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= 8.00 s and T |
= 15.0 s, respectively, are shown in . The figures illustrate that there is large discrepancy between EVDs with different T. At large the mean and the standard deviation of the EVD over a shorter time interval are smaller than those of the EVD over a longer time interval (see (a), compare the curve with different T). Interestingly, in Case 1 the mode of extreme value shown in the curve “T |
= 8” ((a)) is on the left part of the curve while that of “T |
= 15” shows a reverse trend.The EVD is also greatly influenced by the C.O.V. of the random parameters. From it is seen that the EVDs in the cases with different C.O.V. are quite different. The extreme value with smaller C.O.V. (Case 1) of the random parameters distributes narrower. In other words, the standard deviation increases with the C.O.V. of the random parameters increasing. dynamic reliabilities of the structure are evaluated. Listed in are the reliabilities with different thresholds in different cases. From the tables it is seen that the reliabilities computed by the PDEM is of fair accuracy. As is well known that in the dynamic reliability theory based on the level-crossing process, the accuracy is still not ensured. What’s more, although some modifications were studied (say, It is easy to evaluate the reliabilities by Eq. when the thresholds are random variables. shows the typical EVD and PDF of the thresholds (boundaries). Listed in are the results when the thresholds are lognormally distributed random variables with different mean and C.O.V. Some interesting features could be seen from the table. At the same level of C.O.V. of the thresholds, the reliabilities decrease with the means of the thresholds decreasing (see the columns of the table). On the other hand, at the same level of the means of the thresholds, the reliabilities decrease with the C.O.V. of the thresholds increasing when the means of the thresholds are large (see the row with the mean of the threshold > = 0.08). But when the means of the thresholds are small, the reliabilities increase with the C.O.V. of the thresholds increasing (see the row with the mean of the threshold = 0.04). These phenomena imply that local configuration of the PDF of the response are important for dynamic reliability evaluation of structures.On the accuracy of the proposed method, it is worth pointing out that there is no error resulting from the truncation of the expanded series like that in the random perturbation techniques. Therefore, the error of the proposed method mainly lies in the discretization in the numerical procedures, including the error in selecting the representative points from the domain ΩΘ and the error in the finite difference method. To improve the accuracy of the proposed method, these aspects require further investigations in the future.The extreme value distribution of random sampling and stochastic processes is of paramount importance in many disciplines, especially in reliability evaluation of the engineering structures. However, effective method capable of capturing the extreme value distribution for general stochastic problems has not been available as yet. In the present paper, a versatile approach for evaluation of the extreme value distribution and dynamic reliability is proposed based on thoughts of the newly developed probability density evolution method. In the proposed approach, a virtual stochastic process related to the extreme value of the stochastic response of structures is constructed. The extreme value distribution could then be evaluated by dealing with a virtual stochastic dynamical system. Numerical algorithm is outlined. Two numerical examples are investigated. The extreme value distributions of random sampling are compared with the closed form solutions. In dynamic response analysis and reliability evaluation, parts of the results are illustrated. Some features of the instantaneous PDF, the extreme value distribution and the reliabilities are discussed. The studies indicate that, although the accuracy still needs further improvements, the proposed method is effective and versatile.Third body layer—experimental results and a model describing its influence on the traction coefficientWhen adding substances to the wheel–rail contact, they mix with wear particles and form a Third Body Layer (3BL). This layer influences the initial gradient of the traction characteristic.During twin-disc tests presented in this paper, a granular layer consisting of iron and iron oxides with a thickness of up to 50μm was found. In addition, a creepforce model is presented that uses non-linear properties of the 3BL to describe its influence on the traction characteristic. The results of the model were compared to the results of the experiment. A qualitative and quantitative agreement was achieved. This will improve, e.g., the quality of vehicle dynamics simulations, optimizations of control devices for traction and braking, and predictions of wear and damage on wheel and rail.The traction characteristic of the wheel–rail contact is of high importance for the vehicle–track interaction. Thus, accurate models are essential for, e.g., reliable investigations of vehicle dynamics, optimization of traction and braking control devices, or predictions of wear and damage on wheel and rail. Therefore, a lot of research has been done on this topic. Empirical models exist but the necessary parameters need to be fitted for every set of boundary conditions. The advantage of a physical model is that it can cope with different boundary conditions and it leads to a better understanding of the underlying processes taking place in the contact. The most widely used physical model is Kalker's Exact Theory for rolling contact Several effects have been observed in measurements that cannot be explained by Kalker's Exact Theory which assumes a constant μ: different initial gradients have been measured in the micro-creep domain, although the contact geometry and the normal load were not changed A model published by Tomberger et al. is able to reproduce these macro-creep related effects by using physical sub-models for describing local tribological effects This change has been observed when additional substances are present in the contact However, recent research regarding friction modifiers suggest that the effects caused by an artificial or natural 3BL can only be explained by the presence of a third kind of layer in the contact and their interaction There have been investigations regarding the properties of this basic 3BL in the past, but the conclusions differed. While some predicted it to be 1–3 μm thick and attributed it to wear reducing properties This paper focuses on the properties of this basic 3BL and its influence on the traction characteristic. Therefore, experiments were performed on a twin-disc machine under laboratory conditions. This ensures that there are no natural or artificial contaminations in the contact. After the tests, the used discs were optically investigated. The wear debris was collected and analysed by X-ray powder diffraction (XRD) analysis. There, a coherent beam of monochromatic X-rays interacts with a powder and produces spectra. These spectra are then used to identify the materials present in the powder. Additionally, a creepforce model was developed. This model is able to predict the influence of a 3BL on the traction characteristic.The basic 3BL was created by performing twin-disc experiments, which were executed under laboratory conditions. This ensured that only a basic 3BL developed in the contact. Additionally, all necessary parameters could be adjusted independently. shows the schematics of the test machine. The development and operation of the machine was described previously in detail Two kind of discs with a diameter of 47 mm and a width of 10 mm were used in the experiments. The rail discs were made of R260 rail material; the wheel discs were made of ER8 wheel material. All discs were polished and cleaned in an ultrasonic acetone bath before the tests. The mode of operation was that the rail discs were set to a certain velocity while the wheel discs were faster according to the creepage. During the tests, room temperature, which was in between 20 °C and 24 °C, and humidity of air, which was in between 34% and 48%, were measured. Also, the bulk temperature was measured, as it was not possible to measure the contact temperature.After the tests, the discs were embedded in a resin. Then, they were sectioned and the marked area in was investigated with an optical microscope. The results of these investigations were compared to a baseline: an unused pair of discs.During the measurements, a box was placed around the discs to enclose both in order to collect the wear debris which was later investigated via XRD analysis. The wear debris must consist of the same substances as the basic 3BL, although the percentage of their occurrence might vary. Nevertheless, it gives insight into the composition of the layer. shows the traction characteristic for different normal loads and different velocities. The measured bulk temperatures were increasing with creepage and velocity, but all were below 100 °C for the measurements presented. Increasing the normal load leads to a lower level of traction. The same is true for the velocity where a higher velocity leads also to a decrease. This is all in accordance with the results of the model developed by Tomberger et al. . There, the baseline is compared to a used pair of discs. The test conditions were cx=5%, v=0.5ms−1, p0=900MPa in In order to calculate the traction characteristic, it is necessary to calculate the local tangential stress τ(x) and the local normal stress p(x) in the contact. A sketch of the contact is shown in . The thickness of the layer is assumed to be constant and much less than the half size of the contact area: h⪯¡a. Then, the normal contact problem can be solved by Hertz The coordinate system is centred at the centre of the contact area at the interface of 3BL and rail as shown in . It is moving with the velocity v. A 3BL with the thickness h is fixed on the surface of the wheel to agree with the experiment. First, we have to describe the displacement in the area of stick. Here, the total displacement u is the sum of the displacement in the rail uR, the displacement in the wheel uW, and the total displacement occurring in the 3BL u3BL:The kinematic relation in the area of stick reads as follows:Particles on the surface of the rail move with a velocity v through the contact. Particles on the surface of the wheel and in the 3BL move with a velocity ωR because we assumed that the 3BL is fixed on the surface of the wheel and its thickness is much less than the contact width. For steady state and with Eq. The discs used in the experiment can be approximated by cylinders. Therefore, we assume line contact and define the longitudinal creepage cx:Lateral creepage and spin creepage are not considered.One way to model the 3BL is to assume that it is a homogeneous and isotropic material with elastic properties ). We define the material function m(x) using the elastic shear modulus G and the plastic shear modulus k:A1 is the area of the contact where the 3BL deforms elastically, A2 is the area where it deforms plastically. These areas within the area of stick are defined asA1={x||τ(x)|<τc∧|τ(x)|<μp(x)}A2={x|τc≤|τ(x)|<μp(x)}with the coefficient of friction μ and the critical shear stress τc (see ). The layer is assumed to be made of independent brushes because its thickness is much less than the contact width The wheel and the rail are modelled as elastic half spaces with the same material constants, i.e. the same Young's modulus E and Poisson's ratio ν. The strain in the wheel and the strain in the rail are according to Johnson ∂uW/R∂x=−(1−2ν)(1+ν)Ep(x)−1πE⁎∫−aaτW/R(s)x−sdsforx∈Ai,i=1,2with E⁎=((2−2ν2)/E)−1 and the indexes W and R denote wheel and rail respectively. According to , the tangential stresses in the wheel and the rail areThe friction in the area of slip B is modelled according to Coulomb–d'Amonotons law:Then, the tangential stress can be written asτ(x)={τ1(x)forx∈A1τ2(x)forx∈A2μp(x)forx∈B) yields a system of two coupled integral equations for τ1(x) and τ2(x) which are valid for x∈A1 and x∈A2 respectively:(1−cx)hmi∂τi(x)∂x−2−cxπE⁎(∫A1τ1(s)x−sds+∫A2τ2(s)x−sds+∫Bμp(s)x−sds)=−cx(1+(1−2ν)(1+ν)Ep(x))forx∈Aiwith i=1,2. The integral can be solved analytically if τ1 and τ2 are assumed to be polynomial functions with coefficients that are optimized to satisfy Eq. correlates to Kalker's Exact Theory for line contact shows the influence of a 3BL on the local tangential stress in the contact area for two different longitudinal creepages. The elastic shear modulus of the 3BL was set to G=79.3GPa, which is the elastic shear modulus of steel, the plastic shear modulus to k=3 GPa, the critical shear stress to τc=200MPa, and its thickness to h=20μm. Young's modulus of the wheel and the rail was set to E=200GPa and Poisson's ratio to ν=0.29.This different behaviour of the local shear stress leads to a different behaviour of the traction characteristic. This is shown in . Without 3BL, two distinct domains are observable: the micro-creep and the macro-creep domain. With 3BL, three domains are visible: for cx∈T1, the local shear stress looks like shown in (a) with an area of elastic deformation, plastic deformation, and sliding. For cx∈T2, the stress resulting from the elastic deformation within the layer exceeds μp(x). An additional area of slip is formed at the leading edge (see (b)). Area T3 is characterized by total sliding in the whole contact area. The 3BL has a high influence on the creepage at which the transition from micro-creep to macro-creep occurs.A parameter study was made for the four parameters defining the properties of the 3BL to investigate their influence. shows the default values for the thickness h, elastic shear modulus G, plastic shear modulus k, and critical shear stress τc. shows that the influence of the 3BL material parameters increases with the thickness of the layer. The elastic shear modulus changes the gradient in the T1 domain, while the plastic shear modulus changes the gradient in the T2 domain. All four parameter influence the creepage at which the T1 domain changes into the T2 domain. It should be noted that the presented model uses independent parameters and does not take into account any interaction between the parameters, e.g., the thickness of the layer in this model is independent of its mechanical properties. shows the comparison of the developed 3BL model to the results of the measurements on the twin-disc test machine.The coefficient of friction μ was adjusted according to the maximum value of the traction observed in the experiment. The same set of parameters was used to describe the 3BL in every calculation, except for one: the critical shear stress was set to τc=300MPa for p0=1500MPa and τc=200MPa for p0=900MPa. The other parameters used for the comparison are shown in The experimental results showed a 3BL of up to 50μm in uncompressed state that consists of iron and iron oxides. Bucher et al. found an average surface roughness on the rail of 0.41μm and on the wheel of 0.7μm shows that the new model is able to qualitatively and also quantitatively describe the experimental results for the micro-creep domain. The influence of a 3BL on the average relative deviation of the 3BL Model from the experiment is shown in To achieve this, the critical shear stress had to be adjusted for different normal loads. This seems plausible as the layer itself consists of granular materials and the material properties of such a layer are highly influenced by pressure, especially the critical shear stress However, the model does not take into account the interaction of the various parameters themselves. This can be included in the future by implementing a granular description of the 3BL. Therefore, additional investigations of the layer are necessary. Also, twin-disc tests with artificial and natural 3BL need to be performed to gain a better understanding of their influence. It should be noted that this model is only valid for line contact and has to be extended for three dimensional calculations. In addition, this model will be unified with the Extended Creepforce Model by Tomberger et al. Investigations at a twin-disc test machine revealed that a basic Third Body Layer develops in the wheel–rail contact. This layer is up to 50μm thick, which is up to two magnitudes larger than the roughness found on wheel and rail A model was developed to describe the influence on the traction characteristic:The Hertzian Theory was used to solve the normal contact problem because the thickness of the layer is much less than the contact width Line contact is assumed and only longitudinal creepage is considered.The wheel and the rail were modelled as elastic half-spaces.The layer was modelled as an isotropic and homogeneous material with non-linear properties. These properties were described by four parameters: The elastic shear modulus G, the plastic shear modulus k, the critical shear stress τc, and its thickness h.A parameter study showed that these parameters have a high influence on the behaviour of the traction coefficient in the micro-creep domain. They also influence the creepage at which the transition from micro-creep to macro-creep occurs.The developed 3BL model was compared to the results of the twin-disc experiments. The traction characteristics were reproduced qualitatively and quantitatively for two different normal loads and two different velocities. The same set of Third Body Layer properties was used in all cases. The exception was that a different critical shear stress had to be used for different normal loads. This implies a pressure depended behaviour of the 3BL.Macro-mechanical finite element modellingNonlinear finite element model for traditional adobe masonryA huge fraction of the worldwide built heritage consists of adobe masonry (AM) structures, including cultural heritage sites protected by UNESCO and single countries. In Portugal, the Aveiro district is a region where approximately 40% of the building stock is composed of AM structures with high cultural, social and architectural value. This paper presents a macro-mechanical finite element (FE) model that was developed for future performance assessments of AM structures. Based on available experimental data on Aveiro’s AM, the FE model was validated in two different boundary and loading conditions associated with normal and diagonal compression tests. A satisfactory numerical-experimental agreement was found in terms of load-displacement curves, crack patterns, local stresses and deformations. A sensitivity analysis evidenced that compressive and tensile strengths mostly influence the peak load capacity and post-peak softening behaviour of wallettes, whereas Young’s modulus affects the pre-peak rising branch of load-displacement curves.Macro-mechanical finite element modellingAdobe masonry (AM) is one of the most largely used construction technique worldwide due to local availability of constituent materials, low manufacturing cost, simple construction technique and thermo-acoustic properties. AM is a masonry assemblage consisting of adobe bricks and mortar Together with rammed earth, AM falls in the class of earthen construction materials that have been used in various historical ages and countries, starting at least 5000 years ago in Mesopotamia and Turkmenistan Most of studies focused on seismic response and strengthening of AM constructions (see e.g. Therefore, past numerical studies showed the feasibility of both micro-mechanical and macro-mechanical FE models for simulation of both quasi-static and dynamic behaviour of AM structures by means of explicit solution procedures. Nevertheless, other traditional AM constructions still need to be investigated in order to calibrate numerical models with different levels of sophistication. This is the case of Portugal where AM was commonly used until the middle of the 20th century and the Aveiro district is an emblematic region where approximately 40% of the building stock is composed of AM structures. Most of those buildings have an important cultural, social and architectural value, but at the same time and in many situations, a poor state of conservation and structural deficiencies. Therefore, on one hand, a mechanical characterisation of traditional AM of Aveiro district needs to be performed, and on the other, an experimental and numerical assessment of AM buildings is required for their seismic strengthening and risk mitigation. It is noted that adobe units in the Aveiro district were made of arenaceous soil with a reduced silt-clay fraction and air lime according to a percentage between 25% and 40%. Besides, the mortar was typically characterised by a hydrated lime:soil ratio of 1:3 (in terms of bulk volume), where the soil was a sand having 11% of gravel (i.e. particles with size between 2 mm and 9.5 mm) and 4% of clay and silt (i.e. particles with size lower than 0.075 mm).Based on a past experimental campaign by Silveira et al. In this study, a homogeneous FE model is adopted according to the very similar composition and values of mechanical properties of adobe bricks and mortar in the case of Aveiro’s AM After that appropriate values were assigned to strengths and elastic moduli of AM, the mechanical behaviour was simulated in different boundary and loading conditions corresponding to the normal and diagonal compression tests presented in The last part of this study was a sensitivity analysis in which mechanical properties of AM were individually modified to assess nonlinear response variations under different loading conditions. That assessment was considered an important step in relation to the relatively large variability in mechanical properties of the case-study AM. Sensitivity analysis is a powerful tool used to evaluate whether and how nonlinear behaviour of unreinforced masonry may change under varying material/geometric properties, boundary/loading conditions, and retrofit solutions. In this respect, Petersen et al. Experimental data on physical and mechanical properties of the AM under study were collected from the paper by Silveira et al. a and b show, respectively, the experimental setup and load-displacement curves of specimens W1–W5 subjected to normal compression tests. Similarly, a and b show the setup and load-displacement curves related to diagonal compression tests.Experimental tests were carried out with displacement control and AM specimens experienced a quasi-brittle behaviour. All specimens were 1260 × 1260 × 360 mm3 in size and were made of a two-leaf, running bond AM. In detail, adobe units had a size of 460 × 320 × 120 mm3 and their physical and mechanical properties are listed in . Those properties were evaluated on ten adobe units that were randomly selected among those used for the preparation of wallettes. AM joints had a thickness of 20 mm and were composed of an earth-based mortar having the properties outlined in is associated with the typical procedure used in other studies (see e.g. Normal compression tests were performed with loading perpendicular to mortar bed joints. A reaction steel beam was placed above each specimen to distribute the normal compressive load (a). Diagonal compression tests were performed by applying loading through steel shoes in opposite corners of each specimen (a). In all tests, relative displacements on both faces of specimens were monitored by linear variable displacement transducers (LVDTs). As shown below, specimens loaded in normal compression suffered vertical cracks with a rather uniform distribution over both faces. By contrast, diagonal compression produced single diagonal cracks, as observed during past experimental tests on other masonry specimens (see e.g. A macro-modelling FE approach was used to reproduce the experimental results, assigning the same properties to AM constituents in accordance with their very similar composition (see ). Each macro-mechanical model of AM specimen was developed using a regular mesh of eight-node solid elements having a cubic shape with 20 mm edge. Solid elements were preferred over their plane counterparts to allow future extensions of this study to the simulation of AM walls subjected to out-of-plane loading or eccentric compression. The size of finite elements was carefully optimised through a convergence analysis aimed at minimising the computational cost and mesh sensitivity effects of FE simulations, while ensuring a satisfactory simulation of the experimental behaviour. The optimal size of finite elements was found to be equal to the thickness of mortar joints, namely 20 mm. For instance, in the case of normal compression tests, the use of finite elements with 30 mm edge did not produce suitable results in terms of initial stiffness, displacement capacity and strain patterns. This was also consistent with a previous research on tuff stone masonry assemblages that were modelled in accordance with a micro-mechanical approach The numerical models of AM specimens consisted of 63,504 finite elements, regardless of the test setup under consideration (i.e. normal or diagonal compression). A single-point integration scheme was selected and hourglass energy was monitored to get reliable results. Nonlinear static analysis of numerical models was run with displacement control, assuming a monotonic time history with constant displacement rate of 0.8 mm/s. An explicit solution algorithm for nonlinear FE analysis was used in view of potential future assessments of AM structures under dynamic loads, such as earthquake ground motion.Among several material models available in LS-DYNA a). The deviatoric behaviour is governed by a pressure-dependent flow rule with a yield function that depends on the Von Mises stress σe, the hydrostatic pressure p and three material constants a0, a1 and a2. Material crushing is simulated through volumetric deformations. The volumetric pressure-strain behaviour of constituents, that is the function p = p(εv), is usually defined by tabulated values according to experimental tests or numerical calibration. b shows a typical volumetric pressure-strain diagram, having a first branch that defines a linear elastic behaviour by means of the bulk modulus K = p/εv. The definition of material behaviour is also based on the following assumptions: (i) a brittle tensile failure is considered through a cut-off strength; (ii) the attainment of tensile strength induces an elastic unloading according to K from the p-εv diagram; (iii) if the yield condition is exceeded, stresses are scaled down through a radial return algorithm; and (iv) if the hydrostatic tension exceeds the cut-off stress, pressure is set to the cut-off value and the deviatoric stress tensor is set to zero.Material properties of the case-study AM as a whole are outlined in , where ft and fc are the tensile and compressive strengths. The yield constants (a0, a1, a2) of AM were defined according to the mean experimental data and are listed in together with limit volumetric pressures (pv1, pv2, pv3) and limit volumetric strains (εv1, εv2, εv3). The bulk modulus was defined as K = E/[3(1−2ν)] according to the assumption of homogeneous, linear elastic material. Given the lack of triaxial tests on the case-study AM, the volumetric pressure-strain diagram was defined according to experimental curves available in the literature for adobe The yield constants depend on three factors denoted as m, α and k, which were found to be 3.40, 0.315 and 0.12. It is noted that m is the ratio of the uniaxial compressive strength to the uniaxial tensile strength (i.e. m = fc/ft), α is a pressure sensitivity coefficient defined as α=m-1/β and k is a material constant defined as k=2fc/β, where β=3m+1. Further details on behavioural features of the selected material model can be found in, for instance, the paper by Parisi et al. According to the experimental setup, all the nodes located at the base of the model were assumed to be free to move in the horizontal direction (bidirectional rollers), exception made for central nodes that were hinged (a). All nodes located on top were uniformly loaded, in line with the presence of a rigid beam on specimens. It is noted that the full body of specimen was modelled in order to allow the use of the same numerical models in a subsequent study aimed at investigating the nonlinear response of AM walls to eccentric compression, out-of-plane loading (either uniform or non-uniform) and imperfect boundary conditions. Otherwise, a quarter of the AM wallettes could be considered under normal (concentric) compression, as made for instance by one of the authors in a micro-mechanical analysis b shows that the FE model with mean properties allowed a good reproduction of initial stiffness and displacement capacity, ensuring that the numerical load-displacement curve falls in the experimental range. Nonetheless, given that the huge variability in material properties was not simulated through a stochastic numerical model (see e.g. Parisi et al. a) was well captured by the numerical model in terms of plastic strains in the direction of compressive loading (A detailed monitoring of numerical models in terms of local stresses and relative displacements was also carried out. As shown in a, three finite elements were selected at the mid cross section of the numerical model. The spacing between those elements was equal to one-fourth of cross section width in order to detect the distribution of vertical (compressive) stresses as the vertical displacement impressed on top of the FE model increased.b shows that the vertical compressive stress in the central element labelled as #1 reached the mean compressive strength of the AM (i.e. fc = 466 kPa in ) when the vertical displacement of top section attained approximately 2.5 mm. At almost the same displacement level, the vertical stress in the other two elements became very close to fc. The post-peak response of the central finite element was initially more brittle than that of other elements. This was mainly due to the lower level of lateral confinement pressure, as also observed through the thickness of masonry wallettes where splitting vertical cracks firstly occur along the centreline (see e.g. The capability of the FE model to reproduce the relative displacements in the central part of the specimen was also assessed. According to the experimental arrangement of vertical LVDTs in the central part of specimen faces A and B (a and b), six couples of vertically aligned elements were identified on the numerical model (Then, the relative displacements of LVDTs and finite elements in the vertical direction were considered on each specimen/model face and their average values between both faces (i.e. Vi = (ViA + ViB)/2 with i = 1, 2, 3) were computed, as shown in e for specimen W1. It was found that experimental relative displacements were more scattered than their numerical counterparts, regardless of the vertical displacement imposed on top section. f highlights that relative displacements were well captured by the macro-mechanical FE model. The model error evaluated over all vertical displacement levels, denoted by ME = ΔEXP/ΔFEM where ΔEXP and ΔFEM are respectively the experimental and numerical relative displacements, was found to have mean μ = 1.17 and CoV = 15%. These statistics could be used in future probabilistic simulations to include the random error of the FE model in the prediction of the relative displacement corresponding to the displacement impressed on top section.The numerical model used to simulate diagonal compressive behaviour had the same geometry, but different boundary and loading conditions with respect to the case of normal compression. According to the experimental setup (a), compressive loading was applied through a steel shoe on top corner of a 45° rotated specimen. Another steel shoe, which was placed at the base of the specimen (i.e. on the opposite corner) and connected to the basement of the testing machine (a), provided reaction to loading. The steel shoes did not allow translations, so all corresponding nodes of the FE model were assumed to be hinged (The FE model with mean properties reproduced very well the initial stiffness, peak resistance and softening behaviour of specimens (). The numerical simulation perfectly captured the observed crack pattern (a), which was characterised by a main diagonal crack that connected opposite points of the specimen, rather outside the corners restrained by steel shoes.In this respect, it should be noted that local crushing in loaded corners of specimens did not occur during testing and was not observed in the numerical simulation. The deformed shape shown in b is fully compatible with the observed crack pattern.According to the procedure presented in , the numerical-experimental comparison was extended to the monitoring of local stresses and relative displacements in the central part of specimens. In addition to the couple of finite elements located at the ends of horizontal LVDTs (labelled as #1 and #2), the element #3 located in the region involved by diagonal cracking was selected (b shows the horizontal tensile stress in those finite elements under varying vertical displacement imposed on top of specimen W2. It is clearly found that the horizontal stress in element #3 attained the mean tensile strength of the case-study AM (i.e. ft = 137 kPa in ). As the vertical displacement further increased, element #3 was no longer able to sustain stresses.Horizontal relative displacements between end points of LVDTs were also monitored as shown in a and b. Two couples of nodes with spacing equal to 605 mm were identified on faces A and B of the FE model, along the horizontal line connecting opposite corners (e allows experimental and numerical relative displacements to be compared with each other, as the imposed vertical displacement on top corner of specimen W2 increases. Horizontal LVDTs worked until a relative displacement approximately equal to 1 mm was reached. This is because, in that stage of the diagonal compression test, the formation of diagonal cracks in the central part of specimen W2 produced the loss of supports for the horizontal LVDTs. If all five specimens are taken into account, the model error in terms of relative horizontal displacements can be estimated, as done in the case of normal compression. f shows that the macro-mechanical model presented in this paper underestimates relative horizontal displacements, particularly at intermediate damage levels.The model error was thus found to have mean μ = 1.30 and CoV = 42%, which are greater than their respective values related to normal compression. Nevertheless, it is worth noting that the FE model well captures relative displacements associated with ultimate conditions, namely, the largest vertical displacements resisted by AM wallettes.According to the experimental variability of compressive strength fc, tensile strength ft and Young’s modulus E of the case-study AM, the authors of this paper investigated the influence of such mechanical properties on nonlinear behaviour of AM wallettes subjected to either normal or diagonal compressive loading. In this sensitivity analysis, each mechanical property at a time was increased or reduced according to its CoV (see First of all, the role of compressive strength on the initial stiffness, peak load capacity and softening behaviour of AM subjected to normal compression was evaluated. a shows that the initial stiffness was not significantly influenced by fc. By contrast and as expected, the influence of such a parameter on peak load capacity was rather high, allowing the experimental range to be captured when fc was increased by 32%. An intermediate level of increase in fc (i.e. +16%) was also evaluated. That variation produced a small increase in peak load capacity without substantial variations of initial stiffness and residual load capacity (i.e. the load level associated with the maximum axial displacement imposed on top of AM wallettes). Dealing with this latter behavioural characteristic, it should be noted that a 32% increase in compressive strength led to a more pronounced degradation of load capacity compared to that experienced by the FE model with mean mechanical properties (see the solid line in a). When a 32% reduction in compressive strength was considered, the load-displacement curve fell even below the lowest experimental curve.The tensile strength of the case-study AM is the mechanical property with the maximum uncertainty level, measured by CoV = 65%. When ft was reduced by 65%, the numerical load-displacement curve was strongly different from experimental curves, as shown in b (see the dotted line). Assuming that minimum level of tensile strength did not allow the reproduction of the initial stiffness and peak load capacity of AM wallettes, resulting in a sort of exponential (and hence very rapid) softening rather than the experimentally observed parabolic (and hence gradual) softening. Conversely, when a 65% increase in ft was assigned to the FE model, the peak load capacity rose up and a pseudo-ductile behaviour was observed. A similar effect was found when the Young’s modulus was increased by 32% (c), whereas the opposite variation in that elastic property only reduced the load capacity in the pre-peak rising branch.In such loading conditions, variations in compressive strength had relatively minor effects on the load-displacement curve (a). In detail, no significant variations in terms of initial stiffness, peak load capacity and post-peak softening behaviour were found. The compressive strength had only a higher influence on the pre-peak rising branch, resulting in the attainment of peak load capacity at different displacement levels. The initial stiffness corresponding to different levels of compressive strength was the same. Nevertheless, as compressive strength increased, the spreading of cracking reduced, resulting in a less significant degradation of initial stiffness as the load approached the peak resistance of the numerical model.A high sensitivity of nonlinear response to tensile strength can be observed in b. As noted in the case of normal compression, a 65% uniform reduction in tensile strength throughout the whole FE model produced a peak load capacity significantly lower than that provided by experimental tests, followed by a very rapid strength degradation. Nonetheless, a 65% increase in tensile strength allowed the maximum level of peak load capacity to be simulated. In that condition, the FE model was also able to reproduce the highest strength degradation associated with the maximum experimental load capacity.Variations in Young’s modulus under constant Poisson’s ratio determined the same variations in shear modulus of AM. This clearly provides a motivation to the sensitivity of initial stiffness to E, as shown in c. Conversely, both peak load capacity and softening behaviour of AM wallettes were not considerably influenced by Young’s modulus.A nonlinear macro-mechanical FE model of a typical Portuguese adobe masonry was implemented on the basis of the soil and foam material model, which was successfully used in previous studies for other masonry types. Material properties and the volumetric pressure-strain behaviour of the AM were defined according to experimental tests available in the literature. Given that AM constituents (i.e. bricks and joints) were made of earthen materials with similar composition, production and curing process, the authors assigned them the same mechanical behaviour. In order to carry out a robust validation of the FE model, nonlinear numerical simulations were performed in two different boundary and loading conditions corresponding to normal and diagonal compression tests on single-leaf AM wallettes. The authors found a satisfactory numerical-experimental agreement in terms of load-displacement curves and crack patterns, as well as local stresses and deformations in the selected parts of the FE model (i.e. those mostly involved in the damage process). The model error in terms of relative displacements experienced by the central parts of the AM wallettes was statistically characterised as a Gaussian random variable with different mean values and standard deviations for normal and diagonal compression.The macro-mechanical models with mean material properties allowed the initial stiffness, peak load capacity and post-peak softening behaviour to be well reproduced. The sensitivity of such capacity measures of AM wallettes to compressive strength, tensile strength and Young’s modulus was also evaluated. Analysis results highlighted the following characteristics:Compressive and tensile strengths have the highest influence on peak load capacity and softening behaviour of the case-study AM; nonetheless, the lowest level of tensile strength produced load-displacement curves strongly different from those derived by tests.Variations in Young’s modulus always caused a change in the pre-peak rising branch of load-displacement curves; when Young’s modulus was increased, a more appreciable increase in peak load capacity under normal compression was found.The validation of a macro-mechanical FE model with relatively low computational demand allows future developments in the performance assessment of AM structures subjected to several events. In this respect, given that an explicit analysis procedure was used, the FE model presented in this study could be used also in dynamic loading conditions, such as those produced by earthquake ground motion, impact and blast. In that context, opens issues for a complete calibration of the numerical model include an appropriate definition of dynamic modulus and hysteretic behaviour of the adobe masonry under study.Tensile and stress corrosion cracking properties of type 304 stainless steel irradiated to a very high doseCertain safety-related core internal structural components of light water reactors, usually fabricated from Type 304 or 316 austenitic stainless steels (SSs), accumulate very high levels of irradiation damage (20–100 displacement per atom or dpa) by the end of life. Our databases and mechanistic understanding of the degradation of such highly irradiated components, however, are not well established. A key question is the nature of irradiation-assisted intergranular cracking at very high doses, i.e. is it purely mechanical failure or is it stress-corrosion cracking? In this work, hot-cell tests and microstructural characterization were performed on Type 304 SS from the hexagonal fuel can of the decommissioned EBR-II reactor after irradiation to ≈50 dpa at ≈370 °C. Slow-strain-rate tensile tests were conducted at 289 °C in air and in water at several levels of electrochemical potential (ECP), and microstructural characteristics were analyzed by scanning and transmission electron microscopies. The material deformed significantly by twinning and exhibited surprisingly high ductility in air, but was susceptible to severe intergranular stress corrosion cracking (IGSCC) at high ECP. Low levels of dissolved O and ECP were effective in suppressing the susceptibility of the heavily irradiated material to IGSCC, indicating that the stress corrosion process associated with irradiation-induced grain-boundary Cr depletion, rather than purely mechanical separation of grain boundaries, plays the dominant role. However, although IGSCC was suppressed, the material was susceptible to dislocation channeling at a low ECP, and this susceptibility led to a poor work-hardening capability and low ductility.As neutron fluence increases, austenitic stainless steel (SS) core internals of boiling and pressurized water reactors (BWRs and PWRs) become susceptible to irradiation-assisted intergranular (IG) cracking. Although most failed components can be repaired or replaced, such operations are difficult and very expensive. Therefore, extensive research has been conducted in the last ≈20 years to develop our understanding of this form of degradation (For BWR or BWR-like conditions at relatively low damage levels (e.g. ≈1–10 dpa), irradiation-induced grain-boundary depletion of Cr has been considered by most investigators to be the primary metallurgical process that causes irradiation-assisted stress corrosion cracking (IASCC). Very narrow Cr-depleted zones at grain boundaries have been observed by field-emission-gun analytical electron microscopy (). Furthermore, the results of electrochemical potentiokinetic reactivation tests () and the effects of electrochemical potential (ECP) () on the susceptibility of nonirradiated, thermally sensitized material (where Cr depletion is widely recognized as the primary factor) to intergranular stress corrosion cracking (IGSCC) and on susceptibility of BWR-irradiated solution-annealed material to IASCC during slow-strain-rate tensile (SSRT) tests (However, contrary to expectations based on the strong effect of ECP on SCC associated with grain-boundary Cr depletion, IG cracking of highly stressed components has been reported in PWRs () (which operate at low ECPs), and the susceptibility of PWR-irradiated components () to IG cracking at low ECP has been demonstrated in hot cell experiments (, 10%-cold-worked Type 304 SS specimens were tested in Ar at ≈315 °C after irradiation to ≈7 dpa in a PWR. Although the authors considered that these specimens contained IG-type brittle-fracture morphology on as much as ≈35% of the fracture surfaces, actual high-magnification fractographs do not indicate that they are true IG separation, especially when the fracture surface morphology is compared with clear IG cracking in control rod cladding in PWR water (). However, clear IG cracking in Ar gas or low-DO water has been reported by for thermally sensitized Type 304 SS specimens irradiated to ≈0.4 dpa in water at ≈290 °C in the Japan Material Testing Reactor and tested at ≈290 °C. The IG crack morphology was limited, however, to a small fraction (<5%) of the fracture surface near the specimen free surface, which should contain a high concentration of 0 (due to corrosion during service).If we consider this background, there appears to be no real evidence for the occurrence of clear IG cracking in inert gas or air in solution-annealed austenitic SSs at temperatures relevant to light water reactors (LWRs), at least for Type 304 SS irradiated up to ≈7 dpa. However, as irradiation damage is increased to very high levels (i.e. 20–100 dpa), a very significant microstructural evolution occurs, e.g. extensive Cr depletion and extensive segregation of Ni, Si, and other impurities on grain boundaries, and formation of dense defect clusters, microvoids, and irradiation-induced precipitates in grain matrices. The result is that properties at a very high dose, such as hardening, grain matrix deformation, grain-boundary amorphization, mechanical IG cracking, and susceptibility to IGSCC, could differ significantly from those of steels that have been exposed to relatively low doses of irradiation. Information on these properties helps us to better understand the susceptibility of safety-significant core internals (such as BWR top guide and core plate and PWR baffle bolts) to failure at the end of life. To this end, Type 304 SS specimens that had been fabricated from the hexagonal fuel can of the decommissioned EBR-II reactor after irradiation to ≈50 dpa at ≈370 °C were tested in air and water, and post-test analyses were performed by scanning and transmission electron microscopies (SEM and TEM) to elucidate the failure mechanism(s) at very high doses. Initial tests were conducted at ≈289 °C, whereas tests at ≈325 °C in PWR-like water will follow.The geometry of the specimens for tensile and SSRT tests is shown in . The specimens (nominal wall thickness 1 mm, or 0.040 inch) were machined in a hot cell from the hexagonal fuel can of the EBR-II reactor, which was decommissioned after more than 30 years of operation. The fuel can, fabricated from a commercial-grade solution-annealed Type 304 SS, was irradiated in liquid Na at ≈370 °C to a fluence of ≈1.02×1023 n cm−2 (E>0.1 MeV), which corresponds to a damage level of ≈50 dpa. The average grain size of the as-irradiated specimens was ≈35 μm. No records of the composition of the archive ingot or the as-fabricated fuel can were available. The machined irradiated specimens were ground and polished to remove burrs and surface irregularities, and then, the final width and wall thickness of the specimen gauge section were measured at three locations before testing.Tensile properties and susceptibility to IG cracking were determined by SSRT tests on the specimens at 289 °C in air and in water at a strain rate of 2.5×10−7 s−1. All water tests were conducted at 289 °C in deionized high-purity water that contained ≈8 or ≈0.01 ppm DO. Concentration of DO, controlled by purging the deaerated water with an N2/O2 mixture, was measured on the effluent side. The conductivity and pH of the water at room temperature were in the range of ≈0.061–0.067 μS cm−1 and 6.7–7.1, respectively. The electrochemical potential was measured at the effluent side at regular intervals. Further details of the SSRT test procedure are reported in A post-test fractographic analysis was conducted by SEM to measure the percentage of ductile, transgranular, and IG fracture surface morphologies. One or two disks were carefully cut out of the fracture tips (adjacent to the fracture surface) of the cracked specimen. Thin-foil TEM specimens were jet-polished at room temperature in a solution of 25 ml of perchloric acid, 225 ml of acetic acid, and 50 ml of butylcellosolve. TEM analysis was performed at 100 keV in a JEOL 100-CXII scanning transmission electron microscope. shows engineering stress vs. elongation of specimens that were tested in air and water. Feedwater chemistry (i.e. DO, ECP, conductivity, and pH) and results from SSRT tests (i.e. 0.2% offset yield strength, maximum strength, uniform strain, and total strain) are summarized in . Also shown in the table are the results of SEM fractographic analysis (i.e. ductile, IG, and transgranular fracture surface morphology) of the failed specimens.The highly irradiated steel exhibited a good work-hardening capability and a surprisingly high ductility in air, which is manifested by uniform and total elongations as high as ≈3.5 and ≈4.8%, respectively. The tensile properties of the ≈50 dpa material are shown in , with similar data reported for commercial-grade Type 304 SSs that were irradiated to <5 dpa and tested in BWR-like conditions. The strength of the EBR-II material at ≈50 dpa was significantly lower than that of BWR components at <5 dpa that were tested under similar conditions, i.e. ≈680 vs. ≈850 MPa in yield strength and ≈780 vs. 900 MPa in ultimate tensile strength. This finding is most likely due to the fact that the irradiation temperature of the former material was significantly higher than that of the latter (i.e. ≈290 vs. 370 °C).The fracture surface morphology of the air-tested specimen was entirely ductile (see ); no evidence of IG separation was observed in any part of the fracture surface. Many dislocation loops and microvoids were observed in the material (). However, there was no evidence that microvoids, typically ≈20–60 nm in size, aggregated on grain boundaries. This finding is consistent with the observation that the material did not fail by IG separation in air.Results of TEM characterization of the thin-foil specimen, cut out of the gauge section adjacent to the fracture surface, showed that twinning was the predominant deformation mechanism (see ). Twinned grains exhibited characteristic twin reflections in selected area diffraction patterns (SADs), and clear dark-field images of (111) twins could be obtained by using the twin reflections (In contrast to the deformation behavior in air, in an oxidizing environment of the high-ECP water (ECP +202 mV SHE, DO=8 ppm), the material exhibited negligible work-hardening capability and poor ductility, as evidenced by low uniform and total elongations of only ≈0.5 and ≈2.4%, respectively. Deformation steps on specimen side surfaces were absent. However, as indicated by an IG fracture surface morphology as high as ≈90% in one test and brittle cracking near the shoulder-region hole in another, the material exhibited a high susceptibility to IGSCC (see In the low-ECP water (ECP −318 mV SHE, DO=0.01 ppm), the material exhibited a low work-hardening capability and poor ductility (uniform and total elongations ≈0.7 and ≈2.1%, respectively). However, despite the poor ductility, the percentage IGSCC was negligible, and the fracture surface of the specimen was essentially ductile (see ). No evidence of IG separation was observed, showing that low levels of DO and ECP were effective in suppressing the susceptibility of the heavily irradiated material to IGSCC. The free side surface of the fracture tip was characterized by high-density deformation steps, indicating that localized deformation occurred in the low-ECP water (Despite negligible susceptibility to IGSCC, the ductility of the material was significantly lower in low-ECP water (−318 mV SHE) than in air (i.e. total elongation 2.1 vs. 4.8%). Because this behavior indicates that differing types of deformation mechanisms operate in air and in low-ECP water, a TEM analysis was conducted on disk specimens that were carefully excised from the fracture tips of the specimens. The primary deformation mode in the low-ECP water was dislocation channeling (see ). This is in contrast to the observation that the primary deformation mode of the material in air was twinning. In the low-ECP water, twinning was negligible. Twins and dislocation channels exhibit diffraction behavior and dark-field-imaging characteristics that differ distinctively.In addition to dense dislocation loops and microvoids, the highly irradiated material contained dense irradiation-induced precipitates. These dense precipitates were present in all specimens, showing that they did not precipitate during the tests. Dark-field images showed that short line dislocations were frequently ‘decorated’ with precipitates. Although the precipitates could not be identified conclusively at this time, they were cleared in dislocation channels (). Grain-boundary offsets were also observed (see Results from these experiments show that despite the very high dose level, IG failure did not occur in the EBR-II-irradiated steel in air or in low-ECP water. However, similar to Type 304 SS components or specimens irradiated to ≈2–5 dpa in BWRs, the EBR-II-irradiated steel exhibited extensive susceptibility to IGSCC in high-ECP oxidizing water. Furthermore, as shown in , the effects of ECP and DO on the susceptibility of the ≈50 dpa material to IGSCC are very similar to those of Type 304 SS BWR core internal components. This observation indicates that the stress corrosion process associated with irradiation-induced grain-boundary Cr depletion plays the primary role in BWR-like oxidizing water.Obviously, the results of the present experiment do not support the premise that purely mechanical separation of grain boundaries occurs or is likely to occur in water at very high irradiation doses. The results also indicate that if sufficiently low levels of ECP can be maintained, susceptibility to IASCC could be suppressed by use of proper water chemistry even at the end of life, at least in BWR-like conditions at ≈290 °C.It is not clear why dislocation channeling is promoted, and, at the same time, twinning is suppressed in low-ECP water. It is likely that, as suggested by Bruemmer et al., twins are nucleated only when stress in a grain matrix is sufficiently high and reaches a critical stress . If dislocation channeling is promoted by some mechanism in low-ECP water, then strain hardening will be limited to the dislocation channels or to the immediate vicinity of the channels; hence, it will be more difficult for a grain matrix as a whole to reach the critical stress. This premise, then, implies that at very high levels of irradiation, some factor related to the presence of low-ECP water (e.g. hydrogen uptake or vacancy generation) promotes dislocation channeling. Furthermore, the observation that the fine irradiation-induced precipitates were cleared in dislocation channels indicates that dense irradiation-induced precipitation plays an important role in dislocation channeling.Slow-strain-rate tests at 289 °C and post-test microstructural examination were conducted on material from a Type 304 stainless steel (SS) hexagonal fuel can that was irradiated to ≈50 dpa at ≈370 °C in the EBR-II reactor. Although the irradiation conditions are not completely prototypical, the material would represent a limiting end-of-life fluence for boiling-water reactor (BWR) internal components. The major observations and findings are as follows:No intergranular failures were observed in tests in air at 289 °C. This suggests that intergranular failures cannot occur by purely mechanical processes at <50 dpa.As in the case of BWR internal components irradiated to 2–5 dpa, intergranular failures were not observed in tests in water at low electrochemical potentials. However, virtually complete intergranular failure was observed in tests in water at high electrochemical potentials. These results are consistent with the premise that irradiation-induced grain-boundary Cr depletion plays a major role in irradiation-assisted stress corrosion cracking.In the tests in air, extensive twinning leads to relatively high tensile ductilities in Type 304 SS at 289 °C even at ≈50 dpa.In low-electrochemical-potential water at 289 °C, tensile ductilities were low in spite of the fact that intergranular failures were not observed. The twinning observed in the air tests was negligible, and dislocation channeling was the primary process for deformation and failure in the low-electrochemical-potential water. Dense irradiation-induced precipitation and the presence of the low-electrochemical-potential water appear to play important roles in dislocation channeling.© 2021 Elsevier Ltd. All rights reserved.Processing of bulk nanolamellar tantalum and justification of strengthening by grain boundary pre-stressed modelIn the present work, bulk nano lamellar (NL) structured tantalum is fabricated via a two-step process, through primary grain refinement using equal channel angular pressing (ECAP) followed by a secondary geometrical refinement via rolling at different temperatures. Lamella boundary spacings with ~43 nm and ~62.9 nm after liquid nitrogen rolling (LNR) and room temperature rolling (CR), respectively, are produced exhibiting ~1.2 GPa tensile strength. A grain boundary pre-stress (GBp) model is formulated to explain the deviation of yield strength from the Hall-Petch relationship upon reaching the nanoscale. The GBp model explains the contribution to the rise in interface stress due to pre-existing dislocations at non-equilibrium grain boundaries, assisting the interfacial region to yield at lower stress value than the stress predicted by the confined layer slip (CLS) model. As the lamella thickness decreases with simultaneous increase in dislocation density, a critical value is reached where the interface stress will dominate the CLS stress leading to a fall of yield strength for the NL tantalum. The processing route A (strain path), small strain applied during each rolling pass and the suppression of a restoration mechanism at liquid nitrogen temperature are responsible for the near geometric refinement with a uniformity in the lamella structure. The limited tensile ductility of 90% rolled NL tantalum is associated with the formation of a large dislocation density, a smaller lamella spacing, and evolution of a strong (111)<110> fibre texture due to the body-centered cubic (BCC) crystal structure responsible for the formation of stiffened Σ3 grain boundaries.Severe plastic deformation (SPD) has been an attractive technique for fabricating ultrafine and nanocrystalline materials (), which require complex stress state or extensive shearing (). However, producing nanocrystalline structure in unalloyed material requires controlled SPD conditions and is still a challenge for the scientific community. Maximum refinement is achieved by high pressure torsion (HPT) because the technique involves unlimited straining (). The grain refinement achieved by SPD especially for pure metals is often within the ultrafine grain regime (≥100 nm) due to restoration process i.e. during fabrication, which are sensitive to the deformation temperature and the stacking fault energy of the materials (). With additional straining during SPD, the grain refinement reaches stagnation, where the rate of dislocation generation equals that of dislocation annihilation, as well as the grain refinement equals coarsening. Deformation temperature, strain rate and deformation mode are among the important deformation parameters governing the grain refinement stagnation.Deformation at the liquid nitrogen temperature has been beneficial in mechanically assisted grain boundary migration () and retarding the restoration process by the suppression of dynamic recovery (). Therefore, grain refinement is possible even at lower plastic strain for example Cu () etc. Another effective way to obtain grain refinement is by changing the strain path e.g., equal channel angular pressing (ECAP) followed by rolling at ambient temperature, achieved higher grain refinement (). However, heterogeneous microstructure with finer grains dominated by elongated structure along the maximum principal strain direction was obtained. Homogeneous grain structure can only be attained by avoiding the instability caused by strain hardening during SPD (Excellent mechanical property and thermal stability of Nano lamellar (NL) structure materials are attributed to their low excess energy, less mobile low angle grain boundaries (LAGBs), reduced capillary force of grain boundary (GB) migration and texture pinning (). Due to the reason they have gained much interest lately. Lamellar structured materials with lamella thickness less than 100 nm were fabricated by repeated fold and rolling of foils (), surface mechanical attrition treatment (SMAT) (), surface mechanical grinding treatment (SMGT) () and by accumulative roll bonding (ARB) (). Recently, the bulk nano-laminated commercial purity nickel with ~40 nm lamella thickness was fabricated by a two-step processing technique using ECAP followed by liquid nitrogen rolling (). The NL Ni sample showed ~1.5 GPa tensile yielding strength with ~50 °C higher thermal stability than the ultrafine grained (UFG) Ni (). These insight regarding the fabrication of nano lamellar structure with promising microstructure and mechanical behaviour encourages to fabricate the NL structure to achieve further improvement in their properties. Moreover, the deformation mechanism of body centered cubic (BCC) materials is different in comparison to the face centered cubic (FCC) crystal structured materials (The Hall-Petch relationship is well known to be applicable for conventional materials usually when the grain size >1 μm, in-between 1 μm and 100 nm, it roughly holds the classical −0.5 exponent proportionality between strength and grain size (). In the Hall-Petch model, the grain boundaries act as barriers to lattice dislocation motion, thereby inhibiting plastic flow. During SPD, the dislocation density increases substantially with the plastic strain, contributing significant strengthening in materials. A large number of dislocation density based models have been developed to explain the strengthening of UFG and nano-crystalline (NC) materials processed by severe plastic deformation (). These models are based on the contribution to strengthening by statically stored dislocations (SSG), geometrically necessary dislocations (GNDs), and the modified Hall-Petch relationship and so on (). Moreover, the Hall-Petch relationship further breaks down, when the grain size reduces to a few nanometers, known as the Inverse Hall-Petch relation. This is due to the domination of grain boundary assisted plastic deformation mechanism (). To explain the phenomenon many different theories based on transition of classical deformation mechanism at nanometer scale grain size were proposed such as inverse Hall-Petch relationship, grain boundary sliding and coble creep (Nano metallic multilayer (NMM) structures processed by sputtering with BCC/FCC, FCC/HCP and HCP/BCC layers, which act as a trap to glide dislocation and barrier for slip transfer, were widely studied (). The strengthening mechanism of NMM structured can be related to NL tantalum processed by SPD in the present work. The most widely accepted strengthening model for NMM layer was proposed by . The model explains that NL ≥ 50 nm follows the Hall-Petch relationship, NL with size between 50 nm and 5 nm follows the confined layer slip (CLS) stress needed by a single dislocation loop to glide along the layer, below ~5 nm slip transfer through interface takes place resulting softening (). Other models for softening in NMM ≤5 nm based on Kohler stress, misfit dislocations, chemical stress, coherency stress and interface energy (heat of mixing) were also proposed (). However, strengthening model which could contribute to unusual strength and deformation behaviour of SPD processed NL structured by classical deformation mechanism constituting grain size and dislocation density dependence is still absent.Hence, in the present work, Bulk NL structured tantalum is fabricated with distinctive lamellar thickness by processing at room temperature and liquid nitrogen temperature after ECAP. The physics behind grain refinement, structure features and higher mechanical properties in BCC structured NL tantalum is investigated. The cause of deviation of NL tantalum from the Hall-Petch relationship with reduction in lamella thickness is explained by grain boundary pre-stress (GBp) model.NL tantalum was fabricated using two step procedure comprising of ECAP for physical grain refinement followed by geometrical refinement by rolling at different temperatures (). Tantalum with 99.9% purity was procured with the chemical composition shown in . Samples with 12 mm × 12 mm × 80 mm dimension were subjected to ECAP (Channel angle 90° and 20° corner angles) via route A up to eight passes (ε~8) at room temperature. The ECAP processed samples were subsequently rolled at room temperature (CR) and liquid nitrogen temperature (LNR) along the extrusion direction of the ECAP sample by reducing their thickness up to 90% (true strain ~2.3). The samples were immersed in water and liquid nitrogen for 5 min prior to every rolling pass for CR and LNR, respectively. To reduce adiabatic heating multiple rolling passes were applied during rolling and average reduction of ~0.5 mm in each pass. The theoretical geometrical refinement () was calculated using the equation as followsWhere, dgeo is the theoretical lamellar thickness according to geometrical refinement rule, do is the initial grain size before rolling, and ε is the true strain of the rolling. The samples were stored at room temperature for further characterisation using electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), tensile and micro hardness testing.EBSD samples were prepared by polishing on emery papers up to 1200 grit size followed by electropolishing in electrolyte solution consisting 90% sulphuric acid and 10% hydrofluoric acid at 45 °C for 10 min using 15 V electric potential. EBSD with a step size of 50 nm (ECAP samples) and 25 nm (CR and LNR samples) was performed using AURIGA cross-beam scanning electron microscope (SEM) with oxford EBSD detector. The orientation mapping was gathered using channel 5 software package and by using the open source analysis tool for electron and X-ray diffraction (ATEX) developed by the University de Lorraine (). Orientation maps were reconstructed by eliminating the spurious boundaries with ≤ 2° misorientation. The CSL boundaries were characterised by selecting deviation tolerance angle of ±4°.A tecnai G2 T20 operating at an acceleration voltage of 200 kV was used to perform TEM. Thin foils of 0.1 μm were prepared by mechanical grinding followed by twin-jet polishing using an electrolyte of 12.5% sulphuric acid and 87.5% methyl alcohol at −30 °C temperature.Dog bone samples with 10 mm gauge length, 2.5 mm width and ~2 mm thickness (~1.2 after 90% rolling reduction) were used to perform tensile test using UTM 5105 SLXY-H tensile testing machine at ~10−4 s−1 strain rate. Three tensile specimens for each condition was tested to ensure the repeatability in results. Micro hardness was performed using HMV-G micro Vickers hardness tester machine with minimum 10 indent for each condition.The EBSD image of tantalum after 8 pass ECAP via route A is shown in (a). The elongated grains aligned along the extrusion direction, consisting of ~63% high angle grain boundaries (HAGBs, θ ≥ 15°) ((b)) are obtained. Processing by route A cause continuous grain distortion with every pass inclined along the axis of the ECAP die (). High melting point inhibits dynamic recrystallization () as a consequence elongated grain structure is obtained, also evident from (a). The inclination angle of the grains after ECAP via route A depends upon the number of passes, the higher the number of ECAP passes the lesser will be the inclination along the extrusion direction (). The width of the elongated grains (221 ± 51 nm) obtained in the present work is close to the reported grain thickness (200 nm) processed by ECAP route Bc (). Moreover, the processing by route A results in the development of strong fibre texture due to repeated deformation along the same element direction (). The evolution of fibre texture is evident after comparing experimental and ideal (110) pole figure ((c). The details of the fibre texture developed after ECAP and its component are elaborated in section The microstructure obtained after performing 90% CR and 90% LNR is shown in . Elongated grains with strong texture and an average lamella spacing of 62.9 ± 3.8 nm and 42.9 ± 4.1 nm after 90% CR ((d–e)), respectively, can be seen. The lamella thickness is similar with nanolamellar thickness obtained in nickel using the same processing technique somewhere else ( achieved nanostructured tantalum with an average grain size of ~35 nm by using HPT. The selected area diffraction pattern in the inset of shows strong texture along (111) direction, also evident from (a) and (d). The fractograph obtained from the failed tensile specimen of 90% CR ((f)) sample shows dimples and cleavage lines, respectively. Dimples are formed during plastic flow in the material, while the presence of cleavage lines are due to brittleness.The distribution of lamella boundary spacing after 90% CR and 90% LNR is shown in (a). After LNR maximum thickness of lamella is < 100 nm while, few fraction of lamellas with thickness >100 nm after CR are evident. The theoretical geometric refinement () plot, calculated from lamellar spacing of ECAP (Av. spacing~221 ± 51 nm) sample, shows average lamella thickness after 90% rolling should be 23.5 ± 5.3 nm. With the rise in deformation strain, the coarsening of boundary spacing compensates the refinement mechanism of grains. This state of equilibrium between the refinement and dynamic recovery will be responsible for the final grain size (). Since, rolling at cryogenic temperature suppresses dynamic recovery (), the lamellar thickness and geometric refinement curve on LNR tantalum follows a close-to-linear trend as evident from (b). The average lamella thickness after 90% LNR and 90% CR is 42.9 nm and 63 nm, respectively.The fraction of HAGBs after ECAP (62.8%) increased to 67% after 90% LNR and 70.9% after 90% CR as obtained from misorientation distribution shown in (c). The presence of Σ3 (60°/[111]) boundaries in CR (7.9%) and LNR (9.4%) sample are also observable from misorientation profile ((c)). However, no trace of twining from microstructure of NL tantalum was discovered from microstructure (The increase in dislocation density with plastic strain via CR and LNR can be computed by the local orientation distribution determined at individual points along a regular grid on a planer surface from the EBSD images (). The kernel average misorientation (KAM) values are evaluated by only considering the local variations in misorientation between 0° to 5° of a nearby indexed point (). Therefore, the local variation in misorientation with 5° will have highest KAM value. The dislocation density is calculated using the following equationWhere, β is the constant depending on the geometry of dislocation arrangements. The Value of β is taken as 2 for tilt and 4 for twist boundaries. Since, the deformation of BCC materials at low temperature takes place by screw dislocations (). The value of β is taken as 4 because only twist boundaries will be formed (). θ is average KAM value in degrees, b (0.289 nm) is the burger vector and ψ is step size (0.05 μm for ECAP and 0.025 μm for rolled samples). The dislocation density after CR and LNR to different reductions by using eqn. The average Dislocation density stored during rolling of tantalum at different temperature is plotted in (d). A linear increment of dislocation density with decreasing lamella thickness can be seen. the dislocation density 90% CR (63 nm lamella spacing) and 90% LNR (43 nm lamella spacing) is 1.27 × 1016/m2 and 1.41 × 1016/m2, respectively. The dislocation density of ECAP and HPT nanocrystalline tantalum has been reported to be of the order of 1015/m2 and 1016/m2, respectively (). Hence, the obtained dislocation density is well in agreement with these literatures.The hardness increases linearly with decreasing lamellar thickness as shown in (a). The hardness increased from 240 HV to 310 HV after 90% CR, while to 330 HV after 90% LNR. The stress-strain curve of CR and LNR tantalum with different rolling reduction can be seen from (b and c). The enhancement of strength with decreasing lamellar thickness from 846 MPa to 1210 MPa after 90% CR ((c)) can be seen. Deformation at low temperature supresses dynamic recovery there by increasing dislocation accumulation inside the grains. As a consequence, strength and hardness after CR and LNR increases, while ductility is compromised. Additionally, reducing lamellar spacing also contribute to strengthening. Moreover, on comparing the strength with the Hall-Petch relationship, yield strength does not follow (grain size)−1/2 proportionality. The curve deviates from the expected linear relationship as can be seen from (d). The initial yield stress and slope of the linear part of the Hall-Petch curve are consistent with previous investigation (), which might be due to same purity (99.9% pure tantalum) of tantalum used in both the works.Although, strength has increased two fold in the nano lamellar structured sample compared to the coarse grained sample (), sudden fall of ductility (failure after 3.5% for LNR and 4.6% for CR) with uniform tensile elongation after 90% rolling reduction is observed from (b and c). The ductility inside a severe plastically deformed materials is governed by Dislocation density, grain size and grain boundary mobility. After SPD, the high dislocation density is stored inside the microstructure consisting of grain with LAGBs and high energy HAGBs. The high dislocation density restricts the motion of newly developed dislocation. While, there is less possibility of dislocation pileup within smaller grains. Moreover, as the grain size decreases, domination of grain boundaries on deformation mechanism increases. The increasing fraction of HAGBs for all lamellar thickness after CR and LNR to different rolling reductions are shown in . High energy HAGBs are more prone to dislocation accumulation, dislocation absorption and dislocation nucleation, thereby acts as a sink and source to dislocations (). The uniform elongation must be due to dynamic balance between dislocation generation and dislocation annihilation during tensile testing. Additionally, stored dislocation density and increasing strain during tensile testing, contribute to excess dislocations which account for loosing dynamic balance between generation and absorption of dislocations (). However, after 3.5% (90% LNR) and 4.6% (90% CR) uniform elongation, sudden failure of tensile specimen takes place. Failure at tensile strength means no necking or localised elongation, exhibiting limited grain boundary motion during tensile testing. Different types of grain boundaries such as LAGBs, ordinary boundaries or HAGBs and special boundaries or coincidence site lattice (CSL) boundaries have different mobility during straining. HAGBs have higher mobility than LAGBs, since they are of high energy in nature, contributing plasticity in materials. On the contrary, special or CSL boundaries are of low energy and less mobile in tantalum (). LAGBs are also low energy in nature and contribute mostly to hardening. However, slip transfer can take place at high value of stress (). On investigating from EBSD, different significant CSL boundary () fraction after LNR and CR can be seen from (a and b). Σ3 boundary fraction has increased significantly, while no substantial change in fraction of other type of CSL boundaries after 90% rolling is observed. Therefore, the sudden fall of ductility is attributed to increasing fraction of Σ3 boundaries (), dislocation density and decreasing lamella spacing with rolling strain. The Hall-Petch deviation and evolution of Σ3 boundaries by severe plastic deformation is explored in details in the discussion section.The texture of ECAP tantalum after 8 pass by route A is displayed by (110) pole figure and ideal ECAP texture after single pass are shown in (c). The texture components of BCC tantalum are distributed along b1, b2 and b3 fibres displayed by the ODF plotted along φ (0° to 180°), due to monoclinic sample symmetry, as shown in . The b1 fibre belong to consist of Dθ−Eθ−Dθ⟨111⟩θ fibre, b2 contains Fθ−Jθ−Eθ {110}θ and Eθ−D‾θ⟨111⟩θ partial fibres and b3, which is symmetrical to b2, contains Fθ−J‾θ−E‾θ {110}θ and E‾θ−Dθ⟨111⟩θ partial fibres [36]. The Euler orientations of Fθ,Jθ,J‾θ,Eθ,E‾θ,Dθ,D‾θ are shown in ). It can be depicted from pole figure () that the partial fibre Fθ−J‾θ−E‾θ {110}θ with maximum orientation density f(g) = 22.1 near J‾θ orientation and b2 fibre are the main component. The results are similar to the reported literature by . The minor deviation of the components from the ideal orientation can be attributed to the micro texture measurement as compared to bulk texture measurement used in the reported literature (The BCC structures tend to form fibre texture after rolling and recrystallization. The texture orientations comprise mainly of α fibre with ⟨110⟩parallel to rolling direction and γ fibre with ⟨111⟩along the normal direction of rolling plane (). The α fibre begins from {001}⟨110⟩ to {111}⟨110⟩with {112}⟨110⟩in-between, while γ fibre starts from {111}⟨110⟩to {111}⟨112⟩. All these orientations including fibre can be obtained from φ2 = 45°, therefore ODF representations of CR and LNR tantalum confined to the mentioned φ2 section is depicted as shown in (b), respectively. After 90% rolling of tantalum, γ fibre is more prominent as evident from (a and b). A few degree deviation of γ fibre orientation can be attributed to limitation to area measured by EBSD. The grains in 90% CR tantalum are more pronounced towards (111)[011] (36% fraction by volume) and (11 11 8)[4 4 11](26.4% fraction by volume) orientations, while small fraction of (001)[110], (211)[110] and (111)[112] equivalent to 11% fraction by volume each followed by (110)[110] having 2.3 percent orientations. On the contrary, LNR tantalum have more prominent grains orientation along (111)[011](39.6% fraction by volume) and (111)[112](32.7% fraction by volume) followed by (112)[110] (11.2% fraction by volume), (001)[110] (5.6% fraction by volume) and (11 11 8)[4 4 11] (1.8% fraction by volume). The present texture characteristics are similar with the observed 87% cold rolled tantalum (The results explained above exhibit the technique for producing bulk NL tantalum using an ordinary approach. The strange behaviour of the Hall-Petch relationship, uniformity in lamellas and sudden fall in ductility are some of the important phenomenon, which are explored further in the discussion.The yield strength of polycrystalline materials is proportional to the inverse of the square root of average grain size (d−1/2) during deformation, well known as the classical Hall-Petch relationship (). Alternatively, the equation can be understood as when a leading dislocation of a pile up penetrate through a grain boundary into an adjacent grain, the stress ahead of the dislocation should be higher than the critical stress barrier of the grain boundary (). The Hall-Petch relationship will only be applicable when the number of pile up > 6 for single ended, >3 for double ended and >2 for circular dislocations as obtained by elasticity based calculations and is incapable to predict the yield strength, when the number of the dislocation pile is N ≤ 2 (). With the decrease in grain size the pile-up at the grain boundary will diminish, consequently the Hall-Petch relationship deviates from the proportionality of the inversed square root of average grain size, as shown in The confined layer slip (CLS) mechanism (), where glide of single Orowan loop bounded by two interfaces, was developed for predicting plastic yielding of thin film and substrate (). However, it under predicts plastic yielding (), resulting in development of other modified models to predict the yield stress of semi-coherent and coherent systems (). The similarity between NL tantalum and nanostructured film by electrodeposition can be utilized to develop dislocation based model predicting the yield strength using the CLS model.The energy balance equation for applying a shear stress (τ) to propagate a dislocation of burger vector ‘b’ for a unpassivated confined grain boundary (Where, h is lamella thickness and W is the energy of dislocation formed at the interface. For an CLS event, the energy required to form a screw dislocation (, shear stress for a CLS event (τcls) can be obtained asWhere, μ is the shear modulous and α is core cut-off parameter (). On substituting μ = 63700 MPa, b = 0.289 nm, α = 1 for compact core. Multiplying the shear stress value with Taylor factor 2.7 for BCC materials, yield strength can be obtained. The obtained yield strength value is under predicted in comparision to the experimental results, as shown in (a). This observation has also been reported earlier () and further improvement in the model is needed.During severe plastic deformation, dislocation density increases, while the grain size decreases with strain. The non-equilibrium grain boundary formed by severe plastic deformation in UFG and NC materials could have large dislocation density near them (). On applying strain, these boundaries will act as a source of lattice dislocations (). Secondly, the grain boundary has characteristic interface stress (). The pre-existing dislocations at the non-equilibrium grain boundary will arise the interface stress. Due to the implication, interfacial region will be pre stressed and could assist the grain boundary (GB) to yield at lower stress value than predicted by the CLS mechanism. Therefore, the stress generated by pre-existing dislocations over the gliding dislocation loop on the same plane would scale down the stress, needed by the grain boundary to form a new dislocation. The interaction energy between two infinitely long dislocations can be used to compute stress at the grain boundary (interfacial shear stress). The interaction energy between two parallel screw dislocations can be written (Where, λ is the distance between dislocations, can be computed by taking the inverse of the square root of the dislocation density. Since, energy computed by eqn. is for two dislocations, for a single dislocation it can be divided by 2. After dividing and equating eqn. , the interface shear stress (Iss) can be calculated asTherefore, the total stress needed to form a new dislocation loop with pre-existing dislocations on the gliding plane in severe plastically deformed materials can be computed by subtracting the interface shear stress from the CLS shear stress asand after multiplying shear stress ‘τTotal’ with the Taylor factor ‘M’ to obtain normal in-plane stress ‘σTotal’, the equation can be written asOn substituting the value of dislocation spacing, large difference between interface shear stress and CLS stress values can be seen (b). The value of yield stress (σTotal) in is very less because the dislocations considered are isolated glide dislocations without any obstacles in their path. As the dislocation loop glide forward during straining, the pre-existing array of misfit dislocations will interact with the stress field of dislocation loop.With increasing strain, the newly formed dislocation loop during gliding will interact with stress field of the stored array of pre-existing dislocations deposited at the interface. The gliding dislocations will react with the pre-existing dislocations to form new dislocations or form kinks and jogs. In simple form, stress field created against the applied stress to move a dislocation in the array with spacing λ and with screw character can be written as (Where, X and Y are the normalised distance with X = x/λ and Y = y/λ, x and y are the distance towards normal and along the dislocation array, respectively. At small value of x/λ, the stress of eqn. leads to μb/2λ. After adding the stress value approximating the resisting force along the dislocation array to eqn. , Grain Boundary pre-stress (GBp) model is obtained asThe model shows the effect of interfacial pre-stress at the grain boundary generated by pre-existing dislocation density played a crucial role in strengthening of the NL tantalum, which is the reason to be named as the Grain Boundary Pre-stress (GBp) model. With increasing strain, the dislocation density increases and thereby value of λ decreases. On substituting the values of average Taylor factor (M) equal to 3 due to pronounced (111) texture observed in the present work (). By taking the experimental lamella thickness, the value of “λ” is curve fitted and matched to the yield strength using eqn. (c). The λ is the dislocation spacing computed from the dislocation density (ρ) as λ = 1ρ. A good fit between the experimental values and the theoretical values is obtained after curve fitting as shown in (d). The model also validate the strengthening of tantalum processed by HPT ((c and d). The model concludes that apart from the grain size, the strengthening of materials depends upon the dislocation density accumulated inside during deformation., when the value of lamella thickness and dislocation spacing becomes equal, the left side of equation becomes zero. This means that as the grain size decreases, the strength will also decrease after reaching a critical grain size also observed as the Inverse Hall-Petch relationship. For example, in case of 20 nm and 10 nm lamella spacing, fall of yield strength ((c)) is observed after assuming constant λ i.e., maximum dislocation density achieved by tantalum after 90% LNR.Early models were separated in two parts, positive Hall-Petch slope (i.e., based on dislocation pile-up, the GB acting as a source for dislocation, geometrically necessary dislocations, slip distance) () and negative Hall-Petch slope (grain boundary sliding, cobble creep) (), which were also dependent on the grain size and dislocation density. Altogether, these models have been verified extensively on many materials, but no unified model explaining both positive and negative Hall-Petch slope has been developed. The present model is developed only for tantalum, but a generalised GBp model applicable for all the materials can be derived using the present understanding.The rolling after ECAP of materials have been reported by various researchers in the past (). However, the microstructure obtained after rolling above 70% reduction does not show any homogeneity (). During repeated rolling up to higher thickness reductions due to dislocation pileup, instability creates local hotspots and consequences to nonlinearity in material flow (). Hence, either grain refinement or heterogeneity in microstructure is obtained. Rolling coarse grained bulk materials to large plastic strain impart stress concentration at 35° along the rolling plane forming shear bands (). Shear bands are formed due to decrease in the thickness of disoriented dislocation cells with strain and thereby coinciding with each other (). These cells develop texture to slip in a cooperative manner, probably facilitation shear localisation along the maximum shear direction during plastic deformation (). Hence, unstable plastic flow takes place to form shear bands.Also, the deformation of a BCC material is different compared to FCC materials (). BCC materials show 3 stage hardening in both tension () behaviour with temperature. With the decrease in grain size the strength of tantalum increases, while strain hardening and strain rate sensitivity decrease (). Also, after ECAP and HPT the dislocation density of tantalum is found to be of the order of ~1015/m2 to ~1016/m2 (). This makes ECAP processed tantalum more acceptable to shear localisation () compared to coarse grained during LNR. Recent studies showed shear band formation in nano-lamellar nickel (FCC) processed by similar method (). However, in the present work no evidence of shear localisation after rolling of ECAP tantalum is observed.There are few possible explanations for not observing the shear bands in NL tantalum. First, the selection of processing ECAP route A, which produces dislocation cells () aligned along the deformed grains. Since, the shear profile of ECAP route A remains identical (), dislocation cells formed will be aligned at the same angle leading to strong texture and elongated structure ((a)). The aligned dislocation cells during rolling of ECAP tantalum might have restricted the plastic flow along the shear direction thereby producing uniform lamellas also evident from TEM microstructure reported that if stress strain curve during deformation develops a negative slope, homogeneous deformation is no longer the stable response. The lower thickness reduction will assist formation of homogeneous microstructure. Moreover, to achieve homogeneous microstructure in rolling, spacing between grain lamellas and change in billet shape during rolling should have the same ratio. This would be possible only when a balance between strain hardening caused by generation of dislocation and dynamic recovery is achieved. However, during LNR thermally activated restoration process is suppressed resulting higher dislocation density () as compared to CR tantalum. Also, during LNR, the mechanically induced grain boundary migration assisted formation of equilibrium boundaries without any fragmentation in tantalum (). Deformation at room temperature account for inappreciable restoration, consequently deviating lamella spacing from theoretical value.It is well documented that with the increase in strain, the ductility of the material decreases and strength increases can be seen from (b and c). However, on reaching to 90% rolling reduction, there is a sudden failure of tantalum. The misorientation profile ((c)) of CR and LNR tantalum shows 7.9% and 9.4% Σ3 boundaries, respectively. However, no twins are observed from EBSD as well as TEM microstructure already mentioned in section . The EBSD band contrast image highlighting Σ3 boundaries aligned parallel to the lamellas can be seen from (a and b) for CR and LNR tantalum, respectively. These Σ3 boundaries have low energy and are less mobile compared to ordinary boundaries (). Moreover, Σ7, Σ11, Σ13 and Σ27 CSL boundaries also have low energy grain boundary structures (Hahn et al., 2017), still no substantial deviation in their fraction after different rolling reductions of tantalum is observed ((a and b)). Therefore, the increasing fraction of Σ3 boundaries is also accountable to the fall in ductility of 90% rolled tantalum. It can be observed from (a and b) that the critical length fraction of Σ3 boundaries affecting the ductility NL tantalum is ~8%.To perceive the evolution of Σ3 boundary during deformation, local texture from EBSD measurement after 60% and 90% rolling reductions were analysed. Drastic increase in the fraction of Σ3 boundaries after 90% rolling reductions can be seen from (a and b). The ideal texture (110) pole figure for Σ3 boundaries is shown in ). There are many grain orientation relationships to form Σ3 boundaries in materials (). However, the most prominent orientation in the present work is 60° orientation between (111)<110> crystal. The more fraction of grain having pronounced (111)<110> orientation in a polycrystalline material after deformation, the more will be the probability to form Σ3 boundary. The pole figures corresponding to (110) plane after 60% and 90% Rolling at room temperature and liquid nitrogen temperature are shown in (b–e), respectively. The fraction of grains aligned towards (111)<110> direction are 4.1% and 6% after 60% LNR and 60% CR, respectively. While, after 90% LNR and 90% CR, the fraction of grains aligned towards (111)<110> direction are 39.6% and 36%, respectively. Consequently, more grains aligned towards (111)<110> increases the probability to form Σ3 boundaries. Moreover, it can be concluded that with the increase in plastic strain, as more and more grains align themselves along (111)<110> direction. The grains will rotate themselves to least energy orientation and thereby further favouring Σ3 grain boundary formation. also reported the formation of Σ3 in interstitial free steel due to recovery mechanism during equal channel angular extrusion, favouring low energy orientation. Other type of low energy CSL boundary does not evolve due to formation of (111) texture.NL tantalum was fabricated from primary grain refinement by ECAP, followed by secondary geometrical refinement via rolling at liquid nitrogen and room temperature. A GBp model was developed, which shows that high dislocation density and lower lamella thickness are responsible for the deviation from −0.5 exponent proportionality (the Hall-Petch relationship). The following conclusions can be drawn after analysing the microstructure and mechanical behaviour of NL tantalum.The GBp model shows the contribution to the rise in interface stress due to pre-existing dislocations at non-equilibrium grain boundaries, assisting the interfacial region to yield at lower stress value than the stress predicted by the CLS model. As the lamella thickness decreases with simultaneous increase in dislocation density, a critical value is reached where the interface stress will dominate the CLS stress leading to a fall of yield strength. Since, the applied stress needed would only be required to overcome the obstacles faced by the dislocation while gliding.A possible explanation for the sudden fall of ductility after 90% rolling reduction can be correlated with the formation of Σ3 boundaries, apart from high dislocation density and decreasing lamella spacing. The alignment of texture along (111)<110> direction (as predictable in BCC metals) increases the probability for Σ3 boundaries formation.Primary grain refinement by ECAP route A, low applied strain during each rolling pass, mechanically assisted grain boundary migration at liquid nitrogen temperature, and suppression of restoration processing are reasons responsible for the formation of uniform NL structured tantalum, close to the theoretical lamella spacing. The obtained tensile strength is of the order of ~1.2 GPa.The present GBp model is derived after considering the mechanics of dislocation (screw) motion in tantalum. However, using the same principal with minor modifications, a universally applicable GBp model should be possible which will be applicable to materials having different lattice structures.Sunkulp Goel: Conceptualization, Conception and design of study, Formal analysis, Analysis and/or interpretation of, Data curation, data, Writing - original draft, Drafting the manuscript, Revising the manuscript critically for important intellectual content, Approval of the version of the manuscript to be published (the names of all authors must be listed). Y. Wang: Funding acquisition, Acquisition of data, Approval of the version of the manuscript to be published (the names of all authors must be listed). Y.M. Zhu: Funding acquisition, Acquisition of, Data curation, data, Approval of the version of the manuscript to be published (the names of all authors must be listed). Y. Liu: Acquisition of, Data curation, data, Approval of the version of the manuscript to be published (the names of all authors must be listed). J.T. Wang: Conceptualization, Conception and design of study, Formal analysis, Analysis and/or interpretation of, Data curation, data, Writing - original draft, Drafting the manuscript, Revising the manuscript critically for important intellectual content, Approval of the version of the manuscript to be published (the names of all authors must be listed).