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= 50 Hz. The reason is unclear.The S versus f plot is similar to the (ΔZ/Z)m plot in ; however, the position of the maximum sensitivity Sm occurs at f |
= |
fS, different from fm. This indicates that Sm is related not only to the f dependence of (ΔZ/Z), , it is seen that when TA |
= 200 °C is fixed, Sm |
= 3.5%/Oe reaches the highest field sensitivity for the sample after the RFA treatment with F |
= 50 Hz. Further, we have tried various RFA (with different TAs but the same F |
= 50 Hz) treatments. From , we summarize the TA results as follows: in the TA range from 160 to 280 °C, we find (ΔZ/Z)m reaches the maximum value, 72%, when TA |
= 200 °C, and Sm reaches the maximum value, 4.5%/Oe, when TA |
= 160 °C. These results indicate that [A] the low TA RFA method is effective in improving the MI effect; and [B] when TA |
> 240 °C, the effectiveness of the RFA method decreases. Result [B] is reasonable, since according to Ref. , the magnitude of FOM is the largest (1.80% MHz/Oe) for the VAC6025 ribbon sample after the RFA treatment with TA |
= 160 °C and F |
= 50 Hz. In contrast, if the ribbon sample has not been subjected to the RFA treatment, its FOM is only about 0.4–0.7% MHz/Oe.We have introduced a new annealing method to improve the MI effect in the VAC6025 ribbons. This method includes applying a rotating field hR with a frequency F when the ribbon sample has been heated at the annealing temperature TA for 1 h and then field-cooled to room temperature. In terms of the (ΔZ/Z)m improvement, when in the as-cast state, (ΔZ/Z)m is only 34%, but after the rotation-field annealing (RFA) with TA |
= 200 °C and F |
= 1 or 50 Hz, (ΔZ/Z)m reaches 72%. In terms of Sm and/or FOM improvements, for the as-cast sample, Sm |
= 1.8%/Oe and FOM = 0.7% MHz/Oe, while for the sample after RFA (with TA |
= 160 °C and F |
= 50 Hz), Sm |
= 4.5%/Oe and FOM = 1.8% MHz/Oe. Moreover, another important merit of using the RFA treatment is that it does not require high annealing TA. Hence, the ribbon sample remains ductile (good mechanical property) after this annealing treatment.On the mechanics of cold die compaction for powder metallurgyThe main object of this paper is to present a theoretical model for the cold die compaction of powder materials based on the axisymmetric solution of large deformation. The model produces an expression relating the green density of the compact to the applied pressure. The analysis takes into account the internal (restricted movements) coefficient of friction between the particles and the container-compacted powder interface friction. Also, a modified analytical expression for the yield compression stress based on the internal coefficient of friction and the work-hardening of the powder was introduced in the analysis. Experiments were performed on cold die compaction of powder of different particles, having sizes between 45 and 150 μm. Comparison between experimental and theoretical results demonstrated remarkable agreement for all the tested conditions. In addition, and for the purpose of verification of the present theory, other published experimental values were also compared and found to be in very good correlation with the predicted results. Other relevant parameters will also be discussed.distance of the element from the top surface compact-instantaneousheight of the element under considerationinternal coefficient of friction-restricted movements coefficientpowder density at any stage, green, tap, and theoretical densitieseffective stress in compression of the bulk materialPowder metallurgy (p/m in its abbreviated form) in many industries has not received the praise of which it is worthy, but for many years now, has been an established process for the manufacture of precision quality engineering components. Generally, p/m technique consists of the production of a controlled blend of metal powders, pressing the mixture in suitable dies, and subsequent heating (sintering) the compacted powder in a controlled atmosphere and temperature to obtain the required density and strength.The Egyptian iron implements, the Delhi column in India and articles made by the Incas, many centuries ago, clearly demonstrate that pressing of powders into desired shapes is not really new. During the 1920s many parts were made and used commercially, such as tungsten carbides, bronze bushes for bearings, and tungsten filaments for bulbs and others. Since then the p/m industries have expanded more rapidly due to the recognition of the distinct advantages in terms of materials utilization, ease of components manufacture and cost/energy saving and other factors. Despite these outstanding merits, the p/m process does have a few limitations, such as, part design and geometry, initial tooling costs, raw material, i.e. powder, costs are higher than conventional solid bulk, and special care must be taken against corrosion Cold die compaction of powder metallurgy is generally simple to put into practice, however it is extremely difficult to analyze the process theoretically. This may be due to the complex variations of the parameters involved during the compaction process. Nevertheless, much has been published and a great deal of effort has been directed to the development of empirical and theoretical compaction equations to describe the green density-applied pressure relationship. Needless to say, the green density of compact has direct influence on the densification of the product and hence the strength. But it seems that all the previously developed expressions depend totally or partially on experimental factors, due to the unknown parameters. Studies were performed involving the simulation of powder compaction using the FEM and based on the elastic–plastic of large displacement, where the powder is considered as a continuum which exhibits plastic deformation under applied external pressure The main purpose of the present work is to present a theoretical model based on the modified plasticity equations which do not require empirical constants that need to be determined from the powder compaction. However, certain factors such as coefficients of friction are used from previously published work.Generally it is difficult to formulate the mechanism and yielding behavior of the pore bearing materials particularly in cold die compaction process. This may be due to many factors such as fracture, fragmentation, rearrangements, and different deformation behavior of particles. Many published theories have endeavored to express the green density as a function of process parameters. However there has always been difficulty in expressing it fully without relying on experimental values. The present theory relies on the minimum possible experimental parameters and can be used for metallic and other nonmetallic powders with certain properties and geometrical adjustments. Also, the presented equations can be used for isostatic compaction.To establish the process parameters, it is assumed that the powder is housed freely in a container and external pressures are applied simultaneously from both ends, as shown in . As the process of compaction proceeds the powder particles will rearrange to form compacted media. The equilibrium of a small element at a distance z from the upper or lower surface using the cylindrical coordinate (r, θ and z) will be considered Here axial symmetry will be assumed where the cylinder will maintain its form and by excluding torsion, σθz = σrθIn the present work it is assumed that the shear stress is constant (this will be discussed later), and taking into account the geometry of the element, B, then the reduced equilibrium equation in the z direction results inwhere σz is the axial stress at distance z from the surface, σr the radial stress and μ the coefficient of friction between the container wall and the compact powder. However, both the radial stress and the coefficient of friction are assumed to be constant for the present analysis. Needless to say the variation of these parameters will be discussed later. A simplification of Eq. Since there is no change in the diameter of the compacted powder and using the well known expressions of Levy–Mises for the plastic flow of metal, it may be seen that the radial strain (dɛr) = hoop strain (dɛθ). From which it follows that the state of stresses σr = σθ, and using the von Mises criterion for the effective stress (σ¯) of the bulk material, the following relation is obtained: for the case in which sticking does not occur (only sliding) and introducing the boundary condition results inwhere pa is the compact external pressure applied by the punch from both ends simultaneously, and H the height of the compact (varies between the final height (Hf) and the original height of packed powder (Ho)). The final expression for the instantaneous axial stress as a function of the compaction process parameters is given by:On examination of the above expression it becomes evident that a relationship between the density factor (density variation of the compact (dρ) and theoretical density of the material (ρt)) and the stress ratio which is given in Eq. is needed. However, to achieve this, then the true compression strain will be used and is defined as:where H is the actual or the instantaneous height of the compact. From the incompressibility condition where the mass of the powder and the compact are equal at all timesAs previously mentioned, the mechanism of cold compaction is difficult to formulate due to the complicated elastic and plastic deformation during the process and other parameters. Hence, in the present work, a general relationship between incremental stress and incremental strain is proposed and is given by the following expression:where β = (ρt − ρp)/ρt is the density factor, and ρp the tap density of the powder material. It is a known fact that the porosity is not constant and varies considerably with the applied external pressure. Therefore, Eq. can be integrated and substitution of the appropriate boundary condition (σ¯=0 when dρ = ρp) yields green density (ρg) at any compression stage and is given by: permits the determination of the final theoretical green density for any compact conditions, and is given by the following expression:The above formula is a function of process parameters, material and powder properties, and will be discussed later.The above analysis could also be modified to determine the stress distribution at any given point within the compacted sample. For this, once again the condition of axial symmetry is assumed and the effective stress is assumed not to be a function of radius of the element (r), then Eq. where μi is the internal coefficient of friction and L the height of the element from the punch surface The yield stress in compression (σyc) of the material can be expressed by the modified Mohr–Coulomb yield criteria and is given by: that the yield stress in compression depends on the internal friction coefficient μi (or restricted movements coefficient). In order to obtain a modified solution for the metal/ceramic compactions, then the effect of work-hardening of the grains during the compression process must be taken into account. This is done by modifying the effective stress–strain relation as follows:The above equation represents a material which is rigid up to the yield stress (σ0), followed by a strain hardening effect or the work-hardening exponent (n). The logarithmic strain relates to the diameter of the grain before and after compaction, which could be determined beforehand from previous experiments. In addition, it is a well known fact that the grain size has a remarkable influence on mechanical properties of the material. Hence, the effective compressive strength (σ¯) is the most sensitive property and is related to grain size similar to that given in the well known Hall–Petch empirical relationship. The final suggested expression for the strength may be expressed as follows:where σ0 is a basic yield stress that can be regarded as the stress opposing the motion of dislocations.The proposed empirical equation for the general strength of the compact powder is given in Eq. to give the most appropriate effective stress for the process of powder compaction process. The compacting load at any stage of compaction can readily be calculated by equating the applied external load of the punch to the internal resistance of the powder compaction, which is given byFrom the above equation the average applied pressure can also be estimated by dividing it by the cross-sectional area of the punch As mentioned previously, several empirical and semi-empirical expressions relating pressure and relative density during compaction of metal powder have been proposed. This is due to the complexity of the dynamic variation of the parameters during the compaction making it extremely difficult to establish relationships between the process variables. Needless to say, the presented theoretical work is a simplified analysis which could be used with reasonable accuracy. On close examination of the final green density expression, Eq. , it can be seen clearly, that it is a function of the powder and material properties, geometry of the compacted sample and process variables. As mentioned previously the friction coefficient is assumed constant, but in reality it is a dynamic process and function of the pressure, process parameters and porosity. Evidently it becomes difficult to formulate, hence it is an accepted procedure to assume it constant throughout the compaction process. Also the work-hardening can be included through the term of the true stress, Eq. , which would improve the predicted results of the final green density.The raw materials employed in the present experiments were Ancorsteel 85 HP, a water atomized prealloyed 0.85 w/o molybdenum low-alloy steel powder, which have high compressibility and are normally used for high performance applications. The powder was fractioned in six different classes of particle size 45–150 μm according to MPFI standard 05 and compacted without lubricant in a cylindrical die of 9.5 mm diameter and samples height of (10 ± 1) mm. The green density (mass per unit volume of an unsintered part) was calculated using a micrometer and digital balance. shows the compressibility curves of each particle size class, hence the relationship between the green densities of the compacts and the applied external pressures can be determined. Close examination of the figure reveals that there is a small difference of approximately 6% between the compaction of 150 and 45 μm grain diameters show scanning electron micrographs of several powder sizes and it is clearly visible that the powder is irregular in shape after compaction, and almost without porosity. Various micrographs were taken at different locations on the surfaces of the specimens, and all demonstrated the remarks made previously.From the present theory, the green density can be predicted from Eq. by knowing the tap and the bulk material densities, geometry of the initial and final compacted powder and the effective compressive stress of the bulk, friction conditions, and by incrementing the applied pressure values. This finally leads to the theoretical plot of the green density at any applied pressure stage. This procedure is used for the theoretical curves of different types of metallic and nonmetallic powders. Hence a simple computational program was developed for this purpose to facilitate this process., and due to the small difference in density trace curve, it was decided in this present work that the theoretical analysis would be based only on a diameter of 50 μm. Typical comparisons between the theoretical prediction for the green density for d50 and the present experimental results for d150 and d45 are shown in . On close examination of the figure, the remarkable agreement between the predicted values from Eq. and the experimental results can easily be observed. It becomes evident that by using powder with larger particle sizes between 100 and 150 μm, the predicted pressure-density may be increased by 2%, and for smaller particle sizes a decrease by 2% may be needed.The present analysis clearly recognizes the difference between the internal coefficient of friction and the container-compacted powder interface friction. In the case of internal coefficient of friction, Eq. , the movements and rearrangements of the grains and particles of the powder during compaction took place, . Whereas the interfacial friction resulted from the shearing force caused by the radial stress due to the axial compression of the powder, Eq. , which shows clearly these friction marks on the side wall of the compacted powder specimen. These two parameters are generally not equal, however for simplicity, they are assumed to be equal in some cases in the present theory. In fact the present analysis also leads to the determination of the internal/interface frictions which can be estimated from the values which give the closest prediction to the experimental results. In the present experiments it was found that a value of μi = 0.08–0.1, which is a reasonable value compared to values used by other authors . In this case, a different type of experiment must be performed to verify the distribution of the friction as a function of green density. Needless to say, the friction in the dynamic pressing is different from that in the steady or static stage.In general, internal friction plays an important role on the distribution of the compaction pressure in any given plane of the specimen, . The distribution of friction as a function of pressure is illustrated in , in fact this distribution is called friction-hill. The type of distribution has a great contribution towards the required load for the necessary compaction of the powder. Previous work . Therefore, it is fundamental to estimate the friction and geometry of the piece beforehand, also lubrication becomes evident in this process to reduce the required compact load.To illustrate the versatility of the present theory, the compaction of other metallic powders was used for comparison purposes. Several previously published studies were reproduced and some of them are plotted in . All these figures show remarkable agreement between the present theory and the experimental results. All the experimental data are reproduced from the cited published works. In all these a suggested coefficient of friction was employed to yield the best results and varied between 0.09 for iron to 0.35 for copper and others, It is very important to mention that in many cases the compacted part is made up of several powder compositions, as shown in . In these cases it is essential to determine the effective compressive stress of the mixture using the rule of mixture with certain precautions with regards to the presence of voids and other defects. Evidently these will influence greatly the compressive stress of the final compacted part. Needless to say, scanning electron micrographs will be of tremendous help in estimating these defects beforehand, It is evident that there is much the powder metallurgy process has to offer in terms of design and engineering, and the manufacture of parts in a versatile manner in a wide variety of materials for many different types of industrial sectors.The present analysis derives basic equations that govern powder material behavior under cold die or isostatic compaction process. A simple and more reliable theory to predict the green density-applied pressure for any given geometry, powder material size and type, and process parameters was the main objective of the present work. It can also be concluded, despite the approximate nature of the analysis presented, that there is a remarkable agreement between the experimental and the theoretical results. In addition, the experimental results reported here were carried out on powders with different particle sizes. The present theory was also compared to many other published experimental studies and found to be in excellent agreement. Therefore, the present theory can be used with accuracy for ceramic, ceramic/metal, and pure metallic powders, independent of particle shape and size.The outstanding feature of the present model is the reduction in time during the phase of design and testing. Also, it is a very effective method to be used in reducing the number of experimental tests needed for qualifying the compacted part of the required density.It becomes clear from the present analysis that the yield stress of the material plays a major and fundamental role in the final strength and density of the final compacted part. Consequently, in the present theory the Mohr–Coulomb and work-hardening hypothesis were modified to suit the present model, which includes the internal (restricted movements coefficient), die-wall frictions and work-hardening during the compaction process. It is also clear that other parameters can modify the final compacted density and they may include the following factors, which can be deduced from the present model:The theoretical model clearly demonstrates the variation of the initial density of the preform and the pressure distribution from center to edge for a given internal friction. This distribution has the form of friction-hill. Similar distribution is obtained for the variation of initial specimen height. Also, the present analysis admits and takes into account the difference between the interface friction and the internal friction of particles (restricted movements coefficient).Green density distribution will be more uniform for higher initial relative tap density of the preforms. Lubricated powder shows relatively better densification than unlubricated samples. Also, experimental results demonstrated that increasing the particle size of the powder yielded better densification.The present theory can be used effectively to estimate die load from the pressure distributions during the compaction process.In addition to the many advantages mentioned earlier, the powder metallurgy industry is more ecological than many other industries, as it uses re-cycled metals, it is not noisy, and does not generate harmful fumes or pollutants, consequently the future prospects of powder metallurgy are very bright and favorable.TRIP assisted press hardened steel by the anisothermal bainitic ferrite transformationA new steel chemical composition is combined with a new press hardening process, in which die-quenching is interrupted by opening the forming tool to permit slow cooling of the hot formed part through the anisothermal bainitic ferrite transformation. This promotes carbon partitioning to austenite before the forming tool is re-closed and die-quenching is resumed to near-ambient temperature. The final microstructure is predominantly bainitic ferrite with dispersions of martensite and up to 11 % retained austenite. Retained austenite can undergo stress induced transformation to martensite in an automobile crash event. The steel exhibits up to 25 % elongation and 930 MPa tensile strength. In contrast to traditional cold formable Transformation Induced Plasticity assisted steels, where retained austenite is consumed during work hardening of cold forming, here, the desired microstructure is achieved after hot forming meaning the retained austenite is more uniformly distributed within the formed part, which enhances energy absorption. The new steel chemical composition is carefully designed to provide optimal microstructural evolution within the constraints of the new press hardening process, yet relatively lean and manufacturer friendly. The new press hardening process is energy efficient as secondary heating is not required since retarded cooling through the bainitic ferrite transformation is provided by residual heat accumulation of the newly developed titanium alloy forming tool. Development of the new technology is demonstrated by press hardening experiments, tensile testing, microstructural analysis, transversal & axial crush testing of formed parts and numerical simulation of crush testing, including a new modelling technique that more accurately simulates deformation of hot versus cold formed parts. Results show a 22 % increase to energy absorption under axial crushing compared to traditional cold formed Transformation Induced Plasticity assisted steels owing to greater work hardening capacity in formed radii of the part, which are shown to be exposed to the highest stresses during crushing.) first reported the Transformation Induced Plasticity (TRIP)’ effect in 1967 during investigation of austenitic stainless steels. The authors discovered unusually high uniform elongation values, which they attributed to stress or strain induced transformation of austenite to martensite, giving rise to dilatation and internal plastic strain, hence the term TRIP. Mild carbon low alloy TRIP steels, exploiting the same phenomenon discovered by ) were developed by the steel industry in the early 1990s and continue to gain much attention within academic research owing to the impressive combinations of strength and ductility. ) applied different hot rolling, quenching and partitioning sequences to a controlled steel chemical composition to obtain eight different TRIP steel products with different microstructures and then evaluated the effect on mechanical properties. Compared to Dual Phase (DP) steels characterised by microstructures of ferrite and martensite, exhibiting an ultimate tensile strength-total elongation product of approximately 15 GPa.%, TRIP steels exhibit much higher values of up to 25 GPa.%. The characteristically impressive strength-ductility combination of TRIP steels provides superior cold formability and potentially, superior application performance, such as automobile crash performance. conducted impact crash box testing on DP and TRIP steels with equivalent tensile strength. For a given strength category, the TRIP steels with enhanced ductility consistently exhibited superior energy absorption by preventing folded regions of the deformed crash box from splitting. documented development of first generation TRIP steels by the steel industry in the early 1990s. Chemical compositions are typically of 0.15−0.25 % C, 1–2 % Mn and 1.5 % Si and are processed during hot rolling or strip annealing to exhibit a multi-phase microstructure of predominantly (proeutectoid) ferrite, with dispersions of bainitic ferrite, martensite and 10–15 % retained austenite. The silicon content retards iron carbide precipitation during bainite formation giving rise to carbide-free bainitic ferrite with excess carbon over and above the ferrite saturation limit partitioning to austenite and remaining in solid solution. The carbon enriched austenite is then stabilised at ambient temperature. The retained austenite is designed to be stress induced transformed to martensite during plastic deformation, as originally cited by , but in this manner, can be achieved with the inexpensive addition of just 1.5 % Si rather than 20 % (Cr + Ni) in austenitic stainless steel. While TRIP steels inherit their name from the transformation induced plasticity effect originally cited by has mathematically demonstrated that only 2 % of the uniform elongation value may be attributed to the TRIP effect, with for the most part, the impressive strength-ductility combination attributed to ‘composite deformation’ behaviour, where ductility of ferrite is exploited early during deformation and then hardness of martensite resulting from stress induced transformation exploited late during deformation.While economical, the typical silicon content of up to 1.5 % has significantly restricted application of first generation TRIP steels. Slab cracking, high rolling loads, poor weldability and poor metallic coatability are the major drawbacks. To overcome these problems, second generation TRIP steels (sometimes called TRIP assisted DP steels) with silicon content partially substituted by aluminium have been developed. investigated a commercial C-Mn-Cr DP steel and an equivalent experimental steel with the addition of 0.52 % Al. The aluminium addition not only allows for higher percentages of retained austenite, but also broadens the processing window of DP steels by raising the A3 temperature to reduce distribution of mechanical properties.The next problem identified with first and second generation TRIP steels has been relatively low proof to ultimate tensile strength ratio, typically of the order of 0.5, compared to 0.6 of DP steels and 0.8 of martensitic steels. While the low proof to ultimate ratio is indicative of high work hardenability and energy absorption, many automotive structural parts require a minimum proof strength. Therefore, parts may require over forming (work hardening) in order to meet the minimum requirement. To overcome this, third generation TRIP assisted Bainitic Ferrite (TBF) steels have been developed. illustrated the design principles behind TBF steels, consisting predominantly of bainitic ferrite with retained austenite dispersions produced by isothermal holding in the bainitic phase field following rapid cooling from the austenite phase conducted either on the Run Out Table following hot rolling, or during the continuous annealing cycle following cold rolling. developed the original Press Hardened Steel (PHS) technology to overcome poor formability and high springback of ultrahigh strength martensitic steels. The steel blank (typical chemical composition of 0.20−0.25 % C, 1.2 % Mn and 30−50 ppmB) is furnace heated to the austenite phase, transferred to the water cooled forming tool, formed in the austenite phase and then die-quenched to martensite, giving rise to tensile strength and total elongation values of 1400−1600 MPa and 3–6 % respectively. The automotive industry desires lightweighting (primarily to reduce exhaust emissions and fuel consumption). Down-gauging reduces weight, but compromises formability and springback. These compromises are more significant when strength is increased, but they still exist for lower strength steels. Press hardening offers exceptional formability and almost eliminates springback, thus press hardening has gained attention for lower strength parts. developed three C-Mn-Cr steels with chemical compositions of 0.14−0.19 % C, 1.45–1.71 % Mn and 0.01−0.55 % Cr. Following press hardening, the three steels gave rise to multiphase microstructures of ferrite, bainite and martensite exhibiting tensile strength of up to 910 MPa and total elongation of up to 9.3 %.The design principles behind TBF steels are compatible with the press hardening process, consisting of rapid cooling from the austenite phase to bainite and / or martensite. However, in order to achieve the isothermal holding step in the bainitic phase field following rapid cooling from austenite, the original press hardening process requires modification. made an attempt towards this by interrupting die-quenching in the temperature range of 280−320 °C with a secondary isothermal heating step for up to 60 s before die-quenching is resumed to near-ambient temperature. Using a steel with chemical composition of 0.22 % C, 1.58 % Mn and 0.81 % Si, the result was reported to be inter-lath retained austenite within the martensitic matrix, giving rise to a retained austenite volume fraction of 18 %, ultimate tensile strength of 1510 MPa and total elongation of 15 %. While the result is impressive, modification to the press hardening line with the secondary heating step is costly in terms of both infrastructure requirements and energy consumption. introduced a similar idea as above, but instead used a first generation TRIP steel of 0.2 % C, 1.9 % Mn and 1.4 % Si; and instead of isothermal holding, used retarded cooling by pre-heating the forming tool to 200 °C and opening the forming tool in the region of 300−200 °C for up to 60 s to conduct the anisothermal bainitic ferrite transformation. The optimum result was a retained austenite volume fraction of 11 %, tensile strength of 1449 MPa and total elongation of 14.5 %. These impressive results, which represent properties of the formed part are very similar to the traditional cold formable strip TRIP and TBF steels. However, the retained austenite in the latter is consumed during the plastic strain of forming. conducted pre-strain tensile tests on a commercial TRIP steel, showing that pre-strain of 10 % reduced the retained austenite volume fraction from 10 to 5 %. Proof strength was raised from 550 to 825 MPa owing to work hardening, while total elongation was reduced from 30 to 15 % owing to degradation of the stress induced transformation effect. Thus, to compare like for like, the measured mechanical properties of a traditional cold formed TRIP or TBF steel part (in formed regions) will be inferior to the mechanical properties of the part produced by , since in the latter the optimal retained austenite volume fraction and stress induced transformation capability is determined after forming and thus, uniformly distributed throughout the part. However, as previously mentioned, the first generation TRIP steel used by , rich in silicon, is unfavourable because of manufacturing drawbacks and thus, the technology is unlikely to reach commercialisation. Pre-heating the forming tool also necessitates modification to the press hardening line, which increases the infrastructure requirements and energy consumption and reduces the production efficiency. In addition, pre-heating the forming tool decreases the die-quenching rate, limiting capability of the process to produce a variety of microstructures (particularly with limited ferrite volume fractions) across parts with different dimensions and gauges.In this paper, we introduce a new steel chemical composition combined with a new press hardening process in which die-quenching is interrupted by opening the forming tool at a temperature in the bainitic phase field. The resulting slow cooling of the hot formed part through the anisothermal bainitic ferrite transformation allows carbon partitioning to austenite to occur. The forming tool is then re-closed and die-quenching is resumed to near-ambient temperature. The new steel chemical composition is carefully designed to provide optimal microstructural evolution within the constraints of the new press hardening process, yet relatively lean, manufacturer friendly and compatible with conventional steelmaking, strip rolling, metallic coating and welding practices. The new press hardening process is economical and energy efficient as secondary heating is not required, since retarded cooling through the bainitic ferrite transformation is provided by residual heat accumulation of the newly developed titanium alloy forming tool following hot forming. illustrates the principal advantage of the proposed TRIP assisted PHS technology compared to traditional cold formable TRIP (and TBF) steels.The new press hardening process is schematically illustrated by a. The steel blank is furnace heated above the A3 temperature, transferred to the water cooled forming tool and hot formed into the part geometry while in the highly formable and isotropic austenite phase, as per the original press hardening process by . Die-quenching from austenite is interrupted by opening the forming tool at a temperature in the bainitic phase field between the A1 and Ms temperatures, in a similar fashion as per the processes by . However, in this new process, there is no secondary heating step, neither by isothermal heating as by , nor by pre-heating the forming tool to retard cooling as by . Instead, the hot formed part is slowly cooled through the anisothermal bainitic ferrite transformation, with cooling retarded by residual heat of the forming tool following hot forming. b clearly illustrates the novelty of the new process compared to the previous processes. The forming tool is composed of an alloy with relatively low thermal conductivity, such as titanium alloy, as developed by ; and water cooling of the forming tool is disabled during interrupted die-quenching to maximise retardation of cooling. Subsequently, the forming tool is re-closed, water cooling of the forming tool is re-activated and die-quenching is resumed to near-ambient temperature. By employing different parameters, including furnace soaking temperature prior to hot forming and die-quenching; and tool-open temperature-time during interrupted die-quenching, a wide range of microstructures and mechanical properties are theoretically achievable from a given steel chemical composition. However, the principal microstructure targeted is predominantly of bainitic ferrite with dispersions of martensite and retained austenite. Retained austenite is designed to undergo stress induced transformation to martensite during application of the formed part such as an automobile crash event, giving rise to the characteristically impressive strength-ductility combination of TRIP assisted steels.To achieve optimal microstructural evolution within the constraints of the new press hardening process, a new steel chemical composition is required which can achieve austenisation with soaking temperature ideally less than 1000 °C, avoid proeutectoid ferrite formation and achieve sufficient partitioning of carbon to austenite with the limited temperature and time available without secondary heating. The chemical composition of the new steel denoted as 20MnSiAlPB5 is shown in . The design principles are based on the well-known effects of alloying elements on steel, such as those documented by . Carbon content is selected to provide interstitial solid solution strengthening, quench hardenability, low A3 temperature and stabilisation of austenite at ambient temperature following partitioning from bainitic ferrite, where at least 0.1 % C, or ideally at least 0.15 % C is required for the latter, while maintaining sufficiently low carbon equivalent for conventional resistance spot-welding techniques. Manganese content is selected to provide substitutional solid solution strengthening, quench hardenability and stabilisation of austenite at ambient temperature. It also minimises segregation during conventional steelmaking and casting practices (where segregation typically becomes significant with more than 1.5 % Mn) and maintains sufficiently low carbon equivalent. Silicon, aluminium and phosphorus prevent carbide precipitation in carbon enriched austenite during bainitic ferrite formation, thus enabling the Ms temperature of the remaining untransformed austenite to be depressed below ambient temperature. Silicon, aluminium and phosphorus contents are selected to provide the optimal balance of carbide precipitation retardation, kinetics of the anisothermal bainitic ferrite transformation, weldability, coatability and manufacturability. Silicon content is selected as the dominant carbide precipitation retardant, but is limited to minimise formation of surface-bound silicates that impede hot rolling, cold rolling and coating of strip steels when at levels greater than 0.7 %. Aluminium is limited to preserve weldability and minimise nozzle blockage during steelmaking and casting. Aluminium increases kinetics of the anisothermal bainitic ferrite transformation so that appreciable volume fractions of austenite can be retained at ambient temperature during the limited time available during the new press hardening process. Phosphorus is present to limit silicon and aluminium contents and to providing satisfactory carbide precipitation retardation. Phosphorus is limited to around 0.08 % to maintain acceptable weldability. Niobium is added to form niobium carbide precipitates and in turn to provide austenitic grain size refinement that increases the kinetics of the anisothermal bainitic ferrite transformation. Niobium is limited to no more than 0.04 % due to the problems it introduces during strip annealing by narrowing the recrystallisation to austenisation process window. Titanium is added to form titanium nitride precipitates and in turn to enable boron to remain un-bonded in solid solution. Titanium content of 0.03 % reflects the titanium to nitrogen stoichiometric ratio of 3.14:1. Boron is added for hardenability so to avoid proeutectoid ferrite formation. Thus, the targeted microstructure is predominantly bainitic ferrite with dispersions of martensite and retained austenite. The 20MnSiAlPB5 steel was cast, hot rolled and cold rolled to 1.0 mm gauge strip in the laboratory, with the as-received material representing hard-iron (non-annealed) material. Two commercial steels, denoted 10MnSi15 and 20MnSi15, used for producing commercial first generation TRIP steels with minimum ultimate tensile strengths of 580 and 780 MPa respectively, were included for benchmarking (). The as-received commercial materials represented cold rolled annealed products with 1.0 mm gauge. The two commercial steels are designed for cold forming, prior to which, their microstructures are tailored during carefully controlled heat treatment on a continuous annealing line to form retained austenite needed for stress induced transformation capability. It is logical to test our new press hardening process with these existing commercial MnSi steels that are capable of retaining austenite (when subjected to a suitable heat treatment). The next step is then to develop a new steel chemical composition which is bespoke to the new process to yield a superior result. Furthermore, the new steel chemical composition is leaner and therefore more manufacturer friendly than the commercial steels.Press hardening was conducted with a 50 kN thermo-mechanical testing machine equipped with induction heating and PID controller, as shown by b. Three coupons for tensile testing and a sample for microstructural examination by high resolution Field Emission Gun Scanning Electron Microscopy (FEG-SEM) with Electron Back Scattered Diffraction (EBSD) and X-Ray Diffraction (XRD) were machined by Electrical Discharge Machining (EDM) from each press hardened blank, as shown by c. The tensile coupon design, illustrated by d, with gauge length of 5 mm was bespoke to meet the constraints of the experiment. All other parameters of tensile testing conformed to ISO 6892-1:2016. Extension and thus strain was measured by Digital Image Correlation. Throughout, samples were tested in triplicate with mean results presented. illustrates the Continuous Cooling Transformation (CCT) diagram for 20MnSiAlPB5 predicted by numerical simulation using JMatPro commercial software which was used to establish the test-matrix of experimental parameters for press hardening, including soaking temperatures and tool-open temperatures-times as critical variables, as highlighted in a. Heating rate was to be broken into two segments of 10 and 5 °C/s to replicate convective heating rates on industrial press hardening lines. However, the additional segment of 1 °C/s between 750 and 800 °C was necessary due to limited heating rate by induction through the ferrite to austenite transformation. The minimum soaking temperature was selected as 950 °C in light of the predicted A3 temperature of approximately 890 °C. Incrementally higher soaking temperatures of 1050 and 1150 °C, whilst unfavourable for higher energy consumption on industrial press hardening lines, were investigated for the purpose of greater austenitic grain growth and hardenability to retard proeutectoid ferrite formation. Soaking time was set at 30 s to ensure complete austenisation while preserving the testing machine. Transfer cooling rate of 15 °C/s and transfer cooling time of 10 s were selected to simulate natural air cooling of the blank during transfer from furnace to forming tool on industrial press hardening lines. Die-quenching rate of at least 100 °C/s was achieved by applying the 50 kN load (b) while simultaneously water cooling the dies to simulate conditions on industrial press hardening lines and meet the predicted (by JMatPro software) critical cooling rate of 100 °C/s. Dies were fabricated from Ti-6Al-4 V titanium alloy, marked by a relatively low thermal conductivity of 7 W/m.K to minimise heat loss during the anisothermal bainitic ferrite transformation. Tool-open temperatures of 350, 450 and 550 °C were selected to provide a range of temperatures in the bainitic phase field given predicted (by JMatPro software) Bs and Ms temperatures of approximately 580 and 400 °C respectively. Tool-open times of 60, 180 and 300 s were selected to investigate the optimal time for the anisothermal bainitic ferrite transformation. The PID controller allowed for heating and die-motion to be completely automated.Dilatometry was conducted on 12 × 8 mm cylindrical billets to characterise microstructural evolution under the established optimal press hardening parameters. These findings were correlated to EBSD and XRD results to gain understanding of the optimally press hardened microstructure. For EBSD, including texture analysis and phase volume fraction measurement, five images were taken for a given specimen with mean results presented. Owing to the limited surface area that can practically be analysed by EBSD, XRD was used to confirm the austenite volume fraction over a larger surface area of 1 mm2. Tensile strain was then applied to optimally press hardened specimens (using the tensile coupon design of d) to engineering strain values of 5, 10 and 15 % (without fracture), followed by EBSD and XRD examination of the strained gauge lengths to characterise microstructural evolution under replicated deformation (e.g. an automobile crash event) of a formed part. Analyses were conducted normal to the upper-surface.With the optimal press hardening parameters by the same thermo-mechanical testing machine established, Ti-6Al-4V titanium alloy dies were used to form the U-bend open box part geometry of b. Vickers hardness measurements with 10 kg load were conducted at 0.5 mm intervals along the cross-section centreline. This was conducted on three specimens with mean results presented. Additionally, the formed U-bend open box parts were subjected to transversal and axial crush testing under displacement rate of 1 mm/s, as shown by c and d respectively. For transversal crush testing, the former had radius of 3 mm, the span was 30 mm and maximum displacement was 10 mm. For axial crush testing, maximum displacement was 30 mm. Transversal and axial crush testing were conducted on five specimens with mean results presented. Transversal crush testing is used for evaluation of deformation and deflection resistance, of utmost importance to parts of the automobile safety cell for maintenance of a survival space during a crash event. Axial crush testing is used for evaluation of energy absorption, of utmost importance to parts of the automobile crumple zones for smooth, predictable and controllable dissipation of impact energy during a crash event.When numerically simulating formed part performance testing, such as axial crush testing, it is common practice to apply the same material stress-strain data to the entirety of the part. For example, () conducted experimental and numerical simulation of axial crush testing on cold formed DP and TRIP steels. For each material, the authors applied the same stress-strain data throughout the part during numerical simulation. However, this approach can lead to inaccuracies in simulation, since during cold forming, work hardening takes place in the formed regions, giving rise to different material properties in different regions of the part. This is particularly true for TRIP assisted steels owing to their characteristically high work hardening rates and work hardening capacities. Consequently, the load-displacement graphs displayed by exhibited greater disparity between experiment and simulation for the TRIP steel in comparison to the DP steel. To address this issue and thereby correctly evaluate the advantage of the TRIP assisted PHS technology, where the optimal microstructure is achieved after hot forming and with retained austenite and hence mechanical properties more uniformly distributed in the formed part, we propose a new modelling technique which more accurately simulates deformation of hot versus cold formed parts. established a relationship between Vickers hardness (Hv) and yield strength (YS) by investigating over 150 hypoeutectoid steels having a wide range of chemical compositions and a variety of microstructures, including complex multiphase steels composed of bainite, martensite and retained austenite. The relationship is expressed by Eq. acknowledge that while the relationship of Equation 1 is in very good agreement with experiment for ferritic and especially martensitic steels, the relationship is not so good for complex multiphase steels containing retained austenite. Thus, we add a correction factor of -166, giving rise to Eq. . The correction factor was established by comparing predicted yield strength by Eq. to experimentally determined yield strength of the optimally press hardened 20MnSiAlPB5. Since we are concerned with just one chemical composition and just one heat treatment giving rise to just one microstructure, the simple correction factor can be considered valid for this investigation exclusively.The Vickers hardness measurements recorded at 0.5 mm intervals along the cross-section centreline of both hot and cold formed U-bend open box parts were converted to predicted yield strength with Eq. . Predicted yield strength was used to predict tensile engineering stress-engineering strain curves for each region (base, radius and side-wall) of the part geometry. For the hot formed part, predicted yield strength in each region of the part was similar () states that given thickness of 1 mm and bending radius of 2 mm, maximum theoretical bending strain should be 20 %, as per Eq. , where CD = length of outer edge (exposed to maximum tensile strain), AB = length of neutral axis (mm), R = radius of bend to neutral axis (mm), θ = angle of bend (radians) and y = distance from neutral axis AB to axis of interest CD (mm).εmax=δLLo=CD-ABAB=R+y×θ-R×θR×θ=yR=0.52.5=0.2a presents representative engineering stress-engineering strain curves.Engineering stress-engineering strain data were converted to true stress-true plastic strain. Since the true stress-true plastic strain data resulting from the conversion process are valid only during uniform elongation to the commencement of necking, data were extrapolated over the full plastic strain range. This was conducted with Eq. ), where σ = stress (MPa), σu = stress at necking (MPa), k = work hardening rate (MPa), ε = strain, εg = strain at necking and n = work hardening exponent. b presents the extrapolated true stress-true plastic strain curves.Transversal and axial crush testing were numerically simulated using the material data of b and the same part geometry and testing conditions of the physical experiments. This was performed in Abaqus CAE commercial software with a Dynamic Explicit model. Mesh size was 0.5 mm. Element type was Explicit 3D Stress. The isotropic hardening function incorporated in Abaqus CAE was applied. Ductile damage was omitted for simplicity. Elastic modulus was entered as 210 GPa with Poisson's ratio of 0.3 and density of 7800 kg/m3. For axial crushing, contact between the plates (modelled as Analytical Rigids) and box was modelled with a General Contact function carrying a friction coefficient penalty of 0.7. For transversal crushing, contact between the supports / former (modelled as Rigid Bodies) and box was modelled with a General Contact function carrying a friction coefficient penalty of 0.2. The different friction coefficients represent the different nature of contact and geometry; and are recommended for simulations of this kind. Simulation results are shown in the last section of `Results & Discussion`. presents representative time-temperature plots from the start of cooling. Upon interrupting die-quenching and opening the tool, temperature increased due to substantial residual heat accumulation in the dies characterised by low thermal conductivity, before slow cooling commenced by natural air circulation. Even with the lowest tool-open temperature of 350 °C and longest tool-open time of 300 s, minimum temperature did not drop below 255 °C during the tool-open time, demonstrating capability of the new press hardening process to maintain substantial heat for the anisothermal bainitic ferrite transformation and carbon partitioning, without use of secondary heating. Further, it is worth highlighting that in this lab scale experiment, the dies were relatively small, much smaller than dies found on industrial press hardening lines. Such industrial dies would exhibit much greater heat capacity for further retarded cooling. In such a case, water cooling of the dies could be regulated as necessary in order to achieve the exact conditions obtained from this lab scale experiment. presents tool-open start temperature against mean tool-open temperature. With increased tool-open time, mean tool-open temperature decreased due to longer exposure to natural air cooling. As tool-open start temperature increased, or as soaking temperature increased, mean tool-open temperature increased due to greater residual heat accumulation at the moment of interrupted die-quenching. Even with the lowest soaking temperature of 950 °C, lowest tool-open temperature of 350 °C and longest tool-open time of 300 s, mean tool-open temperature was 375 °C, again demonstrating capability of the new press hardening process to maintain substantial heat for the anisothermal bainitic ferrite transformation and carbon partitioning, without use of secondary heating. presents tensile properties of press hardened 20MnSiAlPB5 (error bars have been omitted for clarity, while standard deviations are presented in ). Proof strength (Rp0.2) increases with higher soaking temperature, presumably as the bainitic ferrite volume fraction decreases and the martensite volume fraction increases as a result of greater austenitic grain growth and hardenability. Proof strength decreases with longer tool-open time, likely as a result of increased carbon partitioning from bainitic ferrite to austenite, which reduces interstitial solid solution strengthening of bainitic ferrite, which as the softest microconstituent, dictates proof strength. Proof strength decreases with increased tool-open temperature, which indicates a transition from martensite to lower bainite and then to upper bainite. The same observations can be made for ultimate tensile strength (Rm). Uniform elongation (Ag) is evaluated rather than total elongation (A5) in this instance since the uniform elongation value can be used as a strong indicator of a stress induced transformation enhancing ductility and is less susceptible to error than total elongation due to premature fracture of the test piece or fracture occurring outside the gauge length. Maximum uniform elongation was provided by soaking temperature of 950 °C. This is potentially due to a lower martensite volume fraction and finer bainitic ferrite grain size to enhance carbon partitioning rate and in turn, the stress induced transformation. Uniform elongation increases with soaking temperature raised from 1050 to 1150 °C. This is probably due to a coarser final microstructure resulting from greater austenitic grain growth at the higher soaking temperature. Moreover, after these higher soaking temperatures, the stress induced transformation is not present or negligible due to insufficient carbon partitioning. Thus, ductility of the final microstructure is dominated by conventional microstructural characteristics, such as grain size, rather than stress induced transformation. Uniform elongation increases with longer tool-open time, presumably due to increased carbon partitioning from bainitic ferrite to austenite, which reduces interstitial solid solution strengthening of bainitic ferrite and enhances the stress induced transformation. Validation of the above is provided subsequently in discussion of microstructural analysis. The optimal parameters for 20MnSiAlPB5 can be highlighted as soaking temperature of 950 °C, tool-open temperature of 550 °C and tool-open time of 180 s, as presented in along with the optimal parameters for 10MnSi15 and 20MnSi15. These parameters gave rise to the highest elongation values and the highest ultimate tensile strength-elongation product values (Rm*Ag and Rm*A5). The optimal tensile properties are summarised in presents ultimate tensile strength against proof strength (a) and ultimate tensile strength against total elongation (b) for the three steels press hardened to the full range of experimental parameters. The new press hardened steel 20MnSiAlPB5 failed to achieve the uniform elongation values of the two commercial steels (especially the lower carbon and softer 10MnSi15), which indicates a less effective stress induced transformation, but otherwise achieved similar properties to the commercial 20MnSi15, yet with a leaner and more manufacturer friendly chemical composition. The range of properties achievable from 20MnSiAlPB5 is also wider compared to the two commercial steels, indicating greater scope for a range of products. For example, soaking temperature of 1150 °C, tool-open temperature of 350 °C and tool-open time of 180 s gave rise to ultimate tensile strength of 1418 MPa and total elongation of 9.8 %. For the purpose of a ‘high strength product’, these values are far superior to those achieved from the two commercial steels investigated and moreover, are comparable to results published in the literature, such as by ) as discussed in the introduction section. It should be noted that ) used marginally longer gauge lengths of 10 and 15 mm respectively (here we used 5 mm). Shorter gauge lengths have the effect of exaggerating the tensile elongation values. ) developed an equation for converting tensile elongation values between data obtained with different test-piece geometries. The reader is directed to the reference for further analysis and comparison between results. However, given the marginal difference in gauge lengths used here, by ), for all intents and purposes, the data presented are comparable. Moreover, it is again emphasised that here we achieve these properties with a leaner and more manufacturer friendly chemical composition; and with a more efficient press hardening process since modification to the press hardening line with a secondary heating step is not required. presents dilatometry plots for 20MnSiAlPB5 treated to the optimal press hardening parameters giving rise to the properties of . Note that absolute values of dilatometric strain may be subject to error due to measurement by a modified thermo-mechanical testing machine rather than by a single-purpose dilatometer. However, trends depicted, namely contraction or expansion due to phase transformation, can be considered valid. To avoid variable thermal expansion rates from the heating rates used during press hardening and thus to clearly depict the ferrite to austenite transformation on heating, a continuous heating rate of 10 °C/s to 1200 °C was used (a). The ferrite to austenite transformation is completed by 938 °C, indicating that the new steel 20MnSiAlPB5 is completely austenitic at the soaking temperature of 950 °C and thus, can achieve complete austenisation with a soaking temperature typically used on industrial press hardening lines at present with MnB5 steels without requiring greater energy consumption. Progress of the ferrite to austenite transformation, estimated with the lever rule, is shown by c), thermal contraction begins during the 10 s of transfer cooling time. As die-quenching begins, thermal contraction accelerates. Note that the rate of thermal contraction coincides with cooling rate. Also note that during dilatometry, die-quenching had to be simulated by forced air cooling, with the cooling rate achieved somewhat lower than that of die-quenching, yet sufficiently rapid to avoid the proeutectoid ferrite transformation. This highlights the novelty of the new TRIP assisted steel 20MnSiAlPB5 to provide sufficient hardenability under typical press hardening conditions. After approximately 30 s from the start of cooling, dilatation occurs, corresponding to the beginning of the tool-open time. d plots temperature against dilatometric strain on cooling, from which dilatation and the corresponding phase transformation can be seen at the tool-open temperature of 550 °C. These observations firmly indicate that hot forming can take place in the exclusive austenite phase (for maximum formability) and that proeutectoid ferrite formation is avoided, with the transformation at 550 °C correlating with the predicated bainitic ferrite transformation of . Consequently, α-phase detected by EBSD and accounting for the majority of the microstructure at 48.3 % is clearly bainitic ferrite and not proeutectoid ferrite, as illustrated by representative phase distribution maps of . Further, the average misorientation angle is 37°. The bainitic ferrite has an average grain size (diameter) of 2.7 (±1.8) μm. Despite continuous cooling during the tool-open time, dilatation continues (c), indicating continuous progression of the bainitic ferrite transformation and possible transition to the martensite transformation, given that after bainitic ferrite, the remainder of the microstructure consists of α’-phase (martensite) at 42.6 % and γ-phase (austenite) at 9.1 %. The martensite has an average grain size (corresponding to packet size) of 1.7 (±1.6) μm and average misorientation angle of 79°, distinguishing it from bainitic ferrite. Given the low temperature, displacive and non-equilibrium nature of the martensite transformation, the misorientation angle of martensite can be expected to be significantly higher than that of other phases. The misorientation angle of martensite is often found to be above 50° () and thus significantly higher than that of bainitic ferrite, which is often found to be less than 40° (). For comparison, phase distribution maps are also provided for 10MnSi15 and 20MnSi15 treated to their optimal press hardening parameters (. Since the three steels have been treated to different press hardening parameters, the microstructures are not directly comparable. Nonetheless, due to significantly different carbon content, the microstructure of 10MnSi15 is distinctly different from that of 20MnSiAlPB5 and 20MnSi15. The microstructure of 20MnSiAlPB5 is noticeably finer than the relatively blocky microstructure of 20MnSi15 and the retained austenite volume fraction is more than double. This illustrates the superiority of the new steel 20MnSiAlPB5 when used in combination with the new press hardening process.The austenite volume fraction of 9.1 % measured by EBSD was confirmed by XRD, which recorded a comparable value of 11.7 %. a presents a representative XRD diffractogram, illustrating the austenite peak. The austenite volume fraction is indicative of carbon partitioning from bainitic ferrite during the tool-open time, since such a high volume fraction of retained austenite would not be expected otherwise. The austenite is ultra-fine, distributed between the bainitic ferrite and martensite boundaries with a small block or thin film morphology and with an average grain size (diameter) of 0.3 (±0.2) μm. With increasing tensile strain to 5 and then 10 %, the bainitic ferrite volume fraction remains relatively constant, while the austenite volume fraction deceases and the martensite volume fraction increases, as illustrated by b. This is indicative of a stress induced transformation. With increasing tensile strain from 10 to 15 %, volume fractions remain relatively constant. This correlates with the uniform elongation value of 11.6 % (), since a stress induced transformation would be expected to be completed once strain has reached the uniform elongation value. Again, austenite volume fractions were confirmed by XRD, with similar values presented between EBSD and XRD. The austenite peak of the diffractogram becomes progressively more broad and less defined with increasing tensile strain applied to the specimen (a). This indicates lower reliability of the result and can be attributed to increasing distortion of the crystal lattice creating greater difficulty for the X-ray diffraction pattern to be correlated to the reference parameters. EBSD was thus the preferred characterisation tool for subsequent analyses. Nonetheless, the findings from EBSD and XRD demonstrate that the new steel 20MnSiAlPB5 achieves the objective of delivering a microstructure predominantly of bainitic ferrite, with dispersions of martensite and retained austenite; and with retained austenite undergoing a stress induced transformation to martensite during application of the formed part such as an automobile crash event, giving rise to the characteristically impressive strength-ductility combination of TRIP assisted steels. Moreover, by referring back to and comparison to the two commercial steels, the new steel 20MnSiAlPB5, while relatively lean and manufacturer friendly, provides the optimal microstructural evolution observed within the constraints of the new press hardening process. For example, avoidance of proeutectoid ferrite can be attributed to the novel boron addition to TRIP assisted steels, while the appreciable volume fraction of retained austenite and subsequent stress induced transformation despite limited time in the bainitic phase field under slow air cooling in the hot forming tool can be attributed to the novel Al, Si, P and Nb additions to PHS accelerating the bainitic ferrite transformation and carbon partitioning. presents representative Inverse Pole Figure (IPF) crystallographic orientation maps. Following press hardening, the microstructure is relatively isotropic, both in terms of grain structure and texture intensity, with a relatively weak maximum texture intensity factor of just 1.9 (where texture intensity factor can be interpreted as the proportion of the microstructure that is orientated with the given crystallographic plane and direction combination). Since the final microstructure is relatively isotropic, we can infer that during hot forming, the microstructure was also isotropic. Isotropicity during hot forming is important for obtaining maximum formability. With increasing tensile strain following press hardening, the grain structure becomes progressively more deformed and the (111)[001] texture gradually develops, indicated by a maximum texture intensity factor of 4.3 after 15 % tensile strain.a illustrates representative load-displacement graphs from transversal crush testing. Curves have been corrected for slack take up by the testing machine during approximately the first 1.5 mm of displacement. Thus, maximum displacement is recorded as approximately 8.5 mm rather than the 10 mm applied. Note the two parts are composed of the same 20MnSiAlPB5 chemical composition and have been exposed to the same heat treatment (the optimal press hardening parameters), with the only difference being that one part has been cold formed (representative of traditional cold forming a TRIP assisted steel) and the other part has been hot formed according to the new press hardening process. The cold formed part exhibits higher stiffness (E), yield load (Pyield) and energy absorption (EA), but work hardening rate between 6−8 mm of displacement (k6−8) of the hot formed part is significantly higher so that maximum load (Pmax) of the two parts approach a near equivalent value, as summarised in b illustrates representative load-displacement graphs from axial crush testing. Again, curves have been corrected for slack take up by the testing machine during approximately the first 2 mm of displacement. The cold formed part exhibits higher stiffness (E), but maximum load (Pmax) is similar, while mean load (Pmean) and energy absorption (EA) of the hot formed part are higher, as summarised in c illustrates representative energy absorbed-displacement graphs from axial crush testing, from which the higher energy absorption of the hot formed part beyond approximately 5 mm of displacement, corresponding to conclusion of the first peak of the load-displacement graph, can be clearly observed. Moreover, the relatively smooth and consistent accumulation of energy absorption of the hot formed part, versus the relatively sporadic and non-predictable character of the cold formed part can also be observed. d presents images of parts following testing. While the cold and hot formed parts exhibit a similar appearance following transversal loading, there is a notable difference following axial loading. The hot formed part exhibits a smoother, more consistent and densely folded structure without buckling in the lower section. These differences can be correlated to the load-displacement graphs (b), where for the hot formed part, the rise and fall of load constituting each peak of the graph is of a smoother character. Each peak correlates to each fold of the deformed structure. The smooth and consistent folding behaviour combined with the consistent load maintenance and energy absorption can be correlated to the more uniform microstructure of the hot formed part. This is illustrated by the representative EBSD phase distribution maps. To enhance accuracy, rather than individual phase detection, characterisation is simplified into γ-phase (FCC) and α-phase (BCC). For the cold formed part (a–c), the retained austenite volume fraction decreases from 8.7 % in the base and 9.5 % in the side-wall (non-formed regions), to 3.3 % in the radius (formed region). For the hot formed part, phase volume fractions are similar in the three regions of the part (d–f). While the initial retained austenite volume fraction before cold forming could be assumed to be 7–11 % (), it distributes in a narrow range of 6.5–8.0 % for the hot formed part, but in a wider range of 3.3–9.5 % for the cold formed part. This indicates that the stress induced transformation of austenite to martensite has occurred in the radii during cold forming. presents representative IPF crystallographic orientation maps. For the cold formed part, work hardening giving rise to significant deformation of the grain structure and development of the (111)[100] texture is apparent in the radius, with a maximum texture intensity factor of 3.8. In contrast, for the hot formed part, the microstructure in the radius retains similar isotropic character of the base and side-wall, both in terms of grain structure and texture, with a relatively weak maximum texture intensity factor of just 2.6. The stress induced transformation coupled with work hardening of the cold formed part gives rise to significantly higher hardness in the radius, as illustrated by the hardness distribution profile of a. More uniform phase volume fractions throughout the cross-section of the hot formed part, coupled with no work hardening, gives rise to more uniform hardness throughout the cross-section (b). Hardness actually decreases slightly in the radius. This can be attributed to dynamic recrystallisation during hot forming and a lower cooling rate in the radius due to less homogenous contact with the water cooled forming tool during die-quenching. The differences observed between the hot and cold formed parts can be correlated to the crush properties. During both transversal and axial loading, the radii of the part geometry are critical areas, since the application of load causes the part to bulge at the radii, as illustrated by the annotations in d. The higher hardness in the radii of the cold formed part thus increases part stiffness and yield load. Once yield load has been surpassed, the higher retained austenite volume fraction and greater capacity for stress induced transformation then accelerates work hardening in the hot formed part, giving rise to the higher work hardening rate observed. Once work hardening and the stress induced transformation have been exhausted, the two parts (cold formed and hot formed) are essentially in the same state, hence the maximum load is approximately equivalent. For parts of the automobile safety cell designed to minimise displacement and deflection, the hot formed part is arguably inferior. However, for parts of the crumple zones, designed to deform in a predictable and controllable manner for maximum energy absorption, the hot formed part and hence the new TRIP assisted PHS technology is clearly superior. The more uniform distribution of retained austenite coupled with the maximised stress induced transformation and work hardening capacity maximise mean load and energy absorption, with a 22 % increase to the latter. Moreover, frequency of load peaks and load amplitude are reduced, which are associated with predictable and controllable dissipation of impact energy and crash safety.a illustrates load-displacement graphs from numerical simulation of transversal crush testing, conducted with the material data of b. Curves have been truncated to 8.5 mm of displacement to be comparable to curves from the physical experiment. Compared to the physical experiment, the curves exhibit similar character, except for declining load (negative work hardening rate) beyond approximately 4 mm of displacement. The cold formed part exhibits higher stiffness and yield load, but the hot formed part exhibits marginally higher maximum load and energy absorption, as summarised in . While the work hardening rate between 6−8 mm of displacement is negative, for the hot formed part, the value is closer to zero, thus following the same trend of the physical experiment. Differences between simulation and experiment can be attributed to inevitable inconsistencies in the experiment and imperfections in the material, whereas the simulation represents an idealised environment. b illustrates load-displacement graphs from numerical simulation of axial crush testing. Again, curves have been truncated to 28 mm of displacement to be comparable to curves from the physical experiment. Compared to the physical experiment, the curves exhibit similar character. The cold formed part exhibits higher stiffness and marginally higher maximum load, but mean load and energy absorption of the hot formed part are higher, as summarised in . These results are in very good agreement with the physical experiment and thereby, demonstrate that the new modelling technique, which accounts for the stress induced transformation and work hardening in the cold formed part, more accurately simulates deformation of hot versus cold formed parts. c illustrates energy absorbed-displacement graphs from numerical simulation of axial crush testing, from which the higher energy absorption of the hot formed part can be clearly observed. d presents von Mises stress colour contour maps of parts following loading. Following transversal loading, there is no notable difference between the cold formed part and hot formed part. Following axial loading, the hot formed part exhibits a smoother, more consistent and densely folded structure without buckling of the lower section. The different appearance of the simulated parts closely replicates the physical experiment. Moreover, during both transversal and axial loading, accumulation of maximum stress in the radii of the part geometry, resulting from bulging at the radii, is clearly visible. This vividly demonstrates the importance of the radii to the formed part and thus, the merit of the new TRIP assisted PHS technology, where microstructure and mechanical properties are more uniform throughout the part cross-section, resulting in superior crash performance.The optimised press hardened microstructure of 20MnSiAlPB5 consisted of 48.3 % bainitic ferrite, 42.6 % martensite and 9.1 % retained austenite.The retained austenite can undergo stress induced transformation to martensite during application of a formed part such as an automobile crash event, giving rise to 867 MPa tensile strength and 20.5 % total elongation.Traditional cold forming of TRIP assisted steel reduced the retained austenite volume fraction from 9.1 to 3.3 % in the formed radii, whereas the new TRIP assisted PHS technology more uniformly distributed the retained austenite in the formed part with a near equivalent volume fraction of 9.1 % throughout the part.The higher and more uniformly distributed retained austenite volume fraction enhanced energy absorption by 22 % during axial crushing.Numerical simulation of crush testing, including a new modelling technique which more accurately simulates deformation of hot versus cold formed parts, demonstrated accumulation of maximum stress in the formed radii and thus demonstrated the merit of the new TRIP assisted PHS technology.T. Taylor – Principal Investigator and lead author.K. Kim – EBSD analysis and assistant author.J. Zhang – FEA simulation and assistant author.D. Penney – lab cast processing and assistant author.J. Yanagimoto – project supervisor and assistant author.The authors report no declarations of interest.The effect of laminate stacking sequence and fiber orientation on the dynamic response of FRP composite slabsIn this paper, different stacking sequences (0 / ± 45/90°) of laminated FRP slab under human-induced loads using finite element techniques are investigated to assess the dynamic characteristics of a composite floor and corresponding human comfort problems.Four layers of FRP, with different angles comprising 256 cases, are modeled using ANSYS software. Load models with variable parameters are applied as pattern loads. Material properties and damping ratio are calculated separately for each case with the aid of MATLAB software and considered as input to ANSYS for obtaining the maximum responses in terms of deflection and acceleration from the walking load of people. Then the results are compared with the limiting values proposed by the design standards. A comparison of the two results reveals that 54 cases of investigated FRP laminate seem to be ideal for practical use in satisfying both the acceleration and displacement requirements. This study was carried out to provide a more realistic evaluation of this type of structure when subjected to vibration due to human walking.Laminated FRP composite panels, due to their high structural stiffness, low weight, and low maintenance costs have been recognized as a cost-effective material for use as a floor in structures. One of the features of these anisotropic materials is their ability to be tailored for specific applications by optimizing the design parameters such as stacking sequences, ply orientation and performance targets One of the critical points in designing a structure, is knowing the natural frequency. If a natural frequency of the structure is close to the excitation frequency, then resonance, which is the severe vibration of the structure, could occur. In order to avoid resonance, the natural frequency of the structure must be changed by making suitable adjustments in the design. Allen et al. In terms of the load description for human activity, Alves In recent years, some research has been done on the laminate stacking sequence in applications in different areas Although some research has been carried out on the stiffness and strength evaluations of various types of FRP decks, investigations of the stacking sequence of FRP systems against dynamic load and human activities are limited. The orientation of fibers in a lamina (layer), and, consequently, in the laminate (combination of laminas) plays an important role in the dynamic response of composite floors. Hence, changing the angle of the fibers in the laminate may significantly change the results because of alterations to the stiffness and material properties. Hence, selecting a proper angle and fiber orientation is very important in FRP Laminate panels.In the present work, the main motivation is to examine numerically the vibration characteristics of laminate composite floor structures due to the proportion of fiber orientation and stacking sequence effects when subjected to walking load in order to evaluate their compliance with the serviceability and comfort requirements of the current design standards.In this study, all possible stacking sequences for a 4-layer laminated FRP plate (0°, ±45°, 90°) are examined. A total of 256 cases were obtained for different configurations. In each configuration, there were nine parameters (E1, E2, E3, G12, G23, G13, ʋ12, ʋ23, ʋ13), which addressed the laminated FRP plate's specification. For modeling purposes, an equivalent plate, which was formed by a combination of several laminae, was considered. The properties of the fiber/matrix composite material were deemed for FEM analysis. All 256 possible cases were simulated, and the related dynamic responses, including displacements, accelerations, and natural frequencies were obtained. Accelerations and deflections are compared with AISC design guide 11 and ACI 318-05 standards, respectively Dynamic actions caused by repetitive forces from equipment, machines and human activities such as dancing, jumping, running, and aerobics (gymnastics) or walking produce dynamic actions, which lead to most floor vibration problems. The problem associated with human walking generates special concern because the forces change location and magnitude with each step. In some cases, the applied force is sinusoidal. Also, generally, the structural system's dynamic response involves several vibration modes. Normally, human activities induce dynamic excitations, which could be defined by a combination of harmonic forces, in which the frequencies, f, of the mentioned harmonics are the multiples of the first frequency. For instance, the step frequency, fs, of human activities. These harmonic forces or time‐dependent repeated forces can be represented by the Fourier series, as provided in Eq. αi = dynamic coefficient for the harmonic forcefs = step frequency of the activity of dancing, jumping, aerobics or walking, four harmonics are used in this investigation to generate the dynamic loads. The values for different parameters, which are used in the mathematical model, including phase angle, dynamic load factor, and step frequency, are presented in In this study, a concrete-steel composite and fiber-reinforced laminated composite floor supported by columns at its extremities, and permitting only the floor's linear dynamic response under human walking load was modeled. For convenience, the model is based on an existing structural system . In this modeling, the average weight of a human is considered to be 700 N. The analogous structure is then modeled, changing the concrete slab to FRP laminate, but preserving the type of beams and columns. The detail is offered next.The elastic material properties of laminated FRP composites can be altered by the number, fiber orientation, and stacking sequence of layers. Due to the large demand for such applications in the construction industry, there is a growing need to determine the effects of different configurations of the laminate as a composite material on floor vibration. In the current study, the laminate used to replace the concrete slab is made of AS4 carbon fiber/3501‐6 epoxy matrix with a 0.63 fiber volume fraction. Also, it is composed of four laminae (plies) stacked together with various fiber orientations [0°; ±45°; 90°]. The architecture of a FRP laminate is shown in . The material comprises a number of unidirectional plies of carbon fiber reinforcement impregnated with resins that are stacked together.Different stacking sequences of 4‐layer FRP laminates in the current study resulted in 256 cases in total.It is assumed for the FRP laminate that:All the components are completely bonded together,The effects of adhesives are neglected, andThe behaviors of each deck component as well as the deck system are linear elastic.For modeling purposes, an equivalent plate, which is formed by a combination of several laminae, is considered. The properties of the fiber/matrix composite material are listed in For a description of the laminate's material properties, Ex, Ey, Gxy and vxy are obtained from the constitutive relation defined by the standard classical lamination theory, the ABD matrix:[C¯]=[C¯11C¯12C¯1300C¯16C¯12C¯22C¯2300C¯26C¯13C¯23C¯3300C¯36000C¯44C¯450000C¯45C¯550C¯16C¯26C¯3600C¯66]C11¯=∑K=1NϑKC11(K)+∑K=2N(C13(K)−γ13)ϑK(C13(1)−C13(K))/C33(K)C¯12=∑K=1NϑKC12(K)+∑K=2N(C13(K)−γ13)ϑK(C23(1)−C23(K))/C33(K)C22¯=∑K=1NϑKC22(K)+∑K=2N(C23(K)−γ23)ϑK(C23(1)−C23(K))/C33(K)C¯16=∑K=1NϑKC16(K)+∑K=2N(C13(K)−γ13)ϑK(C36(1)−C36(K))/C33(K)C¯26=∑K=1NϑKC26(K)+∑K=2N(C23(K)−γ23)ϑK(C36(1)−C36(K))/C33(K)C¯66=∑K=1NϑKC66(K)+∑K=2N(C36(K)−γ36)ϑK(C36(1)−C36(K))/C33(K)Where ϑk are the fiber orientations, Cij(k) are the local elastic constants for the kth lamina in the laminate, which take analogous form as those given in Eq. Δ=(∑K=1NϑKC44(K)/ΔK)(∑K=1NϑKC55(K)/ΔK)−(∑K=1NϑKC45(K)/ΔK)2From the effective elastic compliance matrix,E¯z=1S¯33ϑ¯xz=−S¯31S¯11ϑ¯yz=−S¯23S¯22G¯xz=−1S¯55G¯yz=1S¯44In which Sij are the components of [S̅]. In this study, the thickness of the laminate is 150 mm, the same as the concrete‐steel deck. As a result, each lamina has a thickness of 37.5 mm.Also, the damping ratios for the equivalent plate, with the aid of the following equations (Eqs. ) and the results obtained from an experimental observation μi = loss factor for the ith element in the systemWi = strain energy stored in the ith elementn = total number of elements in the