B is less than that of P (the numbers of sp electrons are 3 and 5 for B and P, respectively). Moreover, as manifested by , Tc increases with the B addition, implying that the ferromagnetic exchange interactions among Fe atoms are enhanced by the B addition, which also usually contributes to higher MsThe effects of B substitution for P on the mechanical properties of the present alloys have also been examined by uniaxial compression tests using the as-cast rods. As shown in , the B substitution increases the fracture strength σf but reduces the plastic deformability. With increasing B content from 0 to 3 at.%, the σf increases from 3011 to 3302 MPa, yet the plastic strain εp decreases from 2.5% to 0.4%. When 4 at.% B is added, the alloy exhibits a brittle fracture behaviour at σf of 2152 MPa. It is well known that the strength of BMGs is universally correlated with Tg, Tg gradually increases with the B addition in the Fe–P–C–B BMGs, which conforms to the trend for σf within the range of B content from 0 to 3 at.%. However, there is an exception that σf decreases abruptly when 4 at.% B is added. This is supposed to be attributed to its severe embrittlement, which tends to cause the premature brittle fracture due to the easy cracking at stress concentration sites before the intrinsic material strength can be achieved. Thus the strength is dominated by the extrinsic defects rather than the intrinsic destabilization of the amorphous structures. This can be corroborated by the distinct fracture morphologies of typical samples with 2 and 4 at.% B additions, as shown in . Representative vein patterns indicative of shearing deformation mechanism can be observed on the fracture plane for the Fe80P10C8B2 alloy (x = 2) ((a)). Shear bands can also be detected near the fracture surface ((b)). This may account for the visible plastic deformation of the alloy. Nevertheless, the Fe80P8C8B4 alloy (x = 4 at.%) tend to split into several pieces with mirror-like fracture surfaces, as displayed in (c) and (d), which is the typical cleavage-like fracture feature of intrinsically brittle BMGs.It has been reported that the mechanical properties of BMGs are closely related to their elastic properties, e.g. the ratio between the shear modulus G and bulk modulus K or the Poisson's ratio ν shows the variations of the elastic constants including Young's modulus E, G, K, and ν, of the present BMGs. With increasing B content from 0 to 3 at.%, E and G increase yet ν decreases. Considering the low GFA of Fe80P8C8B4 alloy (x = 4) with dc of 1 mm, it is possible that there may exist tiny crystals, which cannot be detected under the accuracy of XRD, that causes the abrupt increase in E, G and K. It is supposed that the elastic properties are tightly associated with the intracluster metal-metalloid bonds and intercluster metal–metal bonds in the amorphous network. Because the Fe–B bonds contain more covalent component and are stronger than the Fe–P bonds, the partial substitution of B for P may cause the strengthening of the Fe-metalloid connections in the amorphous network and decease the metallic character of them(c)). Thus the Poisson's ratio is decreased, which results in the deterioration of ductility in the Fe–P–C–B BMGs.In conclusion, Fe80P12−xC8Bx (x = 0, 1, 2, 3 and 4 at.%) soft magnetic BMGs have been synthesized by copper mold casting, and the effects of metalloid B substitution for P on the GFA as well as thermal, magnetic, and mechanical properties have been investigated. It is found that the proper B addition enhances the GFA of the alloys with increasing the dc from 1.5 to 2 mm with 2 at.% B addition. The Ms of the alloys gradually increases with the B additions. Also, the B addition increases the σf but reduces the plastic deformability of them. The Fe–P–C–B BMGs exhibit high Ms of 1.35–1.57 T and low Hc of 2.2–7.7 A/m. In addition, these BMGs manifest good mechanical properties featured by a high σf of 3.3 GPa and visible εp of 0.4%–2.5%. The combination of high GFA and good soft magnetic and mechanical properties makes these alloys promising as soft magnetic materials in potential applications.The origin of weld seam defects related to metal flow in the hot extrusion of aluminium alloys EN AW-6060 and EN AW-6082Longitudinal weld seams are an intrinsic feature in hollow extrusions produced with porthole dies. As these joins occur along the entire extruded length, it is desirable that these weld seams have a minimal impact on the structural integrity of the extrudate. In particular, defects associated with weld seam formation should be avoided. In this research, the occurrence of defects related to material flow inside the extrusion tooling is studied. In lab-scale experiments, EN AW-6060 and EN AW-6082 aluminium alloy billets are formed into strips by means of the direct hot extrusion process. By utilising model dies with an internal obstruction similar to the supports present in porthole dies, a strip with a central longitudinal weld seam is formed. The effects of different geometries of the weld-chamber and the processing conditions on the quality of the weld seam are investigated. Characterisation is performed through mechanical testing, focusing on the ability of the weld seam area to accommodate plastic deformation, and microstructural analysis provides insight into the defects related to unsound metal flow. Through computer simulations, conditions related to weld seam formation are modelled and correlated with the experimental results. The experimental results demonstrate that metal flow controlled by the die geometry causes defects leading to inferior mechanical performance of the extrudate. It is further argued that current weld seam formation criteria utilised in finite element modelling need enhancement to incorporate these flow related defects.Aluminium extrusion is a thermo-mechanical forming operation in which a pre-heated work piece (the billet) is pressed though a tooling orifice with a precisely defined opening, leading to elongated parts with a constant cross-sectional geometry. Extruded shapes can be divided into two main categories: solid sections and hollow sections. In (multi-)hollow extrusions, the cross-sectional area is bordered by a single continuous curve defining the outer perimeter and an internal curve for each enclosed void. Hollow sections are generally produced with tools in which cores, or mandrels, are internally suspended in the die by means of legs or bridges. In multi-hollow sections, the number of cores equals the number of voids. In extrusion through porthole dies, the aluminium billet is split into separate metal streams flowing around the legs, to be re-joined in the weld chambers, thus forming longitudinal weld seams. These weld seams occur along the entire extruded length and can therefore not be removed from the extrudate, in contrast to the transverse weld seams, caused by the joining of two consecutive billets, The joining of the metal streams occurs under conditions of pressure, strain/shear and temperature, but without the occurrence of liquid phases, i.e. a solid-state bonding process. Influenced by the particular local process conditions, micro-structural reorganisation processes such as recovery, recrystallisation and grain growth occur () having an obvious bearing on weld-seam formation.Material flow results from the plastic deformation of the workpiece as this is forced from the container and through the die. Material flow in extrusion is governed by the tooling geometry, with secondary influences from the process parameters. Obstructions in the flow path and areas with high friction conditions, such as the mandrel supports, the container wall and the die face lead to stationary areas inside the die, termed dead metal zones (DMZ). In addition, stationary pockets of material can be present at abrupt changes in flow direction and downstream of the obstructions in the die, e.g. as shown by using a model material with a grid pattern, thereby providing a clear representation of the flow pattern. By extending the work to a three-dimensional study in later experiments by utilising a similar set-up, a more complete view of the flow pattern and resulting dead metal zones was obtained.As outlined above, longitudinal weld seams are formed through rejoining of metal streams initially separated by these obstructions. Sub-optimal processing conditions can lead to a number of detrimental features of the weld seam, impairing the structural integrity of the extrudate with varying levels of defect severity, as defined by . These defects can be related to external factors, such as the entrapment of contaminants or gas. Assuming that detrimental external factors are avoided through proper operational measures, appropriate flow conditions are of primary importance in order to establish and maintain contact of the material on the bond plane, resulting in weld seams.Under unfavourable flow conditions, so called “kissing bonds” may occur: a term initially describing an interfacial defect in adhesively bonded structures where there is intimate contact between surfaces but with little bonding (, referring to similar zero volume interface defects occurring in metallic bonds formed in extrusion and friction stir welding. In more severe cases, where insufficient transverse flow occurs behind an obstruction or a DMZ, full rejoining of the metal streams is hindered and partially bonded areas lacking “metallic bonding” are formed due to the formation of gas pockets in the die as described by . The occurrence of gas pockets at the downstream position of the mandrel supports and the detrimental effect on weld seam bonding was further demonstrated by in a series of experiments with a modular die set-up enabling the geometry of the weld chamber to be changed. In these cases the defect is uniquely related to the flow pattern in a particular die. Elaboration of this work by includes the effect of process conditions on the contact behaviour between the aluminium and the mandrel supports, with sticking friction leading to full initial contact of the metal streams or sliding friction resulting in a gas pocket before the metal streams rejoin. Finally, with further exacerbated flow conditions, rejoining of the metal streams is impaired to the point that the gas pocket extends throughout the entire flow path from the weld chamber to the die exit, resulting in a void in the interior of the extrudate cross section.Several methods have been proposed to predict weld seam performance. These methods are largely based on the pressure acting on the bond plane combined with flow-related features, like the residence time in the weld chamber as initially postulated by . Numerical methods are utilised to calculate the relevant input values for weld seam quality criteria, such as originally developed by . Subsequent derivatives of this criterion were developed () with the introduction of a velocity correction factor for different welding paths and () with the introduction of a critical welding indicator implemented in finite element simulations. In a general sense these criteria predict improved weld seam performance for higher interfacial pressure levels and/or longer bonding paths (equivalent to increased bonding times when transit speed through the welding chamber remains unchanged). Although trends can be extracted from these criteria, calibration with experimental data obtained under similar conditions remains necessary to arrive at a quantified assessment of weld seam quality. Moreover, local effects such as the occurrence of a gas pocket as described above, are not captured, as these criteria represent a global value for the entire weld seam in question.As the constitutive behaviour of the material can impact the flow pattern, the occurrence of flow-related defects must be considered in connection with the specific alloy being processed. Insight into the influence of the die on the prevention of flow-related defects can then aid the optimisation of the tooling geometry for the production of sound structural hollow extrusions. In the laboratory-scale extrusion experiments described below, attention is focussed on the flow characteristics related to weld seam defects. Additionally the effect of process conditions combined with the constitutive alloy behaviour on the occurrence of weld seam imperfections is assessed.Extrusion tests were performed on a 500 kN laboratory-scale hydraulic press operating in direct extrusion mode. Billets with dimensions ∅25 mm × 100 mm were machined from industrial direct chill cast billet feedstock in the homogenised condition. The alloys processed in these experiments were EN AW-6060 and EN AW-6082 (hereafter denoted 6060 and 6082, respectively). The compositions, determined by means of optical emission spectroscopy, are shown in . These values are within the limits of the concerned European standard EN 573 (. The aluminium billet is split by the central leg into two separate streams. When these streams are rejoined downstream of the leg a weld seam is formed.Through-thickness transverse tensile samples were machined from the extrudates with shape and dimensions shown in , with the weld seam located at the midpoint of the test piece. Due to the limited size of the available material, the dimensions of the tensile specimens are not compliant with those of standardised tensile coupons. Nevertheless, the results of the tensile tests are still suitable for comparison between the different samples obtained from these extrusion experiments. The uniaxial tensile tests were performed at a temperature of 23 °C and 50% relative humidity at a fixed crosshead speed 0.033 mm s−1. showed that the