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.Simultaneous improvement of mechanical strength, ductility and corrosion resistance of stir cast Al7075-2% SiC micro- and nanocomposites by friction stir processingPresent work investigates the mechanisms of simultaneous improvement of tensile properties, wear properties and corrosion resistance of stir cast Al7075–2 wt.% SiC micro- and nanocomposites through microstructural refinement by friction stir processing (FSP). Optical, scanning and transmission electron microscopy were used to investigate the microstructural evolution. After the FSP, the nanoparticles reinforced composite showed better mechanical properties than that of the microparticles reinforced composite. Tensile strength ( >3 times) and wear resistance were found to increase significantly with simultaneous enhancement of the ductility (10 times). The improvement is ascribed to the grain size reduction, distribution of SiC nanoparticles uniformly within the matrix, increase particle-matrix interface characteristics and elimination of casting defects such as porosity after the FSP. The corrosion potentials of the as-cast composites were found to shift towards noble direction after the FSP. Enhancement of corrosion resistance after the FSP is attributed to the decrease in the heterogeneity on the surface and uniform dispersion of the reinforced particles, which reduced the effective active surface area exposed to the corrosive solution. All such beneficial effects were found to be superior for the nanoparticles reinforced composite due to the improved particle/matrix interface characteristics and dispersion strengthening.Aluminum (Al) alloys are mostly used in structural, aerospace, military and automobile sectors due to their excellent specific strength, high stiffness and outstanding corrosion resistant The FSP technique was originally proposed by Mishra et al. However in a single study, stir casting of Al alloy reinforced with micron- and nanosize particles followed by FSP to modify the microstructures has not been investigated yet. Therefore, in this work, attempts have been made to develop Al7075–2 wt.% SiC micro- (size 20–60 μm) and nanocomposites (size 30–80 nm) using stir casting technique followed by FSP. Aim of the FSP is to modify the cast microstructure thereby enhancing its mechanical strength, ductility, wear resistance and corrosion resistance simultaneously for its practical applicability.Micron size SiC powder (Alfa Acer, average size 20–60 μm) was ball milled in a tungsten carbide grinding media using a planetary mill Pulverisette 6 (Fritsch) for 25 h to produce nanosize SiC particles (30–80 nm). The rotation speed of the mill was set at 300 rpm and the ball to powder mass ratio was kept at 15:1. As a process control agent, toluene was poured in the vial before milling. Subsequently, after the milling, size of the SiC particles was examined by transmission electron microscope (TEM). The TEM sample was prepared first by dispersion of small amount of ball milled powder ultrasonically in methanol and then a drop of the dispersed liquid was drop cast on to the carbon coated copper grid of 3 mm diameter using a micro-pipette and allowed to dry up. After that, the sample with carbon coated copper grid was placed within the TEM for the analysis.Al based composites were produced in a bottom pouring stir casting machine. The experimental set-up used in the production of the composites was already shown in our previous work S as a supplementary material. The FSP was conducted at room temperature without using any coolant. The FSP conditions were kept same for both micro- and nanocomposites for comparisons.Microscopic investigation of the as-cast and friction stir processed (FSPed) composites was carried out using an optical microscopy (Leica DMI 5000 M), scanning electron microscopy (FEI-Quanta 200FE-SEM) and TEM (FEI Technai 20 G2S-Twin TEM). Transverse sections of the FSPed (nugget) zone were taken for microstructural investigation. Standard metallographic procedures were followed to prepare the metallographic samples. Keller’s reagent was used to etch the prepared samples for optical microscopy. TEM was used to investigate the distribution of the SiC nanoparticles in the matrix and other morphology of the nugget zone of the FSPed nanocomposite. The TEM samples were made first by paper polishing of the samples to produce 100 μm thin foil and then 3 mm circular discs were extracted from the foil by Gatan punching system. Electropolishing of the disc specimens was carried out in a solution of nitric acid (30%) + methanol (70%) at −15 °C and 30 V using an FEI twin jet electropolishing unit. The detailed microstructural investigation was carried out using FEI Technai 20 G2S-Twin TEM. Vickers hardness values were measured by applying a constant load of 5 kg for a 15 s dwell time. An average of 6 readings was reported for each hardness value. The uniaxial tensile tests were conducted (Tinius Olsen: H25KS) at a crosshead speed of 1 mm/min at room temperature. For tensile test, sub-size tensile samples with a gauge length of 12.5 mm (ASTM: E8) were prepared from the nugget zone of the FSPed composites (). To ensure the tensile results, minimum 3 tensile samples were tested for each condition. After the tensile test, fractured surfaces were investigated using SEM to correlate the tensile ductility of the corresponding sample.The wear characteristics of the as-cast and FSPed composites were investigated using a pin-on-disc tribometer (DUCOM: TR-201E-M2). A wire electric discharge machining was used to extract the cylindrical specimens of 4 mm diameter from the as-cast and FSPed plates. A specially designed and fabricated specimen holder was used to hold the wear pin (which is the sample itself) against the rotating counter body (made of EN 31 steel having 0.2 μm surface roughness & 65 HRC). The samples were polished using different emery papers (up to 1500 grit size). The specimen weight was measured by using an electronic weighing balance (ML204/A01, METTLER TOLEDO, Switzerland) with a least count of 0.0001 g. All the tests were conducted by applying a normal load of 20 N and sliding speed of 1.674 m/s for a period of 27 min maintaining a constant track radius of 40 mm. After completion a sliding distance of 2000 m, the samples were cleaned with acetone. The dried samples were weighed to calculate the mass loss due to wear. The frictional force to the applied normal load ratio is taken as the friction coefficient. The abraded surfaces were further characterized by using SEM to analyze surface morphology and to investigate the wear mechanisms.. The polarization measurements were carried out from potentials more negative to more positive with reference to the OCP measured at a scan rate of 0.2 mV/s. The current density, icorr and potential, Ecorr were determined from the corresponding polarization plot using Tafel extrapolation method. On the polarization curve, straight line portions of the anodic and cathodic curves were extrapolated and the intersection point of the extrapolated lines gives icorr and Ecorr values Prior to incorporation of micron- and nanosize SiC particles into the molten metal, SEM and TEM analysis have been carried out to examine the size and morphology of micron- and nanosize SiC particles. a,b represent the SEM and TEM images of the as-received (micron size) and ball milled (nanosize) SiC particles. It is observed that (a) the as-received SiC particles have sizes in the range of 20–60 μm. However, the TEM analysis revealed that the average particle size of the ball milled SiC powder is in the range of 30–80 nm (b). An energy dispersive x-ray spectroscopy (EDS) analysis (shown in the inset of b) has been carried out on such particles and approximate quantitative analysis of the particles shows ∼54at.% carbon (C) and ∼46at.% silicon (Si). The approximate stoichiometry of these elements confirms these as SiC particles. The as-received SiC powders were used to produce Al7075-2% SiC microcomposite (MC), and the nanosize SiC powders were reinforced to produce Al7075-2% SiC nanocomposite (NC) both by stir casting process. The SEM micrograph of the as-cast MC and NC, respectively are shown in c & d were recorded after proper etching with the Keller’s reagent. Since c & d are the images of cast micro- and nanocomposites, the grain boundary is not properly developed/revealed in the as-cast state. However, it can be seen from c and d that SiC particles (both micron- and nanosize) are segregated along the interdendritic region and distribution of the particles seems to be inhomogeneous in the as-cast condition. Both the as-cast composites are observed to be a dendritic structure with some casting defects, such as porosities. Formation of the porosity in the stir cast AMCs can be accredited to the poor wettability of the reinforced particles (i.e. SiC) with the melt and air entrapment between the particles e and f show the magnified SEM images with EDS analysis of the MC and NC, respectively. The agglomeration of both micron and nanosize SiC particles at grain boundary area could clearly be seen in the highly magnified micrographs. The EDS peak analysis obtained from the encircled areas of the e and f also confirm the presence of SiC particles in agglomerated form. During solidification, SiC particles are pushed ahead by solidification front, so micron- and nanosize SiC particles predominantly located in the interdendritic regions in both the as-cast composites. To identify the distribution of micron and nanosize SiC particles in the as-cast composites, SEM-EDS elemental mapping (for Al, Si and C elements) was carried out for both micro- and nanocomposites. represent the microstructures along with elemental mapping for the C, Si and Al of the NC and MC, respectively. The elemental mapping shows that the distribution of C and Si are denser at grain boundary areas for both the composites, which indicates the inhomogeneous SiC particles distribution in the as-cast conditions. In , the presence of C rich zones than that of the Si may be due to the experimental factors such as C contamination from the carbon-tape used for sample mounting and adjacent Kα lines overlapping of C, nitrogen (N) and oxygen (O) (N, O present as residual gas). The NC showed a quite finer grain size than that of the MC. Average grain size of the MC is ∼190 μm (d). This can be ascribed to the existence of nanosize SiC particles in the melt, which provide more nucleation sites and consequently finer grain structure was developed in comparison to that of the MC. Some researchers also reported the similar observation in their works In order to improve the particles distribution, the as-cast composites were subjected to FSP using the parameters described in ‘Material and experimental procedure section’. a,b show the microstructures of the FSPed micro- and nanocomposites, respectively. It can be noticed that the FSP leads to the significant breakdown of the dendritic cast structure, develop a uniform dispersion of SiC particles and complete elimination of casting defect. displays the magnified SEM images and corresponding elemental mapping of Si, C and Al of the FSPed micro- and nanocomposites, respectively. By comparing the EDS mapping images and the corresponding SEM image of the FSPed MC (), it can be seen that the micron size SiC particles are more or less evenly distributed in Al matrix after the FSP (except a large SiC particle in the central region) as compared to the cast MC () the reinforcement particles are uniformly distributed and no elemental (i.e. C and Si) rich zone has been detected. This validates homogeneous distribution of SiC nanoparticles after the FSP. Moreover, magnified SEM images of the FSPed composites in Figs. a clearly reveal that the casting defects are almost eliminated after the FSP. This is attributed to intense plastic deformation and frictional mixing, which led to the dynamic recrystallization in the nugget zone a,b), a considerable decrease in the grain size could be observed for both the composites (micro- and nanocomposite) after the FSP. The grain size was determined through linear intercept method using optical micrographs from at least 200 grains such as shown in a and b. The average grain size of the MC and NC after the FSP was found to be ∼9 μm and ∼4 μm, respectively. Some researchers already reported that during FSP, the temperature of the specimen rises to approximately 470 °C The microstructure of the FSPed NC was further examined by using TEM. TEM allows a better understanding of the distribution, especially of the nanosize SiC particles and precipitates formed within the matrix after the FSP of the NC. a shows the TEM image of the Al7075-2% SiC nanocomposite after FSP. As shown in a, the matrix contains two types of second phase particles, i.e. nanosize SiC particle and precipitates, which can be differentiated by their morphologies. The second phase particles with rounded shape (produced due to ball milling) and clear contrast are identified as SiC. The average size of the SiC particles could be estimated to be ∼60 nm, which was evenly distributed within the grains: segregated nanoparticles at grain boundaries have not been observed. However, elongated rod-shaped precipitates were identified as η phase (MgZn2 and/or Mg3Zn3Al2) b shows typical SAED pattern corresponding to the TEM image displayed in a. The SAED pattern shows the spotty continuous rings of Al (220) (200), and (111) planes, and the weak diffraction spots are detected to be from SiC (101) and η (200). These results confirm that the nanoparticles (i.e. SiC) are incorporated well into the matrix of the NC. Gazawi et al. demonstrates the hardness of the as-cast and FSPed composites. An average of 6 indentation measurements has been reported for each hardness value with a standard deviation in parenthesis. The average hardness of the as-cast MC and NC, respectively, are estimated to be 78 HV and 88.5 HV. The hardness value of the as-cast MC is found to be lower than that of the as-cast NC. As discussed above (section ), this may be due to the grain size refinement produced because of nanoparticles presence during solidification (). After the FSP, a considerable enhancement in the hardness value is obtained for both micro- and nanocomposite and these are found to be 101 HV and 121 HV, respectively. This increase in the hardness values is attributed to remarkable microstructural refinement, improved homogeneity of particles distribution and closure of the microporosity by the FSP. Similar trends in results were also reported by other researchers , discussed later). Moreover, it can be noted that in the as-cast state, the standard deviation in the hardness is noticeably higher in comparison to that of the FSPed samples. This is due to the agglomeration and non-uniform SiC particles distribution and presence of residual porosities in the cast composites.The engineering stress-engineering strain plots for the as-cast and FSPed composite samples are shown in . At least 3 samples of each condition were tested to ensure the reproducibility of the tensile tests. a shows the representative stress–strain curves for the FSPed NC to indicate the variation of tensile strength of the composite samples. For comparison, the tensile test results, i.e.%elongation, UTS/YS of the as-cast and FSPed composites are tabulated in . By comparing the stress-strain plots of the as-cast MC and NC (b), it reveals that the addition of nanosize particles by simple stir casting process would not have any major impact on the tensile properties. A slight increase in UTS (from 111 to 139 MPa) and%elongation (from 1.3% to 2.2%) have been observed for the NC as compared to that of the MC. Optimal utilization of the strengthening potential of the nanosize SiC particles (Orowan strengthening) in the as-cast condition is hindered due to the severe agglomeration nature of nanoparticles, which lead to the particle clustering and formation of porosities during solidification c) for both the composites as compared to that of the as-cast state of same. The UTS of the NC is found to increase from 139 MPa (as-cast specimen) to 400 MPa (after FSP) and the%elongation increases from 2.2% to 21%. The UTS of the MC is increased from 111 MPa (as-cast specimen) to 370 MPa (after FSP) and the%elongation is increased from 1.3% to 18.6%. Such improve in the mechanical strength and ductility of the FSPed micro- and nanocomposites are highly attractive for practical applications. The enhancement of the ductility and strength simultaneously is indorsed to the combined effect of grain refinement persuaded by dynamic recrystallization during the FSP, better Orowan strengthening due to the homogenization and redistribution of the SiC particles homogeneously Fractography after the tensile tests was studied by SEM to relate the type of fracture under uniaxial loading. shows the fractographs of the as-cast and FSPed samples. The fractured surface of the as-cast composites, both micro- and nanocomposite (a,b), exhibited a dendritic structure, lack of matrix continuity and presence of associated porosities. It is widely accepted that the existence of such type of defects restricts the plastic deformation capability of the matrix strongly b), is the consequence of the premature fracture due to the debonding in the particle/matrix interface. As a result, the composites behave like brittle materials. In fact, dimples were not observed from the fractured surface. However, a completely different fractured morphology can be observed after the FSP of the composites (c,d). The FSPed composites showed deep and well-defined dimples, which are concomitant to the modified SiC particles distribution within the matrix, formation of recrystallized grains with refined morphology and elimination of porosities. In addition, a noticeable change in the dimples size can be observed between the FSPed micro- and nanocomposites. The dimples are coarser in the FSPed MC (c) as compared to that of the FSPed NC (d). The void size is found to decrease in case of the FSPed NC (d) due to the existence of refined grain structure and reinforcement of the nanosize SiC particles. Such microstructural changes reduced the possibility of premature failure, which led to enhance both the ductility and strength of the FSPed composites To evaluate the tribological behavior of the as-cast and FSPed composites, pin-on-disc wear test was conducted. indicates the change in weight loss of the MC and NC, before and after the FSP. The as-cast MC specimen shows comparatively higher weight loss than that of the other samples. It could be noted () that the wear loss of the as-cast NC specimen is slightly lower as compared to the as-cast MC specimen, which corresponds to better wear resistant of the NC. The enhancement in the wear resistance of the as-cast NC is ascribed to the development of finer grains than that of the cast MC (as discussed in the microstructural section, ). Furthermore, incorporation of SiC nanoparticles into the matrix leads to the reduction of the real contact area. These changes in microstructure substantially influence the wear behavior of the composites. This can be ascribed to the enhancement of the hardness due to the modification of the microstructure. The obtained result is well consistent with the trend observed for the hardness values of the corresponding specimens (, the wear loss of the as-cast composites is reduced considerably after the FSP. The vast reductions in the wear loss of the FSPed composites as compared to that of the as-cast materials can be ascribed to the better dispersion of the hard micron- and nanosize SiC particles within the matrix and proper bonding The worn out surfaces of the as-cast and FSPed composites were analyzed under SEM to recognize the type of wear mechanisms involved. a & b show the SEM images of the worn out surfaces of the as-cast micro- and nanocomposite samples. As illustrated, the as-cast composites exhibit plastic deformation bands along the direction of the sliding and partial irregular pits, which are the clear evidence of the abrasive and adhesive wear. The removal of particles cluster from the matrix during sliding creates pits. Microstructural inhomogeneity and poor particle-matrix interface characteristics are responsible for the pit formation. c,d show the worn surfaces of the FSPed micro- and nanocomposite samples. The worn surfaces are appeared comparatively smoother and are comprised of some shallow grooves with a slight plastic deformation on the grooves’ edges. No craters are evident on the worn out surfaces owing to the uniform SiC particles distribution with in the matrix. These results indicate that the wear mode gradually has modified to abrasive wear from the adhesive type. The enhancement in the wear resistant behavior of the FSPed composites can be ascribed to the improvement in the hardness values due to the refinement of matrix structure, uniform SiC particles distribution after the FSP, increase the bonding between matrix and particles and elimination of the casting defects such as porosities. It is widely known that with increasing the hardness value, wear loss of the material decreases under abrasive wear conditions The electrochemical polarization curves for the as-cast and FSPed composites are displayed in .Tafel extrapolation method was used to determine the values of corrosion current density (icorr) and the corrosion potential (Ecorr) from the corresponding polarization plots summarizes the various electrochemical parameters obtained from the Tafel plots. The Ecorr values of the as-cast MC, as-cast NC, FSPed MC and FSPed NC samples are found to be −1060 mV, −1010 mV, −992 mV and −950 mV, respectively. Moreover, the icorr is determined to be 12.4, 7.46, 3.86 and 2.52 μAcm−2, respectively, for the as-cast MC, as-cast NC, FSPed MC and FSPed NC samples. The corresponding Epit values are found to be −758 mV, −776 mV, −755 mV and −750 mV, respectively, for the as-cast MC, as-cast NC, FSPed MC and FSPed NC samples. It is found that () the corrosion potentials of both the micro- and nanocomposite samples in the as-cast condition are very high. This could be due to the microstructural inhomogeneity and poor particulate-matrix interface characteristics. This type structure is very common in the cast AMCs and facilitates pit initiation which promotes corrosion that the Ecorr of both the micro- and nanocomposite samples were shifted towards noble direction after the FSP. This can be explained in the light of the microstructural features of the corresponding sample after the FSP. As discussed earlier, during FSP, intense heating and frictional mixing refine the microstructure and remove the inherent casting defects (such as porosity, particle clustering and non-uniform distribution of reinforcement) from the as-cast structure. The FSP leads to the uniform SiC particles distribution, decreases surface porosities and enhances the bonding between particle-matrix interfaces. Most importantly, the FSP leads to a substantial grain size refinement. In this work, the grain size (average) reduced to ∼9 μm and ∼4 μm () for the MC and NC, respectively. The Cl− concentration/grain boundary area is reduced for the fine-grained structure of the same material due to the increase in the grain boundary area as compared to its coarse-grained counterpart In the present study, Al7075 alloy composites reinforced with micron- and nanosize SiC particles were manufactured by stir casting route. After that, FSP was used as a secondary processing technique to modify the cast microstructures with the aims to improve the mechanical properties and corrosion resistance of the stir cast composites simultaneously. The major outcomes of this work could be concluded as follows:Al7075 alloy based micro- and nanocomposites (designated as MC and NC, respectively) were successfully manufactured by stir casting route. The cast composites, both micro- and nanocomposites, showed poor mechanical strength and very low level of ductility due to the presence of dendritic structures, inhomogeneously distributed SiC particles along interdendritic regions and casting defects such as porosities in the matrix.FSP led to modify the cast microstructure into uniformly distributed SiC particles within the matrix of refined grain structure with reduced casting defects. Thus, the vast improvement of the tensile strength (∼190%) and elongation (854%) simultaneously for the FSPed nanocomposite (as compared to that of the as-cast counterpart) are mainly due to the microstructural modification arisen after the FSP. The strengthening mechanisms involved in such composite structures are analyzed to be the grain boundary strengthening (i.e. Hall-Petch strengthening), Orowan strengthening through nanosize particle reinforcement and precipitation hardening (η phase).FSPed NC showed superior wear resistance in comparison to that of the as-cast state of the same. This is ascribed to the improved hardness, refined matrix grain size, uniform SiC particles distribution and enhanced bonding between the particles-matrix interfaces.Corrosion potentials (i.e. Ecorr) of the micro- and nanocomposite samples were shifted towards noble direction after the FSP. This can be ascribed again to the modification of the microstructural features comprising with a uniform distribution of SiC particles, reduced surface porosities, refinement of grain size and increased particles-matrix interface bonding characteristics after the FSP. Such beneficial effect became more intense (i.e. shifting towards more noble Ecorr) when the particle size (reinforced in the composite) was reduced from micron to nanometer scale. For the same weight fraction of the reinforcement, the nanosize particles could cover more surface area of the exposed metallic surface to the corrosive solution. Hence, relatively less active opened surface of the NC sample is available for the corrosion leading to more noble Ecorr.Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jmapro.2017.09.005The following are Supplementary data to this article:Structural transitions in nanoscale materialsHigh-pressure studies of mechanical alloyed Ni75Se25 powder mixtureExtended X-ray Absorption Fine Structure and Raman studies were performed to follow the structural and vibrational behavior of mechanical alloyed Ni75Se25 mixture, containing trigonal Ni3Se2 nanocrystalline phase, when exposed to high-pressure conditions. An increase in the local structural order with pressure increasing was observed by means of Debye–Waller factor analysis. The relative Ni nearest-neighbours distances (d) were determined as a function of pressure (P). From the fitting of these d |
× |
P curves with Murnaghan's equation, the inverse linear compressibility of nanocrystalline phases (Ni3Se2 and Ni) and their derivates were determined. The high-pressure Raman experiments resulted in a poor determination of the phonons dispersion curve for Ni3Se2 phase, but they were very important to confirm the absence of nanocrystalline Se in the mechanical alloyed Ni75Se25 mixture, showing that all Se was consumed to form the Ni3Se2 phase.Structural transitions in nanoscale materialsTransition metal chalcogenides have gained much attention in the field of materials science due to their special electronic properties and interesting chemical behavior. In the particular case of nickel selenides, the electronic structure, phase diagram, X-ray spectra and Raman scattering have been studied Inorganic materials with different morphologies can exhibit different properties, even if they are made up of the same elements. Therefore, the synthesis of these materials would be particularly interesting. Due to their unusual morphologies, the nickel selenides are expected to find unique applications, such as solar cells Recently, we have shown that several TM1–xSex (TM—transition metals) alloys can be produced in the nanocrystalline form starting from elemental powder mixtures using MA process One of the goals of this paper was to test the structural stability of both nanocrystalline phases (Ni3Se2 and Ni) found in MA-Ni75Se25 sample following the local environment behavior of the Ni atoms up to 19 GPa by means of high-pressure X-ray Absorption Spectroscopy (XAS) experiments. Furthermore, plotting the relative Ni nearest-neighbours distances as a function of pressure and fitting it using the Murnaghan's equation, the inverse linear compressibility of the nanocrystalline phases (Ni3Se2 and Ni) and its derivate were determined.In order to complement the structural studies, high-pressure Raman experiments were performed. From these measurements, the vibrational profile of the MA-Ni75Se25 sample was followed as a function of pressure. Considering that Ni3Se2 phase stabilization from Ni75Se25 powder mixture is attributed to the existence of non-reacted Ni and that Raman measurements are very sensitive to Se phonons, these studies were very important to complement the information about the atomic diffusion during the phase nucleation process induced by MA.The Ni75Se25 sample milled for 70 h was submitted to high hydrostatic pressures generated by axial forces acting between two small diamonds of a Diamond Anvil Cell (DAC). The high-pressure X-ray Absorption Spectroscopy (XAS) experiments are performed in transmission mode, and consequently, the X-ray beam must pass by the diamonds. Then, several problems arrive. The ordinary XAS set-up using the classic two-crystal monochromator and ionization cameras is strongly dependent of mechanical movements which difficult enormously the beam focalisation. The diamond Bragg reflections must be attenuated or dislocated from the spectral range of interesting by changing the relative position of the DAC with respect with the X-ray beam. As each classical XAS spectrum demands at about 5 min and many DAC positions are, in general, tested, it will be an energetically and time expensive task. The utilization of a Dispersive XAS set-up to collimate the polychromatic beam in a few tens of microns without any mechanical movement coupled with a position-photo-sensible detector is indispensable to realize pressure-induced structural studies. In this set-up, the acquisition time is minimal (tens of 10− 3 s) offering high stability and reproducibility in the measurements that allows to cleaning completely a large energy domain from glitches due to the diamond Bragg reflections in a short period of time.EXAFS experiments were performed in Ni K-edge (8333 eV) at D11 station of DCI in Laboratoire pour l'Utilisation du Rayonnement Electromagnétique (LURE), Orsay, France.The posterior data treatments were done by using the CDXAS-26 Raman scattering measurements were performed at ambient temperature in an XY Dilor monochromator coupled to an optical focal lens (20×) and CCD counting system. The 514.5 nm line of an argon ion laser was used as exciting light always in backscattering geometry and using an output power below 5 mW to avoid the overheating of the sample.The pressure determination during the XAS (Raman) measurements was performed through the pressure-dependent fluorescence of a ruby chip and silicone oil (argon) was used as pressure transmitting medium. shows the XAS spectra of the Ni75Se25 sample milled for 70 h (MA-Ni75Se25) at ambient pressure and at four representative pressures up to 19 GPa. It also showed the XAS spectrum of a Ni metallic foil, which will serve as a good reference. From this figure, one can see that a very good spectral range was obtained, at about 800 eV after Ni K-edge. There is some similarity between MA-Ni75Se25 and Ni foil spectra, especially for E |
> 8.45 keV, but differences in magnitude and spectra profiles are strong evidences of Ni–Se interaction in the MA-Ni75Se25 sample. It is also clear that no important structural changes in the MA-Ni75Se25 sample occurred with pressure increasing up to 19 GPa. shows the XANES region of the XAS spectra as a function of pressure. This region of the X-ray absorption spectra contains information concerning photoelectron multiscattering effects, which gives access to medium-range order (∼ 15 Å) of the atomic structures. Then, it is clear from that the Ni3Se2 phase produced by MA has a very good structural stability with respect to pressures as higher as 19 GPa even in the medium-range distances. The edge values observed for the milled sample are in quite good agreement to that of Ni metal, indicating that there are no electronic features at energy levels smaller than those of metallic form. However, the XANES profiles of MA-Ni75Se25 sample are completely different to that of Ni metallic, indicating different electronic configurations for Ni atoms in the MA-Ni75Se25 sample. shows the EXAFS region of the XAS spectra as a function of pressure. It has observed both phase shift and amplitude magnification with pressure increasing. Once more, the resemblance between the spectra showed that no phase transition occurred in the pressure range tested.The structural effects caused by the pressure increasing become more evident after the EXAFS data treatments where the Pseudo-Pair Distribution Functions (PPDF) were obtained (see ) by means of Fourier transforming (FT) operations on the EXAFS signals. From the PPDF at ambient pressure, one can see that there is a large main peak with maximum intensity at about 2.1 Å and a second small peak, as a shoulder of the main one, located at about 2.6 Å. This corroborates the coexistence of Ni3Se2 and Ni phases in the MA-Ni75Se25 sample observed by previous XRD analysis. In , the shortening of Ni nearest-neighbours average distance and the intensity increasing of the signal amplitude with pressure increasing can be easily observed for both phases. shows the filtered EXAFS signals, χ(k), as a function of pressure. They were obtained by inverse FT operations performed in a selected region (PPDF main peak), which represents the first coordination sphere. EXAFS fittings were proposed to the experimental signals collected at higher pressures (see symbols in ). For that, the total phase shift and amplitude functions were extracted from the EXAFS signal at ambient conditions considering the short-range crystallographic information of Ni3Se2 (coordination number N |
= 4 and average distance d |
= 2.37 Å) and Ni (N |
= 12 and d |
= 2.49 Å) phases shows the pseudo-Debye–Waller (Δσ2) parameters as a function of pressure. The reduction of the Δσ2 parameters with pressure can be explained as a decreasing of dynamical disorder, indicating a local environment order increasing around the Ni atom. From a first analysis, it is evident that the Äó2 obtained for Ni phase is much greater than that for Ni3Se2 one. This fact can be associated with Ni consuming to form the Ni3Se2 during the MA process. Moreover, a slight evidence of Δσ2 increasing for the Ni3Se2 phase for pressures as higher as 15 GPa can be only explained as an increasing in the dynamical disorder of this phase. This suggestion will be further discussed in the Raman measurements.(b) shows the evolution of the Ni nearest-neighbours distance (d/d0) for Ni3Se2 (circles) and Ni (squares) phases as a function of pressure. Reductions of about 2.3% and 5.5% in the nearest-neighbours distances were observed for the Ni3Se2 and Ni phases, respectively, when the pressure reached 19 GPa. Using the Murnaghan's equation The values obtained were BLo |
= 208.7 GPa (fixing BL′ = 5.5) for Ni3Se2 and BLo |
= 85.5 GPa (fixing BL′ = 4.3) for Ni phase. A rough comparison between bulk-modulus of metallic Ni (Bo |
= 186.5 GPa) and that found for Ni in the MA-Ni75Se25 sample showed that the non-reacted Ni in the MA sample is more ductile than in its metallic form. This fact can be explained by superplasticity effects observed in nanostructured nickel and nickel alloys, since that grain-boundary sliding is an important deformation mechanism during superplasticity. On the other hand, the Ni3Se2 phase produced by MA seems to be extremely brittle as compared with the most common metals, such as Fe (164.8 GPa), Co (206.9 GPa), Cu (141.3 GPa) and Pd (191.3 GPa) shows the Raman spectra of Ni75Se25 milled for 70 h as a function of pressure. The plasma line of the laser is indicated as PL in this figure. The first spectrum, at the bottom of this figure, was collected outside of DAC at ambient conditions, which showed good agreement with the previous Raman measurements When the MA-Ni75Se25 sample was introduced in the cell without pressure transmission medium (spectrum named DAC), curiously, the spectrum observed for ambient conditions was not reproduced. Neither the spectrum collected after Argon charging recovered the Raman profiles observed outside the DAC. Up to now, we have no satisfactory explanation for this effect, which was observed in the two runs performed. The DAC spectrum shows basically one feature containing at least two peaks, one located at about 158 cm− 1 and other located at 166 cm− 1.From 1.4 GPa to 5 GPa, the spectra are similar in shape, showing the same 158 cm− 1 and 166 cm− 1 lines previously observed and other two less intense lines at about 128 cm− 1 and 141 cm− 1. It is easy to note that there is an intensity reduction as the pressure increasing for all Raman lines. When the pressure reached 7.3 GPa only the most intense Raman lines were observed, now located at 156 cm− 1 and other located at 167 cm− 1, indicating that the low-frequency line is a soft mode, while the high-frequency one is a hard mode (as the most common behavior of Raman modes with pressure).When the pressure increased to 8.9 GPa, a kind of resonant effect was observed: the baseline increased near to the laser line and the 141 cm− 1, 156 cm− 1 and 167 cm− 1 lines become very intense. For pressures between 10.6 GPa and 15.4 GPa, the spectra showed important changes, displaying an very strong line at 148 cm− 1 and a less intense one located at 167 cm− 1. It is relevant to mention that both lines had their intensities attenuated with the pressure increasing.For pressures higher than 18.1 GPa (up to the highest value tested 23.1 GPa), the spectra become very noisy and practically no Raman active was detected, except by the weak and large band centered at 170 cm−1.Concluding, these Raman results suggest at least one structural/phase transition for the MA-Ni75Se25 sample between 10.6 GPa and 15.4 GPa. Considering that the pseudo-Debye–Waller parameter obtained from XAS experiments presented some evidences about a dynamical disorder increasing of the Ni3Se2 phase for pressures higher than 15 GPa, one can conclude that Ni3Se2 phase could be passing by a structural and/or phase transition. However, to confirm this interpretation, further high-pressure X-ray diffraction measurements are required.Although any concrete evidence about phase transitions was found by these Raman studies, it was clear that there is no free Se in the MA-Ni75Se25 sample at high pressure due to the lack of its characteristic pressure-induced phase transitions. This observation shows that all Se of the initial Ni75Se25 mixture was consumed to form the Ni3Se2 phase in the beginning of the MA process.High-pressure studies of MA-Ni75Se25 sample were performed using absorption X-ray and Raman spectroscopy techniques and the main conclusions obtained were:The coexistence of nanocrystalline Ni and Ni3Se2 phases was corroborated and their crystallographic parameters were followed as a function of pressure up to 19 GPa.A rough estimative of compressibility for both phases (done by fitting Murnaghan's state equation) showed a mixture of ductile Ni nanoparticles and very brittle Ni3Se2 ones.The pseudo-Debye–Waller parameters of Ni3Se2 phase suggested a possible structural/phase transition for pressures higher than 15 GPa.The Raman results corroborate the possible structural/phase transition in the MA-Ni75Se25 sample, but for pressures higher than 10 GPa. Furthermore, the Raman results showed that there is no free Se in this sample, even under high-pressure conditions.A new methodology for the characterization of fracture toughness of filled epoxy films involved in microelectronics packagesFracture toughness is regarded as an important fracture criterion for materials when fracture mechanics is applied to assess the reliability of microelectronics packages. Fracture toughness of a filled epoxy is related to material, process and test conditions. Plane-strain based characterization methodologies have been successfully developed to characterize fracture toughness of bulk filled epoxy materials. However, those methodologies may not be applicable for filled epoxy films, due to the differences in stress-state and degree of curing in the films when compared to bulk specimens. In this paper, strain energy release rate was proposed to be a representative for the description of the fracture behavior of filled epoxy materials. Based on linear elastic fracture mechanics and microdigital image speckle correlation technique, a plane-stress based fracture toughness characterization methodology, including theoretical model, measurement facility, experimental approach and analysis method, was developed. With the methodology, the fracture toughness of a silica filled epoxy film, which is widely used in microelectronics packages as an underfill material, was characterized over a wide temperature range (−40 to 200 °C). The fracture toughness of the film was found to have a nonlinear relationship with testing temperature, i.e., the temperature dependence in the low temperature range is much lower than that in the intermediate temperature range, but is higher than that in the high temperature range.Because of their suitable mechanical strength, favorable viscous properties, light weight and low cost, filled epoxy materials have been widely used in microelectronic packages as molding compounds to encapsulate semiconductor devices, as underfill materials to reinforce the strength of solder joints, and as die attach adhesives to bond silicon chips onto substrates. The use of filled epoxy materials introduces many interfaces and makes packages more complex. As a consequence, the packages are prone to multi-mode damages and failures (e.g., epoxy film buckling, brittle fracture, interfacial delamination, cohesive failure, bond cracking, and environmental failure), when they are subjected to complicated and coupling environmental loading (e.g., thermal, mechanical, moisture, electrical and chemical loading) The linear elastic fracture mechanics (LEFM) technique has been recently employed to study the polymer/inorganic interface strength, crack initiation and propagation, and reliability of various microelectronic packages Generally, fracture toughness is represented by either stress criteria (e.g., stress intensity factor (SIF)) or energy criteria (e.g., strain energy release rate). Fracture toughness of a filled epoxy material depends primarily on three sets of variables. The first set of variables is material related, for example, type of epoxies, type of fillers, type of additives, epoxy/filler volume ratio, and epoxy/filler interfacial bond strength. The second set of variables is process related, for example, curing temperature, curing time, thickness, and humidity level. The last set of variables is testing condition related, for example, testing temperature and testing strain rate ). This means that the calculation based on the geometrical factor, which was determined by the bulk specimens, may not be correct and the fracture toughness determined by the bulk specimen may not represent the actual values of fracture toughness of filled epoxy films (e.g., underfill, die attach). Plane-stress fracture toughness has been widely used in the areas of energy, astronautics and pressure vessel to assess the long-term reliability of various thin plate structures In this study, strain energy release rate was proposed to be a representative of fracture toughness for the description of fracture behavior of filled epoxy films. Based on LEFM and microdigital image speckle correlation (μ-DiSC) technique, a plane-stress based fracture toughness characterization methodology, including theoretical model, measurement facility, experimental approach and analysis method, was developed. With the methodology, fracture toughness of a silica filled epoxy film was determined over a wide temperature range., an infinite plate contains a central penetrative crack with a length of 2a. When the plate is loaded by a uniform biaxial load P, the displacement distributions U(r,θ) and V(r,θ) along the radial line emanating from the crack-tip are given by where μ is the Poisson’s ratio, E is the Young’s modulus, θ is the polar angle, r is the radial coordinate, KI is the mode-I SIF at the crack-tip, κ=(3−μ)/(1+μ) for plane stress and κ=(3–4μ) for plane strain.When one of the displacement distributions, e.g., V(r,θ), is obtained, the nominal SIF K′I at the distance r≠0 from the crack-tip can be determinedfor any given load level Pi (i=1,2,3,…). When the load P reaches to the critical level PC, the crack opens and the specimen fractures. If the displacement distribution V(r,θ) can be obtained at the critical load level, the corresponding nominal SIF K′IC at the distance r≠0 from the crack-tip is then obtainedWhen the surface of a specimen is illuminated by a light source (either laser beam or white light), each point on the surface can be considered as a scattering source. The complex amplitude of the scattered light at any point in space is the sum of the amplitudes of the contributions from each point on the surface. Since the intensity of the scattered light varies with position, randomly distributed light and shade spots therefore appear in the front space of the object surface. This phenomenon is usually called speckle effect. When the specimen is subjected to a loading, the specimen deforms and the speckle spots deform together with the specimen, the speckle effect can therefore be used to measure the deformation of the specimen. Digital image speckle correlation is a technique, which correlates a pair of digital speckle patterns obtained at two different loading conditions and searches for the maximum correlation coefficient Cwhere U and V are the displacement components in x and y directions, respectively; f(xi,yj) and g(xi′,yj′) are the gray-levels at points (xi,yj) and (xi′,yj′) on the subimages before and after loading, respectively. A point pair of maximum C is interpreted as the same point on the sample before and after loading. The deformation components are then determined from the coordinates of points (xi,yj) and (xi′,yj′).A coarse-fine search algorithm is often used to correlate the two images. However, since the algorithm is a full-field search method and tries many possible combinations of the deformation variables within a given range, a large number of calculations must be performed at points (xi,yj) and (xi′,yj′) were introduced into correlation function to improve the search accuracy. Eq. According to the principles of probability and statistics has unimodal character and approximate symmetry. A typical example of correlation coefficient distribution is presented in , the peak of the distribution obtained from Eq. is sole and sharp. This indicates that the improved function is more accurate to find the maximum coefficient C′. Therefore, a line search algorithm, i.e., along the perpendicular direction following by the horizontal direction, can be employed to replace the full-field search algorithm for the determination of the peak point. As a result, the computational time can be reduced by one to two orders and the real-time measurement can be achieved through the improved algorithm.Because of the operational characteristics of video cameras and digitization circuits, the gray-level obtained is discrete in nature. It means that no gray-level information is available between pixels. In order to reach higher accuracy, the bicubic spline interpolation method was employed in this study to smoothen the surface of gray-level distribution and further to determine the values of gray-level at any position in the imageswhere αij is the gray-level at point (xi,yj), and are the distances along x- and y-axis from the point (xi,yj).Two verification experiments were performed to test the accuracy of the improved correlation algorithm in predicting displacements. Rectangular underfill film specimens, which had a length of 3 mm, a width of 1 mm and a thickness of 0.1 mm, were used in the experiments. For the first experiment, two images were acquired without moving the specimen. The correlation was conducted to determine the minimum prediction error. As can be seen from the results given in , the accuracy of the improved algorithm is better than 0.02 pixels for both U and V displacements. In the second experiment, known rigid movements were executed by a nano-stage with accuracy of 5 nm. The algorithm was again employed to correlate the images. By plotting the actual movement versus the correlated movement, the visual picture of the developed correlation algorithm’s validity is shown in . In the figure, the data are arranged around a corresponding 45° ideal line. This indicates that the correlated results are in good agreement with the actual movements.where KIC is the critical fracture toughness at the crack-tip, PC is the critical load, S is the support span, B is the specimen thickness, W is the specimen width, and f(a/W) is the geometrical factor.However, when those methodologies were employed to determine the fracture toughness of filled epoxy films, two issues were arisen. First, since the geometrical factor is geometry dependent, the dimension of specimen used for the determination of fracture toughness must satisfy the size criterion, i.e., plane-strain condition,where σy is the yield stress. However, as listed in , the filled epoxy materials used in most microelectronic packages are in the state of plane-stress rather than that of plane-strain. This means that the degree of curing of filled epoxy films is different from that of bulk specimens and some researchers have reported similar findings where Pmax is the load at the highest point of load–displacement curve, and PQ is the load determined from the point Q, which is the intersection of line OB and load–displacement curve, as shown in . The line OB has a compliance C2, which is 5% greater than the compliance C1 of line OA The load ratio criterion was often found to be unsatisfactory at some testing conditions , is not applicable under those temperatures and for the plane-stress condition this becomes more serious (see ). For the above-mentioned reasons, the fracture toughness determined by using the bulk specimens may not represent the actual fracture resistance of filled epoxy films involved in various microelectronic packages. In other words, the current characterization methodologies are not suitable for the determination of fracture toughness of filled epoxy films.In order to eliminate the effects of specimen thickness, degree of curing and stress-state on the fracture toughness of filled epoxy films, a size criterion, which is usually employed for various thin-plate structures where L is the gauge length of the specimen. Based on this criterion, a double edge crack (DEC) tension specimen was designed, as shown in The material used in this study was Type 3563 silica filled epoxy supplied by Loctite Pte Ltd, which is widely used in flip chip packages as a underfill material. The composition of the material is 60% epoxy filled with 40% silica of size ranging from 1 to 4 μm. By using a thermo-mechanical analyzer, the glass transition temperature (Tg) of the material was determined to be 105 °C.A dispenser, a curing oven and a specially designed mold were employed to prepare the DEC specimens. By following flip chip packaging process, an optimized curing condition was defined to be 165 °C for a period of 8 min. The details of the mold and specimen preparation procedures are given in Ref. Based on the improved correlation algorithm, a noncontact and nondestructive measurement system, so-called μ-DiSC system, was designed and constructed in our laboratories, as shown in . Overall, the system consisted of six main parts: a working table (19); XYZ motorized translation stages (7); a long-working distance microscope (4); a miniature thermal cycling chamber (15); a microforce tester (12) and a computer (1).The chamber (15) was fixed on the table (19). Resistance heaters and thermoelectric coolers were employed to heat and cool the chamber, respectively. A chiller (11) was employed to cool the copper heat exchangers associated with each TEC. A temperature controller (18) was designed to activate the heaters and coolers in order to produce the required temperature in the chamber. The microscope (4) was mounted onto the table via the XYZ stages (7). A stage controller (10) was provided to drive the stages (7) and to further locate the microscope (4) at any desired point in the XY plane and at any desired height over the chamber. A microscope controller (2) was designed to drive and position the zoom module and focus module in order to zoom and focus areas of particular interest in the sample. A ring white light source (13) was mounted to the microscope (4) to illuminate the sample through the glass window (14) on the top of the chamber. A CCD camera (5) was connected to the microscope (4) to acquire images of the sample under any loading condition. The microforce tester (12) was integrated into the system to apply a small mechanical force onto a sample under testing at different temperatures.A central control and image correlation software was developed and consisted of six modules. The chamber control module was developed to generate temperature profiles, monitor temperature levels and save test data. The stage control module was provided to drive the stages, search the sample and also to record and recall the position of the sample. The microscope control module was designed to zoom and focus the sample and display the lens, TV tube, working distance and magnification used for the measurement. The image acquisition module was incorporated to capture, save and display the image of the sample. The microforce tester module was included to generate the mechanical loading profile, measure the force, and save test data. Finally, the image correlation module was implemented to correlate a pair of captured images, calculate the deformation, and visualize the measurement results.Fracture tests were conducted on the microforce tester designed by MTS (Tytron 895.20A-02). The “L” shape fixture with a soft gripper was employed to hold the two ends of the DEC film specimen. A small load cell with accuracy of 0.01 N was used to measure the force applied. TestStarII software was used to control the system and collect the test data. The miniature thermal cycling chamber rated from −50 to 250 °C was employed to produce environment for running the tensile tests at low and high temperatures. In the test, the sample was loaded under far field tension loading. The tests were carried out at seven different temperatures (−40, 25, 75, 100, 125, 150, and 200 °C) with a constant strain rate of 10−3/s. A high resolution CCD camera with 1024 × 1024 pixels was used to capture speckle patterns at different load levels for each testing temperature. After the digital speckle images were obtained, the correlation software was employed to determine the displacement fields around the crack-tip.Typical load–displacement curves obtained at four different testing temperatures of 25, 75, 100, and 150 °C are shown in . It is found from the experiments that at the low temperatures (e.g., −40 and 25 °C), the curves exhibited approximate linear elastic deformation characteristic , if the maximum load that the specimen is able to sustain, Pmax, falls within lines OA and OB, Pmax is taken as the critical load. While if Pmax falls outside lines OA and OB, the load at the intersection of the line OB and the P–V curve, PQ, is taken as the critical load, as shown in . In this study, the critical load and load ratio Pmax/PQ were employed to describe the deformation characteristic of filled epoxy film at different testing temperatures. The results are presented in , the critical load decreased with increasing temperature. However, the temperature dependencies at different temperature ranges were different. At the intermediate temperature range (75–125 °C), the temperature dependence was much stronger than that at the low temperature range (−40 to 75 °C). The weakest temperature dependence appeared at the high temperature range (150–200 °C). On the other hand, the load ratio showed a different trend. It increased with increasing temperature and reached the maximum value at the temperature close to Tg. However, when the temperature increased further from Tg, the load ratio dropped rapidly., when the process parameters and testing conditions are fixed, the fracture resistance of the filled epoxy film depends on the bonding strengths of cross-links in the epoxy matrix and interfaces between the silica particles and the epoxy matrix. Therefore, a possible reason for the above phenomenon was that at the temperatures below Tg, the filled epoxy film was in the glassy state. The bonding strengths of the cross-links and the interfaces were high. Hence, the temperature dependence was not strong and small viscoelastic deformation was obtained. At the temperatures around Tg, the material was in the transition from the glassy state to the rubbery state. Since the bonding strength of the cross-links in the glassy state was much higher than that in the rubbery state, a drastic reduction in the critical load was observed. On the other hand, the bonding strength of the interfaces was remained the same at the temperatures so that being softer epoxy matrix made the film deform easily. Hence, large viscoelastic deformation was obtained. Finally, at the temperatures above Tg, the material was in the rubbery state. The bonding strengths of both cross-links and interfaces were very weak. The change in temperature did not affect the bonding strengths too much. In other words, the temperature dependence was small., it is noted that the load ratio criterion, as given in Eq. , was not satisfied at some temperatures (75, 100, and 125 °C) around Tg. Similar phenomenon was also observed and reported by Pfeil et al. , cannot be used for the determination of fracture toughness, especially for plane-stress condition. This is due to its large viscoelastic deformation at those temperatures as compared to the bulk plane-strain specimens (see Ref. In order to verify the validity of LEFM technique for the filled epoxy materials at the temperatures around Tg (it is valid for low and high temperatures), two kinds of failure analysis experiment were conducted on the film specimens. In the experiment, when the specimen was tested to the point T (as indicated in ), which was over the critical point Q but did not reach the failure point P, the fracture test was stopped. The specimen was then removed from the microforce tester and cross-sectioned along the crack. Afterwards, one side of the specimen was protected and coated with a thin layer of gold. Scanning electron microscope (SEM) was employed to observe the surface morphology around the crack-tip. At the same time, another side of the specimen was polished and coated with a thin layer of gold. The deformation characteristic of the specimen was also studied using field emission scanning electron microscope (FE-SEM).It is interesting to note that when the point T was close to the failure point P, although the artificial crack did not initiate and propagate, many microcracks appeared in the epoxy matrix, as shown in . This observation revealed that it is not safe to use the load at the failure point, i.e., Pmax, to determine the fracture toughness. However, it is very safe to use the critical load PQ to determine the fracture toughness. On the other hand, the surface morphology analysis, as shown in , revealed that there was no obvious crack propagation, but a small plastic zone was found around the crack-tip. The experimental result suggested that SIF is not a good parameter for the description of fracture behavior of the filled epoxy film at the temperatures around Tg. However, it is noted from that the plastic zone is very small and satisfies the small-scale yield criterion, i.e.,where rp is the radius of the plastic zone. When the critical load is used to determine fracture toughness, the radius at the point Q should be smaller than that at the point T, it is therefore reasonable to assume that the LEFM technique is applicable for those temperatures. In this study, in order to eliminate the effects of temperature and plastic deformation around the crack-tip on the change of system energy, the strain energy release rate G was introduced as a parameter to represent the fracture resistance of the filled epoxy film, i.e.,where E′ is the temperature dependent Young’s modulus of underfill film, which is given in the authors’ previous research work , the corresponding nominal strain energy release rate G′IC at the distance r≠ 0 from the crack-tip can be calculated byWith the digitized images obtained before and after deformation, the displacement distribution around the crack-tip can be determined using the correlation software. A typical V field displacement distribution around the crack-tip, obtained at the critical load level of 11 N and the temperature of 25 °C, is shown in . As seen from the figure, when the specimen was subjected to a uniform biaxial load P, an opening displacement field appeared at the crack-tip. The displacement increased as the distance was increased from the crack-tip. Also it is noted the displacement showed an approximate linear relationship with distance except for displacement very close to the crack-tip. Based on the displacement field, by taking θ=90°, the nominal strain energy release rate G′IC can then be determined using Eqs. for any given distance from the crack-tip. Typical results are plotted as function of square root of distance . It is noted that the value of the nominal strain energy release rate G′IC increased as the square root of distance The extrapolation method is often used in finite element method to determine the fracture toughness of material at the crack-tip , the nominal strain energy release rate G′IC showed an approximately linear relationship with the square root of distance . The extrapolation method can then be employed to determine the strain energy release rate GIC at the crack-tip. By curve-fitting the experimental results using a straight line and extrapolating to the y-axis, the strain energy release rate GIC at the crack-tip was then determined from the intersection. By repeating the above procedures, the strain energy release rates were obtained for all the testing temperatures. The results are presented in . It is noted from the figure that the GIC value had a nonlinear relationship with testing temperature. At the low temperature range (−40 to 25 °C), the GIC value decreased with increasing temperature. Since the temperatures were far below the Tg, the material was still in the glassy state, the temperature dependence was not strong. At the intermediate temperature range (75–125 °C), the material was in the transition from the glassy state to the rubbery state. The GIC value decreased sharply in the temperature range. When the temperature was increased further and reached 150 °C, the material was in the rubbery state and the fracture toughness then presented the weakest dependence on temperature.From the above experiments and analyses, the following conclusions were made:• Based on the improved correlation algorithm, a noncontact and nondestructive computer-aided μ-DiSC system was developed. The system was demonstrated to be able to determine fracture toughness of the silica filled epoxy films.• Due to the issues of size and load ratio criteria, plane-strain fracture toughness characterization methodologies, which were developed based on the bulk specimens, were found to be not applicable for the determination of fracture toughness of the filled epoxy layers involved in many microelectronic packages.• Although large viscoelastic deformation was observed at the high load levels for the temperatures around Tg, no obvious plastic deformation and crack propagation was demonstrated by the failure analyses on the surface morphology at the crack-tip and microstructure ahead of the crack-tip. As a consequence, linear elastic fracture mechanics technique was found to be applicable for the description of fracture behavior of the silica filled epoxy films for the whole temperature range. However, the strain energy release rate was suggested to be a representative of fracture toughness in order to take the energy dissipation at the crack-tip into consideration.• A new characterization methodology, including theoretical model, measurement facility, experimental approach and analysis method, was developed for the determination of fracture toughness of filled epoxy films. With the methodology, the fracture toughness of a silica filled epoxy type 3563 was obtained in terms of strain energy release rate. The fracture toughness showed a nonlinear relationship with the testing temperature. At intermediate temperature range (100–125 °C), the fracture toughness was strongly dependent on the temperature. However, it was less dependent on the temperature at low temperature range (−40 to 75 °C) and high temperature range (150–200 °C).• Finally, since the characterization methodology was developed based on a common measurement technique, it is interesting to note that the methodology could be applied for the determination of plane-stress fracture toughness of other metallic and polymer films also.Microstructural analysis of the 〈111〉 and 〈110〉 nickel single crystals subjected to severe plastic deformation by hydroextrusionThe effect of hydrostatic extrusion (HE) on the microstructure and crystalline orientation of the 〈111〉 and 〈110〉 nickel single crystals was examined. The crystals were deformed by two-step hydrostatic extrusion to achieve the true strain εr=2.4. After the extrusion the samples had the form of cylindrical rods. The mechanical properties of the extruded samples (expressed in terms of their microhardness) were compared with the mechanical properties of ultra-fine grained nickel obtained by subjecting polycrystalline nickel to HE. The microhardness of the two deformed crystals appeared to be similar. The microstructure of the samples and the orientation evolution were examined using transmission electron microscopy (TEM), electron back scattered diffraction (EBSD) and X-Ray diffraction (XRD).Both the deformed crystals had an inhomogeneous ultra-fine-grained structure (as observed by TEM). The average grain diameter was 300 nm. The majority of the grain boundaries had high angle disorientations (EBSD).In both the deformed samples the predominating orientation was 〈111〉 (XRD). In the 〈111〉 oriented crystal 95% of the initial orientation was preserved whereas in the 〈110〉 oriented crystal the initial orientation was predominantly transformed into 〈111〉 and 〈100〉.Pure nickel is very rarely used as a structural material because of its high cost per unit. If however its structure is strongly refined, it exhibits good mechanical properties and quite good corrosion resistance. Thanks to these features nickel is an interesting material for the manufacture of the components of micro-electromechanical systems. At present, ultrafine-grained and nanocrystalline nickel is usually produced by the two methods: severe plastic deformation (SPD) Among the available SPD methods the present authors have chosen hydrostatic extrusion (HE). The literature reports on the use of the SPD methods to deform single crystals of metals are very scarce (we can mention only ref. Two nickel single crystals of orientation 〈111〉 and 〈110〉 were examined. The samples were cylindrical in shape and were cut out along the main crystallographic axes 〈111〉 and 〈110〉 of the monocrystals using a spark erosion saw. shows schematically the two orientations of the samples.The HE process was carried out in two steps (from Φ10 mm to Φ6 mm and then to Φ3 mm) so as to be able to observe better the evolution of the microstructure and changes of the mechanical properties. The total deformation value was 2.4.Changes of the mechanical properties were observed by measuring the microhardness on cross-sections of the initial single crystals and of each sample at each stage of deformation using the Vickers method. The microhardness was measured in a ZWICK microhardness tester equipped with a microscope which permitted measuring precisely the indentation diagonal. After the severe plastic deformation (SPD), the microstructure was examined in thin films of the material (specially prepared for transmission electron microscopy (TEM)) using a Hitachi S5500 scanning electron microscope/scanning–transmission electron microscope (SEM/STEM) and the local texture was determined by the electron backscatter diffraction (EBSD) measurement (Hitachi SU70 SEM). The global texture of the materials after SPD was analyzed (qualitatively and quantitatively) by the X-ray diffraction method using a Bruker D8 DISCOVER powder diffractometer equipped with a Cr X-ray source.The HV 0.2 microhardness of the two single crystals 〈110〉 and 〈111〉 was measured on their cross-sections in the initial state and after the hydrostatic extrusion compares the microhardness of polycrystalline Ni Microstructure of the single crystals after the first deformation step contains strongly developed dislocation substructures. The large number of dislocation tangles is typical of plastically deformed materials. The dislocations are agglomerated within the grains and form subgrains defined by the dislocation boundaries. shows the microstructure after the first step of HE (Φ10 mm→Φ6 mm, ε=1) and —this microstructure after the second deformation step (Φ6 mm→Φ3 mm, ε=2.4 accumulated deformation). The microstructural observations allowed us to determine the average grain diameter deq using an image analysis. The average subgrain diameter after ε=2.4 was 305 nm in the 〈110〉 crystal and 295 nm in the 〈111〉 crystal.The microstructure observations also included the determination of the grain misorientations in the deformed material by the EBSD method. Two types of maps were obtained: the distribution of misorientations of the grain boundaries and the distribution of the orientations of the subgrains. shows the maps of the grain orientation distribution in the two crystals (〈111〉 and 〈110〉) after the second step of deformation (εr=2.4).EBSD maps reveal that, in both cases, the misorientation angles above 15° are in majority. The local texture was examined by the same method and the results indicate that the orientations in the investigated area are greatly varied. After HE with ε=2.4, the subgrains in the 〈111〉 crystal are mostly oriented along the 〈111〉 direction whereas those in the 〈110〉 crystal have two main orientations—〈111〉 and 〈001〉. The global texture was measured by the X-ray diffraction method. The pole figures indicate that, in both samples, the texture is strong. In the 〈110〉 oriented sample we have two main texture components 〈111〉 and 〈100〉, so that the original texture of the initial single crystal was strongly transformed during the hydrostatic extrusion. In the 〈111〉 oriented sample the strongest texture component is 〈111〉 which indicates that the HE process yields a substructure with the original orientation. This was confirmed by the quantitative analysis of the texture. shows the pole figures {111} obtained experimentally for the two extruded materials and gives the results of the quantitative texture analysis.The earliest papers describing the texture (examined by X-ray diffraction method) in conventionally extruded rods were published in the mid-20th century by Hill The above examinations have allowed us to compare the microstructure, orientation and microhardness of the 〈110〉 and 〈111〉 Ni single crystals subjected to severe plastic deformation by hydroextrusion. It was also possible to compare these results with the results obtained for polycrystalline Ni subjected to the same process of severe deformation. The microstructure and properties of hydroextruded polycrystalline Ni are well known and described In our experiments the results of microhardness measurements indicate that the single crystal 〈111〉 is harder than the 〈110〉 crystal, which is in good agreement with the theory of slip deformation in single crystals. Also the microstructure analysis is in good agreement with conclusions given by Kulczyk Our results are also in agreement with the results reported by Reed and McHargue gives the percent proportions of the 〈111〉 and 〈001〉 texture components in extrusion-deformed poly- and monocrystals of an FCC metal with the initial orientation 〈001〉 and their percent proportion in a polycrystal with a random orientation.TEM observations revealed that the microstructure contains a dislocation substructure. The average grain size in the deformed 〈111〉 and 〈110〉 crystals was about 300 nm, which leads to the conclusion that the orientation has not much influence on the final grain refinement.The EBSD investigations have shown that the microstructure produced by the HE SPD process mostly contains high angle boundaries. As a result of severe plastic deformation the accumulated dislocations form configurations with high-angle boundaries which further evolve to become homogenous high angle boundaries The SPD process realized by hydrostatic extrusion (HE, ε=2.4) applied to the Ni 〈111〉 and 〈110〉 single crystals yielded a strongly refined microstructures—the average subgrain diameter in both the single crystals was about 300 nm with a majority of high angle boundaries. After the hydrostatic extrusion, the 〈111〉 single crystal preserved its original orientation, whereas the orientation 〈110〉 of the other single crystal has been transformed into two principal orientations 〈111〉 and 〈100〉.Early detection and monitoring of fatigue in high strength steels with MWM-ArraysFatigue monitoring of cyclically loaded shot peened high-strength steel components can be accomplished via magnetic permeability measurements during laboratory tests or in service. These measurements can be performed either continuously using permanently mounted Meandering Winding Magnetometer Arrays (MWM®-Arrays) or intermittently with scanning MWM-Arrays. The results obtained to date suggest that MWM-Array permeability measurements can provide early detection of fatigue damage in steels before conventional methods can detect any changes. This has been demonstrated to be particularly significant in the presence of high compressive stresses introduced by shot peening. One of the fatigue tests was suspended when accelerating changes in local permeability were detected. Examination of the fatigue specimen in a scanning electron microscope detected only a few relatively small cracks, e.g. 50–200 μm long at the surface. Fractography, however, revealed significantly longer cracks. For the same specimen, conventional eddy current and ultrasonic testing failed to provide any indications of cracks, and fluorescent liquid penetrant detected only an inconclusive spot indication. This paper provides a comparison of the permeability changes and fractography data with a fatigue crack growth curve based on a FASTRAN analysis accounting for residual stresses from shot peening. A comparison of the experimental data and crack growth analysis results suggested that MWM-Array magnetic permeability measurements may detect cracks in the compressive stress field when they are about 50 μm deep.Fatigue critical areas, particularly in aircraft components, are often cold worked by shot peening, roller burnishing, or cold expansion to introduce compressive stresses. These compressive stresses significantly increase fatigue life, at least in the case of intermediate and high-cycle fatigue, typically well beyond the design life of the components. If, however, fatigue damage with ensuing fatigue crack initiation and growth does develop, it is important to detect it well before a crack may become critical. Timely detection and characterization of fatigue damage would allow prevention of a failure. Moreover, if fatigue damage is detected early enough, a corrective action, e.g. a minor rework, could become an option. Early damage detection is an integral part of Adaptive Damage Tolerance (ADT), an approach to component life management that requires improved observability of causative factors and material damage Until recently, early detection and characterization of fatigue damage was limited to laboratory methods, such as X-ray diffraction Electrical conductivity and/or magnetic permeability measurements using the ‘Meandering Winding Magnetometer’ (MWM) eddy current sensors and MWM-Arrays The inductive MWM-Array sensor utilizes a meandering primary winding with numerous fully parallel secondary windings (sensing elements). Permanently, mountable MWM-Arrays are particularly suited for continuous fatigue monitoring applications, e.g. for fatigue tests of specimens and components and for in-service monitoring at difficult-to-access locations. Scanning MWM-Arrays with multiple sensing elements provide the capability to generate images revealing, for example, localized damage and cracks. The scanning MWM-Arrays are particularly useful for aircraft and other structures where eddy current testing (ET) is already a widely accepted technique for inspection, while embedded MWM-Arrays provide a potential ‘alternate means of compliance’ for these inspections.In an MWM-Array, a drive winding, with linear drive segments is excited with a current at a prescribed frequency, typically from under 1 kHz up to 40 MHz, which provides a desired spatial distribution for the imposed magnetic field. The drive current produces a time varying magnetic field that induces eddy currents in conducting test materials that follow the drive winding pattern. Inductive sensing elements sense the absolute variations in the magnetic field due to the presence of the test material and local defects or geometric features that alter the flow of the induced eddy currents.In the micro-fabricated MWM-Arrays, the windings are adhered to a conformable substrate, producing a very thin and flexible sensor. The MWM-Arrays used for this study are shown in . Other example MWM-Arrays can be found in a number of papers The design of the drive winding produces a magnetic field in the material under test, such that it can be modeled with considerable accuracy. The software converts sensor impedance magnitude and phase response into material properties, such as electrical conductivity or magnetic permeability. A patented grid method is used to interpret data in real time using a database of responses . Conventional iterative techniques for solving the inverse problem are relatively slow and are not guaranteed to converge to a physical solution. In contrast, the use of grid methods are guaranteed to converge as long as the data point falls within the grid and are relatively fast, making them well suited for the conversion of the image data into property estimates where tens of thousands of data points may need to be processed in real time.The fatigue specimen design was selected based on a specific geometry requirement (presence of a cylindrical cavity) and stress distribution criteria. The key stress distribution criterion—higher stresses in the central portion of the cylindrical cavity—was verified by a finite-element analysis (FEA). In the FEA model, a 100 lb axial pulling force was applied. The resulting stress distribution is shown in . Obviously, the cyclic loads in the tests were significantly higher so that the stresses used later in the fatigue crack growth analysis were scaled up.The specimens were fabricated from 4340M steel heat treated to obtain high ultimate tensile strength (>200 ksi). The specimens were shot peened to generate high compressive residual stresses near the surface. Some of the specimens were also cadmium plated after shot peening to simulate typical high-strength components material constructs.A linear MWM-Array with seven interleaved sensing elements located at 4-mm increments along the array length (see (a)) was mounted on the surface of the central cavity of the specimens. All seven sensing elements were located along the axis of the cavity. The outer sensing elements were located in the lower stress regions near the edges. During the fatigue tests, each of the seven sensing elements of the MWM-Array continuously monitored changes occurring in the material under the footprint of a sensing element. In the tests performed on a 9-ton Instron frame, the specimens were subjected to tension–tension cyclic loading at R=0.1. The impedance measurement instrumentation provided the drive current to produce a spatially periodic magnetic field. The measurements were performed at frequencies of 39, 100, and 251 kHz. In this frequency range, the depth of sensor sensitivity for this steel is, perhaps, between 0.2 and 0.5 mm. However, the sensor can continue to monitor crack growth when a crack grows deeper than 0.5 mm due to crack length and crack opening increase at the surface.The GridStation® software converted these data to local magnetic permeability so that results were obtained in terms of permeability measured at each individual sensing element within the MWM-Array. During fatigue testing, data is recorded continuously, without interrupting the test, at each channel using a seven-channel parallel architecture impedance instrument.Both types of specimens i.e. (1) shot peened and (2) shot peened and cadmium plated, were subjected to fatigue testing using a constant-amplitude loading. Results of the MWM permeability measurements made during a fatigue test of one of the shot peened specimens are presented in . In this test, no significant permeability changes were detected within the first 7000 cycle in any of the seven channels, i.e. over the entire 28-mm long section under the MWM-Array footprint. In the range between 7000 and 31,000 cycle, all seven channels detected gradual permeability changes. However, these changes were significantly faster in the higher stress area compared to the areas near the edges where the FEA indicated substantially lower stresses. At about 31,000 cycle, two of the centrally located channels of the MWM-Array showed a sharp increase of locally measured permeability, and the test was terminated at 33,500 cycle.After the test, the central region of the specimen shown in (inset photo) was examined in a scanning electron microscope (SEM) and about twenty distinct cracks were reported. Most of them were fairly small, on the order of 50 μm long at the surface. The longest of the cracks detected in the SEM and shown in was about 200 μm long at the surface. This irregularly shaped crack appeared to consist of four nearly parallel ‘horizontal’ cracks interconnected by nearly vertical cracks. This specimen was also examined by conventional eddy current, ultrasonic, fluorescent magnetic particle, and fluorescent liquid penetrant inspection. The fluorescent liquid penetrant inspection detected two small round indications, each less than 0.25 mm. The other nondestructive tests did not detect any indications. The cavity was then scanned with an imaging MWM-Array shown in (b, c). During the scanning, the drive was oriented perpendicular to the axis of the coupon cavity, i.e. perpendicular to the anticipated predominant orientation of fatigue cracks. This orientation was the same as in fatigue test monitoring with a permanently mounted MWM-Array shown in (left) shows the permeability image obtained with the imaging MWM-Array. This image shows the distribution of fatigue damage in the high-stress area of the specimen and reveals two adjacent zones within the image with a higher permeability. The zone on the left contains two spots with the highest permeability.After the SEM of the central cavity region and MWM-Array imaging of the cavity were completed, the specimen was notched on the backside and, upon cooling in liquid nitrogen, was broken for a fractographic examination. shows fractography results revealing two nearly coalesced cracks. The larger crack is 1.38 mm deep and at least 2.57 mm long. The combined length of the two cracks is about 4.3 mm. Striation count was carried out at selected locations on both cracks. Estimated crack growth rates, da/dN, at the selected locations are tabulated in The striation count suggested a reduced crack growth rate at some of the deeper locations. This can be attributed primarily to the changes in the applied stresses with depth as indicated by the FEA. Spatial variations in microstructure and residual stress redistribution could also contribute to crack growth rate variations. It appears that some of the MWM-Array sensing elements captured changes in the crack growth rate via changes in the slope of the measured magnetic permeability vs. cycles curves.The FEA indicated that the central region in the test specimen had the highest stresses (see ) and a significant stress gradient through the thickness. An estimate of the normal stresses through the thickness and along the anticipated crack plane is shown by the upper dashed curve in (note that the distance from the surface, x, is plotted on a logarithmic scale). The maximum stress at the free surface (x=0) was 1470 MPa. The assumed residual stresses due to shot peening are based on literature data Using the assumed normal stress distributions along the potential crack plane, the stress-intensity factor (K) at the maximum depth location for a surface crack emanating from the free surface (a/c=1) is shown in . The dashed and solid curves are the K values as a function of crack depth without and with residual stress, respectively. The approximate surface-crack solution was obtained by using a Green's function approach to calculate the stress-intensity factors for an edge crack ). However, the shot-peened specimen developed negative minimum stress-intensity factors for crack depths less than about 0.5 mm. Because most of the fatigue life is consumed for crack less than 0.5 mm, the Kmin value for the shot-peened specimen was assumed to be zero (crack surfaces were assumed to close at zero stress-intensity factor). This is a reasonable assumption for large surface cracks under nearly plane-strain conditions shows the effective stress-intensity factor against fatigue crack growth rate relationship (solid curve) that was used to make life calculations for the specimen with and without residual stress. The crack growth rate data were obtained from Swain et.al. A comparison of calculated and measured crack depth against cycles and crack depth against rate are shown in , respectively. In the calculations, a single semi-circular surface crack was assumed to occur at the maximum normal stress location and propagate through the thickness. For the no residual stress case, R=0.1 loading was used, but the shot-peened specimen was analyzed with R=0 conditions to simulate the contacting crack surfaces under compressive stress-intensity factors. For large cracks, the calculated crack-opening stress levels are essentially the same for R=0 and R<0 for plane-strain conditions. The solid symbols in are crack depths measured on two surface cracks on the shot-peened specimen during the fractographic examination described in . Both cracks were nearly semi-circular and had partly coalesced. shows a comparison of the measured and calculated crack growth rates. The comparison between measured and calculated rates was quite good, but indicated that the measured rates were for cracks that had grown away from the influence of the residual-stress field. Future study is needed to measure rates at smaller crack lengths and to relate the assumed initial crack size to either metallurgical features in the material, machining marks, or to the shot-peened surface roughness. In addition, small cracks emanating from inclusions or surface marks in the steel may develop negative crack-opening stresses under compressive loading due to residual stresses.Based on a comparison of the MWM-Array generated permeability image shown in (left), with the results of fractography, the two highest permeability spots within the left zone in the image correspond to the two adjacent cracks revealed by fractography. Many, if not all, of the other twenty short cracks observed during the SEM of the cavity, i.e. prior to breaking the specimen for fractography, were most likely a part of the two nearly coalesced cracks. The somewhat lower permeability ‘halo’ that surrounds the MWM detected crack indications on the scanned image in the left zone as well as the entire right zone correspond, for the most part, to significant ‘precrack’ fatigue damage. These zones may have contained microcracks, e.g. <3 μm, that could not be reliably detected in the SEM for these machined and shot peened surfaces, and, thus, could have been present but missed in the SEM. Data from the permanently mounted MWM-Array (see ) provides the history of fatigue damage accumulation. It detected an early onset of changes of the measured magnetic permeability and revealed a gradual magnetic permeability increase. It appears that this gradual magnetic permeability increase corresponds primarily to fatigue damage prior to formation of cracks or at least prior to formation of short cracks, e.g. cracks that are shorter than the grain size. shows the FASTRAN generated fatigue crack growth curve and final crack depth values obtained from fractography (crack depth scale on the right) as well as the normalized MWM-Array measured permeability curves (left scale). This figure reveals that the permeability curves for the two central channels, indicating the accelerated permeability increase, reflect faster crack growth toward the end of the test. As an illustration of the MWM-Array capability, shows that at 17,000 cycle when two of the MWM-Array channels indicate a permeability increase as large as 2%, the estimated crack depth is about 50 μm. Note that a 2% change in permeability is an order of magnitude greater than the measurement noise. The MWM-Array can detect significantly smaller permeability changes that are likely to correspond to initial crack growth increments of just a few microns.The results presented here suggest that permanently mounted MWM-Arrays can be used for fatigue studies of steel specimens or components to detect short cracks and monitor their growth. This capability can be used for early detecton of fatigue damage, i.e. early stage diagnostics (prior to formation of cracks detectable by traditional nondestructive methods) and for prognostics, i.e. assessment of how long a steel component can operate safely and when it should be reinspected. When required, MWM-Arrays can be mounted at critical locations on such components for inspections as frequently as required, even after every flight in the case of aircraft components. Scanning MWM-Arrays providing wide-area images of MWM measured permeabilities can also be used as frequently as practical. For some applications, the best solution will be a combination of MWM-Arrays permanently mounted at locations that cannot be reached during inspections, without significant disassembly, and scanning MWM-Array for more accessible locations.Furthermore, when local small cracks can be detected reliably in fatigue critical locations, life extension by local rework could provide a major cost reduction and life extension contribution. Following rework, MWM-Arrays could provide continuous or frequent periodic monitoring of repaired locations. This is relevant both for aging aircraft and design of new aircraft.MWM-Arrays provide the capability for continuous on-line monitoring of crack initiation and growth during fatigue tests of steel specimens and components. In low-alloy steels, permanently mounted MWM-Arrays can detect initial fatigue crack growth increments of just a few microns. In shot peened steel components, both permanently mounted and scanning MWM-Arrays can detect cracks that are difficult to detect by other nondestructive methods.Injectable materials for treating vertebral body fractures or stabilizing osteoporosis defects are demanded to be used in minimally invasive orthopaedic procedures such as percutaneous vertebroplasty (PVP). This technique was introduced a decade ago in