system1Ex=m2E1(m2−n2ϑ12)+n2E2(n2−m2ϑ12)+m2n2G12Here, tlaminate is the thickness of the laminate, d11 is the corresponding inverse term of D11, and I is the second moment of area of lamina. Note that i, j = 1, 2, 3 and i, j = x, y are the lamina and laminate notations, respectively.Finite element (FE) modeling of the composite slab is performed using the ANSYS program is imposed at the center of the slab. From the model, we are interested in the dynamic parameters, such as natural frequency, acceleration, and displacement, for different configurations of laminate, which are then compared to the existing requirements given by the structural design codes; AISC are illustrations of the above-stated description. presents the natural frequencies of the first four modes of the structure. We only show 10 laminate configurations owing to the graph aggregation if outcomes from all 256 cases are displayed. Since our concern here is to make a comparison of the general behavior between the concrete and the laminate decks, coupled with the observation that the responses from the laminates that are somewhat identical, not all the plots are needed., it can be seen that by replacing the concrete deck with laminated FRP material of the same total thickness, the natural frequency of the structure has a significant reduction. The effect of high stiffness in the FRP slabs seems to be less important. This is reflected by their almost identical natural frequencies, within the range of 2.33–6.64 Hz for all 256 cases of FRP slab in the first two modes, even though their stiffnesses are not similar. Generally, for vibration serviceability design and evaluation of floor framing systems, the natural frequency is highly important as it is mentioned extensively in numerous existing design codes.However, it should be noted that the trends of natural frequency variations due to the stacking sequences of FRP laminates are not straightforward.The dynamic amplification factor (DAF) is first assessed to find the critical load frequency that excites the composite floor with the greatest severity compared to other load frequencies. DAF is defined as the proportion of dynamic displacement of the structure over the static displacement at the same point. The highest value of DAF, in this case, is chosen to characterize the resonant frequency and the response of the composite deck corresponding to this particular load frequency. In this case, the acceleration, which is defined as the peak acceleration, is obtained. For instance, in the case of a concrete slab of thickness 150 mm, a load frequency of 1.88 Hz is the frequency at which the structure will be excited severely; as shown in . We denote the peak acceleration as that corresponding to this particular DAF.The peak accelerations for 256 cases of FRP laminate are compared to the AISC design criteria as provided by Murray et al. . The peak acceleration for offices and residences offered by the AISC simplified method is higher than that produced by the FRP models except in three cases, which are shown in pink in (cases 2, 3, and 23). This indicates that the laminated slabs present safe values in terms of floor acceleration in the majority of the cases. Hence, 253 cases are acceptable by this criterion, as shown by the dots under the second limiting curve from bottom in . The peak acceleration increases or decreases based on different stacking sequences of lamina in the laminate. In this particular situation, the peak accelerations do not follow a linear behavior. These trends can be explained based on the interaction between the load and the dynamic characteristics of the structure. In other words, the response of the structure is due to the interaction of the stiffness and mass against the frequency and intensity of the load. It is important to determine which load frequency could excite the structure more severely corresponding to an equal natural frequency.The next interesting observation finds that mode 1 is the most important mode since it reaches a reasonably higher mass participation ratio than the others. The mass participation ratio for a mode provides a measure of how important the mode is in computing the response to the acceleration loads in each of the three global directions. In this study, the vertical direction is the important direction of concern considering the vertical dynamic loading. Since in the first mode, the participation ratio exceeds 70%, and by taking into account that other modes could not be excited by walking load with a frequency higher than this, all the presented responses in the following are based on the first mode excitation.The maximum displacement of the slab in all cases takes place at the mid-span. But, it should be kept in mind that the effect of the dead load, which contains the weight of the slab, is quite considerable compared to the effect of the dynamic and static loads of one person's weight. The serviceability deflection limit has been reported as L/240 for composite floor design , 57 cases seem to be suitable for human comfort fulfilling the criterion (cases shown in pink): L/240 = 9.00/240 = 0.0375 m. In terms of displacement, replacing the concrete‐steel deck with FRP laminate severely influences the responses of the structure. Only 57 cases from 256 cases are acceptable within the safe margin of the serviceability criterion.In terms of acceleration, surprisingly, 253 cases from 256 cases are suitable based on the human comfort level. This means that only three cases are unsafe if serviceability is determined using the acceleration criterion. In other words, the amount of acceleration in 253 cases from 256 cases, is below the acceleration limit amount (0.051 m/s2) presented by the AISC standard. This means that the orientation of fibers in 253 cases is suitable in terms of acceleration. A comparison of the two results (acceleration and displacement) reveals that 54 cases of investigated FRP laminate seem to be ideal for practical use in satisfying both acceleration and displacement requirements. This means that 54 cases from 254 cases have acceleration and displacement below the maximum value presented by AISC and ACI 318-05 Surprisingly, these 54 cases of ply orientation seem to be suitable in terms of acceleration and displacement. Based on the results, FRP laminate slabs with the above configuration (54 cases) may be replaced with concrete-steel slab in the buildings to avoid vibration and provide human comfort.The dynamic characteristics of a FRP laminated composite slab subjected to walking type human loads have been treated using finite element techniques. Different numbers of harmonics, structural damping, and material properties, in particular, the effects of stacking sequences on the structural dynamic behaviors have been considered. For this purpose, a total of 256 configurations of a 4‐layer laminate, with equal layer thicknesses but different stacking sequences, are examined, and the dynamic responses in terms of natural frequencies, displacements, and peak accelerations, have been evaluated. It is not possible to observe an obvious trend of consistency in the natural frequency variation of a structure because of the complicated interaction of the stiffness and mass of the structure. Nevertheless, it is straightforward to see a corresponding reduction in the natural frequencies due to a drop in the equivalent stiffnesses, Eeq. As the bending stiffness of the laminate varies with different configurations of fiber orientations, each particular case requires an independent analysis to find out in detail the exact behavior of the structure. It is found that 54 cases from 256 cases are acceptable in satisfying both the peak acceleration and displacement requirements, within the safe level of serviceability criteria as given by AISC and ACI 318-05 This study has shown that both criteria of composite floor responses -displacement and acceleration- are required to ensure compliance with the comfort level limits. In general, 45- degree layers play a significant role in the dynamic responses of the structure. Therefore, orientations of 45 and 0 degrees can be used with confidence in laminate FRP composite floors to avoid vibration and provide human comfort. This possibility makes FRP laminate materials more attractive since it makes it possible to avoid vibrations in floors without increasing the mass or changing geometry. In practical applications, it means that if a natural frequency excites the structure, the designer can change the material properties and stiffness by changing the laminate stacking sequences instead of re-designing the entire structure.Since the experimental research is so limited in this area, doing some experimental tests could be a way to provide further validation to this study and other similar research.The present study has only examined laminates with a combination of 0, ±45, and 90-degree plies. Obviously, the effects of the use of other fiber angles in FRP laminate remain to be explored, and may influence the results accordingly. Also, different types of walking load description and the distribution of dissimilar layer thicknesses of FRP slab may be taken into consideration in future works. Some testing could be a way to provide further validation of this study.Effect of defects on the local shell buckling and post-buckling behavior of single and multi-walled carbon nanotubesThe local buckling behavior of perfect/defective and single/multi-walled carbon nanotubes (CNTs) under axial compressive forces has been investigated by the molecular dynamics approach. Effects of different types of defects including vacancy and Stone–Wales (SW) defects and their configurations on CNTs with different chiralities at room temperature are studied. Results show that defects largely reduce the buckling stress and the ratio of immediate reduction in buckling compressive stress of the defective CNT to the perfect one, but have little influence on their compressive elastic modulus. SW defects usually reduce the mechanical properties more than vacancy defects, and zigzag CNTs are more susceptible to defects than armchairs. In addition, increasing the number of defects leads to higher deterioration in mechanical properties of CNTs. The results of simulations show that in the case of slender single-walled CNTs, the behavior is primarily governed by the Euler buckling law. On the other hand, in the local shell buckling mode, two distinct behaviors are observed, including the primary local shell buckling mode for intermediate CNTs, and the secondary local shell buckling mode for short CNTs. In the local buckling response, CNTs with smaller diameters sustain higher buckling stresses than CNTs with larger diameters.Due to manufacturing restrictions, the possibility of production of perfect CNTs is much lower than the defective ones The discrepancy between the theory and experiment for the mechanical properties can be attributed to the fact that the existence of defects on the structure of CNTs is inevitable and they are susceptible to defects. In practice, it is almost impossible to find a CNT without any structural defects and imperfections, which are the likely causes of their low ultimate strength. Microscopic observations confirm that defects may be created at the stage of CNT growth and oxidation Despite some drawbacks, defects have also shown advantages in some situations. For example, rehybridization defects increase the interfacial bonding strength between nanotubes and their surrounding matrix polymer On the other hand, CNTs may become mechanically unstable and buckle under compressive axial loads due to their high aspect ratio (length/diameter). Buckling can lead to failure in the form of a sudden decline in the compressive load carrying capacity and undesirable distorted configuration of the structure. Therefore, the possibility of buckling should be considered seriously in devices which use CNT as a compressive component, such as composites, Atomic Force Microscopy (AFM) tip and hydrogen storages. Due to the fact that CNTs are highly prone to structural defects, investigation on mechanical stability and buckling of defective CNTs is inevitable.In recent years, a few studies have been directed towards the buckling analysis of defective CNTs. For instance, the compressive behavior of single-walled carbon nanotubes (SWCNTs) in the presence of chemical functionalization and Stone–Wales (SW) defects was explored by Chandra and Namilae using Molecular dynamics (MD) simulations Investigation of the thermal buckling behavior of defective CNTs has shown that defects reduce the buckling capacities of defective SWCNTs and the degree of reduction depends on the type of defects, chirality and temperature. Simulations have revealed that point defects cause higher reduction in the buckling load than the SW defect After a comprehensive literature review, only a few number of investigations have been found on the buckling and postbuckling analysis of defective SWCNTs and MWCNTs with different chiralities and none of them have examined the effect of defects on the reduction of compressive stress after the buckling. Furthermore, the effect of different types of defects and their interaction on the local buckling analysis of SWCNTs and MWCNTs need to be comprehensively studied.The main focus of this study is to investigate the effects of different types of defects on the local buckling and postbuckling behavior of SWCNTs and MWCNTs through a series of MD simulations. Different parameters such as the number of defects and their relative distance are considered. The stress–strain curves of defective and perfect CNTs under the uniaxial compression are determined, and the buckling stress, the compressive elastic modulus and the immediate reduction in buckling compressive stress of SWCNTs and MWCNTs are examined. In addition, the local buckling mode of SWCNTs with different tube diameters is compared with the Euler buckling theory.The structure of SWCNT is defined by a chiral vector (n,m). In the case of n |
= |
m, the CNT is called armchair and m |
= 0 makes a zigzag CNT. Two or more coaxial SWCNTs with an interlayer spacing of 0.34 nm form an MWCNT. Only double-wall CNTs are studied in this paper. The study is performed on two types of SWCNTs and MWCNTs. SWCNTs consist of a (10,10) armchair and a (17,0) zigzag containing 1660 and 1632 carbon atoms with diameters of 13.56 and 13.31 Å, respectively. The diameters are selected close to each other, but it is not possible to create any zigzag and armchair CNTs with exactly the same diameter. In addition, a (10,10)/(15,15) armchair (with 4100 carbon atoms and diameter of 20.34 Å) and a (17,0)/(26,0) zigzag (with 4128 carbon atoms and diameter of 20.35 Å) MWCNTs are also investigated. The lengths of all nanotubes are 100 Å.Two forms of mechanical defects exist in nanotube structures, namely vacancy (b) which is also known as 5–7–7–5 defect or twinned pentagon–heptagon pairs. The former defect can be formed by removing three convergent covalent bonds and an associated carbon atom from the nanotube structure (a), whereas the latter is a result of rotating a carbon–carbon bond by 90° with respect to its center to a new configuration, as shown in b. It is believed that the effects of defects remain relatively local and limited to the atoms at the vicinity of the defects.The Tersoff interatomic potential function ). This modified version of potential is not capable of handling bond formation mechanisms.Modification of the original Tersoff potential is not necessary in compressive analysis due to the fact that most of carbon bonds are only subjected to compressive forces and even if some of covalent bonds fell into the tensile region, their elongation would not go beyond Rij, so modifying the cut-off function does not significantly affect the overall compressive behavior (The long-range non-bonded interaction between carbon atoms in different layers of MWCNTs is described by the Lenard–Jones (LJ) 6–12 potential. For carbon atoms, these parameters are εC–C |
= 0.00239 eV and σC–C |
= 0.34 nm MD simulations are performed to investigate the buckling behavior of CNTs. At the first stage of simulation, the structure of CNT is relaxed to the room temperature (300 K) by adopting the so-called constant Number of atoms, Volume and Temperature ensemble (NVT ensemble) in 20,000 steps. A random velocity is applied to all atoms in order to reach the specified temperature. Afterwards, the energy minimization procedure is carried out by the conjugate gradient (CG) algorithm in order to remove the existing residual stresses of CNT before beginning the simulation of compression phase.After the system reaches the equilibrium state, buckling simulations can be performed. The axial compression is applied by moving downwards the atoms at the top with the constant velocity of 0.01 Å/fs, while the atoms at the bottom are fixed. The time integration step is set to 1 fs. A total of 1,000,000 time steps are used to simulate the whole buckling response of CNTs.In order to verify the buckling analysis, a perfect (10,0) zigzag SWCNT, previously modeled by Poelma et al. , a good agreement is clearly observed with the reference results.The results of simulations are organized into two main parts. The first part discusses the buckling behavior of defective SWCNTs, and the second part is mainly focused on the influence of defects on the buckling behavior of MWCNTs.The axial strain of CNT is computed as ε |
= |
|ΔL/L0|, where L0 is the initial length and ΔL is the compressive deformation of CNT. The axial stress of SWCNT is obtained by σSWCNT=F/ASWCNT, where ASWCNT=πDt, F is the axial force, D is the tube diameter, and t is the wall thickness. Several authors have recently used the interlayer spacing in graphite (0.34 nm) as the thickness of CNT , does not depend on the cross section and the thickness of the CNT.σDefectiveσPerfect=FDefective/AFPerfect/A=FDefectiveFPerfectThe buckling stress–strain curve for the perfect SWCNT under axial compression is depicted in . The maximum compressive stress for the perfect SWCNT increases almost linearly as the tube is further strained in compression step by step before it buckles abruptly. It should be noted that the Young’s modulus (E) is defined as the initial tangent modulus at zero strain.). Both vacancies and SW defects, which are located in the mid-length of SWCNT, are studied. These defects are located in different angles with respect to each other and the effect of this angle on different mechanical properties such as the buckling stress and the compressive elastic modulus are examined. Then, multiple numbers of defects (both vacancy and SW) are located on circumferences of SWCNT with equal relative angles to investigate their influence on the same mechanical properties.The buckling stress for the perfect (10,10) armchair and (17,10) zigzag SWCNTs are 43.55 and 45.4 GPa, respectively. represents the ratio of buckling stress of defective SWCNT to the perfect one (σDefective/σPerfect) with respect to the angle between two defects. It is worth-mentioning that the effect of vacancy defect on buckling stress of zigzag SWCNT is more than the armchair one. A number of important conclusions can be made by comparing the influence of SW and vacancy defects on armchair and zigzag SWCNTs, as depicted in . Firstly, SW defects always decrease the buckling stress more than vacancies in both types of SWCNTs. Secondly, SW defects show more influence on zigzag SWCNTs than the armchairs, and reduce the buckling stress more significantly (54% reduction).An important point about the SW formation in zigzag nanotubes is that when two SW defects are formed in two adjacent bonds, the distance between the two carbon atoms, which are located on rotated bonds, is reduced from 1.42 to 1.05 Å. This reduction causes a significant increase in the interaction force between the two atoms and so the governing MD equations may diverge. As a result, formation of two SW defects in adjacent bonds seems practically impossible (The results of present simulations indicate that the elastic modules for perfect (10,10) armchair and (17,0) zigzag SWCNT are 1280.8 and 1283.6 GPa, respectively. Variation of elastic modulus ratio of defective SWCNT to the perfect one (EDefective/EPerfect) with respect to the angle between the two defects are reported in . The results lead to the point that the existence of SW defects in both types of SWCNTs always decreases the elastic modulus more than the vacancy defects. However, this reduction for zigzag SWCNT with the SW defect is much more than the armchair one, where a maximum 16% reduction is observed in EDefective/EPerfect. Such a significant amount of degradation does not occur in other models.Most of simulations have resulted in a similar trend and the overall behavior of buckling stress–strain curve comprises of a rise in the stress–strain curve with a constant rate and then, at the buckling point, the stress suddenly falls down, accompanied with occurrence of a significant geometrical deformation in the middle section. Afterwards, the nanotube partially recovers its geometric stiffness and the process of increasing stress continues with a much lower pace.Denoting R as the immediate reduction in the buckling compressive stress (as depicted in ), the ratio of R of the defective to the perfect nanotube can be defined as: shows the variation of RDP with respect to the angle between defects. Accordingly, in all cases, a perfect SWCNT shows more immediate reduction in the buckling compressive stress than the same defective SWCNT for both SW and vacancy defects. This is due to the fact that the perfect tube in the buckling instant bears more compressive stress than the defective one. Consequently, such compressive forces make bigger distortive out of plane deformation in the perfect tube, which leads to the phenomenon that the nanotube structure shows more instability, with occurrence of higher stress reduction. According to , RDP for the armchair SWCNT with SW defects is higher than the zigzag one. In addition, SWCNTs with vacancy defects show higher RDP than nanotubes with SW. This can be attributed to the fact that the bonds between the carbon atoms in SWCNT with SW defects already exist and they can help the overall structure of nanotube to maintain its stability to some extent after the buckling point, while in a vacancy defect, the three covalent bonds connected to a missing carbon atom are completely removed.The next step is to investigate the effect of number of defects on buckling and post-buckling stress of SWCNTs. In this regard, a number of 2–10 defects (both vacancy and SW) with equal angles, are located on circumferences of (10,10) armchair and (17,0) zigzag SWCNTs, as depicted in indicates that when the number of vacancy defects in the middle section of the armchair SWCNT increases, its buckling stress reduces. A more severe degradation in the buckling stress up to 48% is observed in the armchair with vacancy defect. The existence of SW defects in the zigzag SWCNT causes more reduction in the buckling stress than the armchair one up to 57%. also illustrates that in contrast to the effect of vacancy defect, increasing the number of SW defects in both types of SWCNTs, results in convergence of σDefective/σPerfect towards a constant value. In other word, increasing the number of SW defects after a certain number does not affect the buckling behavior. SW defects always cause higher decrease in σDefective/σPerfect ratio in zigzag SWCNT than vacancies, but this is not the case in armchair SWCNT, where by the increase of the number of SW defects from a certain number, vacancy defects could be more critical.Another observation is that during the relaxation phase towards 300 K temperature of armchair and zigzag SWCNTs with large number of SW defects, out of plane distortion occurs in the cross section of SW defects. This distortion for armchair SWCNT is towards the inside of the cylinder, while for the zigzag SWCNT is outwards, as depicted in . In contrast, due to the fact that vacancy defects do not distort the cylindrical structure of nanotube, the overall buckling behavior of nanotubes with vacancy defects remains the same.The influence of SW defects on the elastic modulus of both SWCNTs is far higher than the vacancy defects. In addition, while equal number of SW defects on the zigzag SWCNT reduces the elastic modulus more than the armchair one, the effect of vacancy defects on both types remains relatively identical ( illustrates that the effect of vacancy defects on RDP in both types of SWCNTs is almost the same, and when the number of vacancies increases, RDP is decreased. On the contrary, while the number of SW defects in a section of SWCNT increases, the value of RDP is limited to a specific value, indicating that it does not affect RDP after a certain number of defects. Also, it is worth mentioning that the existence of SW defects results in much lower RDP in zigzag SWCNTs than armchairs with SW defects.Two defects are considered for MWCNTs; one on the inner tube and the other on the outer tube. Then, the effect of the angle between the two defects on mechanical properties is investigated (see b). The stress can be calculated by σMWCNT=F/AMWCNT, where AMWCNT is the area of the cross section of MWCNT,where rin and rout are the radii of the inner and outer tubes, respectively.During the compressive loading, the MWCNT loses its cylindrical shape both on the middle section where the defect exists and on one of the sides (a). Afterwards, the same process is almost repeated on the other side of MWCNT (b). At last, the MWCNT loses its axial stiffness and undergoes eccentric deformation, as depicted in An interesting observation in buckling analysis of MWCNT is that the inner and outer tubes buckle concurrently. At the first glance and based on the basic engineering rules, it seems that the outer tube must be stronger than the inner one (because of smaller ratio of L/D of the outer tube). In order to examine which tube buckles sooner, two (10,10) and (15,15) armchair SWCNTs are analyzed under the compressive loading. Surprisingly, the (10,10) armchair, which is slender, bears more compressive stress (45 GPa) than the (15,15) armchair with 28 GPa compressive stress (). Clearly, this cannot be justified based on the conventional theories of mechanics of materials. The reason is attributed to the fact that occurrence of local buckling dominates the global behavior of SWCNTs. When the diameter of SWCNT increases, the behavior of the specimen changes from a global bending beam model to local out of plane shell mode, where the model becomes more susceptible to the local buckling.In practice, when two individual tubes comprise an MWCNT, both of them buckle concurrently. The reason can be attributed to the fact that when the outer tube is going to buckle, the van der Waals interaction between the inner tube and the outer one imposes out of plane forces on the outer tube and prevents occurrence of buckling in the outer one. This remains to be effective until the inner tube reaches its ultimate buckling stress and at this moment both tubes lose their axial stiffness and buckle almost concurrently (). As a result, the buckling stress of MWCNTs is mainly governed by the size of the innermost tube.In order to further clarify the fact that nanotubes with more slenderness ratio may buckle at higher stress levels, three (7,7), (10,10) and (13,13) armchair SWCNTs with different lengths are modeled. shows that when SWCNTs with different length to diameter ratios (L/D) are subjected to compressive loading, the following distinct behaviors are observed (For L/D ratios greater than around 21 and in the case of slender SWCNTs, there is practically no significant difference in the buckling stress for different diameters and the behavior is primarily governed by the global Euler buckling principle.If L/D ratio is smaller than 21, the Euler buckling behavior of SWCNTs is changed into the local shell buckling mode. In this region two distinct behaviors can be recognized:Primary local shell buckling mode for intermediate CNTs,Secondary local shell buckling mode for short CNTs. In this case, the buckling stress rises with a sharper trend, because the energy required for activation of the secondary mode is always greater than the primary one.In the local shell buckling region, CNTs with smaller diameters sustain higher buckling stress than CNTs with larger diameters. Based on the knowledge of the authors, no published report is available on such a phenomenon yet.For analytical calculation of the Euler buckling stress, it is assumed that the average compressive Young’s modulus of SWCNT is 1250 GPa. Therefore, if the SWCNT behaves similar to an elastic circular cylindrical column, its Euler buckling stress can then be obtained from:where L is the length of nanotube, rgyr is the radius of gyration and ISWCNT is assumed to be the moment of inertia of the nanotube section. The effective length factor for the fixed–fixed SWCNT is assumed to be k |
= 0.5 (the nanotube is modeled as a two-fixed end column).The buckling stress for the perfect (10,10)/(15,15) armchair and (17,0)/(26,0) zigzag MWCNTs with length of 100 Å are 43.35 and 40.38 GPa, respectively. Based on the results of , it is observed that the SW defects reduce mechanical properties (elastic modulus and buckling stress) of both types of MWCNTs more than the vacancy ones. The most reduction in the buckling stress is observed in zigzag MWCNTs with SW defect at about 35% strength degradation. RDP in both types of MWCNTs with vacancy defect is higher than the SW one (). It is clearly observed that, RDP is always less than unity. As expected, the compressive elastic modulus is not largely affected by the existence of defect in MWCNTs and the reduction is negligible (). Also, this decrease in the elastic modulus for inner tube is more than the outer one.In the next step, the effect of number of vacancy and SW defects on buckling and post-buckling stresses of (10,10)/(15,15) armchair and (17,0)/(26,0) zigzag MWCNTs is investigated. Various number of defects (both vacancy and SW) are located on the circumference of inner and outer tubes with equal angles (see In contrast to the result of SWCNTs with multiple defects (), which the buckling stress ratio for armchair SWCNT with vacancy defect is more than the zigzag one, in the case of MWCNT, the buckling stress ratio for the armchair MWCNT is lower than the zigzag one (). The most reduction, which is observed in zigzag MWCNT with SW defect, is about 50%. Similar to the results of SWCNT with multiple defects, the buckling stress for both types of MWCNT is more sensitive to the existence of SW defects than the vacancy one.Although the effect of existence of multiple vacancy defects on the compressive elastic modulus of both types of MWCNTs are the same, but in the case of multiple SW defects, the difference is negligible. In addition, SW defects largely reduce the elastic modulus of MWCNT up to 17% ( illustrates that RDP for MWCNT with multiple SW defects is less than the vacancy defects and this parameter for zigzag MWCNTs with SW defects is minimum. These results prove that RDP in both types of SWCNTs and MWCNTs is always less than unity.The local buckling behavior of perfect and defective SWCNTs and MWCNTs under uniaxial compression has been studied by a series of MD simulations. The findings of the present study have provided further in-depth understanding of the compressive behavior of CNTs, which are frequently used as a compressive component in composites and nanomechanical devices.It has been observed that the defects largely reduce the buckling stress and the ratio of immediate reduction in buckling compressive stress of the defective to the perfect nanotube (RDP) of CNTs, but have little influence on their elastic modulus. Results show that in most cases, the effect of vacancy and SW defects on the buckling stress and elastic modulus of zigzag CNT is more than the armchair one. In addition, SW defects usually show more influence on the buckling stress and elastic modulus for both types of CNTs than the vacancy ones.When two individual tubes comprise an MWCNT, both of them buckle concurrently due to the existence of van der Waals interaction between the inner and outer tubes. It means that the buckling stress of MWCNTs is dominated by the size of the innermost tube. The behavior is primarily governed by the Euler buckling for slender CNTs. On the other hand, in the local shell buckling mode, CNTs with smaller diameters sustain higher buckling stress than CNTs with larger diameters.Detection of crack onset in double cleavage drilled specimens of plaster under compression by digital image correlation – Theoretical predictions based on a coupled criterionGeomaterials such as rocks and concrete are brittle or quasi-brittle materials. Tensile tests carried out to observe the initial phases of crack nucleation are difficult to achieve because of the unstable nature of the tests. Instead, compression tests on drilled specimens offer a greater stability. When subjected to a compressive loading, two opposite cracks take place and grow from the cavity, parallel to the load. This crack nucleation is experimentally studied in rectangular drilled specimens of plaster with a centred cylindrical hole which size is assumed to be small with respect to the dimensions of the specimen. The results are compared to a theoretical prediction of the crack onset derived from the coupled criterion of Leguillon. Due to the difficulty of determining the crack initiation directly by the naked eye, 2D Digital Image Correlation is used. The nucleation event is determined by analysing the history of deformations at some points where the crack is expected to start. The predictions are proving to be in good agreement with the experimental results.In civil engineering and rock mechanics, compression tests like the Brazilian test (see for a review) or the double cleavage drilled compression test (DCDC) () are often preferred to tensile ones because they offer a greater stability. Under a compression load, a tension crack (mode I) initiates in the direction of the compression loading, then it grows gradually and stably as the loading increases without resulting in the complete failure of the specimen. However, it should be noted that in all the above mentioned papers, it is the growth of a crack from a pre-cut that is studied, not the initiation of the crack itself which is the subject of the present analysis.The aim of this paper is to study the crack initiation in quasi-brittle materials using drilled specimens. Plaster is chosen as a model of brittle geomaterial, it is cheap and easy to handle. Moreover some authors pointed out that it can also be a model for industrial ceramics (The prediction of crack initiation cannot be carried out using classical brittle fracture criteria because they lead to a paradox. The Griffith criterion based on energy is unable to predict new crack nucleation and the maximum tensile stress condition often results in unrealistic conclusions. To solve the paradox, one of the authors proposed a coupled criterion, which involves two conditions that must be satisfied simultaneously: one based on energy and the other on stress (). The energy condition derives directly from an energy balance between un-cracked and cracked states. As a consequence of this balance, it is derived that the crack jumps a given length. The stress condition states that the tensile stress must be greater than the tensile strength all along the expected crack path (jump).The verification of this theory is based here on compression tests carried out on drilled specimens made of plaster. The crack onset is experimentally determined using Digital Image Correlation (DIC) (). Our goal is not to definitively validate the theory but only to provide a positive additional element of appreciation for this criterion. In particular, we have tried to show experimentally that the initiation takes place by a jump of the discontinuity and that the model gives acceptable results even if data contain some uncertainty and randomness.Remark: For simplicity reasons, throughout this work, the numerical simulations are conducted within the plane strain elasticity assumption. With axial symmetry, they are the only 2D eligible simplifying hypotheses, especially in the presence of a singularity along a smooth front (crack tip or V-notch root). They are the only ones that allow reconstructing a 3D solution and are frequently used approximations providing satisfactory predictions for failure. This will be discussed again in Sects. Dry plaster is used as a quasi-brittle model material (). Thanks to its short hardening time, a plaster powder of Siniat Company named Prestia Profilia 35® is used in this work. Preparation of plaster samples involves the following steps: The required amount of water and powder are calculated based on the volume of the final sample so as to satisfy a mixing ratio W/P (mass of water to mass of plaster) equal to 0.33. The amount of powder is poured gradually in the mixer containing water. Mixing water and plaster is done at a very low speed (65 rpm) to avoid the formation of air bubbles. In order to homogenize the slurry, the mixture is kneaded by hand with the arm of the mixer. The slurry is then mixed again for 1 min by the mixer at a very low speed. Then the mix is poured into the mould of the desired final sample. The removal of the sample from the mould is done 1 h after pouring. The surface of the obtained specimens looks dry but they are still wet inside. A visual inspection showed no major defects on the surface of the samples. Before drilling and testing, samples of plaster are left for 72 h at room temperature. Note that it is very important to observe a constant period of drying because the mechanical properties of plaster change dramatically all along the drying process (In order to avoid inaccuracies resulting from the drying, Young's modulus, toughness and tensile strength are measured on appropriate samples at the same time.Uniaxial compression tests on samples of dimensions (100 mm × 65 mm × 20 mm) are carried out to determine the Young modulus of the plaster used in the specimens.) are glued on each side (front and back faces) of the plaster samples for strain measurements (lateral and axial strain). Compression machine allows recording the force applied to the specimen during the test. The compression stress is then determined dividing the prescribed force by the loaded surface. Drawing the tangent to the stress strain curve, Young's modulus is computed by taking the slope of this tangent on each sample side. The average of the Young moduli measured on both sides of the samples gives E = 13.5 GPa, but there is some scattering.In order to confirm this value, an optical technique called Digital Image Correlation (DIC) is used. The principle of this technique is detailed in Sect. . It is based on a comparison between successive pictures taken during the loading and acts as a kind of optical strain gauge for strain determination. Before starting the compression test, a black speckle pattern is randomly sprayed on the front face of the samples. When a specimen is compressed, a series of images is captured by a camera. On an image chosen as the reference frame, regularly distributed points are defined in a grid in the upper and lower central parts of the tested specimens (blue points in 3). DIC allows determining in the next images (each image corresponds to a load step) the displacement of the grid points previously defined. The global deformation of the sample at each step (image) is taken as the difference between the average displacements respectively of the upper and lower zones. The strain is determined dividing the result by the height of the specimen (65 mm). Young's modulus is determined by taking the slope of the stress/strain curve (stress given by the machine and strain determined by DIC) in the load direction. The Young modulus found by DIC is E = 12 ± 0.4 GPa not far from the value found using gauges, with a greater confidence in the latter method. Hereinafter E is taken equal to 12 GPa.Three-point-bending tests on un-notched samples (a) are used to determine the tensile strength of the material. In these tests, load is continuously applied at a constant speed equal to 0.1 mm/min. The tensile strength corresponds to the maximum value of the tensile stress reached in the sample along the lower surface (The failure of the specimen occurs in mode I: an opening crack takes place at the middle of the lower edge and then runs through the entire height and width of the sample causing its failure. Cracks repeatedly opening roughly in the middle of the specimen shows that the surface defects are not critical in this measurement. They are small, not visible at the naked eye, and uniformly distributed.The plaster is assumed to be linear elastic (), the Poisson ratio ν is taken equal to 0.3 (where U¯ and σ¯¯ hold respectively for the displacement and stress fields, C is the elastic matrix relying on the Young modulus E and the Poisson ratio ν and ∇x is the symmetric part of the gradient operator with respect to the space variable x.In a plane strain FE simulation, the tensile strength σc is taken equal to the maximum reached by the tensile stress just before failure, i.e. at the Gauss point located in (or close to) the middle of the lower edge where the crack is expected to appear.The experimental values of the tensile strength are given in . As expected in brittle materials there is a significant scattering. The retained value is σc = 4 MPa.The toughness measurements are carried out on notched specimens with same dimensions (4b) (Single Edge Notch (SEN) test). A metal lamella has been added into the mould used for the smooth specimens before casting plaster to form the slit after unmoulding.Griffith's criterion used in brittle fracture allows predicting the crack growth in a structure undergoing elastic deformations. The criterion states that the material fails if an amount of available stored energy reaches a critical value. The criterion can be written Gdif ≥ Gc where Gdif is the energy released by the structure during a virtual unit crack growth (the explanation for the index “dif” will be found further in Sect. ). The constant Gc is the toughness of the material also called fracture energy, a property that describes its ability to resist to fracture.The toughness Gc of Prestia Prifilia35® plaster will be determined by a classical fracture test: the 3-point bending on pre-cracked specimens (4b) and a 2D plane strain numerical simulation. The stress intensity factor KI of the crack tip singularity is determined using a path independent integral (). Its critical value at failure KIc gives Gc through the Irwin formula (plane strain)In addition, a correction is brought to the values of Gc to take into account the influence of the notch-root radius (i.e. one half of the width of the slit, roughly 1 mm) following the procedure proposed by , the final value used in the sequel is Gc = 1.4 J m−2.b) is commonly used to estimate the toughness of brittle materials (). Some authors claimed that the toughness measurement can be dependent on the type of test () comparing SEN, CT and DCB tests on PMMA. However, even if it noticeable (around 20%), from our point of view the scattering remains within an acceptable range for this kind of measurement. But it must be pointed out also that this does not seem to be true in some other cases (see e.g. ) where tests are carried out on rocks (marble). Following this reasoning the measured toughness, determined by the SEN test, may not be applicable to the drilled specimens under a compression loading or this could be at least one alternative explanation for the observed discrepancies between tests and theory (see further on Sects. The coupled criterion was first established in the case of a crack onset at the tip of a V-notch () in a homogeneous material. It combines two conditions to be satisfied simultaneously: energy and stress. Both are necessary and their combination is assumed to be sufficient. This criterion proved to give predictions in good agreement with experiments (The energy condition is based on a balance between an initial un-cracked state and a final state after the initiation of a crack of surface δSwhere δWp, δWk and GcδS are respectively the change in potential energy, the change in kinetic energy and the energy required to create a new crack of surface δS. In usual experiments, the initial state is quasi-static and then δWk≥ 0. According to The coupled criterion is based on the incremental form , which straightforwardly derives from the energy balance without any additional assumption.If the crack growth is continuous, i.e. no jump (additional assumption), the above condition must be true regardless of the value of δS, then considering the limit as δS → 0 (if it exists, another additional assumption) gives the well-known Griffith criterion.where Gdif is the differential energy release rate already used in Sect. . Griffith's criterion is used to study the growth of a pre-existing crack. It cannot be used to study the crack initiation because Gdif = 0 in the absence of crack.The stress condition states that when the opening stress σ, acting all along the anticipated crack path (prior to any crack initiation), exceeds the tensile strength σc of the material, then failure occurs. That is to say the following condition must be fulfilled all over δSTo illustrate this criterion, we will briefly recall how it can be applied to the rupture of a V-notched specimen made of plaster under a 3-point bending symmetric loading (The plane strain elasticity framework is selected (see remark in the introduction section). A 3D FE computation has been carried out on the uncracked specimen ( compares the 3D through the thickness tension σ (i.e. σ11) to the plane strain 2D solution computed by FE (). It is clear that 85% of the 3D points differ by less than 10% of the 2D solution. Furthermore, as will be seen later the mechanism of crack initiation is unstable and if the crack starts somewhere at an inner point, as suggested by the tensile stress profile, it extends quickly to the edge. Thus, it seems reasonable to think that there is only a very short delay between the initiation and the emergence on the outer faces.Within this framework, part of the description of the mechanism is achieved through asymptotic expansions (). It is compared to experiments at the end of the section.At a given load, a crack initiates at the root of the notch (b). The crack length is unknown but, assuming that it is small compared to the dimensions of the structure, we can expand the actual solution U¯l(x1,x2) as (outer expansion)where f1(l)U¯1(x1,x2) is a small perturbation (f1(l) → 0 as l → 0) due to the new crack, and U¯0(x1,x2) the displacement field before crack onset (a). The behaviour of U¯0(x1,x2) in the vicinity of the notch root is given by a Williams' series. is an irrelevant constant, λ = 0.545 is the exponent of the notch singularity, u¯(θ) is an angular shape function associated to λ (eigenfunction) and k is the generalized stress intensity factor. Note that x1, x2 are the Cartesian coordinates and r,θ the polar ones, both originating at the notch root. They are mixed without confusion.At crack onset in the direction θ0 = 0 deg. (i.e. along the bisector of the notch angle), using The index “inc” refers to the incremental form of the energy release rate (see A is a geometrical coefficient depending on the V-notch opening ω and the crack direction θ0 and l is the a priori unknown crack length at initiation (δS = le, where e is the thickness of the sample).Remark: We draw attention to an important consequence of : if failure occurs for a finite loading (i.e. for a finite value of k) then defines a not infinitely small lower bound for the eligible crack length extensions. In other words, there is an instability, the crack jumps (see also As a consequence of the elastic constitutive law (θ) (i.e. sθθ(θ0) = 1), the stress condition can be written. must be simultaneously fulfilled. Then combining gives the crack initiation length., allows writing the criterion in an Irwin-like form involving the generalized stress intensity factor k and its critical value kc), then, either the tensile strength σc is known and the toughness Gc can be determined from or vice versa. To this aim, the notched samples are obtained adding a metal part (having the notch shape) in the mould before casting plaster. The load at nucleation of the crack is measured from experiments and the critical value kc of the generalized stress intensity factor is derived using plane strain elastic simulations (see remark in Sect. ). In this kind of tests, crack is unstable. The crack onset almost coincides with the complete ruin of the structure.Due some scattering, after averaging and using σc = 4 MPa (), the toughness value provided by the coupled criterion is Gc = 4.66 J m−2. This value is then corrected taking into account the notch-root radius (roughly 1.4 mm) following the procedure proposed by . The fracture toughness obtained after correction is Gc = 3.2 J m−2. This value is of the same order of magnitude than that found in Sect. (Gc = 1.42 J m−2) but still differs significantly.On the other hand, λ = 0.545 entails that 2λ − 1 is closed to 0, then σc does not play an important role in the relationship . This makes the inverse determination of σc (Gc being known) very sensitive to the slightest inaccuracy.Samples are 100 mm × 65 mm × 20 mm. An aluminium mould was fabricated with removable faces to facilitate the unmoulding phase (plaster is a special material that swells during drying). This mould was designed and constructed in such a way that the measurement uncertainties are minimal: the faces of the specimen in contact with the press were cast. Furthermore, strict conditions on the parallelism of the faces of the mould were observed during the production of the specimens.The samples are prepared according to the process described in Sect. . A single hole is drilled in each sample. Different diameters of cavities are tested: 3, 4, 5 and 6 mm.Compression tests are performed with a 100 KN press. The load is applied continuously at a speed of 0.2 mm/min. The press is controlled by a computer, which records force and displacement during the test.Despite these care, it must be pointed out that some roughness, lack of parallelism, lack of planarity or particles may still be present at the contact between the platens of the press and the tested specimen. This can cause a loss of symmetry of the loading, or even a stress concentration that may induce cracking at the contact zone and the premature failure of the sample (). To avoid or at least limit these effects while reducing fretting, PMMA sheets are placed on top and bottom of the specimens (). The dimensions of PMMA plates are 100 mm × 20 mm × 20 mm.A high-resolution camera (Baumer HXC20, progressive scan CMOS sensor with 2048 × 1088 pixels, with a pixel size of 5.5 × 5.5 μm2, equipped with a ZEISS Makro-Planar 100 mm macro lens) is used in order to continuously acquire images of the specimen loaded under compression at a frame rate of 20 Hz.The detection of the crack onset with the naked eye (directly on the specimen or on the enlarged images provided by the camera) was not possible. The rupture of almost the whole sample was reached before seeing any crack arising or growing from the cavity in the loading direction. To detect the crack onset, the 2D technique of digital image correlation (2D-DIC) is necessary.As we have discussed elsewhere in the text (Sects. ), the DIC observations are performed on the outer faces of the specimen and could be a poor approximation of what occurs inside. However we are interested only in the crack initiation prediction. This mechanism is unstable at its beginning and we expect that there is only a very short delay between the crack initiation somewhere at an inner point and its emergence on the outer faces. Thus, it is the initiation inside the specimen at a location undergoing approximately plane strain conditions that is detected on the outer faces even if these latter support plane stress conditions.The DIC is an optical non-contact method for measuring displacement fields and strain fields on a surface (or a volume) of a specimen under a mechanical loading. The principle of the technique is to compare two pictures taken at two different stages of loading. The comparison between the two pictures needs the presence of local details on the analysed surface. These details could be naturally present in the material and in this case the surface is used as it is for the analysis by DIC. When the surface of the material has no local details a speckle is applied on the surface (). The random pattern (local details), natural or artificially produced, provides a local contrast essential for the analysis by DIC. The technique provides the displacement field and the strain field by matching, through a correlation coefficient (), pixel grey level values between a current picture at a deformed state and a picture chosen as a reference (The natural texture of plaster specimens has no natural contrast and thus a speckle is applied with a black spray paint at the sample surface so as to create a local contrast. A special light system is added to strongly lighten the surface of the sample. Recording images by the camera is triggered simultaneously with the compression loading. The intensity of light is adjusted so as to have the widest histogram of grey levels on the reference image and prevent saturation phenomena. The number of frames per second is 20. This acquisition frequency proved satisfactory for the detection of the crack initiation.The area of interest captured by the camera during the compression test is a surface of 18 × 10 mm2 centred on the cavity. The home-made CMV software () is used for the DIC analysis. The software allows downloading the sequence of images registered during the compression test. A reference image is defined, and then discretized into a grid of points. A correlation domain D is associated to each point. The software allows searching in the deformed image the most similar domain to D by optimizing the correlation coefficient. This allows computing the displacement field and then the strain field.Once deformations are determined, a map of ɛ11, (i.e. the horizontal component of the strain field, ) is plotted using a colour scale. The map in b shows that there are now two red areas (in the web version) corresponding to strong deformations associated to two cracks emanating from the north and south poles of the cavity in the loading direction. It is seen on this figure that the two cracks, supposed to theoretically grow on the same vertical line, are slightly offset. There are at least two possible explanations: (i) the misalignment is due to a lack of symmetry when setting up the DCDC test as already discussed in Sect. ; (ii) inevitably crack initiates from randomly distributed micro-defects, much smaller than the overall dimensions of the structure (small removals of material when drilling for instance).As already mentioned, the detection of the crack onset is not possible directly from the naked eye and very inaccurate from the digital map. In order to detect the nucleation, the history of ɛ11 is followed on points located on two lines (blue lines in 8) orthogonal to the expected crack path, one close to the top of the cavity and the other close to the bottom (see The history of the local strain ɛ11 at 7 points on the blue line located at the bottom of the cavity (yellow points) is shown in . Although the frame rate is 20 Hz, images were processed every 5 s (1 frame out of 100) which seemed good enough to our purpose and kept some clarity to the figures.The local strain ɛ11 remains small for points located beside the crack path during all the loading time (points 4–7). For points located close to the expected crack location, ɛ11 is small at first and then increases continuously past a given load step. We observe that these growing curves start from a single point and we make the hypothesis that this common point corresponds to crack initiation. In , the curves merge at a time t = 210 ± 2 s. This value is calculated at the intersection of the least square linear functions replacing the three curves having the biggest slope.In such a DCDC test, after initiation the crack growth is extremely stable and the load must be increased more and more strongly to advance the crack. Since we are only interested by the onset mechanism the tests were stopped before the final failure of the specimen which would often occur after having reached the compression strength of the plaster. allows the theoretical prediction of crack nucleation in brittle materials. As before, the plane strain elasticity framework is selected and a 3D FE computation has been carried out again to support this assumption. compares the 3D through the thickness tension σ (i.e. σ11) to the analytical plane strain 2D solution in an infinite domain. The conclusion is the same as in Sect. , 85% of the 3D points differ by less than 10% of the 2D solution. Similarly, the initiation mechanism is unstable, so if a crack starts somewhere from an inner point it must emerge after a very short time on the outer faces of the sample where DIC measurements are performed.Since the diameter of the cavity (3–6 mm) is assumed to be small compared to the dimensions of the plaster specimens (width w = 100 mm, height h = 65 mm, ), and since it is assumed that the crack length at initiation is at most of the same order of magnitude than the hole diameter, a matched asymptotic expansions procedure can be used to model the experiments. It can be carried out with respect to one or the other parameter. For technical reasons related to FE meshes used for solving various problems related to the expansions, these are made with respect to d (this parameter appears sometimes as an index in the expressions) and l is chosen as a variable.Note that, in the opposite case, if cracks are large compared to the diameter of the hole, at the leading order, the presence of the hole might be disregarded and the problem reduces to the study of a crack initiation in a homogeneous medium.Unlike a finite element procedure, asymptotic expansions leads to semi-analytical expressions avoiding the re-meshing for each size of the hole. They consists in solving the problem using two scales: a macroscopic approach called far field or outer problem and a microscopic one named near field or inner problem.On the one hand, the macroscopic approach considers the structure from the point of view of an observer located far away from the structure. In this approach, the perturbation, i.e. the small cavity, is not visible as well as the short cracks emanating from the hole. On the other hand, the microscopic approach considers the structure closely by zooming in around the cavity enlarging the hole and the cracks which become more observable (at this scale).In the outer problem, the diameter of the hole is not visible: mathematically it is obtained considering the limit as d → 0. defines the actual (a) and the outer (b) domains.The displacement field solution to the actual problem in the domain Ωd (Here x1, x2 is the Cartesian coordinate system with origin at the centre O of the hole. The leading term 0 is the solution to the far field problem in the domain Ω0 and the dots denote a small correction to bring to account for the perturbations of the domain (at first the hole and then additional cracks). This leading term can be directly expressed as a uniform compression solution (which plays the role of a one-term Williams' series)where r,θ are the polar coordinate system again originating at O, σ∞ is the compressive remote load and the term r In order to take into account details of the geometry of the perturbation, the space is enlarged by 1/d. Introducing the change of variables yi = xi/d and then passing to the limit when d → 0 leads to define an unbounded domain Ωin (), where the diameter of the hole is equal to 1 and the cracks length is μ = l/d.The displacement field solution to the inner problem, obtained rewriting the elastic equations after the change of variables yi = xi/d, is expanded in a classical asymptotic form (valid for both μ = 0 or not, i.e. without or with cracks):U¯d(x1,x2,l)=U¯d(dy1,dy2,dμ)=F0(d)V¯0(y1,y2,μ)+F1(d)V¯1(y1,y2,μ)+…Where F1(d)/F0(d) → 0 when d → 0. In an intermediate zone, near to the perturbation (the hole and the cracks) in the far field problem and far from it in the inner problem, the two expressions of U¯d(equations ) have to coincide for consistency reasons. The resulting conditions, so-called matching conditions, leads toF0(d)=1;F1(d)=σ∞dV¯0(y1,y1,μ)=U¯0(0,0);V¯1(y1,y1,μ)=ρc¯(θ)+Vˆ¯1(y1,y1,μ)With ρ = r/d. The functions V¯0 and V¯1 are independent of the global geometry and of the applied load and Vˆ¯1 is solution to a well-posed problem in the unbounded domain Ωin (). Especially, Vˆ¯1→0 at infinity. It is determined by an FE computation, the unbounded domain Ωin being artificially limited by a circle of radius R large compared to the dimensionless size of the perturbation 1+2μ (at least 100 times larger).Note that, as already mentioned, the asymptotic expansions have been carried out with respect to d and l is a variable. Thus in the inner problem the cavity diameter is 1 and μ varies. In the FE computations of V¯1 or Vˆ¯1, this is obtained by buttoning/unbuttoning the nodes along the crack without remeshing. From a theoretical viewpoint, expansions could as well be carried out with respect to l with d as a variable but varying the cavity diameter would whenever requires remeshing the inner domain.), the tensile stress along the anticipated crack path can be written according to the constitutive law (∇y is the symmetric part of the gradient operator now with respect to the space variable y)σ11(0,x2,0)=σ∞σˆ11(0,y2,0)withσˆ¯¯(y1,y2,0)=C:∇yVˆ¯1(y1,y2,0)ford/2≤x2≤d/2+landthen1/2≤y2=x2/d≤1/2+μThe bounds for the lower crack are not mentioned here for simplicity reasons. The functionσˆ11(0,y2,0) is a decreasing function of y2 then the stress condition resumes toThe initial state prior to any crack nucleation and the final state after the crack onset are respectively U¯d(x1,x2,0) and U¯d(x1,x2,l). The change of potential energy δWp can be expressed in terms of a path independent integral Ψ (−δWp=Wpd,0−Wpd,l=Ψ(U¯d(x1,x2,l),U¯d(x1,x2,0))withΨ(U¯,V¯)=12∫Γ(σ¯¯(U¯)·n¯·V¯−σ¯¯(V¯)·n¯·U¯)dswhere Wpd,0 and Wpd,l are respectively the potential energy of the initial state (before cracking) and the potential energy of the final state (after the crack onset) and Γ is a contour surrounding the cavity and the cracks. the expressions of U¯d(x1,x2,0) and U¯d(x1,x2,l) derived from respectively for l = 0 and for l > 0 and thanks to the properties of the integral −δWp=σ∞2d2(A(μ)−A(0))withA(μ)=Ψ(Vˆ¯1(y1,y2,μ),ρc¯(θ))Then the incremental energy release rate and the energy condition are writtenGinc=−δWp2l=σ∞2d22l(A(μ)−A(0))=σ∞2dA(μ)−A(0)2μ≥GcThe incremental energy release rate Ginc is an increasing function of μ (checked numerically), whereas the tensile stress σ11 is decreasing. As a consequence, consistency is obtained with equalities and the dimensionless crack initiation length μ0 (l0 = μ0d) fulfils (The critical loading σ∞ at the initiation of two cracks of length μ0 is thenNote that the measured crosshead displacement in includes the deformation of the PMMA plates (Sect. ) as well as that of the machine itself. It shows that plaster keeps an almost linear elastic behaviour under compression loading. A change of the slope in the first part of the curve corresponds to the setting up of the specimen in the jaws, the crushing of asperities …The theory predicts that under a uniaxial compression loading a pair of cracks initiate simultaneously from the two poles of the cavity parallel to the compression loading. Applying the experimental method of crack onset detection detailed in Sect. , the two cracks appear in the direction of the loading but at slightly different times. shows the crack onset from the cavity (diameter 5 mm) already presented in . A first crack initiates at the bottom of the cavity at a loading σ∞ = 7.84 MPa (i.e. a loading force of 15.68 KN), whereas the second crack nucleates at the top of the hole while the first one grows a little, at σ∞ = 8.51 MPa (loading force 17 KN). This small difference (0.73 MPa, roughly less than 10% of the load) can be explained again (see Sects. ) by a lack of parallelism in positioning the specimen, by the existence of small defects around the hole or by the presence of heterogeneities in the plaster at a microscopic scale.While the applied load grows from 14 to 18 KN, i.e. when the two cracks take place at the two poles of the cavity, no discontinuity can be observed in the force/displacement curve (), the curve is very close to being linear. Indeed, the nucleation crack length is small compared to the dimensions of the specimen, for this reason the crack onset has no effect on the global response of the specimen. Moreover, neither cracking sound audible to the ear nor acoustic activity (measured by an acoustic system positioned in contact with the sample during the cycle of loading) is heard during the test until the failure of the whole plaster specimen.Once the crack initiated, the change in length can be followed during the continuation of the compression test. The crack is detected by DIC with a red colour chosen for representing the maximum tensile strain. Knowing the pixel size (5.5 μm), the crack length can be determined in each subsequent picture. It is based on a visual observation of the deformations map. The more accurate method used to detect the crack onset is not applied to follow the crack growth because it would be quite cumbersome to implement, even if it could be done. The uncertainty is about 2–3 grid steps, i.e. 0.2–0.3 mm. shows the normalized crack length (l/d) as a function of the loading. At initiation, up to some uncertainties, the slope of the two curves is almost vertical (see ) and then the curves bend. This tends to prove that the crack onset occurs suddenly as predicted by the coupled criterion (), the crack length jumps from 0 to a given small value. Once initiated the crack grows stably (finite slope). compares the loading predicted by the coupled criterion (solid line) to that found by the DIC analysis (error bars) at crack onset as a function of the cavity diameter. Note that 6 samples were tested for a 3 mm cavity diameter, four samples for diameters 4 and 5 mm, five samples for diameter 6 mm and that the loads at onset of both the upper and lower cracks are reported. Error bars account for the uncertainty on the applied stress at crack initiation. It is directly derived from the uncertainty on the elapsed time measured at initiation (It is observed that the scatter in experimental results decreases when the diameter of the central hole increases. This probably presents similarities to the misalignments observed in Sect. Despite the scattering, both theoretical model and experiments point the influence of the cavity size on the crack onset: the smaller the hole diameter, the higher the failure load at initiation. Of course this size effect has nothing to do with a Weibull statistics, since the sample volume does not change (up to the volume of the hole) and because the cavity acts as a major fault which initiates fracture.There is a satisfying agreement between theory and experiments. The model based on Leguillon's criterion proved to be pretty effective for predicting failure experiments. However, according to , it is important to note that the model predicts that the load at onset increases indefinitely when the diameter d of the hole decreases to zero. Then, undoubtedly the load would exceed the compression strength of plaster (reported to be around 32 MPa for the drying time used to carry out experiments ()) leading to a complete ruin of the specimen in compression before any crack nucleates from the poles of the cavity. But this last mechanism was not addressed herein.The crack onset in drilled plaster specimens under a compression loading cannot be detected by the naked eye during experiments. It has been rather accurately determined by DIC, however the DCDC test is very sensitive to loading adjustment and the experiments have revealed some misalignments and slight load discrepancies at onset of the top and bottom cracks. As a consequence, the wide scattering in the results, common in fracture mechanics, does not allow comparisons as successful as we could have hoped with the predictions derived from the coupled criterion of Leguillon. In spite of that, some positive conclusions can still be drawn. The coupled criterion provides predictions which order of magnitude matches with the experimental measurements. Both experiments and theory have evidenced a size effect, the load at crack onset decreases with the increased diameter of the hole.In order to develop improved models for heterogeneous geomaterials, further investigations will focus on multi-perforated samples (Characterisation and thermal loading of low-Z coatings for the first wall of W7-XLow-Z coatings with a thickness up to 500 μm are being developed as plasma facing material on stainless steel first wall panels for the W7-X stellarator under construction at Greifswald, Germany. The materials under investigation are boron carbide (B4C) and a silicon–boron–carbide (SIBOR, manufactured from Plansee A.G., Austria), both applied by vacuum plasma spraying. Thermal loading was performed in the First Wall Test Facility (FIWATKA) at the Research Centre Karlsruhe. In particular, stepwise increasing heat loads from 50 to 500 kW/m2 and cyclic heat loads up to 1000 cycles of 3 min duration were applied to characterize the thermo-mechanical behaviour of the different coatings. Additionally, 2D and 3D finite element modelling is used to support the experiments and to predict the failure threshold of the coatings, which is also verified experimentally.For the Wendelstein 7-X stellarator (W7-X), which is under construction in Greifswald, Germany, protective ceramic coatings are being developed and will be applied on the plasma facing first wall panels. The total first wall surface area of W7-X is approximately 120 m2. The major part of the internal outboard area of the W7-X vacuum vessel will be protected by actively cooled stainless steel panels () coated with a low Z (atomic number) ceramic material (B4C or Si(C)). The internal inboard area of the vacuum vessel will be protected with graphite tiles clamped on Cu alloy cooling structures. The aim of these low-Z coatings is to inhibit interaction of the stainless steel surfaces with the plasma, which would lead to high-Z impurity influx into the plasma. Because W7-X will be operated in steady state with discharge durations up to 30 min, impurities could accumulate in the plasma, leading to unfavourable radiation and energy loss of the plasma.The plasma spray (PS) technique offers the possibility to coat 3D curved surfaces with materials with very high melting temperatures at reasonable costs. Among the different techniques, ‘vacuum plasma spray’ (VPS) is the most promising method for applying the coatings on the plasma facing surfaces of the first wall panels. This coating process ensures sufficient coverage of the plasma facing surfaces with the low-Z coating for a lifetime throughout the whole operational period of W7-X.The low-Z requirement of the coating materials comes from the energy loss of the plasma by radiation, which is proportional to Z4, with Z being the atomic number of the plasma impurity. Potential candidate materials for first wall coatings, which have already partly been investigated m, impurities below 500 appm (excluding gases).The VPS technique has been chosen for the deposition of the coatings because it offers a good compromise between manufacturing costs and quality of the coating (low impurities and residual gas, good thermo-mechanical properties). Adhesion and cohesion of the coating are key parameters for the successful application of thick coatings. PS-B4C coatings without bonding interlayer have been only deposited up to a thickness of approximately 0.2 mm on large surfaces The thermo-mechanical behaviour of coated components with geometry relevant to the W7-X panels was investigated in the First Wall Test Facility FIWATKA at the Research Centre Karlsruhe The FIWATKA device consists of a large water-cooled vacuum vessel made of stainless steel, with a diameter of 1.8 m and a length of 2.4 m (). Inside the vacuum vessel, a graphite heater with a surface area of 0.6×0.4 m2 is installed. The heater is surrounded with water-cooled copper shields, which allow the aperture of test windows of adjustable size for the installation of test specimens and mock-ups. The mock-ups can be connected to an independent cooling water circuit. The water temperature and pressure at the mock-up inlet can be adjusted from room temperature to 100 °C, and from 1 to 6 bar. Two sets of mock-ups were prepared for the experiment. The first set consists of eight ‘small-scale mock-ups’ (‘SSM’, ), which are made of water-cooled stainless steel substrates of the dimensions 300×80×13 mm3. Six of the eight SSM were coated (VPS) with 18 different coatings resulting from the combination of materials (B4C and SIBOR), different thickness (500, 300, 100 μm) and various interlayer systems (without, Mo, coating materials + stainless steel mixture).Temperature sensors were installed in the mock-ups at three different locations: two points on the cold backside surface and at the end of a hole drilled into the heated steel side, below the coatings ((a)). In two mock-ups strain gauges were also installed on the back surface of the cold side (, scheme). The second set consists of two ‘full-scale mock-ups’ (FSM, ), which are stainless steel (SS DIN 1.4301) prototypes of a W7-X first wall element. The average length of these elements is 550 mm, the width 300 mm and the thickness 14 mm (without coating). The FSM are actively water-cooled and one of the two FSM was coated with B4C of thickness 200 μm (VPS).The SSM were tested with steady state heat fluxes ranging from 50 up to 500 kW/m2. For each load, two cooling water flows were applied, 1 and 2 m/s with inlet temperature 35 °C and pressure 5 bar. The duration of the constant heat load during each step was about 15 min. At the end of the steady state loading, a cycling load () was applied on the two most promising coatings: B4C + (SS-B4C) interlayer and SIBOR + (SS-SIBOR) interlayer. Thousand cycles of 3 min each (in total about 50 h), at 500 kW/m2 and with 1 m/s water flow, were applied. During the experiments, the highest temperature reached on the B4C coatings surface was ∼ 300 °C at 500 kW/m2. No plastic deformation was observed during the thermal cycling experiment.In general, it appears that the coatings with interlayer provide a larger safety margin and allow the application of 500 μm layer thickness due to a reduced residual stress field in comparison to the coatings without interlayer. This statement is also confirmed by other evidence such as observed delamination during the water-jet cutting of the mock-ups, after the experiments. In a few cases the coatings without interlayer detached from the substrate, while the coatings with interlayer did not.) and deformations taking place in the mock-up during the experiment were quite small, also due to the intrinsic geometrical stiffness of the samples. The highest measured tensile strain was smaller than 100 μm/m in the stainless steel. From the finite element analysis, the highest tensile strain, taking place in the B4C, coating is about 1400 μm/m and in the stainless steel, in the position where the strain gauges were applied, about 100 μm/m.At the end of the SSM test campaign, no failure (i.e. cracking or delamination) caused directly by the heat loads was observed on the coatings with interlayer. Only in the SSM coated with B4C, in the region of 500 μm coating thickness, a large piece of coating (80 mm long and 3 mm wide) chipped-off along the edge. The origin of this failure seems to be related to the manufacturing process, after which already fine cracks were observed in the region of later delamination.The FSM were tested with steady state loads ranging from 50 to 500 kW/m2 in the case of the uncoated mock-up, and from 50 to 200 kW/m2 in the case of the B4C coated mock-up. The cooling water inlet temperature was 50 °C (max cooling water outlet temperature 80 °C) and the maximum surface temperature was ∼370 °C on the uncoated mock-up. The FSM experiment showed also a good thermo-mechanical behaviour of the B4C coating. The horizontal displacement of three points (S1, S2, S3, ) was measured during the experiments. Point 2 is located at the centre of the mock-up and points 1 and 3, which lie on the same vertical plane containing point 1, are ∼190 mm distant from the point 2. A deformation parameter S was defined as S=S2−(S1+S3)/2. With the highest heat load 500 kW/m2, the maximum extrapolated deformation of the mock-up edges would have been about 5 mm (i.e. the mock-up elongated) with respect to the central part of the mock-up. To avoid coating failure due to excessive deformation, the heat load in the experiments with the coated mock-up was limited to 250 kW/m2.In support of the FIWATKA experiments finite element analyses have been conducted. Two models, reproducing the SSM with B4C coating (500 μm thick) and the FSM without coating, were generated and the experimental steady state loading conditions were simulated. In the SSM thermo-mechanical analysis the following boundary conditions were applied to the model: 500 kW/m2 uniform heat flux, 30 °C inlet water temperature, 5 bar water pressure. In the FSM thermal analysis the boundary conditions were: 500 kW/m2 average heat flux (not uniform), 50 °C inlet water temperature.The SSM analysis result shows that coating regions at the sample edges are the most critical because the highest stresses and stress gradients develop at these locations (, highest von Mises stress above 200 MPa assuming a B4C Young’s modulus of 100 GPa ). Compared to the SSM, the 5 mm wall thickness, the higher cooling water temperature, the longer cooling water path, the higher heat load peak (600 kW/m2) increase the peak surface temperature by up to 120 °C on the uncoated FSM. The deformation measurement showed that the dynamic water pressure (5 bar inlet, 2.5 bar outlet) does not contribute to the deformation of the mock-up. The numerical results are also in good agreement with the temperatures measured in different locations of the mock-ups during the experiments.The thermo-mechanical tests and the characterization of boron carbide and silicon–boron–carbon coatings on stainless steel substrate showed that thick coatings, with thermo-mechanical and physical properties satisfying the W7-X requirements, are achievable. By the optimisation of the manufacturing parameters it has been possible to manufacture coatings with thermal conductivity above 2 W/m K, low porosity (VPS technique), and good adhesion/cohesion strength (>35 MPa) During the thermo-mechanical test, performed with the FIWATKA device, were applied heat loads up to 500 kW/m2 on the coatings. This value is 2.5 times higher than the W7-X maximum operation first wall heat load that is 200 kW/m2. After both steady state (from 50 to 500 kW/m2 stepwise) and cyclic loading (1000 cycles at 500 kW/m2 in 50 h) no failure was observed in the 500 μm thick B4C and SIBOR coatings with interlayer.Fracture of a compressor rotor made from grey cast ironIn this study, the fracture of a compressor rotor manufactured from grey cast iron is investigated. In order to study the causes of the fracture, specimens prepared from the damaged rotor were subjected to experiments such as hardness and Charpy impact tests. The effect of microstructure on the fracture was also considered. Results showed that the rotor was manufactured from a cast iron containing carbon figures higher than values stated in standards and therefore it has a low impact energy. Geometrical analysis of the compressor rotor revealed that early failure of the structure started from a sharp corner radius by which stress concentrations are created in the rotor.Grey cast iron is a typical brittle metallic material because of its low ductility. This brittle behaviour shows up in tensile testing where the elongation is nearly zero. It is well known that Gray iron is relatively inexpensive and extensively used in applications where the material is subjected to compressive load, such as disc brake rotors and hydraulic valves In this study, the causes of fracture of a compressor rotor made from grey cast iron are investigated. Manufacturing of the rotor is carried out in a military factory. A photograph of the compressor rotor and stator as manufactured in the factory are given in . A number of mechanical and microstructure analyses are carried out to determine the causes of fracture.Specimens extracted from rotor material were subjected to various tests, such as tensile tests and impact energy tests. All tests were carried out at room temperature. For tensile tests, an Instron test machine is used and for impact energy tests, a Psd 300/150-1 test machine is used.Chemical analysis of fractured rotor material was carried out using a spectrometer test machine. The composition of material is given in , corresponding to GG25 cast iron specifications of ASTM A 48 standard Preliminary study of structure led to the view that fracture may have been caused by sharp corners, however, non-failed rotor structures also show similar structural features. Hence it is considered that the cause of failure was unlikely to be sharp corners alone, but their contribution to the failure cannot be underestimated due to presence of stress concentrations.The rotor was broken up into four separate parts and did not bear any indication of fatigue crack growth when the fracture surface was examined, indicating that the failure was of a brittle type of fracture. As shown in , all fractures seem to start at a corner radius because of the high stress concentration at this region which may be compounded by the poor impact energy of the material used. In addition to sharp corners extending to the centre of the rotor, the reduced thickness between the canal and the hub hole added to the failure. To link rotor and stator a wedge shaped blunt hole was drilled in the most critical zone where the thickness between wedge and canal is apparently the least (The structure of the failed rotor material is shown in . There is a mixed structure in which some ferrite exists probably as a result of slow cooling and high Si content. In Following casting, the rotor was subjected to stress relief annealing for 2 h between 650 and 750 °C. Hardness tests were carried out by using the Brinell test method. According to results obtained from hardness tests, it is considered that the rotor bars are probably in the half-hard condition. shows the results of tensile, hardness and impact energy tests.After the fracture, the compressor rotor was separated into four different parts, leading to a brittle fracture. On the examination of fractured parts, it can be concluded that all fractures started at a corner radius due probably to high stress concentrations. The thickness between the hub hole and the canals also has an important effect on fracture behaviour. Examination of the rotor material revealed that the cast iron contained excessive carbon and had a low impact energy.Three different guises for the dynamics of a rotating beamThe dynamics of a flexible beam forced by a prescribed rotation around an axis perpendicular to its plane is addressed. Three approaches are considered, two of them related with simplified theories, within Strength of Materials, and the third one using Finite Elasticity. In the Strength of Materials approaches, the governing equations of motion are derived by superposing the deformations and the rigid motion in the first model, and in the second by stating the stationarity of the Lagrangian (including first- and second-order effects in order to capture the stiffening due to the centrifugal forces) through Hamilton's principle. Two actions are considered: gravity forces (pendulum) and prescribed rotation. Comparison of the two Strength of Materials models with the model derived from Finite Elasticity is carried out. Predictions for the same problems, interpreted in the context of the specific model, are compared and it was found that sometimes they give rather different results, both in the results and in the computational cost. Energy analyses are performed in order to obtain information about the quality of the numerical solutions. The paper ends with an example of a pendulum with a finite pivot including friction and flexibility. When the structural elements are sufficiently slender and the rotational speeds are low, so that the resulting deformations are small, the Strength of Material model that includes the load stiffening and the Finite Elasticity approach, lead to similar results. It can be concluded that the stiffening phenomenon is appropriately considered in the first model. On the contrary, when the Strength of Material hypothesis are not fulfilled, the problem should be addressed via the Finite Elasticity model. Additionally, cases with complexities such as friction at a finite pivot can only be addressed by Finite Elasticity.