ductility, defined by the strain at fracture of uniaxial tensile samples obtained from a hollow AA6082 extrusion is adversely affected by the presence of a weld seam. Donati and Tomesani established that in extruded AA6082 aluminium alloy extrusions with a weld seam the strength properties exhibit minor effects when the welding pressure is above a threshold level, whilst the ductility exhibits a strong relation with the pressure in the weld chamber (). However, in plastic deformation of aluminium alloys containing weld seams as often occurring in post-extrusion forming operations, the ductile performance of the material is insufficiently characterised by a single parameter, such as elongation values (i.e. uniform elongation or total elongation). A complete characterisation should take into account additional factors, such as tensile strength (yield strength, ultimate tensile strength and fracture strength), work hardening behaviour and area reduction. An improved representation of the material response to deformation is formulated by , incorporating relevant values obtained from a uniaxial tensile test, Eq. DVr⋅ln[ln(εu+1)]n[ln(εσ0.2+1)]n2+lnεu+1εσ0.2+120.5+lnσmσfr2+lnεfr−εu+1εu+120.251+rwhere r is the surface area contraction ratio of the tensile specimen, ɛu is the uniform strain, ɛσ0.2 is 0.2% plastic strain, σm is the ultimate tensile strength, σf is the fracture stress and n is the work-hardening exponent.The ductility indicator Dv describes the uniform deformation through the ratios of yield stress and ultimate tensile stress derived from stress values through a power-law relation incorporating the work-hardening exponent, and the elongation ratio of the yield point to the onset of necking (the first two terms in Eq. ). Additionally, post-necking deformation behaviour is characterised by the ratio of the ultimate tensile strength and the fracture strength and the ratio of the instability strain and the uniform elongation (the last two terms in Eq. ) the characteristic values obtained from a simple uniaxial tensile test are thus calculated into a single parameter expressing the deformation characteristics of the sample.Cross-sectional samples from the extruded lengths were prepared for microscopy by means of grinding and polishing of resin-mounted samples up to a final stage of 1 μm diamond suspension. The grain structure of the materials was revealed by electrolytic etching in a 4% HBF solution for 30 s at 20 V DC. Inspection was performed by means of light optical microscopy with a polarised light source. A similar procedure was utilised for inspection of the fractured tensile samples. Scanning electron microscopy (SEM) was employed in characterising the fracture surfaces, relating the morphology of the fracture surface to relevant features of the weld seams.The extrusion process was modelled using a commercial finite-element (FE) code Compuplast®, initially designed for plastics extrusion. The module Virtual Extrusion Laboratory (VEL) was specifically adapted so that the aluminium extrusion process could be modelled. The implicit finite element code utilises a Eulerian formulation, where the aluminium flows through a fixed mesh domain. Constitutive material data for the alloys investigated in this project was implemented in the FE code. The material behaviour was determined through hot compression tests (), using cylindrical samples of 11 mm in diameter and 18 mm height prepared from the billet material as detailed above. The compression tests were performed over a temperature range 450 °C–550 °C and strain rates between 0.1 s−1 and 100 s−1, thus encompassing the ranges encountered in extrusion. Representative flow curves are presented in . The data from the obtained stress–strain curves was subsequently processed into a constitutive model expressing the apparent viscosity as a function of strain rate and temperature through a power-law equation. The simulation model considers a steady-state condition, assuming a billet of infinite length flowing through the container and die. Full 3D models of the dies were constructed, specifically taking into account the design of the leg and the weld chamber geometry. shows the 3D geometry with billet, container, die and rectangular (15 mm × 3 mm) outflow profile.In this set-up of the simulation model only the aluminium in the tool is considered. Thermal boundary conditions were applied utilising experimentally determined temperatures at various locations in the container and the die. At the inlet the ram moves with a constant velocity. This is applied as a constant inlet velocity. At the outlet, a normal velocity condition is applied forcing the outflow in extrusion direction. Sticking friction conditions on the boundary of the aluminium in contact with the extrusion tooling are applied. The container and extrusion die are considered as rigid bodies.In the following the results of the characterisation of the materials obtained from the extrusion experiments will be presented. The relevant samples are labelled in line with the identification of the extrusion tooling. The results of this analysis are presented in for both alloys. Each data point is the average of at least three individual tests, with associated scatter calculated from the standard deviation indicated by the error bars. In this figure the average value for Dv has been scaled according to the maximum value, being the value for 6060 extrudates produced with die B.0, i.e. the die without a central obstruction, at a billet temperature of 500 °C.The microstructures of samples extruded at 450 °C are presented in (alloy 6082). A partially recrystallised microstructure is observed for alloy 6060, whilst alloy 6082 retains a heavily deformed fibrous grain structure. The effect of the obstruction in the extrusion tooling is clear, as in all microstructures except those produced with die B.0 a discontinuity in the grain structure is present, spanning the entire extrudate cross section. This boundary represents the weld seam, formed when the metal streams rejoin in the weld chamber downstream of the obstruction in the die. Around this boundary the morphology of the grain structure reflects the changed material flow pattern caused by the tooling geometry.The detrimental effect of a very shallow weld chamber of 2 mm in die B.2 is evident for both alloys, as incomplete rejoining of the metal streams leads to the formation of a cavity in the centre of the extrudate cross section. Increasing the weld chamber depth to 10 mm (die B.10) prevents the formation of a cavity. However, indications of incomplete bonding are still visible in the central area of the weld seam. At a further increase of the weld chamber depth to d |
= 15 mm in die B.15, the weld seam becomes less clearly defined, but remains visible. Similar defect characteristics are observed in samples B.2 and B.10 originating from the dies with weld chamber depths of 2 mm and 10 mm, respectively produced with a billet temperature of 500 °C.Results of the inspection of the fracture surfaces by means of scanning electron microscopy are presented in . Only the results for alloy 6060 are presented, as the results for alloy 6082 are of a similar nature. The fracture surface of the material without a weld seam (die B.0) exhibits a regular ductile fracture morphology without any distinct features related to material flow in the die. In contrast, the fracture surface of B.2 samples (die welding chamber depth of 2 mm) clearly show a central longitudinally aligned depression, related to the cavity caused by non-converging metal streams in the extrusion tooling. Although no cavity is formed in samples from die B.10 with a welding chamber depth of 10 mm, the morphology of the fracture surface exhibits a considerable area fraction where no bonding appears to have occurred. Increasing the welding chamber depth to 15 mm in die B.15 leads to full bonding in the central region of the extrudate cross section has occurred, indicated by the finely dimpled fracture surface. Along the edges of the fracture surface the fracture surface assumes a more linear morphology. Closer examination of the fracture surfaces of the central area of the B.2 and B.10 samples, presented in , reveals a distinct difference: whereas the morphology of the surface of sample B.2 is indicative of a free extrusion surface where obviously no bonding has occurred, the surface of sample B.10 is comprised of a fine distribution of small dimples, indicating ductile fracture of a bonded surface. The elongated shape and shallow appearance of these dimples however suggest a limited ductile capacity.In order to check the simulation results a comparison was made between the press force measured in the extrusion tests and the calculated press force obtained from the finite element simulations. The results of these comparisons are presented in . The simulation results represent the steady state condition, at approximately halfway through the ram stroke, equivalent to 50% of the billet length extruded.Both experimentally and from the simulations it is readily apparent that higher billet temperatures result in lower forces, as a result of the lower flow stress of the alloys. The different dies exhibit very similar press forces, which may be explained by the fact that, except for the position of the internal die obstruction creating the weld seam, the internal geometry of the dies is the same.In comparing the modelling outcome with the experimental results, it is apparent that in the case of alloy 6060 a somewhat higher value of press force is calculated. Also for alloy 6082 the results of simulation and experiment at a billet temperature of 450 °C show a similar relation, whilst for a billet temperature of 500 °C the press force is somewhat over-estimated. Considering the acceptable correlation between simulation and the experimental results, it may be concluded that the calculated properties can be utilised for correlations between the observed experimental material phenomena and the outcome of the simulations. the hydrostatic pressure distribution inside the aluminium work piece is presented for the dies B.2, B.10 and B.15 for both alloys at a billet temperature of 500 °C. As the lower flow stress at this temperature leads to lower pressures in the weld chamber, this represents the more critical situation regarding weld seam quality according to the weld seam criteria utilising interfacial pressure as a governing factor as described earlier. A gradual decline occurs from high pressure at the inlet to low pressure at the die exit, with highest initial pressure occurring in the die with the deepest welding chamber, i.e. B.15 with a welding chamber depth of 15 mm. From the pressure distributions it is readily apparent that in die B.2 the pressure levels in the weld chamber downstream of the bridge have diminished to very low values. In contrast, higher pressure levels are calculated in the weld chambers for dies B.10 and B.15, with a gradual decrease towards the die exit. the pressure distribution in the aluminium inside the weld chamber is presented in more detail. On the whole there is only a minor difference in the pressure levels for the different alloys at similar locations. Somewhat higher levels are calculated for 6082 as a result of the higher flow stress of this alloy. Nevertheless, the pressure distribution is very similar for both alloys and hence further observations are valid for both alloys. Readily apparent is the “pocket” of low pressure in the central area of die B.2 with a shallow welding chamber of 2 mm, corresponding to the location of the cavity observed in the microstructural investigation. Also close to the press exit of die B.10 (10 mm welding chamber) minimum pressure levels are calculated, however in this die the pressure in the weld chamber where the material flows rejoin remain at a value of approximately 100 MPa for at least 50% of the weld chamber depth before gradually declining towards the die exit. A similar trend is observed for die B.15. the pressure distribution in the aluminium as this rejoins in the welding chamber downstream of the obstruction is presented in combination with the contour of the aluminium die content extracted from the die. Although minor deformation has occurred in removing the aluminium parts from the dies, it is still readily apparent that the contour surrounding the obstruction (notably the area where rejoining occurs) in dies B.2 and B.10 differs from that of die B.15. In the last-mentioned die the contour closely follows the obstruction, whilst in die B.2 and B.10 a more pointed contour is observed where material is displaced from the obstruction.When considering the results obtained in these experiments it is apparent that the inferior weld seam properties of die B.2 are coincidental with the cavity formation due to partial non-converging metal flow in the weld chamber downstream of the obstruction in the die. By extending the weld chamber depth to 10 mm in die B.10, cavity formation is prevented, but weld seam quality as evidenced by the ductility indicator Dv still remains poor, in line with the microstructure in and in particular the fracture surface in . The substandard performance of the material from die B.10 may be explained through the presence of a gas pocket, causing partial surface oxidation of the aluminium. Consequently inferior bonds resembling charge welds are formed. In these cases pre-oxidised metallic surfaces are joined by breaking up the oxide layer and subsequent transverse extrusion of virgin metal though the cracked surface as initially proposed by . This join thus consists of bonded metal-to-metal interfaces with intermittent oxide fragments