France by Galibert and Deramond The cements were prepared at room temperature and injectability was evaluated according to the protocol established. Curing parameters were obtained from the polymerization exotherms. The characterization of the cements was assessed by determining residual monomer content (RMC), glass transition temperature and mechanical properties. Fosfosal release was evaluated in vitro and the behaviour of the cements was studied through the evolution of the surface by microscopic and spectroscopic techniques. Finally, the biocompatibility of the formulations was evaluated in vivo by intramuscular implantation in rats and intraosseous implantation in rabbits.PMMA beads (33 μm of average diameter) were supplied by Industrias Quirúrgicas de Levante (IQL beads) and have earlier been characterized The sol–gel bioactive glasses were prepared as follows: Appropriate amounts of tetraethyl orthosilicate (TEOS), NaNO3, Ca(NO3)2·4H2O and triethylphosphate were mixed with water using a 2 HNO3 solution as the catalyst. A water:TEOS mol ratio of 8 was used in all cases. The mixture was stirred for 1 h and then, placed in a poly(tetrafluorethylene) mould at 70°C for 3 days. After ageing the gel was dried at 110°C for 3 days and then at 150°C for 2 days. The dried gel was ground for 60 min in a rotating mill (Fritsch) at 600 rpm. Finally, the sample was treated at 700°C for 3 h. The nominal composition of the glasses prepared is shown in The particle size distribution was determined by laser ray scattering using a Microtrac SRA-150©, Leeds & Northrup, North Wales, PA analyser: Approximately, 10 mg of the sample were thoroughly dispersed in 2 ml of acetone and, then immersed into an ultrasonic bath for 15 min in order to avoid clusters of the particles. A continuous thin layer of the particle suspension was exposed to a laser ray of 1007 eV of intensity. After a exposure time of 30 s, the ray scattering provided the particle size distribution. An average of three tests were performed for each sample.The bioactive bone cements were formulated using a solid:liquid ratio of 1.7:1. The liquid component consisted of MMA monomer, and DMOH (1 wt% with respect to the liquid phase) as activator of reduced toxicity, in all cases. The solid component consisted of PMMA beads, the corresponding bioactive glass, the drug fosfosal and BPO (1.5 wt% with respect to the solid phase), as the initiator. In the first place, formulations of bioactive cements were prepared with different proportions of glass (20, 40 and 60 wt%) in absence of fosfosal. Secondly, formulations containing 40 wt% of glass and different amounts of fosfosal (20–30 wt%) were prepared. The composition of all the solid phases employed in this work are summarized in Solid and liquid components of the cements were conditioned for 2 h at 23±1°C before the determination. A total amount of 3.0±0.1 cm3 of cement was prepared and charged in a 2 cm3 disposable syringe (Plastipak, Becton Dickinson). A gauge 8 needle (Bone Marrow Biopsy/Aspiration needle, Surecut BMB) 150 mm length was fixed to the syringe and the cement injected to a recipient. The weight percent of cement injected to the recipient respect to the total amount of cement charged in the syringe was considered as the injectability.The exothermic polymerization temperature profile was registered automatically at 25°C using a thermocouple connected to a high sensitivity thermotester and positioned within its junction in the centre of a cylindrical Teflon mould at a height of 3 mm in the internal cavity. The mould (10 mm in diameter and 15 mm high) was placed in a thermostatically controlled bath described in a previous paper Residual monomer was determined by means of 1H-NMR spectroscopy with a Varian XL 300 spectrometer. Three samples of each type were dissolved in deuterated chloroform (5% wt/v), using tetramethylsilane as internal standard and then filtered with Whatman filters (0.2 μm) in order to remove the inorganic component. All the specimens were kept for 7 days in air before the analysis. The residual monomer content (% RMC) in the cured cement was calculated from where AM is the integration of the signal assigned to the methoxyl protons of the MMA monomer (3.80–3.72 ppm), AM+P is the integration under the signals assigned to the methoxyl protons of the MMA and PMMA (3.80–3.40 ppm) and, BV and FS are the amounts (wt%) of the corresponding bioactive glass and fosfosal, respectively, incorporated to the solid phase.Glass transition temperatures (Tg) were measured by Differential Scanning Calorimetry with a Perkin DSC7 interfaced to a thermal analysis data system TAC 7/DX. The dry samples were prepared in the form of thin films (15–20 mg) placed in aluminium pans and heated from 50°C to 200°C at a constant rate of 10°C/min. Tg was taken as the midpoint of the heat capacity transition.Mechanical properties of cured cements were evaluated in compression at room temperature using an Instron 4301 testing machine. A load cell of 5 kN and a crosshead speed of 20 mm/min was used in the compressive testing according to ISO 5833 standard specification Rectangular shaped samples of 30 mm×10 mm and 1 mm thickness were prepared for release experiments. The samples were soaked in 10 ml of phosphate buffer solution (pH=7.0) and they were kept at 37°C. Aliquots were taken at different periods of time and the medium was totally changed by fresh solution. The concentration of fosfosal released was determined by visible ultraviolet spectroscopy (UV-VIS, Perkin-Elmer Lambda 35) analysing the signal at 275 nm corresponding to fosfosal. A calibrated curve of fosfosal was obtained previously by measuring the absorption of the UV signal of solutions of known concentration in the same medium.Discs of 15 mm diameter and 1 mm thickness were immersed in SBF at 37°C. Water uptake and weight loss were determined gravimetrically at different periods of time at 37°C. At appropriate times, the samples were removed, blotted quickly with absorbent paper to remove the water attached on its surface and weighed. In all the experiments a minimum of three samples were measured and averaged. The percentages of hydration degree and weight loss were calculated from where Wh is the weight of swollen specimen at time t, Ws is the weight of the sample dried at time t and W0 is the initial weight of the dry specimen.The morphology of the surface of samples after immersion in SBF was examined by environmental scanning electron microscopy (ESEM), using a Philips XL 30 microscope and by scanning electron microscopy (SEM-EDS) with a Philips XL 30 connected to a microanalyser of X-ray EDAX DX-4. The composition of the surface was analysed by ATR-FTIR spectroscopy (Perking Elmer Spectrum One) and by X-ray diffraction with a Philips-MRD diffractometer using CuKα radiation (λ=1.542 nm).Intramuscular implantation of rods of cured cement (3 mm diameter×15 mm length) were cannulated in the dorsal muscle of female Wistar rats of average weight 300±10 g. Three batches of three animals were operated on and sacrificed after 2, 4 and 8 weeks of implantation. For histological evaluation the samples were fixed first in 10% neutral buffered formalin (phosphate buffered, pH=7.6) and embedded in paraffin wax. Histological sections were prepared and stained by the haematoxylin and eosin technique. The samples were examined in a Nikon Microphot-FXA optical microscope.Intraosseous implantation was studied in New Zealand rabbits of average weight 3.820 kg (3.450–4.260 kg). The rabbits were premedicated with atropine sulphate (0.3 mg/kg, IM) and chlorpromacine (10 mg/kg, IM). General anaesthesia was given by intramuscular injection of Ketamine hydrochloride (50 mg/kg, IM) and fentanile (0.17 mg/kg, IM). A bone defect in the femoral condyle was created by using a slow-speed drill and the bioactive cement BVSP-40-FS-30 was injected and allowed to cure inside. After surgery, the animals were allowed to move freely in their cages without joint immobilization and they were sacrificed at 12 weeks by an intravenous injection of pentotal®.The femoral condyle was cut longitudinally and then was included in methacrylate Acrylic bone cements incorporating bioactive glass and the drug fosfosal have been specifically formulated for use in percutaneous minimal invasive vertebroplasty. Two types of glasses were prepared to that end, BVSP and BVCP, whose nominal composition is shown in , and their particle size distributions are shown in . From the particle size distributions, values of average diameter of 26 and 36 μm were obtained for the BVCP and BVSP glasses, respectively. The injectable formulations developed in this work were based on two components, solid and liquid, which were mixed to produce the cured cement by the radical polymerization of the monomer MMA. The heat produced during the exothermic polymerisation of PMMA formulations has been related to the anti-tumoural effect of PMMA, but it may be sufficiently high in magnitude and long in duration to cause thermal necrosis of bone tissue and intraosseous neural tissue The exotherms of polymerization of the experimental formulations were measured at 25°C and values of the curing parameters are summarized in . It can be observed that the drug-loaded bioactive cements provided an increase of the dough and setting times with respect to the PMMA control which gives time for injection of the material. Also, a decrease of the maximum temperature up to approximately 10°C was measured during the free radical polymerization of the monomer for the formulations containing either fosfosal or bioactive glass, and up to 20°C for those incorporating both components. This result could contribute to reduce the risk of necrosis at a macroscopic level outside the implant, as it has been observed after the injection of N-butyl-cyanoacrylate whose polymerization is less exothermic than PMMA, and exhibited compressive effects on the tumour tissue, but without signs of significant necrosis outside the acrylic tumour cast Vertebral percutaneous puncture is performed using needles of different lengths and diameters depending on the vertebral level . Formulations containing PMMA and fosfosal were also tested giving rise to injectability values around 80% of the mass charged, as high as those obtained with bioactive formulations. However, injection times were longer for the latter formulations. A control of PMMA was also tested but it could not be injected in the same conditions.Cured cements were characterised measuring the RMC and the flexibility of chain by means of the determination of the glass transition temperature (Tg). Results are shown in . RMC remained unchanged for the formulations containing either fosfosal or bioactive glass although this parameter slightly increased for the cements containing both components. However, all these values were in the range of those reported for PMMA cements Among the mechanical properties to be considered in orthopaedics, compressive properties are the most relevant for replacement of cancellous bone whereas tensile properties are important for cortical bone . For dry specimens containing any bioactive glass and fosfosal a significant decrease of the compressive yield strength was observed with respect to PMMA although the values were in the range 90–80 MPa, which are high enough to guarantee the initial mechanical support. Young's modulus increased significantly for cements prepared with the BVCP glass and fosfosal but no significant differences were observed for those incorporating the BVSP glass. Compressive yield strength of the drug-loaded bioactive cements after immersion in SBF for 15 days were in the range 35–50 MPa, considerably lower than those obtained for dry specimens, due to the solution of both glass and drug in the medium, however, they were higher than that of the cancellous bone (5–10 MPa) ). Mechanical properties were similar to those obtained previously in vitro after 15 days of implantation and they remained constant after that time.The release profiles of fosfosal in phosphate buffer of pH=7.0 are plotted against time in . In all cases a moderate burst release around 10% of the drug was obtained in the first hour. This phenomenon is well documented in the literature In vitro behaviour of the drug-loaded bioactive cements was studied in SBF. Results of hydration degree and weight loss for the cements formulated with BVCP or BVSP glass are shown in , respectively. The in vitro behaviour was independent on the composition of the glass. Hydration degree increased with time during the first 2 days and from then on, equilibrium was attained. The values of hydration degree at equilibrium for the cements prepared with any glass and fosfosal were in the range 10–16%, higher than those obtained without fosfosal, as expected due to the hydrophilic character of the drug bearing a carboxylic group. The profiles of weight loss versus time followed the same trend as those of hydration degree, showing that water uptake and solution of glass and drug, are processes that take place simultaneously.The formation of an apatite-like layer on the surface of the drug-loaded bioactive cements was confirmed by experimental techniques such as ATR-FTIR, XRD, ESEM. shows the ATR-FTIR spectra of the cement BVSP-40-FS-30 before and after immersion in SBF for different periods. The spectrum obtained before immersion showed the typical bands assigned to the polymer PMMA: 1721 cm−1 stretching vibration of the carbonyl group, 1400–1435 cm−1 stretching vibration of CH2 and CH3 and 1144 cm−1 stretching vibration of C–O. After 4 days in SBF the spectrum of the surface of the cement showed a new broad band at 1025 cm−1 which was assigned to the vibration of the phosphate groups of hydroxyapatite. Similar results were obtained for the cement BVSP-40-FS-20, however, for the cements prepared in absence of fosfosal, BVSP-40 and BVSP-60, only the cement containing 60 wt% of glass showed deposition of hydroxyapatite but at longer immersion time (13–15 days). This fact indicates that the phosphate groups derived from fosfosal participate in the apatite nucleation accelerating the process, although its detailed mechanism is not yet known. shows the X-ray diffraction patterns of hydroxyapatite and the bioactive cement BVSP-40-FS-30 after 4 days of immersion in SBF. The XRD pattern of the bioactive cement exhibited the characteristic peaks at 2θ=26° and 32° (corresponding to d-spacings of 3.37 and 2.79 Å, respectively) attributable to hydroxyapatite. shows the ESEM photographs of the surface of this cement before and after 15 days of soaking in SBF. The surface of the soaked cement showed spherical particles containing tiny crystals which correspond to the apatite identified by XRD. Apatite started to precipitate after 4 days of immersion in SBF and the spherulites increased in both number and size with immersion time. This phenomenon can be observed in the EDS patterns obtained at different periods of time (). An increase in Ca and P concentrations with immersion time were observed and after 15 days the content of Si decreased considerably and the main components were Ca and P.Formulations prepared with the BVCP glass but in absence of fosfosal presented morphological changes in shorter periods of time compared with those observed in cements containing BVSP. The cement BVCP-40 showed depositions of hydroxyapatite after 10 days of immersion, and the cement BVCP-60 after 4 days, which indicates that the presence of P2O5 plays an important role in the formation of the Ca–P layer. For cements prepared with BVCP and fosfosal, BVCP-40-FS-20 and BVCP-40-FS-30, the apatite layer started to precipitate about 3 days after immersion in SBF which confirms that the phosphate groups of fosfosal accelerates the apatite nucleation process as mentioned above.The biocompatibility of the cured cements was first studied by intramuscular implantation of rods in rats. The histological response to the formulations prepared with bioactive glass and fosfosal was independent on the type of glass, and, as an example, in Secondly, in vivo experiments were carried out by intraosseous implantation of the cement BVSP-40-FS-30 in the femur of rabbits. show the histological results after 12 weeks of implantation. shows a trabecular irregular area corresponding to bone cement surrounded by neoformed osseous trabecular tissue, presumably induced by the cement. shows interdigitating connective tissue surrounding small pellets of cement along with haematopoietic bone marrow, in the right hand, and in the left hand, some aggregates of cement can be seen together with connective tissue and fragments of neoformed bone tissue. In Biomechanical study of a prosthetic solution based on an angled abutment: Case of upper lateral incisorObjectives: To study the complex behaviour of an upper lateral incisor restoration using an angled abutment, a mechanical analysis of the abutment bearing capacity was firstly carried out. The evolution of bone properties around implant was then simulated as a function of time to estimate the maximal load that could be supported by the prosthetic solution without bone damage. Materials and methods: According to the Food and Drug Administration procedure, experimental tests were firstly carried out on five samples. A 25°-angled abutment screwed to an implant embedded into a massive steel bloc was submitted to a static loading. Two finite element models were also built: the first one (I) to interpret and complete the results obtained in the experimental part and the second one (II) to simulate bone remodelling around implant considering a strain energy stimulus. Results: According to experiments, the abutment straightening was observed for an average force of 869 N. Numerical model (I) confirmed this result and indicated that the initial irreversible deformation (yielding) of abutment was obtained for a 283 N compressive force. It could thus be deduced that this abutment can safely be used for an incisor restoration. Model (II) showed that, after 26 months, some of the cancellous bone initially present in an approximately one millimetre thick shell surrounding the implant had reached the density of cortical bone. A safe load notion corresponding to the force leading to the maximal admissible strain value for trabecular bone was introduced. It evolved from 44 N after surgery to approximately 160 N after 26 months.The anterior maxilla morphology often imposes the use of an angled-abutment in the case of an upper lateral incisor restoration. This particular implant orientation leads to a biomechanical behaviour of the prosthetic solution that strongly differs from the one encountered in the case of a straight one.However, the photoelastic models of Brosh et al. Because of the lack of data about the strength of angled abutment, it was necessary to perform a complete mechanical study before envisaging its use for dental applications. Firstly, an experimental characterization was carried out to get information about the limit load and the ruin mode of the abutment. An elasto-plastic finite element analysis simulating the experimental device was then conducted for a deeper understanding of the results obtained and to identify the compressive force leading to the initial yielding of its weakest section. The final step consisted in investigating the behaviour of a prosthetic solution based on an angled abutment for the restoration of an upper lateral incisor. The previous finite element model of implant, abutment and screw was implemented inside a maxilla section and equipped with a ceramic crown. Numerous studies In this study, an attempt was made to describe the remodelling around the implant by simulating the evolution of bone apparent density and Young's modulus over a given osseointegration period. The aims of this paper are then as follows:to define the force level leading to the initial yielding of the abutment and its mode of failure;to evaluate the evolution of bone material properties around implant and then to deduce the maximal load supported by the device.The experimental device described here had to respect the procedure described by the F.D.A. For experimental tests, the implant was glued in a steel cylinder with epoxy glue.The abutment and the screw were composed of the same titanium alloy (TiA6V4) as the implant. Loading was applied vertically, on a hemispheric part situated on the abutment. Five samples were tested under these conditions.Two finite element software packages were used in this work. HyperMesh 7 was applied to create the FEM models. MSC-Marc software was used to solve the problem.Two meshes were accomplished: the first one concerned the experimental device (I) and the second one the prosthetic solution located in its environment (II). present respectively the first and second configuration. The same grid of implant, abutment and screw was used for both cases. This assembly was subdivided into 10,541 elements. The experimental environment was composed of a cylindrical base, epoxy layer and hemisphere. These parts were divided into 19,538 hexa- and tetrahedral elements. The complete model (I) was composed of 30,079 elements and 18,795 nodes leading to approximately 56,400 degrees of freedom.Model (II) was made up of implant, abutment, screw, a maxilla section and a ceramic crown. The geometry of the maxilla was obtained by means of a computed tomography exam of a willing patient. The mean thickness of cortical layer was estimated to 2 mm and supposed to be constant in the finite element model (see ). This maxilla section was divided into 38,475 hexahedral elements and 41,657 nodes to guarantee a high precision of the results in the implant neighbourhood. The maxilla section was chosen with a length of about 80 mm to avoid boundary conditions influencing stress and strain distribution in implant surrounding bone. The mean size of elements near the implant was of 0.35 mm. This value was retained to allow a precise description of bone properties evolution around the implant during the remodelling process.In model I, three materials were used, namely titanium alloy TiA6V4 for implant, abutment and screw, stainless steel 316 L for support and hemisphere and finally epoxy glue (). Because of the globally low stress level in the epoxy interface, its constitutive behaviour was supposed to be simply elastic. To describe the non-linear behaviour of the system, elastic–plastic constitutive laws were introduced for metallic constituents. The constitutive relation of the titanium alloy TiA6V4 () was established by Bonnet-Lebouvier and Klepaczko In model II, four materials were initially used: the same titanium alloy for implant, screw and abutment, cortical and cancellous bones and ceramic for crown. An elastic isotropic behaviour was supposed for bone and ceramic.On the basis of Wolff's “law of bone transformation” ρi+1−ρi=B|(U/ρi)−k−(w/2)|−|(U/ρi)−k+(w/2)|2+Uρi−k(ti+1−ti),where stimulus U is the strain energy density field, w the width of the dead zone and B and k are constants. k characterizes the centre of the dead zone, B is a coefficient governing the rate at which adaptation occurs and i indicates the current time step. It could then be used in the finite element calculations for each element. k and B were chosen to be respectively 0.004 N mm/kg for more details). However, the retained value remains an assumption and the reference to actual time is not pretended to be accurate. Following the work of several authors stated in a review of Doblaré et al. where E0 |
= 18.637 GPa and ρ0 |
= 2.1 kg/m3 correspond to the properties of perfect bone without porosity. A 26 months period of osseointegration was simulated divided into six time intervals. At each time step, the Young's modulus value was re-evaluated thanks to the above relationships. Initial material properties of both models are given in Concerning model I, all translations of its bottom nodes were forbidden in order to reproduce the fastening of the device to the testing machine. The external loading was modelled by applying a vertical displacement Uy function of time (see ), to the top node of the hemisphere mesh. This displacement was varying linearly from 0 to −0.24 mm during computing time. Frictionless contact conditions were managed between the hemisphere and the conical part of abutment.Large displacements and small elastic and plastic strains were considered. A fixed time step algorithm was chosen for the calculations. The displacement of −0.24 mm was applied on forty steps, which leads to a value of Δu |
= −0.24/40 = −0.006 mm per step.The nodes of both maxilla sides of model II were constrained normally to the cut sections in order to reproduce interactions with the rest of maxilla bone. Besides, 32 nodes were vertically restrained to avoid rigid body motion. Contact was defined between implant and bone. A spherical foodstuff was modelled by means of a rigid surface. Another contact was introduced between the crown and the foodstuff. A displacement of the foodstuff was imposed to generate a load on the prosthetic solution in order to get closer to the actual conditions. A mechanically perfect contact was assumed between the angled abutment and the crown as these parts are actually glued. The same hypothesis was considered between implant, abutment and screw.To characterize the mechanical behaviour of the angled abutment, it was chosen to record, on the experimental device, the evolution of compressive force as a function of the displacement of the machine piston. The curves obtained were quasi identical for the five samples tested. An example of such a curve is presented in . At the beginning, a relatively linear relationship was observed between force and displacement. This was followed by a parabolic segment including a maximum and corresponding to the global yielding of the weakest section of the abutment. Then, a buckling phenomenon, materialized by a rapid decrease of the force as a function of displacement was observed. After the complete structure collapse, the force increased to reach a peak, which corresponds to the abutment fracture.The critical force corresponding to the instant of global yielding of the weakest section (or buckling of the abutment) was identified from the force–displacement diagrams. The average magnitude of the critical forces obtained from the five samples was estimated to 869 N as illustrated in . The five samples practically behaved in the same way. A straightening of the angled part of the abutment was observed, consecutive to the local buckling of its weakest wall (To validate our finite element model with respect to the experimental tests, the evolution of the reaction force, at the point of application of displacement Uy, as a function of the imposed displacement is plotted in . It can be observed in this figure that the structure response was elastic during the first three increments, i.e. up to a level of loading of 283 N. At increment 5, for a reaction force of 471 N, the non-linear nature of the answer started to be visible.The curve shows a maximum force of 881 N at increment 16 for a displacement of −0.096 mm. During the next increments, the force decreased to reach 702 N for a displacement of −0.24 mm (increment 40).The equivalent plastic strain defined below was introduced:εeqp=23(ε1p−ε2p)2+(ε2p−ε3p)2+(ε1p−ε3p)2,where εip (for i |
= 1, 2, 3) states for the eigenvalues of the plastic strain tensor.It was observed that for increment 3, εeqp became non-nil and from increment 5 this measure started to be significant (0.325%), see . This yielding was located on the weakest section of the abutment, in the neighbourhood of the junction with the hemisphere. A small yielding of the hemisphere was also noted.A change of apparent density occurred only around the implant. For this reason, it was chosen to present the results about bone's properties evolution in an approximately one millimetre thick shell surrounding this insert (see shows the apparent density distribution inside this shell around the implant for different instants. The highest values of apparent density were situated in bone facing the facial side of the neck. Important values were also noted in the apical region and near the threads tip. illustrates the bone apparent density evolution inside the bone shell. The horizontal and vertical axes represent respectively time and apparent density. Elements of the shell are sorted along the third axis in function of the increasing values of apparent density. This graph shows that the discard of apparent density values increased with time. After 26 months simulated, the tissue properties (E, ρ) of some elements had reached the values of cortical bone whereas for others, they did not change.Due to the abutment angle, a bending of the implant occurred. illustrates axial stress inside implant and angled abutment after a 26 months healing period and for a 160 N external force. The bending is stated by the concentration zones of axial stress situated in the implant on the lingual side of the apex and on the facial side of the neck.Moreover, the bone safe load notion was introduced corresponding to the force leading to a maximal admissible strain value for trabecular bone of ɛt |
= 0.005, see Section for justification. The bone safe load evolution is presented in . At initial time, i.e. just after surgery, the maximal load that can be applied without damaging peri-implant bone was 44 N. This value increased with time to reach about 160 N after 26 months. It can be observed that the safe load evolution slope increased during the first 15 months. The expected saturation phenomenon can be guessed from the end of the studied period.According to the experimental results, the average force value where the whole weakest section of the abutment is yielded, has been identified to RF |
= 869 N. Thanks to finite element simulations, the value of this force could also be determined and was estimated to 881 N. Both values were very close to each other indicating that the FE model accurately represents the static experimental tests until increment 16. It is important to note that a direct comparison of this curve with the experimental one was not possible. Indeed, the experimentally measured displacement was obtained from the machine piston motion that was not taken into account in our simulations.Besides, experimental results did not allow to identify the compressive force leading to the first yielding of the abutment. Conversely, this information was obtained thanks to the finite element calculations. This force was estimated to 283 N. It can be concluded that the abutment is not endangered in case of an upper lateral incisor restoration. In fact, loads supported by these teeth are usually lower than 300 N according to Graig A local buckling phenomenon was experimentally observed for a monotonic loading. It started at the maximal value of the compressive load (869 N) and engendered a straightening of the abutment. The numerical force–displacement curve depicted in indicates that the maximal force was obtained for increment 16. The corresponding plastic strain locally exceeded 4.4% for this increment. Although this value remains relatively low compared to the critical elongation of the titanium (A (%) = 15), the local stability loss leads to the plastic collapse of the abutment.The plastic strain value of 0.325% obtained at increment 5 for a force of 471 N remains quite limited but the repeated loading of the abutment can lead to a cumulated plastic strain inducing a similar deterioration. Such phenomena could occur if the studied abutment was used for molar restoration.Bone apparent density distribution can be explained by the bending phenomenon due to the angle existing between the implant axis and the reaction force of the foodstuff. Indeed, bone apparent density increase happened in order to prevent implant rotation. Areas with the strongest evolution are in accordance with other authors Results about safe load gave some interesting indications about early periods of a single tooth restoration with immediate loading. Our simulations corroborated data available in literature Nevertheless, as the initial safe load value of 44 N for upper lateral incisor is strongly below the bite forces stated in literature It can be noted that bone damages are actually caused in peri-implant bone by surgery Furthermore, it is well known that osseointegration strongly depends on the interface properties of the implant It was also chosen in this study to use the strain energy density as stimulus. Although this stimulus was shown to predict reasonable or good bone apparent density distributions As bone structure is extremely complex, it is difficult to define an “admissible” stress or strain value. This one corresponds to the highest value avoiding the bone damage that could jeopardize implant osseointegration. A strain criterion was chosen here as it is often claimed that the amount of micro motions is the decisive factor for implant survival From all these data, it was finally decided to set the admissible strain at 0.5%. This value was considered as constant even though it may depend on local bone apparent density. In fact, the trabecular structure of cancellous bone can engender higher local strains. However, in our simulations, both bone tissues were supposed to be homogenous in overall sense as defined by Hill In spite of the deficiency of biomechanical data concerning bone remodelling, in particular in the vicinity of oral implants, the present approach gave interesting indications on peri-implant bone response in time and space. Moreover, the introduced concept of safe load and its evolution during the osseointegration period could be incorporated in an oral rehabilitation treatment planning.The abutment studied could safely be used, in the case of an upper lateral incisor restoration, for a range of external forces included between 0 and 280 N. No yielding was observed in this situation. However, if this abutment was used for a molar restoration, a risk of damage would exist as the forces applied may exceed 300 N. Deterioration would then occur by a cumulative yielding resulting from the mastication cycles.The use of an angled abutment generated bending stresses inside bone and implant.Bone remodelling mainly occurred in a one millimetre thick envelope around implant. This remodelling was highly heterogeneous and was more pronounced at thread tips. According to our assumptions, bone within these areas reached the density of cortical bone after 26 months.An attempt was made to determine the safe load preserving bone integrity as a function of osseointegration time. It evolved from 44 N after surgery to approximately 160 N after 26 months. A saturation trend was pointed out. Nevertheless, all these numerical results only indicate tendencies regarding the simplicity of the constitutive model used.Statistical second-order two-scale methodThe statistical second-order two-scale method for thermomechanical properties of statistically inhomogeneous materialsA statistical second-order two-scale (SSOTS) method is established in a constructive way for predicting the thermomechanical properties of statistically inhomogeneous materials. For this kind of composite materials, the complicated micro-characteristics of inclusions, including their shape, size, orientation, spatial distribution, volume fraction and/or material properties and so on, lead to changes of the macroscopic thermomechanical properties, such as stiffness, coefficient of thermal expansion and strength of material. In this paper, a statistical model at an arbitrary position of the composite material is defined to represent the microstructure of the statistically inhomogeneous media at first. And then, the statistical second-order two-scale analysis formulation is derived. Finally, the numerical results for some statistically inhomogeneous composites are calculated by SSOTS algorithm, and compared with the data by experimental and theoretical methods.Statistical second-order two-scale methodWith the rapid advance of science and technology, composite materials have been widely used in a variety of engineering and industrial products. According to their basic configuration, the composite materials can be divided into periodic composites and random composites. Further, the random composites can also be classified, according to the characteristics of random distribution, into statistically homogeneous and inhomogeneous materials. As is seen from , the shape, size, orientation, spatial distribution, volume fraction and material properties of inclusions are gradually changing from one end to the other. This kind of composite materials is called as the statistically inhomogeneous materials, which include functionally graded materials. Due to the microstructure continuously varying, the overall physical and mechanical properties of material gradually change, so the macroscopic material has multi-functional status in physics and mechanics. And these statistically inhomogeneous materials have attracted a deal of attention from scientists and engineers.However, some studies have suggested the need to consider the effect of the microstructure on the macrostructural properties. Based on the concept of a representative volume element, a higher-order theory was developed by coupling the microstructural and macrostructural responses Some finite element methods are employed to predict the thermomechanical behavior of FGM , and their effective computer generation algorithm has been developed by authors For the composites with random inclusion dispersions, all of inclusions in investigated structure are considered in geometry as ellipsoids or the polyhedrons inscribed inside ellipsoids. The size of each inclusion is denoted by the long axis a of corresponding ellipsoid. From the engineering survey and the statistic fitting method of data the microstructure of random composites is represented as followsIn the investigated structure Ω, there exists a constant ε, a≪ε≪L, L is the size of Ω, if at any point inside Ω there exist cells with the same size ε, and in each cell the random distribution model of inclusions is the same, then the composites are called as statistically homogeneous materials. If at an arbitrary point x0 inside Ω there exists a cell with size εx0 and its random distribution model depends on x0, then the composites are called as statistically inhomogeneous materials. In this paper suppose that the size εx0 and the distribution characteristics continuously vary with x0.Each random ellipsoid in the three-dimensional space is defined by 10 random parameters, i.e. the coordinates (x0,y0,z0) of the central point, the orientation (θaxy,θax,θbxy,θbx) of the long and middle axis and the sizes (a,b,c) of the long, middle and short axis. Let the random vector ζ=(x0,y0,z0,a,b,c,θaxy,θax,θbxy,θbx), it includes all the information of an ellipsoid. And suppose that a cell εQx0s (Qx0s denotes the 1-normalized cell) at point x0 contains N ellipsoids, and then its random sample is defined as ωx0s=(ζ1s,ζ2s,ζ3s,…,ζN-1s,ζNs).In this section, a new statistical second-order two-scale analysis formulation is derived by using a constructive way for calculating the thermomechanical behavior of statistically inhomogeneous materials, including stiffness parameters, coefficients of thermal expansion, strain tensor and stress tensor.The thermoelastic problem for the structure Ω is expressed as follows∂∂xjEijhkε(x,ω)∂uhε(x,ω)∂xk-αhkε(x,ω)T=fi(x)x∈Ωuε(x,ω)=u¯(x)x∈∂Ωwhere Eijhkε(x,ω) and αhkε(x,ω) are the coefficients of elasticity and thermal expansion respectively, and ω=ωx0s,x0∈εQx0s⊂Ω. uε(x,ω) is the displacement vector, and T is the temperature increment.We suppose that there exists an expected effective elasticity tensor {E⌢ijhk(x)} on the investigated structure Ω of the statistically inhomogeneous materials. Further the vector-valued displacement u0(x) is defined as the solution of following expected homogenization problem∂∂xjE⌢ijhk(x)∂uh0(x)∂xk-α⌢hk(x)T=fi(x)x∈Ωu0(x)=u¯(x)x∈∂ΩIntroducing the variable ξ=x-x0ε∈Qx0s for ωx0satx0, which denotes the local coordinate defined on 1-normalized cell Qx0s corresponding to x0, and then the material coefficients of microstructure in Qx0s can be expressed as Eijhkε(x,ω)=Eijhk(ξ,ωx0s) and αhkε(x,ω)=αhk(ξ,ωx0s). Since the displacement solution uε(x,ω) of the thermoelastic problem depends on both global behaviors of the structure Ω and local configuration in Qx0s, then it can be expressed as uε(x,ω)=u(x,ξ,ωx0s). Further, suppose that uε(x,ω) can be expanded into the following form in two-scale variables x,ξ.uε(x,ω)=u0(x)+εNα1(ξ,ωx0s)∂u0(x)∂xα1-H(ξ,ωx0s)T+ε2Nα1α2(x,ξ,ωx0s)∂2u0(x)∂xα1∂xα2+Mα1(x,ξ,ωx0s)∂u0(x)∂xα1-K(x,ξ,ωx0s)T+ε3P1(x,ξ,ωx0s)where Nα1(ξ,ωx0s)=(Nα11,…,Nα1n),Nα1α2(x,ξ,ωx0s)=(Nα1α21,…,Nα1α2n),Mα1(x,ξ,ωx0s)=(Mα11,…,Mα1n) are the matrix valued functions defined on Qx0s and H(ξ,ωx0s), K(x,ξ,ωx0s) are the vector valued functions, and u0(x) is the homogenization solution defined on problem Due to ξ=x-x0ε∈Qx0s, respecting the chain rule as ∂∂xi=∂∂xi+1ε∂∂ξi. We now substitute and match terms of the same order of ε, then a series of equations are obtained if the coefficients of εl(l=-1,0,1,2,…) from both sides are required to equal each other. Firstly, from the coefficients of ε-1 the following local problems defined on Qx0s for Nα1m(ξ,ωx0s)m=1,…,n and H(ξ,ωx0s) are constructed∂∂ξjEijhk(ξ,ωx0s)∂Nα1hm(ξ,ωx0s)∂ξk=-∂Eijα1m(ξ,ωx0s)∂ξjξ∈Qx0sNα1m(ξ,ωx0s)=0ξ∈∂Qx0s∂∂ξjEijhk(ξ,ωx0s)∂Hh(ξ,ωx0s)∂ξk=-∂βij(ξ,ωx0s)∂ξjξ∈Qx0sH(ξ,ωx0s)=0ξ∈∂Qx0sIn terms of Lax-Milgram lemma, Korn’s inequality and the symmetry and regularity of Eijhkε(x,ω) and αhkε(x,ω), it is easy to prove that above problems have the unique solution for any specified sample ωx0s.Eˆijhk(ωx0s)=∫Qx0sEijhk(ξ,ωx0s)+Eijpq(ξ,ωx0s)∂Nhpk(ξ,ωx0s)∂ξqdξThus, by taking M samples (ωx0ss=1,2,…,M), M homogenization coefficients Eˆijhk(ωx0s) are obtained, and then from Kolmogorov’s strong law of large numbers, the expected homogenized coefficient at x0 can be calculated in formulaE⌢ijhk(x)x=x0=limM→+∞∑s=1MEˆijhk(ωx0s)M.Similarly, the homogenization thermoelastic coefficients βˆij(ωx0s) depended on sample ωx0s is calculated in formulaβˆij(ωx0s)=∫Qx0sEijhk(ξ,ωx0s)αhk(ξ,ωx0s)+Eijhk(ξ,ωx0s)∂Hh(ξ,ωx0s)∂ξkdξand the homogenization thermal expansion coefficients αˆhk(ωx0s) depended on sample ωx0s can be calculated as followsThe expected homogenization thermal expansion coefficient α⌢hk(x) at point x0 is given by repeatedly calculating αˆhk(ωx0s) for M samples (ωx0ss=1,2,…,M) and Kolmogorov’s theorem of large numbersSecondly, by using E⌢ijhk(x) and α⌢hk(x) the homogenized problem is determined, and then u0(x) is obtained by solving it.Thirdly, from the coefficients about ε0 the following local problems at x0 for determining Nα1α2m(x,ξ,ωx0s), Mα1m(x,ξ,ωx0s)m=1,…,n and K(x,ξ,ωx0s) can be defined, namely∂∂ξjEijhk(ξ,ωx0s)∂Nα1α2hm(x,ξ,ωx0s)∂ξk=E⌢ijhk(x)-Eijhk(ξ,ωx0s)-Eijhk(ξ,ωx0s)∂Nα1hm(ξ,ωx0s)∂ξk-∂∂ξjEijhk(ξ,ωx0s)Nα1hm(ξ,ωx0s)ξ∈Qx0sNα1α2m(x,ξ,ωx0s)=0ξ∈∂Qx0s∂∂ξjEijhk(ξ,ωx0s)∂Mα1hm(x,ξ,ωx0s)∂ξk=∂E⌢ijα1m(x)∂xjξ∈Qx0sMα1m(x,ξ,ωx0s)=0ξ∈∂Qx0s∂∂ξjEijhk(ξ,ωx0s)∂Kh(x,ξ,ωx0s)∂ξk=∂E⌢ijhk(x)α⌢ij(x)∂xjξ∈Qx0sK(x,ξ,ωx0s)=0ξ∈∂Qx0s, it is easy to prove that the problems have the unique solutions Nα1α2m(x,ξ,ωx0s), Mα1m(x,ξ,ωx0s) and K(x,ξ,ωx0s) .of the statistically inhomogeneous materials has formally approximate solution at the pointx0as followsuε(x,ω)≅u0(x)+εNα1(ξ,ωx0s)∂u0(x)∂xα1-H(ξ,ωx0s)T+ε2Nα1α2(x,ξ,ωx0s)∂2u0(x)∂xα1∂xα2+Mα1(x,ξ,ωx0s)∂u0(x)∂xα1-K(x,ξ,ωx0s)Twhereu0(x)is the solution of the homogenized problem, called as the homogenization solution,Nα1m(ξ,ωx0s), H(ξ,ωx0s), Nα1α2m(x,ξ,ωx0s), Mα1m(x,ξ,ωx0s)andK(x,ξ,ωx0s)are the solutions of the problemsFrom the displacement expansion formula , the strains inside εQx0s are evaluated approximatelyεhkε(x,ωx0s)=12∂uhε(x,ωx0s)∂xk+∂ukε(x,ωx0s)∂xh=12∂uh0(x)∂xk+∂uk0(x)∂xh+12∂Nα1hm(ξ,ωx0s)∂ξk+∂Nα1km(ξ,ωx0s)∂ξh∂um0(x)∂xα1-12∂Hh(ξ,ωx0s)∂ξk+∂Hk(ξ,ωx0s)∂ξhT+ε12Nα1hm(ξ,ωx0s)∂2um0(x)∂xα1∂xk+Nα1km(ξ,ωx0s)∂2um0(x)∂xα1∂xh+ε12∂Nα1α2hm(x,ξ,ωx0s)∂ξk+∂Nα1α2km(x,ξ,ωx0s)∂ξh∂2um0(x)∂xα1∂xα2+ε212∂Nα1α2hm(x,ξ,ωx0s)∂xk+∂Nα1α2km(x,ξ,ωx0s)∂xh∂2um0(x)∂xα1∂xα2+ε212Nα1α2hm(x,ξ,ωx0s)∂3um0(x)∂xα1∂xα2∂xk+Nα1α2km(x,ξ,ωx0s)∂3um0(x)∂xα1∂xα2∂xh+ε12∂Mα1hm(x,ξ,ωx0s)∂ξk+∂Mα1km(x,ξ,ωx0s)∂ξh∂um0(x)∂xα1+ε212∂Mα1hm(x,ξ,ωx0s)∂xk+∂Mα1km(x,ξ,ωx0s)∂xh∂um0(x)∂xα1+ε212Mα1hm(x,ξ,ωx0s)∂2um0(x)∂xα1∂xk+Mα1km(x,ξ,ωx0s)∂2um0(x)∂xα1∂xh-ε12∂Kh(x,ξ,ωx0s)∂ξk+∂Kh(x,ξ,ωx0s)∂ξhT-ε212∂Kh(x,ξ,ωx0s)∂xk+∂Kh(x,ξ,ωx0s)∂xhTFrom Hooke’s Law, the stresses inside εQx0s are evaluatedσijε(x,ωx0s)=Eijhkε(x,ωx0s)εhkε(x,ωx0s)-αhk(x,ωx0s)TThen the strains and stresses at any point x inside εQx0s⊂Ω are naturally adopted for evaluating the elastic limit value S(ωx0s) of statistically inhomogeneous materials.The elastic limit strength of statistically inhomogeneous materials is dominated by the strength of particle’s material, matrix and interfaces, as well as the microstructure of composites. And the particle and matrix satisfy their respective strength criterions. For any random sample ωxs corresponding to position x, as the temperature increment T does not change, by using above statistical second-order two-scale formulas the strains and stresses inside εQxs⊂Ω can be evaluated, and then calculate the elastic limit strength value S(ωxs) of the sample ωxs by the proper strength criterions. There exists at least one point x0 on structure Ω, and at x0 the elastic limit of particle’s material/ or matrix/ or interfaces is reach. So, S(ωxs) is the elastic limit strength of structure Ω for ωxs. The expected strength Sˆ of the statistically inhomogeneous composite structure Ω by Kolmogorov’s strong law of large numbers is evaluated as followswhere M is the number of the samples ωxs,s=1,2,…,M.The expected strength Sˆ of Ω is only the average value, so it does not manifest the strength performance of Ω. Therefore, the minimum value of all samples’ strengths is more credible in practical engineering. It is expressed as followsWhen the temperature increment T is different, the strength Sˆ and Smin will be recalculated by SSOTS algorithm.The algorithm procedure of SSOTS method for predicting the thermomechanical properties of the statistically inhomogeneous materials is stated as followsSelect N point xi(i=1,2,…,N) inside structure Ω according to the structural topology and its random distribution feature P(x,x∈Ω).Generate a sample ωxis at the arbitrary point xi(i=1,2,…,N) in normalized cell Qxis according to P(x,x∈Ω), and then generate its FE meshes. in Qxis to obtain Nα1m(ξ,ωxis)(α1,m=1,…,n), and then evaluate the homogenized coefficient Eˆijhk(ωxis) corresponding to sample ωxis by formula in Qxis to obtain H(ξ,ωxis), and then evaluate the homogenized coefficient βˆij(ωxis) and αˆhk(ωxis) corresponding to sample ωxis by formulas Repeat the steps 2–4 for different samples ωxis(s=1,2…,M). The expected homogenized coefficients E⌢ijhk(xi) and α⌢hk(xi) is evaluated by Repeat the steps 2–5 for each point xi(i=1,2,…,N). And then the expected homogenized coefficient functions E⌢ijhk(x) and α⌢hk(x)x∈Ω are determined by N-points interpolation.For the sample ωxis, evaluate Nα1α2m(x,ξ,ωxis), Mα1m(x,ξ,ωxis) and K(x,ξ,ωx0s) by solving problems in Qxis, using the same FE meshes and stiffness matrix as in steps 3 and 4. in the whole structure Ω using E⌢ijhk(x) and α⌢hk(x)x∈Ω obtained in step 6, and solve it to obtain the homogenization displacement u0(x) by FEM.For the sample ωxis, using Nα1m(ξ,ωxis),H(ξ,ωxis), Nα1α2m(x,ξ,ωxis), Mα1m(x,ξ,ωxis), K(x,ξ,ωx0s) and u0(x) to calculate the stain and stress filed of the cell εQxis by Evaluate the elastic limit strength S(ωxis) of the sample ωxis according to the strength criterions of matrix and particles.Repeat the steps from 9 to 10 for different samples ωxis(s=1,2…,M), and M strength S(ωxis) are obtained. Then the expected strength Sˆ and minimum strength Smin are evaluated by In order to verify the feasibility and validity of the statistical second-order two-scale method for predicting the thermoelastic properties of statistically inhomogeneous materials, we have developed the software of SSOTS algorithm. Here some numerical results are shown and compared with experimental data.This example is to calculate the coefficients of elasticity and thermal expansion for the composite material made of Mo particles filled in the continuous, glassy SiO2 matrix, and to compare with the experimental results in The CTE at some points of FGM structure are firstly calculated, and then the spatial variation curves of CTE are drawn by interpolation as illustrated in . The figure shows that the maximum of predicted curve locates at X3≈0.085, where the maximal volume faction is about 0.22 by the approximate function shows the spatial variation curves of elastic properties predicted by SSOTS method. As can be seen from this figure, the moduli and Poisson ratio continuously vary as the particle volume fraction changes. And all maximums are obtained at the maximal volume faction of Mo particles.This example is on the polymer blends in injection molded part . Perpendicular to the melt flow direction, the morphology in the figure is divided into three main zones: sub-skin, intermediate and core zone . According to the observed results of particle dispersions in low injection speed in paper . And the material properties are: EPET |
= 2900 MPa; νPET |
= 0.40; αPET |
= 60 × 10−6 |
C−1; EPE |
= 985 MPa; νPE |
= 0.42; αPE |
= 130 × 10−6 |
C−1. shows that the homogenized material properties are orthogonal-anisotropic. In fact, The PET particles are elongated along the x3 direction during the melt flow process, and the Young modulus, Shear modulus and CTE in the x3 direction are all larger and the Poisson ratio is smaller. These analyses suggest that the morphology of mixed-particles is very important to the thermoelastic properties of blends.By using the SSOTS method in this paper the elasticity limit strengths of the statistically inhomogeneous materials under thermomechanics condition, including tension and compression, bending and twist, have been calculated, and the numerical results on expected elasticity strength and minimal elasticity strength were obtained. For the space limitation of this paper those on strengths of the statistically inhomogeneous materials are omitted here.In this paper, the composites with variable inclusion distributions are defined as the statistically inhomogeneous materials. And the microstructure of the material with plenty of particles is represented.A new statistically second-order two-scale methods for predicting the thermomechanical properties of them is presented, including the second-order two-scale asymptotic expression on the displacement vector, and the formulations of the expected homogenized constitutive parameters, elasticity limit strength.For some statistically inhomogeneous materials, the coefficients of elasticity and thermal expansion are predicted. As a result, the micro-behaviors inside material can be captured exactly by SSOTS method, and the SSOTS results agree with the experimental data. It shows that the statistical second-order two-scale method can be employed to predict thermomechanical properties of the statistically inhomogeneous materials.Artificial intelligence tools and inverse methods for estimating the thermal diffusivity of building materialsThe actual European energy context highlights the building sector as one of the largest sectors of energy consumption. Consequently, the “Energy Performance of Buildings Directive”, adopted in 2002 and focusing on energy use in buildings, requires all the EU members to enhance their building regulations and to introduce energy certification schemes, with the aim of both reducing energy consumption and improving energy efficiency. That is why carrying out an energy performance diagnosis is mandatory, notably when buying or selling properties. Indeed, invisible defaults, like, for example, non-emerging cracks or delaminations, could have a detrimental effect on insulating qualities. Esimaing in situ thermo-physical properties allowing locating these defaults, the present work focuses on proposing new and efficient approaches based on the use of both artificial intelligence tools (artificial neural networks and neuro-fuzzy systems) and inverse methods for characterizing building materials i.e. for estimating their thermal diffusivity using thermograms obtained thanks to a non-destructive photothermal method.The actual European energy context reveals that the building, industry and transport sectors are the three largest sectors of energy consumption. In France, about 25% of GreenHouse Gases (GHG) emissions and 45% of energy consumption are due to buildings In the present work, properties estimation methods, alternative to classic ones, are proposed using thermograms obtained with a non-destructive photothermal method. Its principle is as follows: the sample to be characterized is excited by a light source and its thermal response, called thermogram, is recorded. From the obtained thermogram, one can estimate several thermo-physical properties such as the thermal diffusivity and effusivity or the thickness of a layer for a multi-layer material. These methods can be classified as follows, depending on the time profile of the excitation: one speaks of pulsed methods when the excitation is an impulse and of modulated methods when the excitation is periodic. Pulsed methods are rich in information but impose a high excitation level, which is a problem for fragile or ductile materials. With modulated methods, the excitation is weaker but they give information at the modulation frequency only. A recent solution is to apply an excitation with a random time profile. Previous studies have shown all the interest of this kind of methods ). Inverse method for parameters estimation will be described too. Then, we will be interested in both the simulated data, provided by the GRESPI laboratory, and the artificial intelligence tools we use, i.e. multi-layer artificial neural networks ). Finally, we will present the results about impulse responses rebuilding and thermal diffusivities estimation (Section ). We will end this paper by a conclusion and future works (Section The photothermal experiment, a non-destructive control method, consists in submitting the sample to be characterized to a light flux. As a consequence, the absorption of light causes a local elevation of temperature. The IR emission is recorded (with FT−1 the inverse Fourier transform, Rrand(f) the Fourier transform of Rrand(t) and E(f) the Fourier transform of the excitation. The aim of this paper is to show that correlation analysis techniques can be efficiently replaced by artificial intelligence tools such as multi-layer artificial neural networks or neuro-fuzzy systems.The used database is composed of responses to PRBS, impulse responses and thermophysical properties for the following seven building materials: glass wool, concrete, brick, glass, plaster, granite and stainless steel. Responses to a PRBS () are both composed of 255 points (uniformly spaced in time, Δt |
= 3 s for responses to PRBS while Δt |
= 3 × 10−2 |
s for impulse responses). highlights some of the main properties of the seven considered materials: density (ρ), ranging between 200 kg/m3 and 7900 kg/m3, calorific capacity (Cp), ranging between 670 J/kg K and 960 J/kg K, thermal conductivity (k), ranging between 0.04 W/m K and 16 W/m K, thermal diffusivity (a), ranging between 3 × 10−7 |
m2/s and 4 × 10−5 |
m2/s, and thermal effusivity (b), ranging between 73.21 J/m2 |
K s1/2 and 8028.95 J/m2 |
K s1/2. With the aim of developing the most effective tools, a preliminary study about thermal behaviour has been carried out and allowed choosing the materials used to train or to validate both artificial neural networks and neuro-fuzzy systems. As a conclusion of this study, glass wool, concrete, glass and stainless steel were considered as training materials while brick, plaster and granite were used for validating the developed models. Let us note that, among all these materials, only glass wool is an organic material and, as such, presents a very specific thermal behaviour.The impulse response can be exploited using Parker's technique First, let M*=(M1*,…,Mk*,…,Mn*)T be a vector composed of n experimental measurements uniformly spaced in time between t1 and tn. Next, let M(β) = (M1, …, Mk, …, Mn)T be the model values vector with Mk |
= |
η(tk, β), β being the parameters to be identified. Finally, let SLB(β) be an objective function, defined as the sum of the least square of M* and M(β), to be minimized with respect to the unknown β. It could be written SLS(β)∑k=1n[Mk*−Mk]2=[M*−M(β)]T⋅[M*−M(β)]So, SLS(β) is a scalar function of the searched parameters (β). Searching the best estimate (bopt) of β is searching the SLS function minimum.The sensitivity coefficient Xp related to a parameter βp is given by the first derivative of the model η(t,β) with respect to the just-mentioned parameter. This coefficient depicts the influence of the parameter βp on the model:The criterion minimization method depends on the model linearity versus the parameters. We use methods belonging to the gradient methods class: Gauss–Newton's, Box–Kanemasu's and modified Box–Kanemasu's methods . Model values are firstly calculated with initial parameters, chosen a priori, then, the first criterion value is calculated. If the stopping condition is not satisfied, the algorithm calculates the parameter corrections to make the criterion SLS(β) decreases at the next iteration. New parameters are used to calculate new model values and to resume the process. A recurrence relationship can be written between respective parameter values at kth and (k |
+ 1)th iterations, with Δbi(k) the corrective step applied to parameter bi of b at kth iteration:We frequently use the following criterion (Eq. |bi(k+1)−bi(k)||bi(k)|+δ1<δwithδ1=10−10andδ=10−4The Gauss–Newton's method is one of the simplest and most efficient minimization methods. The Gauss–Newton's step ΔbGN(k) is given by the following expression:ΔbGN(k)=[XT(k)⋅X(k)]−1⋅[XT(k)(M*−M(b(k)))]Let us note that the Hessian approximation XT(k) |
· |
X(k) has to be inversed and needs to be well-conditioned. So, X(k) values must be maximum, small values leading to an ill-conditioned matrix and, as a consequence, the inverse algorithm will not converge. Indeed, the efficiency of the Gauss–Newton's method is dependent on the problem conditioning. Ill-conditioned problems need an adapted method such as the Box–Kanemasu's method.The Gauss–Newton's method is based on a linear approximation of the model. If this hypothesis is really wrong, calculated corrections can oscillate with growing amplitude and the algorithm cannot converge. The Box–Kanemasu's step ΔbBK(k) is calculated as follows:, one can note that a coefficient hBK is assigned to the Gauss–Newton's step ΔbGN(k). This coefficient is obtained thanks to the procedure depicted in . A has a constant value of 1.1 while g(k) is calculated at each iteration in the following way:g(k)=[ΔbGN(k)]−1⋅[XT(k)⋅X(k)]⋅[ΔbGN(k)]−1The Box–Kanemasu's method does not verify if SLS(β) decreases at the next iteration. That is why Bard modified the method, calculating differently the coefficient hBKm(k) assigned to the Gauss–Newton's step ΔbGN(k), as depicted in Two kinds of multi-layer artificial neural networks have been used for estimating, directly or indirectly, the thermal diffusivity of building materials, with the aim of developing a new and effective approach contributing to the energy performance diagnosis of buildings: the commonly used multi-layer Perceptron (MLP) and the Elman recurrent network. Both networks’ topology and the training algorithm used will be described summarily in the present section of the paper.The Perceptron, the simplest neural network, is only able to classify data into two classes ). According to previous tests, more than one hidden layer proved to cause slower convergence during the learning phase because intermediate neurons not directly connected to output neurons learn very slowly. Based on the principle of generalization versus convergence, both number of hidden neurons and iterations completed during the training phase were optimized Feedforward neural networks have been successfully used to solve problems that require the computation of a static function i.e. a function whose output depends only on the current input, and not on any previous inputs. In the real world however, one encounters many problems which cannot be solved by learning a static function because the function being computed changes with each input received. It should be clear from the architecture of feedforward neural networks that past inputs have no way of influencing the processing of future inputs. This situation can be rectified by the introduction of feedback connections in the network ). The delay in this connection stores values from the previous time step, which can be used in the current time step. Because the network can store information for future reference, it is able to learn temporal patterns as well as spatial patterns. The Elman recurrent network can be trained, using an iterative process, to respond to, and to generate, both kinds of patterns. Just as the multi-layer Perceptron, it can approximate any function (with a finite number of discontinuities) with arbitrary accuracy. The only requirement is that its hidden layer must have enough neurons. More hidden neurons are needed as the function being fitted increases in complexity.Several training methods were used, but the Levenberg–Marquardt algorithm where J is the Jacobian matrix that contains first derivatives of the network errors with respect to the weights and biases, and e is a vector of network errors. The Jacobian matrix can be computed through a standard backpropagation technique that is much less complex than computing the Hessian matrix. The Levenberg–Marquardt algorithm uses this approximation to the Hessian matrix in the following Newton-like update:When the scalar μ is zero, this is just Newton's method, using the approximate Hessian matrix. When μ is large, this becomes gradient descent with a small step size. Newton's method is faster and more accurate near an error minimum, so the aim is to shift towards Newton's method as quickly as possible. Thus, μ is decreased after each successful step and is increased only when a tentative step would increase the performance function. In this way, the performance function will always be reduced at each iteration of the algorithm. The main drawback of the Levenberg–Marquardt algorithm is that it requires the storage of some matrices that can be quite large for certain problems. The size of the Jacobian matrix is Q |
× |
n, where Q is the number of training sets and n is the number of weights and biases in the network. It turns out that this matrix does not have to be computed and stored as a whole. For example, if we were to divide the Jacobian into two equal submatrices we could compute the approximate Hessian matrix as follows:Therefore, the full Jacobian does not have to exist at one time. The approximate Hessian can be computed by summing a series of subterms. Once one subterm has been computed, the corresponding submatrix of the Jacobian can be cleared.In the field of artificial intelligence, neural networks and fuzzy logic can be combined in neuro-fuzzy systems in order to achieve both properties of readability and learning ability. Neuro-fuzzy systems synergizes the two techniques by combining the human-like reasoning style of fuzzy systems (through the use of fuzzy sets and a linguistic model consisting of a set of if-then fuzzy rules) with the learning and connectionist structure of neural networks Fuzzy if-then rules are expressions of the form if A then B, where A and B are labels or fuzzy sets characterized by appropriate membership functions. Due to their concise form and through the use of linguistic labels and membership functions, fuzzy if-then rules are often employed to capture the imprecise and subjective modes of reasoning that play a central role in the human ability to make decisions in an uncertain environment Fuzzy inference systems are also known as fuzzy-rule-based systems or fuzzy controllers when used as controllers. Basically, a fuzzy inference system is composed of five functional blocks The acronym ANFIS derives from adaptative network-based fuzzy inference system. A network-type structure, similar to that of artificial neural networks, which maps inputs through input membership functions and associated parameters and then through output membership functions and associated parameters to output, can be used to interpret an input/output map. The parameters associated with the membership functions changes through the learning process. The adjustment of these parameters is facilitated by a gradient vector. This gradient vector provides a measure of how well the fuzzy inference system is modelling the input/output data for a given set of parameters. When the gradient vector is obtained, any of several optimization routines can be applied in order to adjust the parameters to reduce some error measure For simplicity, we assume, first, that the considered fuzzy inference system has two inputs x and y and one output z and, secondly, that the rule base contains only two fuzzy if-then rules of Takagi and Sugeno's type First rule:IfxisA1ANDyisB1THENf1=p1x+q1y+r1Second rule:IfxisA2ANDyisB2THENf2=p2x+q2y+r2Implementing both rules requires the 5-layer ANFIS architecture shown in μAi(x)=11+[((x−ci)/ai)2]biorμAi(x)=exp−x−ciai2μBi(y)=11+[((x−c′i)/a′i)2]b′iorμBi(y)=exp−x−c′ia′i2with {ai, bi, ci} and {a′i,b′i,c′i} two parameter sets. As the values of these parameters change, the bell-shaped functions vary accordingly, thus exhibiting various forms of membership functions on linguistic label Ai Any continuous and piecewise differentiable functions, such as commonly used trapezoidal or triangular-shaped membership functions, can be used. Nodes in the second layer evaluate the premises of the rules, multiplying the incoming signals and sending the product out. So, the ith node output represents the firing strength of rule i. Let us note that many other T-norm operators, allowing performing generalized AND, can be used in this layer The ith node in the third layer calculates the ratio of the ith rule's firing strength to the sum of all rules’ firing strengths (i.e. the contribution of the ith rule), such as:Nodes in the fourth layer evaluate the conclusions of the rules. So, the ith node evaluates the conclusion of the ith rule, with ω¯i the output of layer 3 and {pi, qi, ri} a parameter set. Parameters in this layer can be referred as consequent or conclusion parameters. So:Finally, the single node in the fifth and last layer computes the overall output as the summation of all incoming signals. It is observed that given the values of premise parameters, the overall output can be expressed as a linear combination of the consequent parameters:To train the ANFIS, a data set that contains the desired input/output data of the system to be modelled is used. The modelling approach is similar to many system identification techniques: first, you hypothesize a parameterized model structure and next, thanks to an iterative and hybrid optimization method, basically a combination of least squares estimation and backpropagation gradient descent method As previously mentioned, three new and effective approaches are proposed for estimating the thermal diffusivity of building materials: the neuro-inverse (in this case, artificial neural networks are used for rebuilding impulse responses of building materials, their thermal diffusivity being thereafter determined by means of inverse methods), the neuronal and the neuro-fuzzy approaches.An Elman recurrent network has been trained using the glass wool, concrete, glass and stainless steel responses to a PRBS as network inputs and their respective impulse responses as targets, i.e. as desired network outputs. Let us note, and this is a key-point when rebuilding impulse responses using neural networks (or when directly estimating thermal diffusivities), that responses to a PRBS and impulse responses were presented to the network, during both training and validation phases, as “sequences”. Whatever the response, it is considered as an entity in which all elements are connected to, and dependent upon, each other. The network's number of hidden neurons, the number of iterations carried out during its training phase and the learning rate were empirically optimized. Then, the trained network has been used for rebuilding the impulse responses of brick, plaster and granite using their responses to a PRBS as new and unknown network inputs. This is the validation phase. After rebuilding the impulse response of a material, the inversion algorithm is used for estimating its thermal diffusivity. First, the Gauss–Newton's method has been tried but the inverse problem is very ill-conditioned so we used the Box–Kanemasu's method. A self-made condition has been added, close to the Box–Kanemasu's modified method, to be sure that the criterion to be minimized decreases during calculations (Considering the results provided by the neuro-inverse approach when estimating the thermal diffusivity of building materials, a second approach, named “neuronal approach”, has been tested. Using this approach, the thermal diffusivity of the considered materials is directly estimated, thanks to a multi-layer Perceptron and their respective responses to a PRBS. So, the network has been trained using the glass wool, concrete, glass and stainless steel responses to a PRBS as network inputs and their respective thermal diffusivities as targets, i.e. as desired network outputs (). Let us note that the neuronal approach is really innovative with respect to those usually used for characterizing materials. Indeed, taking advantage of the response to a PRBS instead of its impulse response for estimating its thermal diffusivity is not a common way to do it. However, not having to rebuild the impulse response of a (fragile) material is a good thing because it allows avoiding the use of inverse methods, in some cases not very efficient (for example, when the sensitivity coefficients are weak or because ill-conditioned matrix, close to singular, cannot be well-inversed). The network's number of hidden neurons, the number of iterations carried out during its training phase and the learning rate were again empirically optimized. Then, the trained multi-layer Perceptron has been used for estimating the brick, plaster and granite's thermal diffusivities using their respective responses to a PRBS as new and unknown network inputs.As for both neuro-inverse and neuronal approaches, glass wool, concrete, glass and stainless steel were used to train the ANFIS, while brick, plaster and granite allowed carrying out its validation phase. As a result of the training phase, the membership function parameters are adjusted, the consequent parameters are identified and fuzzy rules are designed. The number of training iterations has been empirically optimized. Considering that the response to a PRBS is correlated with both the thermal diffusivity of the excited material and some of the main characteristics of the PRBS used as excitation, and taking into account expert knowledge about characterization of materials, various set of potential model inputs were tested. As a first approach, the PRBS pulses’ widths and, for each of the pulses, the mean value of the obtained response, were considered. The results being disappointing, the first and the last point of the obtained response were considered instead of its mean value, but no significant improvement has been noted. Finally, the PRBS pulses’ widths (ΔT |
= [ΔT1 |
ΔT2 |
… ΔTn]) and the absolute value of the slopes, calculated, for each of the pulses, considering the line between the first and the median point of the obtained response (s |
= [s1s2 |
… |
sn]) were chosen and proved to be a better option (). The thermal diffusivity of the studied material has been considered as model output (). Let us note that, as when using the neuronal approach, the neuro-fuzzy approach allows not having to rebuild the impulse response of the considered materials. This is, again, a really innovative approach with respect to those usually used for characterizing materials.This section of the paper deals with the results obtained using the three proposed approaches for both estimating the thermal diffusivity of building materials and contributing to the energy performance diagnosis of buildings. Rebuilt impulse responses will be compared with theoretical impulse responses using a widely used similarity criterion (Eq. ). Mean relatives errors will also be computed when rebuilding impulse responses and estimating thermal diffusivities. Let us also note that the topology of the neural networks used and the way the training parameters have been optimized will be mentioned.FIT=100×1−||Rreb_imp−Rreal_imp||2||Rreal_imp−Rreal_imp||2 present the rebuilt impulse responses of brick, plaster and granite, using a log–log scale. Let us remember that glass wool, concrete, glass and stainless steel were used to train the Elman recurrent network used. The network's hidden layer was composed of 8 neurons and 35 iterations have been carried out during the training phase. The learning rate was set to 0.3. The Levenberg–Marquardt algorithm (Section ) allowed optimizing the network's weights. specifies, for the three validation materials, the curve fitting (FIT) and the Mean Relative Error (MRE) observed when rebuilding their respective impulse responses. also presents, using the rebuilt impulses responses and the Box–Kanemasu's method (Section ), the result of the thermal diffusivity estimation. A Relative Error (RE) is calculated.The results provided by the neuro-inverse approach allow, first, validating both the proposed approach and the use of artificial neural networks for rebuilding impulse responses. Whatever the validation material, the MRE is very low, ranging between 0.1% and 0.7%, while the FIT is very high, ranging between 96.5% and 99.1%. Let us note that taking into account the PRBS used as excitation (i.e. using it as network's second input sequence), jointly to the material response, has been considered for rebuilding impulse responses. Finally, and because one can suppose that the response to a PRBS is dependent on both the thermophysical properties of the excited material and the characteristics of the signal used as excitation, only the response to a PRBS was considered as network input sequence., one can also observe that the Box–Kanemasu's method allows taking advantage of the rebuilt impulse responses for correctly estimating the thermal diffusivity of the considered building materials. Relative errors are ranging between less than 1% and 15.7%; this leads to a MRE of about 9%. One could be surprised when analyzing these late results but because both theoretical and rebuilt impulse responses contain very few points in the high sensitivity area, inverse methods are not very efficient. As a consequence, one can expect improving accuracy using both neuronal and neuro-fuzzy approaches.Let us remember that glass wool, concrete, glass and stainless steel were used to train the multi-layer Perceptron used for directly estimating the thermal diffusivity of building materials. The network's hidden layer was composed of 10 neurons and 30 iterations have been carried out during the training phase. The learning rate was set to 0.3. The Levenberg–Marquardt algorithm (Section ) allowed optimizing the network's weights. specifies, for the three validation materials, the result of the thermal diffusivity estimation. A Relative Error (RE) is calculated. Taking a look at , one can observe that the neuronal approach allows improving significantly the estimations’ accuracy. One can note, considering the neuro-inverse results as reference results, that the neuronal approach allows reducing the RE by 40.4% (from 10.4% to 6.2%) and 57.3% (from 15.7% to 6.7%) when estimating the thermal diffusivities of brick and plaster respectively. Concerning granite, the RE increases from less than 1% to 4.5%. One can conclude, and this is a very interesting result, that artificial neural networks are able to provide very good estimations of the thermal diffusivity of building materials, without rebuilding impulse responses, even if the sensitivity of the considered responses to a PRBS is weak. As a consequence, one can highlight that using inverse methods for estimating thermophysical properties of materials is not the only way to do it: artificial neural networks can also do it! Concerning granite, a much more diffusive material than brick and plaster, the sensitivity coefficients are weak in the used identification area, but high enough to obtain a very good estimation of its thermal diffusivity even from its rebuilt impulse response, using the Box–Kanemasu's method.As we did for developing both neuro-inverse and neuronal approaches, glass wool, concrete, glass and stainless steel were used to train the ANFIS allowing directly estimating the thermal diffusivity of building materials. The two model inputs (ΔT and s) and their respective universes of discourse have to be characterized by means of fuzzy sets and membership functions with the aim of designing an appropriate base of fuzzy rules that best maps inputs to single output. Due to the nature of both the signal used as excitations and the obtained responses, the pulses’ widths (ΔT) may be in the range [1s; 8s] while the absolute value of the slopes (s), calculated, for each of the pulses, considering the line between the first and the median point of the obtained response, may be in the range [0; 0.4675]. Both universes of discourse have been split using only two fuzzy sets and trapezoidal membership functions. The thermal diffusivity may be in the range [3 × 10−7; 4 × 10−6]. During the ANFIS training process, the rule extraction method allows generating rules, adjusting the shape of the input membership functions, defined, at the end of the process, as highlighted by (considering four parameters: the left and right base points and the left and right top points), and finally identifying the coefficients of the linear output membership functions (each generated rule has one output membership function) (). 25 iterations have been carried out. depicts the performance of the trained ANFIS. As we did when estimating the thermal diffusivity of the chosen validation materials using the neuro-inverse and the neuronal approaches, a relative error is calculated. One can observe that the neuro-fuzzy approach allows improving significantly the estimations’ accuracy. Indeed this approach provides the best results over the other proposed approaches. Taking a look at the results provided by the neuro-inverse approach (), one can highlight that the neuro-fuzzy approach allows reducing the RE by 72.1% (from 10.4% to 2.9%) and 71.3% (from 15.7% to 4.5%) when estimating the thermal diffusivities of brick and plaster respectively. Concerning granite, both estimations are very similar (1.11 × 10−6 |
m2/s and 1.09 × 10−6 |
m2/s when using the neuro-inverse and the neuro-fuzzy approaches respectively). Taking a look at the results provided by the neuronal approach (), one can remark that the neuro-fuzzy approach allows reducing the RE by 53.2% (from 6.2% to 2.9%), 32.8% (from 6.7% to 4.5%) and 75.6% (from 4.5% to 1.1%) when estimating the thermal diffusivities of brick, plaster and granite respectively. summarizes all the results obtained, for the three proposed approaches.The obtained results validate the neuro-fuzzy approach and highlight the significant contribution of expert knowledge, which has been considered using, as ANFIS inputs, characteristics of both the PRBS used as excitation and the response to this excitation. Again, these results confirm, first, that artificial intelligence tools are useful for characterizing materials and, secondly, that rebuilding impulse responses for estimating thermophysical properties is not mandatory: one can directly estimate the thermal diffusivity of materials using artificial neural networks or neuro-fuzzy systems and responses to pseudo random binary signals. As a consequence, and this is the main result of the study, one can maintain that both neuronal and neuro-fuzzy approaches allow not using inverse methods (these methods are not very efficient when impulse responses contain very few points in the high sensitivity area) and correlation analysis techniques (as previously mentioned, these techniques are very complex to apply, require a large computational time and are, in some cases, not very efficient).With the building sector being one of the largest sectors of energy consumption in Europe, and consequently one of the major causes of greenhouse gas emissions and therefore of global warming, reliable and robust tools are needed for carrying out an advanced energy performance diagnostic and issuing energy performance certificates for buildings. Because invisible defaults, like, for example, non-emerging cracks or delaminations, completely spoil the insulating qualities of buildings, owners (and future owners) would be pleased to locate these defaults. Whatever the situation, the challenge is the same: being able to locate invisible things under a layer of plaster or similar material, which amounts to locate inhomogeneities in a homogeneous medium. These defaults locally modifying the global thermophysical properties of the medium, they can be located by an in situ estimation of these properties.The present work deals with new and effective approaches, alternative to commonly used (and not always very efficient) approaches and based on artificial intelligence tools, for estimating the thermal diffusivity of building materials, using thermograms obtained with a non-destructive photothermal method. Three approaches are proposed, based on responses to a PRBS: rebuilding impulses responses using an Elman recurrent network and then estimating thermal diffusivities thanks to an inverse method (neuro-inverse approach) and directly estimating thermal diffusivities using a multi-layer Perceptron (neuronal approach) or an adaptative network-based fuzzy inference system (neuro-fuzzy approach). The first conclusion of the work is that artificial intelligence tools are useful for characterizing materials. Indeed, whatever the proposed approach, the results are very satisfactory. Let us note that the best results are provided by the neuro-fuzzy approach, highlighting both the significant contribution of expert knowledge and the fact that rebuilding impulse responses for estimating thermophysical properties is not mandatory. One can directly estimate the thermal diffusivity of building materials from responses to PRBS, using artificial intelligence tools. Future works will now focus, first, on considering more materials, and as a consequence more thermal behaviours, for developing global models about thermal diffusivity estimation. In particular, we will be interested in organic building materials, such as, for example, wood or clay. Among all the materials used for developing and testing the proposed approaches, only glass wool is such a material. Characterizing dual-layer materials will also be considered. Finally, future works will also centre on, first, validating experimentally the developed models and, secondly, on extending the range of application of these models to other interesting thermophysical properties (such as thermal effusivity or thermal contact resistance).Poly(3-hydroxybutyrate-co-4-hydroxyvalerate) (P34HB)Ternary blends from biological poly(3-hydroxybutyrate-co-4-hydroxyvalerate), poly(L-lactic acid), and poly(vinyl acetate) with balanced propertiesHerein, poly(3-hydroxybutyrate-co-4-hydroxyvalerate) (P34HB), poly (L-lactic acid) (PLA), and poly(vinyl acetate) (PVAc) were initially melt compounded to prepare a ternary blend with balanced properties. Further, the miscibility, phase morphology, thermal and crystallization behaviors, and rheological and mechanical properties of the blends were studied. The dynamic mechanical analysis (DMA) results indicated that P34HB and PLA were partially miscible; however, PVAc showed full miscibility with PLA and P34HB. PVAc would selectively disperse in the PLA phase when considering low content, whereas it would gradually diffuse into the P34HB phase with the increasing PVAc concentration. A phase-separated morphology was observed for all the blends using scanning electron microscopy (SEM), and the diameters of the dispersed phases increased with the increasing PVAc concentration. The crystallization of P34HB was enhanced by the presence of PLA alone and was restrained by the simultaneous incorporation of PVAc and PLA. The rheological properties of P34HB were significantly improved because of the PVAc phase. Unexpectedly, the toughness and stiffness of the P34HB in ternary blends clearly improved because of the incorporation of PLA and PVAc.Poly(3-hydroxybutyrate-co-4-hydroxyvalerate) (P34HB)The increasing concerns associated with the rapid depletion of finite petroleum resources and environmental problems have resulted in extensive research efforts for the development of biodegradable polymers, especially biobased polymeric materials derived from renewable resources []. Among these biodegradable polymers, aliphatic polyesters, such as polyhydroxyalkanoates (PHAs) and poly(L-lactic acid) (PLA), have drawn considerable attention owing to their biodegradability, biocompatibility, biosynthetic origin, and commercial availability []. PHAs are a type of intracellular polyester mainly used as a carbon source and energy storage substance, which can be synthesized using various microorganisms []. In the family of PHAs, poly(3-hydroxybutyrate-co-4-hydroxybutyrate) (P34HB), which is a copolymer composing 3-hydroxybutyrate (3HB) and 4-hydroxybutyrate (4HB) units, has gained considerable attention because of its remarkable features, including good processing properties and toughness []. Furthermore, the mechanical properties of P34HB change with the changing molar ratio of 3HB and 4HB. Regardless, the widespread application of P34HB is limited by the slow crystallization rate and low thermal stability and melt strength. To overcome these limitations, many efforts, including plasticization, copolymerization, and melt blending, have been made. Physical blending is considered to be the most effective and economical route to improve various properties of polymers [PLA is a widely studied biodegradable polymer. It has been widely used in tissue engineering, packaging, and biomedical applications because of its biodegradability and biocompatibility []. Recently, the reasonable price of industrial-grade PLA and its good processability as well as high mechanical strength have made PLA a potential substitute for petrochemical-derived products in many areas []. However, the intrinsic brittleness and poor heat stability associated with PLA have hindered its large-scale applications in the commercial and biomedical fields.As mentioned above, P34HB and PLA are the most promising candidates for replacing petroleum-based polymers in the future and play an important role in the marketing of different potential applications in case of biodegradable polymers. However, when used alone, neither polymer can fully meet all the performance requirements of structural materials for practical applications. Therefore, binary blends of P34HB and PLA have been extensively studied to enhance the physical properties of pure polymers, such as the thermal stability, crystallization rate, and degradation rate []. However, the main disadvantage associated with binary blends is that some performance improvements are achieved at the expense of other performance characteristics. For instance, the addition of P34HB enhanced the elongation at beak of the blends but decreased the tensile strength and modulus []. Therefore, recently, a blend comprising three or more components has attracted increasing attention from academia and industry because multicomponent polymers exhibit more excellent comprehensive properties []. Poly(vinyl acetate) (PVAc), which is different from biodegradable semicrystalline P34HB and PLA, is an amorphous polymer with high viscosity. It can be blended with some biodegradable polymers to obtain fully miscible blend with improved toughness []. Based on our previous research, PVAc was miscible with P34HB and the introduction of PVAc suppressed the crystallization and increased the toughness of P34HB in blends []. Furthermore, PLA/PVAc was a miscible blend system, and the crystallization of PLA was restricted by the incorporation of PVAc []. Herein, we considered the miscibility of PVAc with P34HB and PLA and the promising complementary performance of the P34HB, PLA, and PVAc polymer components. Further, we selected the semicrystalline P34HB as the matrix, the high-stiffness PLA as the minor phase, and the high-viscosity PVAc as the third phase to prepare a ternary blend system. Finally, the miscibility, phase morphology, crystallization behavior, and rheological and mechanical properties of the multicomponent system were investigated in detail.P34HB, exhibiting a number average molecular weight (Mn) of 5.99 × 105 g mol−1 and a polydispersity of 1.85, was purchased from Tianjin Guoyun Biotech LLC (Tianjin, China). 