► The dynamics of a flexible beam with a prescribed rotation is addressed. ► The stiffening effect is particularly considered. ► Two approaches within Strength of Materials and other with elasticity are studied. ► A pendulum with a finite pivot including friction and flexibility is addressed.In the last decade the problem of a plane rotation of a beam has been studied by several authors due to the importance of the problem. There is the possibility of addressing the present problem with models of different levels of complexity. Usually the technical theories start from a simple model and terms are added to account for various effects. In this work two approaches are explored for the study of rotating beams, i.e. Strength of Materials (SM) and Finite Elasticity (FE), or Nonlinear Theory of Elasticity (NLTE). The aim is to compare advantages and disadvantages of both models. The use of a model within the NLTE frame provides a general tool that allows the validation of the approximated models used in the technical theories. On the other hand, in cases in which the Strength of Materials hypothesis are satisfied, the first method is suitable.Almost exclusively, the study of rotational dynamics of a beam is studied from the viewpoint of Euler–Bernoulli or Timoshenko equation (SM) for the transverse displacement and deformation. In this work, we first add the longitudinal deformation of a rotating-beam model according to the theory SM of Euler–Bernoulli and, second, we propose a model based on the FE of the rotating beam, which allows to take into account more complex and realistic phenomena such as dry friction and other types of nonlinear effects due to large deformations. Two types of actions applied to the flexible beam are considered herein. First, the beam is subjected to only gravity forces (i.e. the well-known “pendulum”, an object that is attached to a pivot point about which it can swing freely) and second, a rotation of a section of the flexible beam is imposed at the extreme point (a flexible beam subjected to a prescribed rotation means that the speed of rotation will be imposed at a section, in this case the end from which it hangs). Note that, since the body is flexible, the rotation imposed at a section may differ from the rotation at another section. Both cases will be considered by the following three approaches: (a) SM with a floating frame, that is, superposition of a rigid-body motion of the floating frame to small deformation about it, (b) SM via Hamilton's principle including the stiffening contributions and (c) Finite Elasticity (in two dimensions, 2D). In the last case, the constitutive equations are stated using the Piola–Kirchhoff stress tensor (see for instance, Truesdell , these equations are presented in the weak form and discretized through finite element via the Galerkin method. The boundary conditions are also discussed given that the equations are stated in a Lagrangian reference in the case of Finite Elasticity. The influence of the stiffening effect in the rotating-beam motion, in the three models are compared. Also, an analysis of the energy conservation is included which permits the control of the numerical convergence. The Finite Elasticity model is taken as a reference. The stiffening effect is shown through the temporal variation of the tip displacement, the natural frequencies, and the mode shapes. Also, the influence on the frequencies of a variation in the Poisson coefficient value is studied using the NLTE approach. It should be noted that the Strength of Materials models do not include this effect. In order to validate this approach, three cases are compared with results found in the literature. A section includes the motion of a 2D pendulum and a comparison with results from the paper of Vetyukov et al. In this section, the equations of plane motion of a rotating beam are stated and discussed. Three approaches are presented and compared. The first two are Strength of Materials (SM) models for a one-dimension continuum in plane motion and the third one belongs to the two-dimensional nonlinear theory of Elasticity (NLTE), that is the beam is a two-dimensional body in planar motion. Whereas the stiffening effect is included naturally in the NLTE approach, in the SM theory a second-order effect should be considered to take into account for it.Two models are stated within the SM theory. One of them is constructed by superimposing a rigid-body motion of the beam with small deformations around the rigid configuration. The other, stating the stationarity of the action (including the second-order effects in order to capture the stiffening effect) through Hamilton's principle. The superposition and Hamilton's principle models will be named as Model SM1 and Model SM2, respectively.The governing equations of a beam undergoing plane rotation are stated superposing the equations governing the small deformations of the beam to the ones of the rigid motion where X is the material coordinate fixed in the frame, t is the time, E is the modulus of elasticity, A is the cross-sectional area of the beam, I is the second area moment, ρ is the volumetric density, u=(u,v)T is the displacement vector, u and v are the longitudinal and transverse displacement components, and f1 and f2 are the normal and transversely applied forces (gravity components). Now ur should be obtained from the equations governing the rigid motion to be replaced in Eq. in order to solve the problem. For instance, in the case of a pendulum of length L and gravity g (see ), one obtains θ¨+(3/2L)gsinθ=0, this equation gives θ(t), and then, ur=X(sinθ−1) and vr=−Xcosθ can be computed. For example, if Q is a point whose coordinates in the inertial system are x and y, and whose coordinate in the rotating frame is X (see where i^ and j^ are the unit vectors that generate the mobile frame. ThenThis model is derived by stating the action. The kinematic transformation equations (The following four energies contributions are introduced:where u, v, x, y are functions of (X,t), W1 is the strain energy due to axial and bending deformations, K is the kinetic energy, P is the gravitational potential energy and W2 is the internal work done by the axial stress that arise from the centrifugal effect and the change in length due to the bending deformation. The stress due to the centrifugal effect is σ=ρω2(L2−X2)/2, where ω is the angular velocity. This contribution, well-known within the classical Strength of Materials, is a second-order effect, yet linear. Bleich and Ramsey kv∂4v∂X4+(v¨−ω2v−2ωu˙)+ω2X2−L22∂2v∂X2+X∂v∂X=G(X,t)where ω=θ˙, kL=E/ρ, kv=(EI)/(ρA), F(X,t)=−(ω2X+gcosωt), and G(X,t)=−gsin(ωt).In this section, the equations of an elastic body in two dimensions for finite displacements and deformations are stated. That is, in these models no hypothesis is made with respect to the size of the deformations. The statement of these equations is made within the frame of the Mechanics of Continuum with the Lagrangian, or material, reference presenting some advantages over the Eulerian, or spatial, reference in the case of Mechanic of Solids problems. In turn, if the problem of the continuum is given by the Eulerian reference, besides the equation of motion (known as Cauchy equation)the mass continuity equation should also be statedwhere Σ is the symmetric Cauchy stress tensor, ρ is the mass density, b is the body force, and a, v are the acceleration and velocity fields, respectively, and div(Σ) is the divergence of Cauchy stress tensor calculated in spatial coordinates (the same is done for the velocity field). It should be taken into account that both a and v are calculated as material derivatives introducing a strong nonlinearity in the differential equations. If the body is subjected to finite displacements in the space, the statement of the boundary equations is a hard problem since the boundary position is one of the unknowns of the motion. Now, if the problem is given in the Lagrangian form, the only vectorial equation of motion to be solved iswhere P is the first Piola–Kirchhoff stress tensor and ∇·P is the divergence of P calculated in material coordinates where F is the deformation gradient, Fij=∂xi/∂Xj. The second Piola–Kirchoff stress tensor S, which is symmetric, is given by P=FS. Then, the equation of motion isThe following constitutive law between the second Piola–Kirchhoff stress tensor S (symmetric) (P=(FS)) and the finite strain tensor E, in which λ and μ are Lame's-type constants, λ=νE⁎/(1+ν)(1−2ν),μ=E⁎/2(1+ν) and E⁎ and ν are constants. Eq. is also known as St. Venant–Kirchhoff material model S is also a function of the derivatives of x. Similarly, for the tensor P, Eq. and the goal of this problem is to find the position vector x (or displacement vector u=x−X) for all X and t subjected to the boundary conditions that will be discussed in the next section.The following subsections describe the numerical scheme implemented to solve the equations of motion.Let ϕj=(ϕj1,ϕj2)T be a finite element basis (admissible functions), i.e. Adm is a set of trial functions defined asAdm=ϕj1,2∣ϕj1,2(0)=0,∂ϕj2∂X∂ϕj2∂X(0)=0and,∫0L∂ϕj1∂X2dX<∞,∫0L∂2ϕj2∂X22dX<∞ by ϕj1 and integrating by parts, one obtainsEA∂ud∂Xϕj10L−∫0LEA∂ud∂X∂ϕj1∂X+ρAp1ϕj1dX=0EI∂3vd∂X3ϕj20L−∂2vd∂X2∂ϕj2∂X0L+∫0LEI∂2vd∂X2∂2ϕj2∂X2+ρAp2ϕj2dX=0In the case of a rotating beam, for the pivot point we chose X=0, then the essential boundary condition requires that the function satisfy ϕj1=ϕj2=∂Xϕj2=0,∀j, and in the free end, X=L, the functions ∂Xud=∂X3vd=∂X2vd=0, are thenThen, the goal of this problem is to find ud=(ud,vd)T such thatud,vd∈Adm∀ϕj1∈Adm⇒∫0LEA∂ud∂X∂ϕj1∂X+ρAp1ϕj1dX=0∀ϕj2∈Adm⇒∫0LEI∂2vd∂X2∂2ϕj2∂X2+ρAp2ϕj2dX=0K1ij=EA∫∂ϕi1∂X∂ϕj1∂XdX,K2ij=EI∫∂2ϕi2∂X2∂2ϕj2∂X2dXQ2j=EI−∂3vd∂X3ϕj20L+∂2vd∂X2∂ϕj2∂X0L+∫f2−ρA∂2vr∂t2ϕj2dXAs before, let ϕj=(ϕj1,ϕj2)T be a finite-element basis of a finite dimension subspace of Adm, the space defined by the essential boundary conditions, and using Eq. by ϕj2 and then integrating by parts, or directly from δ∫t1t2Ldt=0, we obtain the matrix formsK1ij=kL∫∂ϕi1∂X∂ϕj1∂XdX,K2ij=−ω2∫(L2−X2)∂ϕi2∂X∂ϕj2∂XdXQ2j=−kv∂3v∂X3+(L2−X2)∂v∂Xϕj20L+kv∂2v∂X2∂ϕj2∂X0L+∫G−ρA∂2vr∂t2ϕj2dXOnce more, in the case of a rotating beam, at the pivot point X=0 the function ϕj1=ϕj2=∂Xϕj2=0,∀j and at the free end (X=L) the functions ∂Xu=kv(∂X3v)+(L2−X2)∂Xv=∂X2v=0; then the boundary conditions are The variational formulation of the equations of motion is straightforward. Let W be a test vector field (admissible functions) of variables referred to the body in its non-deformed configuration (Lagrangian description). Once again, multiplying the equations of motion by W and integrating over V0 we get: by parts (using Green's formula) and t0 is the stress vector. Here ∂V is the boundary of the region V0 occupied by the body. The surface integral is divided into two parts, ∂V1 and ∂V2. Suppose that the displacement u, and consequently x, is prescribed in a part of the boundary's surface (∂V1, where the essential boundary conditions are imposed) and the stress is given at the other part (∂V2). We will see now how to incorporate the boundary conditionsinto the problem. In the case of non-homogeneous essential boundary conditions, the solution x(X) must satisfy Eq. on ∂V1 but the test function W must satisfy the homogeneous essential boundary condition. Then, in the variational problem , the admissible test functions W are defined asand the natural boundary conditions are automatically imposed where t¯0 is the value of the tension t0 in the boundary.In the case of a pendulum (beam rotating under gravity) the stresses are null on the external body surface with exception of the pivot point p (see (b)). On the other hand, the problem with prescribed motion (beam with prescribed rotation with constant velocity), the stresses are null on the external body surface with exception of the clamped boundary. At these points, essential conditions are imposed. In the Lagrangian description the stress is given by t0=P·N, where t0 is the stress vector of Piola–Kirchhoff and N is the normal vector of the surface in the reference configuration (Finally, the variational problem consists in finding the vector x(X,t), implicit in P, such that∀W∈Adm1,findx∈Adm2,thatsatisfies∫∂V2(t¯0·W)dA0=−∫V[ρ0(b−x¨)·W−P(x)·∇W]dV0Let {ϕj}∈Adm1 be a basis of a subspace of a Hilbert space. In this paper ϕi are shape vector functions. Let the function x(X,t0) be expanded in a series of the vectorial functions ϕi(X)Here ci(t) are functions only of time. The admissible vector functions are ∫∇·P(x)+ρ0b−ρ0∑i=1Nϕi(X)c¨i(t)·ϕj(X)dV0=0for j from 1 to n. P(x) means that the Piola–Kirchhoff stress tensor is calculated from x(X,t) through constitutive relations At last, integrating by parts using Green's formula we get∫∂Vj2(t0(x)·ϕj)dA0+∫Vjρ0b−∑i=1N·ϕic¨i·ϕj(X)−P(x)·∇ϕjdVj=0where Vj is the volume of the jth element.If the problem has non-homogeneous essential boundary conditions, the approximations arewhere ϕ0 is known and ϕ0=x¯ on ∂V1, and consequently x∈Adm2.In this subsection the following models will illustrate the three approaches:A flexible beam rotating in a plane under gravity action is studied using Model SM1, i.e. a Strength of Materials approach with superposition of the beam vibrations to the rigid overall motion.A flexible beam subjected to a prescribed rotation is solved using Model SM2. Since the simulations are done for high-speed rotations, the consideration of the stiffening effect is essential. It was introduced by means of a second-order term into the governing functional (Eq. A flexible beam subjected to both a prescribed rotation and gravity is addressed with Model NLTE.A two body system composed of a flexible pendulum and a finite pivot which is considered rigid is analyzed with the NLTE approach taking into account the friction at the joint.When dealing with the linear SM models, a cubic finite element basis was employed. On the other hand, a quadratic finite element basis was employed to discretize the spatial domain in all the NLTE simulations. Temporal integration was performed using the Gear method (second-order implicit Backward Difference Formula).The first example deals with a beam with L=5 m, a square cross-sectional area A=0.01m2, Young's modulus E=4×107Nm−2, Poisson coefficient ν=0.3 and mass density ρ=7850kg/m3 (). The material properties were chosen to make apparent the differences among the models through larger deformations. The beam is released from a horizontal position with null velocity and restricted to plane motion under the gravitational field. (a) shows the beam motion through 11 instantaneous configurations during the first second of the motion, corresponding to the Model SM1 and Model NLTE with a 2D discretization. Also, the energy variation is depicted in (b). It is seen that the total energy remains constant, a necessary condition for the numerical solution since we are dealing with a conservative system. The total energy Et is the sum of the kinetic, elastic strain and potential energies, i.e. Et=T+Ue+Ug with T=12∫ρ0V·VdV0, and Ug=g∫ρ0x2dV0. It can be proved that for the constitutive law , the elastic energy takes the following expression The number of finite elements and the time step were adjusted after an error study. For this purpose the error was defined as follows:Superscript m denote the present numerical experiment and superscript m′ a reference solution. The reference case was performed with a hundred times more elements and a time step 1/100 smaller than the m case. The aim was to get results with errors less that 1% at t=1 s. The computational time of the reference experiment to simulate the dynamics during the first second was 12,500 s. The duration of the other experiments is depicted in The numerical simulation of the dynamics of a beam subjected to prescribed rotations is now presented. The beam length is L=1 m, the cross-sectional area is 0.01m2, the prescribed angular velocity is ω=3000 |
rad/s, Young's modulus is E=3.4×1010Nm−2, the mass density ρ0=7850kg/m3 and the Poisson coefficient ν=0.3. In particular, a large value of ω was assumed in order to obtain large deformations. Thus, the differences among the three approaches could be highlighted. The beam starts its motion from a zero reference (null displacement) and the initial velocity field corresponds to a rigid rotation. That is, the beam begins its motion from a horizontal position (x(X,t)=X) with a speed given by V1=0andV2=ωX1. The results and comparisons are depicted in . The temporal variation of the coordinate x1 at the free end of the beam during the motion is plotted in in which the values were found with Model SM1, Model SM2, and Model NLTE (2D). The curves are qualitatively similar though the responses found with SM exhibit larger peaks than the NLTE model results. It can be observed that the NLTE leads to a stiffer response. Probably this could be explained due to the choice of a linear Lagrangian constitutive law—S(E). If the second Piola–Kirchhoff stress tensor S is transformed into the Cauchy stress tensor Σ, a stiffening behavior with respect to the SM model would arise. This peculiarity is then not due to the rotation event but to the chosen constitutive model. depicts the variation of the vibration frequency (nondimensionalized with respect to the corresponding frequency at ω=0) when the rotating velocity is increased. The frequency values were found from a Fast Fourier Transform (FFT) plot. The Model SM1 results are shown in dashed lines, the SM2 are shown in dashed-dot line and the NLTE model in full lines. The results are evidently very close in the cases SM2 and NLTE. The case SM1 is indifferent to the rotation speed as follows directly from Eq. . The velocities were assumed small so as to show that the stiffening is not only consistent with the observed physical behavior but that it is also consistent with the NLTE model, in the range of small deformations. Some numerical values of this plot are tabulated in in order to show the differences between the methods SM2 and NLTE. For example, the difference in the frequencies between SM2 and NLTE when ω=50 |
rad/s are 5% for the first mode, 7% for the second, 11% for the third, 14% for the fourth, and 11% for the fifth one. Similar differences are found when ω=0.Since mode shapes are defined for linear problems, and the SM1 model does not reproduce the stiffening effect and, on the other hand, the NLTE model is nonlinear, we can only solve the eigenproblem derived from the SM2 model. But, as can be observed from Eqs. the equations are coupled and yield a nonlinear equation. In order to simplify it and to show representative mode shapes, the coupling terms were neglected and thus, the uncoupled linear eigenproblem was solved for ω=0,50, and ω=100rad/s. It is observed that the influence of the coupling is very small (c.f. ) for these values of angular velocities. shows the first three modes (bending type).Among the effects that can be simulated with the NLTE is the influence of the Poisson coefficient. shows the Poisson effect in the frequencies when the beam is rotating. To highlight this variation, a less slender beam is analyzed. Its cross-sectional area is 0.1m2 and the beam is rotating at ω=50rad/s. The curves are normalized to the corresponding case of ν=0, i.e. fi(ν=0). It is observed that as the Poisson coefficient increases the normalized frequency also increases. Moreover, the behavior is similar for the three frequencies. More slender beams were analyzed and it was found that this effect diminishes as the slenderness of the beam increases.Results found with the NLTE model of the present work are contrasted with results reported in (a) shows the angle vs. time reported in (b) plots the resulting angle from the present study and Fig (c), the superposition of both results. As is observed, and notwithstanding the diverse methodologies, there is an excellent agreement.One should account for geometric stiffening (also load stiffening) when the imposed rotation is large. To the best of the authors' knowledge, the first study of vibration of rotating beams was carried out by Simo and Vu-Quoc ϕ(t)=615t22+152π2cos2πt15−1rad,0≤t≤15s(6t−45)radt>15s. Since the NLTE approach of the present study yields the results referred to the material reference, they were transformed to the rotating rigid frame to allow the comparison. (a) depicts the variation of the axial displacement with time during the 30 s experiment. Approximately at t=12 s an stationary value of 4.676 ×10−4 |
m arises which results in a 9% lower than the value reported in (b) shows the transverse tip displacement. Both curves are very close to the ones reported in the reference paper, despite the different approaches. The small differences may be due to the different constitutive laws in each model. Recall that in the present approach, the constitutive law was stated in terms of the second Piola–Kirchhoff tensor in the Lagrangian reference.The last case analyzed for comparison is the pure bending of a cantilever beam, . Some additional data necessary in the NLTE model are the modulus of elasticity E=5×105 and the height of the beam cross-section in the 2D model, d=24/E3. The moment in the tip to make this configuration possible was found to be M=1.1063(4π) whereas the value reported in Let us now introduce the dry friction into the model. We model the pendulum hanging from a pivot as a flexible body (it constitutes the cross-section of an axis from which the pendulum hangs, and not as a dimensionless point, that includes friction between pendulum–pivot). As we shall see, the technical one-dimensional models cannot reproduce this type of dynamics because they cannot represent a finite-dimension pivot. This is precisely one of the advantages in the implementation of models that take into account the thickness of rotating systems.This model was introduced by Amontons in 1699 and was later developed by Coulomb in 1785 FT≤μ⁎FN→ifFT<μ⁎FN⇒u˙T=0ifFT=μ⁎FN⇒u˙T=−λ⁎FTwhere μ⁎ is the friction coefficient, λ⁎ is a real number and u˙T is the tangential component of the velocity. As can be seen, the friction law must be expressed not only in terms of the normal force, but also of the sliding speed. The static friction is contained in the friction law equation In this case, the boundary conditions imposed on the pendulum are the following. (1) In the outer surface, the stress vector is zero. (2) In the pivot of the pendulum, uN=0 and the tangential component of the stress vector is proportional to the tangential component of the force (tT∼FT) (see ). Since the friction force depends on the normal force at the pivot (which is unknown) the problem is reformulated so that all boundary conditions are in terms of the stress: assumes that each pivot point (axis) corresponds to a normal stress vector proportional to displacementThe friction law formulated in the previous section is non-regular, because there is no univocal functional form that relates tT with u˙T for all values of the velocity. For example, when the velocity is zero the friction stress vector is not defined. For this situation the functional dependence of the friction stress is with respect to other kinematic quantities. However, this law can be regularized,From the numerical point of view this approach will be valid taking ɛ small enough (). The regularization can be performed with different types of functions. For example, ϕɛ1(u˙T)=u˙T/u˙T2+ɛ2, ϕɛ2(u˙)=tanh(u˙T/ɛ), and defined by parts (the one used in this work)ϕɛ3(u˙T)=−1ifu˙T<−ɛu˙T2ɛif−ɛ<u˙T<ɛ+1ifu˙T>ɛWe developed an example to illustrate the influence of the parameters involved, particularly the axis stiffness and friction. A plane pendulum of length L=1 m, width d=0.15 m, and elastic modulus E=6×106N/m2 (again, this value is chosen to highlight the phenomenon), ν=0.3, rotating around an axis (with finite dimensions) of radius R=d/4 centered at d/2 from the tip, that is assumed with different flexibilities through values of stiffness k(N/m3) in Eq. . We have also studied the variations in the friction between the pendulum and the axis. The pendulum is released from rest from the horizontal position. We used a 2D model with 132 quadratic elements.The time response of the pendulum motion was found for different values of the stiffness of the axis (Eq. ): k=αk0 (where k0=2×1011 |
N/m and α=0.1,1,10,100,1000). That is, the flexibility of the axis varies, for increasing α, from flexible to more rigid. The influence of this parameter on the motion is shown in (a) (variations in time of x1 and x2 coordinates corresponding to point C) (see ). It can be seen that if the axis is very flexible (k1) the point C undergoes significant oscillations. As k increases, becoming more rigid (k5), this point tends to remain at rest. The effect of flexibility is also visible in (b) that represents the trajectories of point B (at the free end of the pendulum, see ) for about half-period for the similar rigid model. It can be seen that for a more flexible axis, the point B has a lower trajectory, as expected.The friction between the pendulum and the axis is taken into account with a model of dry friction (Coulomb model). The time response of the pendulum motion was found for different values of μ⁎. We consider two coefficients, one static μs⁎=0.7a and the other, dynamic μd⁎=0.5a, where a is a parameter (a=0.1, 0.25, 0.5, 0.75, 1). (a)) shows, the temporal variation of the x1 component of velocity Vx1 for two values of parameter a (the smallest and the largest, respectively), in all cases with k=k5, and (b) the relation (friction stress)/(normal stress) at point A vs. time (an instantaneous value of friction modulus μ⁎). One can see that this ratio alternates between static and dynamic friction, depending on conditions at each instant.Since the duration of a rigid pendulum period of the same size is about 1 s, every second the pendulum changes its angular velocity and it can be seen that instability occurs (stick-slip) due to an alternation between static and dynamic friction. The stick-slip becomes more evident when the friction module increases. Note that after 6 s the instability increases, coinciding with a decrease in the angular velocity of the pendulum. The instability after 6 s is remarkably noticeable in includes the energy change diagrams for a pendulum without friction (a=0) and with friction (a=1) for k=k5. Note the conservation of total energy in the first case. Similarly to the case of the rigid pendulum, the kinetic energy T is out of phase with the gravitational potential energy Ug. A small part of energy is exchanged with the elastic energy Ue. This analysis is useful for controlling the quality of the numerical solution because, in this case, the system is conservative. In the other case, the pendulum with friction, one can observe how the energy dissipates.This work has presented a brief review of the literature on the geometric stiffening of rotating flexible beams. Some of the several methodologies proposed in the literature to account for the stiffening effect in the dynamics equations were analyzed. The dynamics of a flexible beam under gravity (pendulum) and with a prescribed rotation were addressed with models of Strength of Material (SM) and the Finite Elasticity (Model NLTE). The SM approach was performed with two models, superposition of motions (Model SM1) and Hamilton's principle (Model SM2), in this both cases, the Poisson ratio ν is neglected. The latter included the stiffening effect. In the case of the superposition model, the equations are partially coupled. That is, only the deformation equations are coupled with the rigid motion but the rigid motion equations are uncoupled with the deformations. The nonlinearity is only present in the rigid-body motion. On the other hand, when applying Hamilton's principle, one has fully coupled equations. When the beam is subjected only to gravity, model NLTE yielded similar results to the ones obtained with SM theory (Model SM1). However, in the second example, since a very flexible beam with high rotational velocity was studied, the resulting deformations were not small, and consequently the responses were not identical. Obviously, the more flexible the body, the greater the differences between the linear and the nonlinear models.A flexible beam undergoing prescribed low-speed rotation was also studied. The stiffening effect in Model SM2 makes it possible to determine almost coincident values of frequencies found via finite deformation Model NLTE. As is well known from experiments, the vibration frequencies of a rotating beam increase as the angular velocity ω increases, which is associated with the stiffening effect introduced by the rotation. In the linear one-dimensional theory (Model SM2) the stiffening effect is due to the contribution of the second-order work done by the axial stress caused by the centrifugal force over the bending deformation. For the general case of the dynamics of the elastic body considering finite deformation theory of elasticity, it is not necessary to introduce additional terms in the equation of motion. That is, the SM2 theory can not only model the effect of stiffening due to centrifugal force, but also yields similar results than NLTE. This indicates that the stiffening law is correct. In the conservative pendulum case, the total energy composed of the gravitational, strain and kinetic parts remains constant in time. This is useful to check that the integration scheme introduces neither numerical damping nor instabilities in the solutions. The justification for using the full NLTE model is that it includes all effects and allows to tackle complex geometries. Obviously the CPU times are larger. Besides it allows to handle large deformations that can occur with very flexible beams and high rotational speeds. Furthermore, other complexities such a finite-dimensional pivot can be tackled by this approach. This case also includes the phenomenon of friction in the pivot responsible for the so-called stick-slip. The energy tracking allows, in this latter case, understanding how energy is dissipated in a flexible pendulum.Optical fiber sensor-based detection of partial discharges in power transformersIn this paper, a fiber optic acoustic sensor system is designed and tested for on-line detection of the partial discharges inside high voltage power transformers. The fiber optic sensor uses a silica diaphragm and a single mode optical fiber encapsulated in a silica glass tube to form an extrinsic Fabry–Perot interferometer. Test results indicate that the developed fiber optic sensors are capable of detecting the acoustic signals propagating inside the transformer oil with high resolution and high frequency.Power transformers are the most critical and costly component in power transmission systems. Catastrophic failures of power transformers can occur without warning, resulting in serious oil spills, fires, extensive damage to adjacent equipment, and major disruption of service. The cost of failures can easily drive the total cost of a single transformer failure into the tens of millions of dollars In general, three approaches can be used to detect partial discharges inside the power transformer including electrical, chemical and acoustic methods. The electrical method can provide accurate recordings of partial discharges under laboratory conditions, but it is difficult to be applied in the field on in-service transformers because of the high environmental noise level and lack of accurate calibrations. The current chemical approach detects PDs in transformers by taking gas or oil samples from the transformer. More recent research includes the development of gas sensors and applying them in on-line gas monitors Acoustic PD detection can be realized by mounting piezoelectric acoustic sensors externally on the walls of the power transformer, and very often a suitable couplant is used to ensure good transmission of the acoustic waves. The externally mounted piezoelectric acoustic sensor method offers the advantage of easy installation and replacement. However, the piezoelectric sensor suffers from corruption of the signal from environmental noises such as electro-magnetic interference (EMI). Another problem associated with the externally mounted piezoelectric sensor is that the multi-path of the acoustic wave transmission makes it difficult to locate the exact site of the partial discharges Optical fiber-based sensors have been shown to be attractive to measure a wide range of physical and chemical parameters because of a number of inherent advantages, including small size, light weight, high sensitivity, high frequency response, and immunity to electromagnetic interference. These advantages make optical fiber sensors an excellent candidate for transformer PD detection. Fiber optical acoustic sensors have shown useful in many applications, such as under water hydrophones fiber coupler. One fiber, referred to sensing arm, is exposed to the acoustic signal while the other, referred to reference arm, is shielded from the impact of the acoustic wave. The light beams propagating in the two arms are recombined either by their reflections (Michelson) or transmissions (Mach–Zehnder) to generate interference signals which are modulated by the acoustic waves. The intrinsic fiber interferometric sensors have shown very high sensitivities when a long fiber in the sensing is used. However, they suffer from the fringe fading problems resulting from the random polarization rotation. They are also unstable because of the source wavelength and the temperature-induced changes in the path length difference.More recently, fiber optic extrinsic Fabry–Perot interferometric (EFPI) sensors are under development for the applications of acoustic signal detection In this paper, we demonstrate a fiber optic EFPI prototype sensor system for inside detection of partial discharges in power transformers.The basic principle of the fiber optic acoustic sensor is illustrated in The system consists of a sensor probe, a laser diode, an optoelectronic signal-processing unit, and a single mode fiber linking the sensor probe and the signal-processing unit. The light from a distributed feedback (DFB) laser diode is launched into a 2×2 fiber coupler and propagates along the fiber to the sensor head (to reduce the optical feedback effect to DFB laser, an anti-reflection connector is used after DFB laser). As shown in the enlarged view of the sensor head, the lead in/out fiber and the thin silica glass diaphragm are bonded together in a cylindrical silica glass tube to form a Fabry–Perot sensing element. The incident light is first partially reflected (∼4%) at the endface of the lead in/out fiber due to the Fressnel reflection at the glass–air interface. The remainder of the light propagates across the air gap to the inner surface of the diaphragm. Because the inner surface of the diaphragm is coated with gold which reflects nearly all the incident light (∼96%), the fiber sensor is thus optically self-contained in any environments. This means that the optical signal is only a function of the length of the sealed cavity, and is immune to the diaphragm outer surface contamination resulting from the contact with transformer oil. The two reflections travel back along the same lead-in fiber through the same fiber coupler to the photodetection end. The interference of these two reflections produces sinusoidal intensity variations, referred to as interference fringes, as the air gap is continuously changed. One period of fringe variation corresponds to an air gap change of one-half of the optical wavelength, which in our case is about . As indicated in the enlarged view of the sensor head, the diaphragm is tilted at an angle with respect to the lead-in fiber endface so that only about 4% of the second reflection is captured by the fiber to ensure a maximum visibility of the interference fringes. illustrates the output interference fringes typically obtained from the fiber optic EFPI sensor. In principle, continuous tracking of phase changes in the interference fringes can yield information about air gap changes in the sensor element. The acoustic signal generated by partial discharges causes the deformation of the diaphragm and modulates the sealed air gap length. The sensor therefore gives outputs that correspond to the acoustic signals. Like regular interferometers, the measurement will have ultra-high sensitivity. However, the measurement would suffer from the disadvantages of sensitivity reduction and fringe direction ambiguity when the sensor reaches peaks or valleys of the fringes. Sensitivity is reduced at the peak or valley of a fringe since at that point the change in optical intensity is nearly zero for a small change in the air gap. Fringe direction ambiguity refers to the difficulty in determining whether the air gap is increasing or decreasing by detecting the optical intensity. If a measurement starts with an air gap corresponding to the peak of a fringe, the optical intensity will decrease, regardless of whether the gap increases or decreases. One of the key successes of our sensor is that a controlled bonding technique is used to fabricate the sensor so that the sensor operates only over the linear range of a half fringe. As shown in , the initial operating point is chosen to be the central point of the interference fringe, and the thickness of the diaphragm is designed in such a way that the imposed acoustic signal only deforms the thin diaphragm within the linear part of the sensor response curve. On the other hand, since the maximum amplitude of acoustic wave depend on the PD source and the damaged oil properties, the sensitivity of the sensor is selected carefully for matching different amplitude of the PD acoustic wave. Therefore the sensitivity reduction and fringe direction ambiguity problems can be completely avoided., the sensor head is fabricated by bonding the fiber, ferrule, silica tubing and silica diaphragm together to form a sealed fiber optic extrinsic Fabry–Perot interferometer. The diaphragm vibrates at the presence of an acoustic wave which imposes a dynamic pressure on the diaphragm. It is very important to design the sensor head to ensure high enough frequency response and sensitivity to achieve optimum detection of partial discharges.In the partial discharge detection, the sensitive frequency of the sensor system is suggested to be in the range of 20–, and the acoustic emission frequency of PD is mostly around , the frequency response fn of the sensor in terms of dynamic pressure load is given by the following equation:where α is a constant related to the vibrating modes of the diaphragm, and takes a value of 10.21 for the fundamental mode is the effective radius defined by the inner diameter of the silica sensor-housing glass tubing; h is the thickness of the diaphragm; g is the gravitational constant; w is the specific weight of the diaphragm material; and D is the flexural rigidity of the diaphragm defined bywhere μ is the Poisson's ratio (μ=0.17 for silica glass material at is the Young's modulus of the silica glass material at 25°C). For a fused silica glass diaphragm at . The frequency response of the sensor can thus be calculated by combining where h and R are in microns. As indicated by , the frequency response is proportional to the thickness of the diaphragm and inversely proportional to the square of the effective diaphragm radius. In practice, the diaphragm fundamental frequency is usually designed larger than to ensure the sensor have relative uniform response for the PD acoustic wave.The diaphragm will be deflected when there is a differential pressure p between the inside and outside sealed cavity. The out-of-plane deflection of the diaphragm y is a function of the pressure difference at any radium position r. The ratio between the deflection and the pressure difference is defined as the sensitivity of the sensor, which can be expressed asIn our sensor configuration, the fiber is positioned to the central part of the diaphragm so that only the center deflection y0 is of interest, which is given bywhere y0 is in microns, and p is in the pounds per square inch (psi), so η is in μm/psi. shows a typical sensor sensitivity curve at Based on these equations, the sensitivity and the frequency response of the sensor can be designed to fit different application requirements either by choosing diaphragm materials with different μ and E or by changing the geometric parameters of the sensor head with desired effective diaphragm size R and thickness h. In general, a diaphragm with a larger radius and a smaller thickness will render more sensitive detection of the acoustic signals. However, as indicated above, the operating range of the EFPI sensor head needs to be limited within the linear range, which is a fraction of an interference fringe to avoid the sensitivity reduction and fringe direction ambiguity problems. This imposes a limitation on the thickness of the silica diaphragm.A prototype fiber optic sensor system was built and tested to demonstrate the feasibility of on-line detection of partial discharges in power transformers. The prototype system uses a DFB laser at single mode fiber as the source. A high speed InGaAs detector is used to detect the optical signal from the sensor, and its output is fed to a low noise high gain trans-impedance amplifier. The frequency response of the electronic circuit is limited within a range from 30 to , defined by an additional band-pass filter.The analysis described above provides a clear guideline to the design of the fiber optic acoustic sensor for partial discharge detection. The inner diameter of the silica glass tubing is chosen to be , which limits the effective diaphragm radius to be . To satisfy the frequency response requirement, we choose the diaphragm thickness to be , which provides a upper frequency response of , therefore, the sensor provides a response of about Several sensor heads were made by bonding a single mode fiber, a silica glass ferrule, a silica glass tubing and a thin silica diaphragm together as shown in to . The ferrule used has an inner diameter of ; the tubing used has an inner diameter of . The sensor head is finished by polishing the diaphragm to the thickness of In the sensor fabrication, the initial air gap between the fiber and the inner surface of the silica diaphragm was adjusted to obtain the highest interference fringe visibility. The initial operating point was also adjusted to the central point of a fringe for linear operation and the highest detection sensitivity.To validate the feasibility of using the designed fiber optic sensors for the detection of partial discharges inside power transformers, a field test was performed at J.W. Harley, Inc., in Twinsburg, Ohio, where a specially designed testing facility ( is available to study the partial discharge phenomena power transformers. The testing facility is basically a simulated partial discharge environment inside high voltage power transformers, where a controlled needle-plate partial discharge generator (PDS) is immersed in the transformer oil.The fiber optic acoustic sensor (OFS) was immersed in the transformer oil with the diaphragm towards the needle-plate partial discharge generator, as shown in . The sensor probe was connected to the signal demodulation unit through a single mode fiber cable and an FC connector. After the photo-detection and the signal processing, the output data were digitized and recorded through a digital oscilloscope. shows the typical acoustic signal output from the fiber optic sensor at the events of partial discharges.A comparison test was performed between the Physical acoustic sensor (PZT shown in ) and the fiber sensor, arranged side by side. Their typical output signals upon partial discharges are given in where, (a) is the output from the Physical acoustic sensor and (b) is the output from the fiber sensor. The two sensors’ outputs resemble each other in details. Both the outputs indicate that the acoustic signal generated by a partial discharge comprise of sinusoidal pulses with a gradually decreasing amplitude. also shows that the two acoustic signal pulses detected by the two sensors have the same time period of about . This means that both sensors detected the partial discharge acoustic signal at a frequency of about , which is the typical frequency of partial discharge acoustic waves, as indicated by the literature When an acoustic wave generated by the partial discharge travels in the insulation medium of a transformer, its amplitude will attenuate over distance. Therefore, one of the possible methods to locate the site of the partial discharge source is to monitor the amplitude attenuation of the received acoustic signals. We measured the amplitudes of the acoustic signals detected by the fiber sensor at different distances away from the needle-plate partial discharge generator. The results are shown in which indicate that the amplitude of the acoustic signal has a strong dependence on the location distance between the sensor and the PD source. The largest distance tested was which is limited by the size of the oil tank of the testing facility.In conclusion, this paper has presented the development and testing of fiber optic acoustic sensor for inside-transformer partial discharge detection. The test results clearly demonstrated the feasibility of the developed fiber sensor for the detection of partial discharges inside electrical power transformers. Compared with the conventional acoustic sensors, the fiber optic sensor has the advantages of non-electrically conducting, high frequency response , immunity to the electro-magnetic interference (EMI), chemical inertness, and small size, and the capability of multiplexing more than one sensor in a single fiber, enabling on-line monitor of many power transformers at low cost.Characterization of mechanical and geometrical properties of a tube with axial and circumferential guided waves► Axial and circumferential guided waves are applied for material characterization. ► Theoretical model, laser ultrasound measurements and inversion are employed. ► Dispersion of circumferential guided waves are sensitive to the tube curvature. ► Dispersion of circumferential guided waves can extract the curvature information. ► Both types of guided waves can extract elastic modulus and thickness information.Guided waves propagating in cylindrical tubes are frequently applied for the characterization of material or geometrical properties of tubes. In a tube, guided waves can propagate in the axial direction and called axial guided waves, or in the circumferential direction called circumferential guided waves. Dispersion spectra for the axial and circumferential guided waves share some common behaviors and however exhibit some particular behaviors of their own. This study provides an investigation with theoretical modeling, experimental measurements, and a simplex-based inversion procedure to explore the similarity and difference between the axial guided waves and circumferential guided waves, aiming at providing useful information while axial and circumferential guided waves are applied in the area of material characterization. The sensitivity to the radius curvature for the circumferential guided waves dispersion spectra is a major point that makes circumferential guided waves different from axial guided waves. For the purpose of material characterization, both axial and circumferential guided waves are able to extract an elastic moduli and wall-thickness information from the dispersion spectra, however, radius information can only be extracted from the circumferential guided waves spectra.Motivated by various practical applications, researches in the nondestructive characterization of material or geometrical properties of tubes continue to be interested. For example, in the oil industry guided waves have been used for the inspection of pipelines involving with defects Among various techniques available for nondestructive characterization of material properties, those employing ultrasound techniques have been popular, due to the inherited nondestructive and convenient natures. Ultrasound techniques employing bulk wave technique are frequently used for material characterizations. Recently, ultrasound techniques based on guided waves draw more attention from researcher’s attention due to (a) long range inspection and (b) suitable for thin-walled tubes. Guided waves propagating in tubes can be grouped into two types, namely, axially propagating guided waves and circumferentially propagating guided waves. The axial guided waves can be further categorized into longitudinal mode, flexural mode and torsional mode To extract properties from dispersion spectra of guided waves, inversion process based on simplex algorism is a common procedure. In 1965, Nelder and Mead proposed the simplex method for solving minimum solution This study provides an investigation with theoretical calculation, experimental measurements, and a simplex-based inversion procedure to explore the similarity and difference between the axial and circumferential guided waves, aiming at providing useful information while these two categories of guided waves serve as candidates in the area of material characterization.A laser-generation/laser-detection laser ultrasound technique (LUT) is used for the measurements of dispersion spectra of circumferential and axial guided waves. As shown in , the experimental configuration consists of a pulsed laser for the generation of guided waves and a laser probe for the detection. The excitation source is a Nd:YAG laser with a power of approximately 100 mJ, a 532 nm wavelength, and a pulse duration of 6.6 ns. A laser Doppler optical receiver (OFV 511 and OFV 2700 by Polytec, Germany) is applied to detect the guided waves. A B-scan scheme is used for the measurement of the dispersion behaviors of guided waves. During the scanning, the optical detector is located at a fixed point, while the generation laser beam is scanned in the axial or circumferential direction. Along each of the paths there are 200 scanning steps with a step size of 0.05 mm. By accumulating the 200 steps, shows the B-scan data in a gray scale format for the circumferential guided wave.A two-dimensional fast Fourier transform (2D-FFT), first taken with respect to time and second with respect to scanned position, is used to obtain the dispersion spectra in the temporal frequency versus spatial frequency (ω |
− |
k) domain, where a ridge finding involving with peak-detection algorism is used to identify the guided modes.Following the measurements on the dispersion spectra of guided modes propagating in a tube, an inversion procedure can be employed to obtain properties of the samples. Among many inversion algorisms, simplex method is frequently used together with ultrasound measurements, and is adopted in this research.The procedure using the simplex algorism to extract properties from the measured dispersion spectra is illustrated in a block diagram in . In this algorism, the measured dispersion spectra from the tube are now used as an input data. Theoretical models for the calculations of dispersion spectra can be referred to , the algorism starts by choosing sets of initially guessed properties and adjusts the properties recursively until a tolerance is met to determine a set of properties. By substituting these properties into a theoretical model, a set of dispersion spectra are calculated and compared with the measurement. An objective function defined in the following equation is used as a measure of error between the calculated and measured dispersion spectra:, there are a total of n points selected for the evaluation of objective function. For each point with spatial frequencies ki, the measured and calculated temporal frequencies are represented as ω(ki)Experiment and ω(ki)Theory, respectively. The objective function Fobj is defined as the square sum of difference between the measured and calculated temporal frequencies.A benchmark test is performed before the inversion procedure is used to determine properties from LUT measurement. Purpose of performing the benchmark test is to test the convergence of the procedure related to the objective function, and not covering the effects of noise in the LUT data. In this benchmark test, the measured dispersion spectra in are fed with a set of dispersion spectra calculated using the theoretical model by substituting a set of prescribed properties. The procedure is then used to invert, or back-calculate, the properties, which are then compared with the prescribed properties. Quality of inversion algorism can be evaluated by checking the agreement between the inverted properties and the prescribed properties. In the determination of circumferential and axial guided waves dispersion spectra, there are five independent properties, namely, Young’s modulus (E), Poisson’s ratio (ν), mass density (ρ), wall-thickness (t) and outer radius (OR). In this benchmark test, ρ |
= 7.82 g/cm3 and OR |
= 4.5 mm are fixed while the inversion procedure is used to determine the other three properties, E, v, and t. A set of prescribed properties are given as E |
= 207 GPa, ν |
= 0.3 and t |
= 0.5 mm. shows the initially guessed and determined properties in the t–E subspace. It is shown that the determined properties corresponding to various initial guess converge to sets of values very close to the prescribed properties. Results of the benchmark test advocate the reliability for the inversion procedure in extracting properties from the dispersion spectra.In this research, the investigated sample is a Zircaloy tube with an outer radius of 4.745 mm and a wall-thickness of 0.570 mm. Young’s modulus and Poisson’s ratio from handbook for Zircaloy are 103.8 GPa and 0.315. Mass density is measured to be 6.613 g/cm3 by using the Archimedes principle. shows the calculated and measured circumferential guided waves dispersion spectra for the Zircaloy tube and for the axial guided waves. Although good agreement between the theoretical and measured dispersion spectra are both observed for the circumferential and axial guided waves cases, minor discrepancy can be observed for higher order modes of the dispersion spectra. Minor difference of material properties between the sample and the handbook are suspected to be responsible for the discrepancy. shows theoretical dispersion spectra of circumferential and axial guided waves for the Zircaloy tube for a comparison. These two sets of dispersion spectra merge into a single set in the small wavenumber (k), or long wavelength regime, however depart from each other as the wavenumber increases. Effects of thickness–radius (t–R) ratio on the dispersion behaviors of circumferential and axial guided waves are illustrated in . It is shown that the t–R ratio strongly influences the dispersion of the circumferentially guided waves all over the high-k regimes, while it is limited only to a very small regime in the low frequency part of L(0, 1) mode for the axial guided waves case.The ability in characterizing tube properties with circumferential and axial guided waves dispersion spectra are evaluated with two combinations of properties. For the first combination, similar to that in the benchmark test, E, v, and t are inverted, while ρ and OR are measured independently by the Archimedes principle and calipers. This combination has the purpose of probing the material and geometrical properties not easily obtainable from common measurement techniques. For the second combination, t and IR are inverted, while E, v, ρ are given. This combination has the purpose of probing pure geometrical properties in a non-contact way based on guided waves.For the first combination of inverted properties, a and b shows the guessed and determined properties in the E–v and E–t subspaces while circumferential guided waves spectra are used in the inversion. The initial guessed E values cover a range from 95 GPa to 115 GPa, v from 0.28 to 0.35, and t from 0.2 mm to 0.9 mm. In a simplex algorism, inversion of n parameters needs (n |
+ 1) initial guess values for each run. In , there are twenty initial guessed values for an inversion of three parameters for 5 runs. With circumferential waves, a shows that the determined E converges to a range of 101.88–102.63 GPa and average value at 102.26 GPa, v at 0.330 and t at 0.570 mm. The standard deviation of determined properties also listed at a. While using the axial guided waves spectra, b shows that the average of determined E is 101.80 GPa, v as 0.312, and t as 0.570 mm. The standard deviation of determined E, v, and t are listed at b. For the first property combination, both of inversion processes employing circumferential and axial guided waves show good convergence. Also, a comparison on the inverted t with measurements using optical microscope are listed in . Good agreement with low discrepancies of 0.02% for the circumferential guided waves case and 0.12% for the axial guided waves case are obtained. Finally, while the determined properties are back-substitute into the circumferential and axial guided waves theories, a shows the calculated and measured circumferential guided waves dispersion spectra and b for the axial guided waves. For circumferential and axial guided waves, the theoretically calculated dispersion spectra agree better with the measurements compared with For the second combination of inversion properties, a shows the initially guessed and determined properties in the IR–t space while circumferential guided waves spectra are used. Here, E |
= 102.26 GPa, ν |
= 0.330 and ρ |
= 6.613 g/cm3 are taken as known properties, while IR and t are inverted. a shows that the determined IR from different initial guesses covers a range from 4.136 mm to 4.212 mm, and average value at 4.192 mm. The average of determined values on t is 0.570 mm. Standard deviation of determined IR and t are listed in a. The convergence is tight with a standard deviation 0.74%. For the axial guided waves case in b, although t shows a tight convergence with a standard deviation 0 mm (0%), IR scatters in a wide range of standard deviation 2.005 mm (41.12%). A comparison of inverted IR and t are compared with independent measurements and listed in . Except the highly scattered IR values for the axial guided waves case, the inverted geometrical values agree well with the measurements with low discrepancy below 0.4%. While the determined properties are back-substitute into the theories, shows the dispersion spectra for the circumferential and axial guided waves. It is interesting that all the calculated dispersion spectra agree well with the measurements despite the large scattering in IR values. This phenomenon can be explained by the low sensitivity of IR to the dispersion spectra as shown in This paper reports a procedure and the associated results while axial guided waves and circumferential guided waves propagating in a tube are applied in characterizing properties of a tube. The procedure is based on a laser ultrasound technique for measuring dispersion spectra of guided waves followed by a simplex-based inversion algorism to extract material and geometrical properties. Accuracies of material characterization procedures based on circumferential or axial guided waves are evaluated in two categories of property combinations. While a combination of elastic modulus and wall-thickness (E, |
v, |
t) needs to be determined with the procedure, both circumferential and axial guided waves demonstrate themselves to have high accuracy in the procedure. In this case, the choice of circumferential or axial guided waves is only a consideration of equipment arrangement. However, in another combination of pure geometrical properties (t, |
IR), the procedure based on circumferential guided waves shows good accuracy, but not for the axial guided waves. A major difference between circumferential and axial guided waves is that circumferential guided waves dispersion is sensitive to thickness–radius of the tube but not for the axially guided waves.Experimental and numerical study performed on seismic behavior of irregular external SRC joints in the main plant of CAP1400 NPPThe main plant of steel reinforced concrete (SRC) structure is proposed for CAP1400 nuclear power plant (NPP) in high seismic zone, which not only has better mechanical properties than reinforced concrete structure plant, but also has lower maintenance cost than steel structure plant. The irregular SRC joints are inevitably appeared in the main plant due to the limitations of power generation technology and equipment. In this paper, quasi-static cyclic tests were carried out on three 1:4 reduced scale irregular external SRC joints to discuss the seismic performance of the joints in the NPP, mainly including the damage pattern, hysteretic behavior, load carrying capacity, stiffness degradation and ductility. In addition, the detailed 3D finite element (FE) models were established, in which the bond-slip behavior between the shaped steel and concrete was considered by using the developed software to add a huge number of non-linear spring elements, and the FE models were verified by the test results. Then, the parametric study on seismic performance of irregular external SRC joint was carried out, and the influence of each parameter on the seismic performance of the irregular external SRC joint was analyzed. Finally, the effective and economical reinforcement measures were proposed, and verified by the FE method.Thermal power generation relied on burning coal is the most traditional way of generating electricity, but it has serious problems of polluting the environment and accelerating global warming. Countries are advocating environmental protection and sustainable development The seismic precautionary intensity of the CAP1400 NPP to which the joint studied in this paper belongs is not less than 8 degree, and the design basic acceleration of ground motion is not less than 0.2 g, where g is the acceleration of gravity. The traditional structure can no longer guarantee the safety of the main plant of NPP with large capacity generator in high seismic zone, or it is found uneconomical. The traditional reinforced concrete (RC) structure cannot meet the requirements of structural safety, and the cross-sectional size of the beam and column is too large. The steel structure often has the problems of high maintenance cost and poor corrosion resistance The joint is the most critical position in the structure, which determines the reliability of the structure . The seismic design procedure and load carrying capacity calculation of irregular SRC joints in the CAP1400 NPP main building of SRC structure are not involved in the current code, and the seismic performance is not clear The purpose of this paper is to study the seismic performance of the irregular external SRC joint in the main plant of CAP1400 NPP. Firstly, pseudo-static cycle tests were carried out on three 1:4 reduced scale irregular external SRC joints. Based on the experimental results, damage pattern, force–displacement hysteretic response, force–displacement envelop curve and ductility ratio were discussed. Secondly, the finite element (FE) models of three joint specimens were established by ABAQUS and verified by experimental results. Then, the parametric study was carried out using the validated model to study the influence of the axial compression ratio, the ratio of cross-sectional depth of upper and lower columns, and concrete strength grade. Finally, the effective and economical reinforcement measures were proposed, and verified by the FE method.The irregular external SRC joints in this paper comes from the actual SRC main plant structure of CAP1400 NPP proposed by our research group, and it is composed of SRC beam, upper SRC column and lower SRC column. The design of the joint specimens follows the principle of “weak joint, strong components” to ensure shear failure in the core area of the joints. The three specimens in this paper are designed according to Technical specification for steel reinforced concrete composite structure (JGJ138-2001) The process of designing joint specimens was divided into three steps: The first step was to determine the size of the irregular external SRC joints in the actual main plant structure (the part between the inflection points of upper and lower columns). The second step was to determine the size of the joint specimen according to the ratio of 1:4, and it was necessary to keep the steel ratio and the hoop ratio the same. Finally, in order to ensure that the joint can successfully shear failure, rather than the upper column is damaged due to too high, the upper column height of the joint specimen has been adjusted slightly after the scale reduction. After adjustments, the height of the upper and lower columns was determined to be 1200 mm and 900 mm, respectively. The size of the shaped steel was selected according to the principle of the same steel ratio as the actual structure, and the stirrup was selected according to the principle of the same stirrup ratio as the actual structure. shows the cross sections of the beams and columns of the three specimens, and lists the design parameters of each specimen. The axial compression ratio of all joints is 0.3, and the concrete strength grade is C45. J1 is a regular exterior SRC joint with equal cross-sectional depth of the upper and lower columns (The cross-sectional depth of the upper and lower columns is equal to 400 mm). J2 and J3 are irregular SRC joints with unequal cross-sectional depth of the upper and lower columns (The cross-sectional depth of upper and lower columns is 300 mm and 400 mm, respectively). J2 and J1 only have different cross-sectional depth of the upper column, which are used to study the influence of cross-sectional depth difference between the upper and lower columns on the seismic performance. J3 and J2 only have unequal cross-sectional depth of the beams, which are used to study the influence of cross-sectional depth of beam on the seismic performance.When pouring the joint specimens, the cube test specimens with the size of 150 mm × 150 mm × 150 mm are reserved to determine the strength of concrete of joint specimens lists the strength and modulus of elasticity of steel measured by experiments. These steels in are the steels used in the specimens in shows the loading device for quasi-static cyclic test.An axial force and a horizontal cyclic load are applied to the upper end of the upper column. The bottom of the lower column is hinged to the ground, which limits the translational displacement of the bottom. The vertical translational displacement of the end of the beam is limited by the tie rod. The loading process is divided into two steps: the first step is to apply the vertical load and remain unchanged during the later test process; the second step is to apply the cyclic load in the horizontal direction. When a horizontal cyclic load is applied, load control is used before yielding and the load for each level is repeated once, while displacement control is used after yielding and the load for each level is repeated three times. The loading is stopped when the horizontal load drops to 85% of the peak load The damage pattern of each joint is shown in (a)-(c), and the typical damage pattern is shown in (d). The damage pattern of regular SRC joint (J1) is X-shaped crack along the diagonal of the rectangular core region, which is similar to the conclusion of previous study on regular SRC joint The force–displacement hysteretic curves of the joints are shown in that the force–displacement hysteretic curves of all joints are stable and the pinch phenomenon is not obvious. It is different from the ordinary reinforced concrete joints, indicating that the seismic performance of such joints is better. The comparison of (a) and (b) shows that the force–displacement hysteretic curve of J2 is thinner than that of J1, and the peak of J2 is smaller than that of J1, which indicates that the seismic performance of J1 performed relatively better than J2. The core region determines the seismic performance of the joint. However, the cross-sectional depth of the upper column of J2 is smaller than that of the lower column, resulting in the volume of the core region of J2 being smaller than that of J1. The comparison of (b) and (c) shows that the force–displacement hysteretic curve of J3 is thinner than that of J2, and the peak value is smaller than that of J2. The reason is that the cross-sectional depth of beam of J3 is smaller than that of J2, which results in the volume of the core region of J3 being smaller than J2; therefore, the seismic performance of J2 performed relatively better than J3. shows the force–displacement envelop curves of the joints. The force–displacement envelop curve can more easily reflect the difference of load carrying capacity. that: (1) due to the decrease in the cross-sectional depth of the upper column, the positive and negative peak loads of J2 are reduced by 14.85% and 11.12%, respectively, compared with J1; (2) due to the decrease in the cross-sectional depth of the beam, the positive and negative peak loads of J3 are reduced by 27.15% and 35.32%, respectively, compared with J2.The displacement ductility ratio (u) is used to describe the deformation capacity of the joints, and u=Δu/Δy lists the ductility ratio of each joint. that the ductility of J2 is slightly lower than that of J1, the reason is that the cross-sectional depth of the upper column is smaller than that of the lower column; the ductility of J3 slightly lower than that of J2 because the cross-sectional depth of beam is less than J2.Secant stiffness is used to describe the stiffness degradation of the joint and calculated as follow where: Ki is the secant stiffness of the joint under the i-th load; Pji is the peak load under the i-th load of the displacement j; Δjiis the horizontal displacement corresponding toPji; n is the load cycle times at each level. shows the stiffness degradation curves of each joint in the positive and negative directions. The stiffness of J2 is less than that of J1, and the stiffness of J3 is less than that of J2. It shows that both the decrease of the cross-sectional depth of the upper column and beam will reduce the stiffness of such joints under cyclic loading.Concrete Damaged Plasticity (CDP) model is used to simulate the tensile and compressive behavior of concrete under cyclic load, where the dilation angle is 30 degrees; the eccentricity is 0.1; the fb0/fc0 is 1.16; the K is 0.6667; the viscosity parameter is 0.005. The stress–strain curves of GB50010-2010 is used for concreteThe compressive stress–strain curve is defined as follows:dc=1-ρcn/(n-1+xn)x≤11-ρc/(αc(x-1)2+x)x>1where αc is the parameter of declining stage; fc,r is the compressive strength of concrete; εc,r is the strain corresponding to fc,r; dc is the compression damage evolution coefficient.The tensile stress–strain curve of concrete is defined as follows:where αtis the parameter of the declining stage; ft,r is the tensile strength of the concrete; εt,r is the peak tensile strain of the concrete corresponding to ft,r; dt is the evolution coefficient of tension damage of concrete.The damage factor is calculated according to the following formula obtained by energy method The ideal elastoplastic model is used for the rebars and the shaped steel.The C3D8R, T3D2, and S4R are used for concrete, rebars, and the shaped steel, respectively.The spring2 element in Abaqus is a spring element with two nodes that can be used to simulate the nonlinear relationship between force and deformation. Liu used spring 2 element to conduct a detailed FE analysis of the bond-slip behavior between steel and concrete, which proved that it is reliable to consider the bond-slip behavior with spring 2 element The nonlinear spring element can only be added by modifying the Inp file, which can be divided into three steps: (1) Find the number of coincident shaped steel and concrete nodes at the interface, it is very difficult because the number of the shaped steel and concrete nodes at the interface are randomly distributed. (2) Input to the Inp file in the format required by ABAQUS, as shown in (a). (3) Define the nonlinear force–displacement (F-D) relationship for the spring element, as shown in (b). The method and difficulty for adding the spring element will be described below by taking (a) shows the form of the spring element. In the first line, “type = Spring2″ means that the spring element type is ”Spring2″, and “elset = Spring_upcol_F1″ means that the next spring elements belong to the set named ”Spring_upcol_F1″. The code after the first line is the spring elements, where the first column is the number of the spring element, the second column is the nodes on the shaped steel, and the third column is the nodes on the concrete at the interface. And the coordinate of the steel node and concrete node of each row is completely equal, that is, the positions of the two nodes are coincident in the three-dimensional FE model. Taking the second line (“63, steel-1.50, concrete-1.155″) as an example, ”63″ is the number of the spring element, and “steel-1.50″ indicates the node numbered 50 on the shaped steel; for all nodes on the shaped steel, ”steel-1.“ is fixed. Similarly, ”concrete-1.155″ means the node numbered 155 on the concrete; for all concrete nodes, “concrete-1.” is fixed. It is worth emphasizing that the coordinates of the No. 50 steel node and the No. 155 concrete node are completely equal, that is, the two nodes are coincident in the three-dimensional FE model.(b) shows the form of the F-D curve, and lists the codes of F-D curve of FE model, where the first column is the line number used to explain the code, the second column is the code of the F-D curve in the Inp file, and the third column is the explanation of the code.