degrading the bond integrity. Further elaboration of this phenomenon by focussed on the surface stretching causing the oxide film to break up, with a mathematical treatise to arrive at an approximation of the bond strength. Although this work was performed for cold roll bonding, the principles remain equivalent for other processes in which contacting surfaces with a thin, brittle oxide layer residing on relatively soft substrate is deformed under pressure. In his conclusion the author states that the theory should also be applicable to deformation bonding at elevated temperatures., the pressure on the weld plane increases considerably when the weld chamber depth d is increased from 2 mm in die B.2 to 10 mm and higher, with maximum pressure values in the weld chamber for die B.10 being of the same magnitude as in die B.15. These favourable pressure levels are expected to lead to sound weld seams, as confirmed by the ductility indicator Dv for samples produced with die B.15. In contrast, the low Dv values for samples produced with die B.10 are in conflict with the pressure values determined from the FE analysis. The grounds for the inferior weld seam properties is therefore related to partially unbonded segments, caused by the fractured oxides remnants on the contact surfaces created alongside the gas pocket downstream of the obstruction. As the adopted simulation methodology considers the aluminium domain of a pre-filled die, the occurrence of a gas pocket is only indirectly inferred from the low pressure area spanning the entire path from the obstruction to the die exit in die B.2. In other cases adequate pressure levels are calculated and from the weld seam criteria sound, defect-free weld seams would be predicted. however demonstrates that material flow inside the die does not coincide with the finite element model set-up, assuming a fully filled die. The contour mismatch between the aluminium die content and the shape of the obstruction in the die indicates that loss of contact between the tooling and the aluminium occurs, thereby initiating a gas pocket. Considering the detrimental effect of a gas pocket on weld seam quality, numerical strategies incorporating the flow behaviour leading to the prediction of gas pocket formation is therefore desirable, e.g. as described by In this study the weld seam performance of extruded strips produced by means of dies with a central obstruction was considered. The quality of the weld seam could be clearly discriminated by the ductility indicator Dv, calculated from values obtained from uniaxial transverse tensile tests. These values are compared to those obtained from transverse tensile tests performed on samples from extrusions without a weld seam.Different levels of weld seam quality, related to the severity of a specific defect, were produced by changing the internal geometry of the extrusion tooling. The defect in this study ranges from a cavity in the extrudate cross section to inferior, metal–oxide inhibited bonds. In the latter instance it is suggested that oxidation of the rejoining aluminium surfaces is caused by exposure to a gas pocket downstream of the obstruction in the die.It was argued that current weld seam criteria based on pressure and residence-time related values obtained from finite element simulations are not adequate in predicting weld seam quality for these cases. Capturing of the gas pocket formation phenomenon through flow modelling is therefore essential in accurately predicting weld seam quality.► Web crippling tests of cold-formed channel section with web holes under ETF loading conditions. ► Non-linear finite element models have been developed and verified against the test results. ► A parametric study of cold-formed steel sections with web holes was performed. ► Web crippling strength without openings are compared with current design codes. ► Web crippling strength reduction factor equations are proposed.Experimental and finite element ultimate web crippling load per web;Experimental ultimate web crippling load per web;Web crippling strength per web predicted from finite element (FEA);Mean value of tested-to-predicted load ratio;Coefficient of variation of fabrication factor;Coefficient of variation of material factor;Coefficient of variation of tested-to-predicted load ratio;Horizontal clear distance of web holes to near edge of bearing plate;Elongation (tensile strain) at fracture;Web crippling at points of concentrated load or reaction is well known to be a significant problem, particularly in thin-walled beams ). To improve the buildability of buildings composed of cold-formed steel channel sections, openings in the web are often required to allow ease of installation of electrical or plumbing services. For such sections with holes, web crippling needs to be taken into account.The general purpose finite element program ANSYS A test programme was conducted on lipped channel sections, as shown in The first four notations define the nominal dimensions (d×bf×bl–t1.4) of the specimens in millimetres (i.e. 202×65×13-t1.4 means d=202 mm; bf=65 mm; bl=13 mm and t=1.4 mm).“N32.5” represents the length of bearing in millimetres (i.e. 32.5 mm).Tensile coupon tests were carried out to determine the material properties of the channel specimens. The tensile coupons were taken from the centre of the web plate in the longitudinal direction of the untested specimens. The tensile coupons were prepared and tested according to the British Standard for Testing and Materials , which includes the measured static 2% proof stress (σ0.2), the static tensile strength (σu) and the elongation after fracture (εf) based on gauge length of 50 mm. shows the typical failure mode of web crippling of the specimens. A typical example of the load-defection curve obtained from a specimen both without and with web holes, and the comparisons with the numerical results is shown in The non-linear general purpose finite element program ANSYS One-half of the test set-up was modelled using symmetry about the horizontal planes, as shown in (b). Contact surfaces are defined between the bearing plate and the cold-formed steel section.The value of Young's modulus was 203 kN/mm2 and Poisson's ratio was 0.3. The material non-linearity was incorporated in the finite element model by specifying ‘true’ values of stresses and strains. The plasticity of the material was determined by a mathematical model, known as the incremental plasticity model; the true stress (σtrue) and plastic true strain (εtrue) were calculated as per the method specified in the ANSYS manual (b) show the details of a typical finite element mesh of the channel section and the bearing plate. The effect of different element sizes in the cross-section of the channel section was investigated to provide both accurate results and reduced computation time. Depending on the size of the section, the finite element mesh sizes ranged from 3×3 mm (length by width) to 5×5 mm.The nodes of the cold-formed section were restrained to represent the horizontal symmetry condition. The interface between the bearing plate and the cold-formed steel section were modelled using the surface-to-surface contact option. The bearing plate was the target surface, while the cold-formed steel section was the contact surface. The two contact surfaces were not allowed to penetrate each other.In order to validate the finite element model, the experimental failure loads were compared against the failure load predicted by the finite element analysis. The main objective of this comparison was to verify and check the accuracy of the finite element model. A comparison of the test results (PEXP) with the numerical results (PFEA) of web crippling strengths per web is shown in . Load–deflection curves comparing the experimental results and the finite element results are shown in , respectively. It is shown that good agreement is achieved between the experimental and finite element results for both the web crippling strength and the failure mode.The finite element model developed closely predicts the behaviour of the channel sections with circular web holes subjected to web crippling. Using this model, parametric studies were carried out to study the effects of web holes and cross-section sizes on the web crippling strengths of channel sections subjected to web crippling.A total of 140 specimens was analysed in the parametric study investigating the effect of the ratio a/h. The cross-section dimensions as well as the web crippling strengths (PFEA) per web predicted from the FEA are summarised in A total of 160 specimens was analysed in the parametric study investigating the effect of x/h. The cross-section dimensions as well as the web crippling strengths (PFEA) per web predicted from the FEA are summarised in The effect of the ratios a/h and x/h on the web crippling strength on the reduction factor is shown in for the C202 Specimen. It is seen from these graphs that the parameter a/h and x/h noticeably affects the web crippling strength and the reduction factor.The reliability of the cold-formed steel section design rules is evaluated using reliability analysis. The reliability index (β) is a relative measure of the safety of the design. A target reliability index of 2.5 for cold-formed steel structural members is recommended as a lower limit in the NAS Specification The statistical parameters Pm and VP are the mean value and coefficient of variation of load ratio are shown in , respectively. In calculating the reliability index, the correction factor in the NAS Specification was used. Reliability analysis is detailed in the NAS Specification . Comparison of experimental and numerical results with current design strengths for cold-formed steel sections without web holes.As mentioned earlier, the current cold-formed design standards shows the comparison of web crippling strength with design strength for ETF loading condition. The NAS specification design strength was not considered as the ri/t ratio limit was greater than 3. In the British Standard and Eurocode comparison, the mean values of ratio are 0.99 and 0.99 with the corresponding coefficients if variation (COV) of 0.08 and 0.08, and the reliability indices (β) of 2.46 and 2.46, respectively.Comparing the failure loads of the channel sections having web holes with the sections without web holes, as shown in The limits for the reduction factor in Eqs. are h/t≤156, N/t≤84, N/h≤0.63, a/h≤0.8, and θ=90°.The values of the strength reduction factor (R) obtained from the experimental and the numerical results are compared with the values of the proposed strength reduction factor (Rp) calculated using Eqs. , as plotted against the ratios a/h and h/t in A finite element model that incorporated the geometric and material nonlinearities has been developed and verified against the experimental results. The finite element model was shown to be able to predict the web crippling behaviour of the channel sections for both with and without circular web holes. A parametric study was carried out to study the effects of the different sizes of the cross-sections and web holes on the web crippling strengths of the channel sections. It is shown that the ratios a/h and x/h are the primary parametric relationships influencing the web crippling behaviour of the sections with web holes.Kinetics, mechanism and characterisation of passive film formed on hot dip galvanized coating exposed in simulated concrete pore solutionIt is established that hot dip galvanized (HDG) coatings exposed in simulated concrete pore solution (SPS) develops very stable corrosion products at the coating surface and its corrosion potential gets greatly ennobled due to the formation of a passive layer. This passive layer has been identified as hydrozincite Zn5(CO3)2(OH)6. The passive film is formed in all the constituents of SPS namely hydroxides of sodium, potassium and calcium. Electrochemical impedance spectroscopy (EIS), Raman spectroscopy, scanning electron microscopy (SEM), energy dispersive X-ray analysis (EDXA), XRD studies etc. have been performed to study the kinetics and understand the mechanism of formation of hydrozincite (HZ) at the corroding interface. These studies are expected to provide technique for development of an eco-friendly protective passive layer on galvanized coatings prior to their embedding in concrete.Composites are wonderful materials that acquire synergistic combination of properties of various constituents of composite resulting in entirely new products with dramatically improved properties. Human being had been familiar with composite materials since the beginning of Iron Age. Inventions in newer composite materials started to take place after the understanding of materials was advanced and natural occurring phenomenon was explained by taking the help of principle of science. Amongst the huge number of man invented composites, the reinforced concrete comprising of cement, water, sand, gravel and steel, perhaps is a composite material that had maximum impact in revolutionising the life of human being. After curing, the concrete attains very high strength but remains brittle. To provide ductility, the concept of reinforcing the concrete with steel was conceived. Due to high alkalinity of pore solution of concrete, steel attains a stable passivity due to the formation of a protective film of Fe2O3 on its surface. Unfortunately, this passivity is lost once chloride content in the concrete exceeds a threshold concentration which is reported to be ≈ 0.1% It is well established fact that HDG coating exposed in neutral sodium chloride solution forms corrosion products, which are non-protective and conducting in nature