6.5 mol% of 4HB was present in the P34HB copolymer based on the 1H NMR spectrum, as shown in . PLA (4060D) was supplied by Nature Works LLC (Nebraska, USA). Its weight average molecular weight (Mw) and polydispersity were 1.55 × 105 g mol−1 and 1.3, respectively. PVAc with an Mw of 1.5 × 105 g mol−1 and a polydispersity of 1.54 was supplied by Nuoda New Materials Company (Yantai, China).Prior to blending, P34HB, PLA, and PVAc were dried in a vacuum oven at 100 °C, 50 °C, and 50 °C, respectively, for 10 h. Blends of P34HB/PLA/PVAc with different components were mixed using a Haake batch intensive mixer (Haake Rheomix 600, Karlsruhe, Germany). The mixing parameters included a chamber temperature of 150 °C, a residence time of 7 min, and a screw speed of 50 rpm. The mixing process was continued until the viscosity of the mixture became constant. The blended samples were firstly melt at 160 °C for about 5 min, and then hot-pressed at 10 MPa and 160 °C for 2 min; this was followed by cold pressing at room temperature for fabricating test specimens with a thickness of 1 mm. Neat P34HB and PLA were mixed to achieve the same thermal history as the blends. The mass ratio of P34HB/PLA was fixed at 70/30, and the mass fractions of PVAc in the ternary blends were 5, 10, and 20 wt% based on the total mass of P34HB/PLA binary blends. For convenience, the P34HB/PLA/PVAc blends were designated as P34HB/PLA-X, where X indicated the weight percentage of PVAc in the ternary blends.DMA tests were performed by using a DMA Q800 from TA Instruments (USA) with a tensile mode. The rectangle samples (dimensions 20 × 10 × 1.0 mm3) were heated from −20 °C to 100 °C at a heating rate of 3 °C min−1 and a frequency of 1 Hz.The phase morphology of binary and ternary blends was studied by SEM (FEI Co., Eindhoven, Netherlands) at an accelerating voltage of 10 kV. First, the samples were cooled in liquid nitrogen for at least 5 min, and broken vertically. Then the cryo-fractured samples were etched in the acetone solution for approximately 120 min to remove the PLA phase. The selective etched surfaces of the samples were finally sputtered with a thin layer of gold prior to fractographic examination.The thermal and isothermal crystallization behaviors of all samples were studied on a TA Instruments DSC Q20 (USA) under nitrogen atmosphere. The samples of 5–8 mg were weighted, and crimp-sealed in an aluminum pans. All samples were first heated from −40 °C to 190 °C at a heating rate of 10 °C min−1 (first heating), held at 190 °C for 3 min, then cooled to −20 °C at a cooling rate of 5 °C min−1 (first cooling). After that, the second heating scans were conducted between −20 to 180 °C at a heating rate of 10 °C min−1. The main thermal parameters, such as glass transition temperature (Tg), melting temperature (Tm), melting enthalpy (ΔHm), crystallization temperature (Tc), crystallization enthalpy (ΔHc), cold crystallization temperature (Tcc), and cold crystallization enthalpy (ΔHcc) of samples, were obtained from DSC thermograms. During the heating and cooling scan, the degree of crystallinity of P34HB (Xc) in the blends could be calculated by the following two formulas respectively:where ΔHm0 is the fusion enthalpy of 100% crystalline P34HB with the value of 146 J/g from the literature [], and α is the mass percentage of P34HB in the ternary blends.For isothermal crystallization, all samples were heated to 190 °C at a rate of 100 °C min−1, and held for 3 min. Then they were cooled to 60 or 70 °C at a rate of 45 °C min−1, and kept at the crystallization temperature until the crystallization was complete. The isothermal crystallization exotherm was monitored for further analysis.The flow behavior and rheological properties of all samples were investigated on a rotational rheometer (TA Series AR2000ex, TA Instrument, USA) equipped with 25 mm cone and plate geometry. The frequency sweep tests were carried out in the range of 0.05–100 rad s−1 at 155 °C. The amplitude was set to 1.25% to maintain the response of samples in the linear viscoelastic range.Tensile tests were performed on a tensile testing machine (Instron-1121, USA) at room temperature with a fixed crosshead speed of 10 mm min−1 according to ISO 527-1:2012 standard. At least five specimens of each component were tested, and then averaged.By melt blending P34HB, PLA, and PVAc at 150 °C, hot pressing at 160 °C, and cooling and molding at room temperature, a blend sheet with a thickness of about 1 mm was prepared. The rectangular samples cut from the sheets are opaque. Dynamic mechanical analysis (DMA) was used to examine the mutual miscibility and interfacial interactions of PVAc with the P34HB and PLA components in the P34HB/PLA/PVAc ternary blends. This can be attributed to the fact that various properties and the phase morphology of the blends are considerably dependent on the interaction and compatibility between components. The ratio of the loss modulus (E″) to the storage modulus (E′) (tan δ) exhibits a peak when the decrease rate of E′ is higher than that of E″ with increasing temperature. This peak corresponds to the chain relaxation of the polymer and represents the glass transition temperature (Tg).The tan δ curves of neat P34HB, PLA, and the P34HB/PLA binary and P34HB/PLA/PVAc ternary blends are shown in , and the corresponding Tg values are presented in a, neat P34HB, PLA, and PVAc exhibited a sharp tan δ peak at 12.6 °C, 58.6 °C, and 48.5 °C, respectively, indicating their Tg values. The tan δ curves showed two Tg values in case of the P34HB/PLA binary blend. More specifically, the lower tan δ peak value corresponded to P34HB, whereas the higher one was related to PLA. Moreover, the Tg values of PLA and P34HB shifted to each other compared with pure components. Thus, the P34HB/PLA binary blend was partially miscible.In case of the P34HB/PLA/PVAc ternary blends, two glass transitions could be observed based on the tan δ curves. The transitions at approximately 19 °C were related to the P34HB matrix, whereas those at 49 °C–56 °C were related to the PLA phase. The Tg values of P34HB and PLA considerably increased and decreased with the increasing PVAc content, respectively. In case of the P34HB component in ternary blends, Tg increased by 4.3 °C when the PVAc content was 20 wt%. Such a significant increase in Tg indicated that PVAc (Tg = 48.5 °C) was miscible with P34HB. Similarly, the Tg of the PLA component in ternary blends decreased by 6.6 °C when the PVAc content was 20 wt%, indicating that PVAc was also miscible with PLA. Compared with P34HB, the change in Tg of PLA with the PVAc content was larger, indicating better miscibility of PVAc with PLA. Therefore, PVAc, which was miscible with both PLA and P34HB, was selectively located in the PLA phase; only a small part was dispersed in the P34HB matrix. In addition, PVAc may decrease the interfacial adhesion between the P34HB matrix and the dispersed PLA phase because it exhibits full miscibility with both PLA and P34HB.b shows the storage modulus curves of neat P34HB, PLA, PVAc, and the blends. The E′ of neat P34HB at temperatures below its Tg was approximately 4.5 GPa and decreased drastically at approximately 12 °C because of glass transition. Neat PLA and PVAc showed the highest E′ of approximately 3.2 and 3.1 GPa, respectively, at temperatures lower than their Tg values. The E′ of neat PLA and PVAc decreased when the temperatures were increased to approximately 59 °C and 48 °C, respectively, which can be attributed to glass transition. In case of ternary blends, when the temperature was lower than approximately 12 °C, the concentration of PVAc had no obvious influence on the E′ of ternary blends because all the components were in the glass state. However, ternary blends with high PVAc concentration showed high storage modulus at temperatures below Tg in case of PVAc and above Tg in case of P34HB. This can be attributed to the rubbery P34HB matrix being reinforced by the glassy PVAc and PLA with high stiffness. As the temperature increased to become greater than 48 °C, which was higher than the Tg of PVAc, the PVAc reached a high-elastic state. The E′ of ternary blends decreased with the increasing PVAc content because of the diluting effect of the PVAc segments, which can be attributed to its improved mobility above Tg.The phase morphology of the polymer blends is considerably influential with respect to their mechanical behavior and rheological properties. Further, the relation between their physical properties and microstructure can be obtained based on their phase morphology []. The morphology of the multiphase polymer blends can be studied using various methods, among which scanning electron microscopy (SEM) is an important method. Therefore, the SEM micrographs of the P34HB/PLA binary and P34HB/PLA/PVAc ternary blends after the PLA component was etched are presented in a and b, in case of the P34HB/PLA binary blends, the black pores formed by the removal of the PLA phase were uniformly dispersed in the continuous P34HB matrix as spheres. This typical phase-separated morphology was consistent with the DMA result. The average particle size and distribution of the dispersed phase were obtained via analysis of Nano Measurer 1.2 software and are presented in . The average particle size (D) of the minor phases in the P34HB/PLA binary blends was approximately 0.69 μm. The P34HB/PLA/PVAc ternary blends exhibited a phase-separated morphology. The diameters of the dispersed phases in the ternary blends increased with the increasing PVAc concentration. For example, the D values in case of ternary blends containing 10, 20, and 30 wt% of PVAc were 1.62, 2.02, and 3.11 μm, respectively. Furthermore, the size distribution of the dispersed phase increased significantly with the increasing PVAc content. This proved that PVAc was selectively located in the PLA-dispersed phase. Therefore, majority of the PVAc located in the PLA phase along with the PLA phase constituted the dispersed phase in the P34HB continuous matrix.The P34HB used in this study was a semicrystalline polymer, the thermal, rheological, and mechanical properties of which were considerably dependent on its degree of crystallinity and crystalline morphology []. Therefore, it is considerably important to study the influence of other secondary phases on the thermal properties of the matrix polymer. presents the differential thermal calorimetry (DSC) thermogram of the first heating, first cooling, and second heating scans for neat P34HB as well as the P34HB/PLA binary and P34HB/PLA/PVAc ternary blends. The relevant thermal parameters are presented in a (first heating scan), neat PVAc and PLA showed Tg values of approximately 35.5 °C and 59.6 °C, respectively. The Tg of the PLA phase in the binary blend was 56.7 °C and decreased to become 56.2 °C, 53.4 °C, and 50.5 °C in case of ternary blends with PVAc content of 5, 10 and 20 wt%, respectively. This result was consistent with the change in Tg observed via DMA. The decrease in Tg of the PLA phase in ternary blends with the PVAc content can be attributed to the complete miscibility of PVAc and PLA.Neat P34HB exhibited double melting peaks at 132.2 °C (Tm1a) and 146.4 °C (Tm2a). The low-temperature melting peak (Tm1) and the high-temperature melting peak (Tm2) can be attributed to the melting of the primary and recrystallized crystals, respectively []. The amplitudes of the Tm2a and Tm1a peaks in case of pure P34HB were approximately identical, indicating the production of a certain number of primary crystals in case of neat P34HB. In case of ternary blends, the Tm2a peak was predominant when compared with the Tm1a peak and Tm2a decreased with the increasing PVAc content. This can be attributed to the fact that the PVAc located in P34HB hindered the mobility of the P34HB chains and segments, resulting in more defective P34HB crystals. Furthermore, the presence of PVAc negatively affected the perfection of the recrystallized crystals and the thickness of lamellae.b, the crystallization peak (Tc) of neat P34HB could be observed at approximately 47.3 °C. In general, aliphatic polyesters, such as P34HB and PLA, do not crystalize from the melt under high cooling rate. However, in this work, due to relatively low cooling rate of 5 °C min−1 used, a crystallization peak of neat P34HB could be still observed. The Tc of the binary blend was higher than that of neat P34HB, indicating that the addition of PLA promoted the crystallization of P34HB. This can be attributed to the enhancement of segmental mobility at the interface between P34HB and PLA owing to partial miscibility. Similar results were obtained for other partially miscible blend systems []. However, in case of ternary blends, the Tc decreased with the PVAc content, indicating that the introduction of PVAc into the P34HB/PLA binary blend inhibited the crystallization of P34HB. On one hand, the PVAc dispersed in the P34HB phase hindered the mobility and stacking of the P34HB chains because of its high viscosity and amorphous nature during crystallization. On the other hand, the introduction of PVAc improved the entanglement density between P34HB and PLA, improving the phase adhesion between the dispersed PLA particles and the P34HB matrix []. In addition, the degree of crystallinity (Xc) of the blends was lower than that of neat P34HB and decreased with the increasing PVAc content. This was because the PVAc added to the semicrystalline P34HB was completely amorphous, which considerably restricted the crystallization ability of the P34HB chains, decreasing the Xcb. The Xcb of the P34HB/PLA-20 ternary blend decreased to 6.7%, which indicated that the concentration of PVAc dispersed in the P34HB matrix increased with the content of PVAc in ternary blends, resulting in a more obvious restriction on the crystallization of the P34HB matrix.c (second heating scan), we can observe a cold crystallization peak (Tcc) at 56.5 °C and Tm2c at 145.6 °C in case of neat P34HB. Compared with neat P34HB, the cold crystallization peaks of ternary blends became broader and less intense and shifted to higher temperatures with the increasing PVAc content, indicating that the simultaneous addition of PVAc and PLA restricted the crystallization of P34HB, which became more pronounced with the increasing PVAc content. For ternary blends with 20 wt% PVAc, the Tcc increased by 11.5 °C when compared with that of pure P34HB. During the second heating process, the changing trend of the Tm2c and Xcc of ternary blends with PVAc content was identical to that in the first cooling process.The effect of the presence of PLA and PVAc on the crystallization of P34HB in ternary blends has attracted research interest. The isothermal melt crystallization behavior and kinetics of neat P34HB as well as the P34HB/PLA binary and P34HB/PLA/PVAc ternary blends were obtained via DSC. shows the DSC scans of isothermal crystallization for all samples at 60 °C and 70 °C, respectively. Relative crystallinity (Xt) as a function of crystallization time (t) can be given as follows [where Xc(t) and Xc(∞) indicate the degree of crystallinity at time t and at the end of crystallization, respectively, and dH(t)/dt is the heat flow rate. indicates the changes in relative crystallinity with crystallization time for the isothermal crystallization of all the samples. For each sample, the crystallization time increased with the increasing crystallization temperature; thus, a low crystallization rate can be observed at high crystallization temperatures. For example, for the P34HB/PLA-10 blend, the crystallization at 60 °C required 9 min for completion, whereas that at 70 °C required 18 min. This can be attributed to the decrease in supercooling caused by the increase in the crystallization temperature that reduced the driving force of crystallization, resulting in nucleation difficulties [We used the Avrami equation to analyze the isothermal melt crystallization kinetics of all the samples [where k is the crystallization rate constant related to nucleation and growth and n is the Avrami exponent associated with the nucleation type and crystal growth geometry. shows the Avrami plots for neat P34HB as well as the P34HB/PLA binary and P34HB/PLA/PVAc ternary blends. The k and n values were obtained from the intercepts and slopes of early linear portion of Avrami plots and are presented in . The R2 values were greater than 0.99, indicating that the Avrami equation was appropriate for describing the isothermal crystallization kinetics of this blend system. As shown in , neat P34HB as well as P34HB/PLA binary and P34HB/PLA/PVAc ternary blends had n values of 2.3–2.7, regardless of the PVAc content and crystallization temperature. Thus, neat P34HB and its binary and ternary blends were crystallized using the same mechanism, i.e., simultaneous nucleation and two-dimensional to spherulitic crystal growth []. The k value could not be used to accurately determine the order of the isothermal crystallization rate because the k value was dependent on the n value and n changed with the crystallization temperature and PVAc content.The crystallization half time (t1/2), which is another important isothermal crystallization parameter, is defined as the time required for the degree of crystallinity to reach 50% and can be calculated as follows:The corresponding values are presented in . For the same crystallization temperature, the overall crystallization rates of the P34HB/PLA binary blends were faster than that of neat P34HB. Thus, the isothermal crystallization rates were promoted by the addition of PLA. The enhancement of the isothermal crystallization of P34HB because of the addition of PLA can be attributed to the following reasons. First, P34HB showed limited miscibility with PLA, as discussed above. The PLA phases could activate the mobility of the P34HB chain. After sufficient local activation chain mobility was achieved, the crystallization would improve because of easy dynamic chain alignment. Second, the surface of the PLA domains may serve as a nucleating center, resulting in the enhancement of the crystallization of P34HB in the blends []. The crystallization rate of ternary blends was slower than that of the binary blend and decreased further with the increasing PVAc content. This result could be explained as follows. First, the amorphous PVAc dispersed in P34HB diluted the crystal region and decreased the P34HB chain agglomeration. Second, P34HB and PVAc were highly elastic at crystallization temperatures of 60 °C and 70 °C, respectively. The addition of high-viscosity PVAc enhanced the entanglement density between the P34HB matrix phase and PLA dispersed phase and between P34HB. The increase in entanglement density between P34HB molecular chains not only restricted the formation of the local orientational ordering of the P34HB chains near the interface to reduce the nucleation rate but also limited the diffusion rate of P34HB chains to the crystal front, reducing the crystal growth rate. In addition, our previous study showed that the addition of 20 wt% PVAc to P34HB increased t1/2 from 3.7 to 12.8 min at a crystallization temperature of 60 °C []. In this study, the introduction of 20% PVAc increased the t1/2 of P34HB in the ternary blend to only 5.7 min. Thus, PVAc was maybe primarily located in the PLA phase and only a small part was dispersed in the P34HB phase.Generally, rheological properties are very sensitive to the phase morphology and interface interaction in multiphase polymer systems. The plots of rheological properties versus angular frequency can effectively indicate the microstructure of the polymer blend system. The changes of the components body of the blend, such as molecular weight and degree of branching, can be often observed in high- and intermediate-frequency regions, whereas the low-frequency regions will be affected by the changes in the dispersion state and interface interaction of the components in the blends []. Consequently, we conducted dynamic rheology measurements to better verify our understanding of the miscibility, interface interaction, and variation in bulk properties of the P34HB/PLA/PVAc ternary blends as a function of PVAc content in the blends. The frequency dependence of the storage modulus (G′), loss modulus (G″), complex viscosity (|η*|), and damping factor (tan δ) of neat P34HB as well as the P34HB/PLA binary and P34HB/PLA/PVAc ternary blends are shown in According to the storage modulus data in a, the neat P34HB melt exhibited a liquid-like behavior, indicating a linear relation between G′ and the angular frequency. The G′ of neat PVAc was considerably higher than that of neat P34HB for the entire range of angular frequency because of its higher melt elasticity. For the blends, G′ was higher than that of neat P34HB and lower than that of neat PVAc. The gradual increase in PVAc content in the P34HB/PLA/PVAc ternary blends slightly increased the G′ of the resulting ternary blends. Furthermore, the viscoelastic response of the blends represented a weak frequency dependence at low frequencies, indicating a pseudo-solid-like behavior of the blend melt. This behavior can be attributed to the presence of a network-like structure or the agglomeration of dispersed matter in binary and ternary blends [Similar to the G′ discussed above, the gradual introduction of PVAc into the P34HB/PLA blend from 5 to 20 wt% slightly increased the G″ of blends at intermediate and low frequencies (b). The G″ of neat PVAc was greater than that of neat P34HB at low and intermediate frequencies; however, it was less than that of neat P34HB at high frequencies. Thus, the modulus of PVAc was less dependent on the shear frequency than that of P34HB.c, neat P34HB exhibited a Newtonian behavior in the entire frequency range, whereas neat PVAc showed a stronger shear thinning effect as a function of shear frequency because of its considerably higher viscosity when compared with neat P34HB. The |η*| of binary and ternary blends was greater than that of neat P34HB over the entire frequency range; further, it indicated a non-Newtonian shear thinning behavior. The incorporation of PVAc into P34HB/PLA blends gradually increased the viscosity of the blends at intermediate and low frequencies and reduced the viscosity at high frequencies. This can be attributed to the fact that the viscosity of PVAc was more sensitive to the shear frequency when compared with neat P34HB. As the PVAc content increased from 5 to 10 wt%, the enhancement of modulus and viscosity of the ternary blends was very weak. This was because majority of the high-viscosity PVAc was located in the dispersed PLA phase and only a small part was dispersed in the P34HB matrix at low PVAc content, resulting in the high-viscosity PVAc had little effect on the viscosity of P34HB/PLA binary blends. When the PVAc content increased to 20 wt%, the modulus and viscosity of the ternary blends was improved, indicating that PVAc diffuses into the P34HB matrix at high PVAc content.The loss tangent (tan δ = G″ / G′), as shown in d, is dependent on the mobility of the polymer molecular chains. The larger the tan δ value, the more viscous will be the behavior of the material. On the contrary, the smaller the tan δ value, the more elastic will be the behavior of the material. The tan δ of neat P34HB decreased with the increasing frequency, implying its viscoelastic liquid behavior []. The elasticity of P34HB at high frequencies increased because of the insufficient relaxation time of the P34HB chains. Further, stress dissipation was accomplished at low frequencies primarily via the movement of P34HB segments and chains. Neat PVAc showed much smaller tan δ values in the entire frequency range compared with pure P34HB because of its high viscosity. Furthermore, the blends had lower tan δ than neat P34HB and higher tan δ than neat PVAc. These plots demonstrated that the tan δ of the blends decreased gradually with the PVAc content at high and intermediate frequencies because of the lower tan δ of the PVAc compared with neat P34HB. However, this trend reversed at low frequencies as a function of the PVAc content that can be attributed to the variation of the phase morphology and interfacial interaction of the P34HB/PLA blends with the PVAc content.The Cole–Cole plots can be used to evaluate the miscibility of the ternary blends' components (a, the Cole–Cole curve of neat P34HB showed an arc shape, indicating the relaxation of the time distribution of P34HB. In contrast, neat PVAc had a straight line, indicating its instantaneous relaxation. In case of the P34HB/PLA binary blend, the Cole–Cole curve had two semicircular arcs corresponding to the two relaxation mechanisms of P34HB, i.e., local dynamic relaxation and long-term restricted relaxation. This result indicated the partial miscibility of P34HB and PLA in the blend. In case of the P34HB/PLA/PVAc ternary blends, the semicircular arcs of the Cole–Cole curves became significantly larger with the increasing PVAc content, indicating a longer relaxation process. This can be attributed to the incorporation of PVAc into the P34HB/PLA blend that increased the physical interactions and entanglement density between P34HB and PLA and between P34HB, resulting in the restriction of the relaxation of matrix polymer chains.b shows the G′–G″ plots (Han plots) for all the samples at 155 °C. Chuang and Han [] reported that the Han curves of binary blends exhibited a certain correlation with the blend composition and temperature of various systems. If a blend system was miscible at the molecular level, the Han plots were independent of the blend composition and temperature. Conversely, the Han plots would result in a composition-dependent correlation. Based on b, the Han curves of the blends deviated from those of pure P34HB in the low-frequency region, indicating the partial miscibility of P34HB and PLA. However, the van Gurp–Palmen (vGP) plots (phase angle δ as a function of complex modulus |G*|) provide considerable information about the structural change in polymer systems [c, neat PVAc demonstrated a much lower δ compared to that of neat P34HB because of its high melt elasticity and viscosity. In case of the P34HB/PLA/PVAc blends, the δ values were greater than those of neat PVAc and less than those of neat P34HB. Moreover, they decreased with the PVAc content at high and intermediate values of |G*|. These phenomena suggested that the elasticity of the ternary blends was enhanced with the PVAc content originating from the increased entanglement density of the P34HB and PLA chains in the blends. This result was consistent with the results in with respect to the effect of PVAc content on the frequency dependence of G′, |η*|, and tan δ. Thus, the studies on viscoelastic properties revealed that PVAc affected the rheological properties of the P34HB/PLA/PVAc ternary blends at both low and high frequencies. On the one hand, the melt elasticity and viscosity of PVAc were considerably greater than those of pure P34HB, and the incorporation of PVAc into the P34HB/PLA blend improved the viscoelasticity of the blend system. On the other hand, the introduction of PVAc increased the entanglement density between P34HB and PLA and between P34HB because of the full miscibility of the P34HB/PVAc and PLA/PVAc pairs in the blend system. This improvement of the melt strength of 34PHB is very important for its molding process. presents the representative strain–stress curves of neat P34HB and the P34HB/PLA binary and P34HB/PLA/PVAc ternary blends. Neat P34HB was a rigid polymer and was deformed in a brittle manner with very low tensile strain (5.5%). Generally, the improvement of the tensile strength of a polymer matrix is accompanied by a drastic decrease in toughness in case of binary blends []. In this study, the P34HB/PLA binary blend showed improved stiffness with a yield strength of 33.1 MPa and Young's modulus of 1315 MPa, whereas the elongation at break decreased to 4.7%. This can be mainly attributed to the strengthening effect caused by the incorporation of the high-stiffness PLA phase and the enhancement in the degree of crystallinity of the P34HB matrix after the addition of PLA.The P34HB/PLA/PVAc ternary blends exhibited an excellent balance with respect to their tensile mechanical properties when compared with neat polymers. As can be observed from , all the ternary blends displayed the obvious yield points and stable tensile deformation after yielding, suggesting that the fracture of the ternary blends transformed from brittle to ductile fracture. compares the yield stress, breaking strength, Young's modulus, and elongation at break values obtained from in case of neat P34HB and P34HB/PLA binary and P34HB/PLA/PVAc ternary blends. Compared to the yield strength (24.3 MPa) and Young's modulus (902 MPa) of neat P34HB, ternary blends with PVAc content of 5, 10, 20 wt% exhibited high yield strengths (32.3, 30.4, and 30.3 MPa, respectively) and Young's modulus values (1341, 1527, and 1464 MPa, respectively). Further, these ternary blends showed considerably higher elongation at break values (13.9%, 15.6%, and 26.4%, respectively) when compared with neat P34HB (5.5%). Thus, the elongation at break of the ternary blends clearly increased with the increasing PVAc content, as shown in b. On the one hand, as the PVAc content increased, the dilution effect of amorphous PVAc dispersed in the P34HB amorphous phase became increasingly pronounced. This resulted in the weakening of the intermolecular interaction of P34HB in the ternary blends and easier flow of the P34HB chains, indicating ductility. On the other hand, the decrease in the degree of crystallinity and crystallization rate of P34HB in the ternary blends with PVAc content resulted in a more amorphous P34HB region that could deform and oriented when stretched; thus, ternary blends with more PVAc content exhibited increased toughness.Additionally, the yield and breaking strength of the P34HB/PLA/P34HB blends became slightly lower than those of the P34HB/PLA ternary blend with the increasing PVAc content. Various factors, such as the phase morphology and interfacial strength between the dispersed domains and matrix phase, considerably affect the strength of the polymer blends. On the one hand, the dispersed phase comprising PLA and PVAc in the ternary blends acted as stress-concentrating sites because of the different elastic properties of PLA and P34HB. The debonding at the particle–matrix interface can be attributed to the stress concentration; this resulted in interfacial microvoids, which triggered the fracture of the polymer blends under a tensile test []. With the increasing PVAc content, the particle size of the dispersed phase increased because PVAc and PLA were completely miscible and the debonding at the particle–matrix interface was more likely to occur. On the other hand, PVAc would decrease the interfacial bonding between the P34HB matrix and PLA particles, the degree of which was determined based on the PVAc content in the blends. Consequently, the changes in the yield and breaking strength of ternary blends with PVAc content can be attributed to the combined effects of phase morphology and interfacial strength. The outstanding mechanical performance of the P34HB/PLA/PVAc blends can be attributed to the synergistic effect of the PLA and PVAc phases. In ternary blends with P34HB as the matrix phase, the high-hardness PLA minor phase acted as the strengthening agent, whereas the flexible PVAc third phase played the role of a toughening agent. The interplay between these two minor phases and the P34HB matrix resulted in the excellent balance of mechanical properties in case of the P34HB/PLA/P34HB ternary blends. This unexpected combination of high stiffness and good flexibility that cannot be obtained using traditional binary blends will result in novel applications in case of neat P34HB, PLA, and PVAc alone.In this study, we initially fabricated P34HB/PLA/PVAc ternary blends via melt blending to obtain good multiple performances. The DMA results suggested that P34HB and PLA were partially miscible and that PVAc showed full miscibility with both PLA and P34HB. SEM analysis indicated the phase-separated morphology associated with all the blends. The increase in the particle size of the dispersed phase with the PVAc content in ternary blends suggested that PVAc was preferentially located in the PLA phase. Furthermore, studies of the thermal and isothermal crystallization behaviors indicated that the introduction of PVAc into the P34HB/PLA binary blend reduced the crystallization ability, degree of crystallinity, and crystallization rate of P34HB. The rheological properties of P34HB were improved by the addition of PLA and PVAc. The most intriguing result was that a good balance of toughness and stiffness was obtained for the P34HB/PLA/PVAc ternary blends, wherein the dispersed phase comprising the high-stiffness PLA and amorphous PVAc improved the stiffness, whereas the PVAc located in the P34HB matrix enhanced the flexibility of the ternary blends.Yi Li: Data curation, Writing-original draft, Investigation, Visualization, Resources, Methodology, Conceptualization. Shuangna Yao: Data curation, Investigation, Visualization. Changyu Han: Funding acquisition, Project administration, Data curation, Formal analysis, Supervision, Writing-review & editing, Writing-original draft, Conceptualization. Yancun Yu: Software, Data curation. Liguang Xiao: Formal analysis, Conceptualization, Project administration.A co-rotational curved beam element for geometrically nonlinear analysis of framed structuresCurved beams are sometimes used in practical framed structures due to good mechanical properties and artistic design. In a framed structure, curved beams may undergo large displacement and experience nonlinear behavior as same as the other straight slender beam-column members. Thus, a geometrically nonlinear curved beam element plays an important role in the analysis of framed structures with curved beams. However, most existing curved beam elements are not accurate enough and still need several or even dozens of elements to accurately describe the behavior of a curved beam with a large subtended angle. To fill this gap, this paper presents a novel geometrically nonlinear curved beam element based on the element-independent co-rotational (EICR) method. The proposed element can simulate a curved beam using only one single element in the analysis and design of most practical framed structures. Moreover, this element is directly derived in a Cartesian coordinate system and can be directly and conveniently used with straight beam-column elements in nonlinear structural analysis. In this manuscript, the derivation of the proposed geometrically nonlinear curved beam element is detailed and several benchmark problems are proposed to verify its accuracy and efficiency.Curved beams are preferred by designers and engineers in framed structures for a better appearance at some time. More importantly, curved beams have the coupling effect between bending and stretching, and as a result, they are stronger in resisting vertical loads than straight beams and have better mechanical properties. Slender framed structures may undergo large displacements and large rotations, so geometrically nonlinear behavior of curved beams also gains tremendous attention. However, the coupling effect between bending and stretching makes curved beams more complicated than straight beams in structural analysis, especially when nonlinear behavior is considered.The finite element method (FEM) is an efficient and the most widely accepted method for the analysis of curved beam structures. There have been so many linear finite element formulations about curved beams so far. Early attempts about curved beam elements adopted low-order polynomial interpolations and brought about membrane locking and large errors in results. To avoid this problem, a few approaches, such as reduced or selective integration, high-order or complicated interpolations, mixed elements, etc., were developed A linear two-node curved beam element with high efficiency and accuracy was proposed by Tang et al. Concerning geometrically nonlinear finite element analysis, there are three common categories: total Lagrangian (TL) formulation, updated Lagrangian (UL) formulation, and co-rotational (CR) formulation The concept of EICR was presented by Rankin and Brogan Although EICR formulations are extensively used in the derivation of geometrically nonlinear finite elements, the studies about geometrically nonlinear curved beam elements based on EICR formulations are very rare. Besides, the existing curved beam elements hardly involve the cases using pinned joints as element end conditions, which are common in practical steel-framed structures. Thus, this paper aims to fill these gaps and proposes a novel co-rotational curved beam element for geometrically nonlinear analysis of framed structures.The organization of this paper is illustrated in the following. introduces a linear curved beam element which adopts a trigonometrical mixed polynomial function and has very good performance in the linear analysis of curved beam structures , the formulations of the linear curved beam element with different end conditions including one or two pinned joints are presented. gives a brief introduction to the EICR formulation for the curved beam element. presents several benchmark problems to verify that the proposed geometrically nonlinear curved beam is accurate and efficient for the analysis of practical steel-framed structures. Finally, is the conclusion that discusses the results, limitations of the present study.The planar curved beam element in the basic coordinate system (oxy) only having three degrees of freedom is shown in . This element was derived based on Euler beam theory which neglects transverse shear and warping deformations, while the neutral axis of the element is an arc whose radius and angle are represented as R and α, respectively. Some existing curved beam elements using the same assumptions were derived in a polar coordinate system, and therefore they cannot be conveniently used with straight frame elements for the analysis of the framed structure. To solve this problem, the presented curved beam element was deduced in a Cartesian coordinate system as same as a straight frame element. Also, this element only has three degrees of freedom in the basic coordinate system, so the element formulations are simplified and its natural stiffness matrix is only 3 by 3.The presented linear curved beam element was firstly derived by Tang et al. . Then, the deformation of the curved beam element can be decomposed into the axial part and the bending part through the moving coordinate system o'x'y', and then these two parts can be treated separately and easily.Generally speaking, the bending deformation of the curved beam is greatly larger than the axial deformation in engineering practice, so it is reasonable to neglect the axial deformation of the arch in some cases. Thus, the element formulation only related to bending deformations is firstly introduced in this section. In the coordinate system o'x'y', the infinitesimal element of arc, ds, is regarded as a straight beam segment, and then the strain-displacement relationships can be given by:where u' and v' are the displacements of straight beam segment ds along axis x' and y' respectively, whereas ε', θ' and κ' refer to the axial strain, rotation, and curvature of segment ds, respectively. Due to the omission of axial deformations, the displacement u' and the axial strain ε' are both equal to zero.Then, the vertical displacement produced in the auxiliary coordinate system o'x'y' is assumed as a trigonometrical mixed polynomial function in the following:v′=c0+c1ξ+c2ξ2+c3sinαξ+c4cosαξ,-1/2⩽ξ⩽1/2in which the five unknown coefficients c0 to c4 can be solved through boundary conditions; ξ=φα is the local dimensionless coordinate.It is worth noting that some boundary conditions are only known in the basic coordinate system oxy, so the relationships between the auxiliary coordinate system o'x'y' and the basic coordinate system oxy should be established. At any position of the curved beam element, the pertaining straight beam segment’s incremental displacements in these two different systems have the following relationships:dudv=cos(αξ)sin(αξ)-sin(αξ)cos(αξ)du′dv′Due to the omission of the axial deformation, we havedu′=0 and the displacements in the basic coordinate system can be finally given by the integrations of the incremental displacements as follows:Through Eqs. (4a, b), the displacement functions in the basic system can be obtained. Besides, according to the boundary conditions in the following:the five unknown coefficients c0 to c4 in Eq. (2) can be determined by the nodal displacements e, θ1 and θ2.By substituting these coefficients into the displacement function v' in Eq. (2), we haveN1=α4cos(α2)-4cos(αξ)+α(1-4ξ2)sin(α2)2(α2+αsin(α)+4cos(α)-4)N2=A0+A1ξ+A2ξ2+A3sin(αξ)+A4cos(αξ)16(α-sin(α))(α2+αsin(α)+4cos(α)-4)N3=B0+B1ξ+B2ξ2+B3sin(αξ)+B4cos(αξ)16(α-sin(α))(α2+αsin(α)+4cos(α)-4)A0=80-45α2+6α4+16-8+α2cos(α)+316-α2cos(2α)+4α4+α2sin(α)+24αsin(2α);A1=-28α2+8α4+32α2cos(α)-4α2cos(2α)+16a-2+α2sin(α)+16αsin(2α);A4=-16-21+α2cos(α/2)+2cos(3α/2)+α5sin(α/2)+sin(3α/2);B0=112-15α2+2α4+16-8+3α2cos(α)+16-α2cos(2α)+4a-16+3α2sin(α)+8αsin(2α);Because the axial deformation of the curved beam element is neglected herein, the total potential energy function can be given byin which E is the elastic Young’s modulus and I is the cross-sectional moment of inertia; f={P, M1, M2}T is the element nodal force vector and d={e, θ1, θ2}T is the corresponding element nodal displacement vector.By taking a variation of the total potential energy function, the linear relationship between the force vector and the displacement vector of the element can be given by:where ke is the natural stiffness matrix of the curved beam element in the basic coordinate system with only considering bending deformations and yieldsk22=-CR29-6α2-16cosα+7cos(2α)+8αsinα+2αsin(2α);k23=-CR215+2α2+4(-4+α2)cosα+cos(2α)-12αsinα;When the axial deformation of the arch should be considered in the analysis of framed structure, the natural stiffness matrix shown in Eq. (10) is needed to be modified.First, according to the static equilibrium, the axial force along the neutral axis of the curved beam element can be given byThen, the strain energy due to the axial deformation is:Taking advantage of Castigliao’s second theorem, the nodal displacement at the right end in the basic coordinate system due to the axial deformation can be given byTo simplify the element formulation, the end rotations due to the axial deformation are neglected, since they are much smaller than those due to the bending deformation in general. Thus, the element displacement vector can be modified based on the previous derivation as follows:Rearranging Eq. (14), the final natural stiffness matrix considering the axial and bending deformations can be obtained, and its detailed expression can be found in Ref. In the analysis of framed structures, member end conditions are usually treated as pinned or rigid joints entirely. For rigid joints, the natural stiffness matrix introduced in can be directly used in the analysis. At present, almost all existing curved beam elements only discussed the situation of rigid joints. To fill this gap, the curved beam element with one or two pinned joints are presented in this section.When an element end is assumed as a pinned joint, the moment at this end is zero but the end rotation still exists. For the displacement-based method, it is impossible to derive element formulation with pinned joints by directly using the element model in . Thus, two section-springs with zero length should be assigned in the element ends, as shown in . This method is often used for straight beam elements to consider semirigid joints.The external moment between the section-spring and the other element’s node can be given by:in which Sj is the stiffness of the section-spring; θje and θji are the rotations of the section-spring and the internal element node j, respectively.Also, according to the moment equilibrium conditions at the section-spring, the internal moment between the internal beam element and the section-spring is:In terms of the internal curved beam element between these two section-springs, the element formulation has been introduced in Assembling Eqs. (13)–(15), we have a relationship in the following:M1eM2ePM1iM2i=S100-S100S200-S200k11k12k13-S10k21k22+S1k230-S2k31k32k33+S2θ1eθ2eeθ1iθ2iwhere kij is the entry of the natural stiffness matrix of the curved beam element introduced in It should be noted that the moments M1i and M2i are zero after assembling and the corresponding rotations θ1i and θ2i belong to the internal degrees of freedom of the whole element model consisting of two section-springs and a curved beam element. Through static condensation about these two rotations and the equations: k21 = k12, k31 = k13, k32 = k23 and k22 = k33, we can getPM1eM2e=Keeθ1eθ2e=K11K12K13K22K23sym.K33eθ1eθ2eK11=D2k12k13k23-k132k22+S1-k122k22+S2+k11To simulate a pinned joint, the corresponding section-spring stiffness Sj is set to zero, while Sj is set to infinite to simulate a rigid joint. Thus, the natural stiffness matrix of the curved beam with different types of joint at ends are given as follows:The left joint is pinned and the right joint is rigid:KeS1=0S2→∞=1k22k11k22-k1220k13k22-k12k23000k13k22-k12k230k222-k232The left joint is rigid and the right joint is pinned:KeS1→∞S2=0=1k22k11k22-k132k12k22-k13k230k12k22-k13k23k222-k2320000KeS1=0S2=0=1k222-k2322k12k13k23-k22k122+k132-k11k22-k11k23200000000Finally, making use of Eqs. (17)–(21), the curved beam element with different end conditions is determined. Eq. (17) also can be used for the curved beam element with semirigid joints.To extend the linear curved beam element to geometrically nonlinear analysis, the present study adopts the 2D element-independent co-rotational (CR) formulation for a beam element to transfer the basic element into the global coordinate system. Because the EICR formulation is independent of basic elements, the EICR formulation for a 2D straight beam-column element can be directly used for the present linear curved beam element which is derived in the basic coordinate system. For completeness, the EICR formulation is briefly introduced in this section In an incremental-iterative nonlinear procedure, the tangent stiffness matrix of the curved beam element in the global coordinate system can be given by:where [L] is the transformation matrix from the local to global coordinate system, [T] is the transformation matrix from the basic to local coordinate system and expands three degrees of freedom of the element into six degrees of freedom, while [Ke] is the natural stiffness matrix of the curved beam element shown in and [Kg] is the local geometrical stiffness matrix as same as that for a straight beam-column element. The detailed expressions of these matrices can be found in Ref. In an incremental-iterative nonlinear procedure, once the global incremental displacements have been obtained, the incremental pure deformations for every curved beam element can be extracted from the incremental global displacements through the co-rotational method. The incremental pure deformations Δd are the increments for the three degrees of freedom of the curved beam element, then the basic internal forces of the curved beam element can be updated as follows:where the superscript i−1 means that the quantity belongs to the last element configuration.To assemble the global internal forces of the analyzed structure, the basic internal forces should be transferred into the global coordinate system as:in which the transformation matrices [L] and [T] are updated according to the current element configuration through the nonlinear analysis procedure all the time.To sum up, taking advantage of the CR formulation, the present linear curved beam element with different end conditions can be used for geometrically nonlinear analysis. It is worth noting that the whole analysis procedure based on the CR formulation herein is identical to that for a straight beam-column element, except that the natural stiffness matrix belongs to the curved beam element.To verify the accuracy and efficiency of the proposed curved beam element for geometrically nonlinear analysis, the element formulation was coded in a program and several benchmark problems about practical framed structures with curved members are presented in this section. shows a simple portal frame that contains a curved beam with a 90° or 180° subtended angle and is subjected to point loads. The sections of the curved beam and two columns are all HEB300 whose cross-sectional area and moment of inertia around the strong axis are 149 cm2 and 25170 cm4, respectively. Also, the elastic Young’s modulus is 2.05 × 105MPa. The example investigates four different cases, including (a) the curved beam with rigid joints at both ends, (b) the curved beam with pinned joints at both ends, (c) the curved beam with a rigid joint at the left end and a pinned joint at the right end and (d) the curved beam with a pinned joint at the left end and a rigid joint at the right end. All four different cases adopt the identical load case which is common in practical steel framed structures and makes the columns close to section capacity, as shown in In the geometrically nonlinear analysis of these cases, the straight columns are simulated by one PEP (pointwise equilibrating polynomial) element which is a classical beam-column element for second-order direct analysis shows the response (i.e. horizontal displacement u, vertical displacement v and rotation θ) of Point A obtained by different simulation methods, including linear analysis to highlight the importance of second-order analysis. In this table, LA means linear analysis whereas GNA refers to geometrically nonlinear analysis in which the curved beam is modeled by 90 PEP elements. It was known that enough straight beam elements can get accurate results for the simulation of a curved beam, so the results given by GNA can be regarded as exact values to verify the present study. that the results obtained by the present study which uses only one proposed curved beam element are very closed to those by the method that uses so many straight elements to simulate a curved beam, no matter if the subtended angle of the curved beam is 90° or 180°. Thus, the proposed curved beam element is accurate and efficient for different end conditions of the curved beam in this example and suitable for practical structural analysis and design. Besides, it is worth noting that the difference between the results by linear analysis and nonlinear analysis is very large, which shows that nonlinear analysis is necessary for steel-framed structures in some cases.In this example, we investigated the response of a one-story and two-bay frame with curved beams whose subtended angles are both 60° or 120° (see ). The columns and curved beams are HEB300 and HEA340 sections respectively, while the elastic Young’s modulus is equal to 2.05 × 105MPa. Two different cases about the end conditions of curved beams are tested herein. The ends of curved beams are all rigid in Case a, and all pinned in Case b. In both cases, two vertical point loads are applied to the top of the curved beams.In the present study, each curved beam is divided into two proposed curved beam elements by the points subjected to loads, while the columns are still analyzed by one PEP element per member. Besides, the referenced values of this example are obtained by the models that use 60 straight PEP elements to model curved beams. lists the solutions for Point A of the frame by different methods. illustrates that the results obtained by the present study, in which every curved beam only uses two proposed curved beam elements, are still very close to the referenced values given by the refined element models. Moreover, the accuracy of the proposed curved beam element is not affected by the subtended angle of the curved beam. Thus, the proposed element is accurate and efficient in this example. Besides, it is interesting to find that the difference between the results of linear and nonlinear analyses is not as large as those in the last example. This is because the compression loads to the columns herein are much smaller than those in the last example and the second-order effect in this example is not evident., a two-story frame under point loads is studied in this example to verify the proposed curved beam element. The subtended angles of the curved beams in this frame both are 90° or 180°. The sections of this frame like those in Example 5.2 in which the columns and the curved beams are HEB300 and HEA340 sections, respectively, whereas the elastic Young’s modulus is 2.05 × 105MPa too. Two cases of the curved beams with different end conditions are investigated herein. The end conditions of the curved beams are both rigid joints in Case a and pinned joints in Case b. In the present study, the curved beams and columns only use one proposed curved beam element and one PEP element per member, respectively. Like previous examples, the results by the refined element model which uses 90 PEP elements to simulate one curved beam are taken as referenced values. These results for Point A of the frame obtained by different methods for both cases are listed and compared in In this example of a two-story frame with curved beams, the results obtained by the present study are still in good agreement with the referenced values with only using one element per curved beam, even when the deflections of the frame are very large. Besides, the end conditions and subtended angles of curved beams do not affect the accuracy and efficiency of the proposed curved beam element.This paper presents a novel geometrically nonlinear curved beam element based on an accurate and efficient linear curved beam element and the corresponding EICR method for the analysis of framed structures. Meanwhile, the derivations and formulations of the curved beam element with different end conditions are also proposed. The corresponding analysis procedure was programmed and several examples that are common in practical engineering structures were investigated. Through comparing with the refined element models in these numerical examples, it can be found that the advantages of the present study are evident in accuracy and efficiency.The proposed curved beam element only can be used for large displacement, large rotation, but small strain problems with one element per member. Thus, this element is suitable for the analysis and design of most practical engineering structures. However, the refined mesh of curved beam is inevitable when local pure deformations of the curved beam are large, since the local curved beam element is linear and based on the assumption of small strains. If we need to remove this limitation, a more complicated curved beam element with the consideration of moderate or large strains should be established in the basic coordinate system, which can be studied based on the present study in the future.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.the displacement at the yielding of joints for deformation controlthe measurement from displacement transducer Dithe ultimate strength of bolts used in finite element modelthe elastic modulus of bolts used in finite element modelthe Mooney Rivlin coefficients of rubber used in finite element modelthe first invariant of the right Cauchy-Green deformation tensor of rubberthe second invariant of the right Cauchy-Green deformation tensor of rubberthe initial elastic modulus of rubber used in finite element modelthe initial bulk modulus of rubber used in finite element modelthe initial shear modulus of rubber used in finite element modelthe Poisson's ratio of rubber used in finite element modelthe vertical deflection of the annular thin platethe radial bending moment of the annular thin platethe vertical shear force of the annular thin platethe coefficients associated with the boundary condition of platethe tensile stiffness of joint includes the effects of preload in boltsIn recent years, with the advances in seismic research, more and more researchers pay more attention to the seismic research of non-structural components. Among various non-structural components, process piping systems are particularly important due to their transportation function, complexity of composition, and wide range of layout. Process piping systems are essentially used in industrial buildings to transport fluid manufacturing materials and products, such as liquid and gas. Damage of process piping systems in earthquakes inevitably causes the release of fluids and exposure of chemicals in the environment, which is likely to cause life-threatening hazards and pose disastrous side effects of earthquakes if proper precautions are not taken. Existing investigations showed that pipe joints were more vulnerable to earthquakes than the pipe itself in piping systems []. Particularly in the chemical industry, it is not only necessary to calculate the ultimate load capacity of the joints, but also mandatory to check the tightness of the joints in design [. The nominal diameters of the joints are DN300. According to ASME B16.5, to ensure the behavior of the joint is not affected by the boundary conditions of the pipes, a minimum length of 2.5Rt is required for the pipes, where R and t is the radius and thickness of the pipes. Therefore, the length of the steel pipes connected to the joints in the specimens are chosen as 420 mm in this study. The typical material and detailing of piping joints used in practice are adopted for the specimens, as summarized in . Since the loading and unloading stiffness of the joints are unlikely to be the same due to the hyperelastic behavior of rubber material and complex contact behavior between different parts of the joints, axial load is applied to the joints to investigate the tensile stiffness, load and deformation capacity, and failure modes of the joints. shows the test setup for the experimental study. The test specimen is installed in the self-balance reaction steel frame and connected to a 2000kN servo hydraulic actuator. Hysteretic loading is applied to the test specimen through the actuator and force reaction mechanism of the steel frame. Although the bearing capacity of the specimens under compression is expected to be higher than the tensile capacity under tension, a symmetric loading protocol with axial compression force consistent with axial tension force in each stage of loading is used in the tests. The loading protocol is determined according to the Code for Seismic Test of Buildings (JGJ/T 101–2015) []. The entire loading protocol is shown in (b). During the axial tension loading stage, force and deformation control is used to control the load applied to the specimens before and after the yielding of the joints, respectively. During the axial compression loading stage, only force control is adopted for the control of the loading. To explore the mechanical behavior of the joints under lower levels of loads corresponding to mild intensity levels of earthquakes, five levels of loads, i.e., 0.2Fy, 0.4Fy, 0.6Fy, 0.8Fy, and Fy are used until the yielding of the joints, where Fy is the load estimated using yield strength of 300 MPa for the bolts in the joints. The displacement Δy corresponding to Fy is used for the deformation control of the tests. Δy is determined based on the measurements of the displacement transducers mounted on the specimens at the time of yielding of the joints under Fy.. The joint reached the ultimate tensile capacity of 970kN at deformation of 3.5∆y. The capacity of the joint decreased rapidly due to thread failure and fall out of bolts as shown in The axial force-deformation hysteretic curves of the joints obtained from the tests are as shown in ΔN=12Δ5+Δ6−Δ7−Δ8−Δlp=12Δ5+Δ6−Δ7−Δ8−ε¯⋅lpwhere ∆i (i = 5– 8) is the displacement measurement from displacement transducer Di; ∆lp is the axial deformation between the steel pipe sections 5–5 and 6–6 determined from the average strain within the length of the pipes using Eq. based on the applied force N, and section area and elastic modulus of the pipes.The skeleton curve of the axial force-deformation hysteretic curves is formed by connecting the peak load points of the first cycle of each loading stage and used to determine the initial stiffness, ultimate capacity, ultimate deformation, and yielding capacity of the joints. The initial stiffness of the joint is obtained by linear curve fitting the skeleton curve within the range of 60% of the yielding capacity of the joint Fy that is theoretical determined as Fy = nAbefy, where fy and Abe is the yielding strength and net cross-sectional area of a bolt respectively, and n is the number of the bolts in a pipe joint. The peak axial force on the skeleton curve is taken as the ultimate capacity of the joint, and the deformation corresponding to the ultimate capacity is taken as the ultimate deformation of the joint. Since there are no obvious points on the skeleton curve corresponding to the yielding of the joint, the Park method is used to determine the yielding capacity of the joint under tension []. As yielding under compression was not detected by strain gauges, compression yielding capacity of the joints are not calculated in this study. summarized the initial stiffness, ultimate capacity, ultimate deformation, and tension yielding capacity of the joints. that the hysteretic curves of the two joints have pinching behavior featured with significant stiffness degradation when reloading after unloading and recovery of stiffness when deformation is imposed in the opposite direction. This pinching behavior is caused by the yielding of the bolts and loss of preload in the bolts. However, substantial strength degradation was not observed at the same load levels. As can also be observed in Due to the symmetric layout of the joints and loading, similar strain patterns were developed in the bolts of each type of joint in each stage of loading, thereby, only the strain of one bolt of each joint is presented in this study, as shown in Finite element method is used to analyze the mechanical behavior of the joints using the software program ABAQUS []. The FE model of the joints includes the joints and the steel pipes connected at both ends of the joints. The same dimensions and material properties as the test specimens are used in the FE model. Considering the symmetry of the test specimen and loading, only half of the joint is built in the FE model to reduce computational time and costs is shown in . The material property of the bolts in the FE model uses a bilinear elastoplastic constitutive model with yield strength of fy = 300 MPa, elastic modulus of Eb = 206,000 MPa, ultimate strength of fu = 660 MPa, and strength hardening of 2%Eb. The rubber material used in the joints is nitrile rubber (NBR) treated with fluorine. NBR is a synthetic rubber copolymer of acrylonitrile (ACN) and butadiene widely used in the automotive and aeronautical industry to make fuel and oil handling hoses, seals, grommets, and self-sealing fuel tanks. NBR is generally considered isotropic and volume incompressible, thereby, its constitutive relation is expressed using strain energy function instead of Young's modulus and Poisson's ratio. There are two categories of strain energy functions in ABAQUS: one is based on thermodynamic statistics, such as Neo-Hookean and Arruda-Boyce models; the other is based on continuum mechanics, such as Mooney-Rivlin, Ogden, polynomial, and Yeoh models []. As the Mooney-Rivlin model has been validated to be suitable to simulate rubber seal by Zhao et al. [], it is also adopted to model the rubber gasket in the FE model in this study. The strain energy function of the Mooney-Rivlin model is as following:where C10, C01, and D1 are the Mooney Rivlin coefficients;D1 is used to describe the incompressibility of the material, D1 = 0 when the material is completely incompressible; I1¯ and I2¯ are the first and second invariants of the right Cauchy-Green deformation tensor; and Jel is the elastic volume ratio. The coefficients of C10, C01, and D1 are used to determine the initial shear modulus G0 and initial bulk modulus K0 using Eqs. . The initial elastic modulus E0 of the rubber can be determined given the initial shear modulus and Poisson's ratio ν using Eqs. . For incompressible rubber material with ν = 0.5, E0 is only dependent on coefficients C10 and C01 as Eqs. . E0 = 43.44 MPa with C10 = 5.79 and C10 = 5.79 C01 = 1.45 is used in the FE model of this study.Two reference points RP1 and RP2 are set up at the center of the cross sections and coupled to the cross sections at both ends of the specimen, respectively. Thereby, displacement loading is applied to the specimen by modifying the boundary conditions of the reference points. As no obvious capacity degradation is found in different loading cycles of the same loading level in the tests, monotonic cycle of loading is used in FEA. Before loading of the specimen during the analysis, a preload of 16kN is applied to each bolt using the cooling method. compares the axial force-deformation curves of the joints from FEA with that from the tests. The initial stiffness of the joints obtained by linear fitting of the load-deformation curves are compared in , and the tensile yielding capacity of the joints determined using Park method are compared in . It can be seen that the load-deformation curves from FEA matches reasonably well with the skeleton curves of the force-deformation curves from the tests in the early stage of tension loading, thereby, the initial stiffness and tension yield capacity of the joints from FEA are close to that from the tests. However, significant discrepancy between the FEA curve and test skeleton curve of the SJ1-F joint beyond the yielding of the joint can be observed. The FEA curve obviously deviated from the skeleton curve at loading stages after the yielding of the SJ1-F joint. For the SJ1-F joint, the FEA force-deformation curve has large ultimate deformation and salient two stages of stiffness, while the skeleton curve from the test has limited ultimate deformation and does not have obvious yielding points. These discrepancies can be attributed to two main reasons: (i) the FE model do not capture the shear fracture of bolt threads that occurred in the test, as the threads and shear fracture failure mechanism of the bolts are not explicitly modeled in the FE model; (ii) the bolt material in the FE model is simplified without considering the uncertainties associated with the modeling of the bolts, therefore, does not truly represent the yield strength and strength hardening of the bolts in the test, as the aim of FEA is not to replicate the behavior of the joints in the tests, rather it tries to compare and understand the difference between the test and FEA results. For the SJ1-H joint, shear fracture of bolt threads did not occur in the test, and the FEA curve overall agree well with the test skeleton curve with large ultimate deformation. For both the SJ1-F and SJ1-H joints, the joint deformation under compression from FEA are less than that from the tests. The reason for the discrepancy is that rubber is empirically set as completely incompressible material in the FE model which is not exactly true as the bulk modulus of rubber is not infinitely large. Research on hydrostatic compression test of rubber showed that volume change can reach up to 10% of the initial volume of the rubber in the test []. Using the completely incompressible material in the FE model inevitably causes slightly larger compression stiffness of the joints than the stiffness of the specimens in the tests, which reduced the deformation of the joints under compression in FEA.As process piping systems are used to transport gas or liquid, sealing performance is of significant importance for pipe joints. The yielding of the bolts causes the loss of the preload force in the bolts, which inevitably diminishes the sealing performance of the joints. Therefore, it is practical to use yield capacity rather than ultimate capacity as the failure standard for pipe joints. Although the FE models used in this study do not fully feature the failure mechanism such as bolt thread shear fracture and accurately get the ultimate capacity of the joints, they are able to provide good estimation of the initial stiffness and yield capacity of the joints that matched well with the test data, and therefore, suitable for numerical simulation of the pipe joints.), it is more sensible to take the yield capacity of all bolts as the tension yield capacity of the joints for both safety and economic considerations. Therefore, the tension yield capacity of the joint can be determined as follows:where n is the number of bolts, Ae is the net cross-sectional area of a bolt, and fy is the yield strength of bolts.The comparison between the calculated results using Eq. and the results from tests and FEA are shown in are also smaller than that from FEA, due to the facts that material model with strength hardening is used in the FE model. Overall, the tension yield capacity calculated by Eq. are lower than the results from tests and FEA with some margin of safety, and thereby conservatively suitable for use in engineering practice., where P is the applied tension load uniformly distributed along the pipe wall. is further simplified into the model shown in ] As Mb is the average value of constraint moments distributed uniformly along the edges of the supports, it reduces to zero when the applied tension load increases to the yield load. Therefore, Mbis not considered when checking the sealing performance of the joint under the yield load. The polar coordinate system is used in the simplified model shown in , where ρ is the radial coordinate axis.According to the small deflection theory of axisymmetric circular thin plates, when there is no transverse load uniformly distributed within the width of the plate, the vertical deflection ω, radial bending moment Mρ, and vertical shear force Qsρ of the annular thin plate can be determined using the following equations:A0=−Pa3b22Db2−a2⋅1+ν1−νlnba+M1+M2a2b2D1−νb2−a2C0=−Pa4Da2b2−a2lnba+3+ν21+ν+lnb+M1a2+M2b22D1+νb2−a2where A=−Pa3b2Db2−a2⋅1+ν1−νlnba+Pab4D2lnb+1−Pab2Da2b2−a2lnba+3+ν21+ν+lnb,B=K1+Kwa2bKwD1−νb2−a2+K1a2b+Kwb3KwD1+νb2−a2+1Kw.whereλ=31−ν2a2δ21/4,Dc=Eδ3121−ν2, δ is the wall thickness of the steel pipe. The calculation model for Kn is shown in . Kn can be obtained given the rotational angle θ and bending moment M applied at the support,Kn = M/θ. The boundary conditions of the model in Fig. 14 is: ω|ρ=a = 0; Mρ|ρ=c = 0; Mρ|ρ=a = − M; Qsρ|ρ=c = 0. The coefficientsA0 、 B0 、 C0、D0 can be obtained by substituting Eqs. The rotational angle θ at the support can be derived using Eq. at ρ = a and the coefficients in Eq. (17) as:The calculation model for Kw is shown in . Kw can be obtained given the rotational angle θ and bending moment M applied at the support, Kw = M/θ. The boundary conditions of the model in is: ω|ρ=b = 0; Mρ|ρ=d = 0; Mρ|ρ=b = − M; Qsρ|ρ=d = 0. The coefficients A0 、 B0 、 C0、D0 can be obtained by substituting Eqs. The rotational angle θ at the support can be derived using Eq. at ρ = b and the coefficients in Eq. (22) as:; Step 2: calculate M1, M2 using K1、Kw, and P = F/2πa in Eqs. Since the gasket is compressed in a closed steel groove, the strain in both the radial direction ρ and angular direction φis zero, i.e., ερ = εφ = 0. Using the generalized Hook's law for ερ and εφ, i.e., ερ = [σρ − ν(σφ + σz)]/E = 0, εφ = [σφ − ν(σρ + σz)]/E = 0, and σρ + σφ = 2νσz/(1 − ν), the strain of the gasket in the z direction εz and compression stiffness of the gasketKRcan be obtained as:where AR,hR is the area and thickness of the rubber gasket, and ER=E/1−2ν21−ν.. The value of elastic modulus of the gasket used in the simplified calculation is consistent with that in the FEA, i.e., E = 43.44 MPa with Poisson's ratio of 0.49. KR = ∞ when Poisson's ratio equals to 0.5. is also used for the deflection calculation of the convex ring simply supported at the edge of the stop ring with M2 = 0. The steps summarized in Section 4.2.1 are used for the calculation. Step1: calculate K1 using Eq. where An=−Pa2b22Db2−a2⋅1+ν1−νlnba+Pa24D2lna+1−Pa22Da2b2−a2lnba+3+ν21+ν+lnb.The effect of preload in the bolts is not considered in Eq. can be used to include the effect of preload in the bolts on the tensile stiffness of the ring joint. As shown in for the comparison of the tensile stiffness results from the simplified analysis with the results from the test and FEA of the ring joint. Overall, the results from the simplified calculation method match well with results from the test and FEA. In order to keep the ring joint sealed before the yielding tension load, the preloads in the bolts also need to meet the requirements of Eq. Through an integrated study combining experimental tests, finite element analysis, and theoretical analysis on the load and deformation capacity, tensile stiffness, sealing performance, and failure mechanism of two types of pipe joints under axial loads, the following conclusions are obtained., the simplified calculation method provides estimates of the tensile stiffness of the joints that closely match the results from the tests and FEA., the simplified calculation method is suitable for design of the tension yield capacity of the joints. There is adequate margin of safety against the demand using the simplified calculation method.Specific requirements to ensure the joints to have good sealing performance before the yielding under tension are proposed.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.Experimental Investigation and FE Analysis of CFRP CompositesComposites are one of the most advanced and adaptable engineering materials. The strength of any composite depends upon volume/weight fraction of reinforcement, L/D ratio of fibers, orientation angles and other factors like curing temperature etc. The present work focuses on mechanical properties of carbon fiber reinforced epoxy composite material. Tensile testing of specimens are prepared and tested according to ASTM 3039. Composite properties like Young's modulus (E1), transverse modulus (E2), poisons ratio (υ12), failure stress (σ1) and strain (ɛ1). The experiment is conducted on Computer controlled Universal testing machine with proper mounting of strain gauges and extension meters. Mechanical properties obtained from these samples are input to the FEM model to find the stress and strain distribution in each layer and at interface. Finally the numerical results are compared with experimental results. The variation between Experimental results and numerical results is less than 5%.Linear μ-bending method for the measurement of the residual stress of surface-micromachined MEMSThis study introduces a simple and reliable strategy, called ‘linear μ-bending method’, to measure the residual stress of surface-micromachined micro-electro-mechanical systems (MEMS). The basic theory of the linear μ-bending method relies on the fact that not only the geometry and the material, but also the residual stress contribute much to determine the linear bending stiffness of MEMS. In a reverse way, this study identifies the residual stress after obtaining the linear bending stiffness of MEMS through experimental procedure. In a first step, bending tests for the surface-micromachined cantilevers are performed so that the bending rigidity and the anchor stiffness, which play important role in altering the stiffness of suspending MEMS, are obtained as pre-data. Secondly, the bending stiffness of the surface-micromachined bridge is measured through bending tests. And, as the last step, the residual stress is achieved by putting the obtained data from the bending tests – ‘linear bending stiffness’, ‘the anchor stiffness’, and ‘the bending rigidity’ – into the analytic model presented in this study.The results from the tests about the surface-micromachined poly-silicon structures with various residual stresses demonstrate that the linear μ-bending method is reliable. The output from the linear μ-bending method is that the residual stress of as-deposited poly-silicon film is 142.7 MPa (compressive) with the standard deviation of 3.5% and that the residual stress of the poly-silicon film decreases as the annealing effect grows.MEMS technology has accelerated the miniaturization of sensors and actuators. However, the residual stress of the micromachined structures frequently degrades the reliability of MEMS, particularly the surface-micromachined (SMM) MEMS. Therefore, great attentions have been given to the evaluation and the control of the residual stresses of SMM. Various methods have been introduced to measure the local stress of thin films on the wafer. In cases of micro-bridge and micro-ring methods Nano-indenter systems have been proven to be useful for directly obtaining films’ residual stresses from the load–displacement characteristics of the indenter tip Some researchers have realized an idea – using the nano-indenter or atomic force microscope (AFM) as a bending machine used for applying load to make suspending MEMS bent, in order to identify the material properties of the films This study introduces ‘linear μ-bending method’, to measure the residual stress of SMM. The basic theory of the linear μ-bending method relies on the fact that not only the geometry and the material but also the residual stress make a substantial change of the linear bending stiffness of SMM; the compressive residual stress decrease the stiffness, while the tensile does in a reverse way. The residual stress can therefore be identified if the linear bending stiffness of MEMS structure is obtained through experimental procedure.The bending rigidity and the anchor stiffness also play an important role to alter the bending stiffness of SMM. The former, consisting of the Young's modulus and the second moment of inertia, represents the combined effect of film's material and section's shape. The latter involves flexible anchor structure. As the first step of the linear μ-bending method, the surface-micromachined cantilevers are under the bending tests to discover the bending rigidity and the anchor stiffness. It is assumed that the SMM cantilevers are free from the residual stress and their material composition and their anchor geometries are same as those of the SMM bridges. In a second step, the linear bending stiffness of the SMM bridges are measured through similar bending tests. Finally, the residual stress is obtained by putting ‘the bending rigidity’, ‘the anchor stiffness’, and ‘the linear bending stiffness of the SMM bridge’ into the general analytical model proposed in this study.The linear μ-bending method is useful in that it offers a way to directly obtain the residual stress, not the residual strain. And it is reliable because it deals with the effects of the unknown material properties and the vague anchor's flexibility, which is a part of the entire process.Since the linear μ-bending method needs data from the linear deformation, the bending tests are carried out in the linear range, so that the indention will not occur during the experiments. So, the linear μ-bending method is immune from the problems rising from the nonlinear phenomenon, such as plastic deformation and indentation friction The experimental results about the surface-micromachined poly-silicon structures with various residual stresses demonstrate that the linear μ-bending method is reliable. The results indicate that the residual stress of as-deposited poly-silicon film is 142.70 MPa (compressive) with the standard deviation of 3.5% and that the residual stress of the poly-silicon film decreases as the annealing effect grows.The anchor stiffness and the bending rigidity of SMM cantilever are evaluated at a first step. The anchor stiffness is a measure to the flexibility of the SMM's anchor that cause finite rotation at the boundary. The bending rigidity is the product of the Young's modulus and the second moment of inertia of the beam cross-section shows a SMM cantilever with length l. The applied load at the tip is denoted by P. The analytic model of the SMM cantilever with anchor stiffness, Kθ is described in (b). The anchor stiffness should be considered because the anchor itself deforms as a transverse displacement of a SMM cantilever occurs. The linear load–displacement expression for an elastically deformed cantilever beam is as follows:where K is the linear bending stiffness of the cantilever beam, w the transverse displacement at the loading point, and P the applied load. Note that the present analytic model is linear; hence, the displacement and the applied load have linear relationship.According to the Bernoulli–Euler beam bending theory where E represents the Young's modulus and I denotes the second moment of inertia of the beam cross-section.The bending moment at the location of x along the beam axis is expressed as the product of the applied load and the length of the moment arm, (l−x), as follows:If the anchor is not perfectly rigid, the rotation at the anchor exists and can be expressed as follows:where Mo is the moment at the anchor, and Kθ the anchor stiffness., the linear bending stiffness of the SMM cantilever can be expressed as follows:Note that the bending rigidity and the anchor stiffness in Eq. to two cantilevers with different length gives two expressions. Eqs. show how the linear bending stiffness relates to the bending rigidity and the anchor stiffness for two cantilevers having different length.K(1)=l(1)33EI+l(1)2Kθ−1→l(1)33EI+l(1)2Kθ=1K(1)K(2)=l(2)33EI+l(2)2Kθ−1→l(2)33EI+l(2)2Kθ=1K(2)where the subscript ‘(1)’ and ‘(2)’ represent two cantilevers with different length. The bending rigidity and the anchor stiffness can be calculated from the linear bending stiffness of the SMM cantilevers in the stress-free state using the following equation.1EI1Kθ=l(1)33l(1)2l(2)33l(2)2−11K(1)*1K(2)*where the superscript ‘*’ denotes the very quantities that will be obtained from experiments. The bending rigidity and the anchor stiffness, therefore, become available through simple calculation of Eq. , because all the parameters in the right-hand side are clear from geometry inspection and linear bending tests. shows a schematic drawing of a doubly supported SMM bridge under the applied load P at the center. (b) illustrates the free body diagram for an arbitrary section of the SMM bridge. The reaction moment at the boundary is denoted by Mo. The axial force, Nx representing the residual stress, is expressed by the product of the residual stress σr and the cross-sectional area.where b and t denote the width and the thickness of the SMM bridge, respectively.The analytic model of the SMM bridge is described in . Only the half of the SMM bridge is considered taking the advantage of the symmetry of the loads and the boundary conditions. The moment at the beam section is constituted with the reaction moment, the product of the reaction force and the moment arm, and the product of the axial force and the vertical displacement. Then, the moment at the beam section is described as follows: underlies some assumption about the direction of the axial force. It is assumed that the axial force is parallel to the axis ‘x’ on the basis of the small linear deformation of doubly supported beam, which actually exhibits much smaller rotation of beam section than cantilever one. Accordingly, to perform the bending tests within the linear rage of the deformations is a rule of thumb to validate the linear μ-bending method.The governing equation for the SMM bridge under compressive residual stress is expressed by substituting Eq. To make the formulation process simple, the complex parameter k is defined and the modified form of Eq. incorporating the complex parameter is:where the compressive stress is defined as negative in the present formulation.The vertical displacement satisfying the governing equation is expressed as follows:where A and B are constants determined by the boundary conditions.After applying appropriate boundary conditions and the symmetry conditions at the center of the bridge, the displacement at the loading point, wP, is expressed as follows:wP=−4Kθ+(EIk2l+4Kθ)cos(kl/2)+(klKθ−2EIk)sin(kl/2)4EIk3(EIkcos(kl/2)+Kθsin(kl/2))P=1KcpPwhere Kcp is the linear bending stiffness of the SMM bridge under the compressive residual stress and is expressed as follows:Kcp=4EIk3(EIkcos(kl/2)+Kθsin(kl/2))−4Kθ+(EIk2l+4Kθ)cos(kl/2)+(klKθ−2EIk)sin(kl/2)The linear bending stiffness, Kcp, is obtained experimentally. Then, the complex parameter, k, is only an unknown factor in Eq. , because the bending rigidity, EI, and the anchor stiffness, Kθ are already determined from Eq. is obtained in this study using MATHEMATICA, the commercial software popularly used in mathematical operations.Finally, the expression of the residual stress, σr is obtained through recall of Eqs. Note that the residual stress is easily achievable, because the right-hand side of Eq. consists of all known factors. There is more on the detail formulation process in ‘The governing equation of the SMM bridge under tensile residual stress is similar to Eq. where the axial force driven from the tensile residual stress is defined as positive and the definition of the complex parameter in Eq. Then, the vertical displacement satisfying the governing equation is expressed as follows:where A and B are constants that will be determined by the boundary conditions.After applying appropriate boundary conditions and the symmetry conditions at the center of the bridge, the displacement at the loading point, wP is expressed as follows:wP=4Kθ+(EIk2l−4Kθ)cosh(kl/2)+(klKθ−2EIk)sinh(kl/2)4EIk3(EIkcosh(kl/2)+Kθsinh(kl/2))P=1KtsPwhere Kts is the linear bending stiffness of the SMM bridge under the tensile residual stress and is expressed as follows:Kts=4EIk3(EIkcosh(kl/2)+Kθsinh(kl/2))4Kθ+(EIk2l−4Kθ)cosh(kl/2)+(klKθ−2EIk)sinh(kl/2), the complex parameter, k, is obtained from Eq. . Then, the tensile residual stress, σr is achieved using Eq. details the formulation process in this chapter.The present study conducts numerical simulation to validate the cantilever analytic model of Eq. . The displacements of SMM cantilevers are calculated from the present analytic model and are compared with the results from finite element analysis (FEA).The finite element model for the SMM cantilevers with the length of 30 μm is shown in (a) shows a cantilever incorporating the anchor geometry and (b) illustrates one with rigid boundary. Note that the present 2-D analysis gives results that differ from 3-D analysis less than 2%. FEA simulation is run under the environment of ANSYS version 6.1. shows the load–displacement relationship of the SMM cantilever resulting from the FEA and the present analytic model. It shows also the difference that comes from the effect of the anchor geometry. The geometry parameters and the material properties used in the analysis are obtained from the experiment. demonstrates that the solutions from the present analytic model agree well with those from the FEA solutions in the linear range, while they are different in the nonlinear rage. The deviation of FEA solutions in the nonlinear range comes from the geometrically nonlinear effect , meaning that the flexible anchors significantly affect the kinematics of SMM structures and should be treated as an important factor as long as SMM structures indispensably involve the anchor geometries.Finite element analysis is performed to verify the present analytic model for SMM bridges. The load–displacement relationships are calculated from the present analytic model and are compared with those from FEA. The effect of the anchor geometry of SMM bridge is discussed through the present simulation. Finally, the simulation results are used to explain how the residual stress changes the stiffness of SMM bridges. illustrates the finite element models used for the analysis of the MEMS bridge with the length of 90 μm. (b) with rigid boundary. The simulation strategy is similar to the way of the simulation of cantilevers excepting that in this case the half modeling is used in light of the symmetry condition.The load–displacement relationship of SMM bridge is characterized through the simulation. The results from the present analytic model are compared with those from finite element analysis. It is clear from the figures that the present analytic models gives results matching well in the linear region with the result from the FEA models. Graphical comparison apparently demonstrates that the finite anchor stiffness yields significant difference. In this case, the anchor's flexibility should be incorporated in order to achieve enough accuracy of the analytic model. The geometrically nonlinear effect becomes conspicuous in both figures as the displacement increases. The linear μ-bending method, therefore, negates it by obtaining the linear bending stiffness in the linear range.In the present study, the residual stress is obtained by measuring the bending stiffness of SMM bridge altered by the residual stress. Hence, it is important to characterize the residual stress effects on the bending stiffness of MEMS bridge. shows the bending stiffness of SMM bridge with the length of 90 μm. It is apparent in the figures that the residual stress in MEMS bridge leads to considerable change of the bending stiffness.In this study, experiments are performed to demonstrate that linear μ-bending method is reliable. proposes the entire procedure that is a general process of linear μ-bending method. The specimens of the cantilevers and the bridges in the present test are fabricated by the conventional surface-micromachining process using poly-silicon film. illustrates the overall fabrication process. After the cleaning process of a bare silicon wafer, 2 μm thick TEOS layer is deposited using PECVD process onto the wafer and the base of anchors are made after plasma etching. Then, poly-silicon film with 2.3 μm thickness, the target film in this test, is deposited through LPCVD process with the temperature of 625 °C. Rapid thermal annealing (RTA), the thermal treatment, is applied to the film so that its residual stress decreases. After the RTA, the beam geometry is formed on the ploy-silicon film by using deep reactive ion etching (DRIE). Finally, the TEOS layer is removed in buffered HF solution. In the present work, as listed in , six kinds of specimens are prepared. Each specimen is thermally treated under different RTA temperature so that each one has different residual stress. The RTA is performed for 1 min in nitrogen atmosphere. shows the SMM cantilevers and the SMM bridges fabricated from the above process.Among the prepared specimens, the SMM cantilevers go into the first bending test, resulting in the linear bending stiffness. Then, the bending rigidity, EI and the anchor stiffness, Kθ of the SMM cantilevers are determined using Eq. . If we assume that the axial force from the residual stress does not alter the anchor geometry of the bridges, the bending rigidity and the anchor stiffness obtained from the SMM cantilevers can be applied to the SMM bridges with the same sectional geometry. Such assumption can be reasonable if the anchor geometry is not so high. Next step is to measure the linear bending stiffness of the SMM bridge. Then, the obtained stiffness is compared with the reference stiffness, Kref that is the stiffness of stress-free SMM bridge with the same geometry. The comparison discovers the type of the residual stress in the SMM bridge – compressive residual stress or tensile residual stress. The reference stiffness of stress-free SMM bridge, Kref, is derived from removing the residual stress effect in Kcp and Kts as follows:Kref=limk→0Kcp=limk→0Kts=192EI(2EI+Kθl)(8EI+Kθl)l3Finally, the residual stress is obtained from Eq. after the complex parameter, k is calculated by Eq. . The type of the residual stress determines which class of the formulations is selected (Eqs. shows the load–displacement curves of the SMM cantilevers of ‘the specimen A’ that is deposited without annealing. lists the histories of the six specimens in this test. As observed in the plot, only linear relationship occurred during the test. The linear bending stiffness of the SMM cantilevers is equivalent to the slope of the straight load–displacement curves. shows the linear bending stiffness of the six specimens, the geometries of which are cantilevers with length of 20 and 30 μm. They have similar magnitudes because residual stress is unlikely to affect SMM cantilevers owning to the geometry with free end. The linear bending stiffness of the SMM cantilevers can, therefore, be assumed to be unaffected by the annealing process that tends to decreases the residual stress. The linear bending stiffness of the SMM cantilevers with length of 20 and 30 μm are obtained.The linear bending stiffness of SMM cantilevers are used as a measure to the bending rigidity and the anchor stiffness. lists the bending rigidity and the anchor stiffness for the six specimens of the SMM cantilevers, which result from substituting the linear bending stiffness into Eq. . It is observed in the table that there exists a slight difference in the bending rigidity and in the anchor stiffness among the six specimens. If we neglect the reasonable error during the test, the difference mainly comes from different cross-sectional shapes of the SMM cantilevers. shows the different cross-sectional shapes of the six specimens. This kind of non-rectangular different shapes of the cross-section appear to be inevitable as long as the DRIE process is involved. And, they account for the different bending rigidity and the anchor stiffness. One of the essence of the linear μ-bending method lies on the fact that the bending rigidity and the anchor stiffness are identified through the bending test for cantilevers.After the bending tests for the SMM bridges with length of 90 and 100 μm, their load–displacement curves are obtained and displayed in , respectively. The nonlinear deformations appear in the results, because bridges encounter the nonlinear range earlier than cantilevers with the same length do shows the linear bending stiffness calculated from the load–displacement curves shown in . The results clearly indicate that the linear bending stiffness of the SMM bridges is affected by the RTA temperature. This implies that the residual stress influences on the linear bending stiffness of the SMM bridges. It is observed that the higher the RTA temperature goes, the larger the linear bending stiffness becomes. This indicates that the RTA process reduces the compressive residual stress in the SMM bridges fabricated with poly-silicon.The residual stresses of the SMM bridges are evaluated by applying the linear bending stiffness in on the basis of the type of the residual stress. shows that the residual stress decreases as the RTA temperature increases. It is noteworthy in the figure that almost same residual stress is observed in the test specimen regardless of the length of the bridges. This supports the consistency and the reliability of the linear μ-bending method, because the residual stress must be independent of the geometry.Compared with the conventional nano-indentation method indicates that we could remove the possibility of the slipping on the reasonable base that the slipping is likely to cause large scattering of experimental results.Note that there is no indentation trace in (c), the SEM image around the loading place of the specimens. This implies that the linear μ-bending method does not involve the plastic deformation and the friction between the tip and the surface on the light of the small linear deformation.It is a great advantage of the linear μ-bending method that it incorporates the effects of the unknown elastic modulus and the various shape of the cross-section shown in . The linear μ-bending method deals with them in an experimental way by obtaining the bending rigidity and the anchor stiffness, while many previous researches use the reported value, conduct the tiresome FEA for every case, or just ignore them.It is found from the test results that the measured residual stress of the as-deposited poly-silicon SMM structures is compressive 142.70 MPa with the standard deviation of 3.5% and that the residual stress decreases as the annealing effect grows. compares the residual stresses obtained from the linear μ-bending method and the conventional disk-curvature method based on the Stoney's equation looks reasonable in that the disk-curvature method gives averaged residual stress over the wafer and assumes constant residual stress of the sacrificial layer, not incorporating the annealing effect of the sacrificial layer. reveals how the residual stress changes the linear bending stiffness of SMM bridges with the length of 90 and 100 μm. All the results from the analytic model, the finite element analysis, and the linear μ-bending test agree well.The linear μ-bending method is proposed to quantify the residual stress of the surface-micromachined MEMS. This method gives an entire process to measure the residual stress rather than the residual strain. The effects of the flexible anchor and the unknown parameter of the Young's modulus, quantified through the bending tests for surface-micromachined cantilevers, are incorporated in assessing the linear bending stiffness. The residual stress is obtained from the linear bending stiffness of surface-micromachined bridges. The linear μ-bending method avoids the nonlinear unknown phenomenon, such as the slipping and the plastic deformation by virtue of the linear deformation. Test for the poly-silicon film with 2.3 μm thickness demonstrates that the linear μ-bending method gives reliable results.Detailed solution process is presented for the surface-micromachined bridge with finite anchor stiffness. display the kinematical components used in this study. The contents are divided into two classes depending on the type of the residual stress; the compressive residual stress and the tensile residual stress. They have different signs in the governing equation, leading to the different form of the final solutions.The governing equation based on the free body diagram in (b) describes the moment equilibrium condition as follows:where E is the Young's modulus of micro bridge, I the second moment of inertia of the section defined as bt3/12, and Nx the axial force produced by the residual stress such as σrbt.The compressive residual stress is expressed with the following condition referring to the sign convention.For the convenience of the solution process, the virtual positive axial force is introduced as follows:For the convenience of the solving process, the complex parameter k is defined:After replace the axial force term with the complex parameter using Eq. Then, the solution satisfying the governing equation is assumed such as:The unknown coefficients A and B, and the unknown reactant moment at the anchor denoted by Mo are obtained using appropriate boundary conditions. At first, applying the zero-displacement condition at the boundary results in the following:The anchor stiffness is finite in the present analytic model; thus, the rotation at the boundary is not vanished. The boundary condition about the rotation at the anchor is expressed as follows:The rotation at the boundary is the product of the moment at the anchor divided by the anchor stiffness as follows:The symmetry conditions for the geometry, the boundary, and the loading constraints the rotation at the center of the beam to satisfy the symmetry condition as follows:, the reactant moment at the boundary is acquired and expressed as:Mo=Kθ(1−cos(kl/2))2k(EIkcos(kl/2)+Kθsin(kl/2))P, the displacement solution in the case of the compressive residual stress is as follows:w(x)=(Kθ−(Kθ+EIk2x)cos(kl/2)+Kθcos(k(l−2x)/2)−Kθcos(kx)−kKθxsin(kl/2)+EIksin(kx))2EIk3(EIkcos(kl/2)+Kθsin(kl/2))PBy applying l/2 instead of x, the displacement at the center of the MEMS bridge with finite anchor stiffness is obtained in the case of the compressive residual stress as follows:wP=−−4Kθ+(4Kθ+EIk2l)cos(kl/2)+(−2EIk+klKθ)sin(kl/2)4EIk3(EIkcos(kl/2)+Kθsin(kl/2))×PSolution process for case of the tensile residual stress follows