“NONLINEAR” in the first row means that all spring elements are nonlinear spring elements, and “elset = Spring_upcol_F1″ indicates that the F-D curve is defined for all spring elements in the set named ” Spring_upcol_F1″. The second line is the direction of the spring element. The third row and later represent a specific nonlinear force–displacement (F-D) relationship, where the second column is the deformation D of the spring element and the first column is the force F corresponding to the deformation D. Liu describes in detail the specific requirements and difficulties of adding nonlinear spring element In order to solve the above problem, the software for automatically adding a huge number of nonlinear spring elements was developed in this paper, which greatly improved the efficiency and accuracy of modeling. The graphical user interface of the software for automatically modeling spring elements is shown in F-D curve is the most important property of nonlinear spring element, which should be calculated according to τ-s constitutive relation as follows:Where: F is the force of the spring element, τ is the bond stress of the node where the spring element is located, and Ai is the area around the spring element, as shown in the shaded part in . Ai,corner, Ai,outer,Ai,inner are the area around the corner, outer, and inter spring element, respectively.In this paper, τ-s constitutive relation is defined according to the following formula proposed by Yang Where: τ¯s is the average initial slip strength, τ¯u is the average ultimate strength, τ¯r is average residual bond strength, Su is the slip corresponding to ultimate bond strength, Ssu is the slip of turning point, and Sr is the slip corresponding to the starting point of the horizontal residual stage. These parameters are calculated according to the following formula:The FE model established in this paper is shown in (d) is the assembled model of the joint.In order to get high quality mesh, the concrete and the shaped steel must be properly cut, as shown in the (a)-(b). After cutting, it is ensured that the shaped steel and concrete have coincident nodes at the interface to modeling the spring element.The pressure damage (DEMAGEC) is used to represent the distribution of cracks in the core region of the joint in this paper. shows the distribution of DEMAGEC obtained by FE method and the crack distribution obtained by test. It can be seen from that the damage pattern obtained by the FE method is basically the same as the test, the damage occurs in the core region, and the final damage pattern is the crack along the diagonal of the trapezoidal core region. shows the comparison between the force–displacement hysteretic curve obtained by the FE method and experiment. shows that the FE model proposed in this paper can accurately describe the hysteretic response of irregular exterior SRC joint, of course, it is worth noting that there are still some errors, which may come from the FE model, such as the assumption of material isotropy, the CDP model of concrete, the ideal elastic–plastic assumption of the constitutive model of steel. The error may also come from the test, such as measurement and loading, etc.Since the force–displacement envelop curve can more easily reflect the gap in load carrying capacity, shows the force–displacement envelop curve calculated by the FE method and the quasi-static cyclic test. that the FE model proposed in this paper can accurately simulate the force–displacement envelop curve of such irregular exterior SRC joints. It can accurately calculate the yield load, yield displacement and ultimate displacement of such joints.Based on the validated FE model, more models are further analyzed by the FE method proposed above to study the influence of the ratio of cross-sectional depth of upper and lower columns, the axial compression ratio and the concrete strength on the shear load carrying capacity of the joint. In this paper, η is defined as the ratio of cross-sectional depth of upper and lower columns, which is calculated according to the following formula:where: Hu is the cross-sectional depth of upper column, Hl is the cross-sectional depth of lower column. shows the parameters of the joint specimens used for parametric study.For J-1, 2, 3, only the cross-sectional depth difference between upper and lower column is different, and is 50, 100 and 150, respectively; For J2, 4, 5, 6, only the axial compression ratio is different, and is 0.3, 0.4, 0.5 and 0.6, respectively; For J2, 7, 8, and 9, only the concrete strength grade is different, and is C45, C35, C55, and C65, respectively.J-1, 2, 3 are used to study the influence of the reduction of the cross-sectional depth of upper column on the seismic performance of such joints. The force–displacement envelop curves of J-1, 2, 3 is shown in It can be found that the seismic performance and shear capacity of such joint decrease with the increase of cross-sectional depth difference. Compared with the joint with η equal to 1, the maximum values of the positive loading of joint with η equal to 0.875, 0.75, and 0.625 decreased by 9.83%, 12.34%, and 17.83%, respectively, and the maximum value of negative loading decreased by 5.82%, 7.19% and 12.99%, respectively. The reason is that the reduction of the cross-sectional depth of the upper column leads to the reduction of the volume of the core region of the joint, which weakens the seismic performance of the joint.J2, 4, 5 and 6 are used to study the influence of axial compression ratio on the seismic performance of such joints. The force–displacement envelop curves are shown in shows that the seismic performance and shear capacity of such joints increase with the increase of axial compression ratio. Compared with the joint with Axial compression ratio of 0.5, the maximum values of the positive loading of joint with axial compression ratio of 0.4, 0.3 and 0.2 decreased by 3.52%, 6.43% and 10.00%, respectively, and the maximum value of negative loading decreased by 3.25%, 6.49% and 10.31%, respectively. The reason is that the constraint effect on the concrete in the core region increase with the increase of axial compression ratio.The concrete strength grades of J2, 7, 8, and 9 are C35, C45, C55, C65 respectively, which are used to study the influence of concrete strength on such joints. shows force–displacement envelop curves of J2, 7, 8, and 9.With the increase of concrete strength, the seismic performance of joints is improved. Compared with the joint of concrete strength grade of C65, the maximum value of the positive loading of the joint with concrete strength grades of C55, C45 and C35 decreased by 1.84%, 4.74% and 6.86%, respectively, and the maximum value of negative loading decreased by 3.01%, 6.26% and 9.86%, respectively. It is worth noting that the influence before the peak is bigger, while the influence after the peak is smaller. The reason is that the concrete bears most of the horizontal load before the peak value, and the damage of the concrete after the peak value is more and more serious, and therefore the contribution to the shear capacity is less and less.The mechanics mechanism of the concrete in the core region is the inclined compression rod model, as shown in Before the specimen is cracked, the concrete in the core region of the joint resists most of the shear force. As the load increases, oblique cracks occur along the diagonal direction of the joint, which forms the inclined compression rod. The shear load carrying capacity of concrete depends on the compressive capacity of the inclined compression rod.After the specimen is cracked, the shaped steel in the core region gradually participates in resisting the shearing force. The core shaped steel can be regarded as the “frame + shear wall” system, as shown in The mechanical mechanism of stirrup in the core region is the truss model, as shown in After the steel web yielding, the shear force resisted by the stirrups in the core region increases rapidly, and the strain of stirrup in the core region increases rapidly. At this time, stirrups can not only limit the development of concrete cracks in the core region, but also resist a small part of shear. Stirrups and longitudinal bars in the core region form the truss model.When the load carrying capacity reached the maximum value, the shaped steel and stirrups also yielded. In future research, we will analyze the stress changes of different parts in different stages in detail, and put forward the calculation formula of load carrying capacity based on more finite element analysis.Based on the above analysis, it was found that the seismic performance and load carrying capacity of the regular SRC joint performed relatively better than such irregular exterior SRC joint. However, such joints cannot be avoided in the main power plant of the nuclear power plant. Therefore, such irregular exterior SRC joint must be reinforced. The reinforcement plan and effects will be explained in detail below.The method of adding stiffeners to the shaped steel in the core region of the joint was proposed. The specific measures are shown in . Through the FE analysis, it can be found that these reinforcement methods are economic and effective. The irregular exterior SRC joint with an upper column of 300 mm is used to illustrate the reinforcing effect. shows the comparison of force–displacement hysteretic response before and after reinforcement. shows that the four reinforcement measures can effectively improve the hysteretic performance of the joint. shows the comparison of force–displacement envelop curves before and after reinforcement. that the four reinforcement measures can effectively improve the seismic load carrying capacity of such irregular exterior SRC joints. Compared with the unreinforced joint, the positive peak load of plan 1, 2, 3 and 4 is increased by 13.23%, 7.31%, 8.25% and 9.26%, respectively; the negative peak load of plan 1, 2, 3 and 4 is increased by 12.42%, 8.37%, 7.49% and 9.49%, respectively.Interestingly, the positive and negative peak loads of the unreinforced regular SRC exterior joint in (the cross-sectional depth of the upper column = 400 and the cross-sectional depth of the lower column = 400) are 118.55 MPa and −113.01 MPa, while the positive and negative peak loads of the irregular exterior SRC joints (the cross-sectional depth of the upper column = 300 and the cross-sectional depth of the lower column = 400) strengthened by Plan 1 are 117.66 MPa and −111.80 MPa, which shows that the reinforcement measures of Plan 1 can save about 25% of the steel and concrete, and can ensure that the load carrying capacity does not decline.In order to study the seismic performance of irregular exterior SRC joint in the main building of SRC structure CAP1400 NPP, the quasi-static cyclic tests were carried out on three 1:4 reduced scale irregular exterior SRC joints, and the force–displacement hysteretic response, force–displacement envelop curves, stiffness degradation and ductility of the irregular exterior SRC joint were analyzed. Secondly, the detailed FE model of irregular exterior SRC joints was established, in which a large number of spring elements were used to consider the bond-slip behavior of the interface, and the FE model was verified by test results. Then, the parameter analysis of the seismic performance of such joint was carried out to discuss the effects of different parameters. Finally, the economical and effective reinforcement measures were proposed and verified by the FE method. The key conclusions can be drawn as follows:Through the quasi-static cyclic tests, it was found that the seismic performance of regular joints performed relatively better than irregular exterior SRC joints due to the reduction of the cross-sectional depth of upper column. Irregular joints have lower load carrying capacity, lower ductility and stiffness. The seismic performance of irregular exterior SRC joint decreases with the increase of the cross-sectional depth difference between the upper and lower columns, and decreases with the decrease of the cross-sectional depth of the beam.The method and difficulty of using spring element to consider bond-slip behavior of irregular exterior SRC joints were introduced in detail. In order to solve the problem, this paper proposed the method that can efficiently and accurately build a large number of spring elements in the FE model of SRC members to consider the bond behavior of the interface. Compared with the experimental results, the FE model proposed can accurately simulate the damage pattern, hysteretic performance and force–displacement envelop curve. The proposed model can also accurately simulate the stiffness degradation and ductility because it can accurately simulate the force–displacement envelop curve.Through parameter study, it was found that the seismic load carrying capacity of such joint decreases with the increase of cross-sectional depth difference between the upper and lower column, the reason is that the reduction of the cross-sectional depth of the upper column leads to the reduction of the volume of the core region of the joint. The seismic load carrying capacity increase with the increase of axial compression ratio due to increase of constraint effect on the concrete in the core region. The seismic load carrying capacity of joint increases with the increase of concrete strength, and it is worth noting that the influence before the peak is bigger, while the influence after the peak is smaller. The reason is that the concrete bears most of the load before the peak value, and the damage of the concrete after the peak value is more and more serious, and therefore the contribution of concrete in the core region to the shear capacity is less and less.Four kinds of reinforcement plans were proposed: diagonal reinforcement, short diagonal reinforcement, long diagonal reinforcement, and horizontal + vertical reinforcement. Compared with the unreinforced joint, the positive load carrying capacity of the joint strengthened by these four measures is increased by 13.23%, 7.31%, 8.25% and 9.26%, respectively; the negative load carrying capacity is increased by 12.42%, 8.37%, 7.49% and 9.49%, respectively.Interestingly, the load carrying capacity of the irregular exterior SRC joint (the cross-sectional depth of the upper and lower columns are 300 mm and 400 mm, respectively) strengthened by diagonal reinforcement method is basically the same as that of the regular SRC joint (the cross-sectional depth of the upper and lower columns is equal to 400 mm), which shows that the reinforcement method can save 25% steel and concrete.Biao Liu: In this manuscript, the idea of the manuscript, the reading and review of required references, analysis of test data, establishment of finite element model, development of software for adding spring elements, all finite element analysis, comparison of the results of finite element analysis and test, proposal of reinforcement plan, analysis of mechanism mechanics, the writing of the manuscript, the submission of the manuscript, and the revision of the manuscript were conducted by Biao Liu.Guo-Liang Bai: The specimen design, experiment process and analysis of experiment results were guided by Guo-Liang Bai, and the funding was supported by the fund applied by Guo-Liang Bai.Jin-Quan Zhao: The design of the specimens, the production of the specimens, and the description of the experimental phenomenon were conducted by Jin-Quan Zhao.Jia-Rui Li: The analysis of the experimental phenomena and other auxiliary work were conducted by Jia-Rui Li.All the authors read and approved the revised manuscript.The authors declared that they have no conflicts of interest to this work.Deformation-induced nanocrystallization and its influence on work hardening in a bulk amorphous matrix compositeWith the development of various processes to produce bulk amorphous composites with enhanced plasticity, investigations of the mechanical behaviors of the amorphous alloys in the plastic regime have now become feasible. In addition to dramatically enhanced plasticity, some bulk amorphous composites have exhibited a work hardening behavior during plastic deformation. Considering that most strengthening mechanisms, such as solid solution hardening, martensitic hardening, etc., operative in crystalline metals are associated with dislocations, the work hardening behavior observed from amorphous composites, where dislocations do not exist, is of a special scientific interest. We have observed that quasistatic compression imposed to the amorphous composite induces the homogeneous precipitation of nanocrystallites from the amorphous matrix of the composite, which, in turn, leads to strengthening the amorphous composite. The strengthening mechanism of the amorphous matrix composite is investigated as well.Extensive researches have been carried out to develop various bulk amorphous materials due to their superior mechanical properties suitable for structural applications. The mechanical properties of the amorphous materials can further be improved by promoting the homogeneous precipitation of nanocrystallites within the amorphous matrix.Since amorphous alloys are not in thermodynamic equilibrium, phase transformation from the amorphous to the more stable crystalline phase can take place with the supply of external energy. Temperature and deformation (or stress) are the two most significant categories of driving forces affecting this transformation. Thermal annealing has been typically used to produce thermally induced nanocrystallites that are homogeneously distributed in the amorphous matrix Since mechanical deformation strongly induces nanocrystallite formation, and thermal energy induces a uniformly distributed nanocrystallite formation, the simultaneous application of both mechanical deformation and thermal energy causes an abundant and homogeneous formation of nanocrystallites. Kim et al. Unlike the uniformly precipitated nanocrystallites induced by thermal annealing, the deformation-induced nanocrystallites observed from the earlier studies were viewed only from a very localized area, such as regions near shear bands of the bent specimens or beneath the indent of the indented specimens. Such features are thought to be due to the loading methods and loading time employed in the studies. Under these experimental conditions, higher stress (or deformation) will concentrate only at regions near the propagating shear bands or beneath the indents with a duration of at most ∼10 s. As a result, atoms located at regions away from the bands or the indents, where the stress level is not as high, do not have chances to be supplied with sufficient energy enough to transform into more stable phases. If loading is quasistatic to allow more time for atoms to be rearranged, homogeneous precipitation of nanocrystallites may take place in amorphous alloys even at room temperature. Therefore, it is of interest to examine whether a homogeneous precipitation of nanocrystallites occurs under quasistatic loading at room temperature and to study its effect on the mechanical properties of the amorphous alloy. To our knowledge, no information is currently available on the formation of nanocrystallites during quasistatic deformation at room temperature. Understanding of the formation mechanism of nanocrystallites in the amorphous alloy subjected to quasistatic deformation is important not only to better design amorphous alloys, but also to develop various post-treatment processes suitable for improving the mechanical properties of amorphous alloys.The chemical composition of the bulk amorphous composite used in this study was (Cu60Zr30Ti10)0.95Ta5 (in atomic percent). The alloy was prepared by arc melting the high purity Ti (99.9%), Cu (99.9%), Zr (99.9%), and Ta (99.9%) under a purified argon atmosphere; Master alloy ingots for casting were prepared by first melting Zr and Ta together. This binary alloy was then melted with Cu, Zr, and Ti. The ingot was remelted several times to ensure microstructural homogeneity and then cast into a copper mold to produce a 40-mm long cylindrical rod with a diameter of 1 mm. To compare the thermal properties of the (Cu60Zr30Ti10)0.95Ta5 composite with the Cu60Zr30Ti10 alloy, the Cu60Zr30Ti10 alloy ribbons were prepared by ejecting the melt through a nozzle with an over-pressure of 50 kPa onto a Cu wheel rotating with a tangential speed of 40 m/s. Samples for compression tests were cut from the cast rod. Room temperature uniaxial compression tests were conducted on 2-mm long sections under a strain rate of ∼10−4/s.The thermal properties of the monolithic amorphous alloy and the amorphous matrix composite were examined using differential scanning calorimetry (DSC) at a constant heating rate of 10 K/min in a flowing argon atmosphere. Variations in the hardness of the phases within the composite were measured as a function of the plastic strain using an ultra-micro-Vickers hardness tester under a 10 g load. At least three measurements were made along the specimen’s long axis at positions evenly spaced by 90 μm.The structures of the specimens were analyzed by X-ray diffraction (XRD) with Cu Kα radiation. Samples for transmission electron microcopy (TEM) were perforated by chemical jet thinning using a solution of 10% perchlolic acid in ethanol at a temperature −40 °C. The chemical reaction product covering the disc was removed by subsequent ion milling for about 1–2 min. Detailed structures were examined with high-resolution transmission electron microscopy (HRTEM) coupled with electron energy loss spectroscopy (EELS). is the microstructure of the as-cast (Cu60Zr30Ti10)0.95Ta5 amorphous matrix composite (hereinafter composite), showing the composite structure consisting of uniformly dispersed crystalline particles (white phase) in the amorphous matrix (dark area). is the TEM bright field image and the corresponding selected area diffraction pattern (SADP) recorded from the matrix of the composite, showing the typical characteristics of an amorphous phase. is the bright field image and corresponding SADP recorded from the crystalline particle. Although exact chemical composition of the crystalline particles is not known, based on XRD and SADP of TEM, they were identified as a bcc phase with a lattice constant of 3.25 Å. Considering that the lattice constant of Ta being 3.3206 Å, the particles are thought to be a Ta-rich solid solution containing Ti and Zr. According to the image analysis, the average size and the volume fraction of these particles are ∼10 μm and 8.0%, respectively. shows the DSC traces obtained from the melt-spun Cu60Zr30Ti10 specimen and the injection-cast (Cu60Zr30Ti10)0.95Ta5 composite specimen. The DSC trace obtained from the melt spun Cu60Zr30Ti10 specimen exhibits one endothermic event, i.e., characteristics of the glass transition to a supercooled liquid state, followed by a couple of exothermic reactions associated with consecutive crystallization of the supercooled liquid. The glass transition and the crystallization temperature were 456 and 478 °C, respectively. It is noted that the glass transition and the crystallization onset temperature for the (Cu60Zr30Ti10)0.95Ta5 composite were almost identical to those of the melt-spun Cu60Zr30Ti10 specimen within the measurement accuracy. However, the amount of the exothermic heat for the first crystallization peak decreased from 31.2 to 28.2 J/g. Less heat measured from the composite is considered to be due to the presence of the Ta-rich particles, which, upon heating, do not involve in crystallization. Therefore, it is regarded that the chemical composition of the matrix of the (Cu60Zr30Ti10)0.95Ta5 composite is nearly the same as that of the Cu60Zr30Ti10 alloy. Various thermal properties corresponding to the melt-spun Cu60Zr30Ti10 specimen and the injection-cast (Cu60Zr30Ti10)0.95Ta5 composite specimen are summarized in is the engineering stress–strain curves corresponding to the Cu60Zr30Ti10 alloy and the (Cu60Zr30Ti10)0.95Ta5 composite measured under quasistatic (10−4/s) compression. In each case, the samples were tested to failure. The two materials exhibited elasticity up to the strain of ∼2%, followed by plastic deformation. The Cu60Zr30Ti10 alloy exhibits yielding with the ultimate strength of 2106 MPa and a mean fracture strain of ∼3.5%, while the (Cu60Zr30Ti10)0.95Ta5 composite demonstrates the ultimate strength of 2332 MPa with a dramatically enhanced fracture strain of ∼15.3%. The yield strength (∼1930 MPa) of the (Cu60Zr30Ti10)0.95Ta5 composite is slightly lower than that (∼1983 MPa) of the monolithic Cu60Zr30Ti10 amorphous alloy due to the presence of the ductile crystalline Ta-rich phase. However, the (Cu60Zr30Ti10)0.95Ta5 composite showed work hardening associated with the enhanced plasticity, resulting in the higher fracture strength.It is well known that bulk amorphous metals fail by the formation of shear bands upon loading. Considering that the plastic deformation achieved by bulk amorphous metals is virtually confined at narrow regions near shear bands, the two specimens considered in this study should differ both in the number density and the shape of shear bands. Presented in are the SEM micrographs recorded from the side surfaces of the fractured Cu60Zr30Ti10 and (Cu60Zr30Ti10)0.95Ta5 specimens, showing completely different patterns of shear bands. Observation of the monolithic Cu60Zr30Ti10 sample showed that only a few long and clean-cut shear bands were developed, while a number of shear bands have formed over the entire length of the (Cu60Zr30Ti10)0.95Ta5 composite sample. In addition, as compared to long and clan-cut shear bands observed from the Cu60Zr30Ti10 amorphous alloy, shear bands observed from the composite sample are characterized as short and winding. The major shear bands are oriented at an approximately angle of 48° with respect to compression, which is similar to the direction of the maximum shear stress, i.e., 45°.Although the enhanced plasticity observed from the composite allows us to explore the mechanical behaviors in the plastic regime, detailed mechanisms for the enhanced plasticity will not be treated further in this study and only the strengthening mechanism of the amorphous composite will be discussed. With this regard, it is still questionable if the plastic flow in is accompanied by the work hardening. This questionnaire arises because calculations to construct the stress–strain curves in neither compensated changes in the specimen’s cross-sectional area associated with the formation of shear steps and cracks, nor took the instantaneous changes of the specimen’s cross-section during testing into account. As such, one may consider that the increasing tendency in the stress in could contain a certain degree of unintended artifact caused by the measurement technique. To confirm the work hardening behavior in , a tapered-cylindrical rod for the compression test was machined such that the cross-sectional area of one end of the rod is smaller than the other as shown by the inset of . Such a geometry of the test specimen facilitates plastic deformation in a progressive and controlled manner upon compression, enabling introduction of different amount of strains into the specimen. Prior to compression, the side surface of the specimen was polished to mirror image so that micro-indentation can be made directly on the matrix and the Ta-rich particle at evenly spaced positions along the specimen’s long axis. shows the variations in the hardness of the matrix and the Ta-rich particle measured as a function of the strain subjected to the composite specimen. The hardness of the amorphous matrix was observed to increase linearly with increasing strain, while the hardness of the Ta-rich particle did not vary. This experimental result obtained from micro-indentation again confirmed the work hardening behavior observed from the quasistatic compression test. Work hardening behaviors similar to that observed from the present study can also be found from the other amorphous composites In general, work hardening observed from the crystalline metals is associated with dislocations. Considering that dislocations neither exist, nor are mobile within the amorphous materials, the work hardening behavior shown by the (Cu60Zr30Ti10)0.95Ta5 composite is quite unique and unusual. Since the hardness of the Ta-rich particles did not vary significantly even after compression, actual strengthening of ∼400 MPa associated with the plastic deformation of the composite in cannot be explained based on the strengthening of the Ta-rich particles. This initiated us to probe detailed microstructural changes in the matrix of the deformed composite. is the TEM bright field image recorded from the matrix of the deformed composite, showing the presence of gray spots with an average size of ∼10 nm embedded in the amorphous matrix. The diffraction ring in the SADP pattern in confirms that the image contrast is resulted by the presence of nanocrystallites. The HRTEM image of the gray spots shows lattice fringes as in , further validating the crystalline state of the gray spots. Careful observations of the nanocrystallites confirmed that the nanocrystallites are free from dislocations. Therefore, they can be regarded as a perfect crystal having a theoretical strength. Details regarding the effect of the nanocrystallites on the strength of the composite are discussed in proceeding section.Quantitative analyses on the chemical composition of the nanocrystallites and the remaining amorphous matrix were made using EELS. As can be seen from the jump ratio image in , Cu enrichment was noted from the nanocrystallites, while Cu depletion was observed from the amorphous matrix. Although the measured chemical composition does not represent the exact composition of the nanocrystallites and the remaining amorphous matrix, the average Cu content of the nanocrystallites is approximately 75%, while that in the amorphous matrix is approximately 50%. Such a result is in a relatively good agreement with that obtained by Jiang et al. Judging from the diffraction ring of the SADP as indicated by the arrow in , the degree of crystallinity of the deformed composite appears to be considerable. However, it is very difficult to determine the true volume fraction of the nanocrystallites directly from the TEM images, since nanocrystallites observed from TEM are viewed in superposition. On the other hand, DSC has been widely employed to estimate the volume fraction of a crystalline phase; assuming that the amount of the heat flow associated with crystallization is inversely proportional to the volume fraction of a crystalline phase in an amorphous matrix, the volume fractions of the crystalline phase can be estimated by comparing the amount of the heat flow obtained from the deformed composite with that of the as-cast composite. Shown in are the DSC curves recorded from the as-cast and the deformed composite specimen, showing dissimilar thermal behaviors. When comparing the DSC trace recorded from the deformed composite specimen with that of the as-cast one, less heat associated with the first crystallization as well as the disappearance of the glass transition temperature were noted from the deformed composite specimen. These features obtained from the deformed composite provide direct evidence that homogeneous precipitation of nanocrystallites has taken place to some extent during quasistatic compression. According to the measurement of the exothermic heat corresponding to the first crystallization recorded from the two specimens, it was noticed that the amount of the heat associated with the crystallization in the deformed composite is ∼10% smaller than that of the as-cast composite, indicating that the crystallization has proceeded by ∼10 vol% during quasistatic compression.The effect of the deformation-induced nanocrystallization on the work hardening behavior was studied based on the experimental observations. The strengthening mechanism was theoretically investigated using the phase mixture model.The deformation-induced phase transformations have been known to take place in various materials such as ceramics, polymers, and metals, which have different bonding structures. In some cases, these phase transformations have been successfully applied to commercialization. Crystallization of some commonly used polymers during shaping has long been known as the result of the deformation subjected to the workpiece In general, the hardness of nanocrystallites is higher than that of amorphous phases. This is because the size of the nanocrystallites is so small that both dislocations and other types of defects can neither form, nor be active within the nanocrystallites. Therefore, they can be regarded as a perfect crystal having a theoretical shear strength of τ≈G/2π and the shear modulus of Cu ranges from 37 to 45 GPa depending on microstructures. the normal strength of the Cu-rich nanocrystallites is expected to be 10–12 GPa. Considering that the normal strength of the Cu-based amorphous alloys is ∼2 GPa, nanocrystallites can serve as a reinforcing phase. In addition, in contrast to the localized distribution of the nanocrystallites generated under dynamic loading, the nanocrystallites precipitated due to quasistatic compression were observed to disperse uniformly throughout the amorphous matrix. Such observations can explain the work hardening behavior of the amorphous composite.In order to analyze the strengthening behavior of amorphous composites during deformation, the phase mixture model shows a schematic diagram of the phase mixture model in the partially devitrified amorphous nanocomposites by precipitation in the amorphous matrix. Here, the Ta-rich particles are not shown because they do not contribute the hardening of the composites, as already seen in . As the deformation-induced nanocrystallization proceeds, solute elements rejected from the Cu-rich nanocrystallites are distributed in the remaining amorphous matrix, leading to a change in the solute concentration there (i.e., solute enrichment). It would not be necessary to consider dislocation motion especially in the case of amorphous and nanocrystalline materials, since there are hardly any dislocations. Therefore, the rule of mixtures, Eq. , based on the volume fraction of each phase is eligible to describe the effective strength of the mixture. Indeed, the rule of mixtures based on the volume fraction of each phase agrees well with the results of the finite element analysis of the unit cell model where V is the volume fraction of each phase and the subscripts am, Ta, and Cu represent the amorphous matrix, Ta-rich particles, and the Cu-rich nanocrystallites, respectively. The phase mixture model can be used to predict the overall strength of the amorphous matrix composite. Assuming that the volume fraction and the strength of the Ta-rich particles being 9.2% and 600–700 MPa, the strength of the composite calculated from the phase mixture model was predicted as ∼2600 MPa. Considering that the predicted strength is the upper bound value, the prediction agrees reasonably well with the measured strength, 2332 MPa. shows the schematic plot for the contributions of the strengthening of the residual amorphous matrix due to solute enrichment, Ta-rich particles, and Cu-rich nanocrystallites to the total strengthening of the (Cu60Zr30Ti10)0.95Ta5 composite. Since VTa and σTa are constant during the deformation as can be seen in microstructure and particle hardness measurement in , Ta-rich particles do not contribute to the strengthening of the amorphous composite. Although the hardness increase of the amorphous matrix alone by solute enrichment is high, as is usually found in the Al-based and Zr-based amorphous alloys Therefore, the amount of strengthening in the stress–strain curve () is comparable to the hardness increase in the matrix containing the Cu-rich nanocrystallites (). The more detail numerical analysis is to be performed in the future.The present work confirmed that work hardening does indeed take place in a bulk amorphous composite during quasistatic compression. Unlike most strengthening mechanisms operative in polycrystalline materials, the work hardening observed from the amorphous alloy is due to the formation of homogeneously distributed nanocrystallites that have precipitated in the amorphous matrix of the amorphous composite imposed to quasistatic compression. Nanocrystallites precipitated in the matrix during quasistatic deformation were observed to be a Cu-rich perfect crystal, which is free from dislocations and, therefore, can serve as the reinforcement. The phase mixture model has been successfully applied to quantitatively describe the strengthening behavior and to predict the strength of the amorphous composite.On the joining of steel and aluminium by means of a new friction melt bonding processA new lap welding process for dissimilar materials has been developed and tested for steel-to-aluminium joints. A simple cylindrical tool is rotated and translated over the top steel plate, leading to a transient partial melting of the bottom aluminium plate and the formation of intermetallic reaction layers of FeAl3 and Fe2Al5 as thin as 2.5 μm. Lap shear tests of the welds show very good resistance with fracture mostly in the base materials. |
Assembling dissimilar materials within integrated structures is nowadays a stringent requirement related to improved performance. It is particularly the case for the transportation industry that needs to reduce the weight of structures while still improving their strength and crashworthiness. While efforts are carried out to continuously improve the mechanical properties of new steel grades up to levels unreachable by other materials, as in the case of advanced high-strength steels, Al alloys also present very interesting levels of specific strength that easily ensure lightweight structures, as demonstrated by their ever-increasing use in transport applications. Consequently, the need for an efficient technology to join steel and Al alloys arises in the automotive industry to ensure profitability and lightness of the vehicles in addition to efficient sealing of the joints.The main difficulty in joining steel and Al alloys results from the large difference in their respective range of solid-state stability, but also from their large reactivity leading to the formation of brittle intermetallic layers at their interface Among the various solutions that have been proposed to reduce the heat input and thus to control the interface reactivity Friction stir welding (FSW) is another solid-state joining process which has been widely investigated for welding dissimilar materials, in particular Al alloys and steel, in a butt-joint The present study aims at reporting a new welding technique . The rotating tool then advances along the surface at a predetermined speed. Frictional heat is generated due to the intimate contact between the pressed rotating tool and the top sheet. In addition, plastic deformation occurs below the rotating tool, also contributing to the temperature increase In order to demonstrate the sequence of reactions while avoiding complex metallurgical issues, simple steel and Al grades were first tested. A microalloyed ultralow-carbon (ULC) steel with the composition (wt.%) 0.013C, 0.136Mn, 0.01Si, 0.005S, 0.0132P, 0.002Ti, 0.003Nb,<0.0008N was used as the high-melting-point material. Cold-rolled and annealed sheets 0.8 mm thick with a mean grain size of 13 μm were used. 1 mm thick Al 1050 or 2 mm thick Al 2024 T3 sheets were used as the low-melting-point material. Sheets were 250 mm long and 80 mm wide. The surfaces were cleaned with acetone prior to stacking and welding. A tungsten carbide tool 16 mm in diameter was tilted backwards by 0.5°. The welding machine was controlled in displacement while the rotation rate was set at 2000 rpm for the whole set of experiments. The advancing speed ranged from 100 to 700 mm min−1.After welding, the joints were cross-sectioned by electrical discharge machining perpendicular to the welding direction for metallographic analyses and tensile testing. The transverse sections of the joints were observed by scanning electron microscopy (SEM) with back-scattered electrons (BSEs). In addition, the structure of the joints as well as the diffusion processes were characterixed by energy-dispersive X-ray spectroscopy (EDX) and electron backscatter diffraction (EBSD). Transverse lap shear tests were performed on rectangular specimens with a width of 10 mm, at room temperature and with a crosshead speed of 1 mm min−1. The recorded loads were normalized by the initial transverse section area of the sample at the fracture location, i.e. Al or steel sheets or lap-joints. SEM and EDX were also carried out on the fracture surfaces.The typical microstructure of the joints is illustrated in in the case of the Al 1050–ULC couple welded at 400 mm min−1. Three zones can be distinguished on the SEM micrographs, the Al and steel sheets being separated by a reactive layer. Close to the interface, the Al presents a solidification microstructure with a dendritic structure separated by an eutectic structure containing Fe-rich precipitates. Some large precipitates were indexed by EBSD (see ) as FeAl3, in agreement with Bouché et al. As a consequence of the melting of the Al, an intermetallic reaction layer (IML) is formed at the interface with the steel sheet due to the reactivity between the molten Al and the solid steel. For all advancing speeds investigated, two IMLs were indexed by EBSD. first shows that both FeAl3 on the Al side and Fe2Al5 on the steel side are formed at the interface. These conclusions were validated by BSE SEM micrographs and EDX measurements, even though the different intermetallics have similar chemical compositions requiring accurate measurements. also shows that nanosized grains constitute the FeAl3 layer, while grains of Fe2Al5 are tongue-shaped and larger. These results are consistent with previous studies shows that the thickness of the IML (considering both layers as a whole) decreases similarly for the two Al alloys when increasing the tool advancing speed, which corresponds to a decrease in the heat input during the welding process. Indeed, faster advancing speeds involve locally shorter reaction times. This intuitive result was already observed for other welding techniques, such as friction stir diffusion bonding In addition to the IML thickness, the tool advancing speed also influences to a large extent the Al resolidification process through the resulting cooling rates. In the case of the Al 2024 grade, porosities several microns in size appear in the resolidified Al, 15–20 μm below the IML, when the advancing speed is >400 mm min−1 (see c). This zone corresponds to the last liquid Al that solidifies. This phenomenon was confirmed by EDX analyses that showed larger concentrations of the Al alloying elements (Cu and Mg) close to the porosities, in agreement with the solidus on the phase diagrams a presents the evolution as a function of the tool advancing speed of the engineering strength at the onset of necking of transverse lap shear tests. Three sets of constant levels of strength with the advancing speed can be observed that are related to the location of the necking and fracture; these levels depend on the composition of Al alloy. On the one hand, in the case of the 1 mm thick 1050 Al–ULC steel joints, fracture occurs in the Al sheet at 4.5–5 mm from the centre of the joint, namely in the heat-affected zone. Whatever the advancing speed and the resulting IML thickness, the maximum engineering strengths are similar with a mean value of 76 MPa. The Al 1050 base metal exhibits an ultimate tensile strength (UTS) of 100 MPa, while heat treatments at 620 °C for 3 and 10 min, mimicking the heat-affected zone, lead to UTSs of 90 and 65 MPa, respectively. On the other hand, in the case of the 2 mm thick Al 2024–ULC steel joints, fracture occurs mostly in the steel sheet for low advancing speeds (200–400 mm min−1), as shown in b. The mean strength is roughly similar to the UTS of the base ULC steel (289 MPa vs. 300 MPa). The joints processed at a faster advancing speed (500–700 mm min−1) broke at lower engineering strengths. Indeed, fracture occurs following the porosities resulting from the last solidified liquid Al reported above (see c). Between 400 and 500 mm min−1, both fracture locations are observed, suggesting that this range of welding speeds corresponds to a transition in the fracture mode resulting from a significant level of solidification porosities in the weld.c clearly show that the IML does not initiate fracture, no conclusions can be drawn about the effect of the IML thickness on the weld transverse lap shear strength. For FSW or diffusion bonding in a butt-joint configuration, Tanaka et al. predicted that stronger joints result from thinner IML, with an optimum thickness around 0.5–1.5 μm ) that do not deteriorate the weld strength with respect to the base material, even for IMLs up to 6–8 μm thick.ULC steel has been successfully welded to 1050 or 2024 Al alloys by a new simple and efficient process based on transient liquid bonding. Two IMLs were identified at the Fe–Al interface: Fe2Al5 on the steel side and FeAl3 on the Al side. The thickness of the Fe2Al5 IML decreases with increasing tool advancing speed, whereas the FeAl3 IML thickness remains constant at ∼1 μm. A solidification microstructure with FeAl3 precipitates was observed in the Al alloy. For advancing speeds >400 mm min−1, porosities appear in the last liquid zone of the Al 2024 where larger Cu and Mg concentrations were highlighted. Fracture occurred either in 1050 Al or ULC steel at UTSs close to that of the base materials. However, when porosities appeared in the 2024 Al, fracture occurred in the last liquid zone of the 2024 Al, 15–20 μm below the interface, leading to a slight decrease in the strength. Based on these results, the welding process developed here can be considered a promising technique for joining steel to Al alloys or other combinations of metallic materials with different melting points.A system integration framework through development of ISO 10303-based product model for steel bridgesThis study has developed a product model based on ISO 10303 to overcome problems such as data loss during transferring and sharing project data. The developed product model electronically represents three-dimensional shapes, structural analysis and structural design information of steel bridges. The product model for semantic description of a steel bridge is employed as data structure of an integrated database management system (DBMS) by which steel bridge information can be managed and operated. The DBMS can be made to release restraints such as each different location and heterogeneous computer environments. End-users may be able to freely access steel bridge information of the DBMS on the network. This study also presents a framework for practical management of steel bridge information generated from existing tools by using open standards and web technology. An integrated computer environment can be built by applying this framework composed of product model, data repository, application modules, and programming interfaces to civil engineering fields.Large-scale construction projects are managed by a so-called virtual enterprise, which must coordinate work among different organizations and teams for the whole life cycle. Since this virtual enterprise usually has some restraints such as each different physical location and heterogeneous computer platforms, it causes many problems during transferring and sharing numerous data generated from the same project. Open standards and web technology can be mechanisms that overcome these problems caused by distributed organizations and various computer environments In the construction industry, the development of open standards has made considerable progress with respect to building product model In the case of studies related to product models for bridge structure, Mikami et al. Various studies using web technology have been widely implemented in many fields of the construction industry to facilitate access to needed information. Song et al. In information management of bridge projects, a product model is required so that standardized data such as shape and structural analysis information generated from existing application programs may be reused and shared. However, existing product models related to bridges are not sufficient to satisfy these requirements. Thus, this study has developed a product model for electronic representation of steel bridges based on ISO 10303. The product model aims to electronically describe three-dimensional shapes, structural analysis and structural design information. The product model describes project data of steel bridges with superstructure type such as steel truss, steel plate girder, and steel box girder. The product model is developed according to the methodology for the development of product data specification of ISO 10303. It refers to integrated resources approved as international standard by ISO. Especially, this study uses PART 42 The two approaches are applied to define a product model for the representation of three-dimensional shapes, planning, structural analysis, and structural design information generated over the life cycle of steel bridge projects. The first one shown in applies a hierarchical structure of a product to the steel bridge structure to define the product model. In the manufacturing domain, the definition of the term ‘product’ is described as the object produced by the manufacturing system (a) can be decomposed into some components or assemblies, which are in turn composed of structural bridge members, by applying a hierarchical structure of a product to the physical composition of a steel plate girder. As shown in (b), this study makes abstraction product data corresponding to the physical composition of structural members to semantically represent the decomposed structural steel bridge members of (a). This first approach allows the product model developer to semantically represent the steel bridge data according to the hierarchical structure of a product.The second approach defines product data specifications by using the methodology and application protocols already approved as international standard by ISO 10303. The ISO 10303 development methodology governs the development and standardization of data specifications that are suitable for neutral file exchange as well as providing the basis for shared product databases and archiving. In , this approach for the development of product model is roughly displayed in a graphical diagram form. The data pool of is the conceptual grouping of all information requirements generated by the analysis of project activities. The information requirements are defined by reference to an application activity model (AAM). An AAM is created using IDEF0 (b). Geometric data, which is the three-dimensional shape information separated from the data pool, is replaced by Part 42 or AP 203 EXPRESS This study analyzed the planning, design, construction and maintenance process of steel bridge project according to IDEF0 method. Activities diagrams shown in describe information flow of activities for structural design and its subactivities among whole life-cycle stages. These activities are used to not only analyze information flows of structural design activities, but also determine information scope to be included within a product model. The defined AAM of the steel bridge project is described by AIϕ WIN program of Knowledge Based System, Inc. implementing IDEF0 methodology. Within the AAM, information flow is shown as a number of ICOM arrows. These ICOM arrows may be inputs, controls, outputs, or mechanisms for the activities. The fundamental principle of the IDEF0 methodology is that an input is converted into an output by an activity. A control governs when and how an activity occurs, while a mechanism is something that is used during an activity. A component manufacturer could view this as a way of representing the system whereby raw materials (the input) are processed (the activity) to produce a product (the output) using some manufacturing plant (the mechanism) that is controlled by a production schedule (the control). Of particular interest in the AAM are the inputs and outputs that represent flows of information between the activities. These inputs and outputs are used as aforementioned UoFs and form the basis of the data pool. For example, output arrows–structural analysis results, project technical specification, detailed design results, and design specification–are used as UoFs of product model in the activities of the structural design of This paper presents a product model that is subdivided into seven submodels in order to satisfy the aforementioned information requirements. The submodels cover planning, structural analysis, and structural design information over the life cycle of steel bridge project. Project data generated in the construction and management stage is outside the scope of this study. Especially since bridge maintenance information has been managed by the existing Bridge Management System (BMS), this study considered the connection with the system by using an open standard to exchange the data.To verify whether EXPRESS schema of the defined product model conforms to criteria of EXPRESS language reference manual PROJECT model encompasses project overview, structure overview, and design information. Bridge entity, which is a super-entity for the representation of a bridge structure, is categorized as both steel and concrete structure according to the kind of material (see ). To extend the product model of a steel bridge, a concrete structure may be defined. To represent the product data of a steel bridge superstructure and substructure, a bridge entity refers not only to multiple values of a superstructure entity and substructure entity. The location attribute of a bridge_outline entity represents geographic coordinate data, which can link steel bridge information with the NGIS (National Geographic Information System) developed by the Korean government. Structural_outline entity inherited from bridge_outline entity represents information about various structural design criteria and global load applied to structural design. This submodel covers measurement, magnitude and unit information using types and entities of measure_schema contained in the ISO 10303 Part 41 (fundamentals of product description and support) BRIDGE COMPONENT model describes the major components of a steel bridge structure. Bridge_component entity is subdivided into superstructure and substructure entities (see BRIDGE MEMBER model describes the structural design information of a steel bridge comprised of eight structural members categorized by the BRIDGE COMPONENT model. In the EXPRESS-G diagram shown in This study used the product model, which is defined in the ISO 10303 Part 104 or AP 209 (composite and metallic structural analysis and related design) APPLICATION CONTEXT model refers to entity definitions of application_context_schema of ISO 10303 Part 41 (See ). This model represents an aspect of the application context; a discipline type, which is an identification of the engineering or manufacturing category to which the product belongs; life-cycle stage; market segment type, which is an identification of the category that characterizes potential purchases; and library reference, which is an identification of the library that provides a context for the element of the library as a schema for application protocols to define a frame of reference or context that applies to particular sets of product data. Since an application_context entity is a context in which product data is defined, it represents various types of information that relate to product data and may affect the meaning and usage of that data. This study adopted the entity definitions of application_context_schema to explicitly specify the use of ISO 10303 AP 203 and AP 209. In this study, AP 203 is used to represent three-dimensional shapes of a steel bridge and AP 209 is the representation for structural analysis data of the steel bridge. Especially the application_protocol_definition entity of the schema allows a newly defined product model to include a variety of existing product model. This study also makes use of product_defintion_context entity to represent the life-cycle stage of the product data generated from steel bridge project.SHAPE AND SECTION PROPERTY model is a submodel that represents section properties and geometric shapes of structural members based on the three-dimensional solid model. The section properties of a structural member are constructed by connecting the shape information represented by the three-dimensional solid model. As shown in , the shape entity, which is a super-entity of the shape and section property model, is defined by referring to multiple shape_representation entities as solid_shape attribute values. The shape entity can represent the shape of a structural member by grouping the structural members of a steel bridge. A shape_representation entity, which is one of the AP 203 entities, may represent a three-dimensional geometric shape into a constructive solid geometry (CSG) or boundary representation solid model. This study represents the geometric shape information in accordance with boundary representation solid model corresponding to the AP 203 conformance class 6, which is the implementation level for a commercial CAD/CAE software development. The boundary representation method represents a 3D solid model as a collection of boundary surfaces. The 3D solid data records both the surface geometry and the topological relations among these surfaces. The method can be conveniently used for hidden surface removal and rendering due to the directly available surface information of the modeled objects. The solid is defined by specifying that all points on one side of the boundary of an object are outside and those on the other side are inside of the object. Therefore, 3D shape-based steel bridge information, which is comprised of 3D shape and product data of steel bridges, can be not only recognized by a human being but also interpreted by a computer. A prismatic_shape entity inherited from the shape entity describes the prismatic cross section of a linear structural member and represents the types of member shapes into seven subentities such as angle_shape, rectangle_shape, channel_shape, circle_shape, h_shape, t_shape, and i_shape entity. Complex_shape entity is defined by three subentities to represent structural members with non-prismatic shape. It can be possible to represent bolts and nuts of a joint connection using bolt_shape and nut_shape entity. A cross section with an arbitrary shape can be represented by arbitraty_shape entity. A deck plate of a superstructure can be described by using arbitrary_shape entity. This study only includes 3D shape and description information of concrete members such as deck plate, pier, abutment, and footing.MATERIAL model defines material properties applied to structural members. The material is classified into steel, concrete, and user-defined materials. As shown in EXPRESS-G diagram of , the material entity defines the material properties of a structural member using thermal_expansion attribute, which is the thermal expansion coefficient; elasticity attribute, which is the modulus of elasticity; poisson_ratio attribute, which is the Poisson's ratio; and the weight_density attribute, which is the weight density. The entity also allows additionally needed material data to be expanded. Steel_material, concrete_material, and user_defined_material entities, which are inherited from the material entity, describe the material properties required at the structural design stage. Steel_material entity includes attribute value to define the yield stress of steel material and concrete_material entity includes attribute value to describe the concrete strength, shear strength, and yield stress of a reinforcing bar. Since the material entity is not connected with a structural member, part_element_map entity should be defined to link material property and structural member. That is, the part_element_map entity allows material entity get multiple values of the bridge_member entity.JOINT SYSTEM model represents structural connection among structural members. The connection type is defined by either a welded or mechanical type. As shown in , joint_system entity, which is a super-entity of this submodel, represents the connection among structural members by defining the data type of connected_assembly attribute into bridge_member entity. A joint_system_mechanical entity defining the mechanical type refers to fastener entity with multiple values for the fastener's attribute. The mechanical joint type, which refers to the type specified by joint_system_mechanical_type in the mechanism attribute, is one of a bolted, pinned, and riveted joint type. Accordingly, joint_system_mechanical entity can describe mechanical type of a joint system fastening bolt, nut, washer, and plate. Joint connection information of welded type describes subentities that are categorized by point, line, and surface welding in joint_system_welded entity. The point type describes a spot weld. The line type has an associated curve that defines the path of the weld. The surface is defined to cover a bounded area on a surface. Especially, weld_specification attribute of joint_system_welded entity represents information about welding type and penetration scope.After developing the product model of steel bridges based on the ISO 10303, this paper presents the implementation framework that improves work efficiency and productivity of a steel bridge project by transferring and sharing product data over the project's life cycle in . The presented framework is composed of four subcomponents: product model, data repository, application programs, and application programming interface (API). Since the framework is based on a product model for each application field and various component technologies, an integrated computer environment can be built by various CAD/CAE/CAx tools. Component technologies used to build the framework are the STEP physical file format, EXPRESS-X The PRODUCT MODEL is made up of seven submodels hierarchically representing steel bridge information by the entity–attribute relationship diagram, AP 203 model representing geometric shape information, and AP 209 model representing structural analysis information. Since the product model is described in EXPRESS language, the model allows a computer to parse steel bridge information. The developed product model may be proposed as data structures of data repository to operate steel bridge information in an integrated database management system. In addition, it can be used as a target schema in the mapping process using a structural data mapping language, called EXPRESS-X in the part of INTERFACE I. Also, it can be used in developing application programming interfaces for data input/output as a data structure of STEP physical file format, formally known as ISO 10303 Part 21. To apply the product model into data structures of RDBMS, EXPRESS schema using object-oriented techniques should be translated into SQL schema. This study translated EXPRESS schema into SQL schema by using existing method, defined by ST-Oracle The REPOSITORY is a conceptual term. It is not a single database but a centralized and integrated database that can be accessed by many application programs through the network. After translating entities, attributes, and relationships represented by EXPRESS schema into DDL (Data Definition Language) code for the relational DBMS, the REPOSITORY is constructed by defining table, tuple, and attribute in relational DBMS domain (see ). The operated information within the REPOSITORY covers project overview, structural member, section shape and physical property, material property, and connection information of steel bridges. Also, it covers structural analysis information such as analysis model, analysis results, and load condition as well as three-dimensional solid model information generated from CAD/CAE/CAx programs. Although the product model described by EXPRESS language is developed using object-oriented techniques, the REPOSITORY is implemented by using not object-oriented DBMS, but relational DBMS commonly used in practical work.The REPOSITORY based on the product model of steel bridges can be interfaced from various application programs. This study divides the application programming interfaces into INTERFACE I and II.INTERFACE I saves the STEP physical file into the REPOSITORY or provides information extracted from the REPOSITORY to application programs. To translate a STEP physical file for each different application field into STEP physical file in accordance with product model of steel bridges, mapping process should be accompanied. The mapping process is carried out by mapping schema, written in EXPRESS-X language, between the data defined by the product model of steel bridges and the data defined by another EXPRESS model. However, since this study directly generates a STEP physical file in accordance with the product model of steel bridges within the application program, a mapping schema is not required. The STEP physical file may be translated into relational database management system by the translator.INTERFACE II allows end-users to access steel bridge information operated by the REPOSITORY without limitation to time, space, and computer environment through internet and intranet. REPOSITORY can be accessed through ODBC that provides a standardized set of rules for getting information to and from a database management system. The end-user can search the needed information from the REPOSITORY containing steel bridge information by using DML (Data Manipulation Language) syntax of SQL, used as a query language in relation DBMS. Graphical user interface is also required to create query statement to search information stored within the REPOSITORY. To develop this graphical user interface, this study used ASP and Java script languages on the web service such as the Internet Information Service, which is proposed by Windows 2000 of Microsoft Corp.The application part of the framework shown in is made up of APPLICATION I and II. Two parts correspond to stand-alone CAD/CAE/CAx programs used in practical work and web application programs that reside on the web server.APPLICATION I stands for various stand-alone application programs related to civil engineering fields such as the CAD program for detailed design information and the CAE program for structural analysis. These programs should generate output data into STEP physical file format by individual work process. For example, to transfer and share structural analysis information, the application program should be able to manipulate STEP file based on AP 209 product model of ISO 10303. Thus, every application program within APPLICATION I should include programming interfaces for input/output into the STEP physical file to perform two-way communication with an integrated database management system, i.e., the REPOSITORY.APPLICATION II means a web-based application program that allows the access of steel bridge information and proposes many application functions to end-users with different physical locations. These application programs can be provided on the internet and intranet. This study implemented an application program with which end-users were able to access three-dimensional shapes of steel bridges on the web browser like Internet Explorer and Netscape. These application programs enable overcome restraints by each different physical location and various computer platform environments of the end-user.According to the presented framework for management of steel bridge information, this study implemented a pilot system satisfying requirements of subcomponents of the framework, as shown in To build the repository, any kind of information generated from a steel bridge project over the whole life cycle is required. This study developed a graphical user interface for data manipulation between product data of a steel bridge and the three-dimensional shape information on the AutoCAD program, as shown in . Since the AutoCAD program allows the end-user to draw steel bridge shape using a three-dimensional solid model, the three-dimensional shape can be linked to the product data of a steel bridge like a section or material property of a structural member by the graphical user interface. Therefore, this study adopted AutoCAD as a stand-alone application program that allows end-users to interface with programming classes automatically generated in accordance with product model by standard compiler. AutoCAD was used because it is a computer-aided design program that is most commonly used in construction fields and support functionalities for implementation of graphical user interface.The user interface program for the generation of a STEP physical file in accordance with the presented product model is implemented as follows. As shown in , this study generates product model of steel bridges described by EXPRESS schema into C++ classes using ST-Developer The user interface program allows not only the end-users to use all the AutoCAD functionalities, but also the application developers to embed an additionally required functionality by end-users. Similarly, since the product data assigned to each shape of a structural design member of steel bridge can be imported or exported into/from a STEP physical file format based on the product model through standard input/output interfaces, the product data of steel bridges can be stored into the REPOSITORY.This section represents product data of the Hannam bridge, i.e., the first grade steel bridge which is located on the Han River in Seoul, Korea, and was open at 1969 with the Kyungbu expressway. The design information of a structural member and the three-dimensional shape information for the first span of the seven-span Hannam bridge shown in are generated into a STEP physical file of in accordance with the product model of steel bridges by using the graphical user interface on the AutoCAD program.Since the superstructure of first span of the Hannam bridge called “NM1” is a steel plate girder, the product configuration can be applied to the Hannam bridge. A STEP physical file based on the product model of the steel bridge can be generated. The #32 and #33 stand for the stringer and the #41, #42, and #43 stand for the cross-beam of the first span of the bridge (see ). These structural members can be represented by PART entity, which is one of the entities of the presented EXPRESS schema. The #36, #46, and #47 with bolted-splice joint of is represented by JOINT_SYSTEM entity. Structural members and shape information corresponding to the #32, #33 and #36 of among several steel bridge members are described into STEP physical file format in is called by the name of the structural member “NM1-stringer1” and the member type means a stringer represented into ‘.STRINGER.’ in the type value. The shape information related to structural design member is covered by the #200 and #201. As a representative example, the #200 of stands for structural design member with rectangular cross section shape by instances of RECTANGLE_SHAPE entity. Cross-sectional property of the #32, i.e., the depth of the cross section is 12.0 mm and the width is 400.0 mm, is written in STEP physical file. The #36 of makes using JOINT_SYSTEM entity and referenced entities represent a mechanical connection of stringer in the structural design member. The fastener used at the mechanical connection, as shown in , stands for bolted joints by using JOINT_SYSTEM_MECHANICAL entity. The #36 in the STEP physical file describes the joint type of bolted joints into ‘.BOLTED_TYPE.’ in the type value and lets the shape information of the joint type refer to the multiple shape values, i.e., #206, #210, #212, #213, and #220. Because the #220 stands for the shape and property information of the bolt, it can represent a high-strength bolt connection by ‘.HIGH_STRENGTH_BOLT.’ in the type value and shows that the bolt diameter is 10 mm. Through these processes, the product model for representation of a steel bridge design may be able to write the shape and structural design information of the Hannam bridge into the STEP physical file format.EXPRESS-X is a structural data mapping language. The language enables the specification of the mapping relation between different product models. To manage and operate data of CAD/CAE/CAx program of APPLICATION I within the integrated database management system, as shown in , data mapping between the data should be accompanied. To perform the data mapping, a mapping schema written in EXPRESS-X language should be specified in accordance with interrelation between two product models. Thus, data mapping between two product models needs two product model schema and two mapping schema. The first of the product model schemas is an EXPRESS schema that stands for the individual aspect product models like AP 203, CIS/2, and AP 209 as a source schema. The second of the product model schemas is a target schema, which is an EXPRESS schema representing data structure of the integrated database management system for the manipulation of steel bridge information. The last one is an EXPRESS-X mapping schema that defines the relationship between first EXPRESS schema and second EXPRESS schema. That is, this mapping schema is used to translate a STEP physical file with a product model in accordance with each application field into a STEP physical file based on a steel bridge product model.This study developed a translator using ST-Oracle produced by STEP Tools, Inc. in order to build the REPOSITORY by uploading a STEP physical file of into the relational database management system. The STEP physical file includes three-dimensional shapes and product data of the Hannam bridge generated from AutoCAD by graphical user interfaces. is a schematic form of translation process of a STEP physical file into ORACLE DBMS.The product model written in EXPRESS schema is required to develop this translator. The EXPRESS schema is checked and parsed by a STEP compiler and saved as metadata. The metadata is directly used when it generates DDL statements and code creating table and relation within RDBMS and develops application programming interfaces to upload and download a STEP physical file from RDBMS. Since this study adopted ORACLE as a RDBMS for building and operating the REPOSITORY, the translator is able to upload or download the needed data from the REPOSITORY by using Pro*C, a precompiler. Through these processes, the developed translator allows end-users to automatically store a STEP physical file into the REPOSITORY or extract a needed data from the REPOSITORY.A web application module visually displayed data extracting three-dimensional shape and product information from the integrated database management system, i.e., REPOSITORY, to end-users through a web browser shown in . The end-user can access data that is handled by the REPOSITORY by executing the DML statements through ODBC on the web-based application module shown in . The pilot system, called BIMSS (Bridge Information Management Support System), is developed as a supporting system for operation and management of product data over the life cycle of a steel bridge. The system used VET engine This study presents foundations for the practical use of steel bridge information through linkage between three-dimensional shape and product data of steel bridges. In addition, this study looks forward to applying to information generated from other structures or each application field of the construction industry with the development of a framework based on an open standard like ISO 10303.Microstructural characterization and properties of a Ti-Ta-Si-Ni metallic glass surface alloy fabricated on a TiNi SMA substrate by additive thin-film electron-beam methodAn important factor limiting the wide application of thin-film metallic glass (TFMG) coatings for improving the surface-sensitive properties of structural alloys is the poor adhesion of TFMG to substrates. This problem can be overcome through the synthesis of MG surface alloys (MGSAs) by additive pulsed electron-beam melting of film/substrate systems of high glass-forming ability. In this work, this approach is applied to the [film (Ti60Ta30Si10, at.%, 100 nm)/substrate (TiNi alloy)] system using a low-energy, high-current electron beam (~2.5 μs, ~15 keV, 1.7 J/cm2) at 10 synthesis cycles and 10 pulses per cycle. Using SEM/WDS, XRD and cross-sectional HRTEM/EDS/SAED analyses it has been found that ~1.5 μm thick SA has completely MG structure, in which the near-surface ~500 nm thick Ni-depleted layer has composition ~Ti56Ta23Ni11Si10. Beneath the MGSA, the ~200 nm thick nanocomposite Ti50Ni30÷40(Ta + Si)20÷10 sublayer, consisting of Ti2Ni nanograins embedded in the amorphous phase is formed. The nanocomposite sublayer is followed by the intermediate sublayer with the eutectic columnar nano-grain B2-structure, which provides the diffusion bonding of MGSA with unmelted TiNi substrate. The monotonic depth dependences of hardness, elastic modulus, depth recovery ratio and plasticity, obtained by indentation, indicate the mechanical compatibility of the MGSA and underlying sublayers with the TiNi substrate. The adhesion-related failure of the MGSA during scratch testing proceeds in the ductile mode mainly through the plastic flow of intermediate sublayer. Evaluation of shape memory effect and superelasticity by torsional deformation technique has shown that synthesis of the MGSA results in an almost 2-fold increase in the martensitic shear stress and significant decrease in the stress hysteresis width compared with the untreated TiNi samples. The irreversible residual strain is ~0.8% at a maximum strain of 6%. Potentiodynamic polarization measurements have shown that synthesis of the MGSA results in the significant enhancement in corrosion resistance of test samples in the Lock-Ringer salt solution.Over the past decade, thin-film metallic glass (TFMG) coatings have a drawn remarkable attention due to their ability to significantly improve the corrosion resistance, fatigue and other surface-sensitive properties of metals and alloys as well as metallic biomaterials. The great number of chemical compositions, varied through the synthesis experiments, functional properties of TFMG and the simplified manufacturing routes using magnetron sputtering deposition extend the range of the potential technical and biomedical applications of these materials [The key issue limiting many applications of TFMG, especially for prospective biomedical applications, is the poor film/substrate interfacial adhesion, associated with the lack of mechanical compatibility of substrate with thin-film coatings. An effective way to overcome this drawback is the liquid-phase mixing of such systems using a microsecond low-energy (10–40 keV), high-current electron beam (LEHCEB). Indeed, it has been shown in [] that using moderate irradiation modes (2–5 J/cm2), it is possible to carry out an effective liquid-phase diffusion alloying of ~1 μm thick surface layers from pre-deposited thin (50–100 nm) films under the condition of a limited solubility of film and substrate components in the solid state. The cooling rate of melted layer reaches ~109 K/s [], which is approximately 3 orders of magnitude higher than quenching rate used for production of amorphous ribbons by conventional melt spinning techniques []. The aforesaid arguments show that the LEHCEB is an appropriate tool for the formation of surface alloys (SAs) with an amorphous and/or nanocomposite structure. In the paper [], this method was implemented on a binary system [film (Ta, 80 nm)/substrate (Fe)]: by means of transmission electron microscopy (TEM), a significant fraction of the amorphous FeTa phase in the surface layer after a single-pulse irradiation (0.8 μs, 3.5 ÷ 5.5 J/cm2) was observed. The opportunity of using LEHCEB for amorphous phase formation in the surface layer has recently been demonstrated by Li et al. [] on polycrystalline Al-Co-Ce glass-forming alloy.In recent years, the thin-film electron-beam method used for the synthesis of SAs has been significantly developed, starting with a pulsed melting of individual film/substrate systems to a multiple alternation of deposition of an alloying film of a certain thickness and composition and subsequent liquid-phase mixing of the components of the film with a substrate [], this additive approach was applied to the [film (Ti70Ta30, 50 nm)/substrate (TiNi shape memory alloy (SMA))] system (hereinafter, compositions are given in at. %). It has been found that it leads to the formation of ~1 μm thick Ti-Ni-Ta SA with a depth-graded nanocomposite structure and enhanced mechanical properties compared to the substrate ones. In Ref. [], the similar experiments using the [(Ti60Ta40, 100 nm)/TiNi] system were performed. An increase of Ta concentration in the alloying film and its thickness, compared with Ref. [], as well as the advanced synthesis regime employment, resulted in the formation of TiNi based SA of ~2 μm thickness with a completely amorphous structure, having gradient composition varied within the range of ~ Ti50Ni35÷43Ta15÷7 at the depths from 0.5 to 1.5 μm.In the present paper the [film (Ti-Ta-Si)/substrate (TiNi)] system, in which the film had the composition Ti60Ta30Si10, was chosen. The choice of the ternary composition for the initial film is due to our next steps in the development of the proposed synthesis method for the production of a novel multicomponent Ti-based SA. The selection of Si as the third alloying element in the film was based on the experimental results on amorphization of ternary Ti-Ta-Si [] alloys by melt-quenching techniques, as well as the results of previous studies of phase formation relationships in the Ti-Ni-Ta SA fabricated on a TiNi substrate []. Silicon being an alloying element also promoted the improvement of the corrosion resistance and biocompatibility of TiNi SMA subjected to the ion implantation with Si+ ions []. The aim of the work is to study the elemental composition, structure, mechanical, adhesion and corrosion properties of the synthesized Ti-Ta-Si-Ni SA.The substrates for microstructural characterization, as described in Ref. [], were samples of dimensions 10 × 10 × 1 мм made of 1 mm thick TiNi SMA hot rolled sheet. Its chemical composition is Ti–55.75 Ni–0.020C–0.035 O–0.003 N–0.001H–<0.1 et al. (wt%). The start temperature of the reverse martensitic transformation is AS = 308 K after a two-stage heat treatment performed by the manufacturer (Matek-Sma Ltd., Russia): (i) 750 °C for 20 min, cooling in air, (ii) 450 °C, 50 min, quenching in water. The substrates were mechanically ground, electrolytically polished, and cleaned according to the procedure [The synthesis of SA was performed in a single vacuum cycle on the modified setup “RITM-SP”, that was used in [] for synthesis of the Ti-Ni-Ta SA. Prior synthesis, the TiNi substrates were pre-irradiated by LEHCEB in order to clean the surface layer of inclusions/particles of TiCxOy and Ti2Ni (Ti4Ni2O) that could initiate crater formation []. The LEHCEB-pretreatment was carried out in the following mode: pulse duration τ = 2–3 μs, energy density Es= 2.5 ± 0.5 J/cm2, number of pulses n = 10, repetition rate of 1 pulse/5 s; beam diameter was ~60 mm. Thereafter, using a manipulator, the samples were alternately transferred under the magnetron sputtering system for co-deposition of the Ti-Ta-Si film and then directly under the e-beam gun for pulsed melting of the film/substrate system.Сo-deposition of Ti60Ta30Si10 films was performed by three DC magnetron sputtering sources with the 75 mm diameter cathodes made of Ti (99.95 wt%), Ta (99.95 wt%) and Si (GIRMET, Russia) at room temperature (at the initial stage of synthesis) at pressure of Ar of 0.1 Pa and residual gas pressure of ~10−4 Pa. The TiNi substrate was rotated with 20 rpm during the co-deposition to obtain homogeneous film composition over the substrate. For co-deposition of the film of required composition (Ti60Ta30Si10), the power applied to Ti, Ta and Si magnetron cathodes was PTi ≈ 935, PTa ≈ 252 and PSi ≈ 90 W, respectively, while the film co-deposition rate V = 2.36 ± 0.15 nm/s.The composition of the Ti-Ta-Si film (~1 μm thickness) deposited on monocrystalline Si substrates was determined by energy dispersive spectroscopy (EDS) using the INCA EDS and wavelength dispersive spectroscopy (WDS) systems (Oxford Instruments, UK) installed on scanning electron microscope (SEM) (EVO 50, Zeiss, Germany) at accelerating voltage U = 10 kV. SEM/EDS examination of the Ti-Ta-Si film has shown that this method does not provide satisfactory accuracy due to the significant overlapping of X-ray peaks from Ta and Si (see ). At the same time, according to the SEM/WDS-analysis, which has a higher spectral resolution compared to SEM/EDS, the composition of the coating corresponded to the calculated composition (Ti60Ta30Si10) with an accuracy of ≤ ±5%. The coating practically did not contain carbon, and the oxygen concentration did not exceed several at. %, which is close to the limit of detection (LOD) by the SEM/WDS.The thickness of the Ti60Ta30Si10 film in each deposition-melting cycle of synthesis was 100 nm, as in []. Taking into account the data obtained earlier on the systems [Ti70Ta30, 50 nm/TiNi] [], a liquid-phase mixing of the components of [Ti60Ta30Si10/TiNi] system in each cycle of synthesis was performed in the mode: τ = 2.1÷2.6 μs, Es = 1.7 ± 0.3 J/cm2, n = 10. The number of deposition-melting cycles was N = 10, so that the expected total thickness of the SA was considered to be ~1 μm. The temperature of the substrate at the end of the synthesis did not exceed 200 °C. Using this processing mode, four series of samples with a Ti-Ta-Si-Ni surface alloy were prepared for microstructural characterization, instrumented indentation and scratch testing, shape memory effect and superelasticity (SME-SE) characterization and corrosion testing.The surface chemistry of tested samples was examined by SEM/WDS method mentioned above. LOD was ±2 (Ti, Ni), ±1 (Ta), ± 4 (Si, O) and ± 5 at.% (C).X-ray diffraction (XRD) analysis was carried out on the DRON-7 (Burevestnik, Russia) and Shimadzu 7000S (Shimadzu, Japan) diffractometers using Co-Kα and Cu-Kα X-ray radiation, respectively, in symmetric and grazing incident X-ray diffraction (GIXRD) geometries. In the GIXRD geometry, the incidence angle of the X-Ray beam was α =3°.Cross-sectional TEM studies were performed on JEM 2100 and JEM-2100F electron microscopes (JEOL, Japan) at accelerating voltage of 200 kV in the bright field (BF) and dark field (DF) modes, in the combination with selected area electron diffraction (SAED) and nano-beam diffraction (NBD) patterns (probe beam size ~10 nm). The cross-sectional thin foils were performed by mechanical thinning and ion-sputtering with an EM 09100IS ion slicer (JEOL, Japan). Before measurements, the surfaces of specimens were cleaned by plasma vacuum system HPT-100 (Henniker Plasma, USA) with a (Ar + O2) mixture for ~15 min. Composition-depth profiles were obtained by TEM/EDS technique as described in Refs. []. The regions of TEM/EDS-analysis were rectangular areas (400 × 100 nm), the calculated thickness of foil in the analyzed regions was ~150 nm.The mechanical properties of the surface alloy were examined with the use of nanomechanical equipment NanoTest 600 (Micro Materials Ltd., UK) with a Berkovich indenter under a step-wise increase of the maximum load P from 5 up to 300 mN for each cycle of loading/unloading. The hardness H and Young's modulus E were determined by diagrams of loading/unloading by method of Oliver and Pharr []. The plasticity characteristic δH and the depth recovery ratio η were calculated, as described in Ref. []. The average values of microhardness and Young's modulus of TiNi substrate under static loading (P = 300 mN) are H = 3.0 ± 0.2 GPa and E = 50.0 ± 2.5 GPa.Adhesion properties of the surface alloy on the TiNi substrate as compared with the Ti60Ta30Si10 film (1 μm)/TiNi system were evaluated by the scratch tester Revetest RST (CSM Instruments, USA) equipped with a 200 μm radius Rockwell diamond indenter. The normal load was linearly increased from 0.5 to 1 ÷ 5 N with a rate of 1÷1.2 N/min, the scratch speed was 1.0÷5.4 mm/min and the scratch length was 1 mm. Acoustic emission and tangential friction force were monitored to indicate the detachment or failure of thin film and SA []. The scratch tracks were observed by a built-in optical microscope.The SME-SE characteristics of the samples were determined by the quasi-static torsional tests at a temperature of 293 ± 1 К, as described in Ref. []. Samples with dimensions of 1 × 1 × 16 mm (at least 3 samples for each surface treatment mode) were deformed at a constant shear strain rate ~ 7 × 10−4 s−1, and the maximum accumulated shear strain γ was 6%. When the total torsional deformation reached 6%, the sample was unloaded and the inelastic deformation was recovered by the superelasticity. The shear strain rate remained unchanged upon isothermal torsional loading and unloading. After unloading, the samples were heated up to 373 K, and the residual strain was recovered due to the SME. The effect of surface treatment on SME-SE response was analyzed through the obtaining of the shear stress-shear strain curves.The corrosion properties of test samples were examined by potentiodynamic polarization measurements using a potentiostat P30S (Elins, Russia). A three-electrode cell with an Ag/AgCl (3.5 М KCl) reference electrode, Pt counter electrode and the test sample as the working electrode were used. Polarization curves were determined at 25°С in the Lock-Ringer Salt Solution (LRSS) with ion concentration (mmol/L): Na+ 156.2; K+ 5.6, Ca2+ 2.2; Cl− 161.6 and HCO3− 2.4. The test samples were 2-cm-diameter disks in which the exposed area was 0.95 cm2; two samples were tested for each surface treatment mode. Prior the measurements, all samples were immersed in the LRSS for 1.5 h to stabilize the open circuit potential (OCP). The potential was varied from −400 to 1500 mV versus OCP at a scan rate of 1 mV/s. The corrosion potential Ecorr and corrosion current density icorr were determined by Tafel extrapolation method. The polarization resistance of tested samples was evaluated from polarization curves using Stern-Geary approach []. The corrosion parameters were averaged from the three independent tests. shows the frontal optical and SEM images of the TiNi substrate before (a) and after (b, c) synthesis of the Ti-Ta-Si-Ni SA. It is seen that the TiNi substrate subjected to LEHCEB-pretreatment ( a) has no inclusions inherent to a bulk alloy [], but the irradiated surface contains craters. In Ref. [], it has been also established that the observed craters are nucleated mainly on Ti2Ni (Ti4Ni2O) inclusions. A significant part of these craters, having the smoother edges, is retained after the synthesis of the Ti-Ta-Si-Ni SA. The retention of craters inherited from the TiNi substrate is due to the fact that the synthesis is carried out near the melting threshold of the film/substrate system. At the employed irradiation modes, the thickness and lifetime of the surface melt are too small for mass transfer in the crater region and its smoothing due to the surface tension. The average surface roughness of the Ti-Ta-Si-Ni SA increased by 1.5÷2-fold compared with that of the untreated (electropolished) TiNi substrate (Ra = 0.086 ± 0.014 μm). shows the concentration-depth (x) profiles in the modified surface layer with the Ti-Ta-Si-Ni SA obtained by cross-sectional TEM/EDS (~100 nm ≤ x < ~2500 nm). The average composition of ~500 nm thick near-surface layer determined by surface SEM/WDS-analysis is also given. The principal component of this layer is Ti, the content of which over the entire depth remains at the level of 50 ± 5 at. %, approximately corresponding to that of the TiNi substrate. The modified layer consists of an upper surface layer of 1–1.5 μm thickness enriched with Ta and Si, marking the Ti-Ta-Si-Ni SA, and a transition layer in which the concentration of these components monotonically decreases up to zero., the concentrations of Ta, Si, and Ni determined by both methods in the ~500 nm thick near-surface layer, unlike Ti, noticeably differ from each other. Firstly, according to the SEM/WDS-analysis, this layer possesses the smaller Ni content approximately half of that obtained through TEM/EDS: ~10 and ~ 20 at.% Ni, respectively. Secondly, the Ta content in this layer is ~1.3 times higher, and the Si content, on the contrary, is ~1.7 times lower in comparison with the corresponding data obtained by the cross-sectional TEM/EDS.A noticeable difference in the Ta and Si concentrations, determined at the depths x = ~ 300÷500 nm by the SEM/EDS and cross-sectional TEM/EDS methods, is due to the inability to accurately separate the neighbor overlapping most intense spectral lines of Ta (E = 1.71 keV) and Si (E = 1.74 keV) in the EDS spectra (see d). In turn, the difference in Ni content obtained by the SEM/WDS and TEM/EDS methods may be due to certain limitations of the cross-sectional TEM/EDS: (1) rectangular regions of the TEM/EDS-analysis with a size of ~400 × 100 nm are oriented at a certain angle to the surface plane; therefore, the Ni concentration may be overestimated due to the influence of the TiNi substrate; (2) during the TEM foil preparation (namely, when the Ar+ ion milling/thinning), the sputtered Ni atoms from the TiNi substrate can redeposit on the analyzed region of the foil [From a comparison of the concentrations of Ta and Si in this layer, measured by both methods, it also follows that in both cases the total (Ta + Si) concentration of these elements is approximately the same. It can be concluded that for the Ti-Ta-Si-Ni system, the cross-sectional TEM/EDS method allows to determine with satisfactory accuracy only the total concentration of Ta and Si in depth, significantly underestimating the Ta content and overestimating the Si content.Considering the above-mentioned difficulties of simultaneous identification of Ta and Si by EDS, the SEM/WDS data seems to be more reliable. According to these data, the ~500 nm thick near-surface layer is Ni depleted, and its average composition is Ti56Ta23Ni11Si10 (without considering O and С impurities). In turn, at the depths from x ~ 500 nm up to ~1.5 μm, by the cross-sectional TEM/EDS data, the Ti concentration remains constant at ~50 at. %, while the Ni concentration and the total concentration of Ta and Si possesses inverted behavior with a depth variation. Therefore, the estimated composition of the SA at these depths can be expressed as Ti50Niy(Ta + Si)50-y, where y monotonically increases from 23 at.% (x = 500 nm) up to ~37 at.