In actual practice, however, the results of performance of galvanized coatings in contact of concrete have been conflicting. Hill et al. The mild steel (MS) substrate used for the deposition of the hot dip galvanized coating was in the form of bars of 16 mm diameter. The chemistry of the bar was:C = 0.13, Mn = 0.68, Si = 0.017, S = 0.005, P = trace, Mo = 0.02, Al = 0.09.The bar specimens of size 100 mm length and 16 mm diameter were cut, pickled and polished on grinder followed by polishing with fine emery paper (1200 grade) to get scratch free surface. They were then degreased by tissue paper swabbing with acetone and kept in desiccators. Prior to putting the samples in galvanizing bath, their surface was activated by dipping in 5% hydrochloric acid water solution for 10 s followed by rinsing in running tap water and then fluxed in 50% zinc ammonium chloride solution. The galvanizing was carried out by dipping the bars in electrolytic grade molten zinc (temperature of the zinc bath was maintained at 455–460 °C) for 45 s. Immediately after removing the galvanized bars, they were quenched in cold water and then kept in desiccators to perform further studies. The coating thickness was observed in the range of 70–85 μm. These specimens were used for various types of studies as mentioned in the paper.The electrochemical experiments were performed at fixed temperature of 30 ± 1 °C using a glass cell equipped with constant temperature water re-circulating Teflon tubes dipped into the test electrolyte. Saturated calomel electrode (SCE) and graphite rods (exposed area ≈ 40 cm2) were used respectively as reference and auxiliary electrode. The exposed surface area of working electrode (galvanized bar) in the electrolyte was 10 cm2. To determine the corrosion rate of the coatings, electrochemical impedance spectroscopy (EIS) and direct current (DC) polarization resistance techniques were employed. EIS studies were performed by imposing sinusoidal voltage of 10-mV amplitude at open circuit potential of the working electrodes. No DC (direct current) potential was imposed on the electrode surface during EIS studies. The frequency varied between 100,000 Hz to 0.001 Hz. For DC cyclic anodic polarization studies, the potential was scanned at the rate of 0.2 mV/s. Cyclic polarization experiments for the coated samples were performed to study the effect of formed passive layer on the break down (Ebd) and repassivation (Erep) potentials. In this test, the potentials were increased in anodic direction starting from the corrosion potential of the interface at a scan rate of 0.1 mV/s till the peak current reached to 1.5 mA/cm2. The potentials were then scanned back to the open circuit potential at the same rate. The potential at which a sudden increase in current density during the forward scanning of potential took place was taken as the onset of pitting and referred as break down potential (Ebd). The potential at which the anodic current tended to become zero, was taken as the repassivation (Erep) potential of the pitted surface. The EIS data were analyzed using constant phase element (CPE) and Randle models. The test electrolyte was simulated concrete pore solution (SPS) prepared by dissolving analytical reagent grades of 8.33 g/l NaOH + 2 g/l CaO + 3.36 g/l KOH in double distilled water In order to understand the difference in nature of film formed on HDG surface exposed in the test electrolyte from that in contact of neutral chloride solutions, parallel studies were made in both the solutions. Change in corrosion potential of HDG reinforcement bars in SPS and 1% neutral sodium chloride solution with passage of time is shown in . It is observed from the figure that the rebars exposed in chloride added SPS develop the corrosion potential in the range of − 1400 mV upto the exposure period of 50 h, which indicates its active dissolution in highly alkaline SPS electrolyte (pH ≈ 12.75). After this period of exposure, the potential gradually ennobles and finally reaches to about − 600 mV. A regular visual observation of the corroding interface showed phenomenal periodical changes in the appearance of the surface of the rebars. The surface changed from bright metallic to brownish and then finally dark brown after the exposure of 192 h. During the initial exposures, hydrogen bubbles were observed evolving at the interface who disappeared after 120 h of immersion in the electrolyte. It was initially thought that the alkalinity of the test electrolyte had depleted which has made the test electrode inactive. To remove this doubt, the solution of the cell was removed and fresh solution was added in the test cell. This made no change to the value of potential. Another doubt was generated that the whole zinc coating got dissolved in the test electrolyte and probably the steel substrate had emerged that was providing the nobler potential. After 240 h of testing, the test samples were taken out from the cell and the coating on its surface was thoroughly examined. It was observed that a uniform adherent and hard layer (visual observation) had deposited on the surface of galvanized coating. The thickness of the coating after exposure showed that zinc layer of 80 ± 5 μm existed all over the surface (measured by electromagnetic gauge thickness meter ennobling bare polished steel surface and standards of known thickness as reference). This removed the suspicion that the zinc coating got completely corroded from the rebars surface and substrate steel had emerged out. This exposed interface was then further investigated by using XRD, Raman spectroscopy, EDXA etc. which will be discussed in forthcoming paragraphs. also incorporates the results of change in corrosion potential of HDG rebar exposed in 1% neutral sodium chloride solution. Unlike SPS, the rebars exposed in this solution maintain the corrosion potential of about − 1000 mV (SCE) throughout the exposure period. No ennobling of their potential was recorded even after the exposure period of 720 h. After the exposed samples were removed from this electrolyte, thick, loose and gel type corrosion products were observed on the surface of the test specimen.In addition to the measurement of corrosion potentials of the exposed samples at regular intervals, they were also subjected to electrochemical impedance spectroscopy studies. These studies provided polarization resistance (Rp) and the nature of film formed at the interface. The change in inverse of Rp (which is directly proportional to corrosion rate) for the two systems (HDG exposed in SPS + 1%Cl− and 1% neutral chloride solution) with passage of time is shown in . Initially, a gradual increase in 1 / Rp with time for the electrode exposed in chloride added SPS + 1%Cl− is noted upto the exposure period of 96 h. After this interval of exposure, a sudden decrease in its value is recorded. It is to be noted here that this trend is identical to that recorded for potential-time plots shown in . These findings confirmed that HDG develops a protective passive film after a definite period of exposure in SPS + 1%Cl−, which effectively protects its surface from corrosion. In case of neutral sodium chloride solution, however, a gradual increase in corrosion rate is observed (). These results indicate that the kinetics of corrosion reactions at the interface of HDG and the electrolytes are largely controlled by the nature of corrosion products formed at its surface.A drastic ennobling of potential of HDG in SPS + 1%Cl− after an exposure period of about 120 h was reproducibly noted and aroused interest to study it more in detail. The change in corrosion potential of HDG exposed in different components of SPS namely 0.2(N) NaOH, 0.06(N) KOH and saturated lime solution was followed with passage of time. The results are shown in . It is evident from the figure that the test electrodes in all the components of SPS exhibit initially an ennobling in electrode potential. They get stabilized after the exposure period of about 55 h. NaOH solution attains the nobler followed by saturated lime solution and KOH where the potentials were of the order of − 800 mV and − 900 mV respectively. These results suggest that the HDG surface remains in passive state in all the components of SPS. Development of passive (nobler) potential of HDG exposed in saturated lime solution corroborates the findings of previous researchers who reported that the passivity was caused due to the formation of calcium hydroxyzincate A very distinct difference in time required for the onset of passivation was recorded for the HDG electrode in SPS (, > 120 h) than the electrodes exposed in individual components of SPS (, ≈ 0 h). The longer duration required in the former case was probably due to the presence of higher alkalinity in this solution than the later individual components.The variation in time required for the development of passive layer on HDG surface with the nature of electrolyte shows that change in pH at the corroding interface was very important. It was therefore, necessary to determine the changes in pH of the electrolyte with passage of exposure time in different electrolytes. In order to maintain a constant electrolyte volume and exposed surface area ratio, the electrolyte volume and HDG coated area was maintained same for all the test electrolytes.The results of change in pH of the above four solutions with the passage of exposure time are shown in . It is evident from this figure that initially the pH of limewater and KOH are below 12.5. The pH of NaOH and KOH decrease faster than either lime water or SPS. After the exposure period of 120 h, the pH of lime, NaOH, SPS and KOH decreased by 0.3, 0.75, 0.2 and 1.2 respectively. These facts suggest that the zinc surface reacts faster with NaOH and KOH solution than limewater and SPS solution, which results in faster depletion of alkalinity in the former cases. The potential-time plots indicated that the HDG surface developed passive potentials in the range of − 900 to − 500 mV after the exposure period of approximately 60 h, although the pH of the electrolytes varied to a considerable extent (from 10.8 to 12.75) during this period. These facts suggest that onset of formation of passive films on HDG surface takes place in all solutions after the exposure period of 60 h, irrespective of the pH of the test electrolyte. These findings further indicate that that the passive film formed on the surface of HDG was intrinsic property of zinc and alkalinity at the interface rather than the function of specific electrode–electrolyte interface.In order to understand the mechanism of the film formation at the interface of the corroding systems, electrochemical impedance plots drawn at different intervals of exposure were analysed in Nyquist form. The plots for SPS + 1%Cl− and neutral chloride solutions are shown in respectively. The Nyquist plot for instant exposure of HDG in SPS + 1%Cl− shows a distorted semicircle {(a)}. At 96 h of exposure, the negative value of imaginary impedance at lower frequencies is recorded {(b)}. This inductance behaviour of the coating is attributed to the change in corrosion potential of the interface with time. This corroborates the findings of where it was observed that after 96 h of exposure, a steep increase in potential with passage of time took place. This ennobling of potential is attributed to the formation of a protective layer at the interface. A further increase in exposure time has resulted in a considerable increase in the diameter of the semi circle. It is of the order of 103 Ω for 144 h {(d)}. At extreme right of the curve, which corresponds to the response of the interface at lower frequencies, some scattered points tending to form diffusion tail are recorded. These scattered diffusional points are not very clear in Nyquist complex plots. To understand the behaviour more clearly, the data were plotted in Bode forms which have the advantage over the linear complex plane (Nyquist) plots as it very explicitly track down the changes at the interface. Unlike the Nyquist plots where a compression of spectrum in high frequency region is commonly noted, the Bode's frequency/phase angle plots are very sensitive to the changes taking place at the interface. The results are shown in (e) and (f). The impedance recorded at the lowest studied frequency (0.001 Hz) which is considered as the polarization resistance of the coating surface, is observed to increase with exposure time {(e)}. The frequency/phase shift plots at instant exposure exhibits a single maxima at higher frequency region. This indicates that the surface is responding to only a single faster reaction which in the present case is the dissolution of galvanized coating in SPS solution. With increase in the exposure time, especially above 96 h, two maxima in the frequency phase plots, one at higher frequency and the other at lower frequency zones are recorded. These observations clearly demonstrate that above 96 h of exposure of HDG in SPS + 1%Cl−, a protective layer is formed which hinders not only the electrodic reactions at the interface but also the diffusion of ions through it. The behaviour of HDG exposed in neutral chloride solution, however, is entirely different than that recorded in SPS + 1%Cl− {(a–d)}. In this case, at all the periods of exposure, one semicircle in higher frequency region and a diffusion tail at lower frequency regions are recorded {(a–d)}. It is further observed that the diameter of semicircles recorded at higher frequency region gradually becomes smaller with increase in exposure time. Bode plots also exhibit the same behaviour {(e and f)}. These observations suggest that unlike SPS + 1%Cl− where formation of a protective film resulted in an increased diameter of semicircle with passage of time, in the present case of neutral chloride solution, the layer is totally non-protective and facilitates the electrodic reactions at its surface.In order to confirm further that the passive film formed at the interface drastically reduces the dissolution rate of coating, anodic cyclic polarization studies were performed for the HDG specimens in SPS + 1%Cl solution after pre-exposing the specimen for 2 h and 192 h in the test electrolyte and then running the polarization in fresh solution. The results are shown in . These studies also corroborate the previous results. The plot for the HDG specimen exposed for 192 h have considerably shifted in lower current density region and passive current in this case is about 15 times less than for the other sample exposed only for 2 h of duration. The break down potential (Ebd) which is indicative of the development of pits at the surface, and is characterised by a sudden increase in current density is observed to take place at the open circuit potential of the coating exposed in the test electrolyte for 2 h. In case of the coating exposed for 192 h, this potential is far nobler (Ebd |