similar way to the case of the compressive residual stress. The sign of the tensile residual stress is defined as negative, which results in the negative axial force as follows:The complex parameter k is defined for the positive axial force as follows:Substituting the complex parameter change the expression of the governing equation such as:The assumed displacement solution for the governing equation in Eq. The unknown coefficients A and B, and the unknown reactant moment at the anchor denoted by Mo are obtained using the boundary conditions.Applying the zero-displacement condition at the boundary results in the following:The boundary condition about the rotation at the anchor is expressed as follows:The rotation at the boundary θo is replaced with the moment at the boundary Mo divided by the anchor stiffness Kθ. Then the unknown coefficient can be expressed as follows:The symmetry of the model prohibits the rotation at the center of the bridge as follows:Substituting the expressions of the unknown coefficients into Eq. results in the following expression of the reactant moment.Mo=Kθ(cosh(kl/2)−1)2k(EIkcosh(kl/2)+Kθsinh(kl/2))PAfter substituting the expressions of A, B, and Mo into Eq. , the displacement solution in the case of the tensile residual stress is obtained as follows:w(x)=(Kθ+(−Kθ+EIk2x)cosh(kl/2)+Kθcosh(k(l−2x)/2)−Kθcosh(kx)+kKθxsinh(kl/2)−EIksinh(kx))2EIk3(EIkcosh(kl/2)+Kθsinh(kl/2))PBy substituting l/2 for x, the displacement at the center of the MEMS bridge with finite anchor stiffness is achieved in the case of the tensile residual stress as follows:wP=4Kθ+(−4Kθ+EIk2l)cosh(kl/2)+(−2EIk+klKθ)sinh(kl/2)4EIk3(EIkcosh(kl/2)+Kθsinh(kl/2))×PThe impact response of graded foam sandwich structuresLow velocity impact tests have been undertaken on sandwich structures based on cores fabricated by bonding foams of different densities together. Here, a range of linear PVC, crosslinked PVC and PEI foams were bonded together to produce a three layer core. Carbon fibre skins were then bonded to the core and the structures were loaded by a drop-weight impact carriage with a hemispherical head. It has been observed that the majority of the panels failed in a through-thickness shearing mode, leaving a clear cylindrical hole in the multi-layered core. A limited number of structures also exhibited cone cracking on the exit surface, due to failure in a mixed tensile/shear mode. The impact response of the graded sandwich structures was modelled by finite element analysis and the predicted load–displacement responses and failure modes compared. Agreement between the FE model and the experimental data was good across the range of structures investigated, with the model accurately predicting the impact responses and failure characteristics observed within the panels. It has also been shown that graded core structures can out-perform their monolithic counterparts. Finally when normalised by their unit cost, significant differences in the perforation resistances of the structures have been observed.Although a considerable of experimental work has been undertaken to study the impact and blast response of sandwich beams and panels, few attempts have been made to simulate the perforation behaviour of such structures under impact loading. Lin and Hoo Fatt A number of numerical studies have been undertaken to investigate the dynamic response of functionally-graded foam sandwich structures. Cui et al. Theoretical analyses and numerical modelling studies have also been undertaken on various functionally-graded sandwich structures subjected to static and dynamic loading. This includes continuously, piece-wise, layer-wise and exponentially functionally-graded cores This paper investigates the impact behaviour of graded/layered foam-based sandwich structures made with carbon fibre resin plastic (CFRP) face sheets and a range of PVC and PEI foam cores. The low velocity impact response of the sandwich panels is simulated using three dimensional non-linear finite element models to investigate the influence of core properties and configurations on the perforation resistance of the sandwich structures. Attention is given to identifying the fundamental parameters that govern the impact response of these layered structures.Core materials with varying through the thickness properties were manufactured by bonding three 10 mm thick foam sheets together using a fast-drying contact adhesive, as shown schematically in summarises the properties of the nine different foams investigated in this study. Four of the foams were based on crosslinked PVC foams with densities between 60 and 200 kg/m3. The three linear PVC foams had densities between 60 and 140 kg/m3 and the two PEI foams offered densities of 60 and 80 kg/m3. summarises the stacking sequences of the twelve configurations investigated here, in which the average core density varied from approximately 77 kg/m3 to 113 kg/m3. It should be noted that six of the twelve configurations were obtained by inverting the original stacking sequence, for example Core C2 was simply Core C1 turned upside down. Mode I (opening) and Mode II (shearing) tests on the foams were also conducted to determine the corresponding work of fracture energies, as shown in , to be used in the finite element modelling.Prior to testing, carbon fibre reinforced epoxy (CFRE) skins were bonded to the cores using a two-part epoxy resin. The 0.35 mm thick skins were manufactured by curing two woven CFRE plies (EP121 C15-53 from Gurit Ltd.) in a hot press at 125 °C for 1 h.Impact testing was conducted on 200 mm square panels using a drop-weight impact tower. The panels were placed on a cylindrical support with an internal diameter of 100 mm. The panels were impacted at their centres by a carriage with a 10 mm diameter hemispherical head. The mass of the impactor was 5.56 kg and the release height of the impact carriage was increased up to a maximum of 1.4 m. The displacement and impact force were recorded using a high-speed video camera and a piezoelectric load-cell respectively. The impacted panels were sectioned through the damaged region, ground, polished and photographed in order to highlight the failure mechanisms occurring during the impact process.Finite element models were developed to simulate the dynamic behaviour of the graded foam sandwich panels subjected to low velocity impact loading. The following section discusses the modelling-approach adapted for the various components of the sandwich structures.Prior to damage initiation, the CFRP face sheets were modelled as an orthotropic elastic material. The elastic modulus values of the plain weave skins were assumed to be equal in the longitudinal and transverse directions. Damage initiation was modelled using Hashin’s failure criteria The damage elastic matrix, which relates the stress and strain and controls degradation of the material stiffness, can be expressed as:CD=1D(1-df)/E1(1-df)(1-dm)v12/E20(1-df)(1-dm)v21/E1(1-dm)/E2000(1-ds)GDwhere G is the shear modulus and D is an overall damage variable, dependent upon the current state of fibre (df), matrix (dm) and shear (ds) damage, respectively.Damage evolution was characterised by the negative slope of the equivalent stress–displacement relation after damage initiation had occurred. The fracture energies for the fibre tension GftF, fibre compression GfcF, matrix tension GmtF and matrix compression GmcF failure modes were introduced to determine the energy dissipated during damage development. shows the related material parameters that were used.A crushable foam model was employed to predict the response of the PVC foam core. The properties of the foams are listed in . A phenomenological yield surface for a closed-cell foam material is given by where q is the Von Mises stress, σm is the mean stress, and σy is the uniaxial yield strength (in tension or compression) of the foam. The term α describes the shape of the yield surface, which is related to the ratios of the initial uniaxial yield stress σco and the hydrostatic tensile yield stress pt to the hydrostatic compressive yield stress pco, respectively.The yield stress in hydrostatic compression, pc describes the evolution of the size of the yield surface and is given as:pcεplvol=σcεplvolσcεplvol1α2+19+pt3pt+σcεplvol3where εplvol is defined as the plastic volumetric strain in the volumetric hardening model, which is equal to the compressive plastic strain εplaxial. A compression test on the foam was undertaken to deterime the term, pc. For a rate-dependent material, the strain-rate follows the uniaxial flow rate, which is the strain-hardening function of the equivalent stress q, the equivalent plastic strain ε¯pl, and the temperature parameter θ.The rate-dependent hardening curve is expressed as:in which Rσ and ε¯̇pl are defined as the stress ratio (σ¯/σy) and the equivalent plastic strain-rate respectively.Damage initiation in the PVC foams was modelled using a ductile damage criterion as well as a shear damage criterion A hyperelastic model was employed to account for the elastic response of the large recoverable deformations that occurred during the impact event. This was achieved by introducing a partition beyond the central 40 mm region of the panel. The strain energy potential, defined as the strain energy stored in the material per unit reference volume (i.e., the volume in the initial configuration), was specified as a function of strain at a given point in the hyperelastic model.A tension failure criterion was specified in the lower half of the central region of the panel to model the cone-shaped failure mode observed experimentally. This type of failure was associated with tension–shear loading conditions, and is frequently observed in brittle cores with higher densities.The tensile failure criterion assumes that tensile failure occurs when the pressure stress, p, becomes more tensile than the specified hydrostatic cut-off stress, σcutoff, it can be expressed as,A fully-clamped sandwich panel, based on three layered foam cores, was modelled using ABAQUS/Explicit. The geometry as well as the boundary and loading conditions for the sandwich panel are shown in . One half of the panel was modelled since the panel was symmetric. A rigid cylindrical projectile, with a mass of 5.56 kg, was employed. The initial projectile velocity was set to that based on the perforation energy obtained from the experimental tests. The skin and foam were meshed using continuum shell elements (SC8R) and eight-noded reduced integration solid elements (C3D8R) respectively. A mesh sensitivity analysis was conducted by varying the mesh density within the plane and through the thickness.Low velocity impact tests were undertaken on the twelve core configurations outlined in a shows a typical load–displacement trace for a sandwich panel based on the C100/P80/P60 foam combination. An examination of the figure indicates that the force initially increased up to approximately 500 N at which point it reaches a plateau. The force then remains roughly constant as the projectile perforates the three foam materials, suggesting that the fracture properties of the three foams are similar. Finally, the force begins to increase rapidly as the projectile approaches the rear surface of the target. Here, it is likely that the lowermost foam is crushed between the steel impactor and the rear surface skin. Clearly, the peak force associated with fracture of the rear skin is significantly higher (by a factor of approximately three) than that needed to cause failure in the top skin. Finally, the force drops rapidly at a displacement of 36 mm as the projectile fully perforates the lower skin and passes through the composite. a also includes the load–displacement trace predicted by the finite element model. From a comparison of the experimental and predicted curves it is clear that the model captures all of the major features of the experimental trace, including the pronounced second peak associated with the crushing of the core against the distal skin. b shows cross-sections of the fully perforated sandwich structures, where the presence of a distinct cylindrically-shaped shear zone is evident in both the test specimen and the model.c shows the measured and predicted load–displacement traces for the equivalent inverted structure, i.e. the P60/P80/C100 core configuration. An examination of the figure suggests that there are many similarities with its counterpart in a. Closer inspection highlights the presence of the three cores, with the plateau loads increasing from approximately 250 to 400 to 600 N as the projectile passes through the three foams. The experimental trace also exhibits a more pronounced initial peak and a larger exit peak. The corresponding cross-sections are shown in d, where a cylindrically-shaped perforation zone is again present. Closer inspection of the lowermost foam highlights the presence of a frustrum-shaped zone similar to that observed following impact tests on plain foams a shows the experimental and numerical load–displacement traces for the L80/C60/C200 sandwich structure. The experimental trace exhibits a number of distinct regions as the projectile passes through the various components of the sandwich panel. The initial portion of the trace is linear up to approximately 850 N, at which point the top surface skin fractures and the load drops. The force then oscillates around a value of approximately 750 N, as the projectile passes through the tough L80 foam. The force then reduces as the impactor passes through the more brittle crosslinked foam (C60) before increasing rapidly as it encounters the C200 foam. The final stage of the load–displacement trace exhibits a region in which the force oscillates as the C200 foam is crushed and densifies under the constraint applied by the rear surface skin. b shows that the perforation zone is again cylindrically-shaped, although a small cone crack is in evidence at the exit surface. The load–displacement traces for the corresponding inverted sandwich structure are shown in c. Here, the different fracture responses of the three foams are apparent, with the uppermost, high density C200 foam offering the greatest resistance to perforation and the more brittle C60 system exhibiting the lowest. It is also interesting to note that the force associated with fracturing the lowest skin is less than that apparent in a, due to the lower densification characteristics of the L80 foam. The resulting cross-section from the test, d, highlights the presence of a crack in the uppermost C200 foam that appears to have influenced the subsequent failure locus in the remainder of the structure. This mixed form of failure has been partly captured by the FE model.a shows the force–displacement traces for the L60/P60/L140 sandwich structure. Clearly, there are similarities between this response and that shown in a, with the perforation force increasing in three steps between the peaks associated with fracturing the upper and lower skins. The plateau force resulting from fracturing the tough L140 foam is significantly higher than that required to perforate its lower density L60 counterpart. Finally, the load–displacement response of its inverted counterpart is shown in c. Once again, agreement between the experimental data and the model is very good, suggesting that the FE analysis is capable of capturing the fundamental response of these multi-layered structures.The energy required to perforate the sandwich structures was calculated by determining the area under the load–displacement traces. compares the perforation resistances of the twelve configurations investigated here. From the figure, it is clear that the FE model generally predicts the energy required to perforate the laminates with a high degree of accuracy, with the greatest error being approximately 14%. From the figure, it is clear that the perforation energy varies quite significantly, with the experimental values passing from 21.9 J for the C100/L60/C80 sandwich to 40.8 J for the C200/P60/P80 configuration. If the perforation energy of the layered target is assessed in terms of the average density of the core, the perforation resistance tends to increase with core density. Within each density grouping of structures, there are distinct variations that depend on the specific arrangement of the layers. This is most evident in Panels C9 (P80/P60/C200) and C10 (C200/P60/P80) in which the former has the high density C200 core at the top surface and latter at the rear surface. Placing the higher density and tougher foam uppermost resulted in a 30% increase in the perforation resistance. An examination of the cross-sections of Structure C9 highlighted the presence of a distinct cone-shaped crack in the lower C200 foam. This can be explained from the fact that this form of failure is associated with a mixed mode of loading (Mode I/Mode II) and also the fact that the Mode I work of fracture is much lower than its Mode II value (). Clearly samples that fail in a mixed-mode of failure, such as panel C9, are therefore more likely to offer a lower resistance.Given that the densities of the graded foam cores do vary quite significantly, the perforation energy of the various targets were normalised by the average core density to yield the specific perforation values and these are presented in . When the data are normalised in this way, the previously-observed differences between the foams reduce, although the C200/P60/P80 system still offers the highest performance. The difference between the best-performing and the worst-performing configurations is reduced to 25%. shows a plot of the perforation energy versus average target density, highlighting the benefit of placing the highest density foam on the top surface. An examination of the figure indicates that those laminates in which the highest density foam is placed uppermost tend to out-perform equivalent systems in which the higher density foam is placed against the rear surface skin. The figure also suggests that this enhancement tends to increase with increasing average foam density. Secondary benefits were also observed, such as placing the lowest density foam in the centre of the core and also placing a tough foam against the rear surface of the structure.In the next stage of this investigation, the perforation resistances of the various graded foam cores were compared with those of similar sandwich structures based on one single type of core, for example a C200/C200/C200 construction. Here, the perforation resistances of these “plain” core materials were predicted using the FE model, since previous work has shown that the perforation resistance of plain sandwich panels can be accurately predicted using this approach . The figure indicates that the graded foam core sandwich structures offer a superior perforation resistance to the equivalent monolithic cores.Although performance is a key criterion in selecting a particular core for a given sandwich structure, cost is also an important parameter in the design process. Here, a cost factor was determined by normalising the cost of each foam by the cost of the most expensive foam tested here (this was the P80 foam) and then by multiplying this value by 100. The relative performance of each graded foam was then compared on a cost basis by dividing the perforation energy values by the cost factor, and these results are presented in . An examination of the figure indicates that the perforation energy/cost ratio varies significantly across the range of structures considered. Of particular interest is Structure C5, based largely on low density foams. The performance of this sandwich structure out-performs Structures C1 and C2 by a factor of approximately four.The low velocity impact response of sandwich structures based on layered cores has been studied both experimentally and numerically. Failure in the majority of the sandwich structures occurred as a result of core shear, with the FE model accurately predicting this mode of failure. The numerical model also predicted the associated load–displacement traces and the corresponding perforation energies with a high degree of accuracy.It has also been shown that graded structures can out-perform their monolithic counterparts in terms of their perforation resistance. It has been shown that placing the high density foam core against the top surface skin can lead to an improved perforation resistance relative to sandwich panels in which the higher density foam is in contact with the distal surface. Secondary benefits associated with placing the lowest density foam in the centre of the core and a ductile foam against the lower surface have also been observed. Finally, when the unit cost of the various foams is considered, significant differences are observed between the various sandwich configurations.Industrially fabricated in-situ Al-AlN metal matrix composites (part A): Processing, thermal stability, and microstructureThis study introduces in-situ aluminum (Al)-aluminum nitride (AlN) metal matrix composites (MMCs) manufactured by a powder metallurgy (PM) cost-effective approach realized at a large industrial scale. The Al-AlN MMCs were targeted for structural load-bearing applications with an expected service at elevated temperatures not normally associated with a use of conventional Al-based alloys and MMCs. Commercial Al, magnesium, and tin powders were processed by readily available PM techniques of blending, cold isostatic pressing (CIP), a solid-state nitridation in a static gaseous nitrogen, and a hot direct extrusion. Two sound voids free Al + 8.8 and 14.7 vol% AlN MMCs were reproducibly fabricated in a form of the long extruded bars with the cross-section of 80 × 15 mm. The microstructure of nitrided and extruded MMCs was presented in details. A typical yolk-shell-like microstructure of Al metallic core and nitrided layer was formed homogenously in a volume of the CIP bulky (~25 kg) billets upon nitridation. The microstructure of extruded Al-AlN MMCs consisted of Al grains elongated into the extrusion direction. The Al grain structure was embedded with the evenly distributed micrometric regions formed by a high density AlN nanocrystals in Al matrix. A stability of the tensile mechanical properties of as-extruded Al-AlN MMCs was pursued in transversal and longitudinal directions after the annealings performed at 300–600 °C for 24 h. Owing to an effective stabilization by the stable and fine AlN dispersoids by Zener pinning action no major changes to the mechanical properties took place after annealing up to 500 °C.Aluminum nitride (AlN) features an appealing combination of materials properties, such as a good thermal conductivity (λ = up to 210 and 285 W m−1 K−1 for polycrystalline and single crystal materials, respectively), low coefficient of thermal expansion (CTE = 4.5 10−6 K−1 in the 20–400 °C range), relatively high electric resistance (109–1011 Ω m), low specific weight (ρ = 3.026 g cm−3), high Young's modulus (E = 348 GPa), high compressive strength (2700 MPa) and hardness (12.6 GPa), good thermal stability (up to 2000 K), and good corrosion and thermal shock resistance, in addition to having an ability to absorb a high level of energy From a processing point of view, AlN is better wetted by molten Al when compared to other typical reinforcements in an Al matrix e.g., aluminum oxide (Al2O3). At the same time AlN does not react with molten Al. Thus, problems related to interfacial reactions and inferior interfaces, often present with e.g., Al-silicon carbide (SiC) and Al-Al2O3 MMCs, are circumvented in this way. Numerous ex-situ technological approaches, which utilized discrete AlN particulates, were presented in order to fabricate various types of Al–AlN MMCs In contrast to ex-situ Al–AlN MMCs, in-situ approaches enable more economical and effective fabrication of Al-AlN composite structures with favorable clean interfaces and a fine-nature AlN phase evenly dispersed in the Al matrix, resulting in better mechanical and physical properties. In-situ methods of production of Al-AlN composite structures include diverse techniques. They can be generally divided into those realized in: i) liquid state e.g., nitrogen gas (N2) injection into an Al melt, reactive thermal plasma spraying of Al powders in N2, etc. In the present study (part A) we introduce sound Al + (0–15 vol%) AlN MMCs manufactured at a cost-effective large industrial scale for the first time. In this approach, an Al + 2 wt% Mg + 1 wt% Sn powder blend was at first cold compacted by cold isostatic pressing (CIP) into permeable powder billets (). In the next step a billet was partially nitrided below the melting point of Al in static N2 continuously fed to a chamber at the atmospheric pressure. The nitrided billet was subsequently consolidated by hot direct extrusion (DE) into a composite rod. All feedstock powders and techniques utilized in this study are readily available at the market and in the industry. The microstructure of nitrided and extruded Al-AlN MMCs is presented. This study discusses the thermal stability of the extruded Al-AlN MMCs as reflected in changes to their tensile mechanical properties induced by annealing at 300–600 °C. An ensuing separate study (part B) will report in detail on the mechanical and thermal properties, and creep performance of extruded Al-AlN MMCs that were determined between 22 and 500 °C Al (Kerametal as.), Mg (IMR Metal Powder Technologies GmbH), and Sn (Kovohuty sro.) powders were used for this study (see their properties in ). Their particle size distributions were determined using a laser diffraction system by wet dispersion (Fritsch Analysette 22 MicroTec device). The specific surface area of the powders was determined in accord with the Brunauer-Emmett-Teller (BET) principle following the ISO 9277 standard. The oxygen (O) content of the powders was determined by hot gas fusion analysis (GFA; Bruker G8 Galileo OHN device). Other impurities, apart of O, were determined by inductively coupled plasma mass spectrometry (ICP; PerkinElmer Avio 500 device).An Al + 2 wt% Mg + 1 wt% Sn powder mixture was homogenized in a plough-shear blender (Lodige machine) for 30 min in the air. The Al + Mg + Sn mixture was then pre-pressed by a wet bag method of CIP at 15 MPa (EPSI machine). As the control material, a plain Al powder was CIP for comparison. Porous CIP powder billets had a diameter of ~175 mm and length of ~500 mm, and the weight of each billet was ~28 kg (a). A single Al + Mg + Sn powder billet was inserted into the resistance heating furnace, although the furnace was designed for batch nitridation of six powder billets of the given dimensions at the same time. The furnace chamber with the billet in was evacuated, and the chamber pressure was stabilized at 5 Pa after 1 h. After reaching 5 Pa, the billet was heated at a constant heating rate of 6 °C min−1 to 450 °C. Humidity that was physically and chemically adsorbed on the surface of the Al powder was decomposed and degassed during this stage. The temperature of the billet was monitored by two K-type thermocouples placed 3 cm under the surface. Once the temperature of the billet reached 450 °C the N2 (99.99 wt%) gas was filled into the chamber and heating continued under an N2 atmosphere until the temperature reached the nitridation temperature of 590 °C. After reaching 590 °C heating proceeded at the nitridation temperature and an actual consumption of N2 gas was monitored by a thermal mass flow meter (Bronkhorst EL-FLOW Prestige FG-111B machine) with a±0.5 g precision. The pressure of N2 gas in the furnace was maintained at the atmospheric pressure throughout entire nitridation process. Once the N2 gas consumption reached the targeted value, which corresponded with AlN formation at the surface of the powder particles, the heating was stopped and the inlet of N2 gas closed. Remaining N2 present in the chamber was evacuated. The formation of AlN was confirmed by calculation from the billet weight gain before and after nitridation. In this way Al composite powder billets with an AlN content of 10 and 16.6 vol% were produced. The nitridation period needed for reaching the 10 and 16 vol% of AlN was ~180 and 240 min, respectively (c). The temperature of the extruder container and matrix was set to 500 and 550 °C, respectively. The ram speed during extrusion was set to ~25 mm s−1 and the pressure on the plunger was monitored during pressing. After extrusion the bars cooled down spontaneously in the air and then cold stretched. The extruded bars with a 0, 10, and 16.6 vol% of AlN were labeled as Al0, Al10AlN, and Al16AlN, respectively. As-extruded Al0, Al10AlN, and Al16AlN were sectioned into smaller pieces and annealed at a temperature of 300, 400, 500, and 600 °C under an Ar atmosphere for 24 h.Densities of the extruded materials were determined by Archimedes' principle. Microstructure of the CIP, nitrided, and extruded materials was examined using a scanning electron microscope (SEM, JEOL 7600F) equipped with an energy dispersive X-ray spectrometer (EDS, Oxford Instruments X-Max, 50 mm2) and an electron back-scattering diffraction system (EBSD, HKL technology Nordlys II detector). The N and O content of the extruded materials was determined by GFA. The structure was studied by X-ray diffraction (XRD) using a D8 Advance (Bruker AXS) diffractometer (Cu Kα) in a parallel beam configuration. A Goebel mirror was installed in the incident beam and a 0.23 deg Soller slit and LiF monochromator in the diffracted beam path. The measurement was performed under a constant incidence angle of 10°.Direct microstructural investigations were performed with a probe-corrected FEI/Thermofisher Scientific Titan Themis 300 transmission electron microscope in scanning mode (STEM) at a 200 kV accelerating voltage equipped with an EDS system (Super-X). The probe convergence angle was set to 17.5 mrad for imaging applications; the corresponding probe current was measured to be ~70 pA. EDS spectrum images were acquired by serially scanning across a defined area of the specimen and recording cumulative EDS spectra at each position. EDS chemical maps were produced by integrating the background corrected and fit intensity of the Al Kα, N Kα, Mg Kα and Sn Lα absorption peaks. Scanning micrographs were acquired simultaneously by 3 detectors, namely a high angle annular dark field (HAADF), collection angle 101–200 mrad, annular dark field detector (ADF), a collection angle 24–95 mrad and an annular bright field detector (ABF) with a collection angle set to 13–20 mrad. Investigated samples were ion milled to electron transparency using a precision ion mill (Gatan 691) with LN2 cooling. The final milling stage was done at an accelerating voltage of 1 kV.Mechanical testing was performed with as-extruded and annealed Al0, Al10AlN, and Al16AlN MMCs, both in the longitudinal (L) and transversal (T) directions with respect to the direction of extrusion. Tensile dog bone-shaped specimens had a gauge diameter of 6 mm and a length of 30 mm. Tensile tests were performed using a Zwick Roell 1474 machine at the strain rates of 2.5·10−4 (in the elastic region) and 2·10−3 s−1 (in the plastic region) in accordance with the ASTM E8 standard. The tensile tests were performed at room temperature (RT).Homogeneity of AlN formation in the volume of a CIP Al + Mg + Sn powder billet is crucial as it directly affects the reproducibility of properties across the length and cross-section of a subsequently extruded Al-AlN MMC profile. For this reason, the pressure during CIP of the Al + Mg + Sn powder blend was set to a minimum value of 20 MPa. This assured that the porous precursor with a residual porosity of 30.8 ± 1.6% remained sufficiently permeable. At the same time, the ~28 kg heavy CIP billet reached sufficient strength to endure manipulation and heating operations during processing. The formation of AlN in an N2 atmosphere is preferential to that of Al2O3 only if the partial pressure of oxygen is extremely low ). The thickness of the nitrided layer increased with nitridation duration. It was concluded from SEM micrographs that the average thickness of the nitrided layer was ~2 and ~2.5 µm for the billets with 10 and 16.6 vol% AlN, respectively. It is worth to note that the residual porosity decreased slightly upon the nitridation process. The billets with 10 and 16.6 vol% AlN had a residual porosity of 28.4 ± 1.2 and 27.7 ± 0.6%, respectively. Moreover, a rattle-like microstructure was observed often with voids formed between the nitrided layers and Al metallic cores (Figs. ). This suggests that the nitrided layers grew both inwards and outwards from the surface of the original Al particles, which is in line with previous findings XRD patterns of the CIP Al, and nitrided Al + Mg + Sn powder billets revealed three distinctive phases: Al, AlN and Mg2Sn (). The intensity of the AlN peaks increased with nitridation time while the intensity of the Mg2Sn peaks was rather independent of the AlN content. The presence of fine Mg2Sn intermetallics can also be seen in the EDS maps (). Moreover, the EDS maps pointed out to the traces of iron (Fe) and silicon (Si)-based intermetallics, which could not be detected by XRD and stemmed from major Fe and Si impurities in the as-atomized Al powder ( presents a characteristic cross-sectional STEM image with the representative EDS elemental maps of two adjacent nitrided layers. It is apparent that the nitrided layers consist of two distinctive regions (see the labels in the Al element EDS map in ). In the vicinity of the Al powder core a nitrided shell was formed by a thin inner layer region with a thickness of ~ 80 nm. The inner layer, which was highly enriched with Mg and Sn, consisted of nanoscale AlN crystals with the size of ~10 nm (). Mg atoms decorated the boundaries of those AlN crystals, as it is visible in the Mg elemental EDS map (). Similarly, Sn atoms were found located at the AlN grain boundaries, as is demonstrated by distinct bright areas in the HAADF micrograph (b) and further confirmed by EDS mapping (). The Mg and Sn layers could not be detected by XRD because of their fine nature and thickness of only a few atoms. By contrast, in the outer layer, coarser AlN crystals grew in the form of dendrites in perpendicular directions to the Al core. Unlike the AlN nanocrystals located in the inner layer, the AlN dendrites in the outer layer were embedded within the Al matrix (a). It is in accord with the previous findings ) revealed Mg being incorporated throughout the structure of the nitrided powders i.e., inside the Al core interiors and in the nitrided layers. This was not the case of Sn, which is not soluble in Al, and therefore it was found only in Mg2Sn particles and at AlN crystals in the inner nitridation layer (). Moreover, a detailed microstructural investigation in the present study revealed that the Al matrix found in the outer layer shared the Al lattice orientation with the Al grain core substrate (not shown). This might be rationalized by the epitaxial growth of the outer nitrided layer via the outward-oriented diffusion of Al atoms.It was confirmed earlier that as Sn becomes consumed during nitridation a double layered structure was formed . This was determined for both nitrided powder billets with 10 and 16.6 vol% AlN. However, the present study suggests that a 2 wt% addition of Sn inhibitor was sufficient for the formation of at least 16.6 vol% AlN at a steady, well-controlled rate evenly within the bulky powder billet. Thus, it is evident that the well-controlled nitridation procedure resulted in the formation of similar double-layered nitrided structure as well.Thermal stability of the as-extruded Al-AlN MMCs was studied, as they are intended for applications at elevated temperatures. It was pursued by following changes in their tensile properties induced by annealing at temperatures between 300 and 600 °C during 24 h treatment. show the ultimate tensile strength (UTS), 0.2% strain offset yield stress (YS0.2), and elongation (ε) determined at RT for the as-extruded and annealed Al0, Al10AlN, and Al16AlN measured in the L and T directions. Please note that the annealing temperature of 22 °C represents the as-extruded condition in for the particular stress-strain curves. When compared to the as-extruded state, no major changes to the mechanical properties of both Al-AlN MMCs occurred due to annealing at 300, 400 and 500 °C. The Al-AlN MMCs that were annealed at 600 °C experienced a minor, ~10% decrease in UTS and YS0.2 in both directions. Hence, with respect to potential uses of the Al-AlN MMCs, investigations in this study were limited to operational temperatures up to 500 °C Noticeably, the scatter of measured UTS, YS0.2 and ε values tended to be the smallest for the Al-AlN MMCs annealed at 500 °C. Consequently, the microstructure and properties of only Al-AlN MMCs annealed at 500 °C for 24 h are presented and discussed in the next chapters. It is worth pointing out that the limiting temperature of 500 °C of the UFG Al-AlN MMCs in this study is far above of the recrystallization temperature of conventional wrought and cast Al and Al alloys, which is normally considered to be at a ~ 0.4–0.5 of the melting point. Thus 500 °C is far above the temperature normally associated with the use of conventional Al-based materials and MMCs. compares the YS0.2 values of the wrought commercial purity Al in severely cold worked full-hard condition (A1100 H18) and hot extruded heat resistant Al-Cu-Mg alloy after solution heat treatment and artificial ageing (A2024 T6) determined at RT after annealing for 10 h with the ones obtained for the materials in this study ). This was in line with our previous findings which confirmed a superior stabilizing effect of nanoscale in-situ γ- and δ-Al2O3 dispersoids, c). It should be mentioned that the maximum breakthrough pressure monitored at the plunger during DE of all powdered billets was less than ~550 MPa. This is a reasonable value within the normal pressure capacity of majority conventional industrial DE presses. The residual porosity of the nitrided billets was reduced down to 0.1%, 0.5% and 1.1% for Al0, Al10AlN and Al16AlN, respectively ( shows the XRD patterns of Al0, Al10AlN, and Al16AlN annealed at 500 °C. Following the XRD results of the CIP and nitrided billets, only three distinct phases, namely Al, AlN and Mg2Sn, were detected in the extruded Al0 and Al-AlN MMCs. The intensity of the AlN peaks similarly increased with a higher AlN content. The only slight difference between the XRD patterns of the nitrided billets and extruded MMCs was a change in the intensity of the first two shown peaks of Mg2Sn, The reason behind that is unclear, but it could be assumed that absorption effects were most probably involved. Owing to a fine nature and a low content, no Al2O3 phase was confirmed by XRD in Al0 (). DE induced a rather minor shearing and elongation of Al powder particles decorated with the nitrided layers (a). From a macroscopic perspective, the structure of the MMCs consisted of Al grains elongated along the extrusion direction with embedded cloud-like areas rich in N element, which were evenly dispersed in the Al matrix (b). The micro-sized cloud-like areas consisted of an Al matrix with a high content of embedded AlN nanocrystal aggregates (). It was apparent that the nitrided layers on Al powders fractured and were partially redistributed into the Al matrix during plastic shear hot deformation. The AlN dendrites, which originated from the outer nitridation layers, disintegrated from each other and some of them got smeared towards the Al matrix (). It was observed that the AlN crystals of the dendrite structure were fractured and separated from each other, as is shown in . Nevertheless, a majority of the AlN crystals still existed dominantly within the cloud-like areas. The results on the N content by GFA analysis yielded slightly lower values when compared to those obtained by the measurement of the consumed N2 gas during nitridation and weight gain (). The average AlN contents calculated from GFA resulted in 8.81 and 14.7 vol% for Al10AlN and Al16AlN, respectively.An average Al grain size in T direction of 1.9 µm was confirmed for AlN free Al0 annealed at 500 °C by EBSD. The Al grains in Al0 were elongated and oriented into the dominant< 111 >direction, as was indicated by the main group of 111 spots corresponding to the texture axis parallel to the extrusion axis (a). A small amount of LAGB was confirmed in the annealed Al grain structure of Al0 (a). EDS map of O element illustrates the position of Al2O3 dispersoids at Al HAGB, which originated from the passivation layers on the as-atomized Al powder (b). The determination of Al grain size was rather complicated for Al-AlN MMCs because of the nature of AlN agglomerates located at Al GB. Nevertheless, a similar average Al grain size in the T direction of 1.8 µm, which was slightly lower than of the one found for Al0, was determined for both Al10AlN and Al16AlN MMCs. The mobile dislocations annihilated in Al grain interiors of Al0 and Al-AlN MMCs because of prolonged exposures during nitridation and annealing operations held at the high homologous temperatures of 0.93 and 0.77 Almost no low angle grain boundaries (LAGB) i.e., subgrains, were present in the Al grain structure of both MMCs (a). The EBSD map revealed only a minor flow of patterns in the T direction which the Al grains were aligned into. The pole figures confirmed rather stochastic local vortex flow lines with no major dominant orientation, nor texture (Superior stability of the mechanical properties of the Al0 and Al-AlN MMCs after annealing treatment up to 500 °C was attributed to the Al grain structure stabilized by Al2O3 and AlN dispersoids, respectively. The stable and fine Al2O3 and AlN dispersoids effectively stabilized the Al grain structure by Zener pinning action. The kinetic stabilization approach via nanoscale second phases was shown to be the most effective for UFG and nanoscale structures at the highest homologous temperatures Assuming migrating GBs anchored by the AlN dispersoids present within the cloud-like regions with an estimated 50 vol% population and estimated AlN dispersoids size ~500 nm, the dZ for the Al-AlN MMCs equals to ~170 nm. It is much smaller value than the Al grain size determined in the T direction, which supports the findings on the effective stabilization of HAGBs by a network of the AlN clouds.Al-AlN MMCs were manufactured using a cost-effective approach at a large industrial scale for the first time. In this approach commercially available Al, Mg, and Sn powders were processed by readily available PM techniques of blending, CIP, gaseous nitridation, and DE to produce Al + 8.8 and 14.7 vol% AlN MMCs extruded bars. The microstructure of the nitrided and extruded Al-AlN MMCs, and stability of their tensile mechanical properties were studied after annealing realized at 300–600 °C for 24 h. The following conclusions were made:Solid state nitridation of the permeable billets with a weight of ~28 kg pressed by CIP of an Al + 2 wt% Mg + 1 wt% Sn powder blend in static N2 and at the atmospheric pressure led to a homogenous formation of the AlN component in the entire volume of the billets.By monitoring the actual consumption of N2 gas during the nitridation process, the content of formed AlN was varied by nitridation duration.A typical yolk-shell-like microstructure of an Al metallic core and nitrided layer formed upon nitridation, and the nitrided layers grew in thickness as nitridation duration increased.The nitrided layers consisted of two distinctive regions. The inner layer region was ~80 nm thick and consisted of nanoscale AlN crystals with a size of ~10 nm. The crystals were decorated with Mg and Sn elements. The outer layer was thicker and consisted of AlN dendrites that were embedded in the Al matrix and grew in directions perpendicular to the Al core.DE fully consolidated the nitrided billets into sound extruded profiles with a low residual porosity.The microstructure of the extruded Al-AlN MMCs consisted of Al grains embedded with evenly dispersed AlN-rich agglomerate areas at HAGB. Shear deformation induced during DE accommodated the fracture of the AlN dendrites and disintegration of the AlN nanocrystals within the agglomerate areas. The traces of Mg2Sn intermetallics were found located in the Al matrix.The Al grain structure with the minor flow patterns aligned with the extrusion direction was virtually free of LAGB. The average transversal Al grain size was ~1.8 µm.The stable and fine AlN dispersoids effectively stabilized the Al grain structure by Zener pinning action. This led to a superior thermal stability, and no major changes to the tensile mechanical properties of the as-extruded Al-AlN MMCs were observed in samples annealed up to 500 °C for 24 h.Martin Balog: Conceptualization, Methodology, Writing - original draft, Writing - review & editing, Project administration, Funding acquisition. Peter Krizik: Methodology, Investigation. Peter Svec: Investigation. Lubomir Orovcik: Investigation.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Supplementary data associated with this article can be found in the online version at Effect of welan gum and nanoclay on thixotropy of UHPCThis study evaluates the effect of welan gum (WG) and nanoclay (NC) on thixotropy of ultra-high-performance concrete (UHPC) matrix made with 0.20 water-to-binder ratio. The mortar mixtures were proportioned with a fixed superplasticizer (SP) content and WG and NC contents varying between 0 and 0.09% and 0 and 0.4%, respectively. The dynamic yield stress of these mixtures varied from 40 to 170 Pa. Similarly, UHPC made with different WG and NC contents were prepared with variable SP dosages to maintain initial mini-slump flow of 200 ± 5 mm. Test results indicate that thixotropy can be enhanced by using WG or NC in UHPC with a fixed SP dosage. On the other hand, for UHPC made with variable SP, the incorporation of WG increased thixotropy, whereas the use of NC had limited contribution to thixotropy. Particle flocculation was correlated to the water film thickness (WFT) onto solid particles in UHPC. The rapid increase in static yield stress immediately after mixing (τfloc) showed a linear growth with the decrease of WFT due to enhancement of particle flocculation. A qualitative approach relating particle flocculation and bridging effect of nucleation of early-age hydration products was proposed to describe the rate of linear increase in static yield stress with rest time (Athix). The model yielded good prediction for UHPC prepared with NC, which was not the case for mixtures made with WG where other factors, such as polymer entanglement and association, can play a major role in controlling thixotropy.Ultra-high performance concrete (UHPC) is a promising cementitious composite that can deliver high flowability, high mechanical performance, and superior durability []. Fresh UHPC can exhibit high thixotropy due to the low water-to-binder ratio (w/b) and high binder contents []. In general, the thixotropy describes the continuous increase of rheological properties with rest time, such as static yield stress and apparent viscosity [The thixotropy of cementitious suspensions originates in a change of the microstructure after removing shear stress. The change of microstructure over rest time includes physical structuration and chemical rigidification []. The physical structuration is the formation of network due to flocculation of fine binder particles. The cohesiveness of the network is affected by the attractive surface interactions, including van der Waals force, electrostatic repulsion, and steric hindrance due to adsorbed polymers []. The chemical rigidification corresponds to the formation of bridges among adjacent particles due to the nucleation of hydration products onto binder particle surfaces. The reversible bridge is formed by the early-age hydration products, such as metastable C-S-H phase and ettringite []. As the extension of rest time, the increase of stable hydration products (e.g., stable C-S-H) can transform the reversible bridges to the irreversible bond []. The thixotropy is generally determined by the reversible process of physical structuration and early-age chemical rigidification [Thixotropy can affect the processing properties of UHPC. In the case of high wall and bridge column elements, high thixotropy can decrease the lateral pressure applied on the formwork []. In the case of bridge deck overlay constructed using thin bonded UHPC material, thixotropic UHPC with appropriate fluidity is essential to enable the placement of sloped surfaces []. In the case of 3D printing, UHPC with proper fluidity is needed to secure an easy control of pumpability and extrusion, while high thixotropy can enable the material to transform into a stiff continuous and almost non-deformed filament immediately after printing [The thixotropy of UHPC is influenced by the binder type, w/b, chemical admixtures, and use of nanomaterials. In general, the use of higher binder content and addition of supplementary cementitious materials can increase thixotropy [] evaluated the thixotropy of mortars made with different binder constituents and a fixed 0.4 w/b at different rest time. The results show that mortar made with 72% cement, 22% Class F fly ash, and 6% silica fume led to 50% increase in the structural breakdown area at 30 min of rest compared to that made of 100% cement. The thixotropy can be reduced using superplasticizer (SP), especially at high dosage values [] used the shear stress decay approach determined under constant shear rate to evaluate thixotropy of cement paste made with 0.4 water-to-cement ratio (w/c) and various SP dosages. The authors pointed out that the increase of SP dosage from 0 to 0.1%, by mass of cement, reduced the ratio of initial maximum stress to equilibrium stress from 2.3 to 0.5 when the shear rate was 600 rpm []. The thixotropy can also be affected by the incorporation of a set-accelerating agent (SAA) and a set-retarding agent (SRA) [] used the breakdown area approach to evaluate the effect of SAA and SRA on thixotropy of self-consolidating concrete (SCC) prepared with a constant slump flow of 650 mm. Results indicated that the breakdown areas were 239 and 358 J/m3·s for SCC prepared with SAA and SRA compared to 304 J/m3·s for SCC prepared without any set modifying admixture.The viscosity modifying admixture (VMA) is effective in enhancing thixotropy of cement-based materials [] evaluated the effect of diutan gum on the evaluation of static yield stress with rest time for cement paste prepared with 0.34 w/c. Results showed that the incorporation of 0.25% diutan gum, by mass of cement, enhanced the rate of increase in static yield stress with rest time (Athix) from 0.02 to 0.15 Pa/s compared to cement paste made without any diutan gum. For the cement-based materials made with a constant slump flow, the incorporation of a low dosage of VMA is shown to be more effective to increase thixotropy compared to mixtures with relatively high dosages of VMA and SP. This can be attributed to that the additional SP demand to maintain the required fluidity that can interfere with the effect of VMA [] investigated the thixotropy of SCC made with different dosages of cellulose-based VMA at a constant slump flow of 650 mm. The use of 0.23% VMA and 0.88% SP, by mass of cement, can result in a higher increase in the breakdown area with the rest time, while the incorporation of 0.39% VMA combined with 1.75% SP led to a lower increase of breakdown area compared to SCC made without any VMA. The use of low content of WG can enhance thixotropy [] investigated the shear stress decay of mortar prepared with mini-slump flow of 130 mm under a constant shear rate. Results indicated that mortar prepared with 0.035% WG and 0.3% SP took much longer time to reach equilibrium compared to that made without any WG and SP.The propylene carbonate-based thixotropy-enhancing agent (TEA) is shown to be effective to increase thixotropy of cement-based materials [] reported that the increase in TEA dosage from 0 to 1.1%, by mass of binder, increased breakdown area of SCC from 30 to 500 J/m3·s.The incorporation of nanoclay (NC) can also enhance thixotropy of cement-based materials [] studied the evolution of static yield stress of cement paste prepared with 0.36 w/c. The static yield stress of mixture prepared with 0.5% NC, by mass of cement, increased from 50 to 575 Pa after 60 min of rest compared to 20 to 200 Pa for mixtures prepared without any NC. The combined use of nanoclay and SP can potentially make mixtures with high thixotropy and low yield stress [] indicated that for the cement paste made with 0.4 w/c and dynamic yield stress of 15 mN·m, the ratio of initial maximum stress to equilibrium stress of mixture made with 0.5% NC and 0.2% SP was 20% higher than that of mixture made without any NC and SP.Limited studies focusing on the effectiveness of NC and WG on thixotropic enhancement of UHPC with relatively low dynamic yield stress are reported. Due to the low w/b, the required SP dosage for UHPC is higher than that of conventional cement-based materials to secure a low dynamic yield stress []. The incorporation of NC and WG to improve thixotropy of UHPC would require even higher dosage of SP. Since the high SP dosage can reduce thixotropy [], there is a concern that the combined use of WG and SP or NC and SP potentially have a limited effect on the enhancement of thixotropy for UHPC mixtures with relatively low dynamic yield stress.The objective of the study is to study the coupled influence of using a high content of SP to secure low yield stress and NC or WG to enhance thixotropy. Different contents of WG and NC were incorporated in UHPC prepared with a constant SP dosage and variable SP dosage to maintain a given fluidity. A qualitative approach was developed to describe the thixotropic indices based on wet packing density of the mortar, water film thickness onto the solid particles, and early-age hydration kinetics. Such approach can contribute to the understanding of the mechanisms of using NC and SP or WG and SP on thixotropy of UHPC matrix.The binders employed in this study included ASTM Type III Portland cement, Class C fly ash (FAC), and silica fume (SF). The Blaine fineness values of the cement and FAC are 560 and 465 m2/kg, respectively. The mean diameter and Brunauer-Emmett-Teller (BET) specific surface area of the SF are 0.15 μm and 18,200 m2/kg, respectively. A combined sand including riverbed sand (RS), masonry sand (MS), and pre-saturated lightweight sand (LWS) was used. The specific gravities of the RS and MS are 2.65 and 2.64, respectively. The water adsorption of the LWS is 17.6%, and its specific gravity is 1.81. The LWS was saturated for at least 24 h before use. The particle size distributions (PSD) of binder and sand materials are shown in Welan gum (WG) and nanoclay (NC) powders were used to adjust thixotropy of the UHPC mortar. The WG is a soluble organic material with a specific gravity of 0.8. The NC is a needle-like structure with an approximate length and diameter of 1.75 μm and 30 nm, respectively. A polycarboxylate-ether superplasticizer (SP) with a 26% solid mass content and 1.05 specific gravity was used to enhance fluidity.The water-to-binder mass ratio (w/b) of the UHPC was set at 0.2. The binder consisted of 55% cement, 40% FAC, and 5% SF, by volume. The sand-to-binder volume ratio was set to 1.0. The sand included a combination of 53% RS, 30% MS, and 17% LWS, by volume of total sand. Five different contents were used for each of the WG and NC to enhance the thixotropy of UHPC mortar, as shown in . The contents of the WG varied between 0.5 and 3 kg/m3 that correspond to 0.045% and 0.27% of the binder mass, respectively. Similarly, the NC contents ranged from 2.5 to 16.5 kg/m3. Such values correspond to the 0.25% to 1.5% of the binder mass, respectively. are divided into two sets: mortar with fixed SP dosage (0.28% by active mass of SP compared to binder mass), as well as mortars with variable SP dosages. The slump flow of the reference mixture made without any WG and NC and mixtures in the second group was set at 200 ± 5 mm, which is determined by the mini-slump test without any jolting (ASTM C230/C230M). The upper and lower inner diameter of mini-slump cone are 70 and 100 mm, respectively, and the height is 50 mm.All materials were mixed at room temperature at approximately 20 °C. Before batching, a blender with a 2-L capacity was used to mix the NC, water, and SP for 10 min to obtain a uniform suspension. The pre-prepared solution was then kept at rest for 10 min to enable the foam generated during mixing to vanish. In the case of WG, the WG was dispersed in the SP using the magnetic stirrers at 12.5 rps for 10 min and then the solution was added to the mixing water. The UHPC mortar was prepared using a 12-L Hobart. The mixing procedure was as follows: (1) the various cementitious materials and sand were mixed at a relatively low speed of 1 rps for 2 min; (2) 90% of the water with disputed admixtures was introduced and mixed at 2 rps for 3 min; (3) the remaining water with disputed admixtures was then added and mixed 2 rps for 7 min. The total duration for the mixing of the UHPC mortar was 12 min. The mixing protocol and batching sequence were fixed in this study and were based on best practices adopted by the research team on UHPC given the admixtures and binder materials used in this study. It is important to note that the mixing protocol and batching sequences have a marked effect on rheology, and changes in these parameters can affect test results. For example, Rupnow et al. [] reported that the increase of mixing speed from 2 to 5 rps led to 50% and 65% decrease in viscosity and thixotropy, respectively, of cement paste prepared with 0.43 w/c. Furthermore, the delay in time of SP addition can reduce the yield stress and thixotropy since the chemical interaction between the early hydrates and the SP can reduce the effect of SP on particle dispersion []. The delay time can vary with different types of SP, binder compositions, and w/b [] reported that the optimum delay time of addition of polynaphthalene-based SP was 15 min for cement paste prepared with 0.3 w/c []. Such delay time was limited to 5 min for the mortar made with 0.3 w/c and polycarboxylately-based SP [It is important to note that all mortar mixtures reported in were prepared using three separate batches in order to determine the repeatability of the mini-slump flow measurements and rheological properties. The mini-slump flow was determined by measuring the maximum and minimum diameters of the spread. In general, the maximum difference between the major and minor axes of the mini-slump flow measurements was 10 mm for all tested mixtures, which corresponds to 5% for a mini-slump flow of 200 mm.A Contec 5 coaxial cylinder rheometer was employed to determine the dynamic yield stress and static yield stress of the UHPC mortar. All measurements were performed three times to secure the reproducibility of the results.The rheological measurements started at approximately 15 min after adding the water to mixture. The UHPC was pre-sheared at 0.5 rps for 25 s. Then, the rotational speed was reduced from 0.5 to 0.025 rps in 10 steps. For each step, 25 data points were collected, and the data were checked for equilibrium, plug flow, and segregation []. Finally, the steady state of torque values was selected to calculate yield stress (G) using the Bingham model, as shown in Eq. . The dynamic yield stress (τ0) in fundamental units can be obtained using the G values in Eq. from the Reiner-Riwlin transformation equations, as shown in Eq. where T (N·m) is the torque; G (N·m) is the intercept of the flow curves; H (N·m/s) is the slope of the flow curves; N (m/s) is the rotational velocity; τ0 (Pa) is the yield stress; Ri (m) is the inner cylinder radius of coaxial cylinders; R0 (m) is the outer cylinder radius of the container; and h (m) is the height of the inner cylinder submerged in the materials tested in the rheometer.The static yield stress of UHPC mortar was evaluated after rest periods of 5, 15, and 30 min with the mortar placed in the rheometer, which corresponds to 5, 20, and 50 min after the end of mixing, respectively []. The mortar was subjected to a very low rotational velocity of 0.05 rps for 120 s without any pre-shear. The resulting torque was progressively increased with time to a peak value, then it decreased to an equilibrium value []. The static yield stress (τs) was calculated as follow [where Tmax (N·m) is the peak torque in the process of testing.The wet packing method was used to evaluate the particle packing of UHPC mortar []. The testing procedure was as follows: (1) set a low w/b and prepare the UHPC mortar using the same mixing procedure as ; (2) transfer the UHPC mortar to a 400-mL cylindrical mold after mixing, and fill the mold to excess; (3) compact the UHPC mortar in the cylindrical mold on a vibrating table for 60 s; (4) remove the excess mortar and weigh the mass of mortar; (5) repeat steps (1) to (4) at a successive w/b values until achieving the maximum mass. Taking the reference mixture as an example, the increase w/b from 0.15 to 0.18 increased the mass of the UHPC mortar, and then the mass decreased with the further water addition, as shown in and subsequent figures corresponds to standard deviation divided by the square root of n where n is the sample number (n = 3 in this study). The packing density was calculated as the solid volume fraction at a maximum mass of UHPC mortar, as shown in Eq. . Furthermore, no bleeding was observed for all of the investigated mixtures during the testing of the packing density.where Ф (unit-less) represents the wet packing density; V (mL) refers to the volume of cylindrical mold (400 mL), Vm (mL) refers to the maximum solid volume of the mortar that includes water and SP, which can be calculated by the following equation:where Mmax (g) is the maximum measured mass in the cylindrical mold; ρw, ρsp, and ρs (g/cm3) are the density of the water, SP, and solid materials, respectively; uw, usp, and us (unit-less) refer to the volumetric ratios of water, SP, and each solid material to the total solid materials, respectively.The water film thickness (WFT) is defined as the average thickness of water film coating solid particles in the UHPC mortar. The solid particles included the NC material in the case of the UHPC mixtures prepared with NC. In order to evaluate the WFT, the minimum voids ratio (uv.min) was calculated from the packing density obtained by the wet packing density, as shown in Eq. The mixing water in the UHPC mortar can be divided into void filling water and excessive water []. Thus, the excessive water ratio (ue) can be calculated by the Eq. where uw (unit-less) refers to ratio of the water volume to the solid volume of the granular material.The specific surface area of each solid particle (SSAPSD) can be calculated based on the PSD of each material and the assumed spherical shape for the particles [. Then, the specific surface area of all solid particles (SSAs) can be obtained by Eq. where Vi (unit-less) is the volume fraction passing two successive particle sizes; Di (μm) is the average particle diameter between two successive particle sizes; and Rs (unit-less) is the volumetric ratio of each solid particle divided by the total solid volume.The WFT can be calculated by the excessive water and specific surface area of the particles, as shown in Eq. The influence of WG, NC, and SP on cement hydration was evaluated using the isothermal conduction calorimetry (model: Calmetrix I-CAL8000). The heat flow and cumulative heat of hydration were tested on UHPC mortar samples starting within 1 min after the end of mixing. During the test, the temperature was kept constant at 20 ± 0.1 °C. shows the variations of dynamic yield stress (referred to here as yield stress and to differentiate from static yield stress that will be discussed later) with WG and NC contents. For UHPC prepared with 1% SP dosage, the yield stress increased with the addition of WG and NC. For example, the addition of 0.09% WG and 0.4% NC led to increase in yield stress from 40 to 165 Pa and 40 to 170 Pa, respectively, compared to UHPC made without any WG and NC. For UHPC made with variable SP dosages to secure a slump flow of 200 ± 5 mm, the yield stress ranged between 35 and 43 Pa. Such variations in dynamic yield stress are in a good agreement with the results calculated by a model proposed by Roussel [] where the increase in mini-slump flow from 195 to 205 mm can reduce the dynamic yield stress from 41 to 32 Pa. As the content of WG or NC increased, higher SP dosages were required to maintain the initial slump flow. For example, the increase of WG content from 0 to 0.27% or NC content from 0 to 1.5% led to 185% and 265% increase in SP dosage to maintain the 200 mm of slump flow, as shown in . The enhanced effect of WG on yield stress can be attributed to the long polymer chain of the WG polymer that can fix some of free water, as well as the development of attractive forces among adjacent polymer chains and entanglement of the polymers, especially at low shear rate []. The increase of yield stress with the addition of NC at a given SP dosage can be attributed to that the fine NC particles can enhance the flocculation of binder particles [] showed that the increase of NC from 0 to 3% in cement paste prepared with 0.4 w/b and without any SP enhanced the yield stress from 35 to 75 Pa.The evolution of the static yield stress of the reference mixture with rest time is shown in . The static yield stress increased more rapidly in the first 5 min, then increased linearly with rest time. This is consistent with the results reported by Mostafa and Yahia []. This phenomenon can be fitted by a non-linear model proposed by Ma et al. [] or a bi-linear model proposed by Kruger et al. [. It should be noted that such models are only appropriate to describe the thixotropy of cement-based materials at early age (1 h in this study) since an exponential evolution of the static yield stress with time can take place after the initial linear evolution. For example, Ma et al. [] reported that cement paste prepared with 0.43 w/c exhibited an exponential evolution of static yield stress after rest time of 200 min. Therefore, two thixotropic indices were used to describe the evolution of static yield stress. The τfloc (Pa) refers to the initial increase of yield stress due to the particle flocculation in a short time after shearing, and Athix (Pa/min) refers to the slope of linear evolution of static yield stress.where τs (Pa) is the static yield stress; τ0 (Pa) is the dynamic yield stress. compares the effect of WG (fixed SP) and the coupled effect of WG and SP (fixed slump flow) on the thixotropy of the UHPC mortar. For UHPC mortar mixtures prepared with a fixed SP dosage of 1%, the increase of WG content from 0 to 0.09% resulted in 240% and 135% increase in Athix and τfloc values, respectively. Therefore, the WG is effective to enhance the thixotropy of UHPC. For UHPC mortar with a fixed slump flow of 200 ± 5 mm, the increase in WG content from 0 to 0.18% led to 275% and 110% increase in Athix and τfloc values, respectively. Therefore, high flowable UHPC with WG can achieve low dynamic yield stress and high thixotropy. However, further increase in WG content from 0.18% to 0.27% decreased Athix. This mechanism will be further discussed in The influence of NC (fixed SP) and coupled effect of NC and SP (fixed slump flow) on thixotropy of UHPC is shown in (b). The incorporation of NC enhanced thixotropy; the increase of NC content from 0 to 0.4% led to 215% and 135% increase in Athix and τfloc, respectively, for UHPC prepared with a fixed SP dosage of 1%. For the mortar with a fixed slump flow of 200 mm, the increase of NC content from 0 to 1.5% resulted in 90% and 80% increase in Athix and τfloc, respectively. This indicated that the combined use of NC and SP had a limited influence on enhancement of thixotropy, which can be attributed to that the effect of NC on enhancement of thixotropy was reduced by the additional SP dosage to maintain the fluidity.In addition to using the τfloc and Athix, the coupled effect of τfloc and Athix can be employed to determine thixotropy. This is important since cement-based materials can exhibit higher τfloc values without a considerable change in Athix or similar τfloc values but different Athix results. Therefore, the coupled effect of both thixotropic paramaters (τfloc·Athix) can be considered to evaluate the overall thixotropic behavior of cement-based materials [, the changes in τfloc·Athix confirmed the results evaluated from the individual effect of WG and NC on τfloc and Athix. Both WG and NC are shown to effectively enhanced thixotropy of UHPC made with 1% SP. For example, the increase in WG from 0 to 0.09% and NC from 0 to 0.4% resulted in similar increase in τfloc·Athix from 1600 to 13,000 Pa2/min. However, in the case of UHPC made with a constant slump flow, the influence of WG on enhancing thixotropy was greater compared to that of NC. For example, the increase of WG from 0 to 0.18% increased the τfloc·Athix from 1600 to 13,000 Pa2/min, respectively, compared to using 1.5% NC where τfloc·Athix increased from 1600 to 5500 Pa2/min. The underlying mechanisms are discussed in The effect of WG, NC, and SP contents on the packing density (Φm) of the UHPC mortar is shown in . The value of Φm varied from 0.775 to 0.80. In general, the incorporation of WG and NC both with a fixed SP and variable SP to maintain a fixed slump flow led to a reduction of Φm. The effect of WG or NC addition on Φm for UHPC mortar made with fixed SP dosage was greater than that of mixtures made with variable SP dosages to secure the fixed slump flow. For example, for UHPC mortar prepared with 1% SP, the incorporation of NC from 0 to 0.4% reduced Φm from 0.798 to 0.776. The increase in NC content from 0 to 1.5% decreased the value of Φm from 0.798 to 0.782 for UHPC made with a constant slump flow. Similar phenomenon was observed for UHPC mortar prepared with WG.Two opposite effects of nanomaterials on the packing density of UHPC mortar were reported by Meng and Khayat []. The incorporation of NC can improve the packing density of UHPC due to its fine volume that can fill voids among the coarser cementitious particles. On the other hand, NC can adsorb some of the free mixing water and SP due to its high specific area, which decreased the dispersion of particles. The adsorption effect became dominant when the content of nanomaterial surpasses the threshold value (0.05%, by mass of binder in []), leading to reduced Φm with the increase in NC content from 0.25% to 0.4% in UHPC mortar proportioned with a fixed SP dosage. The influence of WG on reduction in Φm can be attributed to that the adsorption of WG on cement particles decreased the SP adsorption and particle dispersion []. As expected, the increase in SP dosage improved the packing density of UHPC mortar due to its dispersion effect []. For example, the increase in SP dosage from 1% to 1.2% enhanced the Φm value from 0.78 to 0.794 for UHPC mortar with 0.09% WG. These results are in good agreement with work reported by Liu et al. [] where the increase of SP dosage from 1.3% to 1.9% enhanced the packing density from 0.738 to 0.756 for cement paste prepared with 0.2 w/b. shows the effect of WG, NC, and SP contents on water film thickness (WFT) where WFT value ranged between 1 and 12 nm. The incorporation of WG and NC generally reduced the WFT. For example, the increase of NC and WG contents from 0 to 0.4% and 0 to 0.09% resulted in 90% and 95% decrease in WFT, respectively. The effect of NC on reduction of WFT can be attributed to that incorporation of NC decreased the Φm and increased the solid surface area []. For the WG, its long polymer chain can fix part of the free mixing water, and adjacent polymer chain can develop attractive forces and entangle with each other at low shear rate to further block the motion of water []. These modes of action can lower the WFT []. Furthermore, the incorporation of WG can inhibit the adsorption of SP onto cement particles, which can reduce the dispersion effect of the SP [The use of SP led to a higher WFT. For instance, the increase in SP dosage from 1% to 1.2% resulted in 95% increase in WFT for UHPC prepared with 0.09% WG. This can be attributed to the enhanced packing density caused by the strengthened dispersion effect of the SP without significantly increasing the specific surface area of particles of cementitious particles [The influence of WG and NC on reduction of WFT for UHPC mortar prepared with 1% SP was greater than that of mortars made with variable SP dosages to secure the slump flow of 200 ± 5 mm. For example, the incorporation of NC contents from 0 to 0.4% in mortars prepared with 1% SP led to 90% decrease in WFT. Such reduction was 80% for mixtures with increased NC contents from 0 to 1.5% in mortars prepared at a fixed slump flow. Similar results were obtained for mortars prepared with WG. This indicates that the effect of NC and WG on reduction of WFT was greater than the increased influence of SP. Although the slump flow of UHPC mortar was fixed at 200 mm, the WFT value varied with the different combinations of WG and SP or NC and SP. Similar results were reported by Ye et al. [] where the WFT of cement paste prepared with different mineral admixtures varied from 50 to 400 nm given a fixed slump flow of 200 mm.The heat flow curves of the investigated UHPC mortars are plotted in . For mixtures prepared with fixed SP dosage, the increase in WG or NC contents slightly accelerate the early-age hydrations. Similar effect of WG on acceleration of cement hydration was observed by Ciobanu et al. [] where the use of 0.2% WG of the cement mass led to a higher degree of cement hydration for cement paste prepared with 0.32 w/c. This might be attributed to the competitive adsorption between the WG and SP []. That is to say, the use of WG can hinder the adsorption of SP onto the surface of cement particles, which can increase the dissolution and nucleation sites for cement hydration []. The other possible reason is that the WG can adsorb out of free water onto the surface of cement particles []. For UHPC mixture made with a fixed slump flow, the increase in WG or NC content delayed the hydration and reduced the peak value of heat flow. This can be attributed to the additional SP dosage with the increase of WG or NC contents to secure the slump flow of 200 mm. Such higher SP dosage can inhibit the dissolution and nucleation sites for cement hydration [The objective of the study is to investigate the thixotropy of UHPC mortar in the first hour after mixing. Therefore, the cumulative heat of UHPC mixtures during the first hour was analyzed, as shown in . It can be observed that the cumulative heat increased rapidly at first, and then the rate of increase gradually slowed down. This can be attributed to the formation of hydration products covered the surface of binder particles, leading to the delay of hydration []. The cumulative heat of UHPC mortar in the first hour was enhanced with the increase of WG or NC content in mixtures with a fixed SP dosage of 1%. For UHPC mortar with a fixed slump flow of 200 mm, the use of WG content from 0 to 0.09% led to 65% increase in the cumulative heat during the first hour of age. However, further increase in WG content up to 0.27% led to 30% decrease in the cumulative heat. Such reduction was limited to 10% when the NC content increased from 0.5% to 1.5%. This can be attributed to that the accelerated effect of WG and NC on cement hydration was interfered by the higher dosage of SP to secure a constant slump flow.The cumulative heat (CH) can be correlated with the hydration time (t), as shown in Eq. where M and N are constants determined by fitting the relationship between CH and t. M (unit-less) refers to the rate of increase of cumulative heat during the first hour of hydration, and N (unit-less) refers to the difference between the experimental results and regression mode at t = 0.A typical curve of the evolution of cumulative heat during the first hour is shown in . The experimental results can be well-fitted by the derived model from 0.1 to 1 h after the end of mixing. presents the M and N parameters and the values of coefficient of determination (R2) for the derive equation. The high values of R2 indicate good fittings between model and experimental results for all investigated mortars. A lower value of the M parameter corresponds to a higher increase rate of cumulative heat during the first hour of hydration. For example, for UHPC mortar made with a fixed SP dosage, the increase of WG content from 0 to 0.09% led to approximately 5% decrease in the M parameter and 35% increase in the cumulative heat after 1 h.The thixotropy of UHPC mortar can be attributed to the interparticle colloidal interaction and chemical rigidification controlled by early-age hydration products []. At early age, the thixotropy is affected by two phenomenon []: (1) formation of network due to particle flocculation; and (2) formation of bridges due to the nucleation of hydration products. A qualitative approach describing the thixotropy of UHPC mortar was established based on these two phenomena, as described below.The initial yield stress offset (τfloc) of UHPC mortar is caused by the formation of network due to particle colloidal flocculation given the negligible effect of hydration products at very early age after the end of mixing (e.g., 5 min) []. The strength of the particle interaction network depends on the number of contact points and the colloidal surface interaction of the binder particles []. Increased number of contact points can strengthen the particle interaction due to the crowding effect []. In general, the number of contact points can increase with the increase of the solid volume fraction (Φ) and reduction of the packing density (Φm) of the paste or mortar material. Furthermore, the decreased distance between adjacent particles led to a stronger colloidal surface interaction at the contact points []. The WFT is closely related to Φm and can reflect the distance between surface of particles. Therefore, it should be possible to establish a relationship between τfloc and WFT. shows the variation of τfloc with WFT where a linear relationship can be established. The increase in WFT from 2 to 11 nm resulted in 50% decrease in τfloc. This can be attributed to the enhanced value of WFT corresponding to a longer distance among adjacent binder particles, which resulted in a lower degree of particle agglomeration at very early stage after the end of mixing (e.g., 5 min).The network of colloidal particles is gradually rigidified due to the formation of bridges by the nucleation of hydration products at the contact point of binder particles []. Therefore, the bridging effect of nucleation of early-age hydration products should be considered to describe Athix in addition to particle flocculation []. The particle flocculation was characterized by the WFT parameter, as mentioned in ] pointed out that the bridging effect of nucleation of early-age hydration products can be correlated to the covering rate of surfaces of fine particles with hydration products per unit volume of paste or mortar. In this study, the formation of hydration products was characterized by the heat of hydration at early age (e.g., 60 min). Although both the dissolution and rapid formation of the hydration products contribute to the exothermic peak of heat evolution, the contribution of dissolution could be neglected after 15 min of contact between the binder and water []. Therefore, the covering rate of the surfaces of fine particles (including binder and NC) with hydration products per unit volume of mortar can be characterized by the rate of evolution of early-age hydration heat divided by the SSA of the fine particles (EH). As mentioned in Eq. , the 1/M parameter corresponds to the rate of increase of cumulative heat during the first hour of hydration determined from calorimetric measurements. Therefore, the EH parameter can be expressed as follows:where SSAfp (nm2/nm3) refers to specific surface area of the fine particles per unit volume of mortar. The SSAfp can be calculated as follows:where SSAPSD (nm2/nm3) is the specific surface area of each fine particle (including binder and NC); and Rfp (unit-less) is the volumetric ratio of each fine particle divided by the total volume of fine particles.The measured Athix of UHPC mortar prepared with NC reported in is correlated to the WFT and EH parameters, as shown in the Eq. . A good correlation was established with high R2 value, which indicates that Athix is closely related to particle flocculation, characterized by the WFT parameter, and the bridging effect of early-age hydration products, characterized by the EH parameter.A similar approach was applied for mortars prepared with WG. However, as shown in Eq. , the correlation yielded a low R2 value, which indicates that Athix of UHPC made with WG cannot be accurately predicted from the WFT and EH parameters. Therefore, other mechanisms, in addition to the particle flocculation and bridging effect due to cement hydration, can contribute to Athix of UHPC. This includes the polymer entanglement and association of the WG, which is further elaborated in Athix=8.51·WFT−0.21·EH11.23·10−28R2=0.59In view of the above considerations, Athix can be described by the WFT and EH parameters. These two parameters are affected by the combination of WG and SP or NC and SP, as predicted in . Therefore, it is possible to analyze the effect of NC and WG on Athix for UHPC mortar prepared with constant and variable SP contents based on the proposed qualitative approach. shows the effect of NC (fixed SP) and combined use of NC and SP (fixed slump flow) on the values of WFT and EH parameters of UHPC mortar. The coupled effect of the WFT and EH on Athix is shown in . For UHPC mortar made with 1% SP, the increase of NC content from 0 to 0.4% led to 90% decrease in the value of WFT and 10% increase in EH. As shown in , the decrease in WFT and increase in EH led to enhancement of Athix. Therefore, the addition of NC in UHPC mortar at a fixed SP dosage led to a significantly higher value of Athix. For UHPC mortar with a fixed slump flow (i.e., variable SP contents), both WFT and EH parameters decreased by the combined use of NC and SP. This can be attributed to a higher particle flocculation and lower bridging effect of early-age hydration products. Such mechanisms can interfere, resulting in reduced net effect. Therefore, the combination of NC and SP had a limited influence on the enhancement of Athix. shows the effect of WG (fixed SP) and combined use of WG and SP (fixed slump flow) on the values of the WFT and EH parameters. For UHPC with slump flow of 200 ± 5 mm, the increase of WG content from 0.09% to 0.27% resulted in 75% and 5% decrease in WFT and EH, respectively. This indicates a higher flocculation rate of particles and lower bridging effect of early-age hydration products, which cannot significantly increase Athix, as predicted using Eq. . However, the experimental results showed that the incorporation of WG significantly enhanced Athix for UHPC made with a fixed slump flow. Therefore, there should be another mechanism, in addition to particle flocculation and bridging effect of nucleation of early-age hydration products, which can affect Athix of UHPC mortar prepared with WG.The enhancement of Athix using WG might be due to the following physical effect: (1) the WG can fix part of mixing water []; (2) the WG has an anionic character and can adsorb onto the cement particles []; (3) the long polymer chains in WG can entangle with each other and form a relative strong network at a low shear rate when the concentration of WG is high []. Therefore, the network formed by the entanglement of long polymer chains could be the origin of the high Athix. Similar conclusion was reported by Ma et al. [] where the shear stress evolutions of the cement paste incorporating NC and diutan gum under an intermediate shear strain rate of 0.1 1/s were investigated. The results showed that the critical strain corresponding to the maximum shear stress was approximately 0.7 and 0.03 for cement paste made with diutan gum and NC, respectively. This indicated that the incorporation of diutan gum in cement paste formed a strong network to enhance the particle interaction [It is important to note that the increase of WG content from 0 to 0.18% increased the value of Athix, while further increase from 0.18% to 0.27% reduced Athix for UHPC mortar with a fixed slump flow of 200 ± 5 mm, as shown in (a). This can be attributed to the competitive adsorption between the SP and WG []. That is to say, when additional SP dosage was incorporated with increase of WG contents, the adsorption of WG onto cement particle can decrease, resulting in weaker network among binder particles and lower value of Athix []. Further study is needed to evaluate the cohesiveness of the network formed by long polymer chains of WG and adsorption of these polymer chains onto cement particles when qualitatively describing the Athix of UHPC prepared with WG.This study investigated the effect of WG and NC on thixotropy of UHPC mortar prepared with fixed and variable SP dosages. Three indices were used to describe thixotropy: (1) τfloc referring to the rapid increase of static yield stress at rest after the end of mixing (5 min of rest); (2) Athix corresponding to the rate of increase of static yield stress with rest time over 30 min; and (3) the coupled effect of these indices (τfloc·Athix). According to test results, the following conclusions are warranted:For UHPC mortar made with a constant SP dosage of 1%, the increase in WG from 0 to 0.09% and NC from 0 to 0.4% resulted in similar increase in dynamic yield stress from approximately 40 to 170 Pa. The increase of WG from 0 to 0.27% and NC from 0 to 1.5% necessitated a greater SP demand of 185% and 265%, respectively, compared to the reference UHPC made without any WG or NC.The τfloc was found to increase linearly with the decrease of WFT given the effect of WG and NC on the flocculation of binder particles. For UHPC mortar made with 1% SP, the increase in WG from 0 to 0.09% and NC from 0 to 0.4% led to a similar increase in τfloc from 135 to 320 Pa given their similar effect on reducing WFT. On the other hand, for UHPC prepared with a constant slump flow, the increase in WG and NC did not lead to a greater increase in τfloc given the higher SP demand that limits the effect of WG and SP on enhancement of particle flocculation.For UHPC prepared with 1% SP dosage, the use of 0 to 0.09% WG and 0 to 0.4% NC led to of 250% increase in Athix and 720% increase in τfloc·Athix, respectively. For UHPC made with a fixed slump flow, the use of WG was more effective to enhance thixotropy compared to NC. The increase in WG from 0 to 0.18% resulted in 275% and 625% greater Athix and τfloc·Athix values. However, such improvement in thixotropy was limited to 90% and 245% with the use of 1.5% NC.For UHPC mortars made with NC, a qualitative approach was established to describe Athix given the WFT and EH factors that reflect particle flocculation and bridging effect of nucleation of early-age hydration products, respectively. For UHPC prepared with 1% SP, the pronounced effect of NC on enhancement of Athix was due to higher particle flocculation and bridging effect of nucleation of hydration products. However, a limited net effect of NC and SP on Athix was observed for UHPC prepared with constant slump flow given the additional SP demand that can restrict the effect of NC on the bridging effect of nucleation of early-age hydration products.The effect of WG on enhancing Athix is not solely dependent on particle flocculation and bridging effect of nucleation of early-age hydration products. For UHPC made with a constant slump flow, the increase of WG resulted in a higher flocculation of binder particles but lower bridging effect of early-age hydration products. Such net effect cannot explain the increase in Athix. Therefore, other factors, such as physical network formed by entanglement of long polymer chains of WG, should be considered to estimate Athix.Le Teng: Conceptualization, Methodology, Investigation, Writing - original draft. Jiang Zhu: Conceptualization, Methodology, Writing - original draft. Kamal H. Khayat: Supervision, Writing - review & editing. Jiaping Liu: Writing - review & editing.The authors declare that they have no known competing financial interests or personal relationship that could have appeared to influence the work reported in this paper.Tear resistance of a square-wave joint: Experiment versus cohesive zone modelThe load versus displacement response of a double-cantilever beam (DCB) adhesive joint is measured for two interface geometries: a planar interface and a non-planar “square-wave” interface. Joints with a square-wave interface are stronger and tougher than planar joints of equal adhesive layer thickness provided the square-wave amplitude is sufficiently large. Computed tomography (CT) imaging is used to examine the failure morphology of DCB specimens with planar interfaces, and optical fractography is used to observe the failure mechanisms for DCB specimens with square-wave joints of fixed wavelength and selected amplitude; in all cases, the failure mode is similar to those of tensile, square-wave, butt joints. The finite element method is used to predict the cracking response of the DCB adhesive joint. To do so, the adhesive layer is idealised as a plane of cohesive elements with a normal traction versus separation response, as measured independently from square-wave butt joint specimens. Satisfactory agreement exists between the predicted and observed DCB response for all interface geometries, provided the reduction in DCB bending stiffness, arising as a consequence of the square-wave interface geometry, is taken into account.Commonly, adhesive joints are stronger and tougher under shear loading (such as a lap joint) configuration, than under tensile loading (such as a butt joint). This suggests that a strategy for increasing the peel strength and peel toughness of a joint is to inter-digitate the two substrates, and thereby exploit the high strength and toughness associated with a lap-joint configuration, see for example Maloney and Fleck The present study builds on the promising studies on micro-patterned adhesive joints by Matsuzaki and co-workers Crack advance within a joint is commonly modelled by a cohesive zone approach, with the traction versus displacement response of the cohesive zone sensitive to the thickness of the adhesive layer Commonly, the traction versus separation (T-δ) response of the “cohesive zone” is defined by two parameters such as the cohesive strength and work of separation, or cohesive strength and critical separation There is scope for choosing the appropriate level of sophistication in a cohesive zone model, depending upon the research question to be addressed. For example, the role of mode mix on the fracture strength and toughness can be analysed by suitable modification to the traction versus separation law across the cohesive zone, see for example Yang and Thouless The central task of implementing a cohesive zone model is a determination of the traction versus separation (T-δ) law, or “cohesive law”, to define the response of cohesive elements There exist two main methods for measuring a Mode I cohesive law directly from experimental results. The first makes use of the measured J-integral for a crack in a double-cantilever beam specimen, and a simultaneous measurement of the crack tip opening displacement (and crack tip opening angle). The traction exerted by the cohesive layer is the derivative of the J-integral with respect to the crack tip opening displacement. This method has been used by several researchers to derive empirically-based cohesive laws The second method is more straightforward, but there are only limited studies to explore its validity. The Mode I cohesive law is assumed to equal the T-δ response of a tensile specimen so-chosen to represent a thin ligament ahead of the crack. Ivankovic et al. In this study, the load versus displacement response of a double-cantilever beam (DCB) specimen with a square-wave interface geometry is explored as a function of square-wave amplitude. The observed failure mechanisms of square-wave DCB specimens are compared to those observed for tensile butt joints with square-wave interfaces as presented in a previous study A finite element model is used to predict the response of double-cantilever beams with either a planar interface or a square-wave interface. The adhesive layer is represented by cohesive elements with a traction versus separation response as specified by the measured tensile response of a butt joint specimen with the same micro-architecture (planar or square-wave). The accuracy of the finite element model is evaluated by comparing the predicted load versus displacement response to the measurements. Additionally, the accuracy of a J-integral method for predicting the load versus displacement response of DCB joints with planar interfaces is confirmed in the appendix.The adhesive joints comprised a two-part, room-temperature and moisture-curing silyl-modified polymer (SMP) adhesive sandwiched between aluminium alloy 6082-T651 substrates. The adhesive contains filler particles on a scale of 10 μm to control its viscosity in an un-cured state. The double-cantilever beam (DCB) joint is characterised by arms of height H = 25.4 mm, beam lengths l and L of 25.4 mm and 228.6 mm, respectively, and a starter crack of length ao = 30 mm, see (a). The square-wave interface geometry was presented in a previous study (b). The amplitude A ranges from 0 mm (corresponding to a planar interface) to 20 mm, while the magnitude of wavelength λ, adhesive thickness parameters t and s, and depth (into page) B are fixed at λ = 28 mm, t = s = 1.1 mm, and B = 12.8 mm. The pattern wavelength and layer thickness were chosen within the practical range for the manufacturing and test methods adopted. Suitably-shaped substrates were water-jet cut to within a dimensional tolerance of 0.1 mm.Roughening of the substrates was accomplished by manual polishing using 60 grit emery paper; the surfaces were then cleaned and degreased by wiping with acetone. The adhesive was applied in accordance with the manufacturer’s recommendations. A manual applicator gun was used with a static-mixing nozzle. A quantity of adhesive was initially discarded to ensure that both components were flowing freely and to remove any bubbles which may have accumulated in the component tubes. The adhesive layer thickness t was adjusted by shims prior to infiltration of the gap by the