% (x = 1.5 μm). For example, at a depth of 1 μm, which corresponds to the total thickness of the deposited Ti-Ta-Si films, the composition of the SA is Ti49Ni29Ta12Si10.The above-mentioned Ti-Ni-Ta SA with an amorphous structure, synthesized in the similar mode using the [(Ti60Ta40, 100 nm)/TiNi] system (see Section 1), had compositions of ~ Ti50Ni35Ta15 and Ti51Ni38Ta11 at depths of ~300 nm and 1 μm, respectively []. Therefore, the partial replacement of Ta by Si in the alloying film resulted in depletion of Ni not only in the near-surface layer, but also in the much deeper layers. The significant content of Ni in the SA, starting from the depth x >~500 nm, is related with the multiple displacement of Ni from the molten TiNi substrate to the surface at the solidification front.It should be noted that the behavior of the concentration profiles of Ni and Si in SA () is in qualitative agreement with the Ni-rich part of Ni], according to which, for Si concentration up to ~20 at. %, the equilibrium partition coefficient K = CS/CL < 1, where CS and CL are concentration of silicon on the solidus and liquidus line, respectively. Therefore, at least at the initial stage of synthesis, the Si atoms quasi-uniformly dissolved in a Ni-enriched surface melt can be displaced to the surface during superfast solidification. This effect is known to be solute trapping []. However, the contribution of this mechanism, as well as the differences in the diffusivity of Ni and Si in the melt, is difficult to evaluate due to the presence of Ti and Ta in the system. the XRD patterns of the Ti-Ta-Si-Ni SA, obtained in symmetric (a, b) and GIXRD (glancing incidence angle α = 3°) (c) geometries are presented. The diffraction patterns ( a, b), besides the intense peaks of the matrix B2 phase of the TiNi substrate, reveal weak peaks of the intermetallic Ti2Ni and Ti3Ni4 phases, as well as diffuse scattering regions of the first and second orders (DSR1, DSR2) typical for the amorphous structure. DSR1 and DSR2 are observed in the vicinity of the most intense (110)B2 peak (at 2θ ≈ 35÷60°) and in the range 2θ ≈ 65÷90°, respectively. The absence of diffraction peaks of the crystalline phases on the GIXRD pattern ( c) indicates that the modified surface layer of 1.5–2 μm thickness (the approximate layer thickness of half maximum intensity due to the X-ray absorption for α = 3°) containing the Ti-Ta-Si-Ni SA has a predominantly amorphous structure.The results of the cross-sectional TEM analysis of the modified surface layer are shown in a, d, the upper surface layer of 1.0÷1.3 μm thickness, containing the Ti-Ta-Si-Ni SA, has a predominantly amorphous structure, that coincides with the results of XRD analysis (, at the depth greater than x = ~ 500 nm, the glass-forming range (GFR) of the surface alloy is about Ti50Ni23÷37(Ta + Si)27÷13. The amorphous matrix contains embedded nanobubbles up to ~20 nm in diameter, observed mainly in the near-surface layer of thickness ~ 500 nm ( a, b), having the composition of ~Ti56Ta23Ni11Si10 (). Similar nanobubbles were observed in the Ti-Ni-Ta SA []. The formation of nanobubbles can be associated with the trapping and dissolution of gas impurities (argon and oxygen) from the working chamber into the molten surface layer and their subsequent displacement to the surface at the solidification front []. On the surface of the Ti-Ta-Si-Ni SA, a thin (~ 7 nm) supposedly oxide layer is found ( b, c). Absence of diffraction contrast at low-magnification BF TEM image ( b) as well as the lattice fringes on HRTEM images ( c) signifies that this layer possesses an amorphous structure. shows the NBD patterns and the azimuthally averaged diffraction profiles of diffuse scattering electrons [] obtained from the amorphous structure at three depths: ~ 170, 500, and 1300 nm ( a). As can be seen, the radii of the first-order diffuse halos R1amorph on the NBD patterns differ noticeably. The values calculated from the maximum of the radius profiles on the corresponding NBD profiles of the diffuse scattering intensity are 2.37, 2.41, and 2.33 Å−1 at depths of 170, 500, and 1300 nm, respectively. This means that in the Ti-Ta-Si-Ni-SA, not only the chemical composition (), but also the atomic structure of the amorphous phase varies nonmonotonically at the different depths from the surface. Using the TEM/NBD data, it is possible to estimate the radii of the first, second, etc. coordination shells, coordination numbers and other parameters of the short-range atomic order [] of the studied amorphous phase. We are going to prepare a separate work devoted to the study of the atomic structure of the formed amorphous phase.At a depth of more than 1300 nm, beneath the upper amorphous layer, a sublayer of ~300 nm thickness with a nanocomposite structure is formed. The composition of the nanocomposite sublayer varies in depth within the range Ti50Ni30÷40(Ta + Si)20÷10 (). This sublayer consists of a mixture of nanocrystalline grains of 30–80 nm in size ( a) embedded in the amorphous phase, as indicated by the presence of a diffuse halo on the SAED pattern obtained from this region (, SAED b). A small amount of nanobubbles is also observed. Analysis of SAED and NBD patterns (, SAED c, NBDs ① and ②) has shown that nanocrystals are considered to be Ti2Ni grains. No other phases in this sublayer were found by TEM methods.Furthermore, beneath the nanocomposite sublayer at the depth of x ≈ 1.4–1.7 μm, an intermediate sublayer of ~200 nm thickness with a eutectic structure is formed as a result of solidification of a Ti-Ni-based melt depleted in Ta and Si. The eutectic sublayer consists of a mixture of B2- and Ti3Ni4 -phases and a small amount of small R-phase martensite plates (). The B2 phase has a columnar structure (c) with grains of ≤50 nm diameter. Ti3Ni4 nanoparticles with a size of ≤20 nm are segregated along the boundaries of columnar grains. Finally, between the eutectic sublayer and the TiNi substrate an elongated thin-twinned R-phase martensite plate is clearly observed ( d). The martensitic R-phase of TiNi is a strain-induced martensite, as followed by the morphology of the plates, preferred oriented towards the interface between the sublayers. The strain-induced martensitic transformation is known to be an effective mechanism for the relaxation of residual elastic stresses in a TiNi substrate caused by multiple pulsed heating during the formation of the Ti-Ta-Si-Ni SA. The structure of the TiNi substrate located in the heat affected zone at a depth of more than 2 μm is close to the initial one. shows a scheme of a cross-sectional view of the Ti-Ta-Si-Ni SA synthesized on the TiNi substrate based on microstructural characterization (see ). The SA consists of an outer ~1.0÷1.3 μm thick amorphous layer enriched with Ta and Si and inner ~300 nm thick nanocomposite sublayer composed of amorphous phase and Ti2Ni nanograins. Beneath, a transition sublayer with a eutectic columnar granular structure based on the B2 phase is observed, forming a diffusion couple with an unmelted TiNi substrate.From a comparison of this scheme with a similar one for the Ti-Ni-Ta SA synthesized on a TiNi substrate by additive pulsed melting of the [(Ti70Ta30, 50 nm)/TiNi] system [], we can conclude that, as expected, the addition of Si as the third component of the alloying film significantly increases the glass-forming ability of the surface alloy. Moreover, the addition of Si resulted, as expected, in a significant decrease in the Ni concentration in the surface layer with a thickness less than 200 nm. One should expect that Si doping is a promising strategy to form functional Ti-based multi-component metallic glass surface alloys (MGSAs) on substrates made of technical alloys.The dependencies of mechanical properties (hardness H, Young's modulus E, depth recovery ratio η and plasticity characteristic δH) as a function of indentation depth are shown in for initial TiNi substrate and the Ti-Ta-Si-Ni SA. Here, for comparison, similar dependencies are shown for the Ti-Ni-Ta SA with the same concentration of Ta in the deposited film, but without Si []. A gradual decrease in hardness H and Young's modulus E to the values approximately corresponding to the initial TiNi substrate at depth of ~2 μm (~3 and ~60 GPa, respectively) indicates the mechanical compatibility of both SAs and underlying intermediate sublayers with the TiNi-substrate.The high value of hardness H of initial TiNi-substrate at a depth of ~200–700 nm is due to the surface hardening during mechanical grinding ( a, curve 1). The Ti-Ta-Si-Ni SA near the surface (x ≈ 200 nm) possesses increased values of hardness (up to ~8 GPa, a, curve 3) and Young's modulus E (up to ~120 GPa, a, curve 6), compared with the initial TiNi substrate. This is due to the effect of LEHCEB- pretreatment of the TiNi substrate [Comparison of the dependencies H(x) and E(x) for the Ti-Ta-Si-Ni SA ( a, curves 3, 6) and the Ti-Ni-Ta SA (without Si) [ a, curves 2, 5) shows that the maximum values of H and E in both SAs are the same. The difference is that in the upper surface layer with a thickness of up to ~500÷700 nm, the gradients dH/dx and dE/dx for the Ti-Ta-Si-Ni SA are significantly higher compared to the Ti-Ni-Ta SA. Qualitatively, such behavior of the H(x) and E(x) curves in the case of the Ti-Ta-Si-Ni SA is consistent with the high concentration gradients of Si, Ni, and Ta up to the depth of ~500 nm compared to deeper layers of the material (see The parameter η, that characterizes the degree of the recovery of local strain of the Ti-Ta-Si-Ni SA after indentation, gradually decreases from ~60%, which is close to the corresponding value in the initial TiNi substrate, to the values that are ~15% lower compared to the TiNi substrate ( b, curves 1 and 3). It should be noted that in the Ti-Ta-Si-Ni SA under low loading conditions the recovery of strain occurs due to the high Young's modulus ( a, curve 6), in contrast to the initial TiNi substrate, in which the recovery of local strain is caused by the reverse martensite transformation in the matrix B2-phase [ a (curve 2), it can be seen that in the Ti-Ni-Ta SA (without Si) [], near the surface the parameter η is equal 40%, and at the depth of ~500 nm thickness, this parameter decreases to ~30%. Hence, the degree of the recovery of local strain in the amorphous Ti-Ta-Si-Ni SA is significantly higher compared to the nanocomposite Ti-Ni-Ta SA [At last, from a comparison of the dependencies δН (x) in b it follows that the Ti-Ta-Si-Ni SA (curve 6) has an increased by ~10% and ~ 2 times greater plasticity compared to the initial TiNi substrate (curve 4) and the Ti-Ni-Ta SA (curve 5), respectively. The values of δН for the Ti-Ta-Si-Ni SA are consistent with the values of this parameter for Ti-based bulk metallic glasses []. The high plasticity of the Ti-Ta-Si-Ni SA is of great interest for application. This property, in combination with the amorphous structure of the surface layer without grain boundaries or other defects, can provide efficient delocalization of stress concentrations of various nature. Thus, we could expect an enhancement of the fatigue endurance of the material before its fracture.The results of scratch testing of the [(Ti60Ta30Si10, 1 μm)/TiNi] and the [(Ti-Ta-Si-Ni SA)/TiNi] systems are shown in . In a case of film/substrate system, an acoustic emission trace contains two signals, corresponding to a normal load Fn of 0.58 and 0.76 N ( a). The lower normal load corresponds to a penetration depth of ~1 μm, i.e. film thickness; it means that this value reflects the critical load (Lc) of the film failure. The higher normal load corresponds to a penetration depth of ~4 μm; it means that the substrate failure takes place at this load. The low amplitude of both acoustic emission signals and the absence of obvious signs of film detachment (cracking, buckling, etc.) on the scratch track micrograph ( b) indicate a good adhesion of the film. Judging by the track morphology, the considerable thinning of the film by plastic flow and its extrusion by indenter in scratch direction are observed. Thus, the failure of both film and substrate occurs due to the plastic deformation, which is consistent with relatively low hardness of both materials (<5 GPa) [The scratch testing of the [(Ti-Ta-Si-Ni SA)/TiNi] system at the same normal load (Fn = 0.5÷1 N) has shown, that no signs of the SA failure are observed (see c, d). The low penetration depth of indenter (~0.25 μm) is consistent with relatively high hardness of the near-surface layer (~ 7 GPa) as compared with that of the TiNi substrate (see a). The drop of penetration depth observed at Fn ~ 0.8 N can be caused by an indenter passing through an individual crater inherited from the TiNi substrate.Significantly different scratch test results were obtained at Fn = 0.5÷3 N (see e, f). In this case, the penetration depth monotonically increases from zero (surface) to ~1.4 μm in the range of Fn ≈ 0.5÷1.5 N. At the depth of ~1.4 μm, which corresponds to the interface between the amorphous and nanocomposite structures ( a), the distinct kinks of both penetration depth and friction force traces are observed. This means that the onset of the surface alloy failure occurs at Fn ≈ 1.5 N. In turn, the first signal of acoustic emission is detected at Fn ≈ 2.3 N and at the depth of ~2.4 μm, which corresponds to the boundary of modified layer with the unmelted TiNi substrate (see a). After this acoustic emission signal, no distinct kinks of both penetration depth and friction force traces are observed. This means that the failure of the entire modified layer is mainly localized within the intermediate layer ( a), and it occurs at normal load in the range from 1.5 N to 2.3 N. The localization of failure in the intermediate layer is consistent with its layered structure. On the other hand, the microrelief of the scratch track indicates that the entire process of the failure of the modified layer proceeds mainly due to the plastic deformation without noticeable signs of delamination from the TiNi substrate.Thus, a comparative scratch testing of the [(Ti60Ta30Si10, 1 μm)/TiNi] and the [(Ti-Ta-Si-Ni SA)/TiNi] systems has shown, that in both cases a failure of surface layers is due to the plastic flow without signs of delamination of film or surface alloy. The failure of the Ti-Ta-Si-Ni SA corresponds to normal load in a range of 1.5÷2.3 N, which is 2.5÷3 times higher than that of film/substrate system.The effect of surface modification on the SME-SE properties of three types of samples is illustrated in . Here, the torsional shear stress-shear strain curves for the untreated TiNi substrates, and for TiNi substrates with the Ti-Ta-Si-Ni SA and the Ti-Ni-Ta SA [] are presented (T = 293 K). Taking into account the small (1–2 μm) thickness of the Ti-Ta-Si-Ni SA and its mechanical properties (), it was expected that surface modification would not have a significant effect on the SMA-SE characteristics of test samples. However, experiments completely refuted this assumption. First, the martensitic shear stress τМ in the samples with the Ti-Ta-Si-Ni SA is considered to be almost 2 times higher (, curve 3) than that of the untreated TiNi samples (, curve 1) and samples with the Ti-Ni-Ta SA (, curve 2). Secondly, after the synthesis of the Ti-Ta-Si-Ni SA, the shape of torsional shear stress-shear strain curves changed in comparison with the other two types of samples. So, in the untreated TiNi samples (, curve 1) and in samples with the Ti-Ni-Ta SA (, curve 2), the shape of these curves is typical for those of TiNi-based alloys, in which the reversible shear strain is characterized by a wide hysteresis and is provided by both SMA and SE mechanisms [] in a wide range of loads or temperatures. Such TiNi-based alloys are usually used in industry and are not appropriate for medical applications where a good SE in a narrow mechanical or temperature range is required. Samples with the Ti-Ta-Si-Ni SA possess a shape of the superelastic loop with a narrow hysteresis in a shear stress-shear strain curve typical for TiNi-based alloys with the SE effect.The difference in torsional stress-strain loops for the test samples is obviously due to the difference in the structure and mechanical properties of the surface layers, which are involved in the torsional deformation process in the first order. Since the Ti-Ta-Si-Ni SA and the Ti-Ni-Ta SA have similar values of hardness and elastic modulus in the near-surface layer, but higher than those of the initial TiNi substrates ( a), one could expect that both SAs should affect the integral SME-SE characteristics of [SA/TiNi] system. However, the shape of the torsional stress-strain loop in case of the Ti-Ni-Ta SA changes only slightly, whereas in case of the Ti-Ta-Si-Ni SA this effect is manifested significantly. Therefore, this difference can be associated not only with the different structure of SAs (amorphous structure in the case of the Ti-Ta-Si-Ni SA and nanocomposite one in the Ti-Ta-Ni SA []), but also with their various elastic-plastic properties in the deeper layers (Indeed, firstly, the Ti-Ta-Si-Ni SA with an amorphous structure ensures the formation of a higher residual thermoelastic stresses oriented normally to the irradiated surface. This is due to the fact that in the amorphous Ti-Ta-Si-Ni SA there are no crystallographic mechanisms for the relaxation of residual stresses. Secondly, as noted, a sample with the Ti-Ta-Si-Ni SA is characterized by a higher elastic modulus than the untreated TiNi substrate. Therefore, for sample with the Ti-Ta-Si-Ni SA, a higher rotational torque is required to overpass a higher elastic stress limit than that of the untreated TiNi sample. Thirdly, the Ti-Ta-Si-Ni SA layer due to the higher plasticity will be in 2D elastic-stress state without fracture much longer. As a result, a larger volume fraction of the TiNi substrate should be involved in the process of accumulation and recovery of inelastic shear strain in a sample with the Ti-Ta-Si-Ni SA compared to that of the untreated TiNi sample. Fourthly, at the temperature 293 K belonging to the two-phase [B2 + B19’(R)] region on the TiNi transformation temperature-concentration phase diagram [], as soon as an external shear stress τ becomes greater than τМ, the formation of stress-induced martensite is facilitated beneath the layer with the Ti-Ta-Si-Ni SA. This corresponds to the appearance of a horizontal plateau upon loading stage on curve 3 () with shear stress τ ≈ const, close to τM. In turn, during unloading, when external shear stress τ becomes ≤ τМ, a shear strain recovers (almost complete up to γ = 1%) with the formation of a horizontal plateau under unloading stage on curve 3 (On the contrary, in samples with the Ti-Ni-Ta SA, the surface nanocomposite layer almost doesn't have an effect on the stress-strain response of the sample. This is most likely due to the fact that the nanocomposite layer cracks even at the elastic stage of deformation due to its low plasticity. It is planned to study this issue in more detail in the future.It should be noted that the synthesis of both SAs does not lead to a decrease in the reversible inelastic strain. The irreversible strain Δγ ≈ 0.8% (), observed in samples with SA after the loading–unloading cycle is due to the presence of a certain fraction of the martensitic phase that may remain at T = 293 K. When samples with both SAs in-situ are heated up to T ≅ 373 K, a complete recovery of the applied strain is observed as in the untreated TiNi substrates. shows the potentiodynamic polarization curves for TiNi substrates in the initial state, after LEHCEB-pretreatment and after the synthesis of the Ti-Ta-Si-Ni SA. It can be seen that all samples are spontaneously passivated in the anodic polarization process, and the passive current densities are varied in the range of 1÷2 μA/cm2. For TiNi substrates in the initial state (after electropolishing), the corrosion potential Ecorr = −327 mV, the corrosion current density icorr = 0.013 μA/cm2, and a pitting potential for the passive film breakdown Ebr = 890 mV. The LEHCEB-pretreatment leads to a small shift of corrosion potential in the active (negative) direction, a small decrease in the corrosion current density and a significant (almost ~600 mV) decrease in a potential of passive film breakdown. After the synthesis of the Ti-Ta-Si-Ni-SA, an additional small shift of corrosion potential in the negative direction is observed, and the current density decreases by an order of magnitude as compared to the initial state. In this case, no passive film breakdown occurred, i.e. Ebr > 1500 mV. The values of Ecorr, icorr and Ebr of tested samples are given in . In general, the results obtained point to, firstly, the ambiguous effect of the LEHCEB-pretreatment on the corrosion behavior of the TiNi alloy and, secondly, a significant improvement of its corrosion resistance after synthesis of the Ti-Ta-Si-Ni SA.The presence of signs of a decrease in the corrosion resistance of the TiNi alloy after the LEHCEB-pretreatment, as compared with the initial state, at first glance, contradicts with Ref. []. In this paper using samples of a Ti-(50.6 at.%) Ni alloy as well as the similar electrochemical measurement techniques in the Tyrode's simulated body fluid (SBF) at 37 °C, it was shown that the LEHCEB-treatment in the similar mode (1.5 μs, 3 J/cm2, n = 5) led to a significant shift of Ecorr in the more noble direction and a decrease in icorr, i.e. led to a significant increase in the corrosion resistance of the TiNi alloy compared with the initial state. The contradiction is associated, as follows from the aforementioned, with the different initial state of the surface layers of the TiNi alloy (before the LEHCEB-treatment) in our experiments (electropolishing) and in Ref. [] also found that the corrosion parameters of the TiNi alloys in SBFs (Ecorr, icorr and Ebr) are significantly improved after electropolishing (in perchloric acid-based electrolyte) compared to those of mechanical polishing. Through X-ray photoelectron spectroscopy studies they revealed that this effect was associated with a significant increase in the Ti/Ni ratio in the TiO2-based passive oxide film in the case of electropolished samples, compared to mechanically polished samples and, consequently, to an increase in the density and homogeneity of the passive film, which was manifested in a significant increase in the corrosion resistance of the material.To compare the corrosion resistance of tested samples near the corrosion potential, the polarization resistance Rp, inversely proportional to the corrosion rate, was evaluated from the Stern-Geary Eq. [where bc and ba are cathodic and anodic Tafel slopes, derived directly from the polarization curves.The values of Tafel slopes and polarization resistance of tested samples are given in . The average value of Rp of the TiNi substrate is 0.5 MΩ∙cm2, which is of the same order of magnitude as this parameter reported in literature taking into account the different surface finishing (see, e.g. []). After LEHCEB-pretreatment, the polarization resistance of the TiNi alloy increases approximately twofold, which is consistent with some decrease in the corrosion and passivation current densities (see The highest polarization resistance (~3.5 MΩ∙cm2) has been found for the Ti-Ta-Si-Ni SA, which is consistent with the mentioned above highest value of Ebr. It is associated with a completely amorphous structure of the SA to the depth of more than 1 μm (). Such single-phase amorphous structure, free from grain boundaries and other defects, with a uniform distribution of corrosion-resistant elements, determines the high resistance of the surface layer to a pitting corrosion in solutions containing ions of chlorine. It should be noted that surface alloying of a TiNi alloy with both Ta [] by ion implantation also leads to an increase in the corrosion resistance of this alloy in SBFs, that reveals the general mechanisms of corrosion improvements, regardless of the method of alloying with these elements.In this work, the Ti-Ta-Si-Ni MGSA with diffusion sublayer of total thickness 1.5–1.7 μm was successfully synthesized by multiple alternating of magnetron co-deposition of Ti60Ta30Si10 thin (100 nm) film and its liquid-phase mixing with a TiNi substrate using microsecond e-beam surface melting. The depth-graded microstructure, mechanical and corrosion behavior of modified surface layers were examined. Based on these observations, the following conclusions can be drawn.The surface layer of ~1.0÷1.3 μm thickness has a completely amorphous structure, and its composition almost monotonically varies in depth within ~Ti45÷57Ta25÷10Si11÷7Ni10÷35. The near-surface Ni-depleted layer of ~500 nm thickness has composition ~Ti56Ta23Ni11Si10. The MGSA contains nanobubbles (diameter ≤ 20 nm), observed predominantly in the Ni-depleted layer. Beneath the single-phase MG layer, the ~300 nm thick nanocomposite Ti50Ni30÷40(Ta + Si)20÷10 sublayer, consisting of Ti2Ni nanograins (30÷80 nm), embedded in the amorphous matrix is formed. The nanocomposite sublayer is followed by ~200 nm thick intermediate sublayer, which provides the diffusion coupling of the MGSA with the unmelted TiNi substrate. The diffusion sublayer has a B2 phase eutectic columnar grain structure (grain diameter ≤ 50 nm), and Ti3Ni4 nanoparticles (≤ 20 nm) segregated along the grain boundaries.Instrumented indentation has shown that the MGSA possesses simultaneously enhanced hardness, elastic modulus and plasticity compared to those of the untreated TiNi substrate. The monotonic depth dependences of these properties as well as a depth recovery ratio indicate the mechanical compatibility of the MGSA and underlying sublayers with the TiNi substrate.The adhesion-related failure of the MGSA during scratch testing proceeds in the ductile mode mainly through the plastic flow of the intermediate sublayer.Evaluation of characteristics of shape memory effect and superelasticity has shown that the synthesis of the MGSA results in an almost 2-fold increase in the martensitic shear stress and significant decrease in the stress hysteresis width in the shear stress-shear strain loop compared with the untreated TiNi samples. The irreversible part of shear strain (when the γtotal = 6%) is ~0.8%, which is quite appropriate for the biomedical application of TiNi alloy.Potentiodynamic polarization measurements have shown that the Ti-Ta-Si-Ni MGSA with Ni-depleted near-surface layer possesses enhanced corrosion resistance in the Lock-Ringer salt solution compared with untreated TiNi samples.L.L. Meisner: Supervision, XRD, writing-original draft & editingV.P. Rotshtein: Writing-review & editingS.N. Meisner: SEM/EDS/WDS, scratch testingE.V. Yakovlev: Synthesis of surface alloyF.A. D'yachenko: Instrumented indentation, corresponding personThe 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.Influence of ejection temperature on structure and glass transition behavior for Zr-based rapidly quenched disordered alloysWe examined the influence of ejection liquid temperature (Tel) on the structure, thermal stability and crystallization of ZrCu ribbons prepared by the melt-spinning technique. The increase in Tel was found to cause the formation of an oxide phase on the ribbon surface, more loose atomic configurations, the absence of glass transition (GT) and supercooled liquid (SL) region, and the rise of crystallization temperature. The changes in the GT and SL region occur reversibly by controlling the Tel. Neither the change in alloy composition except oxygen nor the difference in crystallized phases is seen. Their hardness increases significantly by the disappearance of GT and SL region. The reversible changes in the appearance and disappearance of GT and SL region was found for different Zr-based glassy ribbons, being independent of alloy compositions. The disappearance is presumably due to the change in atomic configurations from high-coordinated to less-coordinated atomic packing in the melt-spun ribbons by freezing high-temperature liquid. The observed phenomenon of the reversible changes provides a novel opportunity for deep understanding of mutual correlations among liquid structure, GT, stability of SL and bulk glass-forming ability for metallic alloys.A number of bulk glassy alloys have been obtained since the first synthesis of bulk glassy alloy by copper mold casting in 1990 Zr-based bulk glassy alloys (BGAs) exhibit a distinct GT behavior and a wide SL region before crystallization and have been synthesized in a variety of systems by utilizing the high stability of the supercooled liquid to crystallization A number of studies on the influence of the superheating liquid temperature on glass-forming ability, thermal stability and mechanical properties of bulk glassy alloys have been performed in the superheating state up to about Tl +500 K Multicomponent alloys with nominal atomic compositions of Zr60Al10Ni10Cu20 and Zr55Al10Ni5Cu30 (at.%) were chosen for the present study. Pre-alloyed ingots were prepared by arc-melting a mixture of pure metals in a Ti-gettered argon atmosphere. The purity levels of the constituent elements were as follows: Zr 99.9, Ni 99.9%, Cu 99.9% and Al 99.99% (all in wt.%). The alloy ribbons with a cross section of about 0.03 × 1 mm2 were produced by melt spinning of the pre-alloyed liquid from the temperature ranging between Tl +75 K and Tl +770 K. The liquidus temperature was measured by a radiation thermometer and its accuracy is within ±20 K for the relative temperature. The quartz-tube nozzle hole diameter, the copper wheel diameter and the rotation speed of the wheel were fixed to be 0.8 mm, 250 mm and 3000 rpm, respectively. The ejection pressure difference was also fixed as 0.02 MPa.The structure of the melt-spun ribbons was examined by laboratory X-ray diffraction (XRD, D8 Advanced, Brook German), optical microscopy (OM), scanning electron microscopy (SEM, S4800, Hitachi Japan) and transmission electron microscopy (TEM, JEM-2100F, JEOL Japan). The alloy component analysis of the ribbons prepared under different conditions was made by SEM equipped with an energy dispersive X-ray (EDX) spectroscopy. Oxygen content in the melt-spun ribbons was measured using 1 g ribbon samples by a high-temperature thermal decomposition analyzer (HORIBA EMGA-620 W) with an accuracy of 0.01 ppm for oxygen. The sample was heated to high temperature above 3773 K during the measurement.Auger electron spectroscopy (AES, JEOL JAMP 9500F Scanning Auger Microprobe) was also employed in order to study the possible compositional modifications. A Schottky field emission electron gun at 10 kV and 10 nA excited the metallic glass under 10−7 Pa vacuum, where a differentially-pumped ion gun with 3 keV was used to sputter argon ions onto the ribbon samples at a sputtering rate of 27 nm/min for surface cleaning. Different from EDX, the Auger information comes only from the nanometer-range thicknesses, where measurements are conducted after removing the surface contamination. Auger analysis was performed on both faces of the ribbons, i.e., the free surface and the surface in contact with the copper wheel.High-energy XRD was also carried out at the P02 experimental station at PETRA III synchrotron radiation source (DESY, Hamburg) with a photon energy of 59.73 keV and beam size of 250 × 250 μm2 in transmission geometry. The XRD intensity was recorded by a two-dimensional (2D) Perkin Elmer 1621 detector. The diffraction patterns were radially integrated using the FIT2D program Thermal stability associated with Tg, Tx and SL region was evaluated by differential scanning calorimetry (DSC, TGA/DSC 1 STARe system, Mettler Toledo) with a heating rate of 0.67 K/s. The liquidus temperature was measured with a differential thermal analyzer (DTA). Vickers hardness was measured with a Vickers hardness indenter (Tukon™ 1202, Wilson) under a load of 100 gf. Bending ductility was also evaluated by a simple bending test. The deformation and fracture behavior was examined by SEM and OM.(a) shows the DSC curves of the melt-spun Zr60Al10Ni10Cu20 ribbons produced by ejection of the alloy liquids heated at the temperatures of approximately 1350 K, 1665 K, 1735 K and 1925 K, which are higher by 195–770 K than Tl. The ribbon thickness was about 34 μm for the ribbon ejected at the lower (ordinary) temperature (1350 K, Tl +195 K) and about 30 μm for the ribbon ejected at the higher temperature (1925 K, Tl +770 K). For convenience of further discussion, we denote the ribbon obtained by ejection at 1350 K as low-temperature (LT) ribbon and that obtained by ejection at 1925 K as high-temperature (HT) ribbon. Considering that the melt-spinning conditions such as nozzle hole diameter, injection pressure, ejection alloy amount and wheel velocity are constant, the slightly smaller thickness of the HT-ribbon is supposed to reflect the ease of spinning of liquid puddle due to the lower viscosity and the increase of the melt-spinning time resulting from a longer solidification time.The DSC curves of the samples prepared from the lower ejection temperatures of 1350–1735 K show a distinct GT, followed by a SL region of about 90 K and then the onset of crystallization, being almost the same as the previously reported data for the Zr60Al10Ni10Cu20 glassy alloy (b) shows X-ray diffraction patterns of the four alloy ribbons obtained by melt spinning from different ejection temperatures. The XRD patterns from all ribbons consist of only broad peaks without any indication of Bragg reflections, indicating that the four samples are composed of a disordered structure. shows ordinary bright-field TEM, high resolution TEM (HRTEM) images and selected area electron diffraction (SAED) patterns of the Zr60Al10Ni10Cu20 ribbons prepared from the low liquid temperature of Tl +195 K and the high liquid temperature of Tl +770 K. These images reveal maze-like contrast typical for a disordered structure which does not include any fringe contrast characteristic for crystalline phase(s). The electron diffraction patterns also consist only of halo rings. Hence, the XRD, TEM and HRTEM results demonstrate clearly that the melt-spun structure consists of disordered phase.In order to prove the reversibility (appearance and disappearance) of GT and SL region, the Zr60Al10Ni10Cu20 melt was heated once to Tl +770 K in the quartz tube, then cooled to Tl +420 K and ejected onto the rotating Cu-wheel at the same conditions as the above discussed ribbons were obtained. For convenience, we denote such sample as HLT-ribbon. shows a DSC curve of the Zr60Al10Ni10Cu20 HLT-ribbon. The sequent transition of GT, SL and crystallization can be clearly seen on the DSC curve and the glass transition temperature (Tg), ΔTx (=Tx–Tg) and crystallization temperature (Tx) are measured to be 668 K, 90 K and 758 K, respectively. These values are nearly the same as those for the melt-spun ribbons prepared from the lower ejection temperatures. This result demonstrates that the appearance and disappearance of GT and SL region takes place reversibly only by controlling the ejection temperature of alloy liquid. It is noteworthy that the superheating to about Tl +770 K does not cause any appreciable change in alloy composition via evaporation of any alloy component and/or the reaction between the quartz tube and alloy liquid, though the oxygen content increases significantly for the alloy ribbon prepared from the high temperature region. However, as described later, the increased oxygen content is too low to explain the disappearance of GT and SL region. These experimental results suggest that the distinct difference in the DSC curves originates from the difference in the as-quenched structure which reflects the temperature dependence of the liquid structure.The Faber-Ziman structure factors S(Q) for the LT, HT and HLT Zr60Al10Ni10Cu20 ribbons are presented in . In general, all three S(Q)’s are similar. However, a closer look reveals that S(Q) of the ribbon obtained by melt-spinning at the high ejection temperature (HT ribbon) differs from S(Q) of the ribbon obtained at low ejection temperature. For example, the first peak for the HT ribbon is shifted to higher Q-values and the second peak is shifted to a lower Q compared to those on the structure factor of the LT ribbon (see and insets therein). In contrast, the structure factors of the HLT and LT ribbons are almost identical. It has to be emphasized that the structure factors shown in are obtained by high-energy XRD at the sample-to-detector distance of 30.62 cm. Additional high-resolution XRD measurements carried out at significantly increased sample-to-detector distance (1132.23 cm) proved the observed differences and similarities in the peak positions.A similar tendency is observed on the pair distribution functions g(r) plotted in . The g(r) functions for the HLT and LT ribbons are rather close to each other. However, the pair distribution function for the HT ribbon exhibits a notable difference, particularly in the position of the maxima corresponding to the first and the second coordination shells (see insets in ). According to the structural studies of Zr60Cu20Fe20Zr pairs, whereas the peak at about 5.25 Å could principally be related to ZrAl correlations. However, the contribution of Al is certainly very small for the Zr60Al10Ni10Cu20 composition. There is also observed a slight reduction of the short bonds (peak at about 2.78 Å) in the HT ribbon. Bearing in mind the size of the constituent atoms and the results of works At the next step, we have calculated the coordination numbers for the ribbons melt-quench at different conditions. For this, the densities of the ribbons were determined using the reduced density correlation function suggested by Il’inskii et al. The above results indicate that the atomic arrangement in Zr60Al10Ni10Cu20 ribbon obtained by melt-spinning at high ejection temperature differs from that in the ribbons obtained by ejection at low temperature. It is noteworthy that there is virtually no difference in the structure of LT and HLT ribbons (). This points to a reversibility of the structural changes in the melt upon heating and subsequent cooling.The structural features observed for the HT and LT ribbons correlate with those reported in earlier studies of liquid metals and alloys at different temperatures. It was found that the mean interatomic distance in the melts does not necessarily increase with increasing temperature as it is expected from the volume expansion, but even decreases With the aim of confirming further the appearance and disappearance of GT and SL region for the melt-spun alloy ribbons upon variation of the ejection temperature, thermodynamic properties of another typical bulk glassy alloy Zr55Al10Ni5Cu30 was examined. (a) and (b) show DSC curves and X-ray diffraction patterns of the Zr55Al10Ni5Cu30 ribbons prepared by ejection from the lower and the higher liquid temperatures of Tl +75 K and Tl +725 K, respectively. The DSC curve of the ordinary lower temperature ribbon shows a distinct GT, followed by a wide SL region, and the Tg and Tx are 678 K and 775 K, respectively. These values of Tg, Tx and ΔTx are nearly the same as the previously reported values for the Zr55Al10Ni5Cu30 glassy alloy (b) that the XRD pattern of the Zr55Al10Ni5Cu30 alloy samples prepared from the high Tel consists of only broad peaks without a crystalline phase.We further investigated a possibility whether alloy compositions deviate from the nominal values upon superheating of the liquid by examining the differences in oxygen content and alloy components between the high liquid temperature ejection sample and the lower temperature ejection sample. summarizes analytical oxygen contents obtained using the ribbon samples of 1 g by the high-temperature thermal decomposition method with an accuracy of 0.01 ppm for oxygen. The oxygen content of the Zr60Al10Ni10Cu20 ribbon increases from 214 ppm to 3544 ppm by the increase in ejection temperature from Tl +195 K to Tl +770 K. A similar increase in oxygen content is also recognized for the Zr55Al10Ni5Cu30 ribbon, as seen in . The increase in oxygen content might be due to the increase in the degree of the reaction between molten alloy and quartz tube and the increase in solidification time up to the temperature near Tg. However, the oxygen contents keep rather low levels of 3544–4963 ppm. It is notable that all the DSC data for ZrAl-TM base glassy alloys show the distinct Tg and wide SL region in the oxygen content range below 5000 ppm Al-TM base glassy alloys decreases with increasing oxygen content in the range up to 5000 ppm examined up to date shows the EDX intensity profiles of alloy components as a function of energy for the Zr60Al10Ni10Cu20 and Zr55Al10Ni5Cu30 alloy ribbons prepared from the ejection temperatures of Tl +195 K, Tl +770 K and Tl +75 K, Tl +725 K, respectively. No distinct difference is recognized in alloy component concentrations obtained from the EDX profiles, though some scattering is seen. Besides, no appreciable peak of any kind of oxides is recognized, being consistent with the analytical oxygen data shown in . These data demonstrate clearly that there is no distinct difference in alloy component concentrations upon superheating for the Zr-based alloy ribbons with nominal atomic compositions of Zr60Al10Ni10Cu30 and Zr55Al10Ni5Cu30, implying that the superheating of alloy liquid to above Tl +700 K does not cause an obvious deviation of alloy compositions.Furthermore, we analyzed the surface alloy component in the surface region by Auger spectroscopy. (a) – (f) refer to the Zr60Al10Ni10Cu20 ribbons cast from low (normal) temperature Tl +195 K, high temperature Tl +770 K and lower temperature (i.e. Tl +420 K) after the melt was overheated to Tl +770 K, respectively. In all figures, the micrographs (a) show the free surfaces, while the micrographs (b) present the surfaces contacting the Cu wheel by melt-spinning. Due to the formation of typical “air pockets” by melt-spinning, the surfaces show some roughness down to micrometer scale. Therefore, in order to exclude the possible measurement artefacts, the AES analysis was performed on several places, as marked in (a)–(f) by rectangles. As can be observed, the free surfaces show solidified droplets, while such features are absent from the surfaces in contact with the wheel, because it mimics the mirror-like polished wheel. Consequently, the micrographs in (a), (c) and (e) are presented at 500 × magnification, while in the case of (b), (d) and (f) the magnification is set to 2500 × . Due to the fact that in the case of AES the information comes only from a very thin layer on the surface, the analysis was focused to quantify the Zr content (because Zr is the most reactive component and therefore the most susceptible to chemically react with the environment), O content and Si content (Si may be dissolved from the melting crucible during long-time and/or high-temperature heating prior ejection). The data are summarized in . For simplicity, only the mean content is given. In order to understand the distribution of the values, the standard deviation is specified as well (the numbers in parenthesis). All values are in at. %.At the first glance is to remark that the O values are very high clearly indicating the presence of oxides on the surface. Therefore, these values characterize rather the surface of the ribbons than their volume. The Si is also present, being an indication that the molten alloys reacted superficially with the quartz glass containers. Reasonably, Si content is slightly higher in the ribbons melt-spun from high temperature or after the heat treatment in the molten state. The different faces seem to have different Si content, but there is no clear trend: the ribbon cast from high temperature shows larger Si content on the free surface, while after thermal treatment in the liquid state the free surface has lower Si content. Also, the ribbon cast from low temperature shows the same content of Si on both sides. The standard deviation is minimal in the case of ribbon melt-spun from low temperature and then increases (almost) monotonously as the ejection temperature increases.Regarding the O content, there are several aspects which should be considered. First of all, there are differences between the two faces of the same ribbon, usually the free side showing less O than the side contacting the wheel. The standard deviation is much higher in case of the free-solidified side, excepting the ribbon quenched upon thermal cycling, which show very close values for both sides: 44% and 49% from the mean values, respectively. It is interesting that the ribbon cast from low temperature seems to show the maximum O content. This diminishes in the case of ribbon cast from high temperature, decreasing further for the ribbon cast from thermally treated alloy. Further, there are no consistent differences regarding the Zr content measured on different sides of the same ribbon. Also, it is always around 40 at.% for all ribbons, which is 20 at.% lower than the nominal content of the alloy. All together it is to conclude that the AES data put in evidence the presence of oxides on the ribbon surfaces, but there is no significant difference that scales with the melt-treatment before quenching.A fully crystallized structure was also examined for the Zr60Al10Ni10Cu20 samples heated for 3.6 ks at 873 K which is much higher than the overall temperature of the exothermic peak due to crystallization, with the aim of clarifying the influence of the appearance and disappearance of GT and SL region on crystallization structure. The DSC curves in indicate the exothermic peaks for all ribbons. The XRD patterns of the crystallized samples prepared by ejection from Tl +195 K (LT ribbon) and Tl +770 K (HT ribbon) in reveal differences in the intensity of the diffraction peaks. However, most of the peaks can be identified as Zr2Cu, Zr2Ni, Zr3Al2 and ZrNi phases for both the samples, which is independent of ejection temperature. These crystallization phases agree with the some previous data Cu atomic pair has been changed between the HT and LT samples. Considering that glassy alloys with glass transition are formed only in ZrCu atomic pair plays an important role in the achievement of glass transition phenomenon even for the ZrNi glassy alloys. The decrease in the X-ray diffraction peaks of Zr2Cu phase implies the decrease in the number of ZrCu atomic pairs and/or the weakness of the ZrCu atomic pair bonding strength for the HT ribbon, being consistent with the absence of the glass transition and supercooled liquid region for the HT ribbon of the ZrNi alloy. The similar change in the diffraction peaks of each precipitation crystalline phase including Zr2Cu is also observed for the LT and HT ribbons of another Zr55Al10Ni5Cu30 glassy alloy as shown in . In any event, the identification of the same crystallization phases also indicates that both samples do not have distinct deviation of alloy compositions, being consistent with the results obtained by the EDX, AES and high-temperature thermal decomposition methods. The similar crystallization behavior for the Ni60Al10Ni10Cu20 alloy ribbons in glassy and amorphous states is different from the previous studies Moreover, it is established that both HT and LT ribbon samples have a good bending ductility and can be bent through 180° without fracture, accompanied by generation of a high density of shear bands. shows the SEM images revealing the bending deformation behavior on the bent outer surface of the Zr60Al10Ni10Cu20 alloy ribbons produced by ejection from the lower and the higher liquid temperatures. A number of shear bands are observed on the bent surface and there is no appreciable difference in the deformation-induced shear band structures. summarizes Vickers hardness values of the Zr60Al10Ni10Cu20 and Zr55Al10Ni5Cu30 alloy ribbons prepared by ejection from the lower and the higher liquid temperatures. The respective hardness values of the two alloy samples are 495 and 500 for the lower ejection temperature samples and 675 and 748 for the higher ejection temperature samples. Thus, the higher temperature samples have much higher hardness values than those for the lower temperature samples. The difference is interpreted from the change in Tg with ejection temperature. There is a general tendency for Vickers hardness to increase with increasing Tg implies the increase in the bonding force among the constituent elements and the decrease in atomic mobility through the change in the disordered structure, resulting in the higher Vickers hardness values for the HT samples. In addition, the increase in ejection temperature decreases the cooling rate of liquid , a number of slip markings via the generation and propagation of shear bands were observed in the region just near the indenter traces. The density and length of slip markings were more significant for the lower liquid temperature sample than for the higher temperature sample, being consistent with the difference in Vickers hardness. The obvious changes in thermal stability and Vickers hardness by changing the ejection liquid temperature also suggest that physical and engineering properties can be controlled by changing the ejection temperature and consequently liquid structure even for glassy alloys with the same compositions.Finally, it is important to note that the same reversible phenomenon of the appearance and disappearance of GT and SL region has been recognized for many other bulk glassy type alloys such as Zr). Besides, the analytical oxygen contents of these alloy ribbons prepared from the high ejection temperature region were less than 5000 ppm. Thus, this phenomenon seems to be universal for Zr- and CuThe Zr60Al10Ni10Cu20 and Zr55Al10Ni5Cu30 bulk glassy alloys reported up to date exhibited a distinct GT, followed by a wide SL region and then crystallization summarizes the features of thermal stability, precipitation phase and some properties of the melt-spun ZrCu alloy ribbons prepared from the ordinary heated and superheated liquids, together with analytical oxygen contents. Also in the present study, we can recognize GT and SL region for the glassy alloys prepared by melt-spinning in the wide liquid temperature region of Tl +75–580 K. However, we have found that neither GT nor SL region is observed for the melt-spun ribbons prepared from the higher temperature of Tl +720 K and the Tx increases slightly than that for the glassy ribbons prepared from the lower liquid temperatures, in spite of the absence of appreciable change in alloy compositions. In addition, the analytical oxygen contents lie in the concentration range where distinct GT and SL are always observed. It is thus noticed that only the significant increase in the ejection liquid temperature in the melt-spinning production process causes the reversible transition of appearance and disappearance of GT and SL region which cannot be interpreted by the increase in oxygen content.Here we discuss in more details the influence of oxygen which may be dissolved into the Zr-based alloy liquid through the reaction between alloy liquid and quartz tube during the higher temperature melting. On the basis of a number of data on the influence of oxygen on the formation, thermal stability and crystallization of Zr-based glassy alloys, it is known that many properties and decomposition behavior of glassy alloys are affected by the dissolution of oxygen The above mentioned changes in thermal stability and decomposition behavior for the Zr-based glassy alloys containing intentionally added oxygen are essentially different from the present results for the Zr-based alloys prepared from the higher temperature region of Tl +770 K, except for the rise of Tg. In addition, the analytical oxygen contents in the present Zr-based alloys prepared from the higher temperature region are 3544 ppm for Zr60Al10Ni10Cu20 ribbon and 4963 ppm for Zr55Al10Ni5Cu30 ribbon which are nearly the same as those (1400–5000 ppm) It has been reported that the Zr-based multicomponent bulk glassy alloys are composed of high-coordinated icosahedral-like medium range ordered atomic configurations which have considerably high meta-stability The discovered phenomenon of appearance and disappearance of GT and SL region in melt-spun Zr-based ribbons is thought to reflect the as-frozen structure of the melt before quench. Bearing in mind the coordination numbers for the HT and LT ribbons obtained from the high-energy XRD (13.53 and 13.77 atoms, respectively), the disappearance of GT and SL region for the HT ribbons implies that the high-coordinated atomic configurations have been changed to a lower-coordinated configurations in the highly superheated liquid. That is, dynamic long-range cooperative rearrangements of the constituent atoms leading to the appearance of GT phenomenon Ti glassy alloy that the increase in ejection (casting) temperature causes the decrease in cooling rate, resulting in a much relaxed disordered structure Here it is important to point out that the disappearance of GT and SL region is not due to the existence of fine crystallites. As shown in (b), no any trace of crystallites is seen in the XRD patterns, TEM and HRTEM images for the ribbons prepared from the higher liquid temperature. Besides, there is a number of previous studies showing the distinct appearance of GT and SL region even for the glassy alloys including an appreciable amount of crystalline phase It is generally known that the addition of the immiscible elements leading to the positive heats of mixing to glassy type alloys causes the destruction of the high-coordinated medium-range ordered atomic configurations which results in the disappearance of GT and SL region The conventional bulk glassy alloys in Zr-based alloy systems have also been produced by using an arc-melting method We found that the Zr60Al10Ni10Cu20 and Zr55Al10Ni5Cu30 melt-spun ribbons prepared from the lower (ordinary) ejection liquid temperatures of Tl +75–580 K exhibited GT, followed by SL region and then crystallization, while the ribbons prepared from the much higher ejection temperature of Tl +725 K did not show distinct GT and SL region, though their Tx increased slightly. The transition occurred reversibly only by changing the ejection temperature. No appreciable difference in crystallized phases was seen for the lower and the higher ejection temperature ribbons. All studied ribbons exhibited a good bending ductility. The hardness was much higher for the ribbons prepared from the higher ejection temperatures. The new result that the GT and SL region disappear for the higher ejection temperature ribbons, cannot be interpreted by the increase of oxygen content to 3540–4960 ppm. The observed phenomenon is presumably because the frozen structure changes from the high-coordinated atomic configurations, which enable the cooperative atomic rearrangements for GT for the ordinary glassy alloy, to the looser-coordinated structural units with difficulty of the cooperative atomic rearrangements. The finding of the reversible transition between glassy and amorphous structure for typical Zr-based alloys with the same compositions is supposed to be universal for bulk glassy alloys and is expected to cause a further development of science and engineering for ordinary liquid, supercooled liquid and glassy materials by use of the new control method.The following is the supplementary data related to this article:Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.actamat.2016.06.049Electrical and mechanical properties of multi-walled carbon nanotube reinforced Al composite coatings fabricated by high velocity oxygen fuel sprayingMulti-walled carbon nanotube (MWCNT) reinforced Al composite powders were deposited using a high velocity oxygen fuel (HVOF) spraying process to form coatings. High thermal energy and physical contact with atmospheric oxygen were supplied as the MWCNT/Al composite particles were exposed to a gas flow field of high temperature (~ 3.0 × 103 |
K) during HVOF spraying. As a result, the particles underwent full or partial melting and rapid solidification during deposition. Large fraction of lamellar structure was formed in the HVOF sprayed coatings due to the low melting point of Al. The high temperature environment and the exposure to oxygen induced the interfacial reaction of MWCNTs within the splats. The electrical and mechanical properties (elastic modulus and micro-hardness) of the MWCNT/Al composite coatings were evaluated. The variations of measured properties of the MWCNT/Al composite coatings were related to the contribution of the remaining MWCNT and the typical lamellar structure. In this study, the relationship among the properties, structure and the interaction of the MWCNTs with the Al matrix is experimentally and theoretically discussed.► The MWCNT/Al composite coatings were fabricated by HVOF process. ► Microstructure and MWCNT states in the composites were characterized. ► Electrical and mechanical properties of the composite coatings were evaluated. ► Relationship between microstructural factors and properties were investigated.Since carbon nanotubes (CNTs) were discovered in the early 1990s, they have been intensively studied due to their extraordinary physical and mechanical properties, including high thermal and electrical conductivities, elastic modulus and tensile strength MWCNTs reinforced in a metal matrix mechanically interact with the matrix. The dispersed MWCNTs in the metal matrix inhibit dislocation movement, and active dislocation interaction occurs near the MWCNTs, resulting in strengthening of the MWCNT/metal composite by dispersion hardening. MWCNTs reinforced in a metal matrix lead to anchoring effects, as the MWCNTs are able to hold the metal matrix under a severe deformation environment, thereby enhancing mechanical properties such as wear resistance Al, which is widely utilized in industry, has limited industrial applications due to its high ductility. Reinforcement of an Al matrix with MWCNTs enhances Al's mechanical and physical properties. Kim et al. In this study, MWCNT/Al composite powders with MWCNT fractions of 0.5 and 1.0 wt.% were fabricated by mechanical ball milling. The composite powders were subjected to HVOF spraying to form coatings. HVOF spraying is involved with the combustion of fuel gas to form a high temperature gas flow field shows the field emission transmission electron microscopy (FE-TEM) bright-field (BF) image of the initial MWCNTs. The diameter of the MWCNTs ranged in between 20 and 50 nm. The diameter of the MWCNTs was measured through image analysis of FE-TEM BF images. The shape of the MWCNTs showed high aspect ratio. The HREM image of the outer walls of a MWCNT revealed a typical bamboo structure (b). The interspacing of the outer walls was 3.34 Å, which is identical to that of the basal planes in graphene. The MWCNTs had typical structure with no other phases, such as amorphous carbon or impurities, and included the disconnection of the wall. c shows the morphology of the pure Al powder. The Al powder was spherical with diameter of − 45 + 6.5 μm and 99.99% purity.To fabricate the MWCNT/Al composite powder, the Al powder and MWCNTs were blended with 0.5 and 1.0 wt.% MWCNTs for 24 h using a blending machine. The blended powder was ultra-sonicated with ethanol to facilitate the homogeneous dispersion of the MWCNTs. The blended powders were mechanically milled for 5 h using a plenary ball milling machine (Pulerisette5, Fritsch). The rotational speed was 200 rpm and zirconia ball media was used. The ball to powder mass charge ratio was approximately 10:1.A commercially available HVOF spraying system (Hipojet 2100, Plasma Powders) was used to construct the MWCNT/Al composite coatings. Details of the equipment and HVOF spraying process have been explained previously shows the HVOF spraying process parameters, employed in this study. HVOF spraying was performed under ambient environmental conditions, using mild steel (0.19 wt.% C, 0.28 wt.% Si, 0.85 wt.% Mn, 0.035 wt.% P, 0.032 wt.% S) plates as a substrate. Prior to deposition, the substrates were grit-blasted to introduce surface roughness.The thermal reactivity of the initial materials (the MCWCNTs, Al, and composite powders) was analyzed prior to the spraying using a differential scanning calorimetry (DSC) (DSC404 F1, NETZSCH). DSC analysis was performed under atmospheric conditions and the heating rate was 10 °C min− 1. The microstructure of the MWCNT/Al composite powders and coatings were analyzed using a field emission (FE) scanning electron microscopy (SEM) (JSM-7500F, JEOL) and a SEM (JAM5600, JEOL). To observe the microstructure of the coating cross-section, specimens were etched at room temperature with Kroll's reagent (3 ml HF + 6 ml HNO3 |
+ 100 ml H2O). FE-TEM (Tecnai G2 F30 S-Twin, FEI) was employed to analyze the interaction between MWCNTs and the Al matrix during HVOF spraying. High-resolution electron microscopy (HREM) images were analyzed using image analysis software (DigitalMicrograph, Gatan). For TEM sampling, the coatings were mechanically polished with direction perpendicular to the coating surface. The polished thin foils were punched, and electrolytic jet-polished (Tenupol-3, Struers), using 5% perchloric acid and 95% methyl alcohol electrolyte solution. The polishing voltage was 10–15 V, and the temperature was less than − 40 °C. The grain size and distribution were measured by image analysis software (Image-Pro Plus, Media cybernetics).The electrical resistivity of the coatings was measured using a four-point probe (Jandel). Mechanical properties, including the elastic modulus and micro-hardness, were measured. The elastic modulus of the coatings was measured using an instrumented ball indentation test (AIS 300R, Frontics) with a 0.25 mm radius spherical indenter. Multiple-indentations, including 15 loading and unloading cycles, were employed with a maximum indentation depth of 50 μm. Details of the instrumented ball indentation test have been described in the literature The fabricated MWCNT/Al composite powder with 1.0 wt.% of MWCNTs is shown in . The harsh mechanical milling led to severe deformation and rewelding of Al particles, embedding MWCNTs into the Al matrix and preventing observation of the MWCNT surface. A similar phenomenon was observed by Esawi et al. b). The excessively etched cracks exposed MWCNTs as seen in b. The composite powders were nearly spherical with diameter of − 47 + 5.2 μm, which was similar to that of the initial Al.The DSC thermograms of the initial MWCNTs, Al, and composite powders are shown in . The initial MWCNTs had a broad and intense exothermic peak with a range of approx. 530–690 °C. Since the DSC tests were performed under atmospheric conditions, the physical contacts of the MWCNTs with oxygen in the air incur chemical reactions at the elevated temperature after obtaining enough activation energy. The thermally activated oxidation of the MWCNT led to the exothermic reaction. The carbon elements of MWCNTs reacted with oxygen, and then were gasified into carbon oxide or dioxide (CO or CO2). The Al powder showed only sharp endothermic peak near 660 °C due to melting. Although the oxidation of Al might occur, the reaction was not identified in the DSC curve. The MWCNT/Al composite powder (0.5 wt.%) had an endothermic peak at 660 °C and an exothermic peak at 665 °C. As shown in a and b, the MWCNTs were embedded in the Al matrix, i.e., they were not exposed to the surface of particle. The oxidation of the MWCNTs embedded in the Al matrix was delayed until the Al melted at 660 °C since Al inhibited physical contact with oxygen. As the Al melted from the surface, the MWCNT came in contact with oxygen and oxidation occurred. The MWCNT/Al composite powder (1.0 wt.%) showed thermal behavior similar to the that of composite of 0.5 wt.%. As the MWCNT fraction increased, the exothermic heat flow of the MWCNT oxidation increased. shows the microstructures of the MWCNT/Al composite coatings (1.0 wt.%). As all of the powders were sprayed under the same process conditions, the microstructures of the coatings were not significantly different. The XRD patterns of three different coatings in showed the same peak combination and were identical to that of the powder, which indicates that no significant phase transformation or oxidation of Al occurred during HVOF spraying. The MWCNTs were not detected due to their small size and uniform dispersion as well as resolution limitations of XRD.The coating microstructures were primarily composed of lamellar structure and un-melted particles (white arrows in a indicate un-melted parts). The fraction of un-melted particles on the coating was approximately 18% for both the Al and MWCNT/Al composite coatings, indicating that a large fraction (more than 80%) of in-flight particles experienced complete melting. The melted and un-melted area fractions were measured by image analysis of more than ten SEM images.The MWCNTs in the un-melted particle parts were not severely mechanically or thermally affected by the high temperature gas flow and oxygen during HVOF spraying. shows the FE-TEM BF images of un-melted part adjacent to the melted splats of composite coating (1.0 wt.%). The un-melted part included dislocation tangles (black arrows in a) due to plasticity during deposition. The melted splats resolidified producing fine grains with low dislocation density (b). The dislocations (indicated by the black arrow in b) in the lamellar structures might be produced by subsequent impacts of the particles and tensile stress formed by residual stress after deposition.Fully melted particles were thermally affected, and melted during flight. As the liquid droplets impacted the substrate or the previously deposited coating layer, they were transformed into splats (b), and rapid solidification of the splats occurred upon impact. In the literature, the splat cooling rate is between 106 and 107 |
K s− 1b (white arrows). The splat microstructure was composed of fine equiaxed grains with a mean grain size of 280 nm (b). The ultrafine grain formation was attributed to the homogeneous nucleation and high cooling rate of the splats shows HREM images of the MWCNTs in the un-melted part of the partially melted particle and the fully melted splat, respectively. The MWCNT in the un-melted part of the partially melted particle maintained its initial structure during HVOF spraying and had a typical nano-bamboo structure. The interspacing of the walls was 3.34 Å, which corresponds to the interspacing of the (002) basal plane (b). Bent outer walls in the MWCNTs were observed (a). The outer walls may have been bent during mechanical milling rather than during HVOF spraying. Alternatively, the MWCNT surface in the fully melted splat was destroyed (c). The disconnected outer walls were curled, as shown in d), the interspacing of the inner walls was 3.34 Å. But, the interspacing of the outer walls was 3.90 Å, indicating that the outer walls were wider than the inner walls. The width of the upper part of the MWCNT was 18.75 nm, which was less than that of the lower part of the MWCNT (30.79 nm). illustrates the electrical resistivity of the Al and MWCNT/Al composite coatings. The electrical resistivity decreased linearly with an increase in MWCNT. The mean electrical resistivities of 1.0 and 0.5 wt.% MWCNT/Al composite coatings were 6.0 and 7.6 μΩ cm, respectively. The mean electrical resistivity of the Al coating was 10.4 μΩ cm. The mean electrical resistivity slightly decreased with MWCNT fraction. Considering the error ranges, the measured values were similar.The elastic modulus data for the Al and MWCNT/Al composite coatings are shown in . The mean elastic modulus of the Al coating was 64.2 GPa, while the mean elastic moduli of the 1.0 and 0.5 wt.% MWCNT/Al composite coatings were 76.8 and 68.9 GPa, respectively. As the MWCNT fraction within the coating increased, the mean elastic modulus slightly increased. Considering the error range, the elastic modulus of the coatings was similar.The micro-hardness data for the coatings are presented in . The micro-hardness slightly increased with an increase in MWCNT fraction. The mean micro-hardness values of the 1.0 and 0.5 wt.% MWCNT/Al composite coatings were 56.7 and 49.4 Hv, respectively, and the mean micro-hardness of the Al coating was 30.3 Hv.The thermal energy transferred from the gas flow of the HVOF spraying increases the temperature of the particles and induces the melting of the particles. The gas flow in HVOF spraying has a temperature gradient with a Gaussian distribution where dP, h, Tg, TP, ρP and CP are the particle diameter, heat transfer coefficient, gas temperature, particle temperature, particle density and particle specific heat, respectively. The temperature of the particle can be derived from Eq. The un-melted parts of the partially melted particles are at a lower temperature than the melted particles. In the solid state, oxygen diffusion into the particle is not feasible during HVOF spraying. Thus, oxidation of the particle is localized at the particle surface. MWCNTs in the un-melted regions could not come into contact with oxygen during HVOF spraying, therefore protecting them from oxidation. As such, the structure of the MWCNTs in the un-melted part is preserved in its initial state, as shown in a. Fully melted particles are supplied with a high thermal energy and their temperature, which approaches 1.3 × 103 |
K, is relatively high. Thus, oxidation can be thermally activated during HVOF spraying. A mixture of liquid Al and oxygen can form while the liquid Al particle is in-flight. The in-flight state also promotes oxidation by increasing the probability for contact between the liquid Al and oxygen. Accordingly, the MWCNTs in fully melted particles are exposed to high temperature and an activated oxidation environment. The schematics in represent the oxidation of the MWCNT during HVOF spraying. The MWCNT oxidation reduces the fraction of MWCNTs in the HVOF sprayed coatings and the MWCNTs are reduced to a curled-up structure.The electrical resistivity of the HVOF sprayed MWCNT/Al composite coatings is highly influenced by the MWCNT states and microstructural factors of the HVOF sprayed coating. The microstructural factors are the inter-particle boundary, pores, grain boundary and dislocations. These factors play a role as defects for electron transfer within the coating, and increase the electrical resistivity. The electrical resistivity of the Al coating was 10.4 μΩ cm, which was greater than that of coarse-grained Al (2.65 μΩ cm) due to defects in the HVOF sprayed coatings. Approximately 80% of the Al and composite coating area were melted splats consisting of resolidified fine grains. These grains had a very low dislocation density. But, the grain-boundary area increased via rapid nucleation (b). The grain boundaries (arrangement of dislocations) and dislocations increase the electrical resistivity. A dislocation of Al has a specific resistivity value of 1.5 × 10− 18 |
μΩ cm3where fMWCNT is the volume fraction of the MWCNTs in the coating. Based on Eq. , an increase in the MWCNT fraction in the coating led to a decrease in the electrical resistivity. But, the contribution of MWCNTs to electrical conduction was overshadowed by the pores and inter-particle boundaries. The porosity and inter-particle boundaries of thermal sprayed coatings significantly increase the electrical resistivity The mean elastic modulus of the coatings slightly increased with an increase of the MWCNT fraction in the coating, as shown in . Many studies have reported the excellent elastic properties of MWCNTs where EMWCNT is the elastic modulus of the MWCNT, EMWCNT is the elastic modulus of a single-walled carbon nanotube (SWCNT), N is the number of walls, and R denotes the effective wall thickness (h) to the wall inter-spacing (d) ratio (h/d). The elastic modulus of the SWCNT was 4.7 TPa in this study Ecomposite=38fMWCNTEMWCNT+1−fMWCNTEAl+58EMWCNTEAlEMWCNT1−fMWCNT+EAlfMWCNT., the elastic modulus of composites increases with an increase in MWCNT volume fraction. But, in the experimental results, the increase in the mean elastic modulus of the coatings with an increase in MWCNT fraction was not remarkable. The insignificant increase of the elastic modulus is influenced by gasification and destruction of the MWCNTs and structural factors of the Al matrix. The structural factors are residual stress, and pore and inter-particle boundary. In this study, the effects of residual stress on the elastic modulus are difficult to predict because of complexity of the residual stress of HVOF sprayed coatings. It is noted that residual stress of HVOF sprayed coatings is compressive due to high velocity impact and plastic deformation of partially melted particles The micro-hardness represents the plastic behavior of the MWCNT/Al coating, and was determined by a set of factors related to the mechanical interaction between the MWCNT and Al matrix, and structural factors. The hardening factors of the composite coatings are grain boundary hardening, MWCNT dispersion hardening, and strain hardening. The micro-hardness of the Al coating (30.3 Hv) was greater than that of the coarse-grained Al (15.0 Hv), primarily due to the strengthening of the grain boundary and the strain hardening of the Al coating. The Hall–Petch relation describes the contribution of the grain boundary to strengthening and can be expressed as follows where kH is the Hall–Petch constant and d is the grain size. During rapid cooling of the melted splats, grain refinement occurred, reducing the grain size to 278 nm and increasing the strength. The Hall–Petch constant of Al is 0.04 MPam1/2During the mechanical milling process, particles can undergo strain hardening. In the case of the melted splat, dislocations are removed during the melting and resolidification process. Dislocations generated during mechanical milling remain in the un-melted parts, and these dislocations partially contribute to the strengthening of the HVOF sprayed coating. But, strengthening by strain hardening is negligible considering the low fraction of un-melted parts and the high contribution of grain refinement to strengthening.The slight increase in micro-hardness of the coatings with an increase in MWCNT fraction cannot be explained by strengthening due to grain boundary and strain hardening because no significant microstructural differences between the coatings were observed. MWCNTs dispersed in the Al matrix contributed to the increased strength due to dispersion hardening. As the dislocations in the ductile Al matrix intersected with the MWCNTs, they were unable to cut the stiff MWCNTs. As a result, a pile-up of dislocations occurred, promoting hardening of the Al matrix near the MWCNTs. If a higher stress were applied, a dislocation loop could be formed, causing dislocation multiplication and strain hardening.In contrary to the hardening factors, pores and inter-lamellar voids in Al matrix degrade the strength of the composite coatings. Deng et al. reported that the micro-hardness of the sintered MWCNT/Al composite (1.0 wt.%) was approx. 137 Hv, which is greater than the results of this study (56.7 Hv) The fabricated MWCNT/Al composite powders with 1.0 and 0.5 wt.% MWCNT fraction and pure Al were HVOF sprayed to form dense coatings. The relationships among MWCNT state, microstructural factors and the measured electrical and mechanical properties of the composite coatings were investigated. The superior physical and mechanical properties of MWCNTs and their contribution to enhancement in the properties of the HVOF sprayed composite coatings were inevitably overshadowed by loss and destruction of MWCNTs and innate defects of the Al matrix such as inter-lamellar voids and pores. The surviving or remaining MWCNTs in the composite coatings partially contributed to electrical conductivity, elastic modulus and micro-hardness, but the enhancements were insignificant compared with the sintered MWCNT/Al composites. In order to improve the properties of the HVOF sprayed MWCNT/Al composite coatings, increase in remaining or un-reacted MWCNTs and decrease in void, pores and residual stress through process optimization are necessary.Multifield modeling of electromagnetic metal forming processesThe purpose of this work is the formulation of a thermo-magneto-mechanical multifield model and presentation of the numerical strategies applied. In particular, this model is used to simulate electromagnetic sheet metal forming processes (EMF). In this process, deformation of the workpiece is driven by the interaction of a current generated in the workpiece by a magnetic field generated by a coil adjacent to the workpiece. The interaction of these two fields results in a material body force known as Lorentz force. Up to now, modeling approaches found for EMF in the literature are restricted to the axisymmetric case. For real industrial applications however, the modeling of three-dimensional forming operations becomes crucial for an effective process design. The implementation of such a 3D model still represents work in progress. Results shown in this paper are restricted to the axisymmetric case.Electromagnetic forming is a dynamic, high strain-rate forming method in which strain-rates of ≥103 |
s−1 are achieved. In this process, deformation of the workpiece is driven by the interaction of a current generated in the workpiece with a magnetic field generated by a coil adjacent to the workpiece. In particular, the interaction of these two fields results in a material body force, i.e., the Lorentz force and the electromotive power, representing an additional supply of momentum and energy to the material. On the other hand the EM-system is sensitively influenced by the spatio-temporal evolution of the mechanical structure.In recent years considerable effort has been undertaken to simulate such coupled processes. However, approaches tested so far were mainly restricted to 2D or axisymmetric geometries The coupled multifield model for electromagnetic forming of interest here, represents a special case of the general continuum thermodynamic formulation for inelastic non-polarizable and non-magnetizable materials given in 0=∫Br(ρrξ¨−lr)ξ*+KF−T∇ξ*,0=∫R{a˙−LTa}a*+∫R{χ−av}diva*+κEMcurlacurla*,0=∫R∇χ∇χ*,for ξ, a, and χ, respectively. Here, ξ*, a*, and χ* represent the corresponding test fields. Further, R represents a fixed region in Euclidean point space containing the system under consideration in which the electromagnetic fields exist and on whose boundary the boundary conditions for these fields are specified. Here, the system consists of the workpiece, the tool coil, and air (see ). As such, R contains in particular the fixed reference configuration Br, and all subsequent (i.e., deformed) configurations, of the workpiece. Here, F |
:= ∇ξ represents the deformation gradient, and L |
:= ∇v the spatial velocity gradient. Further, κEM represents the magnetic diffusivity, v the spatial velocity field, ρr the referential mass density, K the Kirchhoff stress, and lr |
= det(F)j |
× |
b the Lorentz force in terms of the magnetic flux b |
= curl |
a and the current density j. Note that (1)2,3 follow from Maxwell's equations, while (1)1 represents the weak form of the momentum balance. The above weak field relations are completed by the thermodynamically consistent formulation of the adiabatic thermo-elasto-viscoplastic material model Consider next the finite element discretization of . The difference in electromagnetic and thermo mechanical timescales together with the distinct nature of the fields involved (i.e., Eulerian in the electromagnetic case, Lagrangian in the thermo mechanical large deformation context), argue for a staggered numerical solution procedure in two different meshes resulting in the following algorithmic system:in terms of the arrays xn+1 and a˜n+1 of time-dependent system nodal positions and vector potential values at instance tn+1. The solution of the mechanical part of involves in particular the consistent linearization required for the Newton–Raphson iteration in the context of large deformation inelastic problems. In detail, the staggered algorithm procedure consists of the following steps:Initialize a˜0, x0 and their time derivatives and proceed to (4).A starting value a˜n+1 of the nodal vector potential array is computed for the measured amperage in the tool coil at time tn+1 and the known mechanical state of the system at time tn via (2)2.From a˜n+1, a corresponding value ln+1 for the Lorentz force is obtained. Using this, the system consisting of (2)1 is solved via Newton–Raphson iteration (i.e., at fixed a˜n+1) to obtain xn+1.Proceed to next time step tn+1 |
= |
tn |
+ |
tn,n+1 and proceed with (2). Else, if tn |
≥ |
ts, terminate the simulation, where ts is the total simulation time.Besides its physical motivation, the staggered algorithm offers the possibility to apply custom solutions for both the mechanical, as well as the EM-system. Here, on the mechanical side an effective continuum shell formulation is applied to minimize the computational effort Such elements suffer from their inability to represent sharp transitions imposed by the different EM-properties of the surrounding air and the workpiece. This approach is known from fluid structure interaction as the fictitious boundary method.A more recent approach applies an incrementally progressing mesh-updating algorithm Here, the position of the nodal coordinates of the EM-mesh is determined by means of solving a Laplace problem. On the surface of the workpiece, tool coil and boundary of the computational domain of the EM-system Dirichlet boundary conditions for the Laplace problem are applied: at each instance the boundary of the workpiece moves and prescribes a displacement increment for the new nodal positions of the EM-mesh such that the nodes of both meshes match at the boundary of the workpiece. As a result, at any time, mechanical and EM-mesh exhibit a consistent morphology as depicted in Results shown here are obtained on the basis of an axisymmetric model. Simulations have been carried out for a sheet metal plate consisting of the aluminium alloy AA 6005. The identification of the dynamic viscoplastic material parameters for this material has been carried out with the help of experimental data of the dynamic expansion of metal tubes via a maximum likelihood estimation using finite element simulations together with experimental data . In particular, the distribution of the radial component br of the magnetic flux during forming at 22 μs (above) and 80 μs (below) is shown. The radial component of b drives the forming operation resulting in an axial body force component. Initially, close to the tool coil, the equilibrium values of a and so the Lorentz force are extremely high. When the sheet-plate is accelerated away from the tool coil, however, it moves into a region where a is nearly zero.Forming stages for the plate at various instances are shown in . The contours represent the development of the accumulated inelastic deformation ɛP and the yield stress. Maximum values of the strain-rate reached here are on the order of 104 |
s−1.At the beginning of the process, the center of the plate remains at rest, whereas at a radius of about r |
= 21 mm, the plate experiences high Lorentz forces and begins to accelerate. In later stages, the center of the plate is then pulled along by the rest of the plate and accelerated via predominantly inertial forces, resulting in the cap shaped structure at the end of the process with maximal inelastic strain in the top of the cap. The accompanying yield stress development shown in displays clearly the corresponding maximal increase of the yield stress in the center of the late. The above-discussed results were obtained on the basis of 2D axisymmetric forming processes.Internal stress influence on the coercivity of FeCuNbSiB thin filmsThin films of Finemet-type alloy with thickness varying from 50 to 1000 nm have been deposited by RF sputtering and annealed at temperature ranging from 150 to 450 °C. Their magnetic and structural properties have been characterized using alternating gradient field magnetometry and X-ray diffraction. In addition, the stress in the films has been measured as a function of temperature from the curvature of the wafers using a laser scanning technique.The coercive field of the films first decreases with annealing temperature due to stress relaxation, and then increases again when crystallisation begins. The optimal annealing conditions comprises between the glass transition and the crystallisation temperature.Its is observed that the coercivity of the as-deposited material is continuously decreasing as the thickness increases, following an inverse square root dependence, in relation with the stress-induced magneto-elastic contribution to the total anisotropy. By opposition, it has been found that the coercive field of devitrified and totally relaxed films is inversely proportional to film thickness. In order to explain this evolution, a model is proposed, based on random anisotropy considerations applied to thin films in which the anisotropy was considered localised in the dimension of thickness.The efficiency of electromagnetic microdevices involving soft magnetic materials like actuators, sensors or transformers is most of the time driven by the magnetic losses in the constitutive ferromagnetic layer. In this frame, the research in this domain is oriented to the fabrication of thin films with the softest magnetic properties.However, magnetic softness is highly dependent on the internal stress induced both by the deposition technique and the differential thermal expansion with the substrate:with μw, μf, Ef, υf and ΔT, respectively, the thermal expansion coefficients of the substrate and the film, the Young modulus and Poisson's ratio of the film and the temperature variation involved in the thermal expansion process. The sputtering technique, despite its convenience, is known for inducing high stress in the deposited films. Nevertheless, the contribution of stress to the magnetic anisotropy can be limited by the using of a non-magnetostrictive material or by a specific sample preparation or heat treatment.The permalloy is often used as a soft magnetic material in microsystems, because it is easy to produce by sputtering or electrodeposition. However, this material suffers from a low electrical resistivity, which is detrimental to its high frequency use. Since its discovery in 1988 by Yoshizawa and al. In this work, we present the correlation between magnetic properties and internal stress in Finemet thin films, as a function of the film thickness and annealing temperature. A model based on the random anisotropy model (RAM) will be proposed in order to explain the thickness dependence of the coercive films, taking into account to the internal stress.The amorphous Finemet films were deposited by RF sputtering in argon plasma. The experimental conditions (RF power 250 W, residual vacuum 3×10−5 |