= 0.631 V, SCE) than the freshly exposed surface. The repassivation potential (Erep) where the current diminishes tending to zero, is also quite nobler (− 0.342 V) for the former than the later (− 0.900 V) interface. These facts suggest that the development of the passive film of hydrozincite after longer durations of exposure of the coating, results in an improved resistance not only to general corrosion but also for localized attack. Another interesting observation noted for the polarization curves is two anodic current peaks noted at about − 1.3 V (near corrosion potential) and − 0.65 V (SCE) for the specimen exposed for 2 h. For 192 h exposed specimen, no such peaks are noted. This type of peaks are reported also by previous researchers The specimens after exposure in SPS + 1%Cl− for 192 h were subjected to SEM and EDXA to study the morphology and composition of corrosion products formed at the surface of the test electrodes. Since the studies related to corrosion products formed on zinc surface exposed in neutral chloride solutions are extensively available in literature and are now well established, they were not included for this characterisation. The morphology of the film formed at HDG in SPS + 1%Cl− (exposed for 192 h) is shown in . It is evident from this figure that a uniform and compact film is formed on the surface of the exposed sample. EDXA analysis () showed major peaks of zinc incorporating minor quantities of Si, K and Ca. No peaks of chloride were detected indicating that the corrosion product formed was free of chloride. The minor peaks of K and Ca are attributed to the presence of these elements in the test electrolytes (KOH and Ca(OH)2 are used in the preparation of simulated concrete pore solution). The presence of the peak of Si in the corrosion product was surprising as neither zinc nor test electrolytes had any trace of Si in their composition. The possibilities of this element being picked up from the substrate steel is also ruled out as the surface had about 80 μm of zinc coating even after its exposure of 192 h. This element probably was picked up from the test cell (made of silicon glass) which perhaps dissolved in alkaline test electrolyte during the period of exposure (192 h). We have indeed observed that the test cell used for tests have got corroded during the period of testing of the specimens. These findings indicate that the passive film formed at the interface of HDG is primarily composed of zinc based compounds embedded with minor content of the other elements. In order to have exact composition of this film, the tested specimens were subjected to XRD studies and the spectrum is shown in . This spectrum showed the major peak of hydrozincite {Zn5(CO3)2(OH)6}. In addition to this many minor peaks were also observed that corresponded to zinc hydroxide, sodium bi-carbonate, zinc calcium (CaZn5) etc.Morphology of corrosion products and EDXA analysis as described in above have indicated that the film formed at the exposed HDG had some major components embedded with minor particles that effectively block the pores of passive film. Since XRD is unable to identify minor constituents and amorphous compounds of a mixture, it was considered important to analyse them through Raman spectroscopy. The Raman spectra are shown in . These spectra were collected after focussing the laser beams at different locations of the specimens. shows the Raman spectra of HDG surface before its exposure in the test electrolyte. It is evident from the spectra that only one major peak centred at 560 cm− 1 is noted which is attributed to Zn1+xO, a defective zinc oxide molecule with zinc ion embedded in interstitial positions . These spectra were collected after focussing the beam of laser at different types of visible phases in microscope, (constituents of corrosion products formed at the HDG surfaces). The white spots present in the corrosion products corresponded to oxide of zinc ( two peaks are observed at 562 cm− 1 and 557 cm− 1, which are closer to 560 cm− 1 attributed to defective zinc oxide). The black spots provided Raman peaks at 371, 149 and 3196 cm− 1. The 3196 cm− 1 peak is attributed to vibrational frequency of OH ). Raman peaks noted at 1090, 709, 390 and 140 cm− 1 in ). These results show that the major passivating product hydrozincite forms only after sufficient exposure (≥ 192 h) of HDG surface in SPS + 1%Cl−. This finding is in agreement with the results of time–potential and time–corrosion rate plots shown in where a sudden shift in corrosion potential took place only after 120 h of exposure of HDG in the test electrolyte. As stated above, the peaks between 3200–3600 cm− 1 are caused due to vibrational frequency of OH , where minor phases of hydroxide of zinc and other phases were detected.The above results confirm beyond doubt that the passive film formed at the interface is hydrozincite embedded with other minor constituents such as zinc hydroxide and other compounds of zinc, Ca, Na etc.It is reported that zinc surface in alkaline solutions dissolves under the influence of a number of complex corrosion products formed on its surface further combines with OH− to form zincate ionsThe stability of the zincate ions formed at the surface of zinc depends on different factors such as pH and constituents of electrolytes. In saturated lime solution, e.g. a stable layer of calcium hydroxy zincate is reported to be formed may undergo further transformation to form zinc oxide:However, the present investigation suggests that a major protective hydrozincite layer instead of only oxides and hydroxides reported earlier is formed at the surface of zinc. The reaction that takes place at the interface is probably the reaction of zincate ions with carbon dioxide of air:5Zn(OH)42−+2CO2=Zn5(CO3)2(OH)6(Hydrozincite)+10OH−+2H2OThe above mechanism proposed for the development of passive layer on HDG surface in contact with SPS gets support from the findings described in the of this paper. The presence of hydrozincite on passive surface of HDG was established by XRD and Raman spectra shown in . The fact that during the initial period of exposure, HDG forms unstable corrosion product was evident from spontaneous reaction with visible evolution of hydrogen gas. This indicates that during the initial exposure of HDG in SPS + 1%Cl−, an unhindered spontaneous reaction takes place at the interface. The impedance plots shown in (a and b) for the coating during its initial exposure in SPS + 1%Cl− behaved perfectly like an interface comprising of only resistor and capacitor. The Nyquist real vs imaginary impedance plots exhibit an incomplete semicircle indicating that an unhindered charge transfer reaction was taking place during the initial phases of exposure of the coating in the test electrolyte. Once the coating was exposed for sufficient duration of exposure {(c and d)}, diffusion components characterised by linear real vs imaginary relationship in the domain of lower frequency region was recorded. This is clearly due to the formation of protective layer of hydrozincite, which creates resistance for passage of metal ions and oxygen through it. The two stages of corrosion reactions (instant, 24 h, 192 h and above) taking place at the interface of the coating may be modelled by incorporating various electrical components of the corroding interface. The incorporates only one resistor (R) and a capacitor (C) besides uncompensated resistance and represents the Faradaic components of reaction. At this stage of reaction, the corrosion products formed on the surface of the coating are unprotective such as defective zinc oxide and zinc hydroxide as confirmed by Raman spectroscopy (b on the other hand, in addition to resistor, capacitor and uncompensated resistances also incorporates Warburg diffusion component. The later is caused due to the formation of compact and protective layer of hydrozincite with other minor constituents such as zinc oxide and hydroxide, which are formed after longer duration of exposures.The time required for the development of passive layer of hydrozincite (after exposure of 120 h of the HDG specimen in SPS) is too long and unrealistic from commercial point of view. To make the process commercially viable it is necessary to bring down this period to a reasonably lower value. The results described in this paper indicate that the passivity at the interface of galvanized coating and SPS + 1%Cl− can be accelerated by the incorporation of either CO3− or CO2 generating components. This may result in decrease of long time presently required for the formation of hydrozincite at the coating surface. This possibility is being explored in our lab and will be reported separately.An unusual passive behaviour of galvanized coating exposed in SPS + 1%Cl has been recorded. The coating develops a passive protective film after its exposure of about 120 h and its potential is sharply ennobled from about − 1400 mV to − 600 mV (SCE). This has caused a substantial decrease in its corrosion rate. Raman and XRD studies have confirmed the formation of hydrozincite layer at the surface of the coating. EIS and scanning electron microscopy showed that the layer of hydrozincite formed at the surface of the coating was very protective in nature and incorporates fine particles of zinc oxide and hydroxide in the pores of hydrozincite layer.Electrorheologial properties of hematite/silicone oil suspensions under DC fieldsElectrorheological (ER) fluids composed of α-Fe2O3 (hematite) particles suspended in silicone oil are studied in this work. The rheological response has been characterized as a function of field strength, shear rate and volume fraction. Rheological tests under DC electric fields elucidated the influence of the electric field strength, E, and volume fraction, ϕ, on the field-dependent yield stress, τy. It was found that this quantity scales with E and ϕ with a linear and parabolic dependence, respectively. The viscosities of electrified suspensions were found to increase by several orders of magnitude as compared to the unelectrified suspension at low shear rates, although at high-shear rates hydrodynamic effects become dominant and no effects of the electric field on the viscosity are observed. The work is completed with the analysis of microscopic observations of the structure acquired by the ER fluid upon application of a constant electric field. Electrohydrodynamic convection is found to be the origin of the ER response rather than the commonly admitted particle fibrillation. This fact can provide an explanation to the relationship between yield stress and electric field strength as well as the pattern of periodic structures observed in the measurement geometries.The increase in the viscosity of suspensions upon application of an electric field is commonly referred to as the electrorheological or Winslow effect ER fluids constitute nowadays a very promising area of research and development because of their potential technological applications. These materials have been used as ideal mechanical–electrical interfaces (for transferring and controlling mechanical movement) because of their very fast response time It has long been known that rheological changes in ER fluids are associated with field-induced structures Not many ER devices have been commercialized because of a number of problems that must be solved: their yield stress is not high enough; they have a limited working temperature range; they present problems of suspension stability against sedimentation, and of malfunctions once contaminated; may provoke abrasion of pipes and containers, and others.The limited understanding of the ER activity has also hindered the development of ER suspensions optimized for particular applications, although since the pioneering work of Winslow Another interesting aspect that needs further understanding is the ER response for DC excitation. Elevated suspension conductivities result in prohibitive power requirements to achieve a useful enhancement in viscosity. As a result, many systems are optimized to minimize suspension conductivity, and consequently, the effects of mobile charge carriers are expected to be small. Under these conditions, particle interaction potentials are dominated by the conductivity mismatch between the solid and liquid phases and the interpretation of the rheological properties might be carried out in terms of the electrostatic polarization model However, experimental data cannot be always explained by the polarization model just described, particularly at high electric field strengths, where responses become non-linear. For example, electrostatic forces (as manifested by, e.g., yield stress) are often found to vary as Fel |