adhesive. All specimens were cured in ambient air for one week at room temperature, and G-clamps were used to prevent relative movement of the substrates. A starter crack was generated in all specimens by making use of fresh razor blades: the razor blade was broached to a depth of 5mm, to give an initial crack length of 30mm. Additionally, the uniaxial response of the SMP adhesive was measured by casting a dogbone specimen from the adhesive, of gauge length 20 mm and square cross-section 6.5 mm × 6.5 mm.Mechanical tests were conducted using a screw-driven test machine, as follows.Uniaxial tension tests on dogbone specimens of SMP adhesive were performed in accordance with ASTM D638-14 at machine displacement rates in the range 0.01 mm s-1 to 1000 mm s-1 to characterise the viscoelastic nature of the adhesive.At least three DCB specimens of each joint geometry were tested, and the scatter was expressed in terms of the standard deviation of each set of specimens. The tensile load on each specimen was measured by the load cell of the test machine, while the displacement was measured by the test machine and by a laser extensometer. The machine-measured displacement was corrected for the compliance of the test machine and was used to corroborate the measurements of the laser extensometer, which were used to generate the results presented in the current study. The tests on double-cantilever beam (DCB) joints were conducted at a displacement rate of 0.007 mm/s, and photographs were collected at a frame rate of 0.5 frames per second to monitor crack growth. Additionally, tests on the DCB specimens with planar joints were interrupted and the specimens were placed in a 3D computed tomography (CT) machine in order to observe the formation of voids within the adhesive layer ahead of the crack tip. The CT scan took 30 minutes, and there was little change in the opening profile of the specimen during the scan due to the presence of the wedge. The main purpose of the CT tomography was to examine the process zone within the adhesive joint for the planar specimen. It proved difficult to obtain high resolution images of the square wave joints, and so the study was limited to CT tomography of the planar joint.The tensile traction versus opening displacement of square-wave butt joints was also determined using a machine displacement rate of 8 × 10-3 mm s-1 corresponding to a normalised displacement rate δ̇/t of approximately 7 × 10-3 s-1. At least three specimens of each joint geometry were tested.The uniaxial tensile stress versus strain response of the SMP adhesive is given in for three values of nominal strain rate (3 × 10-3 s-1, 3 × 10-1 s-1 and 30 s-1). Both the nominal and true stress versus strain responses are plotted. Note that the shape of the stress versus strain response is independent of strain rate but the strain to failure (and associated tensile strength) is mildly sensitive to strain rate. As the strain rate is increased from 3 × 10-3 s-1 to 30 s-1, the nominal failure strength, that is, the ultimate tensile strength UTS, increases from 2.5 MPa to 3.6 MPa and the true (logarithmic) strain to failure increases from 0.95 to 1.42, while the Young’s modulus E is almost constant at 2.5 ± 0.2 MPa.The load P versus displacement u response of a double-cantilever beam (DCB) with a planar adhesive layer (A = 0 mm) is shown in (a). No plastic deformation of the aluminium substrates was observed, and this was confirmed by load-unload tests. This is consistent with the relative strengths of the two solids: the aluminium alloy has a yield strength of 250 MPa whereas the SMP adhesive has a UTS of 2 MPa. The non-linear behaviour observed in the initial portion of the DCB load versus displacement response can be traced to the non-linear tensile response of dogbone specimens made from the bulk adhesive, recall Crack growth in the DCB specimens with a planar adhesive layer begins shortly after peak load, and crack advance leads to a decreasing load. CT images of the mid-plane of the adhesive layer are shown in (b) at the following snapshots in time, upon interruption of the testing: (i) initial state, (ii) prior to peak load and (iii) after a crack advance of 42 mm. Recall that the DCB specimens are of thickness B = 12.8 mm (in the z-direction), which can be used as a length scale in interpreting the fracture surfaces of (b) are aligned with the initial crack tip (at a pre-crack length of 30 mm), while the rightmost end of the images are 100 mm ahead of the initial crack tip. (Recall that the specimen ligament is of width 200 mm ahead of the initial crack tip).In the initial state, only a few small voids are visible. At the loading point (ii) of the P versus u curve, microvoids exist within the adhesive, but the voids are too small to be resolved by the CT machine. (Large voids are visible as white circles, while microvoiding is dispersed throughout as grey scale.) Since the effective density of the adhesive is reduced by the presence of the microvoids, the image becomes lighter, as shown in the light grey region ahead of the crack tip in (ii) of (b). The SMP adhesive can sustain a large amount of voiding prior to void coalescence, in contrast to an epoxy, for example. Thus, voids can exist far ahead of the crack tip.Beyond peak load, at point (iii), a new zone of microvoids (light in appearance) is present ahead of the current crack tip, along with a low volume fraction of larger voids. The lighter zone in (iii) is a developing damage zone that progressively fails to give rise to crack advance. Note that the voided zone extends beyond the rightmost end of the image in (iii) of (b). At this stage of loading, a few larger voids have also nucleated and grown ahead of the grey-zone of microvoids. A representative fracture surface is shown in (c): it reveals that the microvoiding occurs from filler particles within the adhesive.The combination of microvoids and occasional larger voids has been observed in the previous study of Maloney and Fleck The load P versus displacement u responses of a planar DCB joint (A = 0 mm) and three square-wave DCB joints with amplitudes A = 2.5 mm, 10 mm and 20 mm are presented in (a). The adhesive layer thickness t is equal to 1.1 mm for all joints. The peak load of the joint with amplitude A = 2.5 mm is 1610 N, and this is 13% less than that of the planar DCB joint (A = 0 mm). Also, the small-amplitude square-wave joint dissipates 25% less energy than that of the planar joint. However, upon increasing the square-wave amplitude A to above 2.5 mm, the peak load and dissipated energy increase monotonically with increasing A.The tensile traction versus separation (T-δ) response of the “square-wave” adhesive butt joint has also been measured as a function of square-wave amplitude A, including the limit of the planar adhesive joint, with the adhesive layer thickness fixed at 1.1 mm. The traction is defined as the tensile load divided by the projected cross-sectional area of the joint normal to the loading direction; the separation δ is the tensile relative opening displacement across the adhesive joint, as measured by a laser extensometer. The traction T versus separation δ responses of a planar butt joint and three square-wave butt joints with amplitudes A = 2.5 mm, 10 mm and 20 mm are presented in (b). It is observed from repeat tests that the average peak traction increases monotonically from 2.2 MPa to 2.4 MPa for joints with square-wave amplitudes in the range 0 mm ≤ A ≤ 10 mm, and jumps to 2.9 MPa for the large-amplitude joint. The double-peak in the T-δ curve for A = 20 mm in (b) is discussed in detail in Maloney and Fleck Recall that the ultimate tensile strength UTS of the dogbone specimens is 2.3 MPa at a comparable strain rate to that of the square wave butt joints, compare (b). Also the nominal failure strain of the dogbone specimens is on the order of 1.6. The planar butt joint (A = 0) has a peak strength of 2.3 MPa, and a failure strain δ/t = 2.0, which are of similar magnitude to those of the tensile dogbone specimens. However, the degree of elastic constraint is significantly higher in the butt joint specimens.The energy dissipated Γ is calculated as the area under the T-δ curve. The value for Γ is based on the projected area of the square-wave, that is the side faces of the square-wave are neglected. This is consistent with the definition of traction T per unit projected area of the joint. The energy dissipated Γ by double-cantilever beam joints and tensile butt joints is presented in (c) as a function of square-wave amplitude A. The cross-sectional area of the DCB arms (ahead of the initial crack tip) was used in the calculation of the energy dissipated per unit area.For both types of specimen, the average dissipated energy initially decreases from values for planar specimens (A = 0 mm) to those for square-waves of amplitude A = 2.5 mm. This is followed by an increase in dissipated energy for square-wave joints of amplitude A = 10 mm and A = 20 mm to levels that exceed those for planar specimens. There is good agreement between the dissipated energy for butt joints and DCB joints for all square-wave amplitudes. For the amplitude range 2.5 ≤ A ≤ 20 mm, the increase in dissipated energy follows an approximately linear trend, similar to the findings of Zavattieri et al. The observed failure sequence of a DCB joint with square-wave amplitude A = 20 mm is presented in . The sequence of debonding in the adhesive layer ahead of the crack tip is compared to the failure sequence of a tensile butt joint from Maloney and Fleck We conclude that square-wave interfaces only provide mechanical benefits (i.e. higher peak load, greater energy dissipation), in the DCB joint and in the butt joint configuration, when the square-wave amplitude A is sufficiently large. Specimens of small amplitude (A = 2.5 mm) fail at a comparable peak load but dissipate slightly less energy than planar joints of the same adhesive layer thickness: only stages (i) to (iii) in the failure sequence of are observed for the small-amplitude square-wave interface, as shear regions fail concurrently with tensile regions. These specimens of small amplitude square-wave possess stress rasers at the corners thereby promoting void nucleation and growth. However, it is somewhat surprising that these specimens are not tougher than the DCB specimens with planar joint in view of the fact that the shear zones of the square –wave act in the manner of a tough lap joint compares to the tensile butt-joint facets of the square wave. For specimens of large square-wave amplitude (A = 20 mm), a substantial increase in dissipated energy over joints with planar interfaces (A = 0 mm) is attributed to the presence of friction between failed shear surfaces, i.e. a pull-out force or the presence of “mechanical interlocking,” as observed in tensile specimens of the same interface geometry in a previous study Finite element simulations were performed with the implicit solver of ABAQUS (version 6.12-2). The two-dimensional finite element model consisted of two rectangular elastic substrates joined by a thin cohesive layer (of negligible thickness tcz = 0.1 mm as the intent is to mimic a traction-separation law across the adhesive joint). The finite element simulation demands a finite thickness of cohesive zone element for its implementation It is emphasised that both the square-wave DCB specimens and DCB specimens with a planar adhesive joint are modelled as planar specimens, but with a cohesive zone of traction-separation law that has been measured from tests on a butt joint of identical joint architecture. The cohesive zone law for the square-wave joint is meant to capture the average traction-separation law associated with several failure events averaged over the wavelength of the square wave. This is a reasonable approach provided the process zone length in the DCB specimens exceeds the wavelength of the square wave. This is clearly the case, recall All double-cantilever beam joints were modelled with the same finite element mesh, and the traction T versus separation δ response of the cohesive elements was used to model the square wave topologies. The aluminium alloy substrates of the DCB joint were treated as linear elastic and isotropic, with a Young’s modulus E = 70 GPa and a Poisson ratio ν = 0.33. The substrates were meshed with 4-node plane-strain reduced-integration quadrilateral elements (CPE4R).Both the square-wave and planar adhesive layers were idealised by a planar cohesive zone (of thickness one element), and was meshed by 4-node cohesive elements (COH2D4). The cohesive elements for the square wave and planar joints were defined by a normal traction versus separation response with three parameters: a normal stiffness K, a critical traction T0 indicating the onset of damage, and a damage variable D(δ) which describes the evolution of damage as the cohesive element undergoes displacement δ.A representative cohesive law is presented in . A maximum nominal stress-based damage criterion is used such that damage is initiated when a critical traction T0 is reached. The normal traction exerted on the interface by each cohesive element is calculated aswhere the initial stiffness K and critical traction T0 are measured values for each of the tensile butt joints of identical micro-architecture to that of the DCB specimens. These values are listed in . The cohesive zone laws for the planar joint and square wave joint are taken directly from the load versus displacement response of the tensile butt joints. Consequently, the initial stiffness K is measured and is geometry dependent.The damage variable D is closely linked to the secant modulus: D evolves from an initial value of zero to a final value of unity, indicating failure of a cohesive element, as the displacement δ increases such that the numerically-constructed curve matches the experimental response. D is defined as follows:damage does not initiate (D = 0) under compressive traction (T < 0);damage also does not initiate (D = 0) for tensile traction less than or equal to the critical traction (T ≤ T0); andfor tensile traction T > T0, D(δ) evolves in accordance with Eq. in order to replicate the measured response of the tensile butt joint specimen.D(δ) was specified at no less than thirty values of δ for each cohesive law and introduced into the finite element simulation in tabular form. For intermediate values of δ, the finite element solver used linear interpolation to determine the value of the damage variable D from adjacent data points.The finite element method is used to predict the response of planar and square-wave DCB joints by a suitable choice of the traction T versus separation δ response of the cohesive elements. The T-δ responses of cohesive elements are constructed from the measured response of tensile butt joints as presented in The predicted load P versus displacement u responses of the finite element model for a planar DCB joint (A = 0 mm) and for three square-wave DCB joints of amplitude A = 2.5 mm, 10 mm and 20 mm are compared with the measured responses in (a). Satisfactory agreement is observed between model and experiment for the planar case and for the small-amplitude (A = 2.5 mm) case. The finite element model underpredicts the peak load of the medium-amplitude (A = 10 mm) square-wave joint, although the difference is on the order of the scatter for these specimens. The model overpredicts the peak load of the large amplitude (A = 20 mm) square-wave joint, and only approximately predicts the shape of the P-u curve for the two square-wave joints of A equal to 10 mm and 20 mm.We note that the bending stiffness of a cantilever beam with square-wave interface geometry may be significantly less than that of a uniform rectangular beam as adopted implicitly within the finite element model. Our modelling approach so far assumes that each substrate of the DCB joint is modelled as a planar substrate of height H = 25.4 mm. This assumption is an approximation particularly for the large-amplitude square-wave DCB joint: although the average thickness of each substrate equals 25.4 mm, the elastic bending stiffness of the beam is sensitive to the distribution of beam height as dictated by beam theory. Note that, for the choice A = 20 mm, the height of the beam varies from 15.4 mm to 35.4 mm. Consequently, the effective beam stiffness in these specimens is substantially lower than that assumed in the finite element simulations and this discrepancy contributes to the mismatch between the results of the cohesive zone model and experimental curves.To address this, the accuracy of the finite element model was improved by assuming an effective beam height Heq in the arms of the DCB specimens such that the bending stiffness of the effective beam equals the average bending stiffness of a cantilever beam with square-wave profile. To achieve this, each arm of the DCB beam was idealised by a single wavelength of square-wave geometry and this arm was subjected to a uniform bending moment at each end in a finite element simulation. The relative rotation of the two ends of the unit cell was determined, and upon dividing this rotation by the length of the unit cell, the average curvature along the length was determined, thereby giving the effective bending stiffness. The equivalent beam height Heq is the height of uniform beam that possesses the same effective bending stiffness as that of the above simulation. This method was used to obtain the equivalent height for substrates of uniform height corresponding to square wave joints of height A = 2.5, 10 and 20 mm. Finite element simulations were then performed on DCB specimens of this equivalent height, and results are compared with the measured responses in (a). The agreement with the measurements is improved, compare The slightly higher residual deviation in load at the tail end of the tests in (b) can be ascribed to slightly larger interlocking and friction in the DCB specimens as a result of slight tilting compared to the butt joint tests (as used to calibrate the cohesive zone model), particularly at large amplitude A. It is appreciated that the butt joint will not deliver an accurate traction versus separation law for use in finite element predictions of the DCB response when the ratio of amplitude A to adhesive layer thickness s is high, by the following argument. Tilting of the mating arms of the DCB specimen will lead to inter-locking at high A/s and thereby to increased dissipation compared to the butt joint specimens. Consequently, the load versus displacement response of the DCB specimens will exceed the finite element prediction at high A/s.Crack growth in double-cantilever beam (DCB) joints with planar and non-planar interface geometries has been measured and predicted for aluminium alloy 6082-T651 substrates and a silyl-modified polymer (SMP) adhesive layer. Load versus displacement responses were measured and the observed failure mechanisms have been determined. The planar DCB joints fail by the growth of voids ahead of the crack tip. Square-wave interface geometries of amplitude A = 2.5, 10 and 20 mm failed by void nucleation at the internal corners of the square-wave interface, followed by void growth and coalescence in the portions of the joint that undergo predominantly tensile loading. Failure of the square-wave joint also entails the growth of cracks from the corners of the joint along the regions of predominantly shear loading. As the amplitude A of the joint increases, the proportion of load carried by the shear regions of the joint increases and the joint switches in character from that of a butt joint to that of a lap joint. The magnitude of energy absorbed in the square-wave joint of the DCB specimens increases with increasing A, with the caveat that the square-wave joint of small amplitude A = 2.5 mm is slightly less tough than that of the planar joint; this is attributed to the presence of the sharp corners in the square-wave joint which leads to early void nucleation.For all interface geometries (both planar and square-wave), the observed failure sequence of DCB joints is similar to the failure sequence of tensile butt joints as presented in a previous study A cohesive zone model is able to predict the load versus displacement responses of double-cantilever beam joints with planar and square-wave interface geometries. In each case, the cohesive zone mimics the tensile response of the adhesive layer, and the cohesive elements are calibrated by the observed response of a butt joint specimen of identical topology (i.e. square-wave, with same value of amplitude A). Satisfactory results are achieved for all joints when the stiffness of the modelled beams is adjusted to match the stiffness of the profiled beams.The approach adopted herein addresses the following question: can the tensile traction versus separation response of a tensile butt joint of square-wave architecture be used to predict the progressive cracking response of a DCB specimen of identical joint architecture? It is not immediately obvious that this will be the case. The critical ratio to consider is the length of the process zone in the DCB specimen compared to the square-wave wavelength. When this ratio is large (as it is in the present study), then it is expected that the current approach will be satisfactory. However, when this ratio of length scales is not large, then it is anticipated that the failure sequence in the DCB specimen may involve void growth only at the crack tip within the adhesive layer, rather than failure at a number of sites ahead of the main crack tip; consequently, the failure mode for the DCB specimen may differ from than in the butt joint specimen.In contrast, a more sophisticated analysis could assume the existing of competing cohesive zones along the adhesive/adherend interfaces or within the adhesive of the square-wave geometry. Additionally, the adhesive could be modelled as an elastic (or visco elastic) solid. This alternative approach is in the same spirit as that of Pardoen et al. As discussed in the Introduction, the traction versus separation law can be derived from the relationship between an elastic calculation of the energy release rate J and the crack tip opening displacement δ. Due to the large deformation before failure of the elastomeric adhesive, it is necessary to include the contribution of rotation of the substrates near the crack tip as a second term in the expression of the energy release rate where ϕ is the opening angle formed by the arms of the DCB specimen at the crack tip.The opening displacement δ and angle φ are each measured from sequential photos of DCB specimens at the location ao of the initial crack tip, see (a). The J-integral is plotted as a function of δ in (b); it is seen that J increases monotonically to a steady-state value Jss.Very close to the crack tip, the J-integral is defined aswhere δc is equal to the local displacement at which Jss is reached. Due to the path-independence of J, the two preceding expressions are equal for a crack in an elastic solid. The traction acting across the interface follows directly from differentiation:This result implies a strong dependence of T(δ) on the form of the equation used to fit the J(δ) data. A detailed study is offered by Zhu and colleagues Traction versus separation curves are calculated and compared to experimental data for tensile specimens in (c). The peak traction of the J-derived cohesive law is somewhat below the experimentally-measured value, and such a discrepancy is to be expected given the fact that entails differentiation of an observed response involving both crack opening displacement and crack opening angle, recall The J-derived T-δ curve is characterised by a non-zero traction at zero displacement, implying an unbounded initial cohesive element stiffness. An unbounded element stiffness is impossible to implement in the finite element model. The highest possible stiffness is instead desirable, so that the energy under the traction versus separation curve remains relatively unchanged. A sensitivity study has been conducted to identify the highest stiffness which the model can handle without encountering numerical instabilities. Based on this sensitivity analysis, an element stiffness of 3 × 1010 Pa/m has been chosen.The load versus displacement response of the DCB specimen is predicted by the finite element model using the J-derived cohesive zone law is presented in (d). The peak load of the cohesive zone model falls below the experimental value. Nevertheless, the cohesive zone model provides a reasonable fit. This method has been used by several researchers to obtain cohesive laws A constitutive model for casting magnesium alloy ZL101 based on the analysis of spherical void evolutionSince casting magnesium alloys contain numerous spherical microvoids, the aggregate of microvoids and matrix can be analyzed using a representative volume element. The representative element can be idealized as a cell containing a spherical void. Through the analysis on the velocity field of the spherical void-cell model, the strain field of the spherical void-cell model was obtained. Defining an intrinsic time that involves the hardening due to plastic deformation and the softening due to voids, a new endochronic model was derived for the elastoplastic and damage behavior of casting magnesium alloys. The corresponding numerical algorithm and finite element procedure were developed and applied to the analysis of the elastoplastic response and the porosity of casting magnesium alloy ZL101. The computed results show satisfactory agreement with experiments.Due to being lightweight, easily shaped and recycled, casting magnesium alloys have been preferred choices for lightweight constructions of components for the automotive industry, for example, steering wheels, door structures and oil sumps The general physical model used here is a representative macroscopic volumetric element (RVE) of a casting magnesium alloy material (an aggregate of microvoids and ductile matrix) (). The representative volumetric element is by definition large enough to be statistically representative of the properties of the aggregate. The RVE can be simplified as a spherical void-cell model shown in . The radii of the void and the cell are a and b, respectively. The radius of an arbitrary point in the matrix of void-cell is r. The matrix of the model is assumed homogeneous and incompressible. Suppose there is a microscopic velocity field vr, vφ and vθ in the matrix of the void-cell model under spherical coordinates, the corresponding microscopic strain rate field ε˙ij in the matrix can be expressed asε˙φ=1rsinθ∂νφ∂φ+νθrctgθ+vrr,ε˙rθ=∂νθ∂r-νθr+1r∂νr∂θ.In the case of axisymmetrical deformationwhere vr and vθ are the function of the r and θ. Noticing that the matrix of the void cell is incompressible, one obtainsε˙r+ε˙θ+ε˙φ=∂∂r(r2vrsinθ)+∂∂θ(rvθsinθ)=0.Suppose the boundary condition at the outer surface of the spherical void cell can be expressed aswhere E˙ij is the macroscopic strain rate of the matrix. In the case that the global axis 3 coincides with the local spherical axis and the deformation is axisymmetricalOne can obtain the boundary velocity field in a spherical coordinate systemvr=b(E˙11sin2θ+E˙33cos2θ),vθ=b(E˙11-E˙33)sinθsinφ,vφ=0.ε˙r=-2A0r3+E˙e6(1+3cos2θ),ε˙θ=A0r3+E˙e6(1-3cos2θ),ε˙φ=A0r3-13E˙e,ε˙rθ=-E˙esin2θ,A0=b33(2E˙11+E˙33)=b2E˙m,where E˙e and E˙m are, respectively, the macroscopic equivalent and bulk strain of the matrix,The microscopic intrinsic time measure is denoted by ζ, which is defined as the Euclidean norm of the deviatoric increment of microscopic strain where dεij′ is the increment of microscopic deviatoric strain. The intrinsic time scale can be defined asF(ζ) is the hardening function which reflects the hardening of the material subjected to plastic deformation, η(f) is the softening function which reflects the softening behavior of material due to void growth during plastic deformation, f is the current void volume fraction of material. For simplicity, to F(ζ) and η (f) are given the following simple forms without considering the strain rate effectwhere β1, β2, γ1 and γ2 are material constants, which can be determined from the curve of a uniaxial experiment. Substituting Eq. into the incremental form of endochronic constitutive equation Δsij(r)=sij(r)-sij(r)(zn)=kr∑r=13[CrΔep-αrsijr(zn)Δζ/F(ζ)η(f)],sij denotes the microscopic deviatoric stress, zn is the intrinsic time scale after n th increments of loading and sijr(zn) represents the r th component of sij at zn, Cr and αr (r |
= 1, 2, 3) are material constants, and G is the elastic shear modulus. By settingone can derive the following expression of the incremental form of the endochronic constitutive equation involving voids:If the effect of voids is not considered (f |
= 0, η(f) = 1), one can prove that Eqs. reduce to the incremental form of the constitutive equation given by Peng and Fan Assuming homogeneous matrix, the homogenization principle can be used in the transition between microscopic and macroscopic quantities Σij=∂Φ∂Eij=1V∫Vm∂ϕ∂EijdV=1V∫Vmskl∂εkl∂EijdV., the macroscopic constitutive equation of casting magnesium alloy can be obtained.The void volume fraction may change during deformation, which is contributed by both the growth of existing voids and the nucleation of new voids, i.e.,Keeping in mind that the matrix is incompressible, the increment of the void volume fraction due to the growth of void can be given byThe new voids, nucleated either by cracking of the particles or by decohesion of the particle–matrix interface, can be described withwhere Λ follows a normal distribution with mean value ζN and standard deviation sN. Similarly to the formula by Chu and Needleman where sN |
= 0.1, fN |
= 0.4, ζN |
= 0.2. The addition of the void nucleation term would more fully reflect the effect of the void evolution on material behavior and improve the predictive ability of the constitutive relation.The material parameters Cr, αr in the constitutive equation Eq. control the stress response and can be determined by a simple tensile test Given a set of measured (σi,eip), we can determine the parameters Cr and αr with the least squares approach.The corresponding numerical algorithm and FE approach were developed based on the constitutive equation presented. The proposed constitutive equation and the corresponding finite element procedure were applied to the analysis of the relationship between stress and strain and the porosity of the casting magnesium alloy ZL101 specimens (with and without notch) under elastoplastic deformation. The material parameters were identified asC1,2,3=(7.853×104,5.463×103,1.326×103)MPa,α1,2,3=1527,278.4,13.8,The geometry of the specimens without a notch is 200 mm in length, and 10 mm in diameter. The size of the specimen with a notch is shown in . The upper right quarter of the two kinds of cylindrical specimens were taken for the analysis due to the symmetry of the problems. The eight-node isoparametric element with 2 × 2 Gaussian points was adopted. The axial displacements were imposed at the end of the specimens with the incremental step of 0.02 mm. The computed results were verified by both macroscopic experiment and microscopic observation.For the specimen without a notch, the relationship between stress and strain was investigated. shows that the computed stress–strain relationship agrees satisfactorily with the experimental data. From it can also be found that the constitutive equation can properly reflect the main character of the material stress–strain curve without a distinct yield point. In order to verify the relationship between porosity and deformation, specimens without a notch were also tested on an Instron 1342 servo-hydraulic material testing system. They were subjected to different deformations, and then unloaded. The tested specimens were cut along the radius at minimum section. After polishing these sections, the changes of porosity in the center parts of the specimens were carefully observed with a microscopic photointerpreter. Since the void distribution is stochastic, a quantitative metallographic method was adopted. gives the comparison of the change of porosity during deformation, which shows satisfactory agreement between the computed and experimental results. also shows that the porosity changes with the developments of plastic deformations according to exponential law. is the SEM photograph at the fractured section of the tested casting specimen, where many dimples can be seen in the fracture section. These dimples are the roots of voids and reflect ductile fracture of the material. For the specimen with a notch the distributions of the stress and porosity on the smallest section of the specimen were studied. shows the contours of the void volume fraction at different applied strain. It can be seen from that voids firstly occur at the root of the notch, where strain is relatively larger, and the porosity takes its maximum in the region near to the root of the notch and decreases with the increase of the distance away from the notch root. show the distributions of the axial stress and the porosity along the notch line at 30 kN, where a is the distance from the surface, coordinate 0 denoting the surface and 5 mm denoting the center of the smallest cross section of the specimen. shows that maximum axial stress arises at the notch root of the specimen, but maximum stress considering voids is lower than that without considering voids. shows that maximum porosity also appears at the notch root of the specimen and agrees well with experimental results.Casting magnesium alloys contain numerous spherical microvoids, the representative void-matrix cell was isolated and idealized as a single spherical cell containing a spherical void. The void volume fraction of the void-matrix cell model equals that of the material. Through the analysis of the velocity and strain of the cell, an elastoplastic constitutive description for casting magnesium alloys was obtained. The change of the void volume fraction during deformation was considered as a combination of the growth of existing voids and the nucleation of new voids. The effect of void evolution on the constitutive equation was considered using a softening function. The corresponding FE procedure was developed and applied to analyze the constitutive behavior and the evolution of porosity of the casting magnesium alloy ZL101 specimens, with and without a notch. It was found that, in the specimen without a notch, the calculated result for the stress–strain relationship for the specimen agrees with experimental data. The variation of porosity follows plastic deformation and is also consistent with experimental results conforming to the exponential function. Study of the notched specimen shows that the maximal axial stress appears at the notch root and that the maximal stress value considering voids is lower than without considering voids. The porosity also reaches the maximum in the vicinity of the notch root and decreases toward the center of specimen, which is reasonable compared with the experimental results.Preparation and regulation of AlCrNiTiSi high entropy alloy coating by a multi-arc magnetic filter cathode vacuum arc systemThe high entropy alloy coatings (HECs), as a breakthrough in the field of increasingly saturated traditional material, have broad development potential, but their applications are restricted by the shortcoming of preparation technology. In this paper, based on the multi-arc magnetic filter cathode vacuum arc system, which is equipped with a 120° Y-shaped magnetic filter duct that has the reasonable match between the geometric size of magnetic filter duct and the uniformity distribution of magnetic field intensity determined by finite element analysis and magnetic field design, the transport of multiple ions is real-time regulated by the relationship among the arc source, focusing magnetic field, the magnetic field of filter duct, arc discharge and ions transmission. Under the detailed process parameters of TiAlSi target arc current of 110 A, CrNi target arc current of 90 A, magnetic field current of 2 A, and negative bias voltage of 100 V, the AlCrNiTiSi HEC is prepared by the novel multi-arc magnetic filter cathode vacuum arc technology for the first time. The AlCrNiTiSi coatings deposited by this system are uniform and dense, and the components are uniformly distributed. The AlCrNiTiSi HEC has good hardness of 13.92 GPa and excellent corrosion resistance in 5 % H2SO4 of the minimum Icorr and Ip of 3.16 × 10−6 and 1.28 × 10−5 A•cm−2.A new alloy with the term “high entropy alloy” was proposed by Yeh ]. For the entropy-based definition, the configurational entropy of mixing per mole could be expressed as ΔS=−R∑i=1ncilnci, where R is the gas constant, ci is the molar fraction of the element, and n is the total number of the constituent elements. Based on the magnitude of entropy, HEA definition separates low (ΔS<0.69R), medium (0.69R<ΔS<1.61R) and high (ΔS>1.61R) entropy alloys. The high mixing entropy effect allows the HEA to easily form disordered solid solutions of single face-centred cubic (FCC) or body-centred cubic (BCC) structures [] instead of complex intermetallic compounds. Due to the variety of alloying elements, a large number of different atoms are dissolved in each other, which will cause serious lattice distortion and hinder the movement of dislocations, so as to obtain the effect of solid-solution strengthening, which is the most common strengthening mechanism in HEAs. At the same time, more excellent properties can be obtained by selecting appropriate elements and regulating the corresponding ratio. The special composition and structure make the HEAs have high strength/hardness ], good corrosion resistance and good oxidation resistance There are many different processing methods for synthesis of HEA bulk materials with a simple solid solution phase such as electric arc melting, casting and plasma sintering ]. Meanwhile, the magnetron sputtering technology has a low deposition rate and requires alloy targets, which usually need to be prepared by powder metallurgy. The alloy targets prepared by this way have a fixed elements ratio that the compositions of coatings cannot be real-time regulated and the production of alloy targets is difficult and costly The cathodic vacuum arc deposition has the advantages of high ionization rate and fast deposition rate, but it has the problem of large particle pollution, which can be solved by magnetic filter system In order to overcome the shortcomings of the two ways mentioned above, a novel multi-arc magnetic filter system is designed and developed, which is simple and easy to operate. The multi-arc magnetic filter cathode vacuum arc technology can realize the preparation of the AlCrNiTiSi HEC by the real-time regulation of the ratio of coating compositions. The research on the preparation of the HECs by magnetic filter cathode vacuum arc technology is firstly reported.The AlCrNiTiSi coatings were prepared by the multi-arc magnetic filter system. The circular TiAlSi target (30 at.% Ti; 60 at.% Al; 10 at.% Si; purity 99.99%) and CrNi target (50 at.% Cr; 50 at.% Ni; purity 99.99%) were used as the cathodic arc source. The 304 stainless steel and Si (100) wafer were used as substrate, which were ultrasonically cleaned in acetone and ethanol for 30 min, respectively. Prior to deposition, the chamber was pumped to 3 × 10−3 Pa and the working pressure was 2.5 × 10−2 Pa. Then the substrates were sputter cleaned for 40 s under substrate biases of −800, −600, and −400 V, respectively. The substrate temperature was around 150°C during the deposition process. The distance between the sample stage and the outlet of main pipe was 100 mm. The positive bias voltage was 24 V. To deposit the AlCrNiTiSi HEC, we adjusted different deposition parameters.Surface and cross-sectional images of the AlCrNiTiSi coatings were observed using a scanning electron microscope (SEM, HitachiS-4800) equipped with an energy dispersive spectroscope system (EDS, EMAX-350) which is used for determining the elemental compositions of the coatings. An atomic force microscope (AFM, Tosca™ 400) in the tapping mode was used to scan an area with a size of 5 × 5 μm to observe the surface morphology. The microstructure of the coatings was investigated by an X-ray diffraction analysis (XRD, SmartLab S2) using Cu Kα radiation with a glancing incident angle of 1° at a step size of 0.02°, and 2theta range varied from 20 to 90 degree. The X-ray source was operated at 40 kV and 40 mA. The hardness (H) and Young's modulus (E) were evaluated by a Nanoindenter G200 (Keysight Technologies) which was equipped with a Berkovich diamond probe tip. The indentation depth was limited to approximately 5-15% of the total coating thickness so as to minimize the effect of substrate, and the test was repeated at least five times to reduce the errors.The electrochemical corrosion test was carried out with a PARSTAT 2273 electrochemical workstation to measure the potentiodynamic polarization of the coatings. A conventional 3-electrode glass cell was used to perform the electrochemical studies in 5% H2SO4 solution. The samples, Pt foil and saturated calomel electrode were used as the working electrode, counter electrode and reference electrode, respectively. The corrosion area of the sample was 0.5 cm2. And the measurement was repeated 4 times to assess the scatter of the measured characteristics.The plasma beam produced by cathode vacuum arc contains electrons, ions, neutral atoms and large particles. Among them, ions are the required particles as film-forming particles, while neutral atoms and large particles, especially large particles, have fatal pollution and damage to the film, which should be completely avoided if possible. There are two main ideas for stripping large particles from cathode vacuum arc plasma: one is to strip large particles from the source of plasma generation, the other is do that during the process of plasma transmission. The stripping of large particles in the process of plasma transmission has become the focus of research because the physical mechanism of plasma generation determines that it inevitably produce large particles []. It is the most effective method to strip the large particles by using the curved charged spiral tube as the plasma transmission duct The plasma is transported in a filter duct where the Larmor radius of the charged particles must be much smaller than the physical size of the filter duct. At the same time, combining the law of plasma movement in electromagnetic field and the Maxwell distribution of electron velocity, the magnetic field formula of magnetic filter is deduced Here, m and Q are the mass and charge state of the particle, respectively, e is the elementary charge and rfilter is the physical size of the filter. Simple calculations show that the Larmor radius of electrons is on the order of hundreds of microns, and that of ions is on the order of tens of centimeters. Thus, electrons will be magnetized in the magnetic filter, but ions and neutral atoms will not be. The magnetized electrons spiral forward in the filter, pulling ions out of the outlet. Uncharged neutral atoms and large particles which are unaffected by the magnetic field will hit the walls of the filter and peel off.The design of the novel magnetic filter duct should not only satisfy the principle of out-of-sight and transmission efficiency [], but also ensure the real-time regulation of compositions ratio by adjusting the transmission of multiple ions. And the plasma drawn from the magnetic filter should be uniformly mixed. According to the above design principles, the schematic diagram of the multi-arc magnetic filter system is shown in the The reasonable matching between the geometric size of magnetic filter duct and the uniformity distribution of magnetic field intensity plays a decisive role in the transmission efficiency and the stable operation of cathode arc source. Therefore, the optimal parameters of the multi-arc magnetic filter system obtained by finite element analysis and magnetic filtration efficiency calculation are as follows: the lengths of the branch pipe and main pipe are 180 and 230 mm, respectively, and the magnetic field intensities are 40 and 90 mT, respectively (]. Under the above optimal parameters, the multi-arc magnetic filter system not only satisfies two basic principles, but also ensures the stable operation of the arc source.We used magnetic filter cathode vacuum arc technology with the multi-arc magnetic filter system, which is equipped with the independent arc sources of TiAlSi and CrNi that do not interfere with each other, to deposit the AlCrNiTiSi HEC by regulating the ratio of coating compositions.The relationship between the arc source, focusing magnetic field, magnetic field of filter duct and arc discharge, ions transmission has been studied by many researchers for many years. There is a strong linear relationship between the arc current and ionic current. By adjusting the arc current, the corresponding ionic current can be adjusted to control the composition ratio in the mixed plasma [], so as to realize the regulation of the ratio of compositions in the AlCrNiTiSi coatings. We first regulate the arc current of CrNi target to 60, 75 and 90 A, respectively, and other parameters remain unchanged. See for specific parameters. The relative contents of each element in the coatings of No. 1, 2 and 3 samples were measured by EDS, and the ΔS of the corresponding coatings were calculated. The results show that the element content or ΔS of these three coatings do not meet the composition-based definition or entropy-based definition of HEA.On the basis of above parameters, the arc current of TiAlSi target was regulated to 90, 110 and 150 A, respectively. Other parameters remained unchanged. See for specific parameters. The relative contents of each element in the coatings of No. 3, 4 and 5 samples were measured by EDS, and the ΔS of the corresponding coatings were calculated. The results show that the element content or ΔS of these three coatings do not meet the composition-based definition or entropy-based definition of HEA.The ratio of compositions in the coating also can be regulated by controlling the magnetic field current and bias voltage []. Therefore, based on the above parameters of the higher ΔS of 1.32 R, other parameters were kept unchanged and the magnetic field current was regulated to 1, 2 and 3 A, respectively. See for specific parameters. The relative contents of each element in the coatings of No. 3, 6 and 7 samples were measured by EDS, and the ΔS of the corresponding coatings were calculated. The results show that the element content or ΔS of these three coatings do not meet the composition-based definition or entropy-based definition of HEA.We regulated the negative bias voltage to 0, 100 and 200 V on the basis of the TiAlSi target arc current of 110 A, CrNi target arc current of 90 A, and magnetic field current of 2 A. See for specific parameters. The relative contents of each element in the coatings of No. 3, 8 and 9 samples were measured by EDS, and the ΔS of the corresponding coatings were calculated. The results show that when the negative bias voltage is 100 V, TiAlSi target arc current is 110 A, CrNi target arc current is 90 A, magnetic field current is 2 A, the elemental content of the coating of sample 9 meet the composition-based definition of HEA.We tested and analyzed the AlCrNiTiSi coatings with different negative bias voltages of samples 3, 8 and 9. The AFM surface morphology of the AlCrNiTiSi coatings with different negative bias voltages are shown in exhibited the elements in the coatings are uniformly distributed. It can be found from the cross-section morphology images () that when the negative bias voltages are 0 and 100 V, the internal structure are uniform and dense, which no obvious impurities and defects have been found. When the negative bias voltage is increased to 200 V, the columnar crystal structure with good crystallinity is formed in the coating. shows the XRD patterns of AlCrNiTiSi coatings with different negative bias voltages. Only one set of peaks representing a face-centered cubic (FCC) structure can be seen in each pattern and no other complex intermetallic compounds in the coatings. Considering the structure and the composition of the coating, it can be concluded that these coatings form a NaCl-type (B1) structure. The high entropy effect of HEAs is the main reason for this phenomenon. When the mixing entropy of the multi-component system is greater than the mixing entropy required to form intermetallic compounds, the formation of intermetallic compounds will be inhibited, which makes HEAs tend to form a stable solid-solution crystal structure. With the increase of negative bias voltages, the XRD diffraction patterns show strong-intensity diffraction peaks. Combining the above test results, the elements content and simple FCC structure of the AlCrNiTiSi coating of sample 9 all satisfy the concept of HEA. Therefore, it is proved that we successfully prepared AlCrNiTiSi HEC by using magnetic filter cathode vacuum arc technology with the novel multi-arc magnetic filter system. shows the mechanical properties of AlCrNiTiSi coatings with different negative bias voltages. With the increase of negative bias voltages from 0 to 200 V, the hardness and modulus of the coating have the same increasing trend, which increased from 11.84 GPa and 179.1 GPa to 15.63 GPa and 224.7 GPa, respectively. Combined with the XRD and cross-section morphology images, it can be found that when the negative bias voltages are 0 and 100 V, these two coatings with high Si content show the characteristics of broadened XRD diffraction peaks, and the internal structure are uniform and dense. As the negative bias voltages increases to 200 V, the coating contains clear columnar crystal structure with good crystallinity, which can also be confirmed from the XRD pattern. Hence, when the Si content is high, the mechanical properties decrease, which may be attributed to the change of the nanometer microstructure of the coating by silicon content ]. Moreover, the severe lattice distortion in the HECs composed of multiple elements can effectively prevent dislocation slip, improving the mechanical properties of the coating. Therefore, under the combination of the advantages of the magnetic filter cathode vacuum arc technology with the multi-arc magnetic filter system and the severe lattice distortion effect of HEA, the hardness of the AlCrNiTiSi coatings prepared by this system were improved, which can be reached to 15.63 GPa.The potentiodynamic polarization curves of AlCrNiTiSi coatings with different negative bias voltages in 5 % H2SO4 are shown in , it is found that the current density (Icorr), passive current density (Ip) and corrosion potential (Ecorr) of the AlCrNiTiSi coatings in 5% H2SO4 are far better than that of the traditional corrosion resistant material 304 stainless steel, indicating that the AlCrNiTiSi coatings have excellent corrosion resistance. This is because the components of the AlCrNiTiSi coating are all easily passivated elements, and a stable passivation film is easily formed in an acid solution. In addition, the composition and structure of the coatings prepared by the novel multi-arc magnetic filter system are stable and uniform, which reduces the electromotive force of the local galvanic cells of the coating, improving the corrosion resistance of the coatings ) that can form a highly dense inert barrier against the penetration of corrosives to improve the corrosion resistance [The multi-arc magnetic filter system with a Y-shaped magnetic filter duct can well solve the problems of the existing coating technology, such as the difficulty in the production of alloy targets, the uncontrollable in the ratio of compositions, the nonuniform in the distribution of elements, etc., and realize the real-time regulation of the ratio of compositions to prepare the AlCrNiTiSi coatings with high quality.By controlling the detailed process parameters, the ratio of compositions in coatings is regulated, so as to realize the preparation of the AlCrNiTiSi HEC by the novel multi-arc magnetic filter system for the first time under the parameter of TiAlSi target arc current of 110 A, CrNi target arc current of 90 A, magnetic field current of 2 A, and negative bias voltage of 100 V.The AlCrNiTiSi HEC has good hardness of 13.92 GPa, and the minimum Icorr and Ip of 3.16 × 10−6 and 1.28 × 10−5 A•cm−2 in 5% H2SO4, which exhibits excellent corrosion resistance.S.N. Chen: Investigation, Visualization, Formal analysis, Writing – original draft. Y.F. Zhang: Methodology, Supervision. Y.M. Zhao: Resources, Methodology. W.Q. Yan: Writing – review & editing. S. Wu: Writing – review & editing. L. Chen: Writing – review & editing, Methodology. P. Pang: Writing – review & editing, Methodology. B. Liao: Conceptualization, Methodology, Validation, Writing – original draft, Writing – review & editing, Supervision, Project administration. X.Y. Wu: Methodology, Supervision. X.P. Ouyang: Writing – review & editing, Supervision, Project administration.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.Harsh environments effects on the axial behaviour of circular concrete-filled fibre reinforced-polymer (FRP) tubesConcrete-filled fibre-reinforced polymer (FRP) tubes (CFFTs) are becoming an attractive system for structural elements proposed to harsh environments. FRP tube provides a corrosion resistant element, reinforcement, confinement for the concrete core, and a stay-in-place formwork. Harsh environments may affect the mechanical performance of the FRP tube, which consequently affect the structural response of the CFFT members. This project investigates the environmental degradation and the durability of concrete cylinders unconfined and confined by filament-wound glass-FRP tubes. Standard plain concrete cylinders and CFFT cylinders were immersed in pure water, salt and alkaline solutions, and exposed to 200 freeze–thaw cycles, between −40 °C and +40 °C. Then, the cylinders were tested under uniaxial compression test to evaluate their performance by comparing the stress–strain behaviour and their ultimate load capacities. Test results indicated that the FRP tube, in CFFTs, is significantly qualified as a sustainable coating material to resist the harsh environments attacks. Theoretical predictions using long term confinement models from CSA and ACI codes are presented.Corrosion of steel reinforcement, in the conventional reinforced-concrete (RC) columns, causes the loss of the member performance and ductility, and consequently decreases the life expectancy of the structures. The use of fibre-reinforced-polymer (FRP) tubes as stay-in-place forms for the reinforced concrete columns is an innovative solution for the corrosion problems. In concrete-filled FRP tube (CFFT) columns, the FRP tube protects the embedded steel and concrete against corrosion, acts as reinforcement in the axial and transverse directions, and confines the inner concrete core. Extensive research has been conducted to investigate the behaviour of CFFT columns under compression load, but there is a limited research regarding their durability. Many environmental conditions may affect the durability of CFFTs such as freeze–thaw cycles, use of de-icing salts, moisture, chemical products, and marine conditions.This project represents another step toward the CFFT technique to be fully implemented in the field of civil engineering structures. The main objective is to investigate the durability of CFFTs by studying their axial behaviour after exposure to harsh environmental factors, and to evaluate their confinement efficiency within the service-life of structures inspired by the North American design codes provisions.Unconfined plain concrete (PC) cylinders and confined CFFT cylinders, 152 mm diameter and 300 mm height, were subjected to various environmental corrosive agents (air, pure water, salt solution, and alkaline solution) while exposing to 200 freeze–thaw cycles, between −40 °C and +40 °C. Then, the cylinders were tested under pure axial compression tests to evaluate their axial performance. The specimens were divided into 25 PC cylinders and another 25 CFFT cylinders, where the concrete was wrapped with a filament-wound GFRP tube. The following sections provide a detailed description of the experimental work.One type of circular glass fibre reinforced polymer (GFRP) tubes, with an inner diameter equals 152 mm, has been used in this study. The tubes were fabricated by filament winding process (as shown in ), using E-glass fibres and vinyl ester resin. Two fibres patterns were used to reinforce the tube; a helical pattern of ±65° and a circumferential pattern of 90°. These patterns were chosen to increase the strength in the hoop direction of the tube and consequently enhance the confinement efficiency. Tension and compression tests were carried out on identical coupons, from the longitudinal direction, following the American standards test method ASTM D3039/D3039M lists the configuration and mechanical properties of the GFRP tube. Finally, the tubes were cut into small tubes, 300 mm length, to provide stay-in-place forms for the CFFT specimens. Note that physical and mechanical properties of the GFRP tube material alone (without concrete) have been evaluated under the same environmental conditions and the results are published in reference A total of 50 cylindrical specimens with identical dimensions, 152 mm diameter and 300 mm height, were prepared for the current study. The cylinders were divided into five groups. Every group contains 10 cylinders divided into 5 PCs and another 5 CFFTs. See . The first group was considered as a reference and was tested after 28 days of casting, while the other four groups were exposed to various environmental conditions before testing. provides the number of specimens according to how they were utilised in the experiments. All cylinders were casted with the same concrete batch using a ready mix concrete. The target mean strength of the concrete mixture was 40 MPa. The ends of the CFFTs were not covered and left to be exposed to the surrounded corrosion medium to simulate the case of piers or piles in marine structure.Four groups of the cylinders would be tested after exposing to 200 freeze–thaw cycles and surrounding by different mediums to simulate various environmental conditions. The specimens were placed in an isolated environmental chamber to control the freeze–thaw cycles. One group was left free to be exposed to the chamber air, while the other three groups were immersed separately, in tanks, in three solutions: pure water, saline, and alkaline solution (see ). The immersion procedure was based on ASTM D570 . It is rational that the actual temperature at the immersed specimens' surfaces is lower than that of the chamber, because the frozen solution isolated the specimens like the case of a frozen lake.The following sections represent and discuss the behaviour of the tested confined and unconfined cylinders under uniaxial compression. The cylinders tested at 28 days old are considered as a reference when studying the environmental effects on the mechanical properties of the standard concrete unconfined compressive strength (fc′) or the confined compressive strength (fcc′). Further comparisons are carried out between the cylinders exposed to freeze–thaw cycles, and immersed in various solution mediums. The specimens' results and behaviour in every group behaved typically. lists the average results in terms of the axial capacity (Pmax), the axial stresses (fc′ and fcc′), the axial strains (εc and εcc), and the stiffness (E1 and E2) as the slope of the stress–strain curve at the elastic and plastic stage, respectively.Confining the concrete cylinders with GFRP tube indicate a large increase in the compressive strength, axial strains, and ductility compared to the unconfined PC cylinders, as shown . The stress-axial strain curves of the CFFT cylinders are typically composed of two main regions, elastic region and plastic region, with a limited transition zone beneath. The initial region is referred to the elastic region where the slope is linearly elastic, as the primary behaviour of PC cylinders, and ascends rapidly up to the ultimate unconfined concrete strength. Afterthought, the concrete core exhibits vertical cracks due to the propagated tensile stresses in the horizontal direction (Poisson's ratio effect). These cracks make the concrete to expand laterally, and the confining GFRP tubes oppose this expansion by tensioning the fibres in the hoop direction. During this stage (the transition zone), the confinement is being activated. The second region is referred to the plastic region. At this stage the concrete core is crushed and the confinement is now fully activated. Also, the stiffness of the CFFT cylinders, which depends on the stiffness of the FRP tube material, is significantly reduced and the curves exhibited a plastic hardening behaviour until the failure load. The average increase in the strength and ductility was about 150% and 1000% over the unconfined PC cylinders, respectively, which indicates the superior performance of the CFFT cylinders.The environmental effects on the PC cylinders and the CFFT cylinders will be presented by comparing the ultimate strength, stiffness, deterioration and failure mechanism. The cylinders tested at 28 days will be considered as control specimens, which consider the standard strength of the concrete (fc′ and fcc′) used in design equations, when studying the environmental effects. Also, the cylinders left in air inside the environmental chamber and exposed to the freeze–thaw cycles will be considered as control specimens when studying the effect of the surrounded medium on the cylinders behaviour. The experimental results of the environmental effects are reported in The control PC cylinders tested after 28 days from casting gave unconfined compressive strength (fc′) of 39.8 MPa, while the PC cylinders kept in air in the environmental chamber attained strength of 51.1 MPa. Note that, the specimens exposed to the environmental effects were tested after 7 months of casting. Hence, there was an increase in the unconfined strength due to hardening of concrete with time especially at the low temperatures of the freeze–thaw cycles, which agrees with the results of Callery et al. . Also, the figures show the minor difference between the results of the PC cylinders exposed to 200 freeze–thaw cycles and immersed in different solutions in the current study. After the freeze–thaw cycles and before testing, there were signs of deterioration on the concrete surface of some PC cylinders as shown in . The PC cylinders immersed in saline reported the worst surface deterioration rather than the specimens kept in alkaline. The deterioration of the specimens immersed in water was limited, while no deterioration was reported in the specimens kept in air. The PC cylinders failed under compression in a typical way with vertical cracks (see ) which occurred once the propagated tensile strength in the horizontal direction exceeded the allowable tensile strength of concrete.Unlike the PC cylinders, the results of the confined CFFT cylinders indicate slight reduction in the average ultimate compressive strength than the control confined specimen tested at 28 days as shown in . That means the environmental conditions exhausted the confining GFRP tube material which is the basic factor in the plastic hardening stage that governs the confined strength of CFFT cylinders. For example; the control CFFT column tested at 28 days failed at a confined compressive strength (fcc′) equals 126.2 MPa, while the CFFT cylinders exposed to freeze–thaw cycles and kept in air failed at f'cc equals 119 MPa with a reduction 6% in strength noting that these specimens were affected by a wide range of temperature from −34 °C to +38 °C.Keeping the CFFT cylinders in water and exposing to freeze–thaw cycles increased the confined strength by 2% more than those kept in air. This is attributed to the surrounded water medium partially isolated the specimens from the wide variation in the chamber temperature, where the recorded temperature inside the water tank varied from −12 °C to +14 °C. Also, the expansion of the frozen water around the specimens pressed them and acted as an active confinement on the specimens. The CFFT cylinders kept in saline reported the lowest confined strength (3% less than that kept in the environmental chamber air and 9% less than that tested at 28 days), which indicates the harmful effect of the salt solution on the FRP and concrete materials. The alkaline did not affect the CFFT cylinders, where their confined strength equals those kept in air.The primary stiffness (E1) of the CFFT cylinders seems to be not changed, because during the first stage the stiffness was depending mainly on the concrete rather than the FRP tube, and the inner concrete core is protected by the outer FRP tube. While the plastic hardening stiffness (E2) reported a clear decrease in its values, because at this stage the stiffness of the CFFT cylinders was depending on the outer FRP tube material which was attacked by the different solutions medium (see ). The saline solution reported the worst decrease in the plastic hardening modulus which was 8% and 11% lower than that of the control CFFT cylinders that kept in air and that tested at 28 days, respectively.In general, no deterioration on the FRP tube surface was observed (), which means a good resistance of such composite structure against corrosion and harsh environments. Also, all the CFFT cylinders failed due to rupture of the GFRP tube in the hoop direction. Popping sounds were heard during the early-to-middle stages of loading which were referred to the dilation of the inner concrete core, micro cracking of concrete, and offset of the aggregate. At higher load levels, the sounds were heard distinctly and the failure was sudden without warning. The ultimate failure was very explosive due to rupture of the fibres in GFRP tube, and the concrete fell out of the tube in a crushed state. See . Thus, one disadvantage of using the FRP tube is the difficulty in predicting when the ultimate failure of the CFFT specimen happens. Visual inspection of the surface failure showed evidence of matrix micro cracking and fibre-matrix de-bonding.The previous results concluded that the environmental conditions affected the confined CFFT cylinders more than the unconfined PC cylinders. Also the results indicated that the degradation in the strength and stiffness was more pronounced during the plastic hardening stage of the CFFT cylinders. Note that, the 200 freeze–thaw cycles conservatively represents a minimum of 6–7 years of outdoor exposure, and this period was calculated based on the geographic location, temperature and weather variations in Canada. Hence, the results will be used to predict the environmental effects on a structure service-life of 50 years by assuming a linear degradation with time for the plastic hardening modulus E2 of the CFFT cylinders. Also the strain will be kept at a constant level of 0.033, since the results pronounced no degradation in the axial strain εc, except for the CFFT cylinders kept in air (). The expected axial confined strength, at 50 years, was calculated by Eqn. , was taken as the unconfined compressive strength of the PC cylinders at the test time.The North American design codes/guidelines as ACI 440.2R-08 Where; ffu and εfu are the new design tensile strength and strain of FRPs, respectively, ffu∗ and εfu∗ are the guaranteed tensile strength and strain of FRPs, respectively, and CE is an environmental reduction factor. The value of CE depends on the fiber type (carbon, glass, aramid), exposure condition (interior or exterior), and the application of the FRP internally or externally to the concrete structure. The value of CE which corresponds to the current study is 0.65 as listed in ACI 440.2R-08 code. This value was applied in the confinement model of the three design codes to calculate the nominal confined concrete strength. Noting that the nominal values of fcc′ were calculated considering the material safety factor φFRP |
= 1.0, and considering the design limits in each model. lists the confinement model of the three codes. lists the expected experimental confined strength of the CFFT cylinders at 50 years old. Also, represent the comparison between the three codes models and the experimental results. indicates that the three codes are very conservative in case of the CFFT cylinders left in air or immersed in water and overestimate the expected service-life strength, however they are slightly overestimate the results in case of alkaline. But, the results pronounce a critical under estimation for the expected service-life results in case of the CFFT cylinders immersed in saline. The environmental factor CE is need to be reduced to be 0.5 to resolve the current under estimation in case of saline, or it is recommended to consider distinctly saline as an aggressive environmental parameter and be included in the category of chemical attacks in Table 9.1 in ACI 440.2R-08 This study presents an experimental investigation on the durability of unconfined plain concrete (PC) cylinders and confined concrete-filled FRP tube (CFFT) cylinders subjected to harsh environmental factors such as as immersing in water, salt, and alkaline solutions and exposing to freeze–thaw cycles. The cylinders were tested under pure axial compression tests to evaluate their axial performance. The main concluded points of this study are:Confining plain concrete cylinders with FRP composite tube improves significantly the ultimate compressive strength and ductility.Plain concrete cylinders confined by a 3.5 mm filament-wound GFRP tube exhibited a 150% and 1000% gain in strength and ductility, respectively, higher than unconfined cylinders.No deterioration on the FRP tube surface in the CFFT cylinders was recorded unlike the PC cylinders, which means a good resistance of such composite structure against corrosion and harsh environments.Salt solution pronounced the most critical degradation on CFFT cylinders. Where keeping CFFT cylinders in saline solution and exposing to 200 freeze-thaw cycles reduced the ultimate confined compressive strength by 9% less than the standards tested at 28 days.The FRP composite tube exhibited a good protection against alkaline.However CFFT cylinders were subjected to 200 freeze–thaw cycles (conservatively represents 6–7 years of outdoor exposure) and immersed in different mediums simulating harsh environments, the reduction in strength is limited which means that the FRP composites are qualified as a sustainable material.On the long term of service life of 50 years, the CFFT cylinders immersed in saline pronounced a critical reduction in strength, and so the design environmental reduction factor should be modified in North American codes.Positron annihilation lifetime spectroscopySynthesis and properties of antibacterial polyurethane with novel Bis(3-pyridinemethanol) silver chain extenderTo synthesize antibacterial polyurethane (PU) films, a novel chain extender, bis(3-pyridinemethanol) silver (BPDS), and a PU prepolymer were also synthesized through coordination and covalent reactions. The effects of incorporating different amounts of BPDS were investigated by characterizing the BPDS/PU films using various instruments: FTIR, TGA, DSC, DMA, XRD, EDX, universal testing machine, contact angle goniometer, and positron annihilation spectroscopy (PALS). With a higher BPDS content, the glass transition temperature, final degradation temperature, and Young's modulus were all enhanced; however, the tensile strength and elongation at break were both reduced. PALS analysis revealed that the more rigid and randomly packed structure of the BPDS/PU films at a higher BPDS content was characterized by a broader free volume size distribution that consisted largely of much smaller free volume holes. Quantitative tests with Staphylococcus aureus and Escherichia coli indicated excellent antibacterial properties, suggesting that the PU films could be used repeatedly.Positron annihilation lifetime spectroscopyPolyurethanes (PUs) are used in a host of applications, especially in the medical field. However, they are easily colonized by fungi and bacteria, which cause recurring infections in patients Researchers have patented their studies The silver ion is active against a broad spectrum of bacteria, and it has a low toxicity; thus, it is probably the most useful of the heavy metal ions shows the chemical reaction involved in synthesizing BPDS. shows the different samples of BPDS/PU, with their corresponding name representation; the amounts of MDI, PTMG, and BPDS; the hard and soft segment content. Equations were used to calculate the hard and soft segment content.Hardsegmentcontent(wt%)=WMDI+WBPDSWMDI+WPTMG+WBPDS×100%Soft segment content (wt%) = 100% – Hard segment content (wt%)where W refers to the weight of each of the following substances (written as subscripts): MDI, BPDS, and PTMG.A Bruker Avance 300 spectrometer (300 MHz) was used for the sample's 1H NMR and 13C NMR spectra. With the use of a PerkinElmer spectrometer (model Spectrum One), the Fourier transform infrared spectra of the samples were obtained by averaging 15 scans in the wavenumber range of 4000–650 cm−1 with a resolution of 2 cm−1. (XPS, Thermo Scientific, K-Alpha) were used to characterize the surface composition of the PU/BPDS films.Thermogravimetric analysis was done using a PerkinElmer TGA (model Pyris 1). Samples (8–10 mg) were heated from 25 to 700 °C under nitrogen at a rate of 10 °C/min.Differential scanning calorimetry was performed on a PerkinElmer DSC (model Jade). Each sample was sealed in an aluminum pan. Scans (−100–80 °C) were made with a heating rate of 10 °C/min under nitrogen purging. The maximum peak in the second scan of the endothermic transition was recorded as the melting point. Samples of 7–8 mg were used for all tests.Dynamic mechanical analysis was conducted with a tension mode, using a TA DMA (model Q800) at 1 Hz with a 5 μm amplitude over a temperature range of −80 to 100 °C and at a heating rate of 3 °C/min. The sample dimensions were 20 mm × 5 mm × 0.2 mm (length × width × height). The peak temperature of the glass transition region in the tan δ curve was taken as the glass transition temperature.The average viscosity of each BPDS/PU solution, depending on its BPDS content, was measured using a Brookfield viscometer (model DV-E).Wide angle X-ray diffraction was obtained by using a Rigaku diffractometer (model RU-H3R). An X-ray beam based on a Ni-filtered Cu Kα radiation from a sealed tube was operated at 60 kV and 300 mA. Data were collected in the 2θ range of 10°–80° with a scanning interval of 0.04°.With the use of an energy dispersive X-ray (model 7021-H Horiba EDX), the silver content and distribution in the samples were obtained. Gold-plated samples, with dimensions of 1–2 mm2, were placed in the EDX chamber operated at 15 kV.Tensile strength and elongation at break were measured using a universal testing machine (model Q Test 5), following the ASTM procedure. A sample had a dimension of 45 × 8 × 0.2 mm3.The antibacterial activity of the BPDS/PU films was tested against either of the following aerobic bacteria commonly found on burn wounds: Staphylococcus aureus and Escherichia coli. Qualitative and quantitative tests were employed. The qualitative test was the so-called disc diffusion method of the US Clinical and Laboratory Standards Institute. BPDS/PU films were cut into circular discs, 15 mm in diameter. Each sample was placed on a Difco Mueller Hinton agar in a Petri dish, and then the microbes therein were incubated at 37 °C for 24 h. If inhibitory concentrations were reached, there would be no growth of the microbes, which could be seen as a clear zone around the sample discs.For the quantitative test, each BPDS/PU film was inoculated with a suspension (0.1 mL) at 30 °C for 0.5 h. The film was transferred to a sterile physiological saline solution, after which it was shaken and washed for 15 min in an aqueous bath. Then, the suspension of bacteria was diluted with a sterile physiological saline solution and was inoculated onto a sterile Petri plate. The plate was then incubated at 30 °C for 24 h. Finally, the grown colonies were counted.CA measurements, using deionized water on the sample, were recorded by a Face instrument (model CA−VP150). The CA reported was the average of values for 3–4 water drops.PALS is a powerful tool that probes the free volume properties of polymers. BPDS/PU films were cut into 10 mm × 10 mm pieces, which were piled up to form a stack 1 mm thick. A radioactive source (20 μCi of 22Na), sealed in a 12 μm thick Kapton film, was sandwiched between two stacks of the BPDS/PU films. The emitted positrons were implanted into the films and were annihilated in the surrounding material, resulting in the release of two gamma rays, each with an energy of 0.511 MeV. A fast–fast coincidence timing system recorded the time difference between the emission of the initial gamma ray of 1.275 MeV during the positron formation and the emission of the final gamma ray of 0.511 MeV during the positron annihilation. Two million counts were collected in each PAL spectrum; the detailed procedure was described in a previous report where y(t) is the experimental lifetime decay data, R(t) is the instrument resolution function, Nj is the normalized count, αjλj is the jth component's intensity, λj is the inverse of the jth component's lifetime, t is time, and B is the background.A positron annihilation technology fitting (PATFIT) computer program The lifetime distribution was determined by using a Maximum Entropy for Lifetime (MELT) computer program where ΔR is an empirical parameter (1.656 Å), determined by fitting well-known cavities is valid for estimating free volume hole sizes for o-Ps lifetimes less than 10 ns. The relative fractional free volume (FFV) can be estimated from Eqs where N3 corresponds to the hole density of the ο-Ps pick-off annihilation lifetime τ3 and was calculated according to Shantarovich and Goldanskii We synthesized BPDS according to the chemical reaction given in . Data from the following verify its synthesis: NMR spectra in a), we identified the following peaks—δa: 8.65 (d, 1H, aromatic Hb); b: 8.55 (d, 1H, aromatic He); c: 7.98 (d, 1H, aromatic Hc); d: 7.56 (q, 1H, aromatic Hd); e: 4.70 (s, 2H, CH2 Ha). From the 13C NMR spectra (b), we identified these peaks—δa: 151.50 (1C, aromatic Cb); b: 140.60 (1C, aromatic Ce); c: 138.53 (1C, aromatic Cd); d: 126.57 (1C, aromatic Cc); e: 62.32 (1C, aromatic Ca).a indicates the characteristic absorption peaks of BPDS: hydroxyl group (−OH) at 3366 cm−1; the pyridine ring C–N–C stretching vibration at 1602 cm−1 and 1040 cm−1; the pyridine ring C–H bending vibration at 832 cm−1. b shows the spectra of different BPDS/PU films, synthesized by varying the amounts of BPDS (see for the reactions involved). These spectra reveal similar peaks that correspond to the following: –NH stretching vibration at 3288 cm−1; hydrogen-bonded CO group of the ester group in PU at 1729 cm−1; CC resonance absorption peak of the benzene ring at 1596 cm−1; bending vibration of –NH group at 1534 cm−1; characteristic C–O linkage of the ester group at 1219 cm−1. However, the intensities of the peaks differ. For example, the intensity of CC is greater at higher BPDS content. At 2240–2275 cm−1, the peak corresponding to the free –NO group does not appear because, during the process of synthesizing BPDS/PU, the prepolymer terminal NCO completely reacted with the OH of the BPDS chain extender. shows the XPS spectra of BPDS/PU films. These spectra show the major peaks for Ag 3d5 (368.4 eV), Ag 3d3/2 (374.4 eV), N1s28, and C1s (286 eV). The binding energies for Ag electron configurations of 3d5 and 3d3 are respectively 368.4 eV and 374.4 eV (a difference of 6.0 eV). These values are also indicated in the literature demonstrate the effect of the BPDS chain extender on the thermal behavior of the BPDS/PU films. reports the thermal degradation temperatures obtained from the TGA curves. Tonset represents the temperature at which the degradation of each film starts.The Tonset values tend to decrease with the increasing amount of BPDS because of the weak coordinate bonding in BPDS. As the BPDS content increases, the coordinate bond effect dominates that of the covalent bond in BPDS/PU; at Tonset, therefore, the resistance to degradation decreases. The degradation temperature at 5% weight loss (Td5wt%) indicates a similar trend.Tend is the temperature at which the maximum weight loss occurs. In contrast to Tonset, Tend increases with higher amounts of BPDS. Coupling effects dominate at high degradation temperatures, as evidenced by the high levels of the material coupling density ) indicate an increasing trend. This result indicates improvement in the polymer heat resistance at higher temperatures (380–420 °C) when the amount of the chain extender increases (from BPDS/PU-01 to BPDS/PU-04). shows the DSC thermograms of the BPDS/PU films. The second column in lists the glass transition temperatures (Tg) based from . At higher content of BPDS, the molecular chains are harder to be disrupted, because the hard segment content of BPDS/PU is also higher as a result of more coupling between the chain extender and the main chain. As such, Tg increases plots the data on tan δ (a) and loss modulus (b) of the BPDS/PU films as a function of temperature, with varying amounts of BPDS as a parameter. The presence of the BPDS chain extender prevents the BPDS/PU polymer chains from being disrupted. Consequently, Tg increases with the amount of BPDS (). The Tg values from DMA were taken at the peaks of the DMA tan δ and loss modulus curves. Similar results were reported in our previous study Within the main peak of 2θ = 20°, the XRD curves of the BPDS/PU films () show broad diffraction patterns, indicating the existence of an amorphous phase. However, the diffraction peak intensities are not the same: 1792, 1186, 800, and 734 a.u. for BPDS/PU-01, BPDS/PU-02, BPDS/PU-03, and BPDS/PU-04, respectively. The film with the highest diffraction peak intensity (BPDS/PU-01) exhibits a relatively sharp peak, which is characteristic of a crystalline phase. This diffraction pattern does not mean that a crystalline or quasi-crystalline morphology is attained; rather, the polymer chains in BPDS/PU-01 are relatively less random. With higher BPDS content, the length of the polymer chains varies. This condition is due to the nonlinear structure of BPDS, which does not favor regular packing of polymer chains.The XRD diffraction patterns of the BPDS/PU films also show minor peaks at 2θ = 38°, 42°, 64°, and 77°, which correspond to the crystallographic planes or Miller indices of (111), (200), (220), and (311) of the Ag crystal in the films shows the stress–strain curves for the BPDS/PU films containing different amounts of BPDS; summarizes the corresponding tensile properties. Incorporating more amounts of BPDS results in lowering the maximum stress, tensile strength, and strain at break; this trend is ascribed to the weak Ag coordinate bond in the BPDS chain extender. However, the Young's modulus is enhanced with increasing BPDS content; the Ag complexes present in the chain extender, which are rigid, restrict the movement of the molecular chains.For the BPDS/PU films, the zone of inhibition toward S. aureus and E. Coli increases with the BPDS content (); furthermore, the sterilization or antibacterial rate at 30 °C and 0.5 h also increases. The BPDS chain extender does provide an antibacterial effect. However, the case of BPDS/PU-01, in which only a small amount of BPDS was incorporated, implies low antibacterial activity, because it fails to create a zone of inhibition in the lawn of bacterial growth, either toward S. Aureus or E. Coli. With a higher BPDS content, the synthesized films demonstrate excellent antibacterial properties, as the zone of inhibition grows significantly. The film's excellent antibacterial activity implies that it could likely be used repeatedly On the basis of the increasing Ag content of the BPDS/PU films (, last column), the antibacterial effect also increases. Toward both S. Aureus and E. Coli, the antibacterial ratio for the BPDS/PU film is less than 86% when the Ag content is below 7.17%; but at such Ag content, the antibacterial ratio becomes very high, reaching 99.8%. illustrates the distribution of elemental Ag as a function of the increasing BPDS content; lists the antibacterial activity of the BPDS/PU films and their Ag content. The white spots in the images represent Ag, which is uniformly distributed in the films. As expected, the distribution of Ag becomes concentrated as more amounts of BPDS were incorporated. The above discussion demonstrates the excellent antibacterial properties of the BPDS/PU films, and these properties are attributed to the presence of Ag and its even distribution in the films., the photographs depict contact angle measurements for the BPDS/PU films, and the obtained data are represented as a bar graph. Relative amounts of BPDS and PTMG were varied to synthesize different BPDS/PU films, with their total amount maintained constant at 4 mol (). The BPDS pyridine units are hydrophobic, so when the relative mole ratio of BPDS to PTMG increases, the contact angle for the synthesized film also increases, which means that the film is less hydrophilic (CA < 90°). Furthermore, with increasing amounts of BPDS, the obtained BPDS/PU film becomes more densely packed because of the enhanced coupling or entanglement of the molecular chains. This condition results in creating more hard segments in the film; the packed structure probably intensifies the film's increasingly less hydrophilic property. The film with the highest BPDS content (BPDS/PU-04, the BPDS to PTMG mole ratio = 1:1) exhibits the highest contact angle, indicating that it is the least hydrophilic. tabulates the free volume characteristics of the BPDS/PU films, which were determined from the three-component analysis using the PATFIT routine. shows the o-Ps lifetime distribution for the films, which was obtained using the MELT analysis. In , the range of the free volume data is wide: the free volume radii (3.50–2.88 Å) are calculated from the τ3 data (2.82–2.02 ns), and the free volume concentrations (similar to FFV, 5.88–2.52%) are related to the I3 data (18.12–14.05%). A similar range of τ3 (1.7–2.9 ns) and I3 (18–28%) for the PU samples has been reported The BPDS chain extender reacts with the PU prepolymer through covalent bonding, and they form coupling with each other. Increasing the BPDS amount relative to PTMG intensifies the extent of the coupling; hence, a more densely packed structure is formed. This dense structure and the presence of BPDS constitute the hard segments in the synthesized BPDS/PU films. The soft segment content depends on the relative amount of PTMG. If the hard segment content dominates the soft segment, then that condition reduces the film's chain mobility.The o-Ps lifetime or τ3 is related to the rates of chain relaxation and mobility in the hard and soft segments of the BPDS/PU films. Hard segments have high packing densities and low free volumes; soft segments exhibit low chain packing densities and high free volumes indicate that the free volume radius decreases with increasing BPDS or hard segment content, a condition in which the chain packing structure becomes denser. This morphology induces a higher Tg (). Moreover, the smaller free volume radius and FFV data at higher BPDS content provide a plausible explanation for the BPDS/PU films' mechanical properties.) indicates a broad distribution of the free volume sizes in the BPDS/PU films. The distribution curve's full width at half maximum (FWHM) indicates that the higher the BPDS content, the broader the free volume distribution. The FWHM values range from 0.973 ns (for BPDS/PU-01) to 1.446 ns (for BPDS/PU-04). The film with the highest BPDS content (BPDS/PU-04) consists of much smaller free volume sizes, but it exhibits the lowest average free volume radius. These free volume characteristics are revealed for the most randomly arranged polymer chains in the BPDS/PU-04 film (according to the XRD patterns in BPDS/PU films were synthesized from a PU prepolymer and a novel BPDS chain extender containing a silver complex. Both reacting materials were also synthesized: BPDS was from a coordination reaction between 3-PDM and AgNO3; the prepolymer was from a covalent reaction between MDI and PTMG. The structure of BPDS and BPDS/PU was confirmed by 1H NMR, 13C NMR, and FTIR spectra. WAXRD patterns showed that the BPDS/PU films were amorphous. With increasing BPDS content, the Tg and Young's modulus of the BPDS/PU films were both raised; however, the initial degradation temperature, tensile strength, and strain at break were all lowered. The films were less hydrophilic when more amounts of BPDS were incorporated, as indicated by the increasing contact angle. Furthermore, the films exhibited excellent antibacterial activities toward S. aureus and E. coli; the antibacterial rates increased at higher BPDS content. With increasing mole ratios of BPDS to PTMG, PALS analysis correlated the denser packed structure and lower mobility in the BPDS/PU films with the lower free volume size and broader free volume size distribution.The authors declare no competing financial interests.Mechanical properties of TiN ceramic coating on a heat treated Ti-13Zr-13Nb alloyIn this paper, mechanical properties of TiN coatings deposited on Ti–13Zr–13Nb alloys prepared by filtered arc deposition were analyzed. The influences of different heat treatment on the abrasion resistance of the substrate were studied, with regards to the coating properties, microstructural features, mechanical properties and the deformation mechanism using wear test and depth-sensing nano-indentation. According to the analysis, the microstructure and enhanced mechanical properties of the alloy substrate play a vital part in affecting the tribological properties of coatings. Parallel scars with patches of surface deformation in TiN coatings on air cooled and water quenched specimens after tribological test are obviously different from those of furnace cooled and aged water―quenched samples. Transformation of β phase into α” phase was triggered by the aging heat treatment, and it was found to be the inducement resulting in the increase of hardness in the substrate. The results show that the aging of the substrate can effectually inhibit the fault activities of the TiN coating and improve the absorption of deformation energy at the surface of the sample, which enhances the coating ductility.The TiN coating on the harder substrate could effectively suppress the fracture activities and absorb the deformation energy, improving the ductility and adhesion of the coating.Act as hard tissue replacements, titanium and its alloys are extensively applied in applications of biomaterials, human implants and other aspects, owing to their high strength to low Young's modulus, weight ratio, superior corrosion resistance and biocompatibility. As the population is aging in most countries, accidents and sports-related injuries are increasing, and hence, the demand for orthopedic implants is ever-increasing. Titanium alloys are categorized as α, near-α, metastable β, stable β, or α+β relying on the microstructure at the room temperature On the other hand, as the release of ions from the implant into the surrounding tissue may cause the biocompatibility problems, the corrosion behavior of alloys must be checked to verify the applicability of a material used for body implants. Viswanathan S. Saji. et al. To enhance the biocompatibility of Ti-13Zr-13Nb alloys, the surfaces treatment to obtain protective coating were often considered using chemical, laser surface modification, ion implantation, plasma spraying, etc. TiN coatings were deposited on Ti-13Zr-13Nb disks of a diameter of 25 mm. Two types of the alloys status were conducted: a) through different ways of heat treatment; b) as received (β solution handled by manufacturer)—set as sample NO.3. The specific treatment is as follows:The alloy phase composition and surface observation were carried out by X-ray diffraction (XRD) and scanning electron microscopy (SEM), respectively.To ensure a uniform deposition surface for the TiN coatings, all the Ti-13Zr-13Nb substrates were polished by the same process before the deposition. Disk samples were polished with a 320 mesh carborundum sandpaper for 4 min, and then the samples were milled using a 15 μm petroleum-based lubricant diamond abrasive for 10 min. The samples were polished for 5 min with an abrasive of a 0.05 μm particle size and a chemical reagent which consists of 25 ml OP-S containing 1.5 ml hydrogen peroxide and 2.5 ml ammonia. Before coating these samples in a Filtered Arc Deposition System (FADS System), all the specimens were submerged in ethanol for a few minutes of ultrasonic cleaning and then dried. After that the FADS system was used to deposite the TiN coating on the polished disk substrates. The pressure of deposition chamber was adjusted to a base vacuum of 6.67 × 10−4 Pa. The substrates were preheated to 300 °C in vacuum, and then the samples were dry etched in-situ using pure titanium ion beam at −850 V high substrate bias. The bias voltage was decreased to −100 V at the beginning of the coating process. During the experiment, a pure titanium buffer layer was deposited on the Ti-13Zr-13Nb substrate, and the working gas of nitrogen was then introduced into the chamber through a mass flow controller with gradual flow rate increase and a final flow rate of 40 sccm to decrease residual stress and enhance adhesion between the substrate and the film. During the deposition process, to avoid the influence of the coating process parameters on the film properties and to ensure a uniform experimental conditions, five Ti-13Zr-13Nb substrates after different heat treatment were deposited on a same disc-shaped stage and the disc was kept revolving at a constant speed during the experiment. The nitrogen working gas pressure was 0.39 Pa. The coating process lasted for 2 h to achieve a film thickness of 1.4 μm.After these, scratch testes were carried out on a scratch tester (CSM, Revetest Xpress) by using an indenter to scratch reactant films to detect the critical load at which TiN coating starts to fail (cracking or removal). The acoustic emission and friction force can be measured synchronously by the apparatus. In order to ensure the accuracy of experimental analysis, five repeated scratch tests were performed on each test specimen to obtain the result of