Pa and working pressure 3 Pa) lead to a deposition rate close to 9.2 nm min−1. The composition of the film has been measured by EDS and is close to Fe72Cu3Nb3Si15B7. It differs sensitively from that of the target, i.e. Fe73.5Cu1Nb3Si15.5B7, in the sense that copper content is slightly higher. The films were processed on 2″ silicon substrates covered by a 200 nm SiO2 layer grown by dry oxidation and a 25 nm titanium adhesion layer deposited by RF sputtering. Samples were annealed for 1 h in a secondary vacuum at temperature ranged between 150 and 450 °C with a heating and cooling rate of 10 °C/min.The magnetic properties of the films were extracted from the hysteresis cycles drawn at room temperature using a Princeton Measurement AGFM. The microstructure has been investigated using a Philips XRD diffractometer with a Co anticathod (λ=1.7889 Å).The internal stress in the films has been measured as a function of the temperature using a FSM 500 TC. This scanning technique detects the deflection of a laser beam on the surface of the wafer, which allows to extract its curvature and finally the internal stress of the film. Indeed, under some conditions (film thickness negligible compared to the wafer thickness, working in elastic domain), the wafer can be considered as a sphere portion and the stress in the film can be expressed aswhere Ew=150 GPa, υw=0.17, tw=280 μm, respectively, Young's modulus, Poisson's ratio and thickness of the substrate are the constants and t, R0 and R are the thicknesses, the curvature radius before and after film deposition, respectively. In order to avoid sample oxidation, the measurements were performed in a forming gas (95% Ar, 5% H2).For reference, a wafer covered with silica and titanium only has been tested using this technique and no evidence of wafer curvature was observed.A set of films with different thicknesses has been deposited and annealed. The coercive field of these films has been measured as a function of the annealing temperature (see ). It has been found that the optimal annealing temperature Topt, resulting in the softest magnetic properties, depends on the film thickness. Topt increases from 225 °C for a 50 nm thick layer to 300 °C for a 1 μm thick layer. Such behaviours have been already observed in previous works, for films of similar composition ) reveals that α-Fe nucleation begin above 300 °C and that changes in microstructure is limited between 300 and 350 °C. The crystallites size remains smaller than that of bulk material, probably in relation with a relatively higher copper content in the films, increasing the density of nucleation sites. For sample annealed at 400 °C, the crystallites contain 5 at% of Si only, their size reaches 10 nm and crystallised volume is about 30%.For a given annealing temperature, the coercive field Hc depends on the film thickness t. The shows that analytical relation between Hc and t is allotropicThe power n has been computed and the results are presented in . It has been found that the coercive field varies from 1/t (as-deposited films) to a 1/t (films annealed at 400 °C) dependence.In nanocrystalline films, local magnetocrystalline and magnetostatic energies only are supposed to be involved in the magnetization process since the stress due to the sputtering has been relaxed by annealing.Following the RAM, the effective magnetocrystalline energy depends on the number of grains N included in the exchange volumewhere x and K1 are the volumic ratio and the magnetocrystalline energy constant of the crystallites, respectively. N is defined by the ratio of exchange volume over the crystallite volumeif t⪡ℓex (thin films). Finally, the exchange length depends on the effective anisotropy and the exchange stiffness A lead to a dependence of the effective anisotropy to the inverse of the film thicknessTaking the usual constants values for α-Fe, K1=48 kJ m−3, A=1.5×10−11 |
J m−1 and using the microstructure features corresponding to the films annealed at 350 °C, i.e. x=10%, and D=4 nm, one obtainsThis result is in good agreement with the experimental values, as far as the 1/t dependence of Hc is concerned. However, the calculated order of magnitude for the coercive field is lower than experimental ones. This can be explained by different phenomena. First, it was not possible to determine precisely the lattice parameter, so it is possible that the Si content in the grains is not null resulting in a lower value of K1. In addition, the increase of the local anisotropy due to the stress induced by differential thermal expansion between the substrate and the film cannot be excluded.On the other hand, the power n for as-deposited films is close to 0.5, which reveals an evolution of Hc with the inverse of the square root of the film thickness. In such a stressed amorphous film, the magnetization process is dominated by domain wall pinning where t is the film thickness and γ the wall energyPrevious works have shown that domain wall pinning in thin amorphous stress-free films leads to a coercive field inversely proportional to the film thickness As Hc varies with 1/t instead of 1/t, this would mean that the stress is proportional to film thickness.In order to verify this hypothesis, the internal stress of the films has been measured. Thin films deposited in the same conditions have been characterized using laser scanning technique. The samples were annealed with a heating rate of 2.5 °C min−1, then maintained at 500 °C for 1 h and finally cooled at 2.5 °C min−1. shows the recordings of the internal stress as a function of the temperature for 550 and 970 nm thick films. As expected with the present sputtering conditions The evolution of stress with temperature is mainly driven by differential thermal expansion effect between the film and the substrate. However, the variations of the slope are characteristic of microstructural modifications. Three domains are visible in : atomic rearrangement at low temperature, supercooled liquid domain and finally crystallisation characterized by the lowest stress. The two characteristic temperatures separating the domains are the glass transition Tg and the crystallisation temperature Tx. As previously shown in Magnetic characterizations compared to stress measurements show that Topt corresponds to the supercooled liquid region, between glass transition and crystallisation temperature. Indeed, for samples annealed below Tg, stress induced by sputtering are relaxed by atomic rearrangment during heating and cooling. Thus, the magnetostrictive energy globally decreases.For samples annealed a temperature between Tg and Tx, the thermal expansion has no effect due to the state of the material, the film deformation following that of the substrate. The magnetostrictive energy remains constant in a first approximation, so do the coercive field and there is no drastic influence of annealing temperature in this range.Finally, if annealing temperature is above Tx, the crystallisation freezes the film in a solid state and modify its mechanical properties, in particular the Young's modulus. As a consequence, the cooling induces a tensile stress expressed as in Eq. with ΔT=Tamb−T. The evolution of this stress during cooling (see ) is about −1.1 MPa °C−1. From this result, one can estimate the thermal expansion coefficient of the films annealed at 500 °C. Assuming Ef=200 Gpa and υf=0.3 (values for iron), one obtains μf=6.4 10−6 |
K−1 This sensitively lower value compared to iron (~10) is explained by the viscous behaviour of the remaining amorphous matrix.The magnetic properties of amorphous and nanocrystallized Finemet thin films have been correlated to the measurement of the internal stress. It has been show that the stress induced by the sputtering is responsible for the high coercive fields of as-deposited film. Following the domain wall pinning model applied to thin films and because the stress increases with the film thickness, the coercive field follows a 1/t law, instead of 1/t for stress-free amorphous material.The coercive field decreases with the annealing temperature, down to a minimum then increases again. The optimal temperature leading to softest material is in the range 225–300 °C. It corresponds to the supercooled liquid region, in which stress due to deposition has been released and differential thermal expansion has no effect.Above this temperature, crystallisation begins at 400–450 °C depending of film thickness, and magnetic properties are affected. At this stage, the magnetic properties of the film are supposed to be the result of the RAM applied to thin films. This model predicts that the coercive field varies as a function of the inverse of the film thickness. In this case, because the material is heterogeneous (nanocrystallites in an amorphous matrix), differential thermal expansion effect between the substrate produces a stress fluctuating at nano-scale resulting in a magneto-elastic energy contribution to the local anisotropy, which is averaged out through random anisotropy process.Experimental study on the quasi-static progressive collapse response of post-and-beam mass timber buildings under an edge column removal scenarioMid-rise to tall mass timber buildings are becoming internationally popular and are required, for instance in the Eurocode or the Australian building code, to be designed against progressive collapse. Designing against progressive collapse is especially important for mass timber buildings as, when compared to reinforced concrete and steel, timber is a more brittle construction material and mass timber buildings are deemed to be more elastic and have limited rotational capacities at the beam-to-column connections. However, whilst the ability of reinforced concrete and steel buildings to resist such an extreme event has been widely researched, limited studies were carried out on mass timber buildings. Their load transfer mechanisms and structural response after the loss of a load-bearing element are currently unclear. Consequently, this paper presents the outcomes of three experimental tests performed on three scaled-down, 2 × 2-bay, post-and-beam mass timber substructures under an edge column removal scenario. The capacity of the 3D substructures to resist progressive collapse was investigated for two types of beam-to-column connectors, namely two tests performed with a connector type commonly used in Australia in mass timber buildings and one test with a proposed novel connector. In the tests, Uniformly Distributed Pressures (UDP) were applied to the floors in two stages: (i) a constant UDP of 4.8 kPa was first applied to the bays not adjacent to the removed column and (ii) an idealised UDP was then increasingly applied to the remaining two bays through a hydraulic jack connected to a six-point loading tree. The load redistribution mechanisms or alternative load paths, structural response and failure modes were recorded and are presented in this paper. Results showed that the applied load was principally transferred to the three columns closest to the removed column and that the Cross Laminated Timber (CLT) panels spanning over two bays were efficient in resisting and transferring the load. The substructure with the proposed novel connector showed an 8.5% increase in capacity and higher ductility than the substructures assembled with the commonly used connector. A simplified theoretical model consistent with the methodology currently used by industry to predict the collapse resistance capacity of post-and-beam mass timber buildings was compared to the test results. The model underpredicted the test capacity by 53%.A local failure of a load-bearing structural element, due to an abnormal load (such as gas explosion, fire, blast, design error or vehicular collision), may propagate through the building and ultimately cause its partial or entire collapse. This phenomenon is referred to as “progressive collapse” The main progressive collapse design guidelines, which include those recommended by the Department of Defence (DoD) Consequently, this study experimentally investigates the structural behaviour of post-and-beam mass timber building systems under an edge column removal scenario. Post-and-beam buildings were chosen as they represent a common office type building in Australia, such as the International House Sydney (opened in 2017) or 25 King Street, Brisbane (opened in 2018). Due to their structural system allowing for large open space floors, they offer less structural redundancy than residential type panelised/shear wall systems. Specifically, this paper quantifies the load redistributions or alternative load paths, failure modes and the overall structural response through the recorded deflections and strain developments in beams and CLT floors. Three experimental tests were carried out on 2 × 2-bay scaled down substructures assembled either from a commercially available beam-to-column connector As a case study, a 5 × 5-bay, six-storey high, representative mass timber office building, on an 8,000 mm × 6,000 mm grid, was designed in . A 10 mm gap was considered between the column and CLT panels.The cross-sectional dimensions of the beams and columns were 600 mm (deep) × 252 mm (wide) and 360 mm × 360 mm, respectively. All beams and columns were LVL structural products. Four types of beam-to-column connectors were designed for this building and are detailed in 2 × 2-bay substructures were extracted from the ground floor of the prototype building for testing as shown in . Note that experimental investigations on the progressive collapse of reinforced concrete and steel buildings are commonly practiced on scaled down substructures, see In total, three substructures were constructed and tested under an edge column removal scenario. Two of these substructures were nominally identical to confirm the repeatability of the tests and both assembled with the Megant type connector described in (Tests EM-1 and EM-2). The third substructure was assembled from the novel connector described in (Test EDP-1). While an edge column is not the most likely column to be damaged from vehicle collision, it still represents a possible removal scenario for which more than one progressive collapse resisting mechanisms (flexural, compressive arch and catenary actions) could develop.hySPAN LVL ordered from Carter Holt Harvey and manufactured from Radiata pine (Pinus radiata) and Douglas fir (Pseudotsuga menziesii) The CLT panels were Radiata pine 3-ply and 75 mm thick (CL3/75) × 712 mm wide and were sourced from XLam shows the perspective and plan view of the extracted substructure with panel and column numberings. The beams, columns and CLT panels are represented by “B”, “C” and “CM”, respectively.The spacing of the screws to connect CLT-to-CLT and CLT-to-beam was different to the representative building as calculated to match the relative shear and axial capacities (a), and (ii) HBS5120 (5 mm × 120 mm) spaced every 222 mm on average to connect the CLT panels to the LVL beams, as detailed in A 500 mm long column stub was used for column C4 to be removed during the experiment (See ). This column was supported by a temporary member during the construction process and test preparation. All other columns were 1,138 mm long and extended 165 mm above the CLT panels.Two different types of beam-to-column connectors were considered to analyse the structural response of the substructures under an edge column removal scenario. The connectors are referred to as “Megant type” connector (M) and the proposed “Double Plate” connector (DP) in The Megant type connector mimicked the Megant connector manufactured by Knapp This connector was specifically designed in (a)). (ii) The column part included two 2.5 mm thick aluminium (T6-6061 alloy) plates inserted through slots pre-cut in the column. The plates overhung on both sides of the column and were connected to it with three rows of six 4 mm steel dowels (s355). Slotted holes were cut in the overhangs to allow the beam to rotate the 0.2 rad (b)). The beam and column were connected “on-site” with six M4 bolts (class 8.8) ( (d)). This connector and its principles of assembly are shown in . Note that while this connector allowed enough rotation to take place for catenary action to mobilise were made straight, they prevented the circular movement of the bolts, thereby generating resistance to the applied load. This connector is only manufactured from aluminium plates which can be cost-effectively waterjet cut. The main cost would be however in the off-site installation of the dowels.Once all the timber elements were cut, the dynamic Modulus of Elasticity (MOE) of each element was measured using a non-destructive acoustic method (b)) which were simply supported on two rubber strips. Then the software Beam Identification by Non-destructive Grading (BING) To measure the bending strength of the LVL beams and CLT panels delivered, five LVL beams and two CLT panels were tested in four-point bending following the Australian standard AS/NZS 4063.1 All LVL products and CLT panels were stored inside the laboratory at ambient temperature and relative humidity. As the samples were not conditioned in a controlled environment, the moisture content (MC) of the timber at the time of both non-destructive (dynamic MOE) and destructive testing of the substructures was measured. Selected samples were immediately cut from the test specimens after testing and weighted. Then the timber MC was determined by the oven dry method according to the Australian standard AS/NZS 1080.1 To measure the material property of the steel components, six 4 mm dowels, five M4 bolts and five M8 bolts were randomly selected from the batches of material that were used in the experimental tests. The middle section of the samples was machined to a nominal diameter of 3.5 mm, 3.1 mm and 6.8 mm over a gauge length of 30 mm, 30 mm and 50 mm for the 4 mm dowels, M4 bolts and M8 bolts, respectively. The samples were tested in a 100 kN Instron universal testing machine following the Australian standard AS4291.1 The Megant type connectors manufactured from the same batch as in The overall view of the test set-up is shown in . The eight permanent columns (i.e. C1–C3, C5–C9), were pin-connected using universal joints to the laboratory strong floor ( (a)). A 250 kN pancake load cell was inserted at the base of each column to measure the vertical reaction force. The load cells were numbered LCVi, where i is the column ID. The load acting on the columns from the level above was also not considered. Additionally, during the construction and Loading Phase 1 (LP1, see ), in which column C4 was temporary supported, a 200 kN load cell (LCVR) was used to measure the vertical reaction force transferred to the temporary support.To simulate the horizontal restraint provided by the adjoining post-and-beam frames and floor panels of the entire building: (i) six peripheral columns were pin-connected horizontally, along the beam longitudinal axes, to rigid frames ((a) & (c)), and (ii) the edges of the CLT panels corresponding to the inside of the building were also pin-connected horizontally, along their longitudinal direction, to rigid frames ((b) & (c)). Two 75 kN load cells (LCH1 – LCH2) were installed to measure the load transfer in the horizontal restraints of columns C1 and C7. Another two 75 kN load cells (LCH3 – LCH4) were also used to measure the horizontal load transfer, but in the restraints connected to CLT panels CM4 and CM6. All load cell numberings are summarised in (c). Due to (i) the nature of post-and-beam mass timber buildings which do not provide continuity of the beams throughout the building, and (ii) the low rotational stiffness of the beam-to-column connections relative to the bending stiffness of the beam The substructural behaviour was further monitored by fourteen linear vertical displacement transducers LVDT (DT), two linear rotational transducers (RT) and twenty strain gauges (ST for the strain gauges glued at the top surface of a timber element and SB for the strain gauges glued at the bottom surface of the element) as:Vertical displacements of the two beams B1 and B2 connected to the removed column, and those of the other two beams B3 and B4 at the middle of the substructure and the CLT panels CM2 and CM5 – CM9 were measured at the key locations shown in The two rotational transducers (RT1 and RT2 in ) were mounted on the beams B1 and B2 on either side of the removed column to record their average rotation θb calculated as,where θRTi is the reading of the rotational transducer number i.Strains at the top and bottom extreme fibres of beams B1 – B4 and CLT panels CM4 – CM6 were recorded at the key locations shown in with 30 mm-gauge length strain gauges. The axial and bending stresses of the beams and the CLT panels at the key locations were calculated as,where εSTi and εSBi are the strain readings from gauge number i glued at the top and bottom of the structural elements, respectively; and EL and EB are the longitudinal and bending MOEs, respectively, of the element measured in . A negative axial stress denotes an element in compression, whereas a negative bending stress indicates an element in positive bending. Note that when a strain gauge was positioned at the top extreme fibre of a beam, a shallow recessed pocket () was manufactured to prevent the strain gauge from direct contact with the CLT panels. Also note that the stresses in Eqs. do not consider any composite action between the beams and the CLT panels.Two different types of Uniformly Distributed Pressure (UDP) were applied to the substructures so that their collapse resistance behaviour could be evaluated A constant load of 4.8 kPa, representing the dead and live loads, was simulated on the two bays not adjacent to the removed column (i.e. bays delimited by columns C2, C3, C9 and C8) through 24 uniformly spaced steel blocks ( (a)). Each block had an average mass of 122 kg and a nominal footprint of 285 mm × 285 mm. The average spacing between any two blocks was 176 mm. Note that the applied 4.8 kPa is about 7% higher than the designed load of 4.5 kPa in the DoD , to accommodate for the size and weight of the steel blocks.A six-point loading tree, similar to the one used by the second and third authors in (a) and consisted of two 50 mm thick triangular steel plates, two steel stands located at the centre of gravity of each plate and one 2,000 mm-long horizontal steel spreader beam. Each corner of the triangular steel plate was bolted to a steel ball inserted into a low friction 50 mm-diameter polyvinyl chloride (PVC) round socket pad. The pads were positioned on 300 mm long × 200 mm wide × 20 mm thick steel plates which were connected to the CLT panels with four CS 8 × 80 mm screws To prevent the development of horizontal forces in the slab from the loading tree, the following precautions were taken:The spreader beam was simply supported through universal joints on the two steel stands. A slotted hole allowed one of the supports to slide along the beam longitudinal axis. Also to ensure stability, the hydraulic jack was connected below the level of spreader beam supports as shown in For each triangular steel plate, the horizontal movements of one support unit ( (a)) were restrained in both the longitudinal and lateral directions while the other two support units could slide in either longitudinal or lateral direction only, as illustrated in The loading sequence was in accordance with the design philosophy in the DoD Loading Phase 1 (LP1): Positioning the loading tree and steel blocks: The loading tree, weighing 10.3 kN, was first positioned on the slab. The steel blocks were then loaded on the remaining two bays. Note that during this phase, the column stub C4 was supported by the temporary member, therefore simulating an undamaged substructure.Loading Phase 2 (LP2): Removal of the temporary support: The temporary support was removed quasi-statically, typically in about 1 min, by gradually releasing the load of the acrow prop which was used to support the column and the load redistribution through the substructure was monitored. To minimise creep deformations, the idle time between LP2 and LP3 was kept to minimum, typically about half an hour.Loading Phase 3 (LP3) - Increasing the UDP until failure: All transducers, load cells and strain gauges were zeroed. Then the hydraulic jack was pin-connected to the spreader beam and its displacement was increased at a constant stroke rate of 5 mm/min, until complete failure at large displacement. Note that, the chosen loading rate allowed the maximum load to be reached in 17 mins on average. This was slower than the recommended time in Standards of typically 3–5 mins, such as in As somewhat already discussed in the paper, similar test set-ups to the one presented in the previous subsections, and consisting of testing scaled-down 2 × 2-bay substructures, are routinely used and accepted in progressive collapse researches to both apprehend the collapse resistance mechanisms and alternate load paths, see and (iv) the UDP typically idealised through 6- or 12-point loading trees. Also testing scaled-down structures may require special attention and changes to the specimen design to correctly replicate the behaviour of the full-scale structure, such as adapting the layout of the reinforcement in concrete structures to match available reinforcement bars while keeping the reinforcement ratio the same between the full-scale and scaled-down structures summarises the average measured dynamic MOE, with associated Coefficients of Variation (COV) on the measurements, of the LVL beams, columns and CLT panels used. presents the MC measured from the selected samples at both the MOE measurements and the destructive testing of the substructures. The MC typically ranged between 8% and 11%. provides the tensile test results for all selected bolts and dowels. Note that the results showed that the yield stress of the M4 bolts used in the experiments was 1.4 times higher than the nominal yield stress of 830 MPa of the ordered class 8.8. The tensile test results for aluminium specimens are summarised in . The average measured strain rates for the steel and aluminium material tests, obtained from the extensometer reading, are given in summarises the four-point bending test results for the LVL beams and CLT panels.The experimental results presented in this section are always given for LP3, with only the load transfer mechanisms and structural overall deflections detailed for LP2. Note that only selected and relevant measurements are presented and discussed in this paper.The load applied by the loading tree versus the measured vertical displacement of the removed column stub is plotted in for the three tests performed. Note that the initial weight of the loading tree was considered in the curves by shifting all curves by 10.3 kN along the y-axis.For the two tests with the Megant type connector (Test EM-1 and repeated test EM-2), the load increased almost linearly to a removed column displacement of about 120 mm (marked as A for Test EM-1 and D for Test EM-2 in ) with an average stiffness of 0.65 kN/mm. A non-linear behaviour with limited inelastic deformation was then observed until reaching the maximum load. For Test EM-1, the maximum applied load of 120.8 kN (marked as B in ), at a removed column displacement of 226 mm, corresponded to the shear failure of the connector linking the interior beam B3 (2nd row) ( (b)) to the interior column C5, as shown in (a). The load then partially recovered until bending failure (marked as C in ) occurred on the same row of beams, but in beam B4 (as shown in (b)). The bending failure was located between CLT panels CM2 and CM3, i.e. at one-third of the beam length and in line with the loading points. From that stage, the load decreased until the test was stopped at a removed column displacement of 374 mm (i.e. about 1/6 of the beam span) with successive localised bending failure of the CLT panels, failure of the CLT-to-CLT and CLT-to-beam screwed connections and bending failure of the beam-to-column connectors attached to the removed column. For Test EM-2, the maximum applied load of 120.4 kN (marked as E in ) was reached at a removed column displacement of 203 mm, corresponded to the bending failure of beam B4, and no shear failure of the interior beam-to-column connector was observed as in Test EM-1. The bending failure was also located between the CLT panels CM2 and CM3. Then the load decreased until the test was stopped. Overall, Tests EM-1 and EM-2 showed similar structural behaviour attesting the repeatability of the tests. The failure modes and the overall deformations of the substructures at the abovementioned key stages and at the end of the tests are shown in The observed behaviour in Tests EM-1 and EM-2 is different to concrete and steel counterparts in which after reaching their first peak load, the structure can often recover from the initial damage by redistributing the load through the system through mobilised catenary action, therefore reaching a second peak load which is generally higher than the first one The substructure with Double Plate connectors (Test EDP-1) showed a different behaviour when compared to the previous two tests. Up until a removed column displacement of 66 mm, the overall behaviour of the substructure was linear with a stiffness of 0.91 kN/mm, i.e. 40% higher than those of Tests EM-1 and EM-2. This difference is attributed to the bending stiffness of the Double Plate connector being 2.3 times higher than the Megant type connector, as determined in ) corresponded to a localised bending failure of the CLT panels CM3 and CM6. The load recovered from this event to increase non-linearly until the maximum load of 130.9 kN (marked as G in ) was reached at a removed column displacement of 236 mm, i.e. about 1/9 of the beam span. This stage corresponded to a bearing failure developing in the aluminium plates of the connectors fastened to the removed column C4, as shown in (a). Note that this failure occurred in the front row of beams (beams B1 and B2) but not in the second row (beams B3 and B4) as in Tests EM-1 and EM-2. This is related to the higher bending stiffness of the Double Plate connectors mentioned above. Indeed, relative to Tests EM-1 and EM-2, EDP-1 enabled the load to be more uniformly balanced and a larger portion of it was resisted by the front frame. After reaching the maximum load, successive localised failures occurred and the load decreased at a slower rate than in Tests EM-1 and EM-2, until the test was stopped at a removed column displacement of 410 mm, i.e. about 1/5 of the beam span. The failure modes and overall deformation of the substructure at key stages and at the end of the test are shown in . Note that to protect the recording devices, all displacement transducers were removed when the test was stopped in . However to further observe the substructural behaviour, the jack was further displaced by 121 mm after removing the transducers and the final states of the substructure shown in (e) and (f) only correspond to this deformation further imposed to the structure.Overall, when compared to Tests EM-1 and EM-2, a more ductile behaviour was observed for Test EDP-1, with the inelastic deformation at Point G equal to about 2.5 times the elastic deformation at Point F in . In terms of UDP, while the 2D post-and-beam systems assembled from the Megant type and double beam connectors The average measured horizontal (axial) force from Load cells LCH1 and LCH2 (see (c)), which provides an indicator if compressive arch and catenary actions were mobilised in the system, is plotted for all three tests in versus the removed column displacement. In compressive arch action, the vertical loads are resisted through the development of compressive forces in horizontally restrained beams A different behaviour was observed in Test EDP-1. Up to a removed column displacement of 225 mm, i.e. corresponding to the maximum applied load, little to no axial force was recorded by the load cells. Then a compressive force, up to 7.3 kN, developed. Contrary to the tests performed on the 2D post-and-beam systems alone which allowed the columns to bend and push back on the horizontal restraints when deforming and likely to the contribution of the CLT panels redistributing the loads (see , tensile forces were recorded in the beams.The beam rotational behaviour for all three tests, obtained from rotational transducers RT1 and RT2 (see , was similar. The maximum rotation when the test terminated for Tests EM-1 and EM-2 was 11.6° on average (0.20 rad) and the maximum rotation when the recording was ceased for Test EDP-1 (see summarises the load transferred from the temporary column C4 to the remaining columns during LP2. A similar behaviour was observed for the three tests. The load resisted by the removed column was predominantly transferred to the three columns the closest to the removed one, with column C5 carrying between 76% and 112% of the redistributed load. plots the column reaction forces during LP3 versus the removed column displacement for the three tests, while plots the percentage of the applied load transferred to each group of columns (i.e. adjacent columns (C1 + C7), interior column (C5), 2nd row side columns (C2 + C8), 3rd row columns (C6 and C3 + C9)) also versus the removed column displacement. Note that (i) the weight of the loading tree is not included in is plotted from a removed column displacement of 10 mm. by summarising the reactions forces and their percentages of the applied load transferred to each group of columns at the maximum load and at the end of the test, respectively.For Tests EM-1 and EM-2, an average of 60.9% of the applied load was transferred to the interior column C5 at the maximum applied load. After bending failure of beam B4, the percentage of the applied load resisted by the 2nd row of columns (columns C2, C5, and C8) decreased while the percentage resisted by the front columns C1 and C7 increased. Importantly and further to the analysis in , a single post-and-beam frame system with Megant type connectors was only able to withstand an equivalent UDP of 0.8 kPa In Test EDP-1, a similar load transfer as Tests EM-1 and EM-2 was observed at the exception that due to the stiffer rotational stiffness of the connector After removing the temporary column in LP2, column C4 displaced vertically by 14 mm on average for Tests EM-1 and EM-2 and by 9 mm for Test EDP-1. The difference is once again attributed to the higher rotational stiffness of the Double Plate connector when compared to the Megant type connector presents the slab vertical displacement at key stages along the diagonal line between columns C2 and C4 for Tests EM-1, EM-2 and EDP-1. Readings from LVDT DT2, DT8, DT10 and DT12, shown in , were used to plot the figure. The bending deformation of the CLT slab can be seen in the figure. Similarly, plots the recorded deformation of the front post-and-beam frame, measured by LVDT DT1, DT2, DT3, DT4 and DT5 as shown in , at key stages for all tests. The figure shows that the bending deformation of the beams was negligible, and all the rotational deformations occurred at the beam-to-column connectors. plot the axial and bending stresses developed in the monitored beams, obtained from the strain gauge readings and Eqs. , versus the removed column displacement for all tests and LP3. The average MOE values for LVL beams reported in (a) shows that for Test EM-1, the front beams B1 and B2 were in compression near the removed column C4 (gauges ST1 & SB1, ST2 & SB2 and ST4 & SB4), however tensile stresses of up to 2.6 MPa were recorded in beam B1 near the side column C1 (gauges ST3 & SB3). This result outlines the likely composite action between the beams and the CLT panels. For Test EM-2 in (a), no axial tension was recorded in beam B1 and the front beams remained in compression. Still for Test EM-2, a tensile axial stress was developed rapidly in beam B4 until bending failure occurred in that beam at a removed column displacement of 203 mm. In Test EDP-1 in (a), tensile axial stresses of up to 3.7 MPa were developed in beams B1 and B2, until the removed column displacement reached 236 mm, corresponding to bearing failure occurring in the aluminium plates of the connectors which were fastened to the removed column (see ). The axial stresses then dropped in those beams but increased again after a plateau stage. A compressive axial stress was recorded in beam B3. Similar to Test EM-2, a tensile axial stress was also recorded in beam B4 which increased rapidly, however no bending failure occurred in that beam.During the loading phase LP3, bending stresses increased by up to 22.3 MPa in the two front beams B1 and B2 in Tests EM-1 and EM-2 ( (b)). A maximum bending stress of 36.9 MPa was found at mid-span of beam B3 in Test EM-1. In Test EM-2, when bending failure occurred in beam B4, a mid-span bending stress of 44.8 MPa was recorded. Considering an initial bending stress of 10.9 MPa recorded in Beam B4 at the end of LP2 (not shown), the total bending stress experience by the beam would be 55.7 MPa. This value is close to the bending strength of 57.7 MPa (see The bending stresses for LP3 in the front row of beams for Test EDP-1, shown in (b), was of the same order of magnitude as Tests EM-1 and EM-2. Also similarly to Tests EM-1 and EM-2, the mid-span bending stress of beam B3 was less than beam B4 due to the asymmetrical configuration of the CLT panels (see ). For beam B4, strain gauge SB6 stopped reading at a removed column displacement of 200 mm, corresponding to a mid-span bending stress of 51.8 MPa, indicating that, considering a recorded bending stress of 6.4 MPa at the end of LP2, the beam was close to fail in bending, despite this failure mode not being observed experimentally. present the axial and bending stresses developing in the CLT panels versus the removed column displacement for all tests and LP3. The average dynamic MOE values for the CLT panels reported in For all tests, the axial stresses in the CLT panels were limited and found to be below 1.4 MPa. The axial stresses were typically higher for the two-bay long CLT panel (CM6) than the one-bay long CLT panels (CM4 and CM5).The bending stresses in the CLT panels at mid-span between the 2nd and 3rd row of beams were typically higher than the stresses at mid-span between the front and 2nd row of beams. Despite CLT panel CM4 spanning one bay and located between the 2nd and 3rd row of beams, and therefore not being in direct contact with the loading tree, it still exhibited bending stress values comparable to the ones encountered by the two-bay long CLT panel CM6. This provides a good indication that through their connection to the two-bay long CLT floors, the one-bay long CLT panels also contributed to resisting the applied load. For Test EM-2, the bending stresses in all recorded CLT panels dropped significantly after bending failure of beam B4, a phenomenon not encountered in Test EM-1 for which the bending stresses only dropped at a removed column displacement of 328 mm, i.e. after both shear failure of the connector and bending failure of beam B4. In Test EDP-1, the bending stresses increased up to a removed column displacement of 91 mm where localised bending failure of CLT panels CM3 and CM6 occurred, as explained in . At this stage, the bending stresses in the monitored CLT panels dropped and did not recover, the load was then transferred to the other panels and the bending stresses of CM5 and CM6 between the front and 2nd row of beams changed from negative to positive bending. For all tests, the absolute maximum recorded bending stress for LP3 of 10.1 MPa was found to be reached in Test EM-1.The experimental load-resistance capacity of the substructure is compared in this section to the design philosophy currently used by the industry in designing mass timber post-and-beam buildings under a column removal scenario. In practice, the front frame with the lost column is ignored in the analysis and the load is considered to be solely resisted by the cantilevered CLT panels spanning two bays. shows the simplified model of the tested substructure used in this analysis, in which only the three two-bay long CLT panels (CM3, CM6, CM9) are assumed to transfer the load back to the 2nd and 3rd rows of beams. Each of the three panels carries the load from two loading points () and the free body diagram of each CLT panel, treated as a simply supported beam with an overhang, is shown in , in which P is the load applied by the hydraulic jack through the loading tree. The maximum bending moment MCLT (in kN·m) carried by each CLT panel, located at the right support B, and obtained from the free body diagram in , is given as a function of P (in kN) as,where 0.25 is in m. The applied load causing failure of the CLT panels can then be deduced from the equation above and the measured bending strength of the CLT panels given in Using the reaction forces of the two-bay long CLT panels in and the one-bay long CLT panels loaded with the constant UDP of 4.8 kPa between the 2nd and 3rd row of beams, shows the free body diagrams of beams B3 and B4 in the 2nd row of beams. The beams are considered to be simply supported, as assumed in the current design practice. The shear forces Vc (in kN) in the beam-to-column connectors can then be calculated from the free body diagram in Additionally, and again from the free body diagram in , the maximum bending moments Mb (in kN·m) carried by each beam can also be calculated in terms of P (in kN) as,where 0.17 and 0.21 are in m. The applied load P inducing shear failure of the connectors can therefore be deduced from the above equations and the connector shear capacity of 33.3 kN for the Megant type connector (measured as part of this study following the same methodology as in The predicted applied loads P at which the CLT panel would fail in bending, the connectors fail in shear and the beams fail in bending are presented in The simplified model predicts a load capacity of 56.8 kN for the bending failure occurring in beam B4. While the failure mode corresponds well to the observed mode for both Tests EM-1 and EM-2, this predicted capacity is conservative and more than half the observed one. The second lower failure load predicted by the model is the connector shear failure occurring at beam B3 at an applied load of 59.5 kN, i.e. marginally higher (4.8%) than the bending failure load of 56.8 kN. This connector shear failure was only observed in Test EM-1. These results show that the current industry practice is overly conservative as some of the resisting mechanisms observed in the experimental tests are ignored, such as (i) the composite action between CLT panels and beams, which enabled the frame with the removed column to resist part of the applied load, and (ii) the rotational stiffness of the connectors which could enhance ductility and redistribute the load through the system.Three ¼-scale 2 × 2-bay post-and-beam mass timber substructures, with CLT floors, were tested under an edge column removal scenario. Tests were performed with two beam-to-column connectors, referred to as “Megant type” and “Double Plate”. The load-deformation behaviour of the substructures, their failure modes and the load transfer mechanisms through the system were reported. The main findings are drawn as below:Repeatability of the tests were confirmed by testing two identical substructures with the Megant type connector, showing similar overall structural behaviours and failure modes.The CLT floors were found to be the critical elements in redistributing the load through the building. Likely through composite action, they also enabled the post-and-beam frame with a missing column to resist a portion of the applied load, an ability that is absent in the 2D frame alone.The substructure with the proposed Double Plate connector showed higher capacity (8.5% higher) and ductility than the substructures assembly with the Megant type connector. When more load was transferred to the 2nd row of beams for frames assembled with the Megant type connectors, both bending failure of the beams and shear failure of the connectors were observed. The novel Double Plate connector, on the other hand, allowed more load to be resisted by the post-and-beam frames attached to the removed column. This type of connection could represent a potential solution to improve the ability of post-and-beam mass timber buildings for progressive collapse prevention.Results showed that the simplified methodology adopted by the industry to design post-and-beam mass timber buildings against progressive collapse is unduly conservative. This methodology is unable to capture the complex 3D load redistribution.Whilst the tests presented in this study were performed on scaled down structures, with the limitations outlined in the paper, they provide an excellent tool to comprehensively understand the behaviour of mass timber buildings under a column removal scenario. The load transfer, failure modes and overall structural response were accurately captured and are readily applicable to understand the progressive collapse mechanisms in full-scale timber buildings.The present study lays a foundation for calibrating numerical models and performing parametric studies to further understand: (i) the role of connections between elements, such as CLT-to-CLT, CLT-to-beam or beam-to-column, (ii) the impact of the CLT layout and (iii) the contribution of upper stories in resisting the loss of a critical column. Additional studies are also needed to further develop robust connections.C.H. Lyu: Conceptualization, Methodology, Formal analysis, Investigation, Writing - original draft, Visualization. B.P. Gilbert: Conceptualization, Methodology, Writing - original draft, Supervision, Funding acquisition. H. Guan: Conceptualization, Methodology, Writing - review & editing, Supervision. I.D. Underhill: Methodology, Investigation, Supervision. S. Gunalan: Conceptualization, Methodology, Writing - review & editing, Funding acquisition. H. Karampour: Methodology, Investigation, 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.Prediction of fatigue crack growth under real stress historiesA damage tolerance analysis methodology for cracks subjected to real loading is presented. A new retardation model, based on material hardening within the overload plastic zone, is developed for irregular stress histories. For the transformation of the irregular stress history into a stress history containing only distinguished cycles, a technique based on the rainflow counting method is used. The methodology is applied to real aircraft loading histories for the conventional 2024-T3 aluminum alloy and the advanced 8090-T8 aluminum–lithium alloy. Predictions agree well with the experimental results. Limitations of the prediction method are also discussed.Aerospace structures operate under highly variable fatigue conditions. To date, fatigue analysis of aerospace structures is based mostly on test results To support fatigue crack growth analysis by crack growth models is not a small task. Real loading histories consist of distinguished load peaks. On the other hand, fatigue crack propagation is a path-dependent process, strongly influenced by load sequence. Therefore, fatigue crack propagation models that support crack growth analysis commonly used under service spectra have been modified to account for load-interaction phenomena. In most cases the modifications aim to consider crack growth retardation It is common belief to attribute the mechanics of the retardation process to localized plastic deformation ahead of the crack and to relate retardation to compressive residual stresses developed after overloads. Amongst such models, those proposed by Wheeler and Willenborg Fractographic analysis has indicated that a significant retardation mechanism is crack surface roughness To improve fatigue crack growth prediction for small initial cracks, models that take into account retardation mechanisms predominant for the initial fatigue stages are required. A model suitable for this case has been developed by the present author and co-workers Application of a model for predicting fatigue crack growth under service spectra can be manageable when transforming the irregular stress history to a sequence of full, distinguished cycles. Furthermore, when plastic deformation is considered to account for damage that accumulates after each event of loading, omission of unloading or compressive events is not justified. To conform with the requirements set above, utilization of the rainflow counting method is proposed. Application of the rainflow method allows one to simulate a service spectrum by an equivalent one which consists of a sequence of full, distinguished cycles; by the transformation, all spectrum events are considered equally if they yield to tensile loading, partial unloading or compressive loading of the material. A serious drawback of the rainflow algorithms is that no attention is paid to the relative position of each event within the service fatigue spectrum during transformation into the simulation spectrum, which in turn implies the a priori assumption of linear damage accumulation during fatigue. In this work, a modification in the application of the rainflow method has been introduced to overcome this shortcoming.For a given load spectrum, the proposed technique proceeds by considering load steps (). For every load step the rainflow method is applied separately ). By using the latter criterion, the consistency between the sequence of plastic zones of the irregular history and the sequence of plastic zones of the derived cycles is satisfied, verifying the observation that it affects fatigue crack growth significantly In the literature several rainflow algorithms are proposed has been used. In contrast, the simulation result has been found to depend on: (1) the length of the discretization step in the fatigue spectrum, i.e., the number of stress events that are defined to constitute a block; and (2) the truncation process of the fatigue spectrum. Both physical parameters might have a significant impact on the simulation result when the service spectra include a great number of events or/and when many small stress events are included.In the vicinity of the crack tip the fatigue damage accumulated within each material element is mainly a consequence of plastic deformation. Therefore, it can be assumed that the material elements in the overload plastic zone are subjected to low-cycle fatigue (LCF) conditions. provides a schematic of the proposed strip–plastic zone model. The length of the overload plastic zone is denoted by rOL while aOL is the crack length after an overload.At the peak of the load rising during an overload, each point near the overload crack tip is stressed with stress S>Syo (). When the overload has been completed, each point within the overload plastic zone has its own new tensile curve. Furthermore, each point has its own new yield stress which is Sy=S. For these points a linear distribution of the value Sy is assumed (). The yield stress of the material ahead of the overload crack tip is assumed to be:where Sf is the cyclic ultimate stress, and β is a parameter lying between Syo/Sf and 1. The exact value of β should be calculated for each overload through stress analysis in the vicinity of the crack tip. However, this is not a small task. To aid development of a simple model, the value of β in has been approximated to be β=1. The validity of this simplification has been verified by the results of a sensitivity analysis for widely used aluminum alloys The length of the plastic zone ωs can be estimated as:The number of cycles to failure ΔN can be determined by the Coffin–Manson rule obtained empirically for low-cycle fatigue conditions. In this expression, ε′f is the ductility coefficient and m an empirical material parameter.In this equation Δδ is the range of the crack-tip opening displacement given by:The parameter h can be evaluated from the condition of monotonic loading:where Kcr is the critical stress intensity factor for fracture.Let λ be defined as a retardation factor given by:The retarded crack growth rate (dα/dN)ret corresponds to the situation in where the crack growth takes place in the overload plastic zone. The nominal crack growth rate (dα/dN)nom corresponds to , in which the crack growth occurs in the absence of any overloads. In view of Note that Syo and Sy are the cyclic yield stress without and with overload plasticity effect (), respectively. It is the relationship between Sy and Syo that determines the change in material response caused by overload. Invoked is a linearly varying function for Sy:, the retarded crack growth rate can be determined from where the nominal fatigue crack growth rate (dα/dN)nom can be derived by constant amplitude loading tests. Application of the model to constant-amplitude loading containing a single overload has resulted in satisfactory predictions [e.g. As mentioned previously, a large class of engineering structures is subjected to service loads that vary randomly. The influence of load interaction on fatigue crack growth rate depends on the interaction of the plastic zones produced. Treating the random loading plastic zone interaction is an extremely difficult task. Therefore, a series of simplifications on existing non-linear models It should be noted that the retardation factor λi of the proposed methodology has absolutely different physical meaning from Wheeler's one The validity of the proposed model is assessed with experimental results. The tests have been performed on bare sheet material of the conventional 2024-T3 aluminum alloy and the advanced 8090-T8 aluminum–lithium alloy. All tests were performed by Deutsche Airbus on standard Center-Cracked-Tension (CCT) specimens with 1.6 mm thickness and Longitudinal (LT) orientation using a standardized load sequence for the upper fuselage shell of the A-300 aircraft of the material element at the crack tip, the approximation β=1 was used. For aluminum alloys such as Al-2024-T3 and Al-6061-T6 the validity of the latter simplification has been verified as reported elsewhere The nominal fatigue crack growth rate is calculated by the Paris rule, that is:where the parameters n and C are fitted to n=4.305−1.316R and C=−2.503×10−15+4.365×10−13R for the Al-2024-T3 alloy, and n=3.837−1.184R and C=−1.08×10−14+1.489×10−12R for the Al-8090-T8, where R is the ratio σmini/σmaxi of each loading cycle. The data have been obtained from constant-amplitude fatigue tests performed by DRA Using the damage accumulation procedure described above, a computer program was developed to predict crack propagation under random loading conditions on the aluminum alloys. Both the accuracy of the calculations and the required computing time depend on the choice of loading step (). The number of reversals assumed to build one step should be a compromise between the gain on computing time and the loss on accuracy. In the present work, for simplicity, it is assumed that the number of peaks in each block is n=60. By executing the program, the prediction of crack length versus number of flights has been carried out for Al-2024-T3 and Al-8090-T8 alloys. The latter predictions are compared with the experimental results in For the Al-2024-T3 and Al-8090-T8 alloys, the predictions agree well only within the areas with α=2–7 mm and 2–16 mm, respectively. The predictions of Willenborg's model are also presented in the same figures. The calculations using the latter model, however, start from larger initial crack lengths; i.e., 5.0 mm for Al-2024-T3 and 4.0 mm for Al-8090-T8. The reason for this decision is the following: for small initial crack lengths Willenborg's model leads to a very large underestimation of the fatigue crack increment per cycle. Therefore, the 32-bit computer used for the calculations is unable to treat such crack increments of the order of 1≎̸10−11 |
mm (i.e., α0+Δαi=α0 when Δαi<10−11 |
mm). The calculations, however, have been carried out in order to arrive at some conclusions concerning the validity range of the mentioned retardation models. clearly indicate that the proposed methodology overestimates the crack growth for larger crack lengths (e.g., >7.0 mm for 2024-T3 and >16.0 mm for 8090-T8) significantly. This behavior could be attributed to the fact that, for larger crack lengths, more predominant retardation mechanisms than the mechanism of material hardening take place. These mechanisms are related to the development of compressive self-stresses around the overload plastic zones. show that the results of Willenborg's model are in good agreement with the experimental results only for large crack lengths.The results lead to the following conclusions:models based only on one retardation mechanism are not able to provide reliable fatigue crack growth prediction for the total fatigue life period;interaction models described in the literature take into account one single mechanism. Therefore, the models are able to predict fatigue crack growth accurately only within the area where this mechanism is predominant; andimprovement of fatigue crack growth prediction for long fatigue life periods requires the development of hybrid models that take into account a larger number of mechanisms. The basic problem that needs further investigation is the definition of the predominant load-interaction mechanisms for each fatigue stage.A transformation technique to change an irregular stress history into a regular one is used. The technique is based on a modification of the rainflow counting method. The advantage of the modified technique is the suitability of using non-linear damage accumulation models and long stress histories.A new retardation model is applied to the transformed irregular real spectra. The model is based on the strain-hardening fatigue mechanism in the plastic zone that takes place during all the fatigue life stages. However, for the alloys 2024-T3 and 8090-T8 investigated, the mechanism seems to be predominant in the early fatigue crack propagation stages. In respect of these alloys and stress histories, the model led to encouraging predictions for the initial crack propagation stages.To improve the fatigue crack growth predictions, it is necessary to investigate the boundaries where each load-interaction mechanism is predominant as well as to develop load-interaction models that take into account more load-interaction mechanisms.A numerical coupling model to analyze the blood flow, temperature, and oxygen transport in human breast tumor under laser irradiationThe aim of this study is to investigate the variation of the blood perfusion rate and distribution of oxygen partial pressure (PO2) in human tumors by a coupling numerical model when laser irradiation is used as an adjuvant method in the treatment of cancer. A two-dimensional finite element (FE) thermal model of a human breast with a tumor was developed. The blood circulation inside the breast was modeled using one-dimensional non-linear equations of pulsatile fluid flow. The distribution of PO2 inside the capillaries, tumor vessels, and surrounding tissue was obtained by the Krogh analysis model. Finally, the variations of the average tumor temperature, blood perfusion, and PO2 during laser heating were computed by coupling the blood circulation, FE thermal, and oxygen transport models.cross-sectional area of blood vessel, m2surface area of blood vessel per unit length, mparameter proportional to the bending stiffness of the tube wall, Par direction in cylindrical coordinate, mz direction in cylindrical coordinate, mThe effect of hyperthermia is not limited to tumor cells but is also observed on the microvasculature. The effect of hyperthermia on tumor vasculature is of considerable interest since controlling the tumor blood flow can improve the efficiency of tumor treatment. For example, in radiotherapy, improving the blood flow can increase the tumor oxygenation; similarly in chemotherapy, increasing the blood flow helps increase the delivery of appropriate pharmacological agents. On the other hand, vascular insufficiency and poor tumor blood flow are desirable in hyperthermia since the blood flow dissipates energy from the tissues.The detailed measurement of microvascular flow The spatial distribution of blood flow in the normal porcine skeletal muscle before, during, and after a period of regional microwave hyperthermia was examined by the radioactive microsphere method The relationship between the changes in oxygen partial pressure (PO2) and blood flow in heated tumors was investigated by animal experiments In summary, exploring the hyperthermia-blood flow-oxygenation relationship is crucial for the realization of targeted drug delivery. Modeling the hyperthermia-blood flow-tissue interaction may be beneficial for the analysis and optimization of the parameters governing planned hyperthermia treatment procedures.Several modeling studies have been conducted to illustrate the effect of variation of blood flow rate under local heating. Shulman et al. On the other hand, some researchers are of the opinion that heat transfer in the tissue and blood vessels should be considered separately using the energy equations in tissue and blood vessels A common feature of the above-mentioned modeling studies is that they intend to capture the variation of blood flow rate with temperature without considering the effects of blood pressure and vessel characteristics. As regards the determinants of tumor blood flow, Jain The purpose of this study is to numerically investigate the response of blood flow and oxygen diffusion to the laser irradiation in a human breast tumor. First, a two-dimensional finite element (FE) thermal model is developed to simulate the absorption of laser energy. Next, the one-dimensional model of fluid flow in elastic tubes is used to model the blood flow in the vessel network with neoplastic vasculature. Subsequently, PO2 distribution is analyzed in normal and tumor tissue units through the Krogh model (a) shows a schematic diagram of a laser-irradiated breast and the solution domain. The breast model is assumed to be hemispherical in shape with a subcutaneous fat layer and gland regions. A 10-mm diameter tumor is located 6 mm beneath the surface with its center on the z-axis. The geometrical data are obtained from the study of Ng and Sudharsan The tumor vessels are different from the vessels in normal tissues, which are permeable, fragile, and larger. Less et al. b shows the modeled blood vessel network in a breast tumor. Here, we consider that the tumor vascular beds are parallel to the normal vascular beds. The geometrical data of the normal blood vessels, including the length and diameters or the cross-sectional areas of the vessel segments, were based on the MRI image The temperature distribution induced by laser irradiation in the target zone and other areas is governed by the bioheat equation ρtct∂Tt∂t=λt∂2T∂2r+1r∂T∂r+∂2T∂2z+Q+ωρbcb(Tb-Tt).When the laser beam hits the skin surface, the laser energy is partially absorbed, scattered, and transmitted. The laser power intensity along the tissue depth is expressed by Lambert–Beer's law, as follows:Heat generation due to scattering is assumed to be negligible; therefore, the specific absorption rate in the target zone can be expressed as follows:Since the diameter of the tumor is 10 mm; the irradiated diameter is set to be 10 mm. For the area not exposed to a laser irradiation, the specific absorption rate is set to be 0.The heat transport in the tissue is subject to the following boundary conditions:At the axis of the symmetry or the base of the breastThe bioheat equation is discretized using the finite element method (FEM). The finite element equation is developed using the Galerkin weighted residual method, and the matrix form is expressed as follows:[ke]=∬eλ∂[N]T∂r∂[N]∂r+∂[N]T∂z∂[N]∂zrdrdz+∬eωbρbcb[N]T[N]rdrdz-∫sh[N]T[N]rds,[c]=∬eρtct[N]T[N]rdrdz,{Ie}=aI0(x)∬e[N]Te-kzrdrdz+ωbρbcbTb∬e[N]Trdrdz,{Se}=∫shTf[N]Trds.The global equation system is then formed from these finite element equations. A forward difference approximation to the time derivative and the conjugate gradient (CG) method are used in order to compute the algebraic equations of temperature.The blood flow in the breast is expressed by one-dimensional non-linear equations of pulsatile flow in an elastic tube. The continuity and momentum equation may be, respectively, defined asThe tube law in the arteries is expressed as in In the above equation, E is Young's modulus, h is the wall thickness, and r0 is the radius of the vessels. The tube law in the microcirculation and veins can be expressed as in where kp is the coefficient proportional to the stiffness of the tube wall and A0 is the cross-sectional area in the initial state. The temperature of blood flow in the vessels is given as in ) are solved by applying the boundary conditions at the inlet, outlet, and the bifurcation. A physiological pulsatile flow is assumed at the inlet qin=qmax(0.251+0.290(cosΦ+0.97cos2Φ+0.47cos3Φ+0.14cos4Φ)),Φ=ωrdt-ωrdπ.Since there is no pulsation of pressure in the veins, the outlet pressure is assumed to be 5 mmHg, which remains constant. At the bifurcations, the pressure is assumed to be continuous and the inflow and outflow are balanced. The inlet blood temperature is assumed to be 37∘C.The two-step Lax–Wendroff method was used to transform the system of partial differential equations into algebraic equations. The energy equation may be solved after obtaining the blood flow rate and cross-sectional area from Eqs. . A detailed description of the computational method can be obtained from . The equation governing oxygen transport in the vessels and the tissue can be expressed as follows:where PO2 is the partial pressure of oxygen, α is the oxygen solubility, D is the oxygen diffusivity, and M is the oxygen consumption rate. At present, the oxygen consumption rate is considered to exhibit zero-order kinetics, that isThe following boundary conditions are supplemented in Eq. x=0,r⩽Rv,PO2=PO20,x=0,Rv⩽r⩽Rorx=L,Rv⩽r⩽R∂PO2∂x=0,r=0orr=R∂PO2∂r=0.With respect to the transformation of the oxygen convective-diffusion equation, a simple explicit scheme, similar to that of energy equation In order to solve the above-mentioned hyperthermia-tissue–blood flow interaction problem formulated above, the weak coupling method was employed. shows the schematic of the data transfer between these models. First, the blood pressure and the flow rate in different vessels are computed through the blood circulation model of the breast. The blood perfusion rate within one heart beat in the normal and tumor tissues thus obtained is transferred to the FE thermal model. Second, the temperature in the normal and tumor tissues under laser irradiation is computed by the FE thermal model and the average tumor temperature is transferred to the blood circulation model. It has been observed that heating a tumor at 41–42∘C for a duration can induce an approximately two-fold increase in the tumor blood flow where A0 and T0 are the cross-sectional area and blood temperature before heating, respectively, and b is the variation coefficient. Based on the experimental results, the value of b may be expressed as follows:Since the cross-sectional area of the blood vessels in the heating area under different tumor average temperatures is computable according to Eq. , the new blood perfusion due to a change in the blood vessel dimensions can be obtained by the one-dimensional blood circulation model and may be transferred to the FE model instead of the old values. Simultaneously, the new blood velocities are input to the oxygen analysis model for the computation of oxygen partial pressure in the normal and tumor tissue units.Three sets of parameters are required for calculating the variation of temperature, blood flow, and oxygen distribution in a tumor field. These include (a) thermophysical parameters for the thermal model, (b) parameters related to blood perfusion, and (c) parameters for oxygen distribution. The thermophysical parameters are compiled from data provided by Shih et al. lists the thermophysical property values used in the analysis.Using the data provided by Sheng et al. The effective diffusion coefficient and the oxygen solubility are assumed to be D=1.5×10-5cm2/s and α=3×10-5cm3O2/cm3/mmHg, respectively. The metabolic rate of oxygen consumption is assumed to be 3.3×10-5cm3O2/cm3/sIn this study, two situations under a laser irradiation of 1.3W/cm2 were considered. In the first situation, the blood is well perfused in the peripheral part of the tumor, whereas in the other situation, the blood is well perfused in the central core of the tumor.(a) shows the finite-element grid network of the computed model. The tumor and gland tissues differ in terms of blood perfusion, i.e., the blood perfusion is higher in the tumor tissue. The temperature distribution at different times under the laser irradiation is shown in (b). As seen in this figure, the laser energy is transferred deeply into the tissue with time, and the average temperature within the irradiated tumor increases.The variations of the average tumor temperature and the tumor blood perfusion are plotted in (a) and (b), respectively. Since the modification of the tumor blood flow induced by the heating treatment depends not only on the therapeutic temperature but also on the heating duration, it is assumed that the variation of the vessels due to the heating treatment occurs 5 min after the heating. (a) shows the average tumor temperature profile for a heating duration of 1200 s. It is observed that the temperature in the tumor without vessels displays the most rapid increase, the temperature in the tumor wherein blood is well perfused in the core displays a lesser increase, while that in the tumor well perfused in the peripheral part displays the least increase. The difference between the highest and the lowest temperatures is 0.6∘C. The variation of the tumor blood perfusion during heating is plotted in (b). In the coupling computing, we addressed the time delay in the variation of the blood perfusion as follows: the blood perfusion variation pattern remains the same within 5 min of heating during the temperature distribution computation; subsequently the computation of the blood flow will be started with a new average tumor temperature. Thus, the blood perfusion within a period of 1 s in (b) corresponds to the blood perfusion within 5 min of heating in (a). Four different types of blood perfusions are observed within 1200 s of heating. Furthermore, it is found that when the tumor has a well-perfused periphery, the blood perfusion rate can be increased for longer durations under laser irradiation, but the tumor temperature in this case is not as easily enhanced as in the case of a tumor with a well-perfused core.(a) shows the distribution of PO2 in the normal tissue unit during a period. PO2 in the inlet of a capillary is assumed to be 50 mmHg, and the pulsatile capillary blood velocity from the one-dimensional model is assigned to the vessel inlets. The tissue volume has a diameter of 60μm and a length of 0.5 mm, and the capillary inside the tissue volume has a diameter of 6μm. Due to the small diameter of the vessels and the low flow rate, the difference in the PO2 levels in vessels and the tissue is less, and the spatial and temporal distribution is almost uniform. The PO2 distribution in the tumor tissue during a period is shown in (b). The tumor tissue volume has a diameter of 120μm and a length of 0.1 mm. The tumor blood vessel is 12μm in diameter. The PO2 distribution in the tumor tissue volume appears different from that in the normal tissue volume. The PO2 gradient in the tumor vessel and the tissue is larger in comparison with that in the normal tissue; thus, the region that is away from the tumor vessel has a lower PO2 than that near the tumor vessel, and the distribution is inclined to become heterogeneous.The variation of PO2 with different blood velocities in the tumor tissue unit is shown in . The solid lines represent the distribution profiles with a lower blood velocity in the initial heating period, and the dotted lines represent the distribution profiles in the later heating period at a higher blood velocity. Since the variation of blood velocity is caused by heating, we can thus obtain the variation of PO2 at different temperature levels.Improving the efficiency of tumor treatments has always been a significant concern. In this study, a coupling numerical model is presented for the study of the tumor blood perfusion and the distribution of PO2 under laser irradiation. The model includes the blood flow rate, temperature distribution, and PO2 distribution inside the vessels and the tissue unit. This model can be used to quantify the interaction of hyperthermia, blood flow, and oxygen distribution. The characteristic feature of this coupling model is to couple the heat and mass diffusion model with a systemic flow model for the determination of blood flow prescribed for the heat and mass diffusion model.Our model has several limitations. First, lumped parameters that are representative of different vessels are required; these parameters are largely dependent on the experiment. Second, it only models the geometric differences between normal and tumor vessels. The tumor vasculature, although similar to the normal vessels in several aspects, has its own characteristic features. The difference in the vessel wall permeability may also be included. In addition, the heat transfer between the larger arteries in the breast and the tissue are not considered. Studies have shown that the thermal effect of larger arteries cannot be neglected In conclusion, the proposed coupling model can be used to investigate hyperthermia-blood flow-oxygen distribution interaction. The initial results show that for the tumors with different blood perfusion distribution, the variation of tumor temperature after heating is different. Accordingly, the tumor blood perfusion displays a different modification tendency. Moreover, the oxygen distribution gradient is greater in the tumor tissue than in the normal tissue, particularly near the tumor vessels.The coupling model presented here provides a tool to analyze the relationship between blood flow, vessel temperature, and oxygen distribution. The ultimate goal of this study is to monitor the spatial and temporal variation of the tumor blood perfusion and its effect on the oxygen distribution in the treatment of cancer. The future extension of this research would be the study of the blood perfusion and oxygen distribution in differently shaped tumors with different heating sources.Y. He received her B.E. (1989) and M.E. (1992) degrees from Dalian University of Technology, China, and her D.E. degree (1999) from The University of Tokyo, Japan. She works as a research assistant at the Computational Biomechanics Unit, RIKEN. Her research interests include numerical and experimental studies of blood flow and heat transfer in living tissues.M. Shirazaki received his B.E. (1992) and M.E. (1994) degrees from Hokkaido University, and his D.E. degree (1999) from The University of Tokyo, Japan. He is an associate professor of the Course of Multimedia Studies in Yokohama National University. His current research interests are fluid-structure interaction including heat transfer and large–scale parallel computing.H. Liu received his B.S. degree (1985) from Dalian University of Technology, China, and completed his M.S.E. (1989) and Ph.D. (1992) from Yokohama National University, Japan. He is a professor at the Department of Electronics and Mechanical Engineering in Chiba University. His research interests focus on computational fluid dynamics, biological fluid dynamics, physiological fluid dynamics, and image-based modeling of cardiovascular arterial vessels.R. Himeno received his B.E. (1977) and M.E. (1979) degrees from Kyoto University and received his D.E. degree (1989) from The University of Tokyo. He is the unit leader of the Computational Biomechanics Unit and the director of the Advanced Center for Computing and Communication, RIKEN. His current interests include computational biomechanics simulation and structure–fluid coupled simulation.Z.G. Sun received his B.E. (1985) from Tianjin University, China, M.E. (1988) from Jilin University of Technology, China, and D.E. (1997) degrees from Gifu University, Japan. He is a senior researcher at Advanced Simulation Technology of Mechanics Co., Ltd., RIKEN. His current interests include computational biomechanics and nonlinear FEM numerical simulation.Residual stress driven creep cracking in AISI Type 316 stainless steelSpecially designed AISI Type 316H austenitic stainless steel 25 mm thick compact tension specimens have been plastically deformed to produce significant tensile hydrostatic residual stresses at the notch root at mid-thickness. These specimens were thermally exposed at 550 °C for 4500 hours in order to study elevated temperature creep relaxation of residual stress and the development of reheat cracking creep damage. Residual strains within the specimens were measured using diffraction techniques before and after thermal exposure. A three-dimensional finite element model was developed both to predict the residual stress within the specimens before and after thermal exposure. No reheat cracking was found near surface, but due to the reduced creep ductility with increasing hydrostatic stress, significant creep cavitation was found mid-thickness. A previously developed creep damage model was applied to predict the onset of reheat cracking. Good correlation has been found between measurements and finite element predictions of strain and stress before and after thermal exposure. The extent of creep damage has also been assessed through destructive examination, providing validation for the creep damage prediction model.Time-dependent plasticity, or “creep”, is an important deformation mechanism at elevated temperatures. If the accumulated creep strains are sufficient to exhaust the creep ductility of the material, extensive grain boundary creep cavitation will develop and cracking initiate. When such creep damage is associated primarily with relaxation of residual stress, the failure mode is commonly referred to as reheat cracking, the term originally being associated with the development of cracking in regions close to or within welds during stress relief heat treatment. Reheat cracks have been detected in non-stress relieved welded AISI Type 316H austenitic stainless steel components operating at elevated temperatures and pressures in UK advanced gas-cooled nuclear reactor plants A method for assessing creep crack initiation in steel components operating at high-temperature can be found in the R5 procedure Central to our study is the reproducible introduction into a simple test-piece geometry of a controlled level of hydrostatic tensile residual stress over a significant region. This has been achieved using a new design for a compact tension (CT) specimen that can be permanently deformed so as to introduce a large tensile residual stress field into the CT notch root area This procedure, combined with post mortem quantification of the level of creep cavitation cracking, has enabled a quantitative assessment of the predictive capability of the reheat crack initiation creep ductility exhaustion model While reheat cracking has been observed in welded engineering structures exposed to long-term elevated temperature conditions For this purpose a CT specimen type of design was chosen. Although such specimens are normally used for fracture or creep crack growth testing under external tensile loading, it has been shown that a tensile residual stress field can be generated by loading in compression beyond yield and then unloading a shows the geometry and dimensions of the CT specimen design adopted. A total of five CT specimens were machined from a 65 mm thick ex-service steam header, supplied by British Energy, taking care to use material remote from original fabrication welds. The steam header, which had been operating at about 525 °C for approximately 60,000 hours, was made from an AISI Type 316H austenitic stainless steel forging (cast number: 55882B3) having the composition shown in A tensile crack opening residual stress field was introduced in the vicinity of the notch of the CT specimens using a pre-conditioning compression treatment. Preliminary two-dimensional (2-D) FE analysis The calculated load was applied to the specimens via ball bearings (25 mm diameter) located in spherical seats on the top and bottom faces of the specimens (see a), at a displacement rate of 0.1 mm min−1. Pre-straining was monitored using the machine load cell and a strain gauge applied to the back-face of each specimen. In this way, pre-straining treatments were carried out in an identical manner on three CT specimens (labelled CT1, CT2 and CT3).In order to validate the 2-D FE analysis of the pre-straining process and to ensure the correct level of plastic strain was introduced, full-field surface strain analysis was undertaken during loading using both electronic speckle pattern interferometry (ESPI) After pre-straining, a 3.5 mm deep pre-crack was introduced into the notch of one CT specimen (CT1). This was achieved by first spark eroding a 0.25 mm wide starter slot to a depth of 1.5 mm into the notch root, and then producing a sharp crack at the slot tip by fatigue load cycling in compression. A total of 128,300 cycles were applied (using loads ranging from −1.5 to −15 kN) to create a maximum total crack length of 3.5 mm. The initial residual strain fields at the mid-thickness plane in all three pre-strained samples (CT1, CT2 and CT3) were measured by high-energy X-ray diffraction (HEXRD) and neutron diffraction, as described in Section 4.The residually stressed notched (CT3) and the notched and fatigue-cracked (CT1) specimens were creep tested by soaking at a constant temperature of 550 °C for 4500 hours in air at normal atmospheric pressure (note: no primary loads were applied in the tests). The extent of cracking was monitored in CT1 during thermal soaking using the potential drop method. The residual strains in the thermally soaked specimens were then remeasured using HEXRD to allow the change in residual stress field in each sample to be determined.Residual elastic strain measurements were carried out using HEXRD at the European Synchrotron Radiation Facility (ESRF) and neutron diffraction on the D1A diffractometer at the Institute Laue-Langevin (ILL), in Grenoble, France. These highly penetrating beams enabled the strain field to be mapped within the CT specimens non-destructively.The HEXRD measurements were carried out on the ID15A beamline utilizing a high-energy white beam. Diffracted X-rays in the 100–300 keV energy range were measured in transmission through the thickness of the samples using an energy dispersive detector. The diffraction gauge volumes for the measurements were defined by vertical and horizontal slits varying from 0.5 × 0.5 mm down to 0.1 × 0.1 mm. The scattering angle was 3° from the incident beam and defined by a static set of horizontal slits 0.1 mm wide. At such low scattering angles this resulted in a maximum gauge length of 10 mm in the through thickness direction using the 0.5 × 0.5 mm slits. That is, the gauge averaged over 5 mm either side of the mid-thickness plane. Only the crack opening (direction 2) residual elastic strains were measured. FE analysis of the residual stress field along the CT ligament showed that the direction 2 component of residual elastic strain was largely constant across the 10 mm thick central portion of the CT specimen Neutron diffraction strain measurements were carried out along directions 1 and 2 (see a) using the 311 peak and a continuous, monochromatic neutron beam of wavelength 1.514 Å with an angular position sensitive detector (PSD). The 311 peak is known to give the most linear response to stress for γ (face-centred cubic) iron After the thermal exposure creep test and the non-destructive diffraction measurements, specimens CT1 and CT3 were examined metallographically in order to assess the nature and extent of creep damage. Both CT specimens were first sectioned by EDM through the mid-thickness plane. One half of each sample was then cooled in liquid nitrogen and immediately cracked open for fractographic analysis. The other half was polished and analysed using standard metallographic methods on the interior (mid-thickness) face. This comprised a repeated light polishing and etching procedure in order to show up any small intergranular cavities or cracks, indicative of creep damage, and to minimize the risk of dislocating grain boundary carbides. Etching was carried out using Marbles Reagent (10 g CuSO4, 50 ml HCl, 50 ml H2O) for <5 s.All FE modelling within this paper was carried out using the package ABAQUS Initially 2-D plane strain and plane stress models were constructed using a 2-D mesh identical to the face of the 3-D mesh shown in b. These models were used simply to determine the load that should be applied in order to introduce a suitable residual stress field, as described above. Pre-strain loading was applied to the dimple via a rigid circle, representing the ball bearing. During loading, the circle was constrained to move only in direction 2 (b) but sliding between this and the sample was allowed. Material property data for Type 316H stainless were obtained from uniaxial tensile tests carried out on samples taken from the same header material and tested at 20, 275 and 550 ˚C (see Subsequently full 3-D modelling was undertaken using a one-quarter geometry 3-D mesh (see b) and symmetry boundary conditions. The model comprised a 2-D mesh effectively extended in the out-of-plane 3-direction. A total of 10 elements was used from mid-thickness to edge giving 30,310 first order (linear) interpolation 8-noded hexahedral brick elements with reduced integration and hourglass control (ABAQUS designation C3D8 R). The residual stress field was produced in the model by applying deformation via a rigid cylinder. Both isotropic hardening and non-linear combined isotropic/kinematic hardening models were used as part of a sensitivity study (). In both cases the yield and proof stress values shown in were used to describe the non-linear nature of hardening for this material. For the combined hardening model the “half cycle” option within ABAQUS was used, resulting in the kinematic hardening parameters being calibrated from the half cycle data shown in shows the predicted residual stress profile after pre-straining along the CT ligament in the mid-thickness plane; the profiles show a significant difference between the two models close to the notch root. The comparison shows that the peak stress of the non-linear kinematic model is approximately half of the isotropic model. Isotropic hardening was selected for all the subsequent FE modelling within this work as the elastic strain profiles from the isotropic model produced better correlation with diffraction measurements near the notch.FE analysis of the thermal soak creep tests was carried out in three stages: (i) the pre-straining treatment was applied (CT1, CT2, CT3) so as to predict the initial residual stress field. This was validated by comparing deformations and strains with those recorded by ESPI, image correlation and diffraction. (ii) For CT1, a crack was introduced into the model by simultaneously releasing the boundary condition constraints on the nodes on the crack face up to 3.5 mm along the ligament plane from the notch root. (iii) For CT1, CT2 and CT3 the FE models were raised to a uniform temperature of 550 °C and a creep deformation modelling step applied in order to predict the relaxation in elastic strain and stress in the test specimens.Creep relaxation and creep strain accumulation can be predicted using non-linear FE analysis with an appropriate creep deformation law. The RCC-MR creep law where ε¯c is the equivalent creep strain, σ¯ is the equivalent von Mises stress and t is the time in hours. C1, C2 and n1 are temperature-dependent coefficients for the material and are given in Ref. In the secondary stage of creep, the creep strain is given bywhere C and n are temperature-dependent coefficients and the variables ε¯ep and tep denote the strain and the time at the end of primary creep, respectively. For each increment of the FE creep analysis, the creep strain for both primary and secondary creep is calculated and the changeover from primary to secondary creep is chosen when the two creep rates become equal.A simple representation of tertiary creep behaviour is also included in the creep analysis subroutine in the following manner:where ε¯cT is the equivalent creep strain that includes tertiary behaviour and Dc is the creep damage function described in Eq. . In this relationship tertiary creep only becomes significant as the level of creep damage approaches unity.It is worth noting that the creep model for the CT specimen was coupled with the pre-straining step so that the prior plastic strain history was stored through subsequent creep and damage simulations. However, the creep models used were not modified to include the effect of plastic pre-straining on subsequent creep behaviour.A ductility exhaustion engineering model, proposed by Hales where ε¯˙c is the instantaneous von Mises creep strain rate at time, t, and εf¯ is the corresponding multiaxial creep ductility, expressed as the von Mises strain at failure, which is a function of the strain rate and stress state. Within the model for reheat crack initiation, an empirical approach has been adopted to describe the effects of stress state on ductility where ϵf,uni is the uniaxial ductility which is a function of the strain rate, σ¯ is the von Mises stress, σ1 is the maximum principal stress and σp is the hydrostatic stress. The first term of Eq. represents cavity nucleation and the second term represents cavity growth by creep deformation. Crack initiation is conceded when Dc |