∝ |
En where n |
< 2 in contrast to the E2 dependence predicted by the polarization model From this, it is clear that several kinds of phenomena may appear as ER response under DC fields. This paper tries to shed light on these facts. We examine the rheological behavior of iron oxide/silicone oil suspensions under DC excitation. The mechanisms accounting for the ER response will be elucidated considering yield stress and viscosity analyses, as well as direct structural observations.The iron oxide (α-Fe2O3 or hematite, density 5.24 g/cm3) powder was purchased from Aldrich, USA, and was used as received. is a SEM picture of the particles: they are irregular polyhedra, with an average size of 105 ± 25 nm. This was determined by fitting a log-normal distribution to the size determinations on about 200 particles on TEM micrographs. The conductivity of the particles is σp |
= (2.6 ± 0.2) × 10−7 |
S/m Different volume fractions (2, 4, 6, 8 and 10%) were prepared by blending of a stock sample with silicone oil in an internal mixer (Cowles type) at 2500 rpm and room temperature during 3 min. The ER suspensions were placed in a vacuum chamber to extract the air bubbles for 2 min previously to any measurements. After that time, the suspensions obtained were completely uniform and no additives appeared necessary.Rheological properties were determined with a Rheometrics Ares 2KFRTN1 (USA) rheometer using a parallel plate geometry with a plate diameter of 50 mm and an electrode gap of 1 mm. The DC field applied was supplied by a GW GFG-89159 wave generator (USA), after rectification and 1000× amplification with a Trek High Voltage Amplifier 609E-6 (USA). The electric field strength ranged from 0.5 to 2.5 kV/mm.All rheological tests were conducted at 25 °C, and consisted of the following steps: (i) preshear the sample during 60 s at 100 s−1 in order to set the same initial conditions in all experiments; (ii) let the sample equilibrate for 40 s, with the electric field applied, so that particle structures can eventually form; (iii) apply a shear rate sweep between 0.059 and 300 s−1.The type of sample cell used to observe the suspensions during application of different strengths of the electric field is shown schematically in . The electrodes were cooper foils, 100 μm thick, glued on the glass plates. The electrode spacing was set for this work at a nominal 1 mm gap.The sample cell was placed on the stage of a Nikon SMZ-2T stereoscopic microscope equipped with a video camera connected to an image acquisition card controlled by a software tailored for these experiments. The magnification used was 50–60×. The amount of ER fluid used to fill up the sample cell was of the order of 500 μl, and the electric field strengths ranged from 0.5 to 2.5 kV/mm, supplied by a HV Dipotonic (USA) power source.Prior to rheological measurements, the response time, τR, of the suspensions was determinated. This is the time that the suspension takes to go from a quiescent state to its final, field-induced structured state. In order to estimate τR, a step-rate test was performed: firstly, the ER fluid was sheared at 100 s−1 for 60 s. This pre-shear step destroyed any previous structure of the suspensions, so that initial conditions were the same in all cases. After that time, an electric field strength of 0.5 kV/mm was instantaneously applied for 120 s while the viscosity was measured at a constant shear rate of 0.03 s−1. At such small rate, one can consider that the structures induced by the field are evaluated in approximately quiescent suspensions. shows the transient response (shear viscosity, η, versus elapsed time), for suspensions of several volume fractions. Note that in the zero-field condition, a minimum flow resistance (a constant shear viscosity), due to dissipative loss from the solid phase, is experienced. When the external electric field is applied, the field-induced interactions cause particles to have an effective motion relative to the liquid phase. This increases the dissipative losses so that a dramatic enhancement in shear viscosity can be observed.Let us note that all the suspensions tested required a relatively long time (of the order of several seconds) to reach a steady state after the electric field was applied. Although the time required for typical ER suspensions to respond to a step increase of electric fields is reported We will consider that τR is the time between the application of the field and the instant at which η reaches a maximum. Results are shown in , where it is demonstrated that τR decreases with volume fraction, and a plateau is suggested at high particle concentration. A similar dependence between reaction time and volume fraction has been described by other authors According to these results, the longest response time is about 30 s for a volume fraction of 2% and 0.5 kV/mm field strength. Since τR decreases with volume fraction and electric field shows the apparent viscosity η of hematite suspensions with 8% volume fraction as a function of shear rate for several field strengths. Similar plots for constant field (1.5 kV/mm) and several volume fractions are given in . Let us first of all note that when no field is applied the suspensions were approximately newtonian. indicate that the samples are shear-thinning, and their viscosity decreases more rapidly with shear rate the higher the field strengths. On the other hand, the effect of the applied field is more pronounced at low shear rates, when hydrodynamic interactions are weaker. Finally, at high-shear rates, curves corresponding to different field strengths tend to merge and reach the values in absence of field, showing that the electric field ceases to have an effect on the measured viscosity. demonstrates that the electrified suspensions display a plastic behavior, with a finite yield stress, τy, more significant the higher the field strength. Similar plots, not shown for brevity, indicate the τy also increases with ϕ. Since the suspensions are newtonian fluids when no field is applied, the yield stress observed in this suspensions must be an ER effect.The yield stress, τy, is plotted as a function of the field strength E and volume fraction in : whatever the volume fraction, τy increases with E, and a roughly linear dependence of τy on the field strength is observed in all cases. This is an indication that other phenomena (such as the above mentioned non-linear conduction effects or ion injection) will prevail over the interfacial (Maxwell–Wagner) polarization mechanism in the overall explanation of the observed ER behavior of iron oxide in silicone oil suspensions. We will return to this point below. shows that a parabolic dependence, τy |
∝ |
ϕ2, describes adequately the variation of the yield stress with the volume fraction of solids. Such dependence is a result also found by other authors As mentioned in the introduction, ER fluids become Bingham bodies when the electric field is applied. This behavior is due to the constant rupture and reformation of the field-induced structures in the suspension at low shear rates. Such a process gives rise to a finite yield stress, τy. From this, the data should be reasonably well fitted by the Bingham equation:Here τ is the shear stress, γ˙ the shear rate and η(∞) is the plastic viscosity. At high-shear rates the viscosity of the suspension approaches that of a simple sterically stabilized dispersion, as hydrodynamic forces dominate over other interactions. The high-shear limiting viscosity can then be fitted to the Dougherty–Krieger where ηc is the viscosity of the continuous medium, [η] the intrinsic viscosity and ϕm the maximum packing volume fraction. For a random suspension of hard spherical particles, [η] and ϕm are 2.5 and 0.605, respectively. However, for particles of different geometries and sizes the intrinsic viscosity and maximum packing volume fraction can reach significantly different values. In order to get information about these parameters for the hematite/silicone oil suspensions, the high-shear rate limiting viscosity of the unelectrified suspensions was fitted to the Dougherty–Krieger equation () resulting [η] = 7.0 ± 0.1 and ϕm |
= 0.3 ± 0.1. The value obtained for [η] is higher than that of suspensions of spherical particles. However, it must be taken into account that intrinsic viscosity is very sensitive to the shape of particles and small changes in the aspect ratio of solids (such as shown by our polyhedral hematite) may give rise to much higher values of this parameter gives a new constitutive equation for our ER fluids shows shear stress as a function of shear rate at different field strengths. The predictions of Eq. for different yield stresses are also shown. Over the whole experimental range of the variables investigated, the Bingham–Dougherty–Krieger model provides an adequate description of the experimental data.The ER effect due to DC fields is much more complex than under AC excitation. Fibrillated arrangements, non-linear conduction, charge injection and/or electrophoretic migration and deposition are some of the possible phenomena which can occur under this condition. For these reasons, a structural analysis is required to elucidate which mechanisms are mainly responsible for the ER response of our hematite/silicone oil suspensions. show photographs of a suspension with a 0.1% volume fraction, taken at different times after application of a constant electric field of 2.5 kV/mm. From a quiescent state (a), particles start to move from the electrodes to the center of the cell (b). This movement is caused by the surface charge of the particles, and if the particles reach the opposite electrode, an injection of charge from the latter will occur until the potential of both particle and electrode are equal; the solids will then be repelled towards the other electrode and so on. This situation collapses into the formation of convection cells where an inter-electrode circulation of particles can be observed (c and d).These phenomena are jointly called the electrohydrodynamic (EHD) instability shows our observations of such periodic particle deposits in a bob and cup geometry, for our concentrated suspensions.These findings can explain the increase in viscosity shown by the suspensions, particularly at low shear rates: viscous dissipation occurs by the tendency of these structures to maintain their integrity and by their friction between each other or with the electrodes ) reflects the shear force required to balance and overcome the tendency of these rings to maintain their integrity which is due to the linear electrical attraction force between the charged particles and the electrodes.Finally, let us note that the structural observations also show the dependence of the response time with the electric field strength. show photographs of a suspension with 0.1% volume fraction at two different electric field strengths (1.5 and 2.5 kV/mm), taken at different times (t |
= 0.45, 2.70, 4.50, 7.20, 22.50 and 45 s). It can be observed how for the highest applied field, the EHD convection cells are completely formed at 7.2 s while for 1.5 kV/mm these structures do not appear until 45 s. These observations show the decrease in reaction time with electric field strength commonly observed in electrorheological measurements.The rheological properties of ER fluids consisting of iron(III) oxide particles dispersed in silicone oil under DC electric fields have been determined. A plastic behavior has been observed, adequately described by a combination of the Bingham and Dougherty–Krieger equations. It is worth to mention that the ER response and, consequently, the yield stress, increase linearly and in an approximately parabolic fashion with the field strength and the volume fraction, respectively. The origin of this ER effect in hematite/silicone oil suspensions has been investigated. Although a slight aggregation between particles is expected (because of Maxwell–Wagner polarization), this is not sufficient to explain the ER response of the suspensions. Qualitative arguments have been given, based on direct images of the particle structures, suggest that electrohydrodynamic convection is an essential feature of the ER response in hematite/silicone oil suspensions. This phenomenon is originated by the charge injection from electrodes to the particles generating their chaotic motion, and, finally, the formation of convection cells. Structural observations such as the patterns of periodic rings in the measurement cells confirm this explanation at high concentration of solids.Fatigue life estimation of an all aluminium alloy 1055 MCM conductor for different mean stresses using an artificial neural networkThis study is aimed to employ artificial neural networks (ANNs) to predict the fatigue lives of the All Aluminium Alloy Conductor (AAAC) 1055 MCM overhead conductor, considering different values of stretching load (mean stress). For ANN training, three Wöhler (S-N) curves are generated for a conductor/suspension clamp assembly. Twenty-seven fatigue tests are carried out with stretching loads, related to everyday stress (EDS) of 17%, 20% and 25.6% of the conductor’s ultimate tensile strength (UTS), corresponding to mean stresses of 48 MPa, 54 MPa and 73 MPa, respectively. Constant life diagrams (at 105, 106, 107 number of loading cycles) for the AAAC 1055 MCM overhead conductor are built using the ANN. The results confirm that the ANN can accurately predict the fatigue