measurements.Tribological tests were performed by pin-on-disc tests on CETR tribometer. In the component of a pin-on-disc, the pin indicated HSS grade material and the disc represented a strip Ti alloys. The pin is designed to mushroom shaped of a radius of 8 mm hemispherical end. Technological conditions of tribological tests are shown in . The choice of Hertz pressure in test parameters was usually relatively mild and approach to the actual hot-rolling environment, which makes it easy to monitor the behavior of antagonistic oxide scales in the contact region without damaging them too quickly After tribological tests, the profile measure of TiN coatings are determined using a Roughness tester of Surf M300 and the weight loss of wear tracks are evaluated. In addition, the weight change of samples were measured by an electric balance with a precision of 0.1 mg made in America (Seen the below Nanoindentation on the TiN coating was made for evaluating coating deformation using the Ultra-Micro Indentation System (UMIS). Coating hardness on Ti-13Nb-13Zr alloy was measured by a Berkovich indenter of a 200 nm radius. Restricted by thermal drift, the resolution in experiment was less than 1 nm/min. The tip was primally calibrated by fused silica as a standard material. Loading and unloading tests of incremental control were within a scale of 3–9 mN to confirm coating hardness. Fracture patterns of TiN coatings were detected through a spherical diamond indenter of a diameter of 5 μm. Since the spherical indenter can result in a more evenly stress field underneath the contact region than the pyramidal pointed indenter, a spherical indenter was putted to use in this fracture study. Test loads in the experiment were set at 160 mN, 260 mN and 360 mN respectively, and the loading-unloading rate of indentations was set at 200 μN/s uniformly. Thin foil samples used to observe TEM morphology were prepared by AFEI XT Nova Nanolab 200 workstation which covers a combination of dual beam Focused Ion Beam (FIB) and a Field Emission Scanning Electron Microscope (FESEM) The XRD patterns and microscopic structures of Ti-13Zr-13Nb alloy substrate treated in different methods are presented in . The substantial coarsening of α lath generated in the furnace cooled specimen presented woven structure consisting of numerous variants of α lath within prior β grains (b). Sample under the condition of air cooling showed fine α–β texture within pre-existing α grains (c). Compared to the two substrates with cooled in the furnace or air, the as received sample showed a subtle scale microstructure of basket weave type. These are typical structures of titanium alloys with β solution treated. As can be seen from the XRD results of a, the air cooling specimen presents α phase with a weak diffraction peak of α” phase notably, and the as received and furnace cooling samples show α phase with a weak β phase peak. Analogous microstructures were observed at relatively fine scales when the samples were water quenched and “water quenched + ageing” from the above condition (e and f). Based on the XRD results, two disperate kinds of martensitic structure i.e. α (hexagonal) and α” (orthorhombic for NO.2 and NO.4) are seen in titanium alloys according to the alloying element content of β. Higher alloying content of β is advantageous to form α” martensitic over α Surface micrograph of TiN coatings on Ti-13Nb-13Zr alloys with different heat treatment under the same deposited conditions are shown in . The tribological test for TiN coatings by a pin-on-disc test were carried out at a normal load of 10 N and sliding speed of 50 mm/s, and the corresponding friction coefficient curves are given in shows the SEM images of pin wear track of the TiN coatings after 1 h tribological test under the experimental technological condition. Among all the specimens with heat treatment in this condition, no significant variation of surface micrograph of TiN coatings was observed. In the case of samples treated by tribological test at a constant load of 10 N, however, the wear surfaces of samples NO.1, NO.3 and NO.5 were found deep parallel scars. This may be triggered by pull-out of stiff particles phase leading to the three-body abrasive wear. Although the interface between TiN coating and Ti alloy substrate can be seen distinctly, there are no visible micro-pores and cracks at the interface, thus the bond between the coating and the substrate is strong. For the samples of NO.2 and NO.4, parallel scars with surface deformed patches were observed. The specimens wear debris were mostly irregularly shaped particles with extremely sharpened edges. Moreover, no visible micro-pores and cracks at the interface are seen. This can be associated with the higher amount of α” phase in Ti alloys, which is conducive to the increase of the hardness of the titanium alloys substrates (Seen the below presents the friction coefficient curve of substrate and TiN coating in typical tribological test. As can be seen from the figure, the friction maintained stability in the very beginning of the test and the friction coefficient of substrate and TiN coating remained at approximately 0.45–0.55 and 0.48–0.58, respectively for the most of the test period. As evident from , there are two marginal changes within each set of date due to the variation of friction coefficient curves, meaning that three tribological stages considered in the pin-on-disc test a, no significant variation of friction coefficient related to disparate heat treatment conditions was obtained except for the air cooled sample of NO.2 that it presented a slight higher in the same testing period. Compared with the friction coefficient of TiN coatings with different heat treatment conditions, stage II time (the second interrupted test) of all samples with TiN coatings on the heat treated alloys increased substantially in the testing period and it increased further to around 1600 s from the start of the test, especially for the air cooled sample of NO.2. However, for the samples treated with water quenched and “water quenched + aging”, Stage I time (the first interrupted test) of the TiN coating showed higher friction coefficient than other samples. In the case of samples for Stage III, no substantial variation in the friction coefficient after disparate heat-treated methods was observed in any media.To further investigate the relationship between weight loss and tribological test of the coatings or substrates, a profile measure of TiN coating after tribological test is obtained (, in the five samples of the experiment, the width of wear track of NO. 2 is the narrowest and the depth of wear track of NO. 4 is the shallowest. Therefore, weight loss of samples NO.2 and NO.4 are calculated to be small, meaning those being good wear resistance. This is consistent with the weighing results in that the weight loss of NO.2 is the smallest and followed by NO.4.The above-mentioned tribological test characterized wear properties of TiN coatings under a constant force. While, there is also a necessary link between wear resistance of coatings and magnitude of force required to break the coatings. In this part, wear resistances of TiN coatings are studied from the perspective of variable force. All of the experimental data of acoustic emission (AE) and friction force are given in demonstrates the micrograph of failure on TiN coatings after scratch tests. On the surface of Ti-13Zr-13Nb alloys for sample NO.1 (a), it is found clearly that as the increase of friction force, the acoustic emission suffered a saltation under a low load conditions of 23,800 mN, indicating that the TiN coating appeared to fail at a load of 23,800 mN. According to the result of sample NO.2 in b, by increasing the friction force, the critical load at which break appears showed a abrupt increase and reached to 48,900 mN. This manifests the specimen of NO.2 (air cooled to room temperature) has a superior resistance to wear than the NO.1 (furnace cooling to room temperature). And that critical load of NO.2 is the maximum of all samples. Scratch test of the NO.3 (as received specimen) surface is presented in c. As can be seen in the diagram, TiN coating of this sample was obviously fail at 25,800 mN, illustrating that in this load the coating seems to have broken. For the coatings deposited on titanium alloys, with the water quench treatment, the value of broken load are relatively high, the specimen of NO.4 was 48,100 mN and the NO.5 reached to 47,700 mN, respectively. The corresponding optical images in d and (e) indicate that under the same water quench environment, the coating of NO.4 specimen with no ageing condition shows better wear resistance ability in scratch test than sample NO. 5. The result is consistent with the above tribological test, indicating that when more force are required to damage the coatings, the wear resistance characteristic of coating's surface to abrasive wear is stronger, and the wear resistance of coating is much better.Wear mechanisms acts a pivotal part in tribological applications, especially in enhancing wear resistance of titanium alloys and restraining environmental degradation. To best investigate the wear mechanisms, studies regarding deformation of the substrate or coating are elucidated. Test loads in the experiment were set at 160 mN, 260 mN and 360 mN respectively, while the results showed that when the test load was too large the alloy substrate would be destroyed, and when the test load was too small the TiN coating could not be deformed or be fractured. As the experiment aims to study the mechanical properties of TiN coatings, the load of 360 mN is the most suitable value. Therefore, only the experimental results of 360 mN load are discussed here.Cross-sectional images of TiN monolayer deformation triggered by the indentation (Selected two samples with different performance for NO.2 and NO.3) are shown in . As shown in the images, thickness of the TiN coating of NO.2 and NO.3 obtained by coating process are substantially the same, both between 1.4 μm and 1.5 μm, and similar edge cracks were found in both coatings with or without heat treatment. On the TiN coatings of sample NO.2, a certain amount of cracks were seen, and most cracks observed in TiN coatings adjacent to the substrate were present in the form of edge cracks b). Compared to sample NO.2, more intensive cracks were distributed in specimen edges of sample NO.3, the intercolumnar shear sliding increased significantly in sample NO.3, and the spacing of step-like rupture at the interface of the TiN coating or substrate was significantly reduced and crack spacing was more intensive. Different deformation process began to occur to consistent with the strain at the two kinds of samples. Cracks were mostly found in the edge of coating or interlayer interface, which are probably caused by the stress concentration in some local areas. Once activated, the edge cracks will propagate on a wider scale and intergranular shear slippage and plastic flow of the titanium interlayers seems to be the primarily factors leading to the coating deformation summarizes the curves of load-penetration depth for TiN coatings, and specific depth results are manfested in b, c, d, e and f. It can be seen in these figures that as increasing the indentation load on TiN coatings, a sudden rupture occurs, indicating the occurrence of pop-in behavior. In addition, pop-in events occurred in sample NO.1, NO.3, NO.4 and NO.5, while no pop-in event was observed for sample NO.2. With the increase in indentation load, more pop-ins can be found in TiN coatings and the pop-in event is mainly caused by the stress-induced plastic deformation Deformation of TiN coatings cannot be separated from the hardness of substrates and coatings. Vickers hardness values of the alloy samples are measured under an experimental force of 500 g, and the average measurement results are shown in As the displacement function associated with the coating thickness or substrate, hardness values of TiN coating and Ti–13Zr–13Nb alloy substrate with heat-treated or not (Selected two samples with different performance for NO.2 and NO.3) are measured through a depth-sensing indentation system. Hardness has a certain influence on the indentation depth. In general, a higher hardness results in a lower indentation depth . From results of the figure, it can be seen that hardness and normalized indentation depth show a negative correlation in the load-penetration process, i.e. the measured hardness for Ti alloys and TiN coatings decrease with increasing indentation depth. The evident increase of hardness at an extremely small indentation depth is chiefly put down to an uninterruptible growth in elastic strain resu1lted from the spherical-tipped indenter. It is reasonable to consider that distinct scatter in individual measures may be associated with the influences of at least two factors , the hardness of specimens are greater and degree of deformation are smaller. Compared with the other four samples, the hardness and critical load (at which break appears) of No.2 are the largest, and weight loss and deformation degree in tribological or deformation test are the smallest. Thus, harder substrates can provide greater support to ceramic coatings and need more external load to break coatings in terms of its favorable resistance to ductile deformation. In a word, the above results explain that harder substrate or TiN coating requires more energy to promote a crack nucleation than that of as received Ti alloys when the two coatings under the same stress.Compared to the as received substrate specimen, the coarsening α lath in furnace cooled or air cooled specimens were found after solution treatment from 760 °C. The water quenched specimen gave rise to growth of a relatively fine scale microstructure.For furnace cooling, as received and “water quenched + aging” specimens, deep parallel scars were found in the wear surfaces. This may be triggered by pull-out of stiff particles phase leading to the three-body abrasive wear. While for air cooling and water quenching specimens, parallel scars with patches of surface deformation in TiN coatings were observed after tribological test. This can be attributed to the heat treatment leading to a transformation of β phase into α” phase.In the pin-on-disc test, the stage II starting time (the second interrupted test) of the friction coefficient curve of TiN coating on the air cooled sample is the longest around 1600 s from the start of the test, leading to the smallest weight loss among all substrate heat treatment conditions.The critical load at which break appears on TiN coatings of NO.2 after scratch tests is the maximum and reaches at 48900 mN, indicating that the air cooling specimen has a superior resistance to wear than others. Compared to sample NO.2, more intensive cracks were distributed in specimen edges of sample NO.3, and the intercolumnar shear sliding increased significantly in sample NO.3.The air cooling specimen has a better hardness and favorable wear resistance than others at same indentation load with no pop-in event occurs in TiN coatings. The increase in Ti-13Zr-13Nb substrate hardness is thought to be caused by the transformation of β phase into α” phase after the heat treatment. And a harder substrate effectually inhibits the fracture activities of the TiN film on top of it and improves the absorption of deformation energy, enhancing the coating ductility and adhesion.A new peeling mechanism of blisters involving surface diffusionA peeling mechanism exclusively driven by surface diffusion has been experimentally observed for the oxide layer covering circular buckles appearing on the free surface of implanted silicon samples when internal pressure resulting from implantation is present below the buckles. A theoretical analysis by means of a chemical potential calculation has been also performed and the possibility for the blisters to peel by a new mechanism has been analysed as a function of pressure. |
Light-ion implantation in elementary semiconductors results in the formation of specific defects at the nanometer scale Si(1 0 0) wafers were first implanted at room temperature and at 15 keV by hydrogen ions at a fluence of 5 × 1016 |
cm−2. Under these experimental conditions, the maximum hydrogen concentration was estimated from SRIM calculations to be located at a depth of 250 nm from the free surface. The Si wafers were then air annealed at 200 °C using a Peltier heater interfaced with an atomic force microscope. The kinetic evolution of the Si-free surface during annealing is displayed in , the scan size of each signal error mode AFM image being 20 × 20 μm2. As previously mentioned in the literature, the implanted silicon surface exhibits circular blisters homogeneously dispatched over the scan area (a) and the thickness of the buckled structures corresponds approximately to the depth of the implanted hydrogen ions. It should also be underlined that the maximum deflection of the blister has been found to be two decades smaller than its radius. At the critical annealing time, small cracks were observed to appear on the buckled structures (see the α blister in b). At this point, it was noticed that a native silicon oxide layer had grown on the sample surface during the annealing process under air. As usual, such an oxide layer is homogeneous, and is only a few nanometers thick. It is believed that the increase in internal pressure in the cavities due to the hydrogen diffusion results in the cracking of the oxide layer, which can no longer accommodate the high level of elastic deformation. The oxide layer is then progressively peeled from the nanocracks located at the top of the blisters to the blister circumferences. After more than 100 h, all the blisters have consequently undergone a complete peeling, as can be observed in d. The time evolution of the profiles of the characteristic α blister (in . As expected from the FvK theory, the blister profile is defined well by an analytic function ). The kinetics of the peeling is found to slow down as the front propagates towards the buckle boundary. At the final stage of annealing, an almost complete peeling of only 3 nm is finally observed for the oxide buckled layer.It is believed that the nanocracks generated through the native oxide layer play the role of precursors that activate the experimentally observed peeling mechanism. This peeling mechanism of the oxide layer was investigated theoretically by considering the hypothesis where the blisters under pressure can be assimilated under stress (resulting from the internal pressure) into thin planar delaminated layers composed of a layer of silicon and a layer of its oxide (see ). This approximation is assumed to be relevant in qualitatively describing the peeling for blisters of low curvature. The difference between the elastic coefficients of the oxide and silicon layers has not been taken into consideration for the sake of simplicity, and the Young modulus E |
= 170 GPa and Poisson’s ratio ν |
= 0.27 of silicon have been used for both layers. An axisymmetrical thin layer of thickness h delaminated on a circular area of radius b which results from the propagation of a penny-shaped crack in a given solid is thus considered in with ϵ0 |
= (1 − |
ν)σ0/E and ϵrr(i)=(1-ν)σ0(i)/E. The condition whereby the delaminated area between the layer and the solid is assumed to be constant during the mass transport process, the buckle being clamped at its edge, is expressed in Eq. . The equilibrium of forces in the plane of the film is satisfied through Eq. . The elastic strain and stress fields were thus determined with the help of Eqs. in both parts of the layer, and the elastic energy stored in the layer was determined to be:Fel=π(1-ν)σ02Ehb2(h-t)b2(h-t)+c2tb(h-t)+ct2In order to characterize the peeling mechanism when diffusion is activated onto the free surface of the layer, the chemical potential for the diffusing atoms is expressed taking into account the elastic energy given in Eq. and the surface energy of the notch. The chemical potential is defined as:with γ the surface energy per unit surface and Ω the atomic volume. Using Eq. with del=Eγ/[(1-ν)σ02] a characteristic length and μ0 |
= Ωγ/del. At this point, it can be underlined that, since the chemical potential expressed in Eq. depends only on σ02, the following analysis may apply to layers submitted to compressive or tensile stress. In order to determine the conditions under which the peeling mechanism is activated, the reduced chemical potential μth/μ0 was plotted as a function of c in a for increasing values of stress σ0, with the parameters E |
= 170 GPa, ν |
= 0.27, γ |
= 1.4 J m−2 characteristic of silicon. Taking b |
= 1.6 μm and h |
= 250 nm, it can be observed in a that, depending on the stress, μth can be positive for c |
∈ [1, |
cmax] such that the peeling can be activated, with cmax the maximum value of the notch width beyond which the peeling should stop. The evolution of this maximum value cmax vs. σ0 is finally displayed in b. It can be observed that cmax increases with σ0, which demonstrates again the key role of stress on the oxide layer evolution. Since the pressure inside the cavities has been found to generate a tensile stress field in the buckled layer of the order of a few hundred megapascals, it can finally be argued from our model that the increasing pressure inside the cavities during the thermal heating is at the origin of the almost complete peeling of the blisters experimentally observed. Moreover, it can be emphasized that the theoretical increase of the stress when cmax reaches the buckle radius b is in good agreement with the experimental results evidencing a slowing down of the peeling phenomenon.In this letter, the peeling of a native oxide layer characterized by in situ atomic force microscopy observations during thermal heatings of irradiated silicon samples has been explained through a chemical potential calculation. It has been demonstrated that this new peeling phenomenon, starting from nanocracks located at the top of the blisters and propagating until the blister circumferences are reached, is activated by the stress inside the buckled layer, which results from the pressure in cavities. It is believed that this study raises several fundamental problems, including the initial cracking of the superficial oxide layer and the kinetics of the peeling phenomenon of the oxide layer and also of the silicon sample. Numerical investigations of these problems should give some insight into the final stage of the film evolution that may lead to the possible coalescence of the pressurized cavities with the free surface.Origin of strong solid solution strengthening in the CrCoNi-W medium entropy alloySolid solution strengthening is one of the most conventional strategies for optimizing alloys strength, while the corresponding mechanisms can be more complicated than we traditionally thought specifically as heterogeneity of microstructure is involved. In this work, by comparing the change of chemical distribution, dislocation behaviors and mechanical properties after doping equivalent amount of tungsten (W) atoms in CrCoNi alloy and pure Ni, respectively, it is found that the alloying element W in CrCoNi alloy resulted in much stronger strengthening effect due to the significant increase of heterogeneity in chemical distribution after doping trace amount of W. The large atomic scale concentration fluctuation of all elements in CrCoNi-3W causes dislocation motion via strong nanoscale segment detrapping and severe dislocation pile up which is not the case in Ni-3W. The results revealed the high sensitivity of elements distribution in multi-principle element alloys to composition and the significant consequent influence in tuning the mechanical properties, giving insight for complex alloy design.The attempts of adding and “solving” alloying element into metallic alloys can be traced back to the Bronze Age. The participation of additional elements in the specific proportion could bring the alloy desirable properties, such as enhanced strength []. Microscopically, the strengthening is mainly provided by the hindering effect on dislocations motion due to the local increase of elastic energy generated by solute and solvent atoms interaction []. The strengthening effect is modulated by the lattice mismatch and shear modulus mismatch in solid solution and the amount of alloying elements within the range of the finite solubility []. However, the basic assumption of this traditional solid solution mechanism is the random solution model, which fails to fully explain the strengthening phenomenon in cases where heterogamous distribution of elements needs to be taken into account []. The multi-principle element alloys containing multiple primary elements in relatively high concentrations [Although in multi-principle element alloys, sluggish diffusion and severe lattice distortion have gotten credit for the special characteristics on the basis of random solid solution [], the abnormal dislocation behaviors and the synergy of multiple deformation mechanisms can only be explained by the heterogeneous distribution of different elements. Heterogeneity in chemical distribution, including local composition fluctuations and chemical short-range ordering, has been found in theoretical studies through computational simulations [], which is proved to have obvious influence on the dislocation behaviors and therefore becomes an important factor that modifies the mechanical properties of multi-principle element alloys []. The magnitude of the composition fluctuation and the short-range ordering structure are sensitive to the difference in atoms size, electric negativity et al. []. Since the effect of the composition fluctuation is often combined and mixed with the traditional solid solution strengthening effect, it remains unclear that how important this unique structural character is to the overall strength of the material compared to traditional solid strengthening mechanism []. Accordingly, it stimulated our further study: how sensitive the heterogeneity of chemical distribution is to doping “different” atoms? What would be the difference after adding alloying equivalent element to a concentrated solid solution and to a single element system, where composition fluctuation does not exist, respectively?In this work, the atomic scale chemical distribution, dislocation structure, dislocation behaviors of CrCoNi, (CrCoNi)97-W3 (named as CrCoNi-3W alloy) and Ni97-W3 (named as Ni-3W alloy) were investigated by conducting multi-scale scanning transmission electron microscopy (STEM) and in-situ transmission electron microscopy (TEM) deformation experiments at room temperature. Previous study showed that adding 3.at% W in CrCoNi, which has large lattice, modulus and electronegativity mismatch with Cr, Co, Ni, can attain maximum solid solution strengthening under the prerequisite of retaining the single phase as well as the initial ductility []. Our results demonstrate that the origin of the strong solid solution strengthening effect is the significant increase of atomic scale local composition fluctuations in the CrCoNi-3W lattice due to the trace amount of W, enhancing the nanoscale segment detrapping [] and resulting in severe dislocation pile up and tangling. In contrast, the equivalent amount of W in pure Ni results in strengthening that can be simply predicted by traditional solid solution strengthening mechanism based on random solution model.All alloys were prepared by arc melting Co, Cr, Ni, W (purity larger than 99.9 %) with designated compositions in a water-cooled copper hearth under Ar atmosphere, with the same method as described previously []. To ensure thorough mixing of the elements, the arc-melted buttons were flipped and remelted at least five times. Then the molten alloy was drop-casted into a cooper mold with the size of 12.7 mm × 25.4 mm × 127 mm. After homogenized for 24 h at 1473 K, the ingots cold-rolled along in the longitudinal direction to reduce the thickness by 90 %. Then the cold rolled CrCoNi-3W alloy was recrystallized at 1373 K for 1 h; and the cold rolled Ni-3W alloy was recrystallized at 1223 K for 1 h.Based on the first principles determination of the misfit strains, the contribution of the size effect to the interaction between the edge dislocation and solute atoms was considered for random solid solution []. The increasing yield stress due to solid solution strengthening effect is predicted by [where M is the Taylor factor, which relates the yield stress in polycrystalline alloys to the critical resolved shear stress and ε is misfit strain, which relates to lattice constant. For CrCoNi-3W, taking M = 3.06 [], μ = 85.38 GPa, ν = 0.30, w = 5b, ε = 0.0137 [], the calculation result is ∼150 MPa; for Ni-3W, M = 3.06, μ = 80.17 GPa, ν = 0.31, w = 5b, ε = 0.0050 [], the calculation result is ∼40 MPa. The derivation process of the function can be found in reference [The TEM samples were first polished with SiC papers down to about 80 μm and then punched into disks with a diameter of 3 mm. In order to achieve regions for observation, the samples were further thinned by electropolishing using different electrolyte for different alloy systems (60 % methanol, 34 % n-butyl alcohol and 6 % perchloric acid for CrCoNi and CrCoNi-3W; 80 % acetic acid and 20 % perchloric acid for Ni-3W, respectively). In situ TEM samples were prepared by attaching the TEM samples to stainless-steel substrates with narrow rectangular windows for transmission of the electron beam.Microstructure characterization were mainly conducted by TEM and STEM-HAADF. In situ straining experiments were launched using a Gatan 654 single-tilt straining holder in a displacement-conctrol mode in a FEI Tecnai G2 F20 TEM operating at 200 kV. Atomic-resolution EDS mapping was carried out by aberration-corrected STEM (FEI Titan Cubed Themis G2 300) operated at 300 kV with a convergence semi-angle of 23.6 mrad, and the details can be found in previous work []. A DCOR plus spherical aberration corrector for the electron probe which was aligned before every experiment by using a gold standard sample were equipped. The beam current was set between 25 pA and 30 pA. The dwell time was 1 μs per pixel with a map size of 512 × 512 pixels; a complete process of EDS mapping took roughly 1.5 h to reach an appropriately high signal-to-noise ratio. Atomic strain maps were obtained using the geometric phase analysis method. We took four aberration-corrected TEM images of the same region with a special mark every 90 degrees and overlying them in the same direction, so as to average the possible influence of vibration during scanning on the strain maps. Although such atomic strain analysis is affected by camera resolution, the qualitative difference in atomic strain maps indicates a substantial difference in lattice distortion between the two alloys.The CrCoNi-3W MEA, CrCoNi MEA; Ni-3W alloy and pure Ni were all produced by arc melting pure elemental Cr, Co, Ni and W metals. The details of production and processing was reported previously [ compares the tensile properties of four alloys at room temperature. From these quasi-static tensile stress-strain curves of different alloys (specific data as seen in Table S1), it is clearly demonstrated that doping W enhanced the mechanical properties in both pure Ni and CrCoNi. However, the strengthening effect of the same amount of W is significantly different between pure Ni and CrCoNi MEA. As shown in and Table S1, pure Ni has the yield strength of 87 MPa and the ultimate tensile strength (UTS) of 340 MPa, while Ni-3W yields at about 140 MPa and shows UTS at about 487 MPa. In contrast, the CrCoNi, a MEA system, has a yield strength of about 500 MPa and UTS of 740 MPa and CrCoNi-3W has yield strength of about 1 GPa and UTS of about 1.3 GPa at a grain size of about 0.8−0.9 μm. Apparently, doping W can inevitably give rise to solid solution strengthening. As the Labusch theory [] suggests, the larger the lattice and modulus mismatch between the alloying and matrix atoms is, the stronger degree of solid solution strengthening the formed alloy has. The Seitz radius of Co, Cr, and Ni are 1.385 Å, 1.423 Å, and 1377 Å []; the shear modulus of Co, Cr, and Ni are 75, 76 and 115 GPa, respectively. W (1.549 Å [] and 161 GPa) is super different from the other elements, which can provide considerable solid solution strengthening effect in both pure Ni and CrCoNi. However, the increase of strength in the MEA system due to W is much higher than that in pure Ni in terms of both absolute value and ratio of rise. Interestingly, such significant strengthening effect in CrCoNi-3W cannot be simply explained by random solid solution model [], which only predicts ∼150 MPa increase in strength. As comparison, the predicted increase in strength of Ni-3W (∼40 MPa) is quite close to the experimental result in this case. (Detailed calculations are presented in 2.2) This indicates that alloying is much more efficient in the multi-principle elements systems than the single principle element systems. And the origin of the much stronger strengthening effect in CrCoNi-3W alloy might be beyond the scope of traditional solid solution strengthening mechanisms.Besides mechanical properties, the effect of W in tuning dislocation structures and their dynamic movement under stress is also quite different accordingly. (a–c) show the TEM image of typical dislocation morphology in Ni-3W alloy, CrCoNi MEA and CrCoNi-3W alloy at ∼2 % engineering strain. The bright-field TEM images in (a–c) were all taken under beam axis [110]. It is found that the dislocation morphology in Ni-3W resembles that in pure Ni, whereas Ni-3W has relatively lower stacking fault energy γsf at about 72 mJ m−2 (compared with the γsf about 132 mJ m−2 for pure Ni as seen Table S1 []). The majority of the dislocations were characterized to be full dislocation with no obvious dissociation. The dislocation lines were quite straight, indicating insignificant pinning on dislocations. The slight wavy image of the dislocation lines is due to the dynamic diffraction in TEM imaging.In contrast, the morphology of typical dislocations in CrCoNi and CrCoNi-3W is distinct. Since their stacking fault energy γsf is low of far less than 20 mJ m−2 (see Table S1), dissociation of dislocations is obvious in both of them as shown in the TEM bright field images in (a) and (b). However, it is obvious that much more significant nanoscale segment detrapping as marked by orange arrows in the corresponding TEM image in (c) existed on dislocations in CrCoNi-3W. As a result, the dislocation structure in CrCoNi-3W shows different variation of dissociation distance in each extended dislocation, curved out in orange lines.The dynamic movement of dislocations in CrCoNi-3W alloy is also distinct to that in Ni-3W alloy and CrCoNi alloy accordingly. To examine dislocation motion directly, we performed in situ straining experiments at room temperature on CrCoNi-3W alloy, Ni-3W alloy and CrCoNi alloy by pulling samples along the same [110] direction, using a Gatan 654 single-tilt straining holder in a FEI Tecnai G2 F20 TEM operating at 200 kV. (a) shows a series of snapshots of dislocation motion in CrCoNi-3W alloy captured from Supplementary Movie 1. Specifically, dislocation motion in CrCoNi-3W alloy is sluggish, indicative of a considerable resistance for glide, primarily involving extended dislocations with various degree of decomposition and nanoscale segment detrapping. Each dislocation line is distinctly wavy, and the morphology keeps changing while gliding, related to temporary pinning effect due to high density and randomly distributed pinning points. For instance, the magnified TEM images on the top right corner of each snapshots show the typical dislocation motion under stress. The exemplificative dislocation is named “dislocation line 1” and marked by red arrow in each snapshot. This extended dislocation, carved out in red line, dissociated unevenly along the dislocation line. Because of the nanoscale segment detrapping, each segment moved with different velocities, hauling the trailing partial toughly. Consequently, severe dislocation piles up was generated, and dislocation tangling was also prevailing. It is worth noting that such nanoscale segments detrapping was also observed in CrCoNi, whereas the phenomenon is less significant, consistent to previous observations [In contrast, image captured from Supplementary Movie 2 in (b) exhibited that, in Ni-3W alloy, dislocation motion (see dislocation line 2 and 2’ marked by yellow and green arrow) are easier and faster, suggesting much fewer pinning points existed. Dislocation pile up was not obvious. Under the similar amount of strain, the dislocation density is much lower than that in CrCoNi-3W alloy and dislocation tangling was not obvious as well. In fact, the deformation in Ni-3W alloy is quite analogous to that in pure Ni in terms of the type of mobile dislocations and the microstructural evolution. The different dislocation behaviors consequently lead to different microstructure in CrCoNi-3W, Ni-3W and CrCoNi alloys. To confirm that our in situ TEM observations are comparable to bulk behaviors, we studied the microstructure of these three alloys under the similar amount of (∼5 %) strain in their bulk counterparts. As shown in , CrCoNi-3W alloy presents a much higher dislocation density. Dislocations from different glide directions are activated and tangles severely. While in Ni-3W and CrCoNi, a relatively small number of dislocations are randomly distributed and only slight tangling was observed.The distinct dislocation behaviors are highly responsible for the different mechanical properties of materials. The harder dislocations move, the higher the applied stress would be. Intrinsically, there are two possible causes of harder dislocation motion: 1) the different dislocation core structure which affects the value of energy barrier that dislocations need to overcome to start moving []; and 2) the different dislocation glide resistance as dislocations continues to move. We first studied the dislocation core structure in CrCoNi-3W, Ni-3W and CrCoNi alloys by using HAADF STEM on ½<110> dislocations in 60° orientation [, the dislocations in CrCoNi-3W and CrCoNi are represented as two partial dislocations with similar dissociation distance, while in Ni-3W it presents a full dislocation related to relatively high stacking fault energy. The atomistic picture of the dislocation core in CrCoNi-3W and CrCoNi are fuzzier presumably due to the nanoscale segment detrapping which results in diffused arrangement of atoms projected on [110] direction in both CrCoNi-3W and CrCoNi. In addition, based on the Z contrast in the HAADF images, no obvious segregation of W is observed in the dislocation core in both CrCoNi-3W and Ni-3W alloys. Thus, the addition of W rarely affects the dislocation core structure. However, our analysis on the glide pathway based on atomic scale elemental mapping demonstrates the significant influence of W addition on the dislocation glide resistance.The glide resistance for dislocations during moving is continuously affected by the local chemical environment. In order to compare the element distribution in three involved alloy systems and reveal the corresponding relationship with dislocation behavior, we investigated the atomic-scale element distributions in Ni-3W alloy, CrCoNi and CrCoNi-3W alloy by using energy-dispersive X-ray spectroscopy (EDS). We adopted a long dwell time, a low beam current and chose samples with proper thickness to obtain atomic-resolution EDS maps with high signal-to noise ratio. presents the three groups of element distribution images for Ni-3W alloy ((c)). On each map for a specific element such as Ni, the concentration of Ni atoms in the atomic column along is positively corrected with increasing brightness in the specific spot. In (a), it appears that a tiny proportion of W atoms is distributed in Ni lattice sporadically and sparsely. By doping W atoms, there is little obvious assemblies of Ni or W. Meanwhile, the atomic fraction of an individual element in the corresponding line profiles, trades narrowly in an average level, which suggested little influence on element distribution in lattice scale. The W concentration varied between 2 % and 4 % from one atomic column to another. Therefore, adding small amount of W atoms into single element solid solution (that can be identified as ideal solid solution), makes little difference and change in atomic scale composition fluctuations.In contrast to negligible random variation in Ni-3W alloy, inhomogeneous fluctuations exist in all elements of CrCoNi-3W alloy as shown in (b). Specifically, as we compare the elements distribution in CrCoNi-3W alloy to that in CrCoNi alloy shown in (c), the role of W in tuning the heterogeneity of chemical distributions is obvious. In detail, certain local aggregations can be identified in Cr, Co and Ni maps by direct observation in (b). Take Ni for instance, local high concentration regimes, where a certain number of Ni-rich atomic columns forming tringles, lines or some other arbitrary shapes, are ubiquitous. Whereas similar patterns were also observed in CrCoNi, what makes CrCoNi-3W different is that such aggregations in CrCoNi-3W alloy is more prevailing than in CrCoNi alloy, and the sizes of the local aggregation regions are relatively larger. The corresponding line profiles of the elements’ concentration in CrCoNi-3W demonstrate that the atomic fractions of Cr, Co and Ni, can reach a high of about 55 % and a low of about 15 %, and even W, a tiny proportion of the total, possesses a high level of variation between 0 and 10 %. By contrast, the atomic fractions of Cr, Co and Ni in CrCoNi MEA in (c) possesses a relatively lower variation of the concentration of all three elements between 25 % and 38 %.It is appealing that adding small amount of W atoms can significantly magnify the amplitude of concentration waves in CrCoNi-3W alloy inherited from CrCoNi alloy. Much higher heterogeneousness in chemical distribution is produced. Consequently, enhancive inhomogeneity of chemical distribution complicates the local chemical environment in lattice scale, which causes fluctuations in bond strength, local stacking fault energy and lattice distortion []. This can be supported by the strain maps (see . It is observed that the atomic scale lattice strain in CrCoNi alloy are more uniform ((a)), whereas higher tensile and compressive strain fields alternate at nanoscale forming substantial atomic scale lattice strain fluctuations in the CrCoNi-3W alloy ((b)), resulting in increased internal stress fields. Together with the increased variation in bond strength, the resistance for dislocation glide in CrCoNi-3W alloy could be much stronger than that in CrCoNi alloy, in particular, tough undulating migration. The more significant nanoscale segment detrapping observed above in CrCoNi-3W alloy should be directly related to the rise of nanoscale composition fluctuations also. Such concentration waves produce high density of pinning points where the strength of each pinning points varies depending on the fluctuation in local compositions.To sum, by comparing the effect of adding equivalent W into CrCoNi and pure Ni through multi-scale and in situ TEM characterizations on elements distribution and dislocation structure and behaviors, it is apparent that the alloying effect on strengthening the materials can be much more significant in multi-principle element solid solutions where the existence of composition fluctuation and the high sensitivity of the elements distribution to composition enables more efficient structural modulation. Its influence on dislocation motion compared to others including grain boundary, phase boundary etc., is more precise, continuous and flexible, which may stimulate even abnormal dislocation behaviors. The results not only provide new understanding on the solid solution strengthening mechanisms in multi-principle element alloys but also shed light on highly efficient alloy-designs in future.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Supplementary material related to this article can be found, in the online version, at doi:The following are Supplementary data to this article:Progressive collapse resistance of 3D composite floor system subjected to internal column removal: Experiment and numerical simulationThis paper presents the results of a large-scale test on a three-dimensional (3D) composite floor specimen under the scenario of removed internal column. A two-bay-by two-bay substructure was 1/3 down-scaled from the prototype building due to laboratory space limitation and tested quasi-statically up to failure by using a specially designed 12-point loading system. The load-displacement responses, failure modes as well as stress development among structural components were obtained and discussed in detail. Corresponding reduced finite element (FE) models was also established afterwards and verified by comparing with test results, based on which extended analyses on the effects of reinforcement meshes, aspect ratios and decking thicknesses were studied. The efficiency of the 12-point loading system utilized in this study was also carefully examined. The experimental and computational results reveal that; (1) the ultimate loading-carrying capacity of 3D composite floor systems after the loss of a internal column is governed by the primary beam-column connections adjacent to the failed column, (2) the steel decking is the main contributor of the floor resistance (up to 65%), while the reinforcement meshes play an secondary role; (3) the 12-point loading system is an excellent substitution of uniform loads in real laboratory environments, but special attention should be paid as the the structural responses are actually underestimated by 20%.Although the structural efficiency of modern buildings subjected to gravity, earthquake or wind loads has been deeply understood and well defined in standardized documents, there is an increasing focus on structural integrity and robustness under extreme loads. This appears far more apparently in recent years due to the increased demands on large-span and high-rise buildings. During the long service period, they are susceptible to local damage caused by some extreme events, for example, earthquakes, vehicle impacts, fires, or even human errors. Despite the low possibility of such events, the catastrophic consequences are definitely unacceptable. Since the risks causing progressive collapse are unpredictable, it is challenging to design buildings via traditional methods. As a compromise, alternate load path (ALP) is recommended in many design codes [] and widely adopted in research programs. In this method, the extreme events-triggered initial damage on main supporting components (columns or walls) is preset without any dependence on the loading types or magnitude, and structural robustness of the building would be estimated to see whether the load originally carried by the damaged columns or walls could be transferred to surrounding components efficiently or not. If there are sufficient ALPs available around, a wider range building collapse could be averted, whereas in the inverse case, progressive collapse might be inevitable. After the failure of one or more columns, the mechanisms resisting progressive collapse such as flexural action, catenary action and tensile membrane action could be mobilized to sustain the redistributed loads. The first one, of course, is also commonly considered in conventional structural design, while another two are characterized in progressive collapse cases.Experimental and numerical studies at steel beam-column connections levels could be found in many open literature []. These studies clearly demonstrated the importance of connection types in resisting progressive collapse, depending on their rotational capacity to mobilize catenary action. Yang and Tan [] conducted a series of experimental and numerical studies on steel frames with six commonly used simple and semi-rigid joints. In their study, the connection responses were studied by applying a displacement-controlled load on the middle column stub until the loss of loading-carrying capacity. The test results revealed the catenary action-dominated resistance at large deformation stage. Besides, the flush end plate and double angle web cleat connections were more favorable to mitigate progressive collapse due to their high strength as well as great ductility at the same time. Specifically, Cassiano et al. [] carried out a detailed parametric analysis on the joint performance of flush end plate connection. The results indicated that, depending on the axial joint-to-beam stiffness ratio, there were two collapse-resisting mechanisms after the missing of a middle column, namely compressive arching-like and catenary-like modes. The latter would be more effective for steel structures with flush end plate connection. Also, for a full development of catenary-like mechanism, the authors creatively proposed a ductility criterion, which in essence guaranteed the individual T-stubs could deform and fail in a ductile way. Wang et al. [] proposed a novel dual-functional replaceable stiffening angle steel component. The test results indicated that the newly proposed beam-column connection can effectively improve the stiffness and strength of the test specimens, and simultaneously had sufficient energy-dissipating performance. Similar connections were also used for reinforced concrete frames, making them meet the multi-hazard design against both earthquake actions and progressive collapse []. Meanwhile, to enhance the tensile strength and rotational capacity of beam-column joints, Ghorbanzadeh et al. [] proposed a new joint configuration by adding duplex stainless steel pins (SSPs) to industry-standard nominally pinned joints. SSPs in their study were strategically placed in a way that they do not interfere with the behavior of the joint under gravity loads. The experimental tests under bending and corresponding numerical simulation revealed that the newly proposed joint details were a reliable retrofit scheme to achieve the required levels of tie force and rotation in a joint when subjected to column removal scenarios. Some experimental tests were also conducted on 3D steel frames []. Except for the 3D frame effect, the conclusions were similar with that drawn from two-dimensional (2D) steel frame tests mentioned above. Also, since these studies were conducted with 2D frames or 3D frames without composite slab, thus the contribution of composite slab in resisting progressive collapse was not included.] presented a computational investigation on the robustness of a typical concrete deck–steel beam composite floor system with simple shear connections under internal column removal scenario. They found that the composite slab contributed significantly in resisting progressive collapse through the diagram action to prevent the exterior columns from being pulled inward and membrane action primarily through the reinforcement mesh and steel decking. Main [] later proposed a simplified method for profiled composite slab simulation, in which the slab is replaced by strong and weak shell elements to account for the nonisotropic slab responses parallel and perpendicular to steel decking ribs. The comparison with the detailed model by Sadek et al. [] parameterizedly studied the effect of concrete and steel strength, as well as reinforcement meshes on structural behavior of a 20-storey composite building. Li and El-Tawil [] also conducted an impressive study on a 10-storey building using 3D FE models. Despite the huge benefits of these numerical works, it could not be denied that these models were not well verified because of limited high-quality experimental tests available in open literatures, as that significantly emphasized by Adam et al. [Experimental studies on 3D floor systems are relatively quite limited. Song and Sezen [] once carried out a large-scale test on an existing building by physically removing four first story columns from one of the perimeter frames, which combined with numerical simulations [] demonstrated the needy of 3D structures instead of 2D ones in investigating progressive collapse. Special focus on dynamic effect after sudden removal of perimeter columns was also provided in their study. Johnson et al. [] conducted an experimental study on a half-scale three-bay by three-bay steel-concrete composite slab system by respectively removing a corner column, two edge columns and an interior column. In their study, water in containers was used to apply loads on the bays incrementally. The load seems to be hard to be accurately estimated since the water in the containers flowed to the locations with the largest vertical displacement, the removed columns in specific words, which makes the applied load varied from uniform loads at the beginning to nearly concentrated loads at large deformation stage. Based on the experimental results, the authors pointed out the necessary of modification to typical steel-concrete composite floor systems used in commercial buildings in extreme events, for example, enhancing deck continuity and slab reinforcement. This suggestion definitely remains questionable considering the cons of the over-enhanced tensile membrane action []. Since there were so many structural elements involved in 3D composite floor system, the contribution of the slab in resisting progressive collapse was hard to be accurately quantitatized from tests. The problem was later partially solved by Fu et al. []. In their study, the collapse resistance from composite slab were recalculated from reaction forces of surrounding columns and restraint frames. However, it seems somewhat overestimated since the contributions of the inner beams were also involved. More recently, Wang et al. [] reported a full-scale test on steel moment-resisting frame with composite floor when removing a penultimate edge column. The test results, together with corresponding numerical simulations [], demonstrated the effectiveness of the moment-resisting connection and the continuous steel decking on improving the load-carrying capacity of 3D composite floor system. However, the author also pointed out that the predicted loads based on yield line theory were always higher that the measured ones, since the contribution of the tensile membrane action in the slab could not be well considered in the yield line theory.By reviewing the literatures, it can be found that the studies on 3D steel frame-composite floor systems are quite limited, especially in relevant experimental tests. The authors once conducted experimental tests on two 3D skeletal steel frames under internal column removal scenarios []. As an extension, this paper presents the test results of a 3D steel frame-composite floor systems after the failure of the internal column. Besides the test, corresponding reduced FE model was also performed, based on which extended analyses on the effects of reinforcement meshes, aspect ratios and decking thicknesses were studied. The efficiency of the 12-point loading system utilized in this study was also carefully examined.The authors previously conducted a comparative study on the progressive collapse of two bare steel frames after removal of the internal column []. One of them was tested under concentrated loads (CLs) (Specimen BSF-CL) while the other subjected to uniformly distributed loads (UDLs) (Specimen BSF-UDL). These two steel frames are similar to the one in this study except for the absence of the composite slab. The test specimen in this study is hereafter referred to as Specimen CF-IC for the sake of convenience. The terms before and after the hyphen represent “composite frame” and “internal column”, respectively. Since the details of the test setup and geometrical dimensions of the steel frame have been described in previous study [], thus only a brief instruction of the current specimen is provided in this section.The overview of the specimen and setup is shown in . Also, limited to the loading capacity of the hydraulic jack as well as laboratory space, the selected substructure was 1/3 down-scaled from the prototype building, resulting in the two-bay by two-bay composite substructure with a layout of 4.0 m × 6.0 m (see ]. Also, the connections were adjusted correspondingly to satisfy relative specifications []. Although the tested specimens might be more like an enhanced 1/3-scaled substructure with enhanced slabs, steel members as well as higher load-carrying capacities, they generally complied with relative design codes and could still be effective to reflect the collapse behavior of 3D composite floor structures under internal column removal scenarios.The restraints from surrounding frames are significant, which would influence lots on the mobilization of catenary and tensile membrane action in steel beams and composite slabs to migrate progressive collapse. To simulate this effect, the steel beams and composite slabs of the selected substructure were extended by 1/4 of neighboring spans, which was supposed to be the positions of deflection points. The ends of these extensions were connected to either the strong reaction wall or ground via a set of vertical and diagonal circular hollow section (CHS) braces with pinning at both ends, as seen in shows the configuration of beam-column connections utilized in this study. The flush-endplate connection was emplyed to join the primary beams and columns together, while double angle-cleat connections to bridge the secondary beams to surrounding structural components.Previous study on two steel frames indicated that, the loading method has a significant impact on the structural response under column removal scenarios. Despite higher operable the concentrated loading is in laboratory environment, it is found to result in a great underestimation of the collapse resistance. To reflect the progressive collapse behavior as real as possible, uniform loads are encouraged. In this study, the uniform loads were approximated by a specially designed 12-point loading system, as shown in . Since the 12-points loading system is controlled by the vertical displacement of the first-tier loading beam, the whole structural response up to final failure could be efficiently captured, whereas only the load-increasing part could be obtained when the “real” uniform load is applied even in numerical simulations. shows the details of composite slab, which consisted of a re-entrant profiled steel decking (40 mm in depth and 0.9 mm in thickness), a C40 concrete slab (65 mm in thickness), and Ф6 hot-rolled ribbed reinforcement mesh (spacing at 200 mm along both primary and secondary beam). The slab was connected to the steel frame by φ13–60 shear studs, which were spaced at 75 mm and 90 mm (the value varied slightly in practice from 85 mm to 93 mm to avoid welding on unsmooth decking surface) along the primary and secondary beams. This means the interaction between the slab and steel frame was designed as full shear.The measurements of displacement and strains were taken at different locations, as shown in . Two linear variable differential transducers (LVDT) were utilized to measure the vertical displacement below the internal column stub (L-F1 and L-F2). These two LVDTs were placed along the diagonal direction, thus the vertical displacement of the internal column could be calculated as the average. Besides, the horizontal displacements at top of CHS braces were captured by 16 YHD transducers. The deformation pattern of the floor was also recorded. However, due to limited instrumentations available in laboratory, the vertical displacement was only measured in a quarter of the tested specimens through 6 LVDTs [V-B8-1(2), V-B9-1(2), V-G6 and V-B10]. Strain gauges were placed at both ends of steel beams and CHS braces to acquire the axial forces. The arrangement of strain gauges in the measured section is shown in Before the test, material properties of steel components including CHS braces, beams, column, end plate, steel decking and reinforcements were obtained from coupon tests. The main material characteristics like yield (fy) and ultimate tensile stress (fu), elastic modulus (Es) and fracture strain (εu) are listed in . In addition, three 150 mm × 150 mm × 150 mm concrete cubes were also prepared at the same time, from which the compressive strength (fc) and elastic modulus (Ec) of concrete were measured and also summarized in with respect to the internal column displacement. The black curve with asterisks represents the load recorded by the load cell on the bottom of the hydraulic jack, while the red curve is one calculated through the strain gauge readings that mounted on surrounding restraints and columns. It can be found that these two curves are in excellent agreements with each other, indicating that the load measurement system was adequate and could be applied for further analysis. Compared with the steel frames in [], the structural response of composite floor systems was fairly complicated since there were so many structural components involved, which makes it difficult to distinguish the curve clearly in terms of collapse resisting mechanisms. For convenient description of the experimental observations, the entire structural response in is artificially divided into three stages.The first stage is defined between the internal column displacement of 0 mm and 263.9 mm. It can be seen from that the vertical load increased rapidly at the beginning of loading. The load and displacement at elastic limit is found to be 210 kN and 4 mm, thus the initial stiffness of the tested system is 52.5 kN/m. Soon after that, the load increased non-linearly with the increment of internal column displacement until reaching an approximate plateau. At this stage, steel fracture initiated at the middle of the web in G3-internal column connection ( (a)). Hereafter, the facture therein propagated widely along the web ( (d)), which resulted in the sudden drop in the vertical load-internal column displacement relationship. Almost immediately, the angles bridging over the secondary beam B8 and the internal column ( (e)) failed. Meanwhile, fractures were also observed in the end plate of C4-G3 connection, as shown in Stage 2 begins after Stage 1 and ends when another sudden drop appeared in at displacement of around 350 mm, which is triggered by the bolt failure in C4-G3 connection, as shown in (a), it can be found that fractures developed centrally in the endplate adjacent to B1. Thus, more forces were shifted to the other part and caused the failure of the upper bolt.In this stage, cracks in the concrete slab gradually widened along the primary beams G1 and G2. Meanwhile, concrete was found to spall around the column C3, exposing the fractured rebars to sights, as shown in (b). It should be noted that, the rebars might already fail as metal fracture-like popping was heard before. However, they are referred in Stage 2 since it is the first time to be clearly observed in the test. Besides, the widely opened cracks were also found around the columns C4 and C5 (see (c)). Concrete between the loading point P5 and the internal column crushed under compression (see (d)). The failure mode of the composite slab in Stage 2 is summarized in The load in the first phase of Stage 3 experienced a slight rebound. After that, a gradual descending is found due to successive peeling off of shear stubs from concrete slab along the secondary beam B8, as shown in (a). The specimen finally lost its load-carrying capacity with the failure of B7-G5 connection at displacement of 452.4 mm ( (b)). In this stage, the structural components continuously deformed with the increase of vertical displacement. The steel decking fractured under the loading point P1 ( (c)). The rebar near the column C4 failed. The crushed and spalled concrete region showed in (e) expanded extensively in this stage, with new concrete spalling generated around the loading point P6 and crushing between the loading points P1-P4 and P1-P2, as shown in demonstrates the overview of the composite slab after test. It can be seen that the concrete failures are not symmetrically distributed in this study. More serious concrete damage near the internal column are obviously caused by the angle fracture of B8-internal column connection, while the differences along the double-span primary beams G1-G2 and G5-G6 are more like to be attributed to the various stiffnesses of surrounding restraints.In this study, sufficient horizontal restraints are provided and the reaction forces were carefully meaasured. Herein, the horizontal reaction forces of the restraints corresponding to the double-span primary (RT-3 and RT-4) and secondary beams (RL-3 and RL-8) are illustrated in , in the early loading stage, the curves representing the reaction forces of RT-3 and RT-4 increased negatively, which means the columns C4 and C5 deformed outward the specimen, causing the generation of compressive arch action. This phenonmenon was also observed in the bare steel frames []. After reaching the ultimate compressive forces, these two curves gradually returned to zero and then shifted into tension until to the end of the test, indicating the development of catanary action at large deformation stage. One may note that the displacement when RT-3 returned to zero was about 180 mm, which is smaller than that observed in the bare steel frames (226 mm −258 mm). This may be attributed to the failure of G3-internal column connection, because of which the structure lost the symmetry and leant to the reaction wall. On the other hand, the curves of RL-3 and RL-8 increased continuously during the entire loading process since the bolted-angle connections used here act as simple connections, thus the secondary beams could rotate nearly freely at beam ends. More importantly, it is found that these two curves were almost the same even though the connection bridging over the internal column and secondary beam B8 fracutured at about 265 mm. This is because, after the failure of B8-internal column connection, the forces originally sustained by the steel angles were transferred to surrounding columns and restaints through shear stubs between the secondary beam B8 and composite slab. This is also the reason why the concrete therein cracks so severely and the shear stubs peelled off from the slab in shows the vertical reaction forces among columns. It can be seen from the left figure that, the loads in the columns corresponding to the double-span primary (C4 and C5) and secondary beams (C2 and C7) experience a rapid increase at the beginning, which, however, decrease gradually after the vertical displacement of around 250 mm. This is obviously caused by the failure of G3-internal column and B8-internal column connections. On the other hand, the reaction forces among the corner columns (C1, C3, C6 and C8) increase continuously during the entire loading process. It is clear that the supporting columns could be classified into three groups, as see in the second figure of . It is interesting to note that the curves of C4 + C5 and C2 + C7 show similar developing trend with a force ratio of around 3/2, which is inversely proportional to the span ratio of the primary and secondary beam. Besides, it can be found that the sum of the vertical reaction force among the corner columns increases rapidly with the increased vertical displacement of the internal column, and exceeds that of C2 + C7 at around 125 mm, eventually equals to that of C4 + C5 after around 285 mm. Considering the small deformation of the peripheral beams (B1, B5, B6 and B10), implies that, after the removal of the internal column, more loads are shifted onto the corner columns through the composite slab. shows the deflection profiles of one-quarter of the tested specimen at different displacement levels of the internal column. Similar to the bare steel frame under concentrated and 12-point loading conditions, the primary beam deformed linearly like simple-supported beams during the entire loading process. This relies in the fact that the primary beam adopted in this study is quite strong with high bending rigidity, thus their bending deformation was so minor and could be just ignored. Honestly speaking, the bending deformation of primary beams could not be ignored in more general cases. However, it may be acceptable considering the fact that stronger beams would make the plastic hinges developed centrally in beam-column connections, thus the structural properties against progressive collapse would be somewhat conservatively evaluated and the designed building would be more on the safe side. The secondary beams, as seen in , deformed in a bilinear manner with the plastic hinges occurred in the loading positions adjacent to the internal column, which exhibits a similar flexural pattern to that under UDLs. shows the strain measurement at ends of double-span primary/secondary beams. The positions and measured sections are illustrated in The strain readings in the double-span secondary beams were illustrated in After the test, a reduced FE model is performed for a numerical study to 1) extend the analysis for a more detailed investigation on the effect of decking thickness, reinforcement meshes and aspect ratio, and 2) check the efficiency of the 12-point loading system. Compared with the detailed modelling approach with components strictly following the real section geometries, the reduced one seems more preferred regarding their much higher computing efficiency and simultaneously similar description of the structural responses [], on the premise that the steel frame (especially the beam-column connection), boundary conditions and composite slab could be well considered.In this study, the steel beams and columns are modelled by one-dimensional beam elements, while connections simulated by component-based models with discrete springs, as seen in . The properties of these springs could be determined from publications by Faella et al. [], or more accurately, by actual component tests []. To enhance the computing efficiency, the component properties are again simplified based on the test results, which is also presented in . It should be pointed out that, in the component-based approach, a rigid shear and out-of-plane rotation spring is applied, which means that the combined effect of shear, tension and torsion are neglected in numerical simulation. In other words, The reduced FE model is valid under the assumption that tensile failure dominates at beam-column connection joints, while shear or torsional failure is negligible.The surrounding restraints applied on the tested specimen is simulated by a set of elastic springs with one end connected to the ends of the cantilever beams while another fixed to the reaction wall or ground. Assuming a uniform strain distribution along the CHS braces, the stiffinesses of these springs (KCHS) could be easily calculated by Eq. . Besides, the column foots that tightly connected to the rigid base in test are all totally fixed in the numerical model.where ECHS, ACHS and lCHS represent the elastic modulus, cross-sectional area and length of CHS braces, respectively.As known, because of the presence of the ribs in steel decking, the composite slab behaves different in the paralleled and perpendicular directions of the ribs. Main [] once proposed an empirical method to describe the nonisotropic slab responses, in which the composite slab was partitioned into couples of strong and weak sections. This method has been proven to be justified for composite slabs with open-section decking, but may be not suitable for this study with re-entrant decking. In the composite slabs of current study, the horizontal deformation of the ribs is restrained by surrounding concrete. This means they contribute little in resisting the applied load in the perpendicular directions of the ribs and can be just ignored, as shown in . However, due to the restraint effect of the ribs, the remaining parts of the decking are tightly connected to the slab. To verify the simplification method, two groups of composite strips are performed. Each group consists of two models, one along the ribs (Model I) while another perpendicular to them (Model II), as seen in as an example. The detailed slab across-section is employed in the first group and the interactions between the concrete slab and steel decking are also considered through “surface-to-surface contact” in ABAQUS []. Whereas the second group uses the simplified slab across-section showed in and the decking is tied directly to the slab. All of them are fixed at both ends and loaded uniformly. The results are presented in that the curves agree quite well with each other when the models deform perpendicularly to the decking ribs. For the strips designed to deform along the ribs, the one using the detailed across-section is found to be slightly higher than another one. This is because the ribs in such case act like deep beams and would contribute in resisting the load through bending and tension. However, it may be not a big issue since the maximum error are less than 8% at large deformation stage.Recognizing the minor effect of the decking ribs and sliding between the concrete slab and steel decking, the composite slab could be simulated by composite shell elements in the reduced model. The material properties of steel components have been given in . In addition, damaged plasticity model is assumed for the concrete, which incorporates compressive and tensile damage through progressive degradation of material stiffness and strength, as shown in The established FE model is finally presented in . The 12-point loading system is simulated by rigid beams, and the ball-and-socket bearings used to connect the second-tier and Y-shape loading beams in test are replaced by “couplings” with three rotational freedoms (UR1, UR2 and UR3) released while the other three translational freedoms (U1, U2 and U3) restrained. So are those between the Y-shape beams and composite slab. The full shear connections between the composite slab and steel frame is modelled by “weld connector” in this study. This is valid as minor deformation were found for the shear stubs until the end of the test.The reduced FE models are calibrated by isolated 3D steel frames subjected to a concentrated load (BSF-CL) in [] and the 3D composite floor in this study. The Specimen BSF-UDL is not adopted here since this specimen was found to partially fail in terms of global bucking of the inner beams B4 and B7, which however, cannot be accurately captured by the one-dimensional beams in the reduced model.For Specimen BSF-CL, the composite slab, weld connector and 12-point loading in are just removed and a displacement-controlled loading is applied on the top of the internal column stub. The simulated vertical load-displacement relationship and the main joint failure in the curve are compared with the test results in . Besides, the axial forces development in double-span primary and secondary beams are also drawn in that the numerical results agree with the test results with acceptable accuracy, which indicates the efficiency of the steel frames and boundary conditions.The numerical predictions for Specimen CF-IC are presented in . Since the strain readings of the double-span primary beams exceeded the normal yield strain (see (a) and (b)), the reaction forces among surrounding columns are selected for a more detailed comparison. It can be found from (a) that the load-displacement curve could be well captured by the reduced model up to the peak at around 247 mm (1086.92 kN vs. 1047.11 kN). However, the loads appear to be slightly higher than the experimental results in Stage II. This is attributed to the concrete spalling occurred near the corner columns C3 and C6 in this stage, which is obviously a structural behavior in slab thickness direction (see (b)) and could not be efficiently modelled by the one-layer shell elements. Note that it is also the reason why the steel angle fracture of B7-G5 connection at the displacement of 452.4 mm could not be well reproduced, and the numerical model finally fail because of both components failure in B8-C7 connection. Even though, it still can be concluded that the reduced FE model is reliable considering the fact the initial stiffness, ultimate load-carrying capacity and main failure characteristics of the composite slab (Having gain the confidence on the reliability of the reduced FE model, extended frame analyses are carried out. One of the objectives is to further identify the impact of decking thickness, reinforcement meshes and aspect ratio on the collapse resistance under internal column removal scenarios as there is only one specimen conducted in the test due to its high cost. In addition, the efficiency of the 12-point loading system, which is now widely adopted as a replacement of UDL, will also be studied in this section.The effect of reinforcements is studied through simulations with various reinforcement spacing (100, 200 and 800 mm) in respective primary and secondary beam directions. The spacing of 800 mm is introduced here as a compromise of no steel reinforcement since the latter is found to give rise to converge difficulties. The results of these simulations were plotted in . Clearly, the steel reinforcements in the primary beam direction affect greater than those in the secondary direction. In particular, doubling the steel reinforcements leads to an increase of the load capacity by 8%, while removing decreases them the load capacity by about 11%. In contrast, the counterparts in the secondary beam direction are around 3% and 6%, respectively. Even though, it can still conclude that the reinforcement meshes are ineffectual on the overall behavior of 3D composite floor systems since the case of no steel reinforcement are performed here just for a theoretical study, which is not practical for a real structural building.Four simulations are carried out in this section to investigate the effect of this parameter as follows: no steel decking, 0.45 mm, 0.9 mm and 1.8 mm (the value of 0.9 mm is adopted in this study). depicts that, compared with steel reinforcements, the decking thickness contribute much more significantly on the collapse resistance of 3D composite floor systems, which is directly related to the initial stiffness and load-carrying capacity. Compared with the one with no steel decking, the ultimate loading capacity is found to be substantially enhanced by 25%, 46% and 65% in the cases of steel decking thickness of 0.45, 0.9 and 1.8 mm. Considering the limited load increases resulted from the densified steel reinforcements (less than 10%) and the serious crack of the concrete slab, it can conclude that the steel decking is the main source of floor's capacity (up to 65% of the overall load-carrying capacity). This indicates that increasing the decking thickness is an efficient measurement to enhance the robustness of structural buildings. However, it should be emphasized that it seems like a double edge sword and could also be detrimental, since the thicker decking accelerates the rotation of the internal column stub towards the column C4, thus the bottom component spring wherein (corresponding to the first peak in the curves of ) occurs earlier and the ductility of the whole structure is somewhat deteriorated. implies that the aspect ratios is another governing parameter on the loading-resisting capacity of 3D composite floor systems under internal column removal scenarios. When the aspect ratio decreases from 1.5 to 1.0, the load-carrying capacity increases by more than 50%. However, it seems to influence little on the vertical displacement corresponding to the peaks. This is because the same dimension in the shorter span (primary beam) results in the same extensions for respective components and the same rotation for plastic hinges. The peak loads, on the other hand, are found to be controlled by the primary beam-column connections adjacent to the removed column, or more specifically, the tensile component spring. This phenomenon could also be found for various cases showed in To reflect the progressive collapse behavior as real as possible, uniform loads are encouraged in experimental program. Problem raise at the same time since in laboratory environment, UDLs are challenging to be applied in a force-controlled way up to failure. In such circumstances, the 12-point loading system was proposed, which is regarded as the most advanced representation of UDL since the load is gradually applied on specimens through the displacement control of the first-tier loading beam, thus the structural components could be fully mobilized and the whole structural responses prior to system failure could be captured. However, it cannot be denied that this loading method is proposed as an approximation of real UDLs and its efficiency has not yet been quantitatively identified in previous studies. In this section, eight simulations with varied steel reinforcement spacing, aspect ratios and decking thicknesses are performed under UDLs. The comparisons between the 12-point loading and UDL methods are given in . Note that the UDLs are applied in load-control algorithm, so that only the load-increasing parts could be obtained. It can be seen from that the curves in the cases of UDLs are in great agreements with those under 12-point loadings. This implies that the 12-point loading system is an excellent option for large-scale testing of composite floors, but simultaneously, special attention must be paid as the structural responses are actually underestimated by 20%.This paper provides an experimental and numerical study of 3D composite floor systems under the scenarios of removed internal column. Quasi-static test was firstly conducted with a special designed 12-point loading system. Corresponding reduced FE model was performed and verified by comparing with experimental tests, based on which extended analyses on the effects of reinforcement meshes, aspect ratios and decking thicknesses were studied. The efficiency of the 12-point loading system was also carefully checked. The following conclusions can be drawn:The ultimate loading-carrying capacity of 3D composite floor systems are governed by the primary beam-column connections adjacent to the failed column, or more specifically, the joint component in tension zone.A simplification method for composite slab with re-entrant decking is proposed in this study, which is proven to be efficient and can be used in reduced FE models.The steel reinforcements in the primary beam direction influence more than those in the secondary beams. Even though, the contributions from increasing the reinforcements are still limited.The steel decking is the main source of the floor's capacity for the studied structure, which accounted for up to 65% of the overall load-carrying capacity. Increasing the decking thickness is an efficient measurement to enhance the robustness of 3D composite floor systems.Aspect ratio is another governing parameter influencing greatly on the robustness of 3D composite floor systems.The 12-point loading system is an excellent option for large-scale testing of composite floors, but special attention must be paid as the structural responses are actually underestimated by 20%.There are no conflict of interests to declare.Probabilistic evaluation on fatigue crack growth behavior in nickel based GH4169 superalloy through experimental dataphysical crack length including physical crack and cyclic-plastic-zone sizefitting parameter relating crack opening to maximum stress intensity factorsnumber of divided interval in probabilistic model establishmentshape and scale parameters in Weibull distributionnormalized crack length to specimen widthmean and standard variance of LDF in interval ifitting parameters for each segment in FASTRAN modelmodified boundary-correction factor for compact tension specimenelastic stress intensity factor at failuremaximum stress intensity factor calculated from the actual crack length athreshold load that terminates crack closurelife distribution factor for specimen j at interval iamplitude of stress intensity factor calculated by actual crack length aTurbine disc, a critical rotating component of an aero-engine, experiences significant level of mechanical and thermal stresses induced by centrifugal loading and temperature gradient, respectively. Fatigue properties of materials should be systematically investigated to obtain reliable design of turbine disc. Safe-life principle was employed in critical systems that are difficult to repair or may cause severe damage, requiring an extremely low level of risk based on testing and analysis data. However, this technique considered the most dangerous state of the engines, contributing to an over-conservative design thereby requiring more resources than those are actually needed. After the catastrophe happened in Sioux City, 1989, which was due to a fatigue crack originating from a critical area of the stage I fan disc Nickel based superalloys, e.g., GH4169 superalloy studied here, are usually used in high temperature turbine discs for their unique combination of microstructural stability and fatigue resistance, due to the high volume fraction of precipitates γ′/γ′′ that uniformly distribute in disordered γ phases The probabilistic FCG models are usually derived from the deterministic FCG models, with a probabilistic process of parameters fitted from experimental data. However, since the deterministic FCG models always include more than one parameter to be fitted Several numerical models of plasticity-induced crack closure (PICC) have been developed for the calculation of ΔKeff, such as the FAtigue crack growth STRuctural ANalysis (FASTRAN) model by Newman In this paper, systematic experiments for the materials of the GH4169 superalloys at different locations, corresponding service temperatures, and different stress ratios were conducted to calculate the stochastic FCG performance. Based on the experimental data, probabilistic FCG model under the consideration of crack closure was established. Contents are organized as follows. In Section , material properties and experimental procedures are presented. In Section , the detailed development of the probabilistic model is introduced. Section presents the results and discussion based on both the experiments and the model. The paper is concluded in Section The chemical composition of the GH4169 superalloy include: C (0.035 wt%); Si (0.08 wt%); Mn (0.03 wt%); S (0.003 wt%); P (0.006 wt%); Cr (18.93 wt%); Mo (3.02 wt%); Ti (1.03 wt%); Nb (5.11 wt%); Al (0.53 wt%); B (0.003 wt%); Co (0.08 wt%); Fe (19.46 wt%); balance Ni. The superalloy was cut from an actual turbine disc.Aging treatment with solution and stabilization, which has been widely used to control the grain size and mechanical properties of nickel based superalloy, was applied to the disc as: solution heat treated at 950–980 °C for 1 h, followed by air cool; aging at 720 °C for 8 h, cooling to 620 °C at 50 °C/h, aging at 620 °C for a another 8 h, and then finishing with air cool.Compact tension (CT) specimens for the FCG experiments were cut from a turbine disc with a radius of 110 mm. Three discs with radius of 110 mm from different batches were selected for the fatigue tests. CT specimens, of which the geometry is shown in . Initial notches of 0.2 mm were created on all the specimens by wire-cut electro discharge machining (EDM).A 100 kN Instron 8801 servo-hydraulic testing machine was used for fatigue tests under stress control with triangular waveform. FCG tests were performed at a frequency of f = 10 Hz, two stress ratios of Rσ = 0.1 and Rσ=0.5, and service temperatures of 550 °C for location A and 330 °C for location D, respectively.Experimental conditions and specimen numbers are summarized in . In each test group, 18 specimens were tested to obtain the stochastic FCG data. All the procedures of pre-cracking, load imposing, heating and measuring are in accordance with ASTM To examine crack closure, a Questar long-distance microscope with a 2 μm resolution was used to measure the crack length and capture sequences of images during load cycles for Digital Image Correlation (DIC) analysis. Matlab code by Eberl et al. The experimental procedure for studying crack closure was referred to Matos et al. . In each case, the original length of L1 remained unchanged.In order to establish the FCG model that includes the crack closure effect, fitting was conducted on the experimental FCG data. FASTRAN model where c is the physical crack length including both the actual crack length a and the cyclic-plastic-zone size Δrp, N is the number of cycles, Ci and ni are two fitting parameters for each segment, ΔKeff is the effective SIF involving crack closure, Kmax is the maximum SIF at a specific crack length c, KIe is the elastic SIF at failure, and q = 1.5 is an empirical constant.The effective SIF ΔKeff, derived from imposed load on cracked material, instant crack length and geometry factor for a specific specimen type, can be described as:where Smax is the maximum applied stress, Sop is the crack opening stress, and F(α) is boundary-correction factor, which accounts for configuration effects on the SIF, α = c/W representing the normalized crack length c to specimen width W. ΔKeff reflects the existence of crack closure with a specific specimen type. As for CT specimens studied in this paper, it can be transformed to:where Pmax is the maximum tensile load, Pop is the imposed threshold load that terminates crack closure, B and W are the geometrical dimensions (i.e., 3.75 mm and 25 mm respectively as shown in ) of the CT specimens, and G(α) is boundary-correction factor for CT specimens, and can be expressed as G(α)=2+α(1-α)3/2(0.886+4.64α-13.32α2+14.72α3-5.6α4)The crack length c defined in this model is determined by the actual crack length a and the cyclic-plastic-zone size Δrp, asAnd the cyclic-plastic-zone size Δrp is a function of the ratio of crack opening load Pop to maximum tensile load Pmax, and plastic zone size rp, asThen the Dugdale strip-yield model is employed for the calculation of plastic-zone size rp, aswhere Kmaxa is the maximum SIF calculated from the actual crack length a, and σys is yield strength of the material., the elastic SIF at failure KIe is determined by the Two-Parameter Fracture Criterion (TPFC) where KF and m are fracture parameters that are equal to material fracture toughness KIc, and 1 (for ductile materials), respectively, and Su is the plastic-hinge stress equal to the ultimate tensile strength σu. Thus Eq. , the deterministic FCG model is established, in which the material fracture toughness KIc and the crack opening SIF Kop are determined by standard fracture toughness testing and crack closure experiments.Based on the deterministic FCG model proposed in Section , the probabilistic evaluation of FCG rate at a specific testing condition can be developed by adding a LDF factor according to the study of Yang et al. In log–log diagram, XL,ij (LDF) represents the deviation of FCG curve for specimen j relative to that fitted from the whole set of data at interval i. The value of XL,ij is positively related to FCG life, thereby negatively related to FCG rate. By assuming a normal distribution, i.e., N(μi,σi), where μi and σi are the mean and the standard variance of LDF calculated in interval i, scattering property of FCG can be illustrated piecewisely throughout the process of crack extension, as shown in Grain size distribution, γ′/γ′′ precipitates and δ phases in location A and D have been investigated in previous study . Results exhibit that parameter λ and average grain size d¯ vary at location A and location D. Average grain size d¯ was determined to be the main factor for the deferent FCG rate of specimens from different locations. Thus, in this paper, we suppose that the grain size variance will contribute to the stochastic property of FCG rateStochastic FCG rate da/dN vs. ΔKa (i.e., the SIF range calculated from actual crack length a. Experiments on the specimens from locations A and D were conducted at service temperature of 550 °C and 330 °C, respectively. Two stress ratios, i.e., 0.1 and 0.5, are investigated for a more comprehensive representation of stochastic FCG behavior.Fractographic analysis was then performed following the fracture of the test specimens. Here we provide the representative fractographic observations from specimens #A01 and #A19 at 550 °C and specimens #D01 and #D19 at 330 °C for simplicity. For each specimen, SEM observations were conducted at both low and high stress intensity factor ranges, i.e., a = 6.75 mm (ΔKa = 31.55 MN/m3/2 for Rσ = 0.1 and ΔKa = 26.29 MN/m3/2 for Rσ = 0.5, see ) and a = 9.25 mm (ΔK = 40.86 MN/m3/2 for Rσ = 0.1 and ΔKa = 34.05 MN/m3/2 for Rσ = 0.5, see ). Obvious fatigue striations are found throughout the process of FCG from those SEM images, indicating that transgranular fracture is dominant. This mode of fracture suggests that the crack growth is ductile in nature. Widths of striation are measured at different experimental conditions and crack lengths, of which the values can be used to validate the data obtained from fatigue tests.In addition, material fracture toughness KIc were obtained at corresponding conditions for locations A and D as the input for the probabilistic FCG model previously established in Section The crack opening SIF Kop with respect to the maximum SIF Kmax is determined by crack closure experiments assisted by DIC observations. At a specific crack length, crack opening distance (COD) can be calculated from initial position L1 and loaded position L2, as illustrated in . For instance, measured COD and imposed load with respect to frame number at a = 7 mm at each experimental condition is illustrated in , some portions of the COD/CODmax curve are nearly equal to zero when imposed load is relatively low, which represent the conditions at which the crack is closed. Therefore, a crack opening load, Pop, can be determined as shown in . To investigate the crack closure behavior at each condition, Pop is measured at crack length of 7.00 mm, 8.00 mm, 9.00 mm, 10.00 mm, and 11.00 mm following the same process above. Corresponding results are shown in , Kop is always larger than Kmin, indicating that crack closure exists for the whole crack extension process, as well as all the test conditions. In order to establish a proper model for the description on crack closure behavior, i.e., relationship between Kop and Kmaxa, fitting process is carried out on the following linear functionwhere h is a fitting parameter obtained from the data above, of which the values are listed in With the material parameters determined in Sections , the probabilistic model can be employed to describe the scattering of the FCG data obtained from experiments. The