⩾ 1.The above ductility exhaustion model has been incorporated into the ABAQUS FE creep subroutine , the effect of prior plastic strain history is not explicitly included in the creep damage model; however, it is indirectly considered by the use of a lower bound ductility associated with heat-affected zone (HAZ) material that had previously experienced cyclic thermoplasticity. This topic will be discussed in greater deal in Section During the compressive pre-straining of specimens CT1, CT2 and CT3 the surface strains were monitored by image correlation and ESPI in order to confirm that the intended residual strain fields had actually been introduced. shows a comparison between the total surface strains predicted by the plane stress, plane strain and 3-D FE models at the end of the treatment and those actually measured for CT2. Good agreement is observed between the surface strain fields measured by image correlation and ESPI and the 3-D FE model. The measured fields both show lobes of compressive strain (e.g. note the −1.5% contour) emanating from the notch at approximately ±45° above and below the central ligament, with a tensile strain of ∼1% being reached towards the back-face of the specimen. The agreement with the 2-D FE models, however, is not so good, despite the fact that similar tensile strain levels are predicted in both cases to those observed. The predicted strains around the notch are very different, with the characteristic lobes of strain observed experimentally absent from both analyses. This difference is significant, necessitating the use of a full 3-D model, as it is the plasticity around the notch root that generates the final residual stress field within the specimen.In view of the fact that hydrostatic stress is believed to play an important role in reheat cracking a compares the predicted and measured residual opening (direction 2) elastic strain variation along the central ligament at mid-thickness of the pre-strained, notched CT specimens (CT2 and CT3). Measurements of residual elastic strain were made using both HEXRD and neutron diffraction techniques. The close agreement between the two measurement techniques on two separate samples encourages a high level of confidence in the measurements made. The only disparity in the measured residual strains is close to the notch root. This is due to the difference in measurement gauge volume used for the two techniques. The larger gauge volume of the neutron measurements (2 × 2 × 1.5 mm compared with 0.5 × 0.5 × 10 mm) has resulted in a greater smearing effect in the region where the strain gradient is highest. The error bar plotted at each HEXRD measurement corresponds to the uncertainty of the multiple peak fit of the diffraction spectrum, and is much smaller than the point-to-point scatter of the data. The agreement between measured and predicted initial residual strains along the mid-thickness ligament line is very good. The predicted and measured (HEXRD) tensile strains at the notch root surface correspond to crack opening stresses of around 800 MPa.The residual elastic strain field at mid-thickness in the pre-cracked CT sample (CT1) was mapped by HEXRD. The stress concentration associated with the presence of the pre-crack is clear from the elastic strain map acquired mid-thickness in a. It is also evident in the line profiles of a taken across the central ligament. The residual stresses predicted by the 3-D FE model are very similar to those predicted for the notched sample (a) except in the immediate vicinity of the crack itself where, unsurprisingly, the tensile field is more intense and has advanced slightly deeper into the ligament corresponding to the length of the crack tip. It is noteworthy that the magnitude of the measured residual strain at the crack tip in a is somewhat smaller than the measured strain at the original notch and that predicted for the pre-crack. This may be because the length of the crack tip varies slightly through the thickness of the sample and therefore the gauge volume samples material at various distances from the crack, smearing out the measured stress to a lower value. for the notched (CT3) and pre-cracked specimens (CT1). For both samples the creep crack can easily be distinguished from the fast fracture crack formed on breaking open the sample due to the oxidation-induced darkening of the creep crack surface. Unsurprisingly, significantly more creep damage can be seen in the centre of each specimen in comparison to the surface. This is due to the higher triaxial constraint in the middle of the specimen, leading to a considerable reduction in the creep ductility (see Eq. ). Extensive creep cracking was expected in CT1 due to the stress intensity generated by the 3.5 mm pre-crack. However, the occurrence of creep cracking for a blunt notch in CT3 was less expected. In both cases, the creep cracks appear not to be fully contiguous. shows optical micrographs from regions around the CT notch root taken from the mid-thickness planes. a exemplifies the discontinuous nature of creep cracking ahead of the pre-crack, while the close-up in b confirms that microcracking occurs by the link up of creep cavities nucleated along grain boundaries c shows the extensive region of creep damage around the blunt notch of CT3. A number of discontinuous cracks emanating from the notch root, parallel to the CT ligament, can clearly be seen. Here, the dominant creep crack is approximately 1.7 mm long and comparable with that in CT1; however, clearly shows that overall creep cracking is more extensive in the pre-cracked specimen CT1.b compares predicted strains in the notched specimen with HEXRD measurements on specimen CT3 after prolonged thermal exposure. Comparing these results with the pre-strained case (a) shows that the peak tensile strains have relaxed significantly over the course of the 4500 hours exposure, reducing from ∼3000 × 10−6 at the notch to around zero. This combined with the fact that the peak tensile strain is now 3 mm from the notch reflects the extensive level of creep damage to this depth. Further from the notch the stress profile has been retained, but approximately halved in magnitude. It is notable that the point-to-point scatter in measured strain in b is significantly larger than the measurements in a because of poorer grain sampling statistics associated with the smaller gauge volume employed (0.1 × 0.1 × 3.4 mm compared with 0.5 × 0.5 × 10 mm).a shows the predicted evolution in crack opening residual stress with thermal exposure. It is clear that significant changes occur as soon as the temperature is raised due to the lower yield stress at elevated temperature compared to room temperature. After 100 hours considerable creep relaxation of tensile stress has occurred over the first 3 mm or so, with peak stresses reducing from an initial peak residual stress of 800 MPa to below 400 MPa with an accompanying reduction in compressive stresses along the ligament. After 1000 hours there is a marked change in the stress profile at the notch root, the magnitude of the peak residual stress falling to about 250 MPa, and the peak stress moving to 4 mm from the notch root. Less dramatic changes are predicted thereafter.The modelled and measured relaxed strain profiles in b for the notched specimen are in very good agreement. The discrepancy in strain (∼300 × 10−6) within 2 mm of the notch root is probably be due to that fact that the FE creep model is not configured specifically to simulate the observed microcracking (c). In practice this will tend to significantly relieve the crack opening stress locally; nevertheless in line with observation the high level of creep damage predicted there () significantly reduces the capacity to maintain significant stresses.b shows predicted residual stress distributions at 20 °C for the fatigue pre-cracked specimen CT1 before and after creep at 550 °C for 4500 hours. A peak stress of ∼1150 MPa is predicted at the 3.5 mm pre-crack tip for this model. After thermal exposure the peak stress falls to ∼400 MPa and the stress gradient adjacent to the crack tip is also reduced. Again there is reasonably close agreement between the measured and predicted residual strain profiles both before and after thermal exposure (). As mentioned above, the model does not model the physical formation of creep cavities or the growth of a dominant creep crack. This is probably why it fails to fully capture stress relaxation between 3.5 and 5 mm due to the 1.4 mm (average length) creep crack (The creep damage model applied in the present work has been used extensively by British Energy to assess the susceptibility of non-stress relieved welded stainless steel plant components operating at high-temperature (500–600 ˚C) to the risk of initiation of reheat cracking In our case, the nature of the FE model used to predict initiation of reheat cracking differs significantly from models used in previous plant weld assessments Predicted damage results for the notched specimen CT3 have been examined and compared with the fractographs in . This shows that the extent and shape of the creep damage zone predicted by the FE model is in good agreement with the observed creep crack and that the crack size is over-predicted. The over-predicted size of creep damage is probably related to the use of a lower bound value of the uniaxial creep ductility. The FE results show that the creep damage is associated with a region of high initial hydrostatic stress (∼310 MPa) located at the centre of the specimen at the notch root. This reduces the local multiaxial creep ductility to about 0.01 of the original uniaxial creep ductility (Eq. ). A metallurgical definition of the crack length-scale representing initiation of reheat cracking based on an order of magnitude greater than the average grain size is proposed here for discussion purposes. The grain size in the CT specimens ranged from 10 to 200 μm with an average value of 44 μm based on mean linear intercept method measurements. This defines a crack initiation length-scale of ∼0.5 mm. On this basis the observed maximum depth of cracking of 2 mm in the specimen suggests that some crack growth has occurred in the soak test. shows the predicted evolution of creep damage with thermal exposure time. At earlier thermal exposure times creep damage is seen to form ahead of the notch root; this is most likely due to the higher levels of trixiality present there. It is seen that the creep model predicts crack initiation on this basis (0.5 mm length-scale) at a time earlier than 150 hours. As the model simulates the development of creep damage in the form of cracking, it is likely that the accuracy of the model will deteriorate with subsequent thermal soaking time. This may also explain the over-predicted size of creep damage zone for CT3. Further thermal exposure tests on similar pre-compressed notched specimens are desirable to clearly define reheat crack initiation length-scales, to provide more precise validation of the prediction model at earlier thermal soak times (size, shape, location and time), and to determine whether crack growth predicted by the model can be correlated with the size of observed damage. In the meantime, the CT3 results demonstrate the validity of the model for a reheat crack initiation size of about 2 mm, which is at the low end of the size range of damage that has been found in plant welds by ultrasonic inspection.With regard to the pre-cracked specimen (CT1), as mentioned above, the reheat crack initiation model is not designed to predict creep crack growth from an existing or developing crack, as it does not explicitly include crack mechanisms, including the complete loss of load bearing capability. Nonetheless, predicted damage results for the cracked specimen CT1 have been examined and compared with the corresponding fractograph (see . It is remarkable how the predicted extent and shape of cracking correlates closely with that observed. The level of conservatism for CT1 is lower than CT3 due to the extremity of the stress state being simulated for CT1. In the case of CT3 a blunt notch is investigated using a lower bound creep ductility, whereas for CT1 the same creep ductility is used but with an addition of a pre-crack. The pre-crack would be expected to produce the most extreme levels of stress concentration and triaxiality and hence reduce the level of conservatism in the creep damage prediction compared to the blunt notch of CT3. It also noteworthy that the orientation of cracking (directly ahead of the crack tip at 0°) in a for CT1 does not follow the 45° lobes of measured peak residual strain ahead of the crack tip mapped in a. This is in line with the FE model which predicts the greatest reduction in local creep ductility ahead of the crack tip at the 0° orientation. This is due to higher levels of stress triaxiality according to Eq. at this location. This highlights the importance of the triaxiality of the stress field for driving reheat cracking.The close correlation between the creep damage observations of CT1 and creep damage predictions suggests that the reheat crack initiation model can provide reasonable results for short increments of crack growth. Indeed, these results further underwrite the robustness of the creep damage model for predicting reheat crack initiation in plant components where the definition of “initiation” and “crack growth” tends to be somewhat imprecise.There is some experimental evidence that plastic strain reduces the creep deformation rates, and particularly the creep ductility, of austenitic material b) implies that an appropriate creep law has been used, but strictly this only confirms that the correct end state is reached and does not necessarily validate the creep deformation–time path. The creep ductility used in the creep damage analysis was originally When comparing the residual stress state of the CT specimen with typical welds in plant structures it is clear that the long-range residual stress fields may be markedly different. In general, structural welds have approximately weld metal yield magnitude residual stresses acting in the longitudinal (welding) direction, maximum levels of ∼60–70% parent yield magnitude in the transverse direction, and ∼10% parent yield in the normal direction. Reheat cracking starts to become a potential concern when levels of transverse stress increase and the normal stress exceeds ∼20% parent yield, i.e. as the level of triaxiality (hydrostatic stress) begins to increase. In the CT specimen the pre-deformation treatment introduces a significant long-range residual stress distribution in the crack opening direction. However, local to the notch the treatment has created a sufficiently high level of triaxial stress to promote creep damage. As the reheat cracking model only takes account of the local stress state and the level of triaxiality in particular, it is not important that the long-range residual stress states in weld and CT test-piece are not identical.As discussed in the preceding section, the secondary issue of plastic strain levels is also important. In the modified CT specimens plastic strain is introduced isothermally in a single deformation cycle, whereas in welds, plastic strains are introduced by several cycles of thermoplasticity as weld metal is laid down bead by bead. In both cases the plastic strain levels vary rapidly, either moving away from the notch, or moving away from a weld fusion boundary. Based on practical experience, approximately 3% plastic strain would be expected in parent material a few millimetres from the fusion boundary of a single pass stainless steel weld; so total plastic strains could potentially exceed 10–20% in multi-pass welds.Three specially designed 25 mm thick CT specimens were pre-strained equally in compression, introducing a well-characterized residual stress state. A 3.5 mm deep pre-crack was introduced by fatigue into one of the specimens after pre-straining. Post mortem comparison of the mid-thickness vs. the exterior of the specimens following the thermal exposure tests has demonstrated very large differences in damage level consistent with modelling and demonstrating the importance of the hydrostatic component of the tensile stress. This confirms the need for testing of thick test-pieces and for monitoring the strain and damage in the bulk. In this respect non-destructive mapping of residual strains in the interior combined with subsequent post mortem fractography has proven to be an excellent way of examining the capability of the creep damage model to predict the evolution of stress and damage during elevated temperature exposure. The main findings are as follows.A 3-D FE analysis of the pre-straining treatment of the notched CT specimens, using an isotropic hardening model, predicted the initial residual strain/stress field with high accuracy when compared with IC and ESPI surface strain measurements and interior synchrotron and neutron diffraction residual (elastic) strain measurements. Neither plane strain nor plane stress models were found to be appropriate descriptors of these samples.The 3-D FE model predicted that considerable relaxation of the initial residual stress state would occur by creep deformation after 4500 hours thermal soaking at 550 °C. The predicted creep relaxation was in good agreement with mid-thickness synchrotron diffraction strain measurements on both notched and pre-cracked specimens before and after the thermal soak test. Slight disparities were found in regions of high creep damage where macro-cracks had initiated.The thermal soak test results have demonstrated the validity of the creep damage predictive model for a reheat crack initiation depth of about 2 mm, where it is likely that some limited crack growth has occurred. The model provided a good indication of the location and shape and over-predicted the size of initiated reheat cracks in both the notched and pre-cracked specimens.Further thermal exposure tests on similar pre-compressed notched specimens are desirable to clearly define reheat crack initiation length-scales, to provide more precise validation of the prediction model at earlier thermal soak times (size, shape, location and time), and to determine whether crack growth predicted by the model can be correlated with the size of observed damage.It should be remembered that in our case the means of introducing residual stress by compressive plastic deformation is very successful at generating sizeable and reproducible stress fields capable of causing reheat cracking, even in the absence of an applied load. Residual stresses introduced by welding austenitic stainless steel differ from the case studied in that plastic strains are introduced via multiple compressive–tensile strain cycles. If the nature and magnitude of plastic strain is a factor in creep ductility exhaustion mechanism, this may affect the extent to which our results are transferable to such cases. The influence of plastic strain on creep ductility is an important topic for further study.Preliminary studies on the suitability of rheocast Al alloys for deep drawingThis work analyses comparatively the behaviour of AlMg 5052 alloy sheets, in rolled and rheocast conditions, in deep drawing operations. Tensile tests and Erichsen cupping tests were performed to evaluate deformation behaviour in the two types of structures. Results showed higher deformation at lower required forces for rheocast material. Tensile test showed %EL four times higher, YS three times smaller and UTS two times smaller in the rheocast sheets compared to the rolled condition. Erichsen tests showed failure of rheocast at Fmax 24% smaller and total displacement 38% higher than rolled sheets. Fracture analysis showed distinct patterns, coalescence of dimples leading to fracture in rolled material, intergranular crack in rheocast. To produce the same degree of deformation, rheocast material requires 50% of the force required for rolled sheet. General results shows therefore, in terms of processing, that rheocast material can be an interesting raw material for deep drawing operations, meaning significant energy savings and formability improvement.Among the new manufacturing technologies developed in the last years aiming to achieve the best relation quality/costs, thixoforming of metallic alloys has been occupying an important position Thixoforming, meaning shaping of parts from raw material in the semi-solid rheocast condition (where the solid constituent presents morphology of spheroids), has been widely reported mainly related to casting and forging operations by the so called thixocasting and thixoforging processes. More recent studies also report the possibility of extruding bars in the semi-solid state, for which significant reduction in required forces is observed The flow behaviour of the rheocast slurry (thixotropic, non-Newtonian) allows its processing at low energy consumption and the production of high quality near net shape parts. Fine, equiaxial and residual stress-free and pore-free structures are usually obtained in thixoformed products.Despite the high formability of rheocast structures, already well known and the basis of thixoforming by die casting or forging processes As a process of significant commercial importance, deep drawing could take big advantages of the particular properties of rheocast materials, improvement in the geometry complexity due to the high plasticity of the rheocast material in the solid state or even higher in the semi-solid condition (naturally, low liquid fraction would be required to keep material cohesion in this case), reduction of necessary forces, energy savings. The possibility of deep drawing in the rheocast, solid or semi-solid conditions, could make it possible to form low plasticity alloys, those today impossible to be shaped by this process.Besides, the highly refined and isotropic structures in the rheocast raw material can lead to better processing performance, resulting in products with better surface quality and more homogeneous mechanical properties.Therefore, the analysis of the feasibility of forming materials in the semi-solid state would bring a new challenge for deep drawing operations, materials and products.This work relates the preliminary results in getting globular rheocast structures in sheets of a particular AlMg alloy and submitting such structures to standard formability tests, still in the fully solid state. Results in formability tests are compared to those obtained for conventional rolled sheets.Commercial wrought AlMg 5052 alloy, with chemical composition shown in Square samples of 100×100×0.8 mm thick were prepared from as received cold worked (by rolling) sheets and heated to a specific temperature above Tsolidus, to induce partial melting in order to produce rheocast structures. Solidus and liquidus temperatures for investigated alloy were determined by DTA analysis as follows, Tsolidus=629 and Tliquidus=655.8°C. According to previous experimental works, temperature and time of heat treatment were determined as 636°C and 7 min, respectively. Under such conditions it is expected total spheroidisation of the solid in the presence of intergranular liquid, or in other words, to produce rheocast structures.To avoid blisters in the surface of samples caused by absorption of hydrogen from atmosphere, Ar as protective gas was used throughout heating and holding at high temperature. After treatment samples were quenched in water. Resulting rheocast samples as well as initial sheets had their microstructures characterised by optical microscopy and SEM. Micropobe analysis was used to evaluate composition of observed precipitates and distribution of main alloying elements in the Al matrix, in the rheocast condition.Formability of wrought and rheocast sheets were evaluated by tensile tests and Erichsen cupping tests; the former also used to evaluate general mechanical properties.An universal strength testing machine — MTS was utilised for both sort of tests. For Erichsen tests, 100×100 mm and 50×50 mm square samples were used, deformation speed applied was 20 mm min−1. For tension tests, sub-size sheet-type specimens according to ASTM E8M standard were used, deformation speed applied was 0.02 mm s−1. Fracture topography and surface quality were observed by SEM. shows microstructures of (a) wrought material, in rolled condition and (b) after heat treatment to produce a rheocast structure.It can be observed in (a) very fine and homogenous distribution of precipitates (average dimension of precipitates 2 μm) due to the high deformation ratio in rolling operations, grain boundaries are not easily detected.Microstructure after treatment at T>Tsolidus shows fine globular structure, typical of rheocast materials. In this case the solidified rheocast alloy presents as main constituents the Al-α primary phase with globular morphology, surrounded by secondary phases, which were liquid in the semi-solid condition. The heating treatment imposed caused spheroidisation of original structure by mechanisms involving the steps: recrystallisation of originally deformed structure during heating; followed by liquid formation in grain boundaries by melting of secondary phases when Tsolidus is reached; liquid penetration in the newly formed recrystallised boundaries (in cases where γcg>2γsl, where γcg is the energy associated to the grain boundary and γsl is the energy of the liquid/solid interface) and detachment of the recrystallised grains to the surrounded liquid, where they can grow equiaxially with holding time. This growth is dependent on t1/3 or t1/4 (t=holding time), depending on the liquid fraction present in the slurry When such mechanisms are present, the globular solid particles observed in the rheocast material are actually individual grains, as discussed elsewhere Microanalysis results show two different types of precipitates, both with needle morphology and located in grain boundaries, one rich in Mg, Al and Si (typical chemical composition showing ∼21Si-57Al-22Mg) and another rich in Al and Fe (∼67Al-29Fe). shows these precipitates in more detail and , their chemical composition. This kind of particles, considering their hardness, size, morphology and distribution, can be seriously deleterious to the material’s mechanical properties.. The indicated points lie in a straight line (distance 7 μm between two consecutive points), linking the centers of two neighbour grains.High values of Fe and a depletion of Mg in the particular grain boundary examined indicates the proximity of a FeAl precipitate.Taking in account the high temperature, as well as heating and holding times involved in the production of a rheocast slurry, homogenisation of gradients of dissolved elements in the Al matrix is expected.On the other hand, liquid formation in grain boundaries above Tsolidus stimulate enrichment of elements in this region, where their solubility is higher. This enrichment was already reported elsewhere: works on Al-4,5%Cu alloy Results of tensile tests in AlMg 5052 sheets in both rolled and rheocast conditions are presented in . It can be observed the drastic decrease in YS and UTS and increase in percentage of elongation, when comparing rolled sheets and rheocast material. This behaviour was expected, once full recrystallisation takes place when heating the material at high temperatures to produce the rheocast condition.The low value of UTS and YS can be attributed to the usually coarse boundaries found in this sort of material, due to the enriched liquid in the slurry in these regions, leading to the formation of coarse phases when the slurry is frozen to the solid state, as observed in the microstructures.However, rheocast material presents significant higher %EL, due to its recrystallised, non-dendritic structure. These high values of elongation can be of significant importance in terms of processing, shaping complex geometry with lower required forces can mean a whole new range of wrought materials (for instance alloys with low ductility) and products.It was also pointed out that subsequent heat treatment to promote solubilisation of secondary phases can substantially increase mechanical properties of rheocast products.Therefore, mechanical properties deficiency in rheocast materials can be solved when properly controlling the rheocast process to obtain very fine grains, or by means of proper heat treatment in the final product.Advantages of improved processing should compensate losses in mechanical properties, therefore, thixoforming has a specific field of application, i.e. for those products where compromise between facility of shaping is mandatory over mechanical properties.It was also tested imperfect rheocast sheets produced by heat treatment in absence of protective gas. In this case blisters were produced on the surface due to hydrogen absortion (). In this condition the material had their Y, UTS and %EL reduced and was not considered in the analysis.General results obtained in Erichsen cupping tests for AlMg 5052 alloy in both rolled and rheocast sheets are shown in graphics show variation of applied force with displacement until failure was observed in the sample.It can be observed that failure occurred at a maximum force of 5 kN in the rolled sheet while the rheocast material could not afford more than 3.8 kN (24% lower).It can be also observed that failure does not occurs abruptly in the rheocast sheet, some deformation is still in course after Fmax is reached. The total displacement produced in rheocast sheets is substantially higher (38%) than in rolled condition, 5.2 against 7.2 mm, respectively.These results are compatible with the behaviour observed in tensile tests, which had already shown the higher plasticity of rheocast materials. that the necessary force to achieve determined level of deformation can be reduced up to 50% when using rheocast globular material instead of wrought sheets. also shows results obtained for samples with blisters on surface, as mentioned before. It can be noticed the strong influence of surface quality in the required force for deformation, rather than in the resulted displacement itself. In the present case, force inducing failure is 3.8 and 3.4 kN, respectively, for samples with good and poor surface quality.Fracture topographies and surface appearances near split edges after Erichsen tests were observed by SEM. Typical results for wrought sheets is shown in In the first case it can be clearly observed the presence of dimples, indicating fracture mechanism based on coalescence of voids generated by deformation of the matrix around hard precipitates; dimensions of dimples are compatible with precipitates dimensions (about 3 μm). The external surface near the fracture region is smooth with visible slipping lines.In the case of rheocast material, fracture topography shows the presence of dimples with high dimensions (however compatible with precipitates observed in the structure) and high degree of plastic deformation in the Al matrix.The presence of big cavities around globules of primary phase can be seen, caused by intergranular fracture. In some regions the grains seem to be completely detached. This behaviour could explain the high degree of plasticity of the rheocast material (also observed in tension tests) and the appearance of decohesion in the failed surface. Surface topography near the edge is rough with visible shift of grains, forming hills and valleys as well as cracks passing through grains boundaries.As the structure of rolled and rheocast materials are completely different, the failure patterns and mechanical properties has to be also quite distinct, as observed. The absence of dendritic formations and the internal homogeneity of primary phase in rheocast result in the high plasticity observed in this kind of material. In the other hand, the presence of secondary coarse phases causes failure by intergranular fracture, resulting in a sort of decohesion or separation of globulae.Appropriate heat treatment to eliminate these coarse phases in the rheocast product could improve its mechanical behaviour, still keeping the high plasticity.This work shows that deep drawing operations are feasible in AlMg 5052 sheets presenting globular rheocast structures. In such state the material presents high plasticity, requiring lower forces to form: for a specific displacement, such force can be reduced to 50% related to that required for conventional raw material in rolled condition. Failure in rheocast material occurs by intergranular fracture, resulting in the separation of the globulus of the primary phase.Mechanical properties in the rheocast product however, must be improved either by redefinition of parameters in rheocast process to prevent coarse precipitates in the grain boundary and to decrease grain size, or by means of suitable treatments in the final product to solubilise intergranular coarse phases.Acta Mechanica Solida Sinica, Vol. 21, No. 6, December, 2008 ISSN 0894-9166 Published by AMSS Press, Wuhan, China. DOI: 10.1007/s10338-008-0863-9 WAVE LOCALIZATION IN RANDOMLY DISORDERED PERIODIC PIEZOELECTRIC RODS WITH INITIAL STRESS** YizeWang1 Fengming Li12* Kikuo Kishimoto2 Yuesheng Wang3 Wenhu Huang1 (1P. O. Box 137, School of Astronautics, Harbin Institute of Technology, Harbin 150001, China) (2Department of Mechanical Sciences and Engineering, Tokyo Institute of Technology, 2-12-1, O-okayama, Meguro-ku, Tokyo 152-8552, Japan) (3 Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, China) Received 19 June 2008; revision received 20 November 2008 ABSTRACT The elastic wave localization in disordered periodic piezoelectric rods with initial stress is studied using the transfer matrix and Lyapunov exponent method. The electric field is approximated as quasi-static. The effects of the initial stress on the band gap characteristics are investigated. The numerical calculations of localization factors and localization lengths are performed. It can be observed from the results that the band structures can be tuned by exerting the suitable initial stress. For different values of the piezoelectric rod length and the elastic constant, the band structures and the localization phenomena are very different. Larger disorder degree can lead to more obvious localization phenomenon. KEY WORDS piezoelectric phononic crystal, initial stress, random disorder, localization factor, localization length I. INTRODUCTION In recent years, many people have studied the elastic wave propagation in periodic structures (or called phononic crystals)[1-8]. These artificial periodic structures can be used in many engineering applications, such as transducers, filters and vibration isolation technology. Among various phononic crystals, the system with smart materials (e.g. piezoelectric materials) appears. Due to the adaptive ability this new kind of phononic crystal has special applications. The problems on the elastic wave propagation in the intelligent material structures have received special attention[9-19]. In practical applications, on one hand, due to mismatch of material properties, the presence of the initial stress in composite structures is unavoidable during the manufacture process. On the other hand, the initial stress is often introduced to prevent the piezoelectric materials from brittle fracture. It leads to dramatic change of wave dispersion relation. The effects of the initial stress on the wave propagation in piezoelectric structures have been reported by some researchers [20-25]. This study is motivated by the works of Li et al.[26] and Yang et al.[27]. In Ref.[26], the elastic wave localization in randomly disordered periodic piezoelectric rods was analyzed. But the initial stress has not been introduced and the wave mode is longitudinal. Then the elastic wave propagation in * Corresponding author. Tel: +86-451-86414479, Email: [email protected] ** Project supported by the National Natural Science Foundation of China (Grant Nos.10672017 and 10632020), the China Postdoctoral Science Foundation, Heilongjiang Province Postdoctoral Science Foundation and Japan Society for the Promotion of Science (JSPS) to perform research work at Tokyo Institute of Technology, Japan. 530 ACTA MECHANICA SOLIDA SINICA 2008 periodic piezoelectric rods was investigated by Yang et al. for two-dimensional analysis in which the thickness-twist mode was considered[27]. In the present work, the localization factors and localization lengths in randomly disordered periodic piezoelectric rods with the initial stress are discussed. It is found that the initial stress has pronounced influences on band structure properties. Moreover, some new and interesting physical phenomena can be observed. The results suggest that we can tune the band structures by properly adjusting the initial stress. As a result, the effects of initial stress on band gap properties can be understood further. This paper is organized as follows. In I, the equations of wave motion and the transfer matrix are given. In II, the localization factor and localization length are presented. Numerical calculations are preformed in V. In , the conclusions of this study are drawn. II. EQUATIONS OF WAVE MOTION AND TRANSFER MATRIX Figure 1 shows the periodic piezoelectric rods consisting of elastic materials and piezoelectric ceramics periodically. The lengths of elastic and piezoelectric constituents are a1 and a2, respectively. For the case of small perturbation, the general motion differential equations for the piezoelectric material with initial stress are expressed as[28,29] Di,i + (uijD0),i = 0 (1a) (1b) where ?2 is the mass density of the piezoelectric material, sij the elastic stress tensor, Di the electrical displacement vector, ui the elastic displacement vector, sk0j the initial stress tensor, D0 the initial electrical displacement vector and dot denotes differentiation with respect to the time t. We assume that the longitudinal wave propagates along the x-axis and there is only one constant initial stress sx0 in each unit cell[23]. The governing equations of the longitudinal wave for piezoelectric ceramics are given by ?2u2 ?2?2 (E2 + sx)~?x~T + e33 ? 2 - ?2 ?2u2 ?2?2 e33^r^- -e33^7^- =0 ?x2 ?x2 ?2u2 ?t2 = 0 (2a) (2b) where u2 (x2, t) is the longitudinal displacement of the piezoelectric material, E'2 the Young modulus, e33 the piezoelectric constant, e33 the dielectric constant and ?2 (x2, t ) the electrical potential function. According to the similar procedure in Ref.[26], Eqs.(2) can be changed to 0?2u2 ?2u2 (E2 + sx)^r2- ?2 = 0 ?x22 ?t2 (3) where E2 = E'2 + e33/e33 is the equivalent Young modulus of the piezoelectric ceramics. Similarly, the governing equation for the elastic material is (E1 + sx0) ?2u1 ?2u1 ?x2 21- - ?1' ?t2 =0 (4) where u1 (x1, t) is the longitudinal displacement of the elastic material, E1 the Youngs modulus and ?1 the mass density. The harmonic solutions of the displacements can be expressed as ui(?i, t) = [Ci sin(ai?i) + Di cos(ai?i)] exp(-i ?t) (i = 1, 2) (5) Fig. 1. The schematic diagram of an elastic rod periodically inserted with piezoelectric ceramics. Vol. 21, No. 6 Yize Wang et al.: Wave Localization in Randomly Disordered Periodic Piezoelectric Rods 531 where i = y^1, Ci and Di the unknown coefficients to be determined by the boundary conditions, ? the circular frequency, ai = kia the non-dimensional wave numbers, ki = ?/ci (i = 1, 2) the wave numbers, ci = \/(Ei + sx)/?i the wave velocities in the elastic and piezoelectric materials, ?i = xi/a1 the non-dimensional coordinates, a1 the mean value of the length of the elastic rod. So the non-dimensional length of each component is defined as ?i = ai/a1 (i = 1, 2). As shown in Fig.(1), each unit cell includes two sub-cells (sub-cells 1 and 2). Based on the continuity conditions at the interfaces of the (j 1)-th, j-th and (j + 1)-th unit cells, the relation of the state vectors for the two consecutive unit cells is given by[26] (j) v 2R = T (j-1) v 2R (6) where v2r is the state vector at the right side of the j-th unit cell and Tj is the transfer matrix between the two constitutive unit cells. For the detailed elements in v(2 jr and Tj, one can refer to Ref.[26]. III. WAVE LOCALIZATION Lyapunov exponent measures the average exponential rate of convergence or divergence between two neighboring orbits in phase space. Appling the Lyapunov exponent, we can calculate the localization factor which describes the average exponential decay rate of elastic wave amplitudes. It has been proved that for 2m x 2m transfer matrices, the Lyapunov exponents occur in pairs and the m pairs of Lyapunov exponents have the following property[31,32] ?1 > ?2 > > ?m > 0 > ?m+1(= ?m) > ?m+2(= ?m-1) > > ?2m(= 1) (7) According to the algorithm presented by Wolf et al. to calculate the Lyapunov exponent[32], we can get the smallest positive Lyapunov exponent which represents the localization factor. In the present work, the dimension of the transfer matrix is 2 x 2 and the first Lyapunov exponent ?1 is the localization factor. For the detailed expression of Lyapunov exponent, one can refer to Ref.[26]. For wave propagating in the disordered periodic structures, the wave amplitudes exponentially decay as exp[/l(?)] with the distance, where ? is the circular frequency of the elastic wave and x is the position coordinate along the disordered periodic structure. Then l(?) is called the frequency-dependent localization length which represents the distance of wave propagation along the structure[33]. The non-dimensional localization length L which denotes the similar physical meaning as l(?) can be given L = 1/?1 (8) IV. NUMERICAL RESULTS AND DISCUSSIONS In this section, the numerical calculations of localization factors and localization lengths in disordered periodic piezoelectric rods are performed. The structures are made up of epoxy and piezoelectric ceramics. The material constants are E1 = 4.35 GPa, p = 1180 kg/m3, E'2 = 88.07 GPa, ?2 = 7600 kg/m3, e33 = 18.62 C/m2, e33 = 5.92 x 10-9 F/m[26,35 1 4.1. Localization Factors In order to analyze the influence of the initial stress on band structures, different values of the negative initial stresses are considered. The localization factors varying with wave-number a1 for the ordered periodic piezoelectric rods with the initial stress are displayed in Fig.2. Four different values of the initial stress are considered (i.e. j sx0 j = 0,10, 20 and 50 MPa). The non-dimensional length of the piezoelectric ceramics is 0.5. The localization factors being zero correspond to the pass bands and the other regions denote the stop bands. It can be seen from Fig.2 that the initial stress has pronounced influences on the band structure for large wave numbers. And the influence of initial stress is not obvious for small values of (e.g. Fig. 2 Localization factors ?i vs. wave-number ai for ordered periodic piezoelectric rods with the consideration of the effects of the initial stress. 532 ACTA MECHANICA SOLIDA SINICA 2008 |sI =10 MPa). However, the effects can not be negligible when the initial stress is larger than 10 MPa. The peak value of the localization factors becomes larger and the stop bands are gradually broadened with the increase of the initial stress near the frequency interval a\ g (44, 45). So, it can be concluded that the band structure characteristics can be tuned by the initial stress. In order to introduce the randomness into the periodic structure, the non-dimensional length ?2 of sub-cell 2 is assumed to be an uniformly distributed random variable with mean value ? and coefficient of variance d. For d = 0, the structures are perfectly periodic. For d > 0, the structures are randomly disordered. The variations of the localization factors vs. non-dimensional wave number with the effects of the length of the piezoelectric ceramics are displayed in Fig.3. The initial stress \s is 20 MPa and the values of d are 0 and 0.1. The non-dimensional length of the piezoelectric ceramics is 0.5, 1.0 and 1.5, respectively. It can be seen from Fig.3(a) that the first pass band tends to be narrower with the increase of the length of the piezoelectric rod. The locations and widths of the pass bands and stop bands are remarkably changed for different values of ? . We can observe from Fig.3(b) that for the disordered periodic piezoelectric rods the passband regions corresponding to the complete periodic structure will vanish (e.g. for the passband near a\ = 5 of the dashed line) or become narrower (e.g. for the passband near a\ = 6 of the dashed line). So in disordered periodic structures, the wave localization phenomenon appears. In order to investigate the effects of the material constants on the dynamic behavior of the wave propagation and localization, the localization factors for different values of E'2 (60, 70 and 80 GPa) are computed and displayed in Fig.4. The value of ? is 1.0 and the initial stress is 20 MPa. We can Fig. 3. Localization factors ?1 vs. wave-number a1 for disordered periodic piezoelectric rods with the consideration of the effects of ? . (a) 5 = 0 (b) 6 = 0.05 Fig. 4. Localization factors ?1 vs. wave-number a1 for disordered periodic piezoelectric rods with the considering of the effects of E'2. Vol. 21, No. 6 Yize Wang et al.: Wave Localization in Randomly Disordered Periodic Piezoelectric Rods 533 observe from Fig.4(a) that in lower frequency region the effects of the material constant on the band gap properties are slight. But in higher frequency region, the material constant has significant influences. With the increase of the elastic constant E'2 some stopbands will become wider (e.g. for the stopband at ai = 4) and others will become narrower (e.g. for the stopband at a\ =6). And similar to Fig.3(b), for disordered periodic piezoelectric rods, the wave localization phenomenon occurs. 4.2. Localization Lengths In this section, the localization lengths in randomly disordered periodic piezoelectric rods with initial stress are calculated to study the wave localization characteristics. The elastic constant of the piezoelectric ceramics, E^ is assumed to be a uniformly distributed random variable with mean value Ef2 and variance coefficient d. The non-dimensional length of the piezoelectric rods is 1.0. For different variance coefficients of the elastic constant (d = 0.01, 0.02, 0.05 and 0.2), the localization lengths varying with the non-dimensional wave number a\ are displayed in Fig.5. The initial stress, |sj!|, is assumed to be 20 MPa. It can be observed from Fig.5 that there are some narrow intervals in which the localization lengths are not zero for the whole considered frequency regions. This means that some waves can propagate a longer distance along the disordered periodic structure and others are localized near the disturbance source. Moreover, we can see from Fig.5(a) that for smaller variance coefficient d, there is a peak value of the localization lengths in the interval of ai G (5, 6). But this peak value is reduced to a lower one with the increase of the variance coefficient. Finally, it tends to be zero for a large value of the variance coefficient in Fig.5(d). The width of the peak in the interval of ai G (3, 3.3) also becomes narrower, which means that these waves cannot transmit along the disordered periodic structures. These phenomena are due to the fact that the wave localization is strengthened with the increase of the disorder degree. Fig. 5. Localization lengths vs. the wave-number ai for disordered periodic piezoelectric rod. 534 ACTA MECHANICA SOLIDA SINICA 2008 V. CONCLUSIONS In this paper, the elastic wave localization in disordered periodic piezoelectric rods with initial stress is studied. The mechanical and electrical coupling is considered. The random disorder of the length and elastic constant of the piezoelectric material are investigated. Both of the localization factor and localization length are calculated. Numerical calculations are performed to draw the following conclusions: (1) For ordered periodic structures, the band gaps can be tuned by changing the initial stress, especially in higher frequency regions. 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[17] Cao,X., Jin,F. and Wang,Z., On dispersion relations of Rayleigh waves in a functionally graded piezoelectric material (FGPM) half-space. Acta Mechanica, 2008, 200: 247-261. [18] Jin,F., Wang,Z. and Kishimoto,K., Basic properties of Rayleigh surface wave propagation along curved surfaces. International Journal of Engineering Science, 2005, 43: 250-261. Vol. 21, No. 6 Yize Wang et al.: Wave Localization in Randomly Disordered Periodic Piezoelectric Rods 535 [19] Jin,F., Wang,Z. and Wang,T., The Bleustein-Gulyaev (B-G) wave in a piezoelectric layered half-space. International Journal of Engineering Science, 2001, 39: 1271-1285. [20] Liu,H., Wang,Z.K. and Wang,T.J., Effect of initial stress on the propagation behavior of Love waves in a layered piezoelectric structure. International Journal of Solids and Structures, 2001, 38: 37-51. [21] Liu,H., Kuang,Z.B. and Cai,Z.M., Propagation of Bleustein-Gulyaev waves in a pretressed layered piezoelectric structure. Ultrasonics, 2003, 41: 397-405. [22] Du,J., Jin,X., Wang,J. and Zhou,Y., SH-wave propagation in a cylindrically layered piezoelectric structure with initial stress. Acta Mechanica, 2007, 191: 59-74. [23] Du,J., Jin,X. and Wang,J., Love wave propagation in layered magneto-electro-elastic structures with initial stress. Acta Mechanica, 2007, 192: 169-189. [24] Yang,J.S. and Wang,J., Dynamic anti-plane problems of piezoceramics and applications in ultrasonics a review. Acta Mechanica Solida Sinica, 2008, 21: 207-220. [25] Akbarov,S. and IIhan,N., Dynamics of a system comprising a pre-stressed orthotropic layer and pre-stressed orthotropic half-plane under the action of a moving load. International Journal of Solids and Structures, 2008, 45: 4222-4235. [26] Li,F.M., Wang,Y.S. and Chen,A.L., Wave localization in randomly disordered periodic piezoelectric rods. Acta Mechanica Solida Sinica, 2006, 19: 50-57. [27] Yang,J.S., Chen,Z.G., Hu,Y.T., Jiang,S.N. and Guo,S.H., Propagation of thickness-twist waves in a multi-sectioned piezoelectric plate of 6 mm crystals. Archive of Applied Mechanics, 2007, 77: 689-696. [28] Shang,F.L., Wang,Z.K. and Li,Z.H., An exact analysis of thermal buckling of piezoelectric laminated plates. Acta Mechanica Solida Sinica, 1997, 10: 95-107. [29] Fahmy,M.A. and EI-Shahat,T.M., The effect of initial stress and inhomogeneity on the thermoelastic stresses in a rotating anisotropic solid. Archive of Applied Mechanics, 2008, 78: 431-442. [30] Castanier,M.P. and Pierre,C., Lyapunov exponents and localization phenomena in multi-coupled nearly periodic systems. Journal of Sound and Vibration, 1995, 183: 493-515. [31] Xie,W.C., Buckling mode localization in ribtiffened plates with randomly misplaced stiffeners. Computers and Structures, 1998, 67: 175-189. [32] Wolf,A., Swift,J.B., Swinney,H.L and Vastano,J.A., Determining Lyapunov exponents from a time series. Physica D, 1985, 16: 285-317. [33] Scales,J.A. and Van Vleck,E.S., Lyapunov exponents and localization in randomly layered media. Journal of Computational Physics, 1997, 133: 27-42. [34] Li,F.M., Wang,Y.S., Hu,C. and Huang,W.H., Wave localization in randomly disordered periodic layered piezoelectric structures. Acta Mechanica Sinica, 2006, 22: 559-567. [35] Hirsekorn,M., Delsanto,P.P., Leung,A.C. and Matic,P., Elastic wave propagation in locally resonant sonic material: Comparison between local interaction simulation approach and model analysis. Journal of Applied Physics, 2006, 99: 124912. Wave localization in randomly disordered periodic piezoelectric rods with initial stressThe elastic wave localization in disordered periodic piezoelectric rods with initial stress is studied using the transfer matrix and Lyapunov exponent method. The electric field is approximated as quasi-static. The effects of the initial stress on the band gap characteristics are investigated. The numerical calculations of localization factors and localization lengths are performed. It can be observed from the results that the band structures can be tuned by exerting the suitable initial stress. For different values of the piezoelectric rod length and the elastic constant, the band structures and the localization phenomena are very different. Larger disorder degree can lead to more obvious localization phenomenon.Microstructural manipulation and improved mechanical properties of a near α titanium alloyIn this study, a newly developed near α titanium alloy with a typical Widmannstätten as-cast microstructure was subjected to isothermal multidirectional forging (IMDF) at 15 °C below β transus temperature. Microstructural observations reveal that the prior β grain boundaries disappeared and α laths transformed into spheroids gradually with increasing the IMDF pass. Ultrafine α grains with an average grain size of 1.57 μm was achieved after four-pass IMDF. Microstructural homogeneity was enhanced and the fraction of recrystallized grains increased remarkably with increasing IMDF pass. The spheroidization process of α laths is a result of the recrystallization during IMDF, including the dissociation of α laths and the migration of subgrains. Compared to the as-cast titanium alloy, both the tensile strength and elongation to failure at room temperature were improved, which is primarily attributed to the microstructure refinement and spheroidization of α laths. In addition to grain refinement, dislocation hardening and substructure strengthening are also the critical mechanisms for the increased strength observed in the samples after IMDF.Titanium (Ti) alloys are considered critical materials for the aerospace industry in virtue of their high strength-to-weight ratio, excellent corrosion/oxidation resistance, and preeminent creep resistance at elevated temperatures []. Among Ti alloys, near α alloys, in particular, possess good creep resistance, weldability, and toughness. They are considered a good candidate for certain applications in aerospace []. However, ineluctable casting defects and coarse microstructure lead to relatively poor mechanical properties, which largely limit the application of near α titanium alloys [A large number of reports are available on the deformation behaviors of Ti alloys by traditional hot-working technologies, such as forging, extrusion and rolling []. As compared to traditional hot-working technologies, severe plastic deformation (SPD) methods including high-pressure torsion and equal channel angular pressing are proven more effective to achieve ultrafine-grained microstructures []. Among these SPD techniques, isothermal multidirectional forging (IMDF) is gaining attention because of its cost-effectiveness and simple operation []. For instance, Ansarian et al. used this technique to have refined the grain size of pure Ti from 64 μm to 1 μm after 6 passes of IMDF. As a result, they achieved in the pure Ti 2.5 times greater tensile and shear strength than in an annealed Ti []. In another recent study, Zhang et al. found that both yield strength and elongation were significantly improved, as compared to the as-cast Ti-6Al-4V alloy []. Another previous study by the same group revealed that the mechanism of grain refinement caused by IMDF includes both continuous dynamic recrystallization and discontinuous dynamic recrystallization []. It is generally agreed that IMDF can lead to grain refinement and therefore improving yield strength. In addition to grain size reduction, the morphology of α laths is also changed to spherical shape during IMDF. However, the evolution process of the α laths is still largely unknown. For example, in one study of Ti-7333, Fan et al. proposed that spheroidization involves four steps: lath shearing, dislocation generation, nucleation of dislocation interface and interface migration []. Yoshinori et al. pointed out that the formation of α/α boundaries during hot deformation in Ti-6Al-4V alloy leads to a splitting of α laths in subsequent annealing, which is considered as spheroidization of α laths []. Yan et al. proposed that the dynamic recrystallization (DRX) process of commercial-purity Ti during hot deformation could be divided into a twin-active DRX stage and discontinuous DRX stage []. Despite its importance, thorough investigations into the spheroidization process in near α Ti alloys are still lacking. Therefore, we attempted to elaborate on the spheroidization mechanism in this type of Ti alloy during IMDF.The service temperature of the conventional Ti-Al-Sn-Zr-Mo-Si near α alloys is below 600 °C. In order to further improve the high-temperature performance, a newly developed near α Ti alloy with nominal compositions of Ti-6Al-3.5Sn-4.5Zr-2.0Ta-0.7Nb-0.5Mo-0.4Si was designed []. In this study, we applied IMDF to this newly developed near α Ti alloy. The IMDF processes were undertaken at 15 °C below β-transus temperature. The main objective was to investigate how IMDF affects the microstructural evolution and mechanical properties of this Ti alloy. The spheroidization mechanism and strengthening mechanism were discussed as well.The thermomechanical processing procedures including open-die forging and IMDF are shown in . The β-transus temperature of the current alloy measured metallographically is approximately 1308 K. Based on the β transus temperature, the as-cast ingot was subjected to open-die forging at 1373 K with a total height reduction of 75%, followed by air cooling. Samples for the IMDF process were obtained from the open-die forged rectangular billet by an electro-discharge machine. In the IMDF process, the dimensions of the billet 35 mm × 35 mm × 70 mm were maintained unchanged, while the loading axis was changed by 90° after each IMDF step. The IMDF was undertaken at 1293 K with a strain rate of 0.01 s−1. One-pass IMDF consists of three steps, as shown in . The samples that underwent one, two and four passes were labelled as sample 1-IMDF, 2-IMDF and 4-IMDF, respectively. After IMDF an annealing step was conducted at 923 K for 6 h, followed by furnace cooling to relieve the residual stress during IMDF.Microstructures were observed using an FEI Quanta 200F scanning electron microscope (SEM) with an electron backscatter diffraction (EBSD) attachment and a Philips CM12 transmission electron microscope (TEM). Tensile tests were carried out on an INSTRON-5500R testing machine with a crosshead speed of 0.5 mm/min. shows the initial microstructure of the as-cast titanium alloys. A typical microstructure is shown in (a). A close-up SEM micrograph presents a typical Widmanstatten structure consisting of alternate layers of thick α and thin β laths in the colonies. The average size of the colonies and the width of α laths were measured to be 472.5 μm and 2.61 μm, respectively.Obviously, the microstructure morphology of the as-cast titanium alloys has changed after IMDF. As shown in (a), after one-pass IMDF, the microstructure is still mainly composed of α laths. A small amount of equiaxed α can be observed in a higher magnification micrograph, as shown in (b). By increasing the IMDF pass, the prior β boundaries start to disappear, and α laths transform into spheroidal α grains gradually. After 4 passes of IMDF (4-IMDF), a large number of equiaxed α are observed, as shown in . Moreover, quantitative analysis by EBSD shows that the average size of α grains is reduced gradually, from 2.13 μm after one-pass IMDF to 1.57 μm after 4 passes (The phase constituents in the as-cast and as-forged samples are shown in , revealing that α-Ti is the only phase observed. This indicates that the alloy is near α Ti; the content of the β phase is too small to be detected by XRD. demonstrates the distribution of deformation twins along {101‾2} twin planes. These twins are thought to belong to the well-recognized {101‾2} <1‾011> deformation twinning system in Ti alloys []. The twin boundaries and the grains around them are highlighted by red and yellow lines, respectively. The volume fraction of the deformation twins increases to 0.76% after four passes of IMDF, (d). However, the volume fraction of the deformation twins is too small to play a considerable role in mechanical properties. This phenomenon is different from previous research on Ti alloys subjected to cold deformation, which leads to a large number of deformation twins []. We speculate that the twins are gradually replaced by fine recrystallized grains formed during high-temperature IMDF and subsequent annealing treatment.(a) – (c) present the EBSD analysis results, including Kernel Average Misorientation (KAM) or local misorientation, Schmid factor and recrystallization fraction at different IMDF passes. A high KAM value indicates a high dislocation density. All the samples have similar KAM value distribution and the average KAM in sample 2-IMDF is slightly greater than in the other two samples, as shown in (g), (h) and (i). This might be caused by the continuous occurrence of dynamic recrystallization (DRX) during IMDF. The recrystallization proceeds by consuming dislocations to form the new dislocation-free grains, decreasing dislocation density []. The Schmid factor distribution in basal slip systems for different IMDF passes is presented in (d) – (f). The average value of the Schmidt factor is 0.32, 0.31 and 0.19 for the three samples. In addition, as shown in (j)–(l), the recrystallized grains account for 15.6% after 1 pass IMDF and the percentage of the recrystallized grains increases to 61.8% after 4 passes. further presents the average value of Schmid factor distribution in both prismatic slip and pyramidal slip systems, as compared to the basal slip system ((a) suggests that no obvious slip systems dominate in the Ti sample after one pass IMDF. After 4 passes of IMDF, the average Schmid factor of both prismatic slip and pyramidal slip systems increases to 0.42 and 0.43 respectively. In contrast, the average Schmidt factor of the basal slip system decreases to 0.19, (f). This indicates that the prismatic and pyramidal slip systems in this Ti alloy start and dominate gradually, at the expense of the basal slip system [ represents the EBSD results showing the orientation and grain boundaries distribution of α grains in the Ti samples. (a), (d) and (g) are respective orientation maps recorded with reference to the inverse pole figures (IPF), shown in the inset of these respective figures. As seen in (a), (d) and 8(g), the dominant orientation of α-Ti changes from <0001> to <011‾0> in the normal direction (ND) with the increase of deformation passes. Numerous equiaxed grains with high-angle grain boundaries (HABs) are visible in (b), (e) and 8(h) (labelled by red lines). The fraction of the HABs increases from 53.3% in sample 1-IMDF to 75.9% in the sample 4-IMDF ((c) cf. 8i). This is in good agreement with the increment of recrystallization fraction shown in with the increase of deformation passes.Typical tensile stress-strain curves of the Ti alloy samples at room temperature are shown in and the corresponding tensile properties are summarized in . Distinct characteristics of strain hardening can be observed in after yielding. In addition, the stress increases notably with increasing the IMDF pass. It is worth noting that the ultimate tensile strength (UTS) and elongation to failure (δ) of the Ti samples have been significantly improved after IMDF. For example, the sample after 4-pass IMDF has an increase of UTS and yield strength by 22.5% and 31.8% respectively. In the meantime, the elongation to fracture also increases by 166%, as compared to the as-cast counterpart.Fracture surfaces of the samples are shown in (a), brittle quasi-cleavage fracture features in the fractography of the as-cast sample. A high-magnification SEM micrograph taken in the red box in (a) shows that both quasi-cleavage facets and tear ridges are visible, along with small amounts of dimples around them ((b)). In contrast, sample 1-IMDF reveals many deep dimples on the fracture surface, (c) and (d). The presence of a large number of deep dimples is a typical characteristic of ductile materials. The fractography results are consistent with the tensile properties as shown in IMDF has led to the spheroidization of α laths. The degree of spheroidization increases with the number of IMDF pass. Judging from the microstructural evolution (), a correlation between recrystallization and spheroidization of α laths can be established. In a previous study, Ye et al. [] observed that a high-energy electropulsing treatment promoted the recrystallization and phase transformation, leading to morphological change. In order to decipher the spheroidization mechanism, detailed TEM investigations were performed in this study. reveals the dislocation entanglement at the boundaries of some recrystallized grains. Small amounts of subgrains and dislocation polygonization are also visible.The most common slip system in Ti is {101‾0} <12‾10> prismatic slip. However, the number of the {101‾0} <12‾10> prismatic slip systems is insufficient to accommodate an arbitrary plastic deformation. Therefore twining is commonly observed in Ti and other close-packed hexagonal metals []. However, during IMDF, the average Schmid factor in the forged samples is above 0.4 in both prismatic slip and pyramidal slip modes (), indicating that non-basal slip plays a major role in achieving plastic strain in α grains deform. illustrates schematically the spheroidization process of α laths during IMDF. First, the large amount of plastic deformation results in a significant increase in dislocation density in α laths. The subsequent dynamic recovery reconfigures the dislocations into small-angle boundaries to form subgrains. Afterward, α laths are subdivided into fine substructures under the repetitive action of grain boundary diffusion and grain boundary sliding. Ultimate separation of these sub-microstructures gives rise to the disintegration of α laths. Zherebtsov et al. [] also found that grooves with various depths have been observed in Ti-6Al-4V during warm deformation. The existence of thermal etching ditches results in the concentration gradient of alloying elements near the α lath interface, which drives the interface to migrate. After the disintegration of α laths, under a joint effect of grain boundary concentration gradient and grain boundary sliding, the grains are gradually spheroidized to reduce the interfacial energy and homogenized.The increased strength is believed to arise from grain refinement, enhanced dislocation density and substructure strengthening. According to the classic Hall-Petch equation, the strength increment is expressed as:where ΔσH−P is the yield strength increment as compared to the as-cast Ti alloy,Ky is the strengthening coefficient with a value of 0.4MPa⋅m1/2 for Ti [], dy and d0 are the average grain sizes of the forged and as-cast samples. The calculated yield strength increment is 29.36 MPa, 46.48 MPa, and 71.60 MPa respectively for the IMDF samples after 1, 2 and 4 passes. The results are shown in In addition to grain size reduction resulting from severe plastic deformation, the morphological alteration of α laths plays a critical role in enhancing mechanical properties. During the entire IMDF process, the α phase changes from laths to spheroids. It is believed that the formation of spheroidal α brings about the improvement of both strength and ductility because the spheroidal grains cause much less stress concentration and therefore less likelihood of premature cracking. Our results are different from a previous study by Srinivasu et al. [] but consistent with another study reported by Li et al. [Previous studies have shown that increased dislocation density is also beneficial to the improvement of strength [, dislocation entanglement and subgrains near the recrystallized α increase the resistance of dislocation slip, thus increasing the strength of the forged Ti samples. Microstrain (ε) can be derived by the Williamson-Hall method, and expressed as [Where β is the full width at half maximum (FWHM) of the peak, θ is the angle corresponding to the diffraction peak ((b)), K is a constant, λ is the wavelength of X-rays (0.154184 nm in this study), and D is the crystal size (2.13 μm and 1.57 μm). The value of ε can be calculated from the slope of the linear fit of β cosθvs. 4sinθ plot, using three diffraction peaks (101‾0), (101‾1‾)and (101‾2).The microstrain in metal and the stored dislocation density are related to:where b is Burgers vector, and base on Eq. , the increase in strength caused by dislocation hardening can be quantitatively expressed as follows:where M is average Taylor factor, a is a constant, and G is the shear modulus. The calculation results are listed in , showing that the contribution from dislocation hardening is 58.32 MPa and 72.44 MPa in sample 1-IMDF and 4-IMDF respectively. It is clear that dislocation hardening (58.32 MPa) plays an important role in the improvement of yield strength.In addition to grain boundary strengthening and dislocation hardening as discussed previously, subgrain structure strengthening is also a notable contributor to the increased strength. The existence of substructures as shown in can hinder the movement of dislocations, thus increasing plastic deformation resistance.The elongation in the Ti samples increases gradually with the IMDF pass, which is similar to the previous studies. For example, Shi et al. observed high ductility in a fine-grained Mg-Zn magnesium alloy and attributed the enhanced ductility to the reduced grain size [] observed elongation of 47% in a fine-grained AZ31 magnesium alloy and suggested that the activated non-basal slip systems and dynamic recovery are responsible for the large tensile ductility. In addition, the Ti samples after IMDF demonstrate spheroid α grains that might be beneficial for uniform deformation during the tension test.The main conclusions arising from this study are summarized as follows:The as-cast Widmannstätten microstructure has gradually transformed into equiaxed α after isothermal multi-directional forging (IMDF). Spheroidal α grains and ultrafine grain size (~1.57 μm) were observed in the Ti sample after 4-pass IMDF.The spheroidization of α laths is related to the dynamic recrystallization during IMDF. Microstructural homogeneity and the fraction of the recrystallized grains increase significantly with increasing forging pass. The spheroidization process of α laths mainly involves the breakdown of α laths and the migration of subgrains.Both strength and elongation are improved by IMDF. Grain refinement, dislocation hardening, and substructure strengthening contribute to the increased strength. Grain refinement is a major contributor to the enhanced ductility observed in the Ti samples after IMDF.The raw and processed data are not available at the time of submission because they are part of the ongoing research project.Effect of surface treatments on the fatigue life of titanium for biomedical applicationsMany surface treatments that are used in cementless and endosseous implants modify the topography and the roughness to increase the implant-bone contact area and thus favor bio-mechanical anchorage, shortening the period of osseointegration. Nevertheless, the effects that the surface treatments can have on the fatigue life of the material are not generally considered. In this sense, the superficial condition of the component is one of the features that affect the fatigue strength, specially the fatigue crack nucleation.The fatigue behaviour of annealed commercially pure titanium grade 4 was studied. The surface treatments used were acid etching, shot blasting and a dual treatment of blasting + acid etching. An as-machined surface condition was used as a reference. Topography, roughness, surface defects, microstructural changes and residual stresses were characterized in each case. Rotating-bending fatigue tests of each surface condition were conducted at room temperature with a frequency of 33 Hz. S–N curves and Basquin equations were obtained based on the results of these tests. Tested samples were also characterized to evaluate fatigue damage.The acid etching decreases the fatigue endurance, while the blasting and blasting + acid etching treatments showed a similar behaviour with respect to the reference condition. For acid etching, the modifications introduced (stress raisers) contributed to accelerate the nucleation of cracks. On the other hand, the treatments with a blasting stage besides generating stress raisers, introduced compressive residual stresses and superficial plastic deformation that tend to improve the fatigue endurance of the material.Within the great family of biomaterials, metallic biomaterials are extensively utilized due to their wide range of applications in musculoskeletal implants, such as artificial hip and knee protheses; screws, plates, nails and intramedullar fixation devices; and dental implants (). Titanium and its alloys are recognized within the biomaterials due to both their excellent biocompatibility and high chemical inertness of the oxide that covers their surfaces, as well as their mechanical and their osseointegration properties that promote their regular use in biomedical applications (In the case of titanium implants, surface roughness is one of the most important surface characteristic in reducing the period of osseointegration, stimulating greater bone regeneration and improving mechanical stability by interlocking the surrounding bone tissue with the implant (). Indeed, the modifications introduced by surface treatments developed for cementless and endosseous implants are based on the empirical evidence that there is a surface roughness range where the osseointegration is optimized (Within the great variety of surface treatments used in biomaterials to improve osseointegration and to reduce the healing time, nowadays, blasting, acid etching and a combination of both (blasting + acid etching) are widely used (The implants usually bear cyclic loads during their service life, and therefore, the fatigue endurance of the materials will play a very important role when trying to estimate the long-term performance of the device (). Furthermore, the surface condition of an implant is one of the main features that can affect the fatigue properties, mainly the crack nucleation stage. The surface factors, which affect the fatigue life of a implant can be divided roughly into three categories: (i) surface roughness or stress raisers at the surface, (ii) changes in the fatigue strength of the surface metal, (iii) changes in the residual stress condition of the surface (). Generally, the presence of notches in a loaded specimen accelerates the initial stage of crack growth (stage I), due to the stress raiser effect and the triaxiality produced at the root of the notch that lead to a high local stress and a decrease in the material yielding capacity. In contrast, the introduction of superficial compressive residual stresses (by means of blasting, thermomechanical treatments, etc.) can severely increase the fatigue strength. Therefore, although the surface treatments applied to bone engaging implants introduce important improvements in tissue responses, the fatigue life of the treated implants can be significantly affected, due to the residual stresses introduced during the treatment, the surface roughness, the generation of defects, the superficial hardening by plastic deformation, etc. (The aim of the present work is to study the effect of the surface treatments: blasting, acid etching and blasting + acid etching, in the fatigue life of commercially pure titanium. Additionally, the influence of the surface modifications introduced for each treatment is analyzed.The experimental procedure was divided into three stages: (i) base material characterization, (ii) surface treatments’ and surface characterization of treated samples, (iii) evaluation of the treatments effects on the fatigue life by rotating-bending fatigue tests and characterization of tested samples.The material characterization was carried out by metallographic analyses, tensile tests and Vickers microhardness measurements.Metallographic samples were prepared to characterize the microstructure, which was etched with Kroll’s reagent (10% HF, 5% HNO3, 85% H2O- Reagent No. 186 ASTM E407) (). The mean grain size was determined according to the ASTM E112 (). A Universal Machine Shimadzu UH-1000 kNA was employed for the tensile tests, where the ultimate tensile strength, yield strength, elongation and reduction in area were obtained. A Microhardness Tester Shimadzu HMV-2000 was used to obtain Vickers microhardness. The obtained results for the microhardness test were an average of five measurements.Four different surface conditions were selected to evaluate their effects on the fatigue life: as-machined condition (M: without any surface treatment), acid etching (A), blasting (B), and dual treatment of blasting and acid etching (BA). The M condition was used as a reference.Topography was characterized with a scanning electron microscope (SEM) Phillips model SEM 505. Besides, to confirm the presence of foreign particles embedded in the surfaces, energy dispersive spectroscopy (EDS) adapted to the SEM was performed.To characterize the superficial roughness, the mean roughness (Ra), total roughness (Rt) and the mean spacing (Sm) were determined using a Taylor Hobson model Surtronic 3 + profilometer. The values reported for each condition were the average of five measurements carried out on a fatigue sample. These measurements were done on five different generatrices of the sample.Longitudinal sections of the fatigue samples were prepared for metallographic observation to investigate the surface and subsurface microstructure. Light microscopy (LM) and SEM were applied to characterize the superficial defects introduced and the changes produced on the material’s microstructure.The presence of residual stresses was qualitatively analyzed with a RIGAKU diffractometer using radiation Cu-Kα (λ=1.5418Å) radiation by comparison between different treated samples. The X-ray pattern was obtained for the family of (2 1 3) planes, which diffracts at 2θ=139.5°. A rough estimation of residual stress levels was carried out by means of expressions reported elsewhere (The rotating-bending fatigue tests (R=−1) were conducted in a M.O.P. Type CT 8/30 machine at room temperature in air, with a frequency of 33.33 Hz (2000 rpm). The samples were tested with constant stress amplitude, at different load levels. The maximum stress applied was on the order of 2/3 of the ultimate tensile stress of the material. The number of cycles to failure was recorded at complete fracture of the specimens. A criterion of infinite life of 107 cycles was also adopted. The test configuration corresponds to a cantilever beam, loaded in an extreme. The geometry and dimensions of the samples can be observed in . The number of samples was n=5 for the as-machined condition and at least n=10 for the A, B, and BA surface treatments. σa–Nf curves were plotted based on the results of these tests. Tested samples were characterized by SEM and LM observations of longitudinal sections to evaluate the superficial damage. shows LM images of the microstructure of a cross section of the original material. The metallographic analysis revealed the presence of α phase equiaxial grains in both the longitudinal and cross section. The mean grain size measured was No. 7 according to the ASTM E112 using the comparative method A (Sheet II) (). The values obtained from the tensile and microhardness tests are gathered in . These data meet the requirements of the ASTM F67 standard for commercially pure titanium grade 4 (The analysis of the surfaces by SEM indicated that the topographies obtained were similar to those reported in the literature ( shows SEM images of the different surfaces studied. (a), corresponding to the M condition, reveals equidistant parallel marks characteristics of the machining process. Treatment A introduced modifications in the sample topography, as shown in (b). Microholes characteristic of this treatment are clearly observed (). In some cases, intergranular corrosion could be detected. This feature has been reported as a topographical characteristic of acid etched surfaces in osseointegration studies (). The B-samples presented an irregular rough surface with evidence of plastic deformation and material tearing ((c)), and embedded particles were occasionally found. These irregularities presented a random distribution, which was also reported by other authors (). Regarding the topography produced by BA treatment, (d) evidences a rough surface with a two-level roughness in agreement with the literature (). At low magnifications, the SEM images revealed irregularities which were similar to the ones observed in B-samples, while at higher magnification, the microholes characteristic of treatment A could be observed. The distribution of the microholes was homogeneous in the whole surface and zones with severe attack but corroded grain boundaries as in the A-samples were not differentiated.The results of the surface roughness measurements are reported in for each condition. The values of Ra, Rt and Sm obtained are expressed with their standard deviation (D). All the treatments increased the roughness parameters with respect to the M condition. For the Ra, this increase was about 3 μm. The values obtained in the present work are similar to those reported in the literature for these types of treatments and they are within the roughness range that improves osseointegration (). The A treatment presented the lowest Ra value, while the B and BA treatments produced similar Ra values. The results of the Rt measurements show a similar tendency to that obtained for the Ra values. In contrast, the treatment that showed greater Sm was A, while the BA treatment caused the smallest Sm value.The material microstructure near the surface for each studied condition is shown in . No severe superficial defects were observed in the M-sample ((a)). Treatment A did not modify substantially the macroscopic profile of the surface with respect to the reference condition as can be appreciated in (b). However, at higher magnifications the profile associated with the microholes and the intergranular corrosion previously mentioned, was observed. Here, V-shaped notches could be distinguished at the grain boundaries.