lives of an overhead conductor for various levels of mean stress also when limited experimental data is used for training.minimum bending stiffness of the conductorThe demand for electricity is increasing worldwide as the global population grows. Simultaneously, new power lines have been built, and networks are upgraded to satisfy the demand. In some countries, like Brazil, the transmission networks can have hundreds of thousands of km Besides the dynamic forces caused by the wind, the conductor is also submitted to static loading, due to the tensile load applied when installing the transmission lines. Different stretching loads can be used, depending on the size of the span and type of conductor. The mean stress on the conductor is one of the main factors that influences its fatigue resistance, since an increase in the stretching load not only rises the normal stresses in each one of the aluminium wires but also interferes in their inner contact mechanics, hence it will certainly play an important role on the fretting fatigue process. Thus, the mean tensile stress superimposed onto alternating stresses generated by aeolian vibration significantly reduces the fatigue resistance of the conductor Diagrams correlating mean and alternate stresses at a specific number of cycles to failure (fatigue life) have been used to observe the effect caused by mean stress on fatigue resistance of materials and components. Several diagrams have been proposed and used, including those by Gerber To compute the remaining fatigue life of a overhead power line, the Conférence Internationale des Grands Réseaux Électriques (CIGRÉ) proposed a methodology that requires not only measuring the actual vibration levels of the conductor, but also its S-N curve (where S is the bending stress amplitude in a strand in the outer layer of the conductor at the point diametrically opposite to the last point of contact (LPC) between the conductor and the suspension clamp. S is calculated by using the Poffenberger–Swart A preliminary study by some of the present authors applied ANNs to estimate the effect of a mean stress on the fatigue life of an aluminium conductor steel reinforced (ACSR) This publication aims to predict the fatigue lives for various mean stresses (stretching loads) of overhead conductors, by using a technique that requires a lower number of laboratory and reliability tests. This makes possible to predict the fatigue lives of an overhead conductor when submitted to different mean stress levels.This section will present in details the materials and methods applied to carry out the fatigue tests on an Aluminium Alloy Conductor 1055 MCM (AAAC 1055 MCM) to generate the S-N curves for different stretching loads (mean stresses).The AAAC 1055 MCM is made of aluminium alloy 6201-T81. Aluminium is widely used in power line conductors due to its high conductivity and low cost compared to other metals. The structural and dimensional characteristics of AAAC 1055 MCM are shown in reports some geometrical and mechanical properties of such a conductor.With a view to standardising the tests, CIGRÉ Fatigue of an overhead conductor occurs at the points where its movement is restricted ). Therefore, the P-S model provides the nominal bending stress (zero to peak), σa, at a material point on a strand of the external layer diametrically opposed to the LPC. More specifically, such bending stress amplitude is calculated as:being K the Poffenberger–Swart constant where E and da represent the modulus of elasticity and the diameter of the aluminium strand, respectively and x () is the distance between the LPC and point where the bending displacement of the conductor (Yb) is measured, i.e., 89 mm. Finally, p is a stiffness parameter, which is given by:where H is the conductor stretching load and EImin is the minimum bending stiffness of the conductor, given by:n is the number of aluminium wires in the conductor.The S-N curve can be built by applying different peak to peak bending displacements (Yb), which is related to the bending stress amplitude by the Poffenberger–Swart formula The fatigue tests with the AAAC 1055 MCM are conducted in the Laboratory of Fatigue and Structural Integrity of Overhead Conductors at the University of Brasilia. illustrates the configuration of the test bench. Each of the three benches is around 47 m long, divided into two spans: the passive and active spans. The conductor is anchored in two blocks (fixed block 1 and 3 in ), which are fixed on ground of the active and passive spans, respectively. The conductor is excited by an electromechanical shaker positioned on the fixed block 2 in the active span. This shaker is connected to the conductor by a custom clamp, mounted on an alignment device that avoids the transmission of lateral forces to the shaker. An accelerometer1 used just to monitor forces and displacements transmitted to the shaker is installed on the top of such a clamp ((a)). At the extreme of the active span is the suspension clamp ((b)), which is held on a thick mettalic plate inclined at 10° to the conductor (sag angle). The tests are carried out under displacement control and an accelerometer, installed on the conductor at 89 mm from the LPC between conductor and clamp, is used to this end (here it is worthywhile noting that all accelerometers and others sensors used during the test campaign were properly calibrated by an external contractor). The tests are performed in the 18–20 Hz frequency range, in the optimal working region of the shaker. A vibration sweep of the resonance frequencies is performed to select the most appropriate one to conduct the fatigue test. reports the test parameters selected to build the S-N curves of this AAAC 1055 MCM conductor/suspension clamp assembly. To count the number of fatigue cycles experienced by the conductor, a laser displacement sensor is placed below the clamp used to position the accelerometer on the conductor, as shown in b. As mentioned before, the criterion to stop the test is the complete failure of 6 strands (i.e., 10% of the aluminium wires of this conductor). The detection of broken wires inside the suspension clamp is made by a device installed at the first node of the overhead conductor from the LPC. This device consists of two rulers attached to the conductor node by a screw clamp and two laser sensors (). One should notice that, after the failure of a single wire, there will be a redistribution of forces among the remaining unbroken strands, which will provoke a minute rotation to the conductor. Therefore, the rulers are used to amplify such an effect while the laser sensors measure the displacement and, at the end of them, allowing the calculation and the record of the rotation angle.The stretching load (every day stress – EDS) applied to the conductor is controlled and read by a load cell connected to the anchor clamp (see detail in ). The conductor is stretched by using at one end of the bench a hand traction winch and by the dead weigths at the other extreme. After the target mean load is reached, the conductor is left to accommodate for six hours. In this test campaign S-N curves are constructed for three different mean loads: 26.07 kN, 30.65 kN and 39.03 kN.These loads correspond to every day stress levels of 17%, 20% and 25.6% of the conductor’s ultimate tensile strength (UTS). Dividing these mean stretching loads by the total cross section area of the conductor one obtains the following mean stresses: 48 MPa, 54 MPa and 73 MPa. Here, it is worthy emphasizing that each wire will experience during the test a combination of the mean stress generated by the static stretching load plus an alternating stress due to the cyclic bending. This cyclic stress, as it was explained in section 2, can be computed by the Poffenberger-Swart formula (Eq. ) at a point on a strand of the external layer diametrically opposed to the LPC.At the end of the fatigue test, a sample of the conductor, which is inside the suspension clamp, is properly identified and cut for further inspections. Besides confirming the number of broken wires, this inspection reveals the number of failures per layer and position of such failures with respect to a reference point on the clamp (or on the conductor). The number of broken wires and their respective number of cycles are recorded according to the fracture graphs available in the test monitoring room. Thus, the S-N curves of the test specimen (conductor AAAC 1055 MCM/suspension clamp assembly) can be obtained.Costly long-term tests are needed to construct constant life diagrams of conductors. Thus, developing a numerical model capable of estimating the Wöhler curve (S-N curve) of conductors for a certain mean stress level would benefit industries by predicting conductor behaviour before its use. To that end, a mathematical representation of the problem must consider two variables as input elements: the number of cycles to failure (N) and mean stress (σm). The bending stress amplitude (σa) is the value obtained by the model. In the present study, we used a multiple-layer perceptron network. ANN training was conducted via the backpropagation algorithm using the rule of the moment, with architecture consisting of two input neurons, mean stress (stretching load) and number of cycles, and one output neuron (bending stress amplitude), in order to obtain the following function shown in Eq. ANN architecture, and their normalised values, are shown in (where Nmax is 107 cycles). In the hidden layer, 1 to 30 neurons were used to select the most appropriate architecture to model conductor fatigue behaviour. Each hidden neuron shows bias and a sigmoid activation function, with a linear function used for the output neuron. The use of sigmoid activation functions is suitable for these types of network as the smoothness is their main characteristic, making it possible to obtain their derivatives. These derivatives are essential to develop the training algorithm for this type of network architecture Several engineering problems were successfully solved with a multiple-layer perceptron network, thus the authors will use the same network for this work. Its traits include the ability to learn about a problem through training and generalising for cases not presented to the network , the values of A and b are constants obtained by the least square method (). This table also shows the ultimate tensile stress (σult) of the AAAC 1055 MCM conductor. illustrates an ANN training flowchart. (a) shows that during training, the synaptic weight matrix (w) is a variable which changes by means of the training algorithm. The training was conducted by using the S-N curves obtained experimentally by Eq. (Training data), which represents the desired value (d). Initially, the random synaptic weights (w) and theirs output values (z) were defined for the ANN and thereafter these values are compared with the desired values (d). From this result, one can use the error obtained between these values from the training algorithm to modify the synaptic weights (w) of the ANN (which is represented by the arrow cutting the ANN chart, (a)) and to restart the process. Each time the process is repeated there is a training season. At the end of the training, the results are compared with the values obtained experimentally (b), demonstrating the ability to generalize. For the training, the backpropagation algorithm with the moment rule was used with the constant moment and learning rate are 0.7 and 0.1, respectively.The cross-validation method is used for ANN training, employing two S-N curves with a mean stress of 48 MPa and 73 MPa, respectively, as the training set, and an S-N curve with mean stress of 54 MPa to validate the network. These curves are presented in . The root mean square (RMS) is calculated using the Eq. where Q is the size of the dataset, di are the desired responses, and zi is the the final actual response of the output neuron. To distribute the data more evenly and to improve the computational performance of the training process, the input and output neurons were normalised. The implementation of the algorithms is made with the MATLAB software.ANN training is performed using the cross-validation method, where a training set (S-N curves at mean stress of 48 MPa and 73 MPa) and a validation set (S-N curve at a mean stress of 57 MPa) are used. During the training, the RMS (Root Mean Square) was assessed for each training epoch, selecting the best result where the lowest RMS value of the validation set (RMSmin) is found, as shown in . The training performed reveal that the lowest value obtained by RMSmin was 0.0001. Thus, a stopping criterion in the training of this ANN architecture for other conductors of the same family can be applied in the range of around this number, using 10 to 20 hidden neurons.The results and discussions about the fatigue tests carried out on the AAAC 1055 MCM conductor are presented in this section, followed by the constant life diagrams obtained after ANN training with the experimental data.Three Wöhler (S-N) curves are generated for a AAAC 1055 MCM conductor. Twenty-seven fatigue tests are carried out with stretching loads, related to everyday stress (EDS) of 17%, 20% and 25.6% of the conductor’s ultimate tensile strength (UTS), corresponding to mean stresses of 48 MPa, 54 MPa and 73 MPa (i.e. nine fatigue tests for each mean stress value). reports, not only the loading conditions, but also the fatigue lives (for break of the sixth aluminium wire) obtained in each test.The S-N curves generated using the results from for three different mean stress levels (EDS values). Analysis of the data on the graph shows that the higher the mean stress, the