range of ΔKeff in logarithmic scale at each experimental condition is divided into 5 intervals corresponding to the process of crack extension, then parameters Ci and ni (i = 1,…,5) in FASTRAN model are determined piecewisely through fitting procedures of all the data included in corresponding interval.Then, in each interval i, LDF for individual specimen j (i.e., XL,ij) is calculated to evaluate the variance of FCG rate relative to the whole data set. Parameters μi and σi in assumed normal distribution can be calculated by statistic procedures based on obtained XL,ij values. Thus, parameter σi represents the stochastic property of FCG as the crack extends in interval i. illustrates the values of parameter σi in each interval. No obvious difference of FCG variance is found between locations A and D at both stress ratios. Moreover, a decrease-to-increase trend can be found according to the experimental in this study. Reasons can be explained as follows.More prominent scatter of FCG rate in coarse grains presents more prominent scatter of FCG rate in coarse grains (location D) than fine grains (location A). Specifically, at Rσ = 0.1, the standard variation σ of FCG in coarse grains (location D) is always larger than that in fine grains (location A). At Rσ = 0.5, the standard variation σ of FCG in coarse grains (location D) is larger than that in fine grains (location A) in interval 2, 4 and 5, smaller in interval 3 and similar in interval 1. If we consider the average value, the conclusion is identical that more prominent scatter can be found in coarse grains., parameter k is similar between locations A and D while parameter λ is not. Considering the scale parameter λ in Weibull distribution represents the scatters of involved data, analogical to the standard variance in natural distribution, we employ the normalized value of λ/d¯ as a criterion to evaluate grain size variance. As for locations A and D, λ/d¯ are both 1.13 approximately, which means the scatter of grain size are almost the same. By excluding the influence of grain size distribution, we can determine that the average grain size alone can also contribute to the scatter of FCG rate.It is well known that FCG behavior exhibits obvious microstructural dependence when the crack length is comparable to grain size, since the grain/twin boundaries in polycrystalline material hinder the extension of the dislocations as well as the crack, contributing to continuous accumulation of local plastic strain As for the early section of FCG in stage II, which is represented by interval 1 in this paper, FCG rate is dependent on material microstructures as the crack length is relatively small. With the increase of crack length, crack length and corresponding plastic zone size tend to be larger than the grain size (represented by intervals 2–4), and FCG rate becomes less dependent on microstructures. Thus, the variance of FCG decreases. With the crack extending continuously, it finally approaches the unstable condition. Although the crack growth is still stable before it goes into section III, the crack growth rate is obviously higher than that of the previous conditions. The high FCG rate is usually accompanied with prominent fluctuations of the crack path, leading to the uncertainty of stress condition around crack tip. Therefore, the FCG rate turns out to be more stochastic. In this way, the decrease-to-increase trend of FCG rate variance is formed.From the results and discussion above, calculating results are in good agreement with experimental data. Thus, we can determine that the established probabilistic model can effectively reflect the stochastic property and corresponding variance along with the crack extension, indicating a promising tool for probabilistic FCG rate prediction.The deterministic FCG model was proposed by combining the piecewise FASTRAN model and the Dugdale strip-yield model to incorporate the crack closure effect in FCG behavior. Material parameters in the deterministic FCG model was obtained by performing FCG experiments, which were conducted at service temperatures of specific locations with stress ratios of 0.1 and 0.5 and a frequency of 10 Hz, in accordance to ASTM -15. The fracture toughness KIc was measured at specific temperatures according to ASTM -03. DIC was employed to measure different levels of crack closure at tested conditions, which was represented by the linear relation between crack Kop and Kmaxa .Based on the deterministic FCG model, the probabilistic FCG model was established by introducing the LDF to represent the scattering level of data of each specimen in a specific divided interval. LDF was assumed to subject to normal distribution and the mean and standard deviation are obtained through a statistical process. By excluding the influence of grain size distribution with a normalized value of λ/d¯, we determine that the average grain size alone can also contribute to the scatter of FCG rate. It turns out that FCG rate variance follows a decrease-to-increase trend as crack extends, which can be interpreted as the changing microstructural dependence of FCG and stress condition uncertainty when crack approaches unstable state. Thus, proposed probabilistic model effectively reflected the stochastic property of FCG, offering a promising tool for probabilistic DTA.Poly 4-hydroxyphenyl methacrylate-carbon nano-onions (f-CNOs)Rational design and engineering of carbon nano-onions reinforced natural protein nanocomposite hydrogels for biomedical applicationsIn the current study, poly 4-hydroxyphenyl methacrylate-carbon nano-onions (PHPMA-CNOs = f-CNOs) are synthesized and reinforced with natural protein gelatin (GL) to engineer GL/f-CNOs composite hydrogels under the sonochemical method. The influence of f-CNOs content on the mechanical properties of hydrogels is examined. Cytotoxicity of hydrogels is measured with the human osteoblast cells. The results revealed good cell viability, cell growth, and attachment on the surface of the hydrogels, and results are f-CNOs dose-dependent. Specifically, the GL/f-CNOs (2 mg/mL) hydrogel showed the highest cell viability, enhanced tensile strength, elastic modulus, and yield strength as compared to pristine GL and GL/f-CNOs (1 mg/mL) hydrogels. It reveals the extent of physisorption and degree of colloidal stability of f-CNOs within the gel matrix. Furthermore, GL/f-CNOs hydrogels efficiently load the 5-fluorouracil (5-FU) and show a pH-responsive sustained drug release over 15 days. Nevertheless, these CNOs based composite hydrogels offer a potential prospect to use them in diverse biomedical applications.Poly 4-hydroxyphenyl methacrylate-carbon nano-onions (f-CNOs)Hydrogels are emerging three-dimensional (3D) networking scaffolds used for a range of tissue engineering approaches due to their highly hydrated nature, and diffusive transport property (). Generally, hydrogels are classified into two types such as physical hydrogels and chemical hydrogels. Physical hydrogels are held together by molecular entanglement. Chemical hydrogels are covalently functionalized structural networks (). Numerous hydrogels have fabricated from synthetic and natural polymers with an emphasis on biomedical applications including drug delivery, regenerative medicine, and tissue adhesives (). Specifically, The hydrogels used in biomedical applications mimic the native extracellular matrix (ECM) and support cellular growth as well as tissue regeneration (). Besides, 3D culturing, cell-cell interactions, cell-matrix, differentiation, cellular proliferation, and migration have studied using hydrogels (). For this, naturally occurring biopolymers have demonstrated potential advantages over the synthetic polymers (). For instance, alginate, chitosan, hyaluronic acid, fibrinogen, collagen, and gelatin (GL) have reported (). Among the natural biopolymers, the GL will benefit more because of its wide availability, and less immunogenicity. Therefore, it is evocative to fabricate GL-based hydrogel scaffolds for biomedical applications.GL is a natural protein comprises many arginine-glycine-aspartic acids (RGD) and metalloproteinase (MMP) residues. The residues induce cell attachment and cell remodeling (). Usually, coatings, nanoparticles, nanofibers, and hydrogels have been used as biomedical scaffolds (). Among them, GL-based hydrogels are potential implantable scaffolds for cartilage tissue engineering (). For example, carbon nanotubes (CNTs) reinforced into GL hydrogels to improve mechanical properties without inhibiting 3D cellular growth and porosity (). Graphene oxide (GO) has also been used as a second phase additive to improve the cell viability and proliferation in 3D hydrogel scaffolds (). In addition, reduced graphene oxide-based silk nanofibrous were developed for nerve and cardiac tissue engineering applications (). However, there are some concerns, including poor water resistance, rapid degradation, and low mechanical strength, which are impeding the biomedical applications of GL-based hydrogels. It is worth to mention that graphene and its derivative have effected membrane organelles, plasma membrane, and cytoskeleton (e.g., nucleus, lysosomes, and mitochondrion) (). The CNTs could passively penetrate into tissue membranes through enhanced permeability and retention (EPR) (). Further, synthetic techniques of CNTs are tedious. Consequently, it is highly appropriate to engineer a facile method to fabricate carbon-based hydrogels with superior mechanical properties, and excellent biocompatibility.Carbon nano-onions (CNOs) are a new class of quasi-spherical nanomaterials containing concentric graphitic shells, which were described by Ugarte in 1992 (). Because of their outstanding physicochemical properties, CNOs have used in numerous applications, such as lithium-ion batteries, catalysis, supercapacitors, cell imaging, therapeutic, diagnostic, and other biomedical applications (). Among different carbon nanomaterials, CNOs are most propitious for biomedical applications, since they are tolerable to transport in the circulatory systems with great biocompatibility and negligible toxicity (). PEG conjugated CNOs, oxidized CNOs, and pure CNOs are nontoxic and exhibited more than 85% of cell viability with fibroblasts (). Also, poly 4-mercaptophenyl methacrylate (PMPMA) was covalently attached to the CNOs surface to fabricate ultra-high molecular weight polyethylene (UHMWPE)/PMPMA-CNOs nanocomposites (). A small quantity (0.1 wt%) of PMPMA-CNOs was significantly enhanced the biocompatibility, mechanical, and thermal properties of UHMWPE. Recently, zein/PMPMA-CNOs hydrogels were developed for pH-responsive controlled drug release (). However, the synthesis of PMPMA-CNOs was laborious and lengthy (48 h) due to the less reactive mercaptophenyl functional group. Zein protein is not soluble in water, which required organic solvent (1,4-dioxane) to prepare zein/PMPMA-CNOs hydrogels. In addition, 1% of glutaraldehyde (GA) was used to cross-link zein and attain stable hydrogels. However, 1% of GA is toxic, and GA might release into the host due to the degradation of the hydrogel scaffold (). Zein/PMPMA-CNOs showed slightly improved cell viability over 3 days, but after 3 days, the viability was decreased. Besides, strong basic conditions (pH = 9.0) are required to obtain drug release from zein/PMPMA-CNOs hydrogels. These demerits of zein/PMPMA-CNOs hydrogels provoked us to design and synthesize more reactive poly 4-hydroxyphenyl methacrylate-carbon nano-onions (f-CNOs) as well as to fabricate GL/f-CNOs hydrogels. Consequently, it is of great importance to explore the application of f-CNOs as novel hydrogels in the biomedical research field.The synthetic route of nanomaterials plays a pivotal role in biomedical applications. Sonochemistry is a newly developing method to synthesize nanomaterials. Sonochemistry is an easy, simple, and short-time physicochemical method contingent on the high-intensity ultrasound (). Sonochemical effects of ultra-sonication depend on the acoustic cavitation phenomenon. This synthetic route relies on various parameters including concentration, and type of the reagent, ultrasound frequency, intensity, dissolved gas, and the position of the reaction vessel in the ultrasound system. Several nanomaterials have developed using a sonochemical method for controlled drug delivery (). In the past, several graphene-based nanomaterials have explored using the sonochemistry method (). Therefore, it is hypothesized that f-CNOs could be uniformly dispersed and reinforced homogeneously within the GL matrix by the sonochemical method. The uniform dispersion of f-CNOs can improve the mechanical properties of GL/f-CNOs hydrogels with splendid cytocompatibility and biodegradability. The biomaterials based controlled drug release systems have fascinated for the treatment of cancer. Among chemotherapeutic agents used for cancer treatment, 5-FU is one of the most extensively used drugs for malignant cancer (). However, 5-FU has some pharmacokinetic limits, such as short half-lives and unfavorable maximum drugs (). Besides, oral absorption and intravenous injection of 5-FU exhibited gastrointestinal lesions, and atrophy, respectively (). The pharmacokinetic limitations and side effects are associated with oral, and intravenous delivered 5-FU have reduced when encapsulated into hydrogels (). Therefore, there is a clear and unmet need to develop novel GL-based hydrogels, which can be employed to deliver chemotherapeutics with admirable biocompatibility.In the current study, we have designed and synthesized reactive f-CNOs within 2 h to fabricate GL/f-CNOs hydrogels by the sonochemical technique. Only 0.4% of GA was used to cross-link GL and obtain stable hydrogels. GL/f-CNOs showed excellent cell viability over 14 days of incubation. In the wet state, the GL/f-CNOs hydrogels could bear a compressive strain up to 65% and recover its original shape after the stress was released. These results indicate that the GL/f-CNOs hydrogels exhibit good mechanical durability and elasticity. The porosity and degradation of GL/f-CNOs hydrogels were improved with the inclusion of f-CNOs. In consequence, the present study can clarify the potential cytotoxic effects of f-CNOs on osteoblast cells. Both mechanical and cytocompatibility results were f-CNOs dose-dependent. Furthermore, to explore the efficacy of GL/f-CNOs composite hydrogels as drug vehicles, 5-fluorouracil (5-FU) drug release was studied under physiological conditions. Remarkably, f-CNOs bearing composite hydrogels showed pH-responsive sustained drug release over 15 days.All the reagents and organic solvents were purchased from commercial suppliers and used without further purification. Gelatin (GL) from porcine skin, glutaraldehyde (GA), 5-Fluorouracil (5FU), methacryloyl chloride (MA), hydroquinone, 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide (EDC), and N-hydroxysuccinimide (NHS) were purchased from Sigma Aldrich (St. Louis, MO, U.S.A). Osteoblast cells were obtained from the American Type Culture Collection (ATCC, Manassas, VA). Phosphate buffered saline (PBS) pH 7.4, Dulbecco's modified Eagle's medium/F12 without phenol red (DMEM/F12), penicillin/streptomycin, fetal bovine serum (FBS), and trypsin were bought from Gibco Invitrogen (CA, U.S.A.). CellTiter96®AQueous One Solution Cell Proliferation Assay was acquired from Promega (WI, U.S.A.). LIVE/DEAD Cell Imaging Kit was purchased from Molecular Probes, Life Technologies Corp. (CA, U.S.A.). Alizarin Red S, G418 disulfate salt, ascorbic acid, dexamethasone, β-glycerophosphate, and cetylpyridinium chloride were purchased from Sigma Aldrich (MO, U.S.A.).Hydroquinone (1.0 g, 9.08 mmol) and N, Nʹ-diisopropylethylamine (1.42 mL, 8.17 mmol) were dissolved in anhydrous tetrahydrofuran (THF), and the reaction mixture was probe sonicated for 30 min. Then, methacryloyl chloride (887 μL, 9.08 mmol) was added dropwise into the above solution and continued the probe sonication for 60 min. After completion of the reaction (monitored by TLC), 50 mL of THF was added into the reaction mixture to generate diisopropylethylamine hydrochloride salt, and this salt was filtered off. The excess THF was evaporated, and the crude product was purified by column chromatography with hexane as eluent to provide 4-hydroxyphenyl methacrylate as a key monomer. The target molecule was properly characterized by NMR.1H-NMR (500 MHz, DMSO-d6): δppm 7.6 (2H, d, J = 8.3 Hz, o,oʹ-ArH), 6.9 (2H, d, J = 8.3 Hz, m,mʹ-ArH), 6.3 (1H, s, CCH), 2.00 (3H, s, CH3). 13C NMR (125 MHz, DMSO-d6): δppm 164.9 (CO), 154.6, 134.9, 131.8, 128.8, 124.2, 123.7, 18.0.; HRMS (ESI) calculated for C10H10O3 [M + H] 179.06, found 179.08.4-Hydroxyphenyl methacrylate (200 mg, 1.12 mmol) and 1 wt% of AIBN were dissolved in anhydrous THF and probe sonicated for 60 min. After that, the reaction mixture was diluted with 75 mL of diethyl ether to precipitate the polymer. The solids were filtered off and washed with dichloromethane (DCM) to remove unreacted monomer and catalyst. Then the crude product was dissolved in 3 mL of methanol and re-precipitated through diethyl ether. This precipitate was filtered off and dried in a hot oven at 45 °C for 12 h to obtain the PHPMA as white solid. The polymer was characterized using NMR and GPC analysis. 1H-NMR (500 MHz, DMSO-d6): δppm 7.6 (2H, br s, o,o′-ArH), 6.9 (2H, br s, m,m′-ArH), 2.36 (2H, br peak, CH2 polymeric), 1.31 (3H, br peak, CH3 aliphatic). 13C-NMR (125 MHz, DMSO-d6): δppm 175.0, 154.3, 132.14, 126.0, 124.4, 124.0, 122.8, 119.5, 117.9, 45.9, 20.0. GPC analysis: Weight-average molecular weight, Mw (g/mol) = 31, 893 and polydispersity index = 1.2.CNOs with a carboxylic acid functional group (50 mg), EDC (285 mg), and NHS (175 mg) were dissolved in anhydrous DMF and probe sonicated at 12W power for 45 min to activate the carboxyl groups of CNOs. Then, 100 mg of PHPMA was added into the above solution and probe sonicated for 120 min. The reaction mixture was then centrifuged at 7000 rpm to eliminate larger aggregates and excess unreacted reagents. The resulting solid was washed with DMF/triethylamine (9.9: 01) and dried under vacuum to produce poly 4-hydroxyphenyl methacrylated CNOs (f-CNOs) as a black solid. Finally, the black solid was stored in a refrigerator at 4 °C for further use. 1H-NMR (500 MHz, DMSO-d6): δppm 7.7 (2H, br s, o,o′-ArH), 7.0 (2H, br s, m,m′-ArH), 2.0–1.8 (2H, br peak, CH2 polymeric), 1.4–1.1 (3H, br peak, CH3 polymeric). 13C-NMR (125 MHz, DMSO-d6): δppm 177.2, 174.5, 153.8, 131.9, 124.5, 124.0, 123.2, 122.0, 119.4, 45.3, 19.4. GPC analysis: weight-average molecular weight, Mw (g/mol) = 34, 670 and polydispersity index = 1.3.Pristine GL (3% w/v) was dissolved in PBS (pH 7.4) and probe sonicated for 60 min. After that, crosslinker glutaraldehyde (0.4%, w/w) was added to the above GL solution, and sonication was continued for 15 min to form the gelation. The dry pristine GL hydrogel was obtained by a freeze-drying process. For the preparation of GL/f-CNOs (1 mg/mL) hydrogel, initially, 1 mg/mL of f-CNOs was probe sonicated for 30 min in PBS (pH 7.4) for the uniform dispersion. Then, the prepolymer solution of GL (3% w/v in PBS) was added into the CNOs solution, and probe sonication was continued for 60 min to attain a black solution containing GL-coated CNOs. Next, crosslinker glutaraldehyde (0.4%, w/w) was added into the above solution, and sonication was continued for 20 min to obtain GL/f-CNOs (1 mg/mL) composite hydrogel. The freeze-drying process was used to obtain dry GL/f-CNOs (1 mg/mL) composite hydrogel. Similarly, GL/f-CNOs (2 mg/mL) hydrogels were also prepared with a target concentration of 2 mg/mL of f-CNOs. To prepare the drug-loaded hydrogels, 5 mg/mL of 5-FU was added to the above solutions (pristine GL and GL/f-CNOs) before the addition of crosslinker.Fourier transform infrared (FTIR) spectroscopy (PerkinElmer Universal ATR Sampling Accessory Frontier) was utilized to scrutinize the functional groups of f-CNOs and hydrogel samples. The NMR spectra of target molecules were recorded using JEOL Model JNM ECX (500 MHz) NMR spectrometer, and deuterated dimethyl sulfoxide (DMSO-d6) was as a solvent. Q-TOF mass spectrometry was used to record mass spectra of monomer, and data were analyzed using the built-in software. The molecular weights and polydispersity index (PDI) of targeted polymers were measured using gel permeation chromatography (GPC, Agilent Technologies 1260 Infinity Series instrument) analysis with PL gel mixed C and B 10-μm columns.The Malvern Nano-ZS instrument was used to perform DLS measurements and analyzed by Zetasizer software. The f-CNOs with a final concentration of 500 μg/mL were dispersed in water, and DMEM cell medium or PBS 0.01M. The f-CNOs samples were probe sonicated for 60 min and then diluted into 50, 25, 5, and 1 μg/mL in water, and DMEM cell medium or PBS 0.01M, respectively. After that, the size of the particle was measured. Zeta potential measurements were recorded using dispensable zeta potential cuvettes on the same apparatus. All the zeta measurements were carried out three times per sample and averaged to obtain the final results.Swelling measurements of hydrogels were obtained by gravimetrically on a definite amount of dried hydrogel samples. Initially, the freeze-dried and pre-weighed hydrogel samples were immersed in PBS and DMEM, respectively, and kept at 37 °C for 4 h until the equilibrium of swelling had been reached. The swollen hydrogels were removed, and excess water was soaked mildly with filter paper and weighed with a microbalance. The equilibrium swelling ratio (ESR) was measured using the following equation:where Ws is the weight of hydrogels at equilibrium state and Wd is the weight of the hydrogels at the dry state.Degradation of hydrogels was measured with respect to weight loss. For this, initially weighed hydrogel specimens (W0) were immersed in Dulbecco's Modified Eagle's medium (DMEM) and incubated at 37 °C for 25 days. Then, the samples were taken out from the medium at specified time intervals, washed and dried in the desiccator for 12 h and weighed (Wt). The weight loss ratio calculated as 100×W0−WtW0. The weight remaining ratio was calculated as. 100−[100×W0−WtW0]In vitro 5-FU release from the hydrogels was measured using UV-spectrophotometer (Agilent Technologies, 89090A). 30 mg of 5-FU-loaded hydrogel samples were immersed in 10 mL of DMEM and gently incubated at 37 °C. At specified time intervals, 2 mL of 5-FU released medium was collected and replaced with 2 mL of fresh DMEM medium to retain the solution volume constant. The drug release was determined at λmax = 265 nm to obtain 5-FU concentration. The 5-FU release from hydrogel samples against release time was demonstrated. The pH-values (pH 5.0 and 7.4) of the DMEM medium were adjusted with 1 M HCl or 1 M NaOH to measure the pH-responsive drug release. Triplicate experiments were carried out. The drug release (%) was calculated from the following formulaDrugrelease(%)=MassofdrugloadedGel−MassofdrugreleasedMassofdrugreleased×100The In-vitro cytocompatibility of samples was evaluated with human osteoblasts (bone-forming cells). The cytotoxicity of GL/f-CNOs hydrogel specimens has studied by culturing osteoblasts on the surface of samples with specified concentrations of f-CNOs (1 mg/mL and 2 mg/mL). Furthermore, cell morphology and viability were measured.CellTiter96®AQueous One Solution Cell Proliferation Assay was used to measure cell viability. For this, disk-shaped (∼6.3 mm in diameter) pristine GL and GL/f-CNOs composite hydrogels were cut into thin sections to measure the proliferation and cell viability. Before seeding the cells, the thin-sectioned hydrogel specimens were sterilized by ethanol (70% v/V) followed by UV irradiation. Then, the tinny sections of hydrogel samples were decorated on 96 well plates. Next, the bone cells at a density of 1 × 104 cells per well (∼3.12 × 104 cells/cm2) were seeded on the surface of the hydrogels. On the next day, the non-adherent cells were removed by changing the medium. The cell number was calculated after 1, 3, 7, and 14 days post-seeding using CellTiter96®. Furthermore, the LIVE/DEAD Cell Staining Kit was used to measuring the cell viability of hydrogels, and the images were recorded using fluorescence microscopy. The tissue culture plate was used as a control. The experiments were run in triplicate.Prior to cell seeding on 24 well plates, pristine GL and GL/f-CNOs composite hydrogels were cut into a disk shape to decorate on 24 well plates. After that, osteoblast cells at a density of 1 × 104 cells/mL were seeded on the surface of hydrogels in DMEM/F12 medium supplemented with 0.3 mg/mL of G418 disulfate salt, 2.5 mM of L-glutamine, 1% of penicillin/streptomycin and 10% of fetal bovine serum. The cells were incubated for 24 h in a humidified atmosphere at 5% CO2. Then, the medium was transferred from the well plates and washed several times with phosphate buffer solution. After 14 days of incubation, cell images were recorded by an optical microscope (Model IN200A-5M, Amscope, Chino, CA).The cell culture experiments were conducted to measure the cell attachment and cell proliferation of hydrogels. The morphological features of cells cultured on the surface of hydrogels were recorded by using SEM analysis. For this, osteoblast cells seeded hydrogel samples were incubated for fourteen days. Then the samples were washed with PBS and treated with 2.5% glutaraldehyde for overnight. Next, the specimens were dehydrated by ethanol and dried by vacuum desiccator for overnight. Before the SEM analysis, the hydrogel samples were coated with gold.All the experiments were carried out in triplicate, and the results were presented as mean ± standard deviation (SD). Tukey post hoc, and one-way analysis of variance were performed to determine statistical analysis and statistical significance was considered at p ≤ 0.05.Previously we synthesized poly 4-mercaptophenyl methacrylated CNOs starting from a thioester coupling of 4-mercaptophenol with COOH–CNOs followed by methacrylatation and polymerization (). The synthetic route was laborious and the reaction required a longer time to obtain the final materials. Therefore, in the current study we have synthesized poly 4-hydroxyphenyl methacrylated CNOs, the reaction was started from highly reactive hydroquinone (1,4-dihydroxybenzene) using versatile sonochemistry technology (). Hydroquinones constitute an essential group of substrates, and their chemical moiety is often found in natural and synthetic organic compounds. () Usually, they undergo redox transformations between quinones and hydroquinones. Plastoquinones and ubiquinones play vital roles in energy production based on the hydroquinone-quinone redox reaction (). Thus, we hypothesized that hydroquinones moiety would provide good cytocompatibility.Initially, hydroquinone was treated with methacryloyl chloride in the presence of diisopropylethylamine to provide 4-hydroxyphenyl methacrylate (HPMA) as the key monomer, and this reaction was completed within 60 min through probe sonication method. The chemical structure of (HPMA) was confirmed by 1H and 13C-NMR analysis (, supporting information). Next, HPMA was polymerized using a catalytic amount of AIBN, and the poly 4-hydroxyphenyl methacrylate (PHPMA) was accomplished within 60 min via probe sonication (). The chemical structure and molecular weight (Mw) of the PHPMA were confirmed by NMR and GPC analysis, respectively (See in supporting information). Specifically, the GPC measurements of PHPMA exhibited a weight-average molecular weight (Mw) of 31,893 with a polydispersity index (PDI) of 1.25.Finally, the PHPMA was coupled with COOH–CNOs via ester coupling in the presence of EDC and NHS (). The reaction was conducted in DMF via the sonochemical method, and the targeted product poly 4-hydroxyphenyl methacrylated CNOs (f-CNOs) was obtained within 120 min. The f-CNOs were characterized by NMR and GPC analysis (see in supporting information). The GPC measurements of f-CNOs reveal that the synthesized f-CNOs showed approximately 34,673 of Mw with 1.32 of PDI.To accomplish the greater physicochemical properties of f-CNOs based hydrogel, first, it is required to disperse the CNOs particles throughout the gel matrix homogeneously. In this context, the CNOs would be stabilized uniformly in physiological buffer or aqueous environments. Many reports have revealed on the stabilization of those CNOs in aqueous environment by using surfactants and fluorescent molecules (). Consequently, we synthesized poly 4-hydroxyphenol methacrylated CNOs through probe sonication technology. The synthesized f-CNOs were probe sonicated in water, and stabilized dispersion was observed over 12 months. It is postulated that PHPMA chains could covalently be attached to the surface of CNOs to stabilize in the aqueous environment. The acoustic cavitation or sonic wave is the best stringent source of exfoliation of 2D nanomaterials.The acoustic cavitation occurs in the liquid environment due to the fluctuation of pressure that generates bubbles growth followed by bubble collapse and internal turbulence. Finally, this ultrasound energy converts into enormous temperature and confining pressure. Ultrasound waves can negotiate through CNOs, which are held by π-π stacking and/or van der Waals forces. During this process, CNOs have stratified in a liquid environment. The stabilization of colloidal CNOs is attained by chemical conjugation of HPMA macromolecular chains onto the CNOs surface. Consequently, probe sonication would be a great choice to accomplish the homogeneously dispersed and stabilized CNOs in the aqueous environment. Highly stable CNOs produced by ultra-sonication are very effective to improve the tensile, electrical, and elasticity properties of the nanocomposites. The dispersion and stability of synthesized f-CNOs were systematically investigated in different environments including water, PBS and DMEM using DLS measurements. The pristine COOH–CNOs showed around 32 ± 1.7 nm of diameter in water and 212 ± 1.1 nm of diameter in PBS (b). The diameter values of COOH–CNOs did not change with the time and concentration, suggesting a low tendency of agglomeration even at comparatively high concentration. Similarly, the hydrodynamic diameter of f-CNOs was also measured and found 38 ± 1.2 nm in water and 219 ± 1.5 nm in PBS (We performed DLS measurements in DMEM to monitor the agglomeration behavior of CNOs under physiological conditions. The dispersion of pristine CNOs in DMEM showed an average diameter of 211 ± 2.1 nm. The f-CNOs exhibited an average diameter of 264 ± 1.9 nm in cell medium (b). The results demonstrate that there is no significant difference in the dispersion of f-CNOs in both PBS and DMEM. Besides, the zeta potential of pristine CNOs and f-CNOs was verified in PBS and DMEM. The pristine CNOs exhibited −31 ± 1.0 and −29 ± 1.0 mV of zeta potential values in PBS and DMEM, respectively (b). The results indicate that the COOH group has a significant effect on the charge capacity of pristine CNOs. Whereas, f-CNOs showed a positive charge effect with +10 ± 1.0, and +7 ± 2.0 mV of zeta potential values in PBS and DMEM, respectively (b). Thus, positive zeta potential values confirm the successful chemical conjugation of HPMA moiety on the surface of CNOs. Then, stabilized and uniformly dispersed f-CNOs were reinforced with GL to fabricate GL/f-CNOs composite hydrogels by the probe sonication method (a). Initially, f-CNOs were dispersed by probe sonication, and GL solution (3%) was added into it. After 60 min of probe sonication, glutaraldehyde was added as a cross-linker to form the gelation of composites. The gelation process was very fast, and the gelation was completed within 30 min. The digital photo of GL/f-CNOs composite hydrogel with 2 mg/mL of f-CNOs was illustrated in c, and the overturned image exhibits proof of the gelation.The microstructure morphologies of composite hydrogels were obtained from the SEM analysis. The cross-sectioned SEM images of hydrogels were illustrated in . As shown in the SEM images, the composite hydrogels displayed a continuous and porous structure. The internal morphology and porosity were dependent on the concentration of f-CNOs. The higher f-CNOs content bearing GL/f-CNOs composite hydrogel displayed improved pore sizes.The porosity of hydrogels plays a critical role in drug release experiments. Therefore, we measured the porosity of the GL/f-CNOs composite hydrogels, and the results were presented in (supporting information). GL/f-CNOs (1 mg/mL) hydrogel specimen showed 3.08 μm of average pore diameter (), whereas GL/f-CNOs (2 mg/mL) hydrogel sample exhibited 4.95 μm of average pore diameter (). This porous morphology can improve the water uptake properties of the composite hydrogels.A DSC analysis was used to measure the melting temperature and crystallinity of composite hydrogels, and the results were depicted in a. Pristine GL hydrogel exhibited 35.02 ± 0.17 of a degree of crystallinity (DOC), and GL/f-CNOs composite hydrogel with 1 mg/mL of f-CNOs showed 46.19 ± 0.37 of DOC. On the other hand, GL/f-CNOs composite hydrogel with 2 mg/mL of f-CNOs displayed 51.12 ± 0.13. Furthermore, all the hydrogels showed a melting temperature in a range of 95–155 °C (a). Overall, DSC analysis revealed that the crystallinity and melting temperature of the composite hydrogels were significantly enhanced with the inclusion of f-CNOs. The TGA plot of freeze-dried hydrogels was depicted in b. The TGA results suggested that the thermal stability of composite hydrogels was proportional to the concentration of f-CNOs. The gradual increment in the thermal stability of composite hydrogels was observed with increasing the f-CNOs content. Particularly at 112 °C, around 12–14% of weight loss was observed, which could be due to the removal of entrapped water within hydrogel samples. The hydrogels displayed thermal decomposition in the temperature range of 295–425 °C. Specifically, pristine GL hydrogel showed initial degradation temperature (T0.1) around at 298 °C and midpoint degradation temperature (T0.5) at 345 °C. GL/f-CNOs composite hydrogel with 1 mg/mL of f-CNOs showed T0.1 at around 345 °C and T0.5 at 420 °C. Whereas, GL/f-CNOs composite hydrogel with 2 mg/mL of f-CNOs exhibited T0.1 at 347 °C, and T0.5 at 424 °C. Thus, TGA results demonstrated that the onset temperature of the GL/f-CNOs composite hydrogels was considerably improved with the addition of f-CNOs due to the high conductivity of CNOs as well as van der Waals or noncovalent electrostatic interaction between f-CNOs, and GL chains.FTIR analysis was performed on pristine GL and GL/f-CNOs composite hydrogels to study the possible interactions between GL and f-CNOs (a, pristine GL hydrogel showed the absorption bands at approximately 1649 cm−1 for stretching vibration of CO bond and amide I. Whereas, 1537 cm−1 for C–N bond and amide II, respectively (). The absorption bands of C–H stretching vibrations of aliphatic groups appeared in a frequency range of 2956–2967 cm−1. Whereas, N–H bending and C–N stretching peaks of pristine GL were observed at 1446, 1240, and 1084 cm−1, respectively.An N–H stretching vibration of amide A appeared as a broad peak in the absorption range of 3480–3110 cm−1. Furthermore, the FTIR spectra of pristine f-CNOs showed the major bands approximately at 1701 cm−1 for the CO group and 1560-1418 cm−1 for vibrational starching of phenyl ring moiety. All the peaks of f-CNOs have contracted in the FTIR spectrum of GL/f-CNOs composite hydrogel, which reveals the effective π-π stacking or hydrophobic interactions between f-CNOs and polymeric chains of GL. As shown in a, GL/f-CNOs (2 mg/mL) composite hydrogel exhibited a broad absorption band in the range of 3500–3025 cm−1 for amide A (N–H stretching vibration). Besides, GL/f-CNOs (2 mg/mL) composite hydrogel showed 1647 cm−1 for CO stretching vibration and amide I, whereas 1535 cm−1 for amide II and C–N bond, respectively. Similarly, C–N stretching and N–H bending peaks of composite hydrogel were shifted to lower frequency range, which revealed that f-CNOs were mingled into the hydrogel matrix. Thus, FTIR spectra show physicochemical interactions among f-CNOs and GL.Sustained deformation and tolerance of high loads of the hydrogel are important properties in tissue engineering, and drug delivery applications. Therefore, the tensile properties of composite hydrogel were measured, and a non-linear stress/strain curves were presented in b. With the inclusion of f-CNOs, the tensile strength of composite hydrogels was significantly improved. Thus, GL/f-CNOs (2 mg/mL) composite hydrogel showed 4.75 MPa of tensile strength, whereas GL/f-CNOs (1 mg/mL) hydrogel displayed 2.42 MPa of tensile strength. The tensile results suggested that GL/f-CNOs composite hydrogel with 2 mg/mL of f-CNOs exhibited lower strain and higher tensile strength than GL/f-CNOs (1 mg/mL) hydrogel. This could be due to the hydrogen bonding or electrostatic interactions between GL and f-CNOs. Furthermore, the tensile strength of the GL/f-CNOs (2 mg/mL) hydrogel was compared with pristine GL hydrogel (1.61 MPa). The GL/f-CNOs (2 mg/mL) hydrogel showed three times greater tensile strength than pristine GL hydrogel. Thus, tensile results suggest that f-CNOs content (2 mg/mL) could be critical to attaining improved mechanical properties. Therefore, tensile results of composite hydrogels revealed that there could be hydrogen bonding interactions or electrostatic interactions between f-CNOs, and GL.A compression test was performed to estimate the mechanical stability behavior as well as the durability of the hydrogels. The cyclic compression tensile (stress-strain) curves of the GL/f-CNOs hydrogels at different rates of maximum compression (35, 50, and 65%) were presented in . The GL/f-CNOs hydrogels unveiled good shape recovery behavior. When the strain was increased from 35% to 65%, GL/f-CNOs hydrogels were showed increased hysteresis loops. Specifically, GL/f-CNOs hydrogels were exhibited larger hysteresis loops than the GL hydrogels at different rates of maximum compression (a–c). The cyclic stress-strain curves of the f-CNOs loaded hydrogels confirmed that the GL/f-CNOs (2 mg/mL) hydrogels could be compressed to large strains, specifying that the hydrogels are elastic materials. Moreover, it shows that the energy dissipation of the GL/f-CNOs hydrogels was more effectual during the loading/unloading cycles.This could be due to the delayed restoration and destruction of the hydrogen bonding interactions or electrostatic interactions between the f-CNOs and the GL at different strain values during the cyclic test. Overall, cyclic compression results indicated that the GL/f-CNOs composite hydrogels exhibited good elasticity and high mechanical durability.The degradation properties of hydrogels play a vital role in tissue engineering and drug delivery. Hence, we measured in vitro degradation of composite hydrogels as a function of incubation time in DMEM at 37 °C, and the results were presented in a. The f-CNOs content has a considerable impact on weight loss. The pristine GL hydrogel showed around 96% of weight loss in 25 days. On the other hand, the composite hydrogels lost their weight steadily up to 25 days (a). The GL/f-CNOs composite hydrogel with more f-CNOs content (2 mg/mL) exhibited a slower weight loss rate than hydrogel with less f-CNOs content (1 mg/mL). Particularly, GL/f-CNOs (2 mg/mL) composite hydrogel showed 42% of degradation in 25 days. Whereas, GL/f-CNOs (1 mg/mL) composite hydrogel displayed 63% of degradation in 25 days. This could be due to the existence of electrostatic interactions between f-CNOs and GL or the greater hydrophobicity and higher tensile strength of f-CNOs.In addition, the equilibrium-swelling ratio of pristine GL and f-CNOs filled composite hydrogels was also measured under physiological conditions (PBS and DMEM), and the results were presented in b. The swelling ratio was decreased along with the increase of f-CNOs content. Pristine GL hydrogel showed around 65%, and 60% of swelling in DMEM and PBS, respectively (b). The swelling ratio of pristine GL in PBS was a little lower compared to those in DMEM. The GL/f-CNOs (1 mg/mL) composite hydrogel displayed around 44%, and 42% of swelling in DMEM, and PBS, respectively, indicates f-CNOs have a detrimental effect on the swelling.The water uptake was extremely relying on f-CNOs content into the gel matrix. Whereas, GL/f-CNOs (2 mg/mL) hydrogel exhibited approximately 35% and 32% of swelling in DMEM and PBS, respectively (b). Predominantly, water uptake reliant on the effective concentration of the polymer chains present in the hydrogel matrix. With increasing f-CNOs filler in the hydrogel matrix, the swelling was decreased due to additional physisorption, which deeds as physical crosslinking sites of the polymer chains. The swelling results have also consistent with some nanofiller reinforced composite hydrogels.It is reported that lysosomes and endosomes embrace higher acidic nature with a pH range of 5.0–6.5 than the cytoplasm (). Under these conditions, 5-FU release from the hydrogels was studied at pH 5.0 over 15 days of incubation and illustrated in a, GL/f-CNOs (2 mg/mL) composite hydrogel showed around 31% of burst release within 24 h. After that, around 61% of the prolonged drug was observed in 15 days. This could be due to the van der Waals forces or strong π-π stacking among 5-FU, f-CNOs, and GL polymer chains. These characteristics might have reduced the diffusion rate of 5-FU from the composite hydrogels. It is also anticipated that solubility of 5-FU decreases in the presence of f-CNOs, and dawdled the 5-FU diffusion from the composite hydrogels. Whereas, GL/f-CNOs (1 mg/mL) hydrogel exhibited around 36% of burst release within 24 h. Then, the sustained drug release was observed for up to 15 days. After 15 days of incubation, around 84% of drug release was detected from GL/f-CNOs (1 mg/mL) composite hydrogel. These results suggest that the diffusion of the drug is the major mechanism of drug-loaded composite hydrogels. Thus, it is postulated that GL polymer chains, slow degradation, and mobility of f-CNOs were exhibited a key role in the drug release. In contrast, pristine GL hydrogel showed around 67% of burst release within 24 h. After that, sustained drug release was noticed, and approximately 97% of the drug was released in 15 days and reached a plateau.The pH of the intracellular and extracellular environment of cancer cells and normal cells is different (). The pH of the intracellular environment of normal cells and blood is around 7.4, whereas intracellular pH of cancer and normal cells is around 7.2 (). Corresponding to these conditions, 5-FU release was measured in DMEM at pH 7.4, and slower drug release was observed (b). The GL/f-CNOs (2 mg/mL) composite hydrogel showed around 29% of burst release on the first day of incubation. Next, the sustained drug release (60%) was observed for up to 15 days. The GL/f-CNOs (1 mg/mL) hydrogel exhibited 31% of burst release on the first day, and 82% of sustained drug release was noticed at the end of 15 days of incubation. Besides, pristine GL hydrogel displayed 66% of burst release within 24 h, and the remaining drug was released in a sustained manner over 15 days of study. Specifically, pristine GL hydrogel exhibited 99% of drug release in 15 days and reached a plateau. It could be due to the hydrophilic nature of 5-FU within the gel matrix, which led to faster diffusion of the drug from the hydrogel into the medium. The results at pH 7.4 attributed π-π stacked 5-FU molecules on the surface of f-CNOs. Thus, it is posited that due to the enhanced permeability, and retention (EPR) effect, 5-FU can transfer into cells through endocytosis and expose to a low pH environment and facilitates active drug release from composite hydrogels.The cytotoxicity of GL/f-CNOs composite hydrogels was also measured with human osteoblast cells using CellTiter96® AQueous One Solution, as shown in . The human osteoblast cells were seeded on the pre-sterilized thin-sectioned hydrogel samples. Pristine GL and GL/f-CNOs composite hydrogels exhibited very similar cell viability on the first day of incubation. However, enhanced cell viability was observed in GL/f-CNOs composite hydrogels on the seventh day of incubation, whereas pristine GL hydrogel showed comparable cell viability on the same day (Remarkably on day fourteen, GL/f-CNOs (2 mg/mL) hydrogel displayed superior cell viability compared to pristine GL and GL/f-CNOs (1 mg/mL) hydrogels. This could be due to the lower degradation rate, enhanced tensile strength, and higher hydrophobicity of GL/f-CNOs (2 mg/mL) hydrogel. The cytotoxicity results demonstrated that the cell viability was depended on the f-CNOs content. Besides, the results suggested that the GL/f-CNOs composite hydrogels could use as potential drug carriers with high cytocompatibility. It is worth to mention that 3D hydrogel scaffolds with good porosity, the desired shape, and mechanical properties are necessary for cartilage tissue engineering (). GL/f-CNOs hydrogels exhibited good porosity, cell viability, compressive strain, and shape recovery, good mechanical durability, and elasticity. Therefore, these properties suggest that the GL/f-CNOs hydrogels scaffolds are adequately mechanically stable to withstand implantation and to maintain regenerated cartilage.The morphology and cellular interactions of osteoblast cells on the surface of thin-sectioned hydrogel specimens were achieved using SEM analysis, and the results were depicted in . After fourteen days of incubation, the cellular attachments were enhanced on the surface of GL/f-CNOs composite hydrogels (a). Particularly, osteoblast cells were stretched and adhered to the surface of the GL/f-CNOs composite hydrogels (b–d). After fourteen days, full-fledged and improved cellular extensions of osteoblast cells were observed on the surface of the composite hydrogels (b–d, white arrows). Thus, the cell colonization, cell population, and size of osteoblasts were extensively enhanced over fourteen days of study. Nevertheless, GL/f-CNOs composite hydrogels revealed good cell attachment, proliferation, and cytocompatibility of f-CNOs.The cytotoxicity of f-CNOs was also evaluated by LIVE/DEAD kit in cell culture medium containing GL/f-CNOs composite hydrogels, and the optical images of the cells incubated for fourteen days were depicted in . The cell culture plate has taken as a controller, and it showed a decent percentage of DEAD cells over fourteen days (Whereas, pristine GL hydrogel showed a decent percentage of LIVE cells with a certain degree of DEAD cells (b). Surprisingly more than 90% of LIVE cells were detected in GL/f-CNOs (2 mg/mL) composite hydrogels (d). GL/f-CNOs (1 mg/mL) composite hydrogel also exhibited 85% of LIVE cells with few numbers of DEAD cells (c). These results revealed that osteoblast cells were well attached to the surface of composite hydrogels, and the cell growth was significantly improved with f-CNOs content. This might be due to the less degradability, excellent biocompatible of CNOs, and HPMA moiety on the surface of f-CNOs. The GL/f-CNOs composite hydrogels showed excellent cell growth compared to pristine GL hydrogel and tissue culture plate. The results also reveal a positive effect of f-CNOs on the survival of osteoblasts. Besides, stretched morphology was noticed on the surface of composite hydrogels. This could be due to the surface morphology, a contact angle with cell media, and the surface chemical interactions that have played a major role in the development of cell growth. Besides, it is also postulated that f-CNOs were well dispersed within the gel matrix and wrapped by GL polymer chains offered strengthened GL/f-CNO composite hydrogels with amenable cytocompatibility.We have validated the sonochemical method as a versatile approach for the development of highly surface-modified CNOs by ester coupling with poly 4-hydroxyphenyl methacrylate (PHPMA). The sonochemical method played a significant role in the control of the dispersion and size of the CNOs. A small quantity of f-CNOs has exhibited an impeccable impact in the improvement of mechanical properties, and cytocompatibility of GL/f-CNOs composite hydrogels. The GL/f-CNOs (2 mg/mL) composite hydrogel exhibited the highest improvement in tensile strength as compared to GL/f-CNOs (1 mg/mL) and pristine GL hydrogels. The strengthening mechanism was greatly influenced by the degree of colloidal stability, concentration, and physisorption of f-CNOs within the gel matrix. The GL/f-CNOs composite hydrogels showed excellent cell viability with osteoblast cells, and the cytotoxicity was dose depended. The LIVE/DEAD results of GL/f/f-CNOs hydrogels revealed more than 90% of osteoblast survivability. Besides, the composite hydrogels showed pH-responsive and sustained drug (5-fluorouracil) release under physiological conditions. Collectively, our results represent new perspectives in the application of conjugated CNOs in biomedicine. The mechanical and cytotoxicity properties of composite hydrogels are highly dependent on their physicochemical characteristics, and critically, that surface chemical conjugation of CNOs allows significant control over these properties. Thus, these surface-functionalized CNOs bearing composite hydrogels can be useful as potential carbon nanocomposites in cartilage tissue engineering and drug delivery.The Authors have no conflict of interests.The following are the Supplementary data to this article:GPC, 1H and 13C-NMR spectra for all new polymers.Supplementary data to this article can be found online at Pull-in response and eigen frequency analysis of graphene oxide-based NEMS switchIn this work, finite element analysis of shunt capacitive switch having Gold/Graphene oxide (GO) bridge structure is reported. The pull-in voltage analysis of two structures, intact and circularly perforated Gold/GO-based shunt capacitive switch is performed. The pull-in voltage of 5.6 V and 4.75 V are obtained for intact and circularly perforated structure respectively for 2 µm long, 0.3 µm wide and 4.9 nm thick GO suspended beam. The pull-in voltage gets reduced by making circular holes (perforations) in the suspended beam. Also, the extraction of basic modes of vibration of the switch is done using eigen frequency analysis. The eigen frequency analysis for both the structure is performed. The eigen mode obtained in eigen frequency analysis gives information about the desired functioning of NEM switch. The obtained eigen frequencies for primary eigen modes are 3.8 MHz and 3.21 MHz for intact and circularly perforated NEM switch structure. The perforations in the beam reduce the flexural rigidity of the beam hence the frequency of eigen mode is less.In Radio frequency (RF) communication systems, the demand for high-performance devices has grown drastically. Microelectromechanical systems (MEMS) technology has empowered the availability of devices having low loss, small size, high linearity and low power consumption In this paper, pull-in voltage and eigen frequency analysis of a NEM switch using gold/GO as beam material is presented. Gold/GO-based switch designing is done in finite element modeling (FEM) based tool COMSOL Multiphysics. The switching operation of NEM switch is achieved by the electrostatic actuation mechanism. For actuation, one gold electrode is used as bottom actuation electrode and another gold electrode is placed just above GO. The pull-in voltage and eigen frequency analysis for both intact and circularly perforated structures have performed.In this work, a double clamped shunt capacitive switch is proposed in which electrostatic actuation is used. Electrostatic actuation offers benefits like less power consumption, small electrode size and high switching speed etc. In this paper, a double clamped shunt capacitive switch has reported in which GO has used as suspended beam. The side view of GO-based NEM switch is shown in (a) and circularly perforated beam structure is shown in (b). In this switch structure, two gold electrodes are used, one is used as bottom electrode at which voltage is applied. Another gold electrode is used just above the suspended GO beam. The top gold electrode is kept at ground potential. The geometrical dimensions of the suspended beam/bridge, electrodes, and circularly perforated beam are given in FEA of NEM shunt switch has done in COMSOL Multiphysics. GO has used as double clamped suspended beam structure. The electromechanics module solves the coupled equations for electric field and structural deformation. In FEM simulations, the GO beam is set with Poisson ratio of −0.567 and Young’s modulus of 27 GPa In electrostatic actuation, voltage is applied at one electrode while the other electrode is kept at ground potential. When applied voltage is increased, the electrostatic forces try to pull the suspended beam towards the actuation electrode. The mechanical force in the suspended beam tries to retain the initial position. When electrostatic force overcomes mechanical force, the beam snaps down and comes in contact with the bottom electrode. The voltage at which the suspended beam snaps down and touches the actuation electrode is known as actuation/pull-in voltage g = gap between beam and actuation electrodeIn NEM switches, low actuation voltage is desired. The pull-in voltage can be decreased by either changing spring stiffness of suspended beam, by changing the device dimensions, by using perforations or by using meander structure. By making perforations in the beam, the mass of the beam reduces and the air below the suspended beam get easily squeeze out. Thus, it reduces the actuation voltage. In the perforated structure, the change in actuation voltage is highly dependent on the size/shape of perforations Eigen frequency also known as fundamental characteristic frequency/natural frequency, is a frequency at which a device vibrates. When a device vibrates at a certain eigen frequency, structural deformation takes place in a particular mode. This analysis provides information about the shape of eigen mode. Each eigen mode has different eigen frequency value. The desired motion is represented by the primary eigen mode . The next high mode f1 of eigen frequency can be determined by Eq. The spring constant depends upon the Young’s modulus of the bridge material and device dimensions. The high eigen modes depends upon the inertia of the beam and device dimensions.In this paper, finite element analysis (FEA) of a shunt capacitive switch is done in COMSOL Multiphysics. The pull-in voltage analysis is performed for both intact structure and circularly perforated structure. The pull-in voltage of 5.6 V is obtained for the intact structure of GO-based NEM switch. The (a) shows the total displacement of 50 nm achieved at voltage 5.6 V. The pull-in voltage of 4.75 V is obtained for the circularly perforated structure. The (b) shows the total displacement of 50 nm at voltage 4.75 V. The actuation voltage depends upon the spring stiffness of suspended beam. The spring stiffness of the suspended beam gets changed by making perforations in the beam. By making perforations, the mass of the beam reduces and the beam becomes less stiff. While other parameters are same for both cases but the spring stiffness for both intact and perforated beam is different. Hence, different voltage values are obtained. shows the gap vs applied voltage plot for both structures. When the applied voltage is 0 V, the suspended beam remains in upstate. As the applied voltage increases, the gap between the actuating electrode and suspended beam decreases. When the applied voltage is equal to pull-in voltage (intact structure = 5.6 V and circularly perforated structure = 4.75 V), the beam touches the actuating electrode and the gap becomes zero. The results show that the pull-in voltage can be reduced from 5.6 V to 4.75 V by making circular perforations in suspended beam.Eigen frequency analysis has done for both intact and circularly perforated GO-based NEM switch structures. The first six eigen frequency modes are obtained for both intact and circularly perforated structure. The obtained eigen frequency modes are given in The basic modes of oscillation of the device are represented by eigen frequency analysis. In the analysis, different eigen modes can be obtained. The primary eigen mode represents the desired motion of the device while the higher eigen modes represent the undesired modes. For both intact and circularly perforated structures, six different eigen frequency modes are obtained using FEA as shown in . For intact GO NEM switch structure, the obtained values of eigen frequencies are 3.8 MHz, 19 MHz, 21.1 MHz, 65.1 MHz, 80.1 MHz, 125 MHz. For circularly perforated structure, the obtained values of eigen frequencies are 3.21 MHz, 16.3 MHz, 18 MHz, 62 MHz, 72.5 MHz, 123 MHz. The primary eigen modes in both cases are 3.8 MHz and 3.21 MHz for intact and circularly perforated structure respectively. For the circularly perforated structures, the eigen frequency values are less as compared to intact structure. By making a circularly perforated structure, the flexural rigidity of the suspended beam is reduced which reduces the inertia of the beam. The reduction in inertia further reduces the eigen frequency.The pull-in stability and eigen frequency analysis of gold/GO-based NEM switch have performed in this work. In the switch structure, gold/GO has used as suspended beam and gold electrode has used as actuation electrode. The FEM of gold/GO-based intact and circularly perforated structures are done using COMSOL Multiphysics. The circularly perforated structure gets actuated at a voltage less than the intact structure. By making perforations, the air below the suspended beam is easily squeezed out through the perforations, hence reduces the actuation voltage. Eigen frequency analysis for both the structures is performed to find out the primary eigen mode. It is observed that by making perforations, the pull-in voltage and eigen frequencies are reduced. The pull-in voltage can be further reduced by changing the perforation size/shape.Rekha Chaudhary: Methodology, Software, Writing. Prasantha R. Mudimela: Supervision, Validation, Writing - review & editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Microstructural properties of the mid-facial bones in relation to the distribution of occlusal loadingAlthough the concept of the occlusal load transfer through the facial skeleton along the buttresses has been extensively studied, there has been no study to link microarchitecture of the mid-facial bones to the occlusal load distribution. The aim of this study was to analyze micro-structural properties of the mid-facial bones in relation to occlusal stress. The study was performed by combining the three-dimensional finite element analysis (3D FEA) and micro-computed tomography analysis (micro-CT). Clenching was simulated on the computer model of the adult male human skull which was also used as a source of bone specimens. After the FEA was run, stress was measured at the specific sites in cortical shell and trabecular bone of the model along and between the buttresses. From the corresponding sites on the skull, twenty-five cortical and thirteen cancellous bone specimens were harvested. The specimens were classified into high stress or low stress group based on the stress levels measured via the FEA. Micro-architecture of each specimen was assessed by micro-CT. In the high stress group, cortical bone showed a tendency toward greater thickness and density, lower porosity, and greater pore separation. Stress-related differences in microstructure between the groups were more pronounced in trabecular bone, which showed significantly greater bone volume fraction (BV/TV) and trabecular thickness (Tb.Th) in the high stress group. Our results suggest that the mid-facial bones in the adult dentate male skull exhibit regional variations in cortical and trabecular bone micro-architecture that could be a consequence of different occlusal stress.Early descriptions of the maxillofacial architecture were made at the beginning of the 20th century, when a few researchers observed pillar-like areas within the mid-facial skeleton composed of a thick cortical bone However, recent investigations of the buttresses via finite element analysis (FEA) brought new findings related to the pattern of occlusal load distribution to light. Stress along buttresses was frequently registered only in the anterior maxilla, whereas it was distributed uniformly over the posterior maxilla having no form of buttresses Along with the analyses of the mid-facial biomechanics, recent investigations of the facial bone structure revealed tremendous regional variations in cortical and trabecular bone architecture in dentulous individuals Therefore, the aim of this study was to investigate bone micro-architecture in the different regions of the mid-facial skeleton in relation to the occlusal load dissipation. The study was performed by combining the three-dimensional finite element analysis (3D FEA) and micro-computed tomography analysis (micro-CT). We hypothesized that regional differences in micro-architecture exist in both cortical and trabecular bone as a consequence of different functional demands during mastication.The 3D FEA was used to show the pattern of occlusal load distribution through the mid-facial skeleton and to allow direct measurement of von Mises stress to which cortical and trabecular bone is subjected during clenching, respectively. Unlike the previous FE studies After 3D FEA was run, we measured Von Mises stress at the specific points in cortical shell and trabecular bone of the mid-facial skeleton on the loaded side (). Twenty-five and thirteen measurement sites were selected in cortical shell and trabecular bone, respectively, bearing in mind location of buttresses proposed by the classical theory and the distribution of occlusal load obtained during FEA. In the cortical shell, stress was measured at the following sites (a): along the alveolar process of the maxilla at the level of the apices of the tooth roots (5 points), 5 mm above the apices of the tooth roots (4 points), at the site where the posterior maxilla meets the pterygoid processes (1 point), in the body of the maxilla and the zygomatic bone along the buttresses (9 points) and between the buttresses (6 points). Stress in trabecular bone (c) was measured: along the alveolar process of the maxilla at the same level as it was measured in the cortical shell (8 points), in the frontal process of the maxilla (2 points), and within the zygomatic bone (3 points).The bone specimens were taken from the same skull for which computer model was developed. We chose the skull of a young adult male with a full dentition from the skeletal collection from the Laboratory for Anthropology, Institute of Anatomy, Faculty of Medicine, University of Belgrade. Twenty-five cortical and thirteen trabecular bone specimens were detached from the sites of the maxilla and the zygomatic bone at which von Mises stresses were measured (b, d). The vicinity of anatomical structures, such as tooth roots, infraorbital foramen, orbital rims, etc., was used to ensure a consistent site selection and co-registration of stress and micro-CT parameters and also to avoid inter-site overlapping during measurement. The specimens were classified into high stress or low stress group based on the observed tendency of calculated stresses to concentrate at the lower or higher level on the stress scale. Thus, cortical bone specimens subjected to stresses above 2.25 MPa were classified into the high stress group, while specimens from areas experiencing up to 1.49 MPa were classified into low stress group. Similarly, trabecular bone specimens that experienced stresses below 0.46 MPa and above 0.49 MPa were classified into low stress and high stress group, respectively.Cortical and trabecular bone specimens from both groups were scanned by micro-computed tomography (Scanco Medical μCT 40; Switzerland). Each sample was placed in a holder with a consistent cranio–caudal orientation and scanned in dry conditions. The samples were foam padded to avoid any movement artifacts during scanning. Images were obtained at 55 kVp and 144 μA, at isotropic resolution of 10 μm, 2048 × 2048 pixels per slice. The integration time per each projection was 200 ms. The micro-architecture of the cortical and trabecular bone was automatically evaluated using micro-CT evaluation program V6.5-1 with direct 3D morphometry. The following micro-architectural parameters were determined for cortical bone: cortical thickness (Ct.Th, mm), cortical porosity (Ct.Po, %), pore diameter (Po.Dm, mm), pore separation (Po.Sp, mm), total volume density (TV.Dn, mg HA/cm3), and bone volume density (BV.Dn, mg HA/cm3). Micro-architectural parameters measured for trabecular bone included: bone volume fraction (BV/TV, %), trabecular number (Tb.N, 1/mm), trabecular thickness (Tb.Th, mm), trabecular separation (Tb.Sp, mm), structure model index (SMI), connectivity density (Conn.D, 1/mm3), degree of anisotropy (DA), total volume density (TV.Dn, mg HA/cm3), and bone volume density (BV.Dn, mg HA/cm3).Statistical analysis was performed in SPSS statistical software (version 15.0). The data related to stress and micro-architecture of the cortical and trabecular bone specimens from both groups were presented as mean with standard deviation. The Shapiro–Wilk test was used to ascertain the normality of the data distribution. The differences in micro-architectural parameters between the high stress group and low stress group were assessed by Student's t-test or Mann–Whitney test, depending on the normality of the data distribution. The correlation analysis was used to determine the relationship between von Mises stresses and micro-CT parameters of cortical and trabecular bone, as well as the relationship between the individual micro-architectural parameters. The full range of stress was used in the correlation analysis. The statistical significance was evaluated at the level of 0.05. displays an average value of von Mises stress registered within the cortical shell in both groups. In the high stress group stress varied from 2.25 MPa to 2.75 MPa, whereas the low stress group experienced stress between 0.65 MPa and 1.49 MPa during clenching. The micro-architectural parameters of cortical bone measured in both groups are also summarized in . Greater cortical thickness and slightly greater bone volume density were found in the regions where cortex was subject to a high occlusal stress. In the same areas, cortical bone was less porous with increased distance between the pores in comparison to the low stress group (). Similar pore diameter was detected in both groups. Described differences in cortical bone micro-architecture between the groups were not statistically significant.Although a significant correlation between stress values and particular microarchitetural parameters was not statistically detected (), we noticed differences in Ct.Po and Po.Dm between individual cortical bone samples of similar thickness that experienced significantly different stresses during clenching. The greatest differences were detected between the cortex of the anterior wall of the maxilla below the infraorbital foramen and the posterior maxillary wall (). Cortical bone from the posterior maxilla was three times more porous with two times greater pore diameter than the cortical bone from the anterior maxillary wall (). Other cortical bone samples of similar Ct.Th and BV.Dn but different stresses also showed similar variations in Ct.Po and Po.Dm, e.g., cortex of the zygomatic arch and the inferior orbital rim, with the two times greater Ct.Po in the latter.Correlation analysis between micro-architectural parameters of the cortical bone samples showed that increase in cortical thickness (Ct.Th) is accompanied by significant increase in bone volume tissue density (BV.Dn) and pore separation (Po.Sp) (). Other parameters, such as cortical porosity (Ct.Po), also showed a significant positive correlation with Po.Dm, whereas it correlated negatively with pore separation (Po.Sp) and cortical density (TV.Dn and BV.Dn).For the trabecular bone, the stress ranged from 0.49 to 1.67 MPa in the high stress group, whereas the low stress group experienced between 0.25 MPa and 0.46 MPa (). There were also differences in trabecular bone micro-architecture between the groups (). Trabecular bone experiencing high stress had significantly greater bone volume fraction (BV/TV), trabecular thickness (Tb.Th), and tissue volume density (TV.Dn) when compared to the low stress group. Trabecular number (Tb.N), degree of anisotropy (DA), and bone volume density (BV.Dn) were also greater in the high stress group, but the differences did not reach statistical significance.Correlation analysis showed that an increase in stress magnitude is accompanied by a significant increase in trabecular BV/TV (). The statistically significant positive correlation was also noted between BV/TV and Tb.N (). Increase in BV/TV was also accompanied by a significant increase in both TV.Dn and BV.Dn. Trabecular number showed a negative correlation with Tb.Sp, whereas it correlated positively with Conn.D, TV.Dn and BV.Dn (Although the concept of buttresses in the mid-facial skeleton has been extensively studied as well as the principle of structural bone adaptation to functional loading In our study of the complete mid-facial skeleton, cortical bone demonstrated a tendency toward greater thickness (Ct.Th) and density (BV.Dn) in the areas experiencing high occlusal stress. This finding is in line with the study of Menegaz et al. However, the differences in Ct.Th and BV.Dn between the high stress and low stress groups were not significant. This might suggest that, beside occlusal stress, more factors are included in the determination of the cortical bone thickness and density in the mid-facial skeleton. Similar assumption was made by Thongudomporn et al. The porosity of cortical bone is also important micro-architectural characteristic due to its ability to predict bone strength More obvious regional differences in micro-structure between the sites experiencing high and low occlusal stress were observed in trabecular bone. The greatest stress-related differences between the groups were detected in bone volume fraction and trabecular thickness (). Bearing in mind that BV/TV and Tb.Th are usually the first to change during the alteration of occlusal loading Trabeculae in our study showed more concave surfaces (negative SMI) in the regions subjected to high occlusal stress when compared to more plate-like trabeculae in the low stress group. Similarly, Yeh and Popowics Our results corroborate recent experimental studies that suggested occlusal loading as an important determinant of the facial bone micro-architecture In finite element studies, certain necessary simplifications could potentially limit the interpretation of the results. Although assumption of bone anisotropy would seem more reliable for the FEA, this procedure may also influence the results negatively By performing FEA and micro-CT analysis of the same skull, the influence of sex and age-related differences in the facial bone structure and morphology was avoided as well as the influence of dentate status. Therefore, our findings might be not representative for other bone specimens. Further studies are needed to explore if the relationship between occlusal stress and facial bone microstructure differs in skulls of different sex, age and dental status.Within the limitations of the study, cortical and trabecular bones of the mid-facial skeleton exhibit regional variability in micro-architecture that could be a consequence of different occlusal stress. In the areas subjected to high stress, cortical bone showed a tendency toward greater thickness and density, lower porosity, and greater pore separation. Stress-related differences in microstructure were more pronounced in trabecular bone, which showed significantly greater bone volume fraction (BV/TV) and trabecular thickness (Tb.Th) in the areas under high occlusal stress. These areas also contained slightly denser and more numerous trabeculae with predominantly concave surfaces. To our knowledge, this study is the first to link micro-architecture of the mid-facial bones to occlusal stress in a mature dentate individual.The elastic behavior of dense C3N4 under high pressure: First-principles calculationsWe have carried a detailed theoretical study on the geometry, density of states, elastic properties, sound velocities and Debye temperature of α-, β-, c- and p-C3N4 compounds under a maximum of pressure up to 100 GPa by using first principles calculations. The optimized lattice constants under zero pressure and zero temperature agreed well with the previous experimental and theoretical results. The band gaps of the four types of dense C3N4 were widened gradually with the increase of pressure. The calculated Poisson’s ratio γ and B/G values suggest α-, c- and p-C3N4 are brittle materials under 0–100 GPa, whereas β-C3N4 will become a ductile material as external pressure reaches 57 GPa. We found that the Debye temperature of the four dense C3N4 gradually reduces in the order of c-C3N4>p-C3N4>α-C3N4>β-C3N4 at 0 GPa and 0 K. However, the Debye temperature of c-C3N4 was lower than p-C3N4 when external pressure exceeds 6.3 GPa. It may hint that the results could be served as a valuable prediction for further experiments.Super-hard materials are of great importance in scientific development and industrial production because of their applications in cutting, grind, polishing and precision instrument processing, etc For the last few decades, various studies have been performed to explore covalent compounds formed by light elements, namely, boron, carbon and nitrogen due to their ability of forming short and strong three dimensional covalent bonds In this study, we preformed the first principles calculations to investigate the geometry, density of states, elastic properties, sound velocities and Debye temperature of α-, β-, c-C3N4 and p-C3N4 compounds under a wide pressure range (0–100 GPa). Besides, the elastic properties of dense C3N4 were compared with diamond and c-BN, and the results indicated that dense C3N4 could be a substitution of the diamond and c-BN.The alpha (α-), beta (β-) and cubic (c-) together with pseudo-cubic phases C3N4 (p-C3N4) were investigated based on the Density Functional Theory (DFT) Structure of unit cell plays a very important role in understanding the nature of solid materials. shows the three-dimensional structure of four dense C3N4 phases. The N atoms are 3-fold coordination by three C atoms. The α-C3N4 is trigonal structure with space group of P-31c, each cell includes four units. The β-C3N4 is trigonal structure as well and belongs to space group of P-3, each cell includes two units. The c-C3N4 and p-C3N4 have higher symmetrical structure which are cubic (with I-4̄3d space group) and tetragonal (with P-4̄2m space group) structure respectively. One cell includes four units in c-C3N4 while one unit in p-C3N4.The calculated lattice parameters, bond overlap population and bond length as well as other available values of four dense C3N4 at 0 GPa and 0 K are shown in . And the computed results are in agreement with the experimental and previous theoretical results well, which imply that our calculation methods and results are reasonable and authentic.In order to investigate the variation of structural properties of the four types of dense C3N4 phases under different pressures, we displayed the pressure dependence of the normalized structural parameters a/a0 and c/c0 as well as V/V0 with the pressure ranging from 0 to 100 GPa as shown in . The values a0, c0 and V0 are the equilibrium structure parameters at 0 GPa as listed in (a) shows that, as pressure increased, all the lattice parameters decreased, especially the ratio of a/a0 of α-C3N4 decreased more quickly compared to the others. The ratio of a/a0 of c-C3N4 decreases the slowest, which means that a-axis of α–C3N4 is the most easily compressed in the four types of dense C3N4. (b) shows that, as pressure increased, the volume of c-C3N4 decreased more slowly than other allotropes. Besides, the volumes of α-C3N4 and p-C3N4 decreased more quickly and the both curves almost coincide with each other. The bulk modulus B is a measure of resistance against a change of volume of a material caused by external pressures Most covalent compounds formed by light elements (such as boron, carbon and nitrogen) are more likely to be super-hard materials (a) shows the average C–N bond length of four dense C3N4 with pressure from 0 to 100 GPa. All the bond lengths decreased with the increasing of pressure, indicating that the dense C3N4 phases will be more “hard” under high pressures. (b) shows that all the bond overlap populations of C3N4 increased with the increasing of pressure, which demonstrated that the covalent characters were enhanced over these changes. However, the overlap population of p-C3N4 remained almost unchanged in the pressure range of 40–100 GPa, indicating that the covalent character of p-C3N4 changed little as the external pressure exceeds 40 GPa.We further analyzed the electronic properties of the four dense C3N4 at different pressures in details. The total and partial density of states of the four dense C3N4 phases at zero and high pressures are shown in . The Fermi level is set to 0 eV. We can see that the four dense phases of C3N4 are semiconductors due to their relatively wide band gap, which is consistent with other similar theoretical reports shows that the band gaps of compounds are widened as the pressure increases. The valence bands and conduction bands keep away from the Fermi level and the peaks of the DOSs are dropped with the pressure increasing.Elastic constants of solid compounds are important because of their close relations with various fundamental physical properties, such as elastic modulus, Debye temperature and phonon spectra . The mechanical stability tests is satisfied for all systems of the four dense C3N4, the as-obtained results are in close proximity to previous values, though there is slight disparity caused by the precision setting and method of calculations. Additionally, we find the elastic constants C11 and C44 of diamond are larger than the four types of dense C3N4, but C12 is much smaller. Interestingly, the elastic constant C14 of α-C3N4 and β-C3N4 are equal to zero, which indicate that both of the compounds are transversely isotropic For understanding the variation of elastic constants at different pressures more clearly, we use to illustrate these data. It could be concluded from the figure: (1) as pressure increases, all the elastic constants increase monotonically, demonstrating the elastic properties of the four dense C3N4 can be enhanced by high pressure. We also found the lines of the elastic constants C11 and C33 located far above the other elastic constants. To the best of our knowledge, the elastic constant C11 (C22 and C33) represents the elasticity in length, which can change with longitudinal strain, and C12 (C13 and C23) and C44 (C55 and C66) are related to the elasticity in shape (d), the lines stand for elastic constants C11, C12 and C44 overlap with C33, C13 and C66, respectively, which demonstrate that the elastic properties of p-C3N4 is similar to that of c-C3N4.The bulk modulus B, shear modulus G, Young׳s modulus E and Poisson׳s ratio γ can be directly derived with these elastic constants by the Voigte–Reusse–Hill approximations (VRH) GR=52C2(C44C66−C142)3KV(C44C66−C142)+C2(C44+C66)and the Reuss bound on the bulk modulus is same to BV.For tetragonal phase, the Voigt bound bulk modulus is given according to Eq. , while the Voigt shear modulus can be defined as GR=15[18BV/C2+6/(C11−C12)+6/C44+3/C66]−1The elastic modulus based on Hill approximation is an average of Voigt bound and Reuss bound The Young׳s modulus E and Poisson׳s ratio γ can be calculated by the following formulas The calculated elastic modulus B, shear modulus G, Young׳s modulus E, Poisson׳s and ratio γ of four dense C3N4 and diamond as well as c-BN at 0 GPa and 0 K are listed in . From the Table, we note that our results are in agreement with previous values well. Beyond that, c-C3N4 has the highest bulk modulus of 441.12 GPa, which is slightly larger than diamond. The shear modulus (385.30 GPa) and Young׳s modulus (895.25 GPa) of c-C3N4 are the highest in the four type of dense C3N4, which are also less than that of diamond.The Poisson׳s ratio γ can be judgment of ductility and brittleness, for a brittle material γ<0.26, while for a ductile material γ≥0.26 that the four types of dense C3N4 including diamond are brittle materials because of their Poisson׳s ratio are smaller than 0.26. In addition, diamond exhibits the smallest brittleness in these compounds. On the other hand, according to Pugh׳s criteria The bulk modulus BH, shear modulus GH, Young׳s modulus E and Vickers hardness Hv as a function of pressure in present work are illustrated in (a), we can see the bulk modulus of c-C3N4 is the largest in the four types of dense C3N4. Simultaneously, the bulk modulus of α–C3N4 is very close to that of p-C3N4, which confirms our previous predictions. (b) and (c) show the shear modulus and Young׳s modulus increase with the increasing of pressure. The shear modulus and Young׳s modulus of c-C3N4 are the largest at ambient temperature, however, they are smaller than that of p-C3N4 as the pressure is over 7.4 GPa and 36.0 GPa, respectively. It is well known that shear modulus G can be used to measure materials’ resistance to deformation and Young׳s modulus E can be a measurement of materials׳ rigidity (d) shows the hardness of C3N4 increase monotonically with increasing pressure, demonstrating C3N4 will be more “hard” under high pressure again. illustrates the change of ductility and brittleness of the four types dense C3N4 under different pressures. As shown in , the Poisson׳s ratio γ and B/G values increase monotonically, which suggest that higher pressure can weaken the brittleness of these compounds as the pressure increases. However, all the compounds are brittle materials even the pressure reaches 100 GPa except for β–C3N4. When P≥57 GPa, β–C3N4 will turn to ductility material. Actually the higher pressure is, the better the ductility of β–C3N4 is.Elastic anisotropy analysis is of great significance in understanding the mechanisms of materials׳ microcracks and durability Where BV, BR, GV and GR represent bulk modulus and shear modulus in the Voigt and Reuss approximation, respectively. The shear anisotropic factors provide a measurement to the degree of anisotropy in the bonding between atoms in different planes. The shear anisotropic factor for the {1 0 0} shear planes between the 〈0 1 1〉 and 〈0 1 0〉 directions isFor the {0 1 0} shear planes between 〈1 0 1〉 and 〈0 0 1〉 directions isand for the {0 0 1} shear planes between 〈1 1 0〉 and 〈0 1 0〉 directions isIn our paper, the calculated anisotropic parameters mentioned above at zero pressure and zero temperature are listed in . For a crystal, a value of zero represents elastic isotropy and a value of 1 (100%) represents the largest possible anisotropy shows the pressure dependence behavior of elastic anisotropy for the four dense C3N4. We can observe that, all the elastic anisotropy index AU increase monotonically with the pressure increasing. Typically, the change of elastic anisotropy index AU under high pressures is much larger than the others. Notably, (b) shows that AB of α-C3N4 increase monotonously with pressure increasing, whereas AB of β-C3N4 decreases with the increasing of pressure and both anisotropy values are equal to each other at 61 GPa. AB for c- and p-C3N4 is equal to 0 even at high pressure, which indicates that the external pressure has no obvious effect on the anisotropy of their bulk modulus.The Debye temperature is an important parameter of solid materials, it can be used to calculated the vibrational internal energy, heat capacity and entropy. One of the standard methods for calculating Debye temperature is from elastic constant, since Debye temperature Φ is proportional to the average sound velocity vm by the equation Where h is the Planck constant, k is Boltzmann constant, q is the number of atoms in the molecule, N is Avogadro׳s number, ρ is the density and M is the molecular weight of the solid. The average sound velocity vm can be defined as follows The vs and vl represent shear wave velocity and longitudinal wave velocity, respectively, and can be calculated as follows Where B and G stand for isothermal bulk modulus and shear modulus, respectively, and the wave velocities and Debye temperature calculations are based on BH and GH. The calculated shear wave velocity vs, longitudinal wave velocity vl, average sound velocity vm and Debye temperature Θ of the four dense C3N4 phases at zero pressure and zero temperature are listed in . Notably, crystal with low density and high modulus may have large Debye temperature as well. The Debye temperature of the four dense C3N4 gradually decrease in order of c-C3N4>p-C3N4>α-C3N4>β-C3N4. Unfortunately, there are few reports on the Debye temperature of these compounds till now. Therefore, our calculated data can provide information for further experimental researches. shows the dependence of Debye temperature on the pressure range from 0 to 100 GPa. The c-C3N4 has the highest Debye temperature with external pressure ranging from 0 to 6.3 GPa. However, the Debye temperature of c-C3N4 is lower than p-C3N4 as external pressure exceeds 6.3 GPa. Besides, we find the Debye temperature of β-C3N4 changes a little with pressure increases, which indicates that the Debye temperature of β-C3N4 is less sensitive than that of the other three compounds. However, for the first time the Debye temperature of the four type of dense C3N4 under different pressure are calculated, so there are no experimental and theoretical values for comparison. Hence, our calculation results provide a very important prediction for future experiments.In short, the geometry, density of states, elastic properties, sound velocities and Debye temperature of α-, β-, c- and p-C3N4 compounds under pressure ranging from 0 to 100 GPa were investigated by first-principles calculation with generalized gradient approximation. The calculated results show that the a-axis of α–C3N4 is the most easily compressed in the four dense C3N4. The VB and CB are move away from the Fermi level, which induces the widened band gap of these compounds as external pressure increases. The elastic modulus can be obtained based on Voigt–Reuss–Hill approximations. The bulk modulus of c-C3N4 is the largest in the four dense C3N4, and the bulk modulus of α-C3N4 is very close to that of p-C3N4. The shear modulus and Young׳s modulus of c-C3N4 is the largest at ambient temperature, however, it is smaller than that of p-C3N4 as the pressure is over 7.4 GPa and 36.0 GPa, respectively. According to the Pugh׳s criterion, we conclude that α-, c- and p-C3N4 are brittle materials under 0 and even under 100 GPa. However, β–C3N4 will turn to ductile material as the external pressure exceeds 57 GPa. Elastic anisotropy analysis shows that α-, β-, c- and p-C3N4 are anisotropic materials, and the anisotropy decreases in the following sequence: c-C3N4>β–C3N4>p-C3N4>α–C3N4. Besides, we calculated the sound velocities and Debye temperature of α-, β-, c- and p-C3N4 compounds. The results show that c-C3N4 has the highest Debye temperature with external pressure ranging from 0 to 6.3 GPa, while the Debye temperature of c-C3N4 is smaller than that of p-C3N4 when external pressure exceed 6.3 GPa.Through-the-thickness direction stitchesEffects of through-the-thickness stitches on the elastic behavior of multi-axial warp knit fabric compositesIn order to improve the resistance to delamination and some in-plane and out-of-plane properties of composite materials for structural integrity, through-the-thickness reinforcement must be provided. The reinforcement is achieved by using the stitched multi-axial warp knit (MWK) fabrics as preforms for the fabrication of composite structures. In this study, the influence of stitches on the elastic behavior of MWK fabric composites under tensile and shear loadings was investigated by utilizing a unified micromechanical model. In the analysis, the in situ constituent properties and fiber volume ratios of insertion and stitching fibers determined from the geometric parameters set by the representative volume were used. The crucial step in the analysis was to correlate the averaged stress states in the constituents by adopting the bridging matrix. The experimental results were compared with the predicted results. It was found that the predicted results are in reasonably good agreement with the experimental results.Through-the-thickness direction stitchesRecently, composite materials have been widely used in many high performance structures due to their high specific strength and stiffness coupled with cost effectiveness over traditional materials. Mostly the fabrications of high performance composite materials for structural applications are limited by stacking prepreg tape materials in the multi-directional orientation In this study, the bridging model developed by Huang In order to establish a model for the analysis, an appropriate representative volume, which is the smallest repeating unit of structure, must be identified. Then, overall dimensions, geometries, such as cross-sectional shapes of insertion fiber bundles and stitching threads, and key geometric parameters must be obtained based on experimental observation. The key geometric parameters are the number of insertion fiber bundle axes, the orientations of bias insertion fiber bundles, fiber volume ratio of insertion fiber bundles, type of stitch, stitch line spacing, stitch pitch, diameter of stitch of the representative volume. The geometric limits applied to the structure must also be identified. It would be most reasonable to have a symmetrical representative volume which consists of a complete stitch and insertion fiber bundles. The shapes of insertion fiber bundle and stitch thread cross-sections were determined by observing the cross-sections of the composite specimens cut perpendicular to their warp direction using an optical microscope. From the observation, the insertion fiber bundle is assumed to have a race track cross-section and stitch thread is assumed to have a circular cross-section because it has less tendency to spread out. The modified lock stitch is considered in this study since the disruption of laminate by any interior looping processes between the bobbin and needle threads can be avoided. shows the idealized representative volume models for unidirectional (UD) and double bias longitudinal transverse (DBLT) fabric composites. The curved loop of stitch fibers is idealized to a rectangular shape assuming tightest loop.The representative volume of DBLT fabric composites consisted of warp (0°: x-direction), weft (9°: y-direction) and bias (±θ) insertion fiber bundles are stitched together in the through-the-thickness direction whereas that of UD fabric composites are stitched only warp (0°: x-direction) insertion fiber bundles.The geometric parameters of the representative volume for MWK fabric composite are determined from . From the figure, X, Y, Z are the dimensions of the representative volume in the x, y, and z directions, respectively. The thickness and width of insertion fiber bundle and diameter of stitch thread are t, w and d, respectively. The dimensions of insertion fiber bundles for DBLT fabric composites are given as follows:where w, t, ds and f are the width of insertion fiber bundle, thickness of insertion fiber bundle, diameter of stitch thread and aspect ratio of insertion fiber bundle (width-to-thickness ratio), respectively. l∗, m∗ and n∗ are numbers of fiber bundle in the warp, weft and bias directions. The subscripts indicate their directions.The cross-sectional areas of insertion fiber bundles and stitch thread arewhere S are cross-sectional area of insertion fiber bundle and stitch yarn, respectively.The fiber volume ratios of the insertion fiber bundles in the warp, weft and through-the-thickness directions and fiber volume ratios of the lock stitching threads arewhere p∗, q∗ and r∗ are the numbers of layers of fabrics in the x, y, and θ directions, respectively and κi and κs are fiber packing fractions of insertion fiber bundle and stitch thread, respectively.The total fiber volume ratios of the insertion fiber bundle, stitch thread and composite in the representative volume areThe volume average stress tensors of the MWK fabric composite, fibers and matrix are determined by expanding the bridging model developed for the unidirectional composites where σf, σm, Vf and Vm are volume average stress tensor of fiber, volume average stress tensor of matrix, total fiber volume ratio and matrix volume ratio, respectively.The corresponding volume average stress tensors of fiber and matrix are expressed by the following equations:where M, Vfi and Ai are the number of insertion fiber bundles and stitch threads, fiber volume ratio and bridging matrix of each insertion fiber bundle or stitch thread, respectively. Since all insertion fiber bundles and stitch threads have their own orientations with respect to the global coordinate system, the bridging matrix for each insertion fiber bundle or stitch thread must be transformed from the principal coordinate system to global coordinate system.where Tσ is stress coordinate transformation matrix. The bridging matrix in the principal directions is available in the literatures . The local coordinate system is designated 1–2–3 where 1 coincides with the axial direction of insertion fiber bundle or stitch thread. The global coordinate system is indicated as x–y–z. The stress coordinate transformation matrix is given by following relation:Tσ=l12m12n122m1n12n1l12l1m1l22m22n222m2n22n2l22l2m2l32m32n322m3n32n3l32l3m3l2l3m2m3n2n3m2n3+m3n2n2l3+n3l2l2m3+l3m2l3l1m3m1n3n1m3n1+m1n3n3l1+n1l3l3m1+l1m3l1l2m1m2n1n2m1n2+m2n1n1l2+n2l1l1m2+l2m1where li |
= cos(i, |
x), mi |
= cos(i, |
y), ni |
= cos(i, |
z) and i |
= 1, 2, 3.Suppose the average stress of each insertion fiber bundle or stitch thread is correlated with volume average stress tensor of fiber by following relation such thatwhere ai is fiber correlation matrix. Substituting Eqs. The volume average stress tensor of fiber is obtained directly from Eq. σm=1Vf∑i=1M′VfiAiai∑i=1M′Vfiai+VmVf∑i=1M′VfiAiai-1σThe corresponding volume average strain tensor for the composite is obtained asε=∑i=1MVfiSfiai+VmVfSm∑i=1MVfiAiai∑i=1MVfiai+VmVf∑i=1MVfiAiai-1σ=SσFrom above equation the compliance matrix S of the MWK composite is obtained