(c) shows the severely plastically deformed surface layer produced in the B-samples. The deformed layer was relatively uniform along the entire treated surface with a thickness ranging from 10 to 20 μm. Twinning was the predominant deformation mode in the region below the severely deformed surface layer, as expected for this type of material (). In addition, notch-shaped superficial defects were distinguished. They were associated with the sharp edges of the alumina particles. The dimensions of these defects were greater than the ones observed on the A-samples. A detail of a particle embedded on the surface and its EDS pattern are shown in (b) reveals a significant Al content in the particle, which indicates that it is one of the alumina particles employed in treatment B. The presence of gold in the spectrum is associated with the sputter coating used for the sample preparation.The surface profile generated by the BA treatment observed at low magnification was similar to the profile of the B-surface. A severely deformed surface layer and notch-shaped defects were also observed over the whole treated surface. Nevertheless, at higher magnifications microholes produced by treatment A could be distinguished as well ((d)). Furthermore, the distribution of these microholes was homogeneous in the whole surface, with neither zones with differentiated etching nor significant intergranular corrosion being detected. shows the Intensity vs. 2θ graph obtained around the angle 2θ=139.5° for every analyzed condition. The estimated residual stresses were around zero for the M and A condition. Nevertheless, the M condition presented slightly tensile stresses as could be expected for this type of process (). The peaks corresponding to treatments involving the blasting stage (B and BA treatments) appeared shifted towards lower angles and were also wider than for the other conditions. These results were associated with the existence of compressive residual stresses () and were estimated in the range of 280–380 MPa. This result is in agreement with those expected for blasted titanium (). Furthermore, a decrease of the intensity was observed for these peaks, which implies the occurrence of a certain texture in the treated surfaces ( shows the measured σa–Nf curves for every surface condition. Experimental data were fitted with the Basquin equation, which is used for modelling this type of tests. The values obtained for the M condition are consistent with data previously reported (). For the A condition the fatigue strength was approximately 150 MPa smaller than for the M-samples in the whole analyzed range. In terms of fatigue life, for a given stress amplitude, the decrease of the number of cycles to failure was around 2 orders of magnitude. On the other hand, the B-, BA- and M-samples showed similar results. Nevertheless, the fatigue life obtained for the BA condition tended to be slightly over that of the B condition. All the values obtained are within the usual scatter for this type of tests (). The Basquin equation’s constants and the correlation factors R2 obtained from every fitting are: M:σa=811.9∗Nf−0.058R2=0.8290A:σa=1016.3∗Nf−0.121R2=0.7945B:σa=1060.8∗Nf−0.083R2=0.8435BA:σa=878.2∗Nf−0.063R2=0.7864 These expressions provide useful information for design, because they allow modelling of the material fatigue behavior for each surface treatment. shows images of longitudinal sections of the tested samples. As can be seen, the superficial defects acted as stress raisers and were preferential sites for fatigue crack nucleation. The sample with treatment A showed a larger amount of fatigue cracks, which were longer than those observed for the other surface treatments. In the case of B, BA and M conditions, few cracks were detected, even in samples tested at high stress amplitudes. In the M condition, the cracks nucleated from a smooth surface without severe superficial defects. The nucleation mechanisms involved were related to strain concentration and cyclic sliding (). Moreover, deformation twins and secondary cracks were observed ((a)). Nucleation of fatigue cracks was observed at the V-shaped superficial defects of the A-samples, which acted as stress raisers ((c), the notches originated by the alumina particles projection, acted as stress raisers and were preferential sites for the fatigue crack nucleation in the B-samples. In BA-specimens the fatigue crack nucleation also took place at notches generated during treatment B ((d)). Nevertheless, fatigue cracks were not nucleated at the surface defects caused by treatment A after treatment B. Therefore, it is concluded that the microholes generated by treatment A were not preferential sites for fatigue crack nucleation in a BA-surface.It is known that fatigue life, related to fatigue crack nucleation, could be affected by several factors like roughness, surface defects–acting as stress raisers–, surface hardening and residual stresses, among others ( summarizes the effects produced by each treatment with the aim of carrying out a qualitative analysis of the relative importance regarding fatigue life of the different surface modifications.The defects produced by treatment A resulted from a generalized surface corrosion (microholes + intergranular corrosion). Intergranular corrosion defects were more severe stress raisers than microholes, promoting crack nucleation due to their geometry and location.The surface defects generated in samples with a blasting stage (B- and BA-) were randomly distributed on the studied surface samples. The obtained results showed that the geometry of these defects is closely related to the alumina particle geometry. The notches were associated to the sharp edges of the particles, which was confirmed by the observation of alumina particles embedded in the surface. It is interesting to establish the differences in the effect of treatment A on the material surface, depending on the presence or not of the prior treatment B. As mentioned previously, treatment A produces microholes and intergranular attack. For the case of treatment A after B no evidence of intergranular attack was observed. This would be explained due to the plastic deformation introduced during the B treatment that increases the surface energy, diminishing considerably the greater grain boundary activity. Thus, treatment A after B, finds a homogeneous surface without a definite grain boundary feasible to be attacked, and produces a superficial modification with homogeneously distributed microholes.In comparison with the M condition, the surface treatments significantly increased the surface roughness of the samples along with the generation of superficial defects. Although the generation of surface defects led to a roughness increase, the observations of the surface profiles showed that the defects had geometric features and distributions that the contact profilometry did not differentiate. Therefore, although the roughness measurement is an important technique to characterize surfaces for biomedical applications, in this case, the roughness values obtained by a contact profilometer are not the most suitable features to explain the effects of the different surface treatments in fatigue life, because they do not differentiate between the characteristics of the defects generated by them. In this work, the roughness values measured on the treated surfaces had no major differences, but in term of stress concentration, the stress raisers generated by treatment A were more severe than the ones generated by the B or BA treatments. Alternative methods such as light interferometry should be used to avoid this problem (The A treatment did not generate either superficial plastic deformation or residual stresses. The treatments involving blasting can introduce compressive residual stresses and strain hardening at the surface, thus the material fatigue endurance can be sensitively affected (), the B and BA treatments introduced compressive residual stresses. In addition, the appearance of a severely deformed surface layer with a twinning zone in the subsurface, evidence a strain hardening by cold working (The A-samples presented a worse fatigue performance than the other analyzed conditions. As mentioned previously, this treatment introduced neither superficial plastic deformation nor induced considerable residual stresses with respect to the reference condition. Nevertheless, the treatment generated defects that acted as effective stress raisers for fatigue crack nucleation. In this sense, the decrease in fatigue life of the A-samples would be linked to the decrease of the number of cycles that are necessary for the nucleation of fatigue cracks from the preexisting defects. This is consistent with the larger amount of propagating cracks of greater length observed in the A-samples ((b)). Treatments introducing compressive residual stresses had a better fatigue performance than the A treatment. This result is in agreement with the bibliography since the compressive residual stresses can reduce and even eliminate the effects of the stress raisers (). Furthermore, the severe plastic deformation gave rise to strain hardening in the surface layer that improve the fatigue behavior. Therefore, the B and BA conditions are more favorable.A metallurgic-mechanical analysis has been applied to explain the effect of surface treatments on the fatigue life of c.p. titanium. Surface treatments use to improve osseointegration properties of metallic implants were characterized. The different surface modifications produced by the blasting, acid etching and blasting + etching treatments have been characterized according to the location and geometry of surface defects, surface hardening, and compressive residual stresses. A strong dependence of the fatigue crack nucleation mechanism on the surface conditions was observed. Acid etching treatment generated stress raisers, but neither introduced compressive residual stresses nor hardened the surface, and was the treatment that showed a lower fatigue endurance of titanium. On the other hand, treatments with a blasting stage had a better fatigue behavior that was associated to the presence of a severely plastic deformed surface layer, the strain-hardening related to it, and the compressive residual stresses. This fact counteracts the negative effect in fatigue life of the stress raisers introduced by the treatments.Much better technical figures and weather resistance then regular sleepers from woodMore than 1300km track are running on FFU since 1985Sleeper height experiences from 10 to 45cmFFU synthetic sleeper – Projects in EuropeIn the 1970s JR Japanese Railways after many years of maintenance observation realized that around 70% of installed sleepers from wood have a very short life time, this because the existing weather influences where leading to molding and rotting of wood. JR decided to develop alternative material so that life time of sleepers can be increased and track behavior advantages of wooden sleepers can be retained.The letters “FFU” stand for “fiber-reinforced foamed urethane”, the material used in Japan to develop a synthetic sleeper. Back in 1978, a company called Sekisui was awarded several prizes in Japan for this technological development, which initially went under the name of “Eslon Neo Lumber FFU”.FFU synthetic sleeper is from a material that has the same material properties as natural timber and can be handled and processed as easily as it can. The synthetic material has virtually the same specific mass as the natural one, yet a very considerably longer service life than the latter, and its weathering proper ties are also superior. In 1980, the Railway Technical Research Institute (RTRI), working in cooperation with the Japanese railways, laid sleepers made of this material on two experimental sections of track in Japan. Following on from a period of five years of practical experimentation, in which all the specified requirements were fulfilled, FFU has since then been used by the Japanese railways as a standard product on steel structures, under points and crossings and in tunnels in combination with both ballasted and ballast less track. In 1996, the RTRI removed the first synthetic sleepers from the experimental track sections and subjected them to a new series of tests. Extrapolating the results recorded at that time, FFU would be expected to have an in-situ service life of more than fifty years.Since 2004, railway sleepers made of FFU have been in use in Europe on railway bridges with open load-bearing structures made of steel as well as under points and crossings. In September 2008, Munich’s University of Technology wrote the final report on a research project into such sleepers, drawing positive conclusions. 2011 DB AG – German Railways installed first time FFU on a 60 m long bridge in Vilsbiburg. 2012 DB AG used FFU for two 60.000 t/day switches in Wurzburg In 2011, 30 years after the first field test, RTRI again did laboratory test with sleepers removed from first field test. This 30 years old and under regular train operation used sleepers showed that the technical figures have been decreased a little. The conclusion of this test was that RTRI wrote a letter to JR – Japanese Railway operator – that they can still use these FFU sleepers for the next 20 years.Much better technical figures and weather resistance then regular sleepers from woodMore than 1300 km track are running on FFU since 1985Sleeper height experiences from 10 to 45 cmThe technique used for the manufacture of FFU synthetic wood is pultrusion. Oriented glass-fiber strands are drawn through a pulling device, coated in polyurethane and cured at a high temperature, to result in a particularly high-grade, pore-free material. If so ordered, it is possible to manufacture the synthetic wood ex works as semi-finished products in the shape of railway sleepers and bridge timbers with millimeter precision. Some of the different processes that the manufacturing works is capable of applying to its semi-finished products with such tight specifications are listed in Each of the synthetic sleepers produced in the works to meet a precise special requirement is given a unique marking, to make sure that it is laid at the intended location on the engineering site.Following forms of preparations are already available in the manufacturing works:Milling out the space for the rivet heads.If all the sections of railway track on which FFU synthetic sleepers have been laid since 1985 are added together, then the total number of kilometers is more than 1.300.Some of this has been on light-rail systems and some on really heavy rail systems with axle loads in excess of 30 tones. The predominant use of FFU synthetic-wood sleepers in Japan has been on the Shinkansen high-speed network, along with applications on regional, cross-country and metro lines.The first project using FFU synthetic wood in Europe was implemented in 2004. It was part of the general overhaul of the Zollamt Bridge in Vienna, an open engineering feature with its load-bearing structure made of steel, which had been designed by Otto Wagner and built originally between 1896 and 1898. The overhaul of the bridge included the replacement of its corrosion protection and the entire track superstructure.The bridge is used by the U4 metro to cross the river Wien. The bridge was closed to all traffic for a period of ten days and during that time the superstructure, which had suffered very considerable damage due to the elements, was replaced, and new anti-corrosion measures were applied to the load-bearing structure underneath it. After that, the bridge timbers made of FFU synthetic wood were trimmed and laid in place. The rails were correctly positioned and welded together. Finally, the decking elements were laid and, in order to create an interesting experimental situation, it was decided to use FFU synthetic wood for just half of them. The metro operator, Wiener Linien, has announced new maintenance intervals for the future (If this maintenance schedule works out in practice, at least another fifty years are going to elapse before passengers are again forced to change to a substitute mode of transport during a metro closure. Since them Wiener Linien already installed all of their open steel bridges. They also will install it on 78 switches in the area of their rolling stock garage, starting 2013. Wiener Linien also will change all polyurethane sleepers from VAE on their existing tracks within the next 15 years with FFU.It was in 2005 that the Austrian Federal Railways (ÖBB) first used FFU synthetic sleeper on the Hackingerstrasse railway bridge, which crosses over a road in Vienna. This bridge is located in the approach to a home signal on a curve with a high cant, and large numbers of freight trains pass over it every day. The ÖBB opted to use FFU synthetic sleeper, given that the bridge had had a very costly maintenance record. The sleeper screws had needed retightening several times a month. It had also been necessary to replace the former natural bridge timbers repeatedly at intervals of only a few months. The condition of the FFU synthetic sleepers on the bridge in 2011 has remained as good as new since they were laid in 2005. The sleeper screws have remained reliably firm at all times. The positive experience with FFU led to the decision to use it for the sleepers on the Karwendel bridge over the river Inn in Innsbruck, in Ostbahn bridge over the river Danube in Vienna and one more than 7 other bridge projects of their network. In 2010 ÖBB installed first double slab with synthetic sleepers in the area of the new main train station in Vienna.Turning to Germany next, there Voestalpine BWG laid the first points with a length of approximately 74 m on FFU synthetic sleeper in June 2008. The lengths of the point sleepers range from 2.20 to 4.50 m. BWG used a type of milling cutter to make the necessary holes. It is reported that the geometric stability and evenness of the FFU material was found to be very favorable for preparing the sleepers economically in this way in the factory. This set of points has now been laid in Chempark Leverkusen.ProRail from Netherland installed three bridges with FFU in 2012.BLS, SOB, RHB railway companies from Switzerland will install first projects in 2013 with FFU and already consider using FFU on projects coming in 2014 and 2017.NetworkRail considers installing FFU also as longitudinal sleeper in 2013. London metro is ready to do the first trial with FFU in the near future.The initial discussions with the objective of creating the preconditions for FFU synthetic wood sleepers to be authorized by the EBA (German Federal Railway Authority) for use on the track belonging to infrastructure managers in Germany (i.e., “DB Netze”) took place in January 2008.The tests to be carried out were defined jointly with the transport infrastructure engineering department at Munich University of Technology and the test laboratory linked to it.Sekisui provided twenty FFU synthetic sleepers for the tests with the dimensions of classical natural wooden ones (26 × 16 × 260 cm/width × height × length). It attached Vossloh KS rail fasteners to six of these. The sleeper screws were fastened with a torque of 220 Nm.The following sections present the results of each of the individual tests and examinations.The fatigue test was carried out using the “scissors-lever vibrator” at Munich University of Technology.The length of rail used for this test had had 15 mm of material removed from the top of it by milling in accordance with DIN EN 13481-3. The dynamic stiffness of the rail pad corresponded to a spring coefficient of greater than 200 kN/mm. The top load in the test was 140 kN, the bottom load 10 kN, and the load-application frequency was 3 Hz. The test load thus matched that in the experimental fatigue load applied to a sleeper laid in a track subjected to wheel-set loads of 225 kN (see shows the deflection of the rail relative to the sleeper after three million load cycles at ambient temperature. These are values which experience has shown to be within the admissible range.Another test phase involved an additional 1.28 million load cycles at the higher temperature of 48 °C. The values measured were of the same order of magnitude as those at ambient temperature.It can be concluded from this that the system’s mechanical behavior is not generally affected by higher temperatures.For this particular test, recesses are milled into two opposite sides of the shafts of two sleeper screws and strain gauges are glued into these. The screws are calibrated in a centered tensile test, in which it is possible to assign the elongations registered to the corresponding tensile forces. The tensile force in the sleeper screws diminishes as a function of tightening torque and time.For the extraction test, a central tensile force is applied to the sleeper screws, and the values are recorded using an inserted pressure cell. The tests are carried out on all eight screws in a single synthetic sleeper. The load is increased continuously until the screw is pulled out.The extraction force needed for this was found to be 61 kN, which is very considerably higher than that needed for natural wooden sleepers, for which Munich University of Technology had measured a value of only 35 kN in the same test in 1997.The purpose of an impact test is to establish how sleepers would behave if subjected to impact loads as the result of the derailment of railway vehicles.This is done in accordance with the technical supply conditions laid down by Deutsche Bahn for “reinforced concrete sleepers – basic principles for dimensioning, design and approvals”. This document states that each sleeper tested must undergo two impact tests (I and II).For the first of these tests, the point of impact is 25 cm away from the center line of one of the rails and parallel to the axis of the track. For the second test, the point of impact is 15 cm away from the end of the sleeper, in other words on the outside of the rail.In the case of the second impact, the fibers were loosened as far as the sleeper’s end face, and a wedge-shaped end piece was separated from the sleeper. That is not critical for the sleeper’s load bearing capacity in this area, near its end. It scarcely needs mentioning that the screws holding the ribbed base plate into place are not negatively affected by such loads.The FFU synthetic-wood sleepers did not show any signs of warping or twisting as a result of the impact loads. This also means that the track gauge remained constant.The electrical resistance of the synthetic sleepers was measured between two 50 cm-long sections of UIC-60 rail, fastened to them. A layer of insulation was inserted between the sleeper and the ground and rain was simulated by sprinkling water on it from four nozzles for two minutes. Electricity was applied to the two lengths of rail at 30 V/50 Hz. The tests were performed on subsequent days, giving the synthetic-wood body sufficient time to dry off between the individual measurements.The standard underlying the test, DIN EN 13146-5, requires a minimum resistance of R33 ⩾ 5 kΩ as the mean of three measurements. The tests produced a value of R33 = 71.9 kΩ for the electrical resistance of FFU, so it was shown to satisfy the permissible minimum value with a very big safety margin.In order to examine the behavior of an FFU synthetic sleeper under conditions of bending stress, a static test was applied to the middle of the sleeper basically along the lines of DIN EN 13230-2, with a distance between supports corresponding to the mean distance between the centerlines of the rails, namely 1500 mm. The width of the load plate was 100 mm. The test force applied initially was 20 kN and this was then increased in increments of 5 kN, during which the amount of deflection in the synthetic-wood sleeper was recorded on four dial gauges.Up as far as a load of 240 kN (which corresponds to a bending tensile stress of 74 N/mm2 on the underside of the sleeper) no crack was detected in the bent zone.On the basis of the measured deflection, the modulus of elasticity of the synthetic-wood sleeper was calculated to be around 7000 N/mm2.An analogous test was performed on a wooden sleeper made of beech with the same dimensions. For the same test setup, that sleeper failed under a load of 80 kN in the zone affected by the bending tensile stress.How the synthetic-wood sleeper behaves when subjected to repeated loads was investigated in the form of a fatigue test (using the same width between supports of 1500 mm as for the static test).The load was applied through an articulated support with a width of 100 mm and was increased from its original value up to 100 kN. After that, the fatigue test was performed with the following load parameters: top load = 86 kN, bottom load = 21.5 kN and frequency = 2 Hz.The maximum bending moment produced was 30 kNm, which corresponds to the test value laid down for sleepers in DBS 918 143 (DBS = Deutsche Bahn Standard) – in other words, these were extremely critical test conditions.No damage was detected on the synthetic sleeper in the course of the whole fatigue test of 2.5 million load cycles. The elastic deflection after this time was only 0.4 mm more than it had been at the start of the test.The deformation followed a more or less constant course throughout the whole duration of the test, and no signs of fatigue occurred. Nor was there any perceptible difference in the measured elongation after 2.5 million load cycles.Finally, the synthetic-wood sleeper was subjected to a load of 175 kN, corresponding to a bending tensile stress of 56 N/mm2, but no cracks occurred.The compressive fatigue test under the rail pads follows the basic principles of DIN EN 13230-2 (which actually deals with reinforced concrete sleepers), with a spacing of 600 mm between pads. The load is applied through the fastenings for the ribbed baseplates with the complete rail fastening in place. A force of 150 kN acting through the rail pad was chosen for the fatigue test. This corresponds to unfavorable conditions in real life, such as a poorly positioned track, uneven distribution of loads through the rails, stiff rail supports and a high dynamic allowance for a static wheel-set force of 250 kN.No damage to the synthetic sleepers was observed during the fatigue test with two million load cycles. The elastic deflection at the end of this period was only 0.2 mm greater than beforehand.No plastic deformation was detected up to a load of 150 kN, while the maximum plastic deformation of 0.8 mm was measured for a load of 300 kN.These tests were carried out at ambient temperature and at −10 °C, with a spacing of 1.0 m between supports and a test force going up to a maximum of 200 kN.In the case of the low-temperature tests, the synthetic sleepers were kept at −20 °C for two days previously in a climate controlled storeroom.The results of these tests confirmed that the deformation of FFU synthetic-wood sleepers subjected to bending-moment stress is only marginally temperature-dependent. No embrittlement occurred at low temperatures. There was no significant change in deformation between the first and third load application.From this, it may be concluded that the fibers do not even fracture at low temperatures when a bending stress with this intensity is applied (see On behalf of SEKISU Chemical GmbH, investigations were to be carried out on SEKISUI manufactured FFU synthetic wood sleepers with dimensions of 12 × 26 × 260 cm for the use in track construction.Following consultation with the EBA (German Railway Authority) and DB (German Railways) the following investigations were to be carried out on the synthetic wood sleepers:Behavior of the sleeper under vertical and horizontal loads in the vibration fatigue test. Support in ballast bed in line with DIN EN 13481-3 (requirements for fastening systems of wooden sleepers).Static and dynamic testing of synthetic wood sleepers based on DIN EN 13230-2.Extraction tests on sleeper screws according to DIN EN 13481-2.The loading parameters were: a |
= 33°, Po,v |
= 140 kN, X |
= 15 mm, f |
= 3 Hz, 3.0 million load cycles, RT (23 °C). The displacement of the rails with respect to the sleeper after 3 million load cycles can be seen in . Standards DIN EN 13481-3 and 13146-4 define no requirements in this regard. Measurement of the deformation was done with dial gauges according to Based on the experience to hand, the values shown above are within the permissible range. They indicate comparable or lesser deformation than was observed in Research Report No. 2466.In addition, both the horizontal and vertical movement of the ribbed plate (outer side) was registered. After 3.0 million load cycles, a maximum resilient sinking of 0.23 mm and a maximum permanent sinking of 0.18 mm was registered at the ribbed plate. The horizontal movement (resilient and permanent) of the ribbed plates was around 0.6 mm on average.Subsequent visual examination of the underside of the sleeper after removal from the ballast bed revealed only slight pressure marks.In order to investigate sleeper behavior when subjected to bending load, static tests were conducted on the center of the sleeper in line with DIN EN 13230-2. A sleeper with 120 mm height was used. The support spacing was 1.5 m and load plate width was 100 mm. The initial test load was set to 10 kN. Subsequently the load was increased in increments of 10 kN, with sleeper bending registered on four dial gauges. Based on the measured deflection, Young’s modulus (E) was determined using the following equation:E |
= Young’s modulus (N/mm2), l |
= support spacing 1500 mm, I |
= moment of inertia (mm4), f |
= bending deflection (mm).Young’s modulus for synthetic wood sleeper under bending load is approx. 8800 N/mm2. With a load of 70 kN the deflection of the sleeper is 15 mm.In order to investigate the behaviour of the synthetic wood sleeper under repeated load, a fatigue test of 2 million load cycles in the center of the sleeper was conducted in line with DIN EN 13230-4. The deflection of the sleeper was recorded during the entire testing procedure in the region of maximum torque. The support spacing during testing was 1.5 m, and the load was applied in accordance with DIN EN 13230-4 via a 100 mm wide hinged support.The applied load was initially up to 65 kN. The fatigue test was then conducted under the following boundary conditions:The above load produced a torque of 23 kNm. This torque corresponds to an axle load of 250 kN and train speed V |
> 200 km/h.No damage to the sleeper could be established during the fatigue test of 2 million load cycles. It indicates that the resilient deflection after 2 million load cycles is only 0.25 mm greater than at the start of the test. The deformation remained nearly constant throughout the entire fatigue test, i.e., there were no signs of fatigue.The purpose of the fatigue test on the rail seat (compressive load) is to determine how the sleeper behaves under high compression. The fatigue test was conducted on three sleepers.The fatigue compression test on the rail seat was conducted in line with DIN EN 13230-2 (concrete sleepers). In compliance with the stated standard, a support spacing of 600 mm was selected. In the first fatigue test, the load was applied via a ribbed plate with the dimensions 160 × 370 mm. Since there were no screw holes in the sleeper, the ribbed plate was just set down in the rail seat area and thus not clamped to the sleeper. A load of 150 kN was selected for the fatigue test. This corresponds to an axle load of 250 kN and a train speed V |
< 200 km/h. A static load of 1.2 × 150 kN = 180 kN was applied before the fatigue test. After the fatigue test the static load was increased to 2 × 150 kN = 300 kN.The test setup can be seen in attachment 3. The following boundary conditions were chosen:A sleeper deflection of about 3 mm was recorded at the start of the fatigue test. After 2 million load cycles this increased to about 4 mm, which is roughly twice the figure recorded under the same boundary conditions for the sleeper with 16 cm height according test report 2466.No damage to the sleeper could be established during the fatigue test of 2 million load cycles. The ribbed plate was subsequently removed. Plastic deformations of approximately 0.85 mm were detected on the surface of the sleeper’s upper side under the ribbed plate. Aside from this, no other damage could be found.In consultation with the client, the fatigue test was conducted on the rail seat at two further sleepers using ribbed plate Rph 1 with dimensions 160 × 345 mm. In addition, a 0.5 mm thick synthetic pad was fitted underneath the ribbed plate. The first sleeper was subjected to 5 million load cycles and the second sleeper to 2 million load cycles. The upper test load remained unchanged at Po |
= 150 kN while the lower test load Pu was 50 kN.For a load of 150 kN the deflection registered was 4.8 mm (sleeper No. 2, 5 million load cycles) and 4.2 mm (sleeper No. 3, 2 million load cycles). With the exception of plastic deformation on the rail seats, no damage could be detected on the sleepers.In the extraction tests, a centric tensile force is applied to the sleeper screws and measured by an interposed load cell.The tests were conducted in line with EN 13481-2 attachment A on 12 sleeper screws Ss 8-140 and synthetic wood sleepers with a height of 120 mm. According to the client, the standard diameter of the holes for screws Ss 8-140 is 19 mm. To investigate the effect of a larger diameter on the extraction force, 8 further holes of 20 mm diameter were drilled by the client with wood and steel drills in sleepers delivered to the testing institute.The test was subsequently executed. The load was increased gradually until the screw was extracted. The maximum extraction forces are compiled in For the Ss 8-140 sleeper screw, the table shows mean extraction forces of 57 kN (19 mm standard hole diameter) and 51 kN (20 mm hole diameter). Previous extraction tests on wooden sleeper screws showed extraction forces of approx. 35 kN (see Research Report No. 1687 of 30.06.1997).In the 1970s JR Japanese Railways after many yours of maintenance observation realized that around 70% of installed sleepers from wood have a very short life time, this because the existing weather influences where leading to moldering and rotting of wood. JR decided to develop alternative material so that life time of sleepers can be increased and track behavior advantages of wooden sleepers can be reached.FFU synthetic sleeper for the use in railway tracks was developed in 1978 and since 1985 has been used for more than 1.300 km of track in Japan, the People’s Republic of China, Taiwan, USA and Europe.It has been in use in Europe since 2004 on open load-bearing structures in steel and under railway points and crossings. In September 2008, Munich University of Technology presented the final report on a research activity into the properties of FFU synthetic sleepers, and its findings can certainly be summarized as positive.In terms of mechanical properties and inherent mass, synthetic sleepers are comparable with classical ones in natural timber. Their bending stiffness is higher than that of classical sleepers made of beech, while their bending tensile strength has even been found to be very much higher. Synthetic sleepers are thus capable of undergoing very much greater elastic deformation without the formation of cracks. In the fatigue tests carried out by Munich University of Technology regarding plastic deformation caused by high rail-pad forces, sleeper-screw extraction forces and impact-test behavior, the FFU synthetic sleepers performed brilliantly. Moreover, they have a markedly high electrical resistance between two rails fastened in the normal positions and show no signs of embrittlement caused by low temperatures.The EBA (German Federal Railway Authority) granted its approval for FFU synthetic wood in April 2009. German federal railway DB installed since 2011 bridges and switches with FFU sleepers.In 2011, 30 years after the first field test, RTRI again did laboratory test with sleepers removed from first field test. This 30 years old and under regular train operation used sleepers showed that the technical figures have been decreased a little. The conclusion of this test was that RTRI wrote a letter to JR – Japanese Railway operator – that they can still use these FFU sleepers for the next 20 years.Ceramic-on-polyethylene: The experience of the Ranawat Orthopaedic CenterTraditionally, metal-on-polyethylene has been the gold standard bearing in total hip arthroplasty. Ceramics were introduced as an alternative bearing because of their superior mechanical properties. Our institution has found that ceramic-on-polyethylene has consistently shown lower in vivo wear rates compared to metal-on-polyethylene. The latest generation of ceramic-on-polyethylene, BIOLOX delta-on-highly cross-linked polyethylene, has shown an excellent linear wear rate (0.006 mm/yr), which is much lower than previously found wear rates for cobalt–chrome-on-highly cross-linked polyethylene (0.011 mm/yr). The minimal wear rate of BIOLOX delta-on-highly cross-linked polyethylene provides the potential to increase long-term survivorship and become the new gold standard bearing in THA.Optimal bearing choice in primary total hip arthroplasty (THA) remains a hotly debated topic. Increasing demands of younger patients and advances in fixation technologies have accentuated the importance of bearing choice to provide excellent outcomes. Aseptic loosening is often cited as the leading cause of revision THA Our institution has performed several in vivo wear studies on various generations of both MOP and ceramic-on-polyethylene (COP). In our experience, BIOLOX delta-on-HXPLE has shown excellent results and has become the bearing of choice in our practice. This study outlines our experience with current MOP and COP.Metal-on-polyethylene is widely accepted as the most common bearing surface used in THA. Over the years, several different metals have been used including stainless steel, titanium alloy, and cobalt–chromium (CoCr) alloy. Most metal femoral heads used today are made of a CoCr alloy. A typical CoCr alloy used for a femoral head is composed of 66% cobalt, 28% chromium, 6% molybdenum, and trace percentages of other elements. The microstructure of a CoCr femoral head consists of a cobalt-based matrix with chromium and molybdenum interspersed throughout, which increases the hardness and provides corrosion resistance. A secondary carbide phase also exists, which contributes to the mechanical properties of the material. All of the femoral heads also undergo several hardening mechanisms, such as ion-implanting, hot isostatic pressing, annealing, spark plasma sintering, and homogenation. The excellent mechanical properties of CoCr () are responsible for the durable, excellent survivorship when coupled with polyethylene The major disadvantage of MOP bearings is they are associated with higher polyethylene wear rates Ceramics were introduced to THA because of their superior mechanical properties. Ceramics are well known to be biologically inert, hard, with high wettability. Early ceramics were known to have high in vivo fracture rates BIOLOX delta (CeramTec, Plochingen, Germany), the latest generation of ceramic, has been available since 2003. BIOLOX delta is an alumina matrix composite composed of roughly 74% alumina, 25% yttrium-stabilized tetragonal zirconia particles (Y-TZPs), and other oxides such as strontia and chromia, the latter of which is responsible for giving this generation its unique pink color. The Y-TZPs that are evenly distributed throughout alumina serve to strengthen the material significantly with minimal sacrifice to other mechanical properties. CeramTec also claims two additional strengthening mechanisms to the material that reduce crack propagation. One mechanism is that other oxides in the material come in the form of large platelets that can deflect cracks as they propagate through the material. The other is that evenly distributed Y-TZPs create localized pressure peaks that act similar to an air bag to reduce crack propagation. These mechanisms have shown to significantly increase the fracture toughness, while maintaining the hardness (The primary reason why ceramics have been unable to supplant the use of metals as a femoral head material is because of the risk of ceramic fracture. Ceramic fracture has been well documented throughout the literature. First-generation alumina femoral heads have been reported to have as a high as a 13% rate of fracture Since the 1960s, polyethylene has proven to be a highly successful bearing in THA. John Charnley introduced polyethylene to THA after he recognized the great tribological potential of the material. Ultra-high-molecular-weight polyethylene (UHMWPE) is a tightly packed polymer of ethylene, which has a very high molecular weight, low coefficient of friction, high wear resistance, good chemical resistance, and has good chemical and thermodynamic stability, making it an ideal material for use in vivo. Since 1998, HXLPE has become the standard of care in THA. Cross-linking is the process in which polyethylene is irradiated, creating free radicals that are able to create covalent bonds between two adjacent carbon chains. Many of today's current polyethylenes undergo a cross-linking process with a gamma dose of roughly 5–10 Mrad, which has been shown to well decrease in vivo wear rates Our institution has conducted several in vivo wear studies comparing wear rates of various bearing articulations (). We conducted a long-term study comparing the first generation of alumina with CoCr-on-UHMWPE Many have shown the benefit of cross-linking polyethylene In 2011, our institution reported on our preliminary results using the latest generation of ceramic-on-polyethylene, BIOLOX delta-on-HXLPE Optimal bearing choice remains one of the most hotly debated topics regarding THA. Advances in fixation technologies and the increasing demands of younger patients have further emphasized the importance of optimal bearing choice. The optimal bearing choice for a patient is one that has the lowest wear rate and lowest associated complications. Low wear rates can increase survivorship by reducing histiocytic activity that leads to the leading cause of revision THA: aseptic loosening Several mid- and long-term studies have compared the steady-state wear rates of the early generations of alumina-on-UHMWPE with those of CrCo-on-UHMWPE BIOLOX delta has also been well shown to reduce wear rates compared with early versions of ceramic. BIOLOX delta has only been available for a short time, limiting the mid- and long-term studies available. Our institution performed a short study looking at the wear rate of BIOLOX delta-on-highly cross-linked polyethylene at 1 and 2 year intervals MOP has also been associated with several catastrophic complications. Not only has CoCr-on-polyethylene been associated with high wear rates, it has also been associated with some of those complications seen in MOM articulations In our experience, current COP hips have a lower wear rate than corresponding MOP hips, with fewer complications. The minimal wear rate seen among BIOLOX delta-on-HXLPE (0.006 mm/yr) can provide the potential for COP bearings to last 20, 25, or even 30 years, with excellent survivorship. Longer follow-up is necessary, but in our experience BIOLOX delta-on-HXLPE is the gold standard at our institution.Traditionally, metal-on-polyethylene has been the most widely used bearings worldwide. Advances in both polyethylene and ceramics have provided superior results to the traditional metal-on-polyethylene. Short-term studies have provided excellent results with the latest generations of ceramic-on-highly cross-linked polyethylene. Currently, long-term survivorship of ceramic-on-polyethylene is between 90% Evolution of mechanical properties of steel fiber-reinforced rubberized concrete (FR-RC)In this work, the evolution of strength (compressive, tensile, and flexural) and toughness of steel fiber-reinforced rubberized concrete (FR-RC) with various fiber dosages and rubber contents was studied. The toughness of FR-RC was investigated using both four-point bending unnotched beams and three-point bending of notched beams. The toughness characteristics were quantified using toughness indexes proposed in ASTM K fracture model. The results show that the compressive strength of FR-RC is dependent on both rubber content and fiber dosage, while the flexural and tensile strengths are dominated by the fiber dosage. Although steel fiber can slightly increase the modulus of elasticity of FR-RC, it is mainly controlled by the rubber content. In addition, the first peak strength of FR-RC is influenced by both rubber and steel fiber inclusion, which is in agreement with its strength development. The steel fiber controls the straining hardening and softening behaviors of FR-RC. According to the double-K fracture model, it is found that the rubber content dominates the initial fracture toughness, while the steel fiber dominates the unstable fracture toughness.Concrete is one of the most widely used construction materials in the world due to its low cost, abundant availability of raw materials, and strong compressive strength. The basic ingredients of concrete, i.e., sand and gravel bound together with a hydraulic binder, and water, have been used at least as far back as Egyptian times. The original formula of concrete has been extended to incorporate various additives or admixtures (e.g., fibers, superplasticizers, industrial byproducts) that can result in improvements in strength, ductility, durability, workability, and sustainability of concrete. The development in concrete technology enables the selection of proper materials and design of concrete mix that satisfies the performance requirements at low economic and ecological costs. For instance, it is widely known that traditional concrete has a high rigidity and stiffness (low toughness); the inclusion of rubber into concrete (i.e. rubberized concrete) through partially substituting aggregates can increase its toughness, ductility, energy dissipation capacity, and impact resistance []. These unique properties enable rubberized concrete to become a promising material for some specific applications, including highway pavements, crash barriers, and sound absorbers []. In addition, the use of rubbers recovered from end-of-life tires contributes to the greenness and cost-effectiveness of concrete, as well as solve the environmental problems caused by the accumulation of millions of waste tires worldwide [Many previous studied showed that the strength and modulus of elasticity of rubberized concrete decrease significantly with the increasing proportion of rubbers []. For instance, it was reported a 65% reduction in compressive strength of concrete when the fine aggregate is fully replaced with crumb rubbers []. The modulus of elasticity of rubberized concrete decreases with the increasing replacement level of crumb rubber. A further parametric analysis suggested that the replacement ratio of rubber particles should be less than 20% to avoid significant reduction in strength []. However, the performance of rubber in concrete is also influenced by the stiffness, particle size, gradation, and surface properties of rubber particles [Due to the considerable reduction in strength, rubberized concrete has been proposed recently to be reinforced by steel fibers to improve strength while maintaining its excellent flexibility and toughness [] studied the compression toughness of fiber-reinforced rubberized concrete (FR-RC) with various rubber contents and concluded that increasing the rubber content up to 15% results in improvement in the compression toughness. Similarly, Abaza and Hussein [] showed that the failure mode of rubberized concrete under compression changed from fragile to ductile due to steel fiber reinforcement. The flexural toughness of FR-RC is highly enhanced due to the combined use of crumb rubber and steel fiber in the concrete mix, due to the bridging effect of fibers and high elasticity of rubbers. Nevertheless, a systematic and quantitative analysis of the evolution of mechanical properties of FR-RC with various fiber dosages, rubber contents, and curing ages is still missing. The combinational effect of steel fiber and rubbers on the mechanical properties of concrete composites are far less known. It remains unclear how the rubber and steel fibers separately or jointly affect the flexural and fracture characteristics.To fill the aforementioned knowledge gaps, this study first investigates the evolution of strength and modulus of elasticity of plain concrete, rubberized concrete, steel fiber-reinforced concrete, and steel fiber-reinforced rubberized concrete. This study focuses on mixes with less than 20% replacement ratio of rubber since a higher ratio would result in a significant reduction in mechanical properties and unsuitable for practical use. The toughness characteristics of steel fiber-reinforced rubberized concrete with various fiber dosages and rubber contents were then studied in detail. It is expected to reveal the mixture parameters that control the mechanical properties of FR-RC and contribute to the mix optimization of FR-RC.The ordinary Portland cement (OPC) with a grade of P.O. 42.5 was used (The P.O. 42.5 indicates that the 28-day compressive strength of hardened cement paste is at least 42.5 MPa, according to Chinese standard GB175-2007). The fine aggregate was river sand with a fineness modulus of 2.64, and the coarse aggregate was crushed gravel with a particle size ranging from 5 to 20 mm. The hooked-end steel fibers with an ultimate tensile strength not less than 1070 MPa were used. The cross-sectional shape of the steel fibers is circular with a length/diameter ratio of 80 and length of about 30 mm (see (b)) were from the waste tires that were crushed and ground into particles ranging from 1 to 3 mm.In this work, plain concrete (denoted as PC), concrete with sands being partially replaced by rubbers (rubberized concrete, RC), concrete with steel fiber addition (fiber-reinforced concrete, FC), and concrete with both rubber replacement and steel fiber addition (fiber-reinforced rubberized concrete, FR-RC) were studied. The PC mixture was prepared by mixing OPC, tap water, river sand, crushed gravel, polycarboxylate superplasticizer in a ratio of 457: 164.5: 599: 1303: 2.74 (kg/m3). Since previous studies recommended that the replacement ratio of rubber should be less than 20% for practical use [], the RC concrete has the rubber replacement ratio of 5%, 7.5%, 10%, 12.5%, and 15% (by mass) of the sand, which is equivalent to the amount of rubber in concrete being 14.42, 21.63, 28.84, 36.05, and 43.26 kg/m3, respectively. For FC or FR-RC mixtures, the steel fiber was added at the percentage of 0.5%, 0.75%, and 1.0% by volume with respect to concrete, which is equivalent to the amount of steel fibers being 39.0, 58.5, and 78.0 kg/m3, respectively. In the nomenclature used in this paper, the number after concrete denotation represents the rubber replacement ratio and steel fiber percentages. For instance, FR-RC-10-1.0 represents the fiber-reinforced rubberized concrete with the rubber replacing the 10% sand and with 1.0% steel fiber addition. All specimens were demolded after casting for 24 h and cured in a controlled environment with 20 °C and 90% relative humidity till testing.The compressive, tensile, flexural strengths, and static modulus of elasticity of PC, RC, FC, and FR-RC were measured at various ages. The compressive and tensile strength was measured on cubic specimens with a side length of 150 mm at a loading rate of about 0.4 MPa/s. The flexural strength was conducted on prismatic specimens with a dimension of 100 mm × 100 mm × 400 mm, in accordance to ASTM /C78M-16. The modulus of elasticity was conducted on cylindrical specimens with a diameter of 150 mm and a height of 300 mm, in accordance to ASTM /C469M-14. To consider the heterogeneity nature of the concrete specimens, at least three replicates were measured.Flexural toughness tests were performed on FR-RC at the age of 1, 3, 7, 14, 28 days. The unnotched specimens with a dimension of 100 mm × 100 mm × 400 mm were four-point loaded at a displacement controlled rate of 0.05 mm/min, as shown in (b). The load-deflection at the middle span (i.e., P-δ) curves of specimens during loading was recorded. According to ASTM toughness indexes, I5, I10, and I20, can be calculated based on the load-deflection curve of fiber-reinforced rubberized concrete, following:In which, A1, A2, A3, and A4 represent the area under the load-deflection curve in which the deflection reaches δ, 3δ, 5.5δ, and 10.5δ, respectively. The δ is the deflection corresponding to the first crack point, which is on the load-deflection curve at which the form of the curve first becomes nonlinear. Therefore, residual strength factor, R5,10 and R10,20, can be calculated from the value of 20(I10Fracture toughness tests were performed on FR-RC at the age of 1, 3, 7, 14, and 28 days. The notched beams with a dimension of 100 mm × 100 mm × 400 mm and a notch of 30 mm in length and 0.7 mm in width were prepared. The load – middle span deflection (i.e., P-δ) curve and load-crack mouth opening displacement (i.e., P-CMOD) curve were recorded using a three-point bending test, as shown in (c). The deflection and CMOD were recorded using gauges. To quantitatively analyze the fracture characteristics, double-K fracture model proposed by Xu and Reinhardt was used []. In comparison to other fracture models (such as Bazant's crack band model []), double-K fracture model enables the determination of fracture parameters only by measuring the ascending branch of the P-CMOD curve. According to the double-K fracture model, the initial fracture toughness, KICQ and unstable fracture toughness, KICS, can be calculated using:KICQ=1.5(FQ+mg2×10-2)×10-3⋅S⋅a01/2th2f(α)KICS=1.5(Fmax+mg2×10-2)×10-3⋅S⋅ac1/2th2f(α)f(α)=1.99−α(1−α)(2.15−3.93α+2.7α2)(1+2α)(1−α)3/2,α=achKICQ is initial fracture toughness [MPa⋅m1/2]; KICSis the unstable fracture toughness [MPa⋅m1/2]; Fmax is maximal load [kN]; FQ is the initial cracking load [kN]; m is the mass of the specimens within the two end supports [kg], which can be calculated proportionally to the span; g is the gravitational acceleration constant, i.e., 9.81 m/s2; S is the span length within two end supports [m]; ac is the effective length of the crack [m]; t is the thickness of specimen [m]; h is the height of specimen [m]. show the time-dependent evolution of compressive, tensile, and flexural strength of PC and RC with different rubber contents, FC with different fiber dosages, and FR-RC-10-1.0 at various ages. The strength of other FR-RC mixes at 28 days is listed in . It can be seen that regardless of rubber content, the strength developed rapidly in the first 7 days, reaching about 75% of the 28-day strength. However, the strength of RC decreases with the increasing amount of rubber content, with the largest extent for compressive strength and least extent for flexural strength. This finding is consistent with previous findings and attributed to the formation of large voids and defects at the interfaces of rubber and cement matrix. For FC, adding no more than 1.0% steel fibers into concrete did not considerably affect the compressive strength development, but slightly improved the tensile and flexural strength. The improvement in tensile and flexural strength was observed merely at later ages (>3 days), which indicated that the interfacial bonding of steel fibers and hydrating cement matrix played an important role. On the other hand, adding steel fibers into rubberized concrete noticeably increased its tensile and flexural strength, while its effect on compressive strength depended on the rubber content. For example, it can be seen that the highest strength in FR-RC-10 was FR-RC-10-0.75, rather than FR-RC-10-1.0. The tensile and flexural strength of FR-RC was primarily controlled by the fiber dosage, while the compressive strength relayed on the optimum combination of rubber and fiber. The decline in compressive strength due to a high amount of fiber dosage in FR-RC might be associated with the poor compactness.The modulus of elasticity of concrete decreased considerably with rubber inclusion. Although adding steel fibers can increase the elastic modulus of rubberized concrete, it was still smaller than plain concrete. It suggests that the development of modulus of elasticity of FR-RC was dominated by the crumb rubber content. The appropriate combination of steel fibers and rubber has the potential to produce highly ductile concrete with sufficient strength. shows the representative P-δ curves of the unnotched FR-RC beams, which can be divided into three stages: elastic stage prior to first crack, strain hardening, and strain softening. The first crack strength of FR-RC increased with the specimen age, which was attributed to the strengthening of concrete matrix and interfacial bonding between steel and rubber with concrete. Increasing the rubber content in FR-RC decreased the first crack strength and modulus of elasticity (slop of the curve at the elastic stage), but had little effects on the strain hardening and softening behaviors. Increasing the steel fiber dosage improved the first crack strength and strain hardening behaviors; however, it negatively impacted the strain softening behavior. These findings implied that the first peak strength was influenced by both rubber and steel fiber inclusion, which is in agreement with the strength development of the same mixes. However, the straining hardening and softening behaviors were mainly controlled by the steel fiber dosage in FR-RC. It suggested that after the first crack, the anchoring effect of steel fibers embedded in the cracking concrete matrix played a dominant role. lists the toughness indexes, I5, I10, and I20 and residual strength factors, R5,10 and R10,20 of FR-RC-10-0.75 at various ages. It can be seen that I5, I10, and I20 increases over time with the most rapid development before 7 days. It indicates that curing of concrete improved its flexural toughness, which was attributed to improved binding between fibers and concrete matrix and anchoring effect over time. According to the ASTM the residual strength factors R5,10 and R10,20 values up to 100, this kind of material can be regarded as perfectly plastic material. shows that almost all R5,10 and R10,20 values exceed 100, implying the great plasticity of FR-RC. lists the toughness indexes and residual strength factors of FR-RC with various fiber dosages and rubber contents. It can be seen that the toughness indexes of FR-RC concrete first increased then decreased with the increasing amount of fiber dosage, reaching the maximum value at the dosage of 0.75%. It indicated that there was a combinational effect of the rubber and fibers on the flexural toughness of concrete. Adding high dosage of fibers potentially resulted in fiber dispersion problem that adversely impacted the performance of FR-RC. Increasing the rubber content in concrete did not considerably affect the toughness indexes, but enlarged the deformation (reduce stiffness) at the first crack. shows the representative P-δ and P-CMOD curves of notched FR-RC beams. It can be seen that the first crack strength and ultimate strength of FR-RC increase with ages, which is consistent with the development trends of strength and flexural toughness in unnotched specimens. In addition, the evolution of first crack strength for FR-RC with varying rubber contents and fiber dosages agreed with the trends observed in strength development of cubic and unnotched specimens. It can be seen in (b) that the first crack strength tended to decrease with the increasing rubber content, while the strongest strain hardening behavior occurred in mix FR-RC-10-0.75. In (c), the strain hardening behavior was only observed in the mix with a fiber dosage higher than 0.75%, while the first peak is highest for mix FR-RC-10-0.5. It suggests that the steel fiber dominated the strain hardening performance of FR-RC, and the first peak strength was influenced by both rubber and steel fiber inclusion.The initial fracture toughness, KICQ, and unstable fracture toughness, KICS, of steel fiber reinforced rubberized concrete are listed in . The curing age increased the KICQ and KICS. The highest KICQ at 28 days was observed for mix FR-RC15–0.75, which had the highest rubber content; while the highest KICS at 28 days occurred in mix FR-RC10–0.75, which had the highest strength and flexural toughness. Further increase of steel fiber content to 1% decreased the toughness mainly due to the insufficient compactness of concrete matrix. It indicates that the rubber content dominated the initial fracture toughness, while the steel fiber controlled the unstable fracture toughness.This study investigates the mechanical properties of steel fiber-reinforced rubberized concrete (FR-RC) with various rubber contents, fiber dosages, and curing ages. The following conclusions can be drawn based on this study:The compressive strength of FR-RC is dependent on both the rubber content and fiber dosage, while the flexural and tensile strengths are dominated by the fiber dosage.The modulus of elasticity of FR-RC is mainly controlled by the rubber content.The strength and toughness of FR-RC increase with curing age, which can be attributed to the enhanced anchoring effects of fibers in a hydrated cement matrix.Based on the bending tests of notched and unnotched beam specimens, the first peak strength of FR-RC is influenced by both rubber and steel fiber inclusion, while the straining hardening and softening behaviors are mainly controlled by the steel fiber.According to the double-K fracture model, the rubber content dominates the initial fracture toughness, while the steel fiber dominates the unstable fracture toughness.Microstructure and mechanical properties of the near-beta titanium alloy Ti-5553 processed by selective laser meltingThe aerospace industry continuously demands new materials with high strength and low density like the investigated near-β titanium alloy Ti-5553. Lately, a new need for parts with designs concerning the force flow instead of the process ability with conventional methods is rising. Therefore, additive manufacturing methods are gaining more and more in importance. In this study we processed the Ti-5553 alloy by selective laser melting (SLM), which is one of these methods. Bulk samples with a density of 99.95% were built. X-ray and electron backscatter diffraction show a pure β-phase microstructure. Mechanical tests exhibit a tensile strength of about 800 MPa and a strain up to 14%. These results demonstrate the possibility of processing this alloy by SLM.The aerospace industry has a huge demand for new alloys with lower density and higher strength. One promising candidate fulfilling these requests is the near-β titanium alloy Ti-5553 (chemical composition see ) with a nominal density of 4670 kg/m3 and an ultimate tensile strength up to 1300 MPa Normally the production of parts made of Ti-5553 includes a complex sequence of different thermo-mechanical steps to gain the desired microstructure A new upcoming route for customized part production with tailored geometry and properties are additive manufacturing methods Selective laser melting (SLM) is one representative of additive manufacturing processes Moreover, additive manufacturing shows a great potential compared to subtractive methods concerning the processing of Ti-5553. Normally, the conventionally machining of this alloy is characterized by some difficulties through a short life time of the tools and a low cutting speed First studies of processing titanium and its alloys via selective laser melting were focused on cp-Ti and Ti-6Al-4V. Therefore, the properties of both materials have been extensively examined. The influence of the process parameters like the scanning strategy on the microstructure of Ti-6Al-4V, for instance, was investigated by Thijs et al. This current study focuses on the processing of Ti-5553 via SLM evaluating the microstructure by scanning electron microscopy (SEM), electron-backscatter diffraction (EBSD) and the mechanical properties by tensile tests.The starting material was gas-atomized powder (GAP). The atomization was realized by applying the EIGA method. This method utilizes electrode induction melting under a protective argon atmosphere (purity 99.999%) to obtain a spherical-shaped powder. The electrode consisted of an extruded rod of Ti-5553. In this study, a powder fraction from 25 to 45 μm (d50 |
= 35.71 μm) was employed showing a limited flow ability mainly originating from satellite formation A SLM Solutions 250HL device equipped with a 400 W (theoretical power) Nd:YAG laser (λ = 1064 nm) was used to produce all SLM samples. The spot size of the laser beam was about 80 μm in diameter in the focal point. High purity argon (purity 99.999%) acted as protective gas during the building process. The substrate plate consisted of commercial pure titanium.Starting point for the SLM experiments were single melted tracks on a substrate coated with a thin powder layer of 45 μm. This method is well known for allowing examination of a wide range of different parameters )) as well. Finally, two types of bulk specimens were produced applying the parameter setting with the highest density: Cubic samples (side length 8 mm, chessboard scheme) for microstructure analysis and cylinders (chessboard scheme) with diameter of 6 mm as basis for round specimen (DIN 50125 shape A by turning) for the tensile tests. Other parameter combinations were not investigated due to insufficient density.The metallographic preparation of the embedded samples consisted of grinding and polishing. The final step of the preparation was either etching with Kroll's agent, OPS with 10% H2O2, or a treatment by glow discharge optical emission spectroscopy (GD OES) Two methods of X-ray diffraction analysis were employed: A D3290 PANalyticalX'pert PRO with Co-Kα radiation (λ = 0.17889 nm) in reflection mode and a STOE P in transmission mode with Mo-Kα radiation (λ = 0.07093 nm).Tensile strength measurements were realized with an INSTRON 5869 by applying a cross-head speed of 1 × 10− 3 |
mm/s.The setting up with the highest density (180 mm/s, 100 W, hatch overlap 5%) constitutes for the stripe scheme 99.0% relative density for all tested combinations. By applying the chessboard strategy (5% hatch overlap) for this combination, the relative density can be increased up to 99.5%.To double-check the density of the main parameter combination, one cubic sample (with the chessboard scheme) was analyzed with a μCT device (). The determined pore volume accounts to about 0.11%. In addition to the measurement of the density, the characterization of the pore distribution is possible. Sample A exhibits a pore channel from the bottom to the top of the cube along the building direction (A). This effect can be explained by a too low overlap in the intersection zone of the four fields of the chessboard scan scheme (A). The remaining pores in sample A show an isotropic distribution in the volume. The second measured sample B (B) was processed with the same parameter combination as sample A (field overlap 60 μm), only changing the overlap of the four scan field to a higher value (120 μm). Thus, sample B demonstrates an isotropically distributed porosity (B) throughout the whole specimen without any indication of the existence of a pore canal in contrast to sample A. Apparently, a smaller overlap of the four scan fields mentioned earlier prohibited the pore channel formation. Thereby, the porosity decreases additionally down to 0.05%.Same as the GAP the x-ray diffraction pattern of the longitudinal cut of the cubic sample only shows reflections of a pure β-phase (Im-3m) microstructure with no indication of a second phase ( displays the microstructure of the cubic samples. The section of interest is a lengthwise cut parallel to the building direction. Scan track boundaries appear as nose-shaped to ball-shaped thick white lines and define a solidified melting pool. In contrast, grain boundaries can be distinguished as thin white lines developing vertically. Furthermore, grains with a size up to several 100 μm have grown across the melting border. Their elongation along the building direction () dominates the aspect ratio of the grains. This effect is well described for titanium and its alloys produced by additive manufacturing B). A direct correlation between scan track boundaries and grain boundaries is not definable. In general, the grains show a quite irregular shape.A SLM-typical epitaxial growth dominates the solidification A and B). This leads to a change of the solidification morphology from planar front to cellular and cellular-dendritic structures inside the grains (In general, grains contain several cell clusters with only small differences in orientation. Orientation differences inside the grains are represented by small-angle grain boundaries (). These small-angle grain boundaries or dense dislocation walls normally indicate a deformation of the grains or the microstructure EBSD measurements reveal an overall texturing of the sample (). The 〈100〉 direction of the unit cell is aligned along the building direction and its intensity is about six times random intensity. In general, the crystallization of undercooled melts takes place in the so-called easy-growth directions, as demonstrated by Walton and Chalmers already in 1959 In order to understand the microstructure formation better, a grain size analysis was done for the cubic sample, giving a mean size of the grains of d = 146 μm (area weighting). The measured area of the cubic sample was located in the middle of the lengthwise cut. In the measured area, more than 1000 grains were taken into account using the software ESPRIT 2.0 by examining a large EBSD map. To obtain statistics that are more reliable and to further check the influence of different hatching strategies and the main SLM parameters further investigations are necessary.) show an ultimate tensile strength of around 800 MPa and a maximum elongation of 14% for the SLM-prepared samples. These values are similar to what is known from literature for the mechanical properties of Ti-5553 with a pure β-phase microstructure indicates a not yet fully optimized parameter setting; even if it was the choice of the best parameter combination with a density over 99.9% as already mentioned. Considering the development of the stress-strain curve, a slight stress drop occurs after reaching the yield strength. This stress drop is common for materials with bcc crystal structure at low deformation temperature The premature failure of sample 3 can be traced back to a typical SLM defect. On the fractured surface a smooth area covering certain melted tracks is visible which is probably caused by insufficient coating combined with deficient melting of the powder bed due to the poor flowability previously mentioned. This minimizes the loaded area, increases the residual stress level in the microstructure, and promotes crack initiation.Almost fully dense Ti-5553 samples were produced using the selective laser melting technology. The microstructure consists of pure β-phase. The shape of the grains is elongated in building direction with a cellular to cellular-dendritic morphology. Electron backscatter diffraction revealed a weak texturing with an alignment of the 〈001〉 direction along the building axis.During this early phase of Ti5553 SLM process parameter development, the selective laser melted Ti-5553 specimens exhibited an ultimate tensile strength of about 800 MPa and a maximum elongation of around 14%. It is expected that an enhancement, at least in ductility, should be possible by improving the evaluated parameter setting. An additional post processing heat treatment, eventually even combined with hot isostatic pressing, should deliver significantly better strength properties. This will be topic of future investigations.In general, this study proves the possibility of processing Ti-5553 via SLM with a sufficient density (99.95% relative density) for a first analysis of the mechanical properties. This offers new and promising perspectives for industrial applications of this type of alloy.True and secondary-bifurcation D-G interactionOn the distortional-global interaction in cold-formed steel columns: Relevance, post-buckling behaviour, strength and DSM designThis work reports the available results of an ongoing numerical (shell finite element) investigation on the post-buckling behaviour, strength and design of fixed-ended cold-formed steel columns undergoing distortional-global (D-G) interaction. Columns with different cross-section shapes are analysed, namely plain lipped channel (LC), web-stiffened lipped channel (WSLC) and zed-section (Z) columns, in order to investigate distinct D-G interaction natures: involving either distortional and (global) flexural-torsional buckling (LC and WSLC columns) or distortional and (global) minor-axis flexural buckling (Z columns). In particular, the relevance of these D-G interaction types is discussed, by assessing when they affect visibly the column ultimate strength and/or failure mode. The results presented and discussed concern columns with various geometries and yield stresses, thus ensuring a wide variety of range combinations involving (i) global-to-distortional critical buckling load ratios (RGD) and (ii) squash-to-non critical buckling (distortional or global) load ratios (Ry) and leading to non-negligible failure load erosion. The possible occurrence and failure load impact of “secondary (distortional or global)-bifurcation D-G interaction” (RGD |
< 1.0 or RGD |
> 1.0 and high Ry) are investigated - it is well known that such impact may be significant in columns experiencing “true D-G interaction” (RGD |
≈ 1.0). The above results consist of (i) relevant non-linear (elastic and elastic-plastic) equilibrium paths, (ii) deformed configuration evolutions along those paths, evidencing D-G interactive effects, and (iii) figures providing the failure mode characterisation. Then, the numerical failure load data obtained are compared with their predictions by (i) the currently codified DSM (Direct Strength Method) column global and distortional strength curves, and (when necessary) (ii) proposed DSM-based design approaches, specifically developed to handle D-G interactive failures - a few design considerations are drawn from these comparisons.True and secondary-bifurcation D-G interactionThe complex shape and high wall slenderness exhibited by the open thin-walled cross-sections commonly used in cold-formed steel (CFS) members make them highly susceptible to several instability phenomena, involving either individual (local, distortional, global - L, D, G) and/or coupled (L-D, L-G, D-G, L-D-G) buckling modes. In fact, the efficient design of such elements is far from well established, since interactive buckling phenomena may emerge even when the corresponding critical buckling loads/moments are significantly apart. Therefore, in order to assess the structural behaviour of such members it does not suffice to acquire in-depth knowledge about their “pure”/individual buckling and post-buckling behaviours, since couplings involving two (or even three) buckling modes may occur. Naturally, such coupling effects may erode, to a smaller or larger extent, the member ultimate strength (depending on the corresponding slenderness), thus leading to a high likelihood of reaching unsafe designs.As far as interaction phenomena involving distortional buckling in CFS columns are concerned (e.g., Camotim et al. []), most of the existing studies, comprising experimental investigations, numerical simulations and/or design proposals, deal with L-D interaction - it is worth pointing out the works of Kwon and Hancock []. However, the amount of studies available on columns undergoing D-G interaction is much scarcer and, therefore, a significant research effort is needed before safe and accurate design rules against this type of interactive failures can be established/developed. Indeed, to the authors' best knowledge, the existing works addressing the influence of this coupling phenomenon on the post-buckling behaviour and ultimate strength of CFS columns consist of (i) experimental investigations on rack-section uprights, with and without holes [ and, more recently, web-stiffened lipped channel columns [, and (ii) shell finite element numerical investigations on simply supported (locally/globally pinned end cross-sections with free or prevented warping) and fixed-ended lipped channel columns [], and simply supported and warping-prevented rack-section uprights with or without holes [], and (iii) a Generalised Beam Theory (GBT) numerical study on the mechanics of fixed-ended lipped channel columns affected by this type of interaction [Although all the above studies provided clear evidence of the detrimental influence of D-G interaction on the column strength, an investigation quantifying relevance and addressing the DSM (Direct Strength Method) design against the corresponding failures is still lacking - this work aims at contributing towards filling this gap. Therefore, the objective of this paper is to report the available results of an ongoing numerical (shell finite element) investigation on the post-buckling behaviour, strength and design of fixed-ended CFS columns undergoing different D-G interaction levels, types and natures. Two different D-G interaction natures are considered, which differ in the global buckling mode involved: either major-axis flexural-torsional (plain and web-stiffened lipped channel columns are analysed) and minor-axis flexural (zed-section columns are analysed). In particular, the relevance of D-G interaction is discussed, in order to assess when the column ultimate strength and/or failure mode are visibly affected by its development. It is necessary to identify combined ranges of (i) global-to-distortional critical buckling load ratios (RGD) and (ii) squash-to-non critical buckling (distortional or global) load ratios (Ry) that lead to a non-negligible failure load erosion. Both columns experiencing “true D-G interaction” (RGD |
≈ 1.0) and “secondary (distortional or global)-bifurcation D-G interaction” (RGD |
< 1.0 or RGD |
> 1.0 with high Ry values) are investigated - particular attention is paid to the former, since its impact on the failure load is more significant. The numerical results presented consist of (i) relevant non-linear equilibrium paths, (ii) deformed configuration evolutions along those paths, evidencing D-G interactive effects, and (iii) figures providing the failure mode characterisation. Then, the numerical failure load data obtained are compared with their predictions provided by (i) the currently codified DSM column global and distortional strength curves, and (ii) proposed DSM-based design approaches, specifically developed to handle D-G interactive failures - design considerations/guidelines are drawn from this comparison.To summarise, the methodology adopted in this work consists of (i) selecting/identifying, through buckling analysis, fixed-ended column geometries (cross-section dimensions and lengths) associated with the several cross-section shapes considered and exhibiting the required RGD ratio range (), (ii) performing a column sensitivity analysis to the critical-mode initial geometrical imperfection shape, by means of elastic post-buckling analysis, particularly aimed at determining the most detrimental initial imperfection shape (), (iii) assessing the relevance of the three possible types of distortional-global interaction, namely by carrying out and extensive parametric study to assemble elastic-plastic failure load data (), and (iv) addressing the DSM design of columns affected by D-G interaction, which includes the proposal of preliminary DSM-based strength curves, on the basis of the previously gathered failure loads (The identification/selection of CFS (E |
= 210GPa, v |
= 0.30) column geometries (cross-section dimensions and lengths) prone to D-G interaction can be obtained on the sole basis of elastic critical buckling loads, i.e., by performing “only” linear buckling analyses. Since it is well known that global buckling may have different natures (depending on the cross-section shape), involving either (i) pure flexure (usually minor-axis), (ii) pure torsion or (iii) flexure (usually major-axis) and torsion, the corresponding D-G interaction also exhibit different natures - the same applies to L-D-G interaction (e.g., []). Therefore, three cross-section shapes, namely (i) plain lipped channels (LC), (ii) web-stiffened lipped channels (WSLC) and zed-section (Z) columns are considered in this work - while the first two are “expected” to undergo interaction between distortional and (major-axis) flexural-torsional buckling, the last one experiences interaction between distortional and minor-axis flexural buckling. As done in similar studies, such geometries were selected through GBT buckling analysis sequences in the user-friendly code GBTUL [The output of this selection procedure are 41 columns exhibiting RGD values in the range 0.0 < |
RGD |
≤ 2.0 with the critical local buckling load (PcrL) higher than the global and distortional ones (PcrL/Pcr.Max |
> 1.0, with Pcr.Max |
= max{PcrD; PcrG}), thus ensuring that no interaction with local buckling occurs (i.e., precluding L-D-G interaction) - they are labelled X1 to X41, where “X” may be either “LC”, “WSLC” or “Z”, and their characteristics can be found in ), respectively (all WSLC columns contain “v-shaped” intermediate stiffeners formed by two walls with 45° inclination and width equal to 102 |
mm). In order to investigate the effect of strong D-G interaction and the possible occurrence of “secondary (global or distortional) bifurcation D-G interaction”, 20 columns were selected in the 0.90 < |
RGD |
< 1.10 range and 19 columns are obtained by varying this ratio in 0.10/0.05 until 2.00 and 0.50. The remaining two columns were chosen to assess the merits of the currently codified DSM global design curve in estimating the failure loads of columns collapsing in pure global modes (addressed in ) and, therefore, are characterized by very low RGD values – a more in-depth study concerning the accuracy of the currently codified DSM distortional design curve has been recently reported by Landesmann and Camotim [For illustrative purposes and in order to clarify the nature of the global buckling modes of columns prone to D-G interaction, show the variation, with the length L (logarithmic scale), of the critical buckling load Pcr for columns with the three cross-section shapes and RGD |
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