faster is the fracture progression of conductor wires. This behaviour is associated not only with the increase of the tensile mean stress in the individual wires, but also with the rise in contact forces among wires (triggered by the higher loading), thereby increasing the contact stresses. Notice that, for a same stess amplitude level, the curve with the EDS corresponding to 25.6% of the conductor’s ultimate tensile strength (UTS) will provide a smaller life (number of cycles) than those with 20% and 17%, i.e., the increase in stretching load significantly reduced the fatigue strength of the conductor Data from the 27 experimental tests conducted with the AAAC 1055 MCM are used to train a multiple layer perceptron architecture. The graph in shows the results of constant life diagrams for such a conductor obtained by the application of the ANN. This is a graph of bending stress amplitudes versus mean stresses for a specific constant life. Three curves have been plotted for 105, 106 and 107 fatigue cycles. The regions below each one these curves correspond to the combination of alternate and mean stresses that the AAAC 1055 MCM can safely withstand at that specific number of vibration cycles.Each increase in mean stress is followed by a decline in stress amplitude with the purpose of obtaining the same fatigue life for the conductor. Clearly, one can see that, in regions where winds cause higher stress amplitudes, the transmission utilities need to establish a compromise between a required durability (number of cycles) and the wish to use higher levels of the stretching load, which again will directly impact in the costs of construction of the line. Also it should be noticed that raising the stretching load of the conductor increases vibrations (as self damping is decreased) and reduces its useful life These results make it possible to predict the fatigue behaviour of the AAAC 1055 MCM conductor for different mean stress values. It is important to emphasise that, without using ANNs, approximately 80 conductor samples would be needed to obtain the constant life curves depicted in , where each sample is 50 m long. The time required to build these curves would be around 13 months without interrupting the tests. The use of ANNs makes it possible to estimate S-N curves at many different mean stress levels from small experimental samples, while substantially reducing the time and resources needed to conduct an experimental programme of this magnitude. Worth of notice is the fact that only moderate levels of mean stress were considered in test program, which generates some uncertainty of the curve at low and high mean stress. Anyway, in pratical terms the transmission lines are usually designed to operate within the range of mean stresses used in this work. shows the Wöhler curve or S-N fatigue curves, where the bending stress amplitude values, found by the ANN, are plotted with the respective number of cycles to failure for mean stresses of 48, 57 MPa and 73 MPa. This shows that an increase in mean stress on the conductor decreased its fatigue strength, and that the results obtained for this conductor are in line with literature data, as those produced for Aluminium Conductor Steel Reinforced Conductors (ACSR) such as reported in Fadel The use of ANNs proved to be promising, since they can assess the fatigue behaviour of a power transmission conductor using three S-N curves, thereby enabling power line companies to predict the fatigue life of their conductors submitted to different mean stresses, saving time and money.The results have show that the S-N curve for the AAAC 1055 MCM under a EDS of 25.6% UTS, corresponding to a mean stress of 73 MPa, presents an average reduction of 43% of the fatigue life compared to the life of the conductor under 20% UTS, which corresponds to a mean stress of 57 MPa. The ratio of 49% has been observed between the fatigue life obtained using the EDS of 17% UTS and 25.6% UTS. Thus, an increase of conductor stretching load (mean stress) significantly reduced its fatigue strength.Accurate results have been obtained after ANN training with experimental data using the three S-N curves. The curves obtained under EDS of 17% and 25.6% UTS, with mean stresses of 48 MPa and 73 MPa respectively, have been used to train the neural network and the curve with 20% UTS (mean stress of 57 MPa) to validate it.The regions where the conductor could work safely are been determined via the constant life diagrams using the ANN. It is important to emphasise that a decrasing in stress amplitudes is required to obtain the same useful fatigue life of the conductor when mean stress increases.The use of an ANN made it possible to predict the fatigue behaviour of the AAAC 1055 MCM for different mean stress values, using a small sample of experimental data for network training. As such, power transmission line designers can predict the fatigue life of conductors subjected to different mean stresses, thereby saving time and money.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Confirmatory investigations on the flux effect and associated unstable matrix damage in RPV materials exposed to high neutron fluenceThis paper provides additional experimental data on the neutron flux effect on RPV hardening and embrittlement and on the so-called unstable matrix damage that was suggested to occur at high flux. Six materials taken from the first irradiation surveillance capsules of Belgian PWRs with a fluence not exceeding about 1.5 × 1019 |
n/cm2 were further irradiated in the BR2 high flux reactor to additional fluences ranging between about 1 and 1.5 × 1020 |
n/cm2 at 290 °C. Eight additional RPV materials were selected to investigate the flux effect on irradiation hardening. No statistically-significant difference in irradiation hardening for low and high flux could be evidenced from the null hypothesis test applied with the general linear model. This is confirmed by additional experiments where fourteen irradiated specimens of various RPV materials consisting of low to high Cu and Ni contents were annealed at 350 °C for 5 h to eventually reveal some recovery of the unstable matrix damage. The results did not show any recovery upon heat treatment, which indicates that unstable matrix defects did not appear in these materials during irradiation at high flux.Effect of neutron flux on irradiation embrittlement of reactor pressure vessel (RPV) materials has been extensively debated for many years but to date still no consensus could be reached among the scientific community. This difficulty of reaching a consensus stems from a number of reasons, among which the absence of reliable data that can unambiguously clarify the flux effect, the absence of archive material that can be irradiated at higher flux, the difficulty to separate neutron flux from spectrum effects, and last but not least the experimental uncertainties.The flux effect is an important issue because it addresses the opportunity of using high flux material test reactor (MTR) data to provide not only insight on irradiation damage occurring on pressurized water reactor (PWR) vessels but also help for developing embrittlement trend curves. This is very important in the perspective of long term operation.In the low fluence regime, say below about 1 × 1019 |
n/cm2, E |
> 1 MeV, it is generally accepted that high flux reduces the rate of the Cu-rich precipitate kinetic but the plateau (saturation) value corresponding to complete Cu-precipitation is unaffected by neutron flux. For high fluence levels, and in particular in the perspective of long term operation, this question remains open. In a previous paper, we investigated the neutron flux effect on a reactor pressure vessel material and found that flux effects were not significant The insignificant effect of flux was also supported by post-irradiation annealing experiments at low temperature performed on four RPV materials, in which no sign of recovery of the mechanical properties could be detected Two main mechanisms are usually considered to model the irradiation hardening and embrittlement of RPV materials, the Cu-rich precipitation (CRP) and the stable matrix damage (SMD) In order to clarify the behavior of the HSST-02 material, and to eliminate the potential effect of difference in initial properties, HSST-02 material taken from the broken Charpy specimens of the first surveillance capsule irradiated at low flux (∼1 × 1011 |
n/cm2, E |
> 1 MeV) for about 3–4 years, was used to manufacture a number of small tensile specimens. These specimens were re-irradiated in the BR2 reactor at significantly higher fluxes, of the order of 1013 |
n/cm2, E |
> 1 MeV. The objective of this re-irradiation is to directly compare the tensile data obtained on the subsequent surveillance capsules with the high flux data obtained after re-irradiation.In the following, two experimental works will be described, analyzed and discussed:A comparison of low flux irradiation hardening of HSST02 and other surveillance materials with high flux data, with the aim of clearly establishing whether flux effect is effective or not.Post-irradiation annealing at 350 °C/5 h over a variety of material compositions to evaluate eventual recovery due to UMDs.It is important to emphasize here that the answer to such a question is not binary but will be expressed in statistical terms, namely significant or negligible differences, taking into account the experimental uncertainties. This is inherent to the scatter that is usually observed and that cannot be ignored.Eight RPV materials were selected for this study among which six materials for which archive materials were not available (one plate, four forgings and one weld) and two from archive materials, one forging and one weld From previous RADAMO irradiations, some spare tensile specimens were available The chemical composition of the investigated materials for both irradiation (set I) and post-irradiation annealing (set PIA) are summarized in . As it can be seen, the available range of chemistry encompasses a large variety of RPV chemical compositions.The tensile specimens were irradiated in the BR2 reactor at a nominal temperature of 290 °C ± 5 °C to five different fluence levels. Of course, as the irradiation time was kept constant, about 21 days, the differences in fluence are proportional to the flux differences. All specimens are in contact with the pressurized water, typical of PWR conditions and the water temperature was continuously monitored. The average recorded temperature is close to 290 °C. The fluence (resp. flux) distribution in the in-pile section of the Callisto loop located in the BR2 reactor is shown in are consistent and using the fluence distribution curves, a neutron fluence, resp. flux, could therefore be attributed to each individual specimen.All tests were performed at room temperature at a strain rate of about 1 × 10−4 |
s−1. One of the important outcome of this experimental exercise is the significant scatter that is associated with the tensile data. Indeed, because of the limited availability of irradiated material and the high testing costs, one single specimen per condition is generally tested. This was the case in the previous experimental work reported in Ref. of the present work, it becomes obvious that the large scatter can easily affect the overall interpretation. Therefore, it is important to incorporate the experimental scatter in our data interpretation. In the case of , the inherent experimental deviation on the measured yield strength is about ±25 MPa leading to the indicated trend curves (average, lower and upper bounds). This means that differences lower than 25 MPa cannot be considered as meaningful. Nevertheless, it is possible to find sometimes outliers that exhibit tensile test results that are clearly outside the uncertainty bounds and that can likely be associated to the specimen fabrication process that can eventually induce unintended deformation. Fortunately, such observations are marginal. Finally, it is important to mention that all eight materials analyzed in this work exhibit such a scatter, of the order of ±25 MPa.The overall test results on the eight RPV materials are shown in . As it can be seen, because of the large scatter, it is obvious that it becomes difficult to clearly and unambiguously determine whether flux has an effect or not on the tensile properties. Another difficulty is associated with the fluence levels that are not always the same for comparison between low flux and high flux. There are only few cases for which the fluence is similar.To analyze the data, in a first stage, the following procedure is used to compare the low flux to the high flux data. In order to normalize the data to similar fluence levels, a mathematical fitting is used. Two alternatives were used. In the first one, the data are normalized by adopting the following relationship:ΔσynormalizedΔσyexperimental=ΦnormalizedΦexperimentalαUnfortunately, the large scatter does not allow to unambiguously assess the data. An example is shown in In the second alternative, for each data set, low flux surveillance on one hand and high flux MTR-BR2 on the other hand, a simple mathematical fit is selected such that the deviation is minimized. The fits that are used are mostly a power law type but first to second order polynomial functions are also used for data clearly deviating from the power law. Then, specific fluence levels are chosen within the range where interpolation is possible. For example, in the specific case of RBM6 steel shown in , the four fluences that were chosen are 1.75, 3.5, 4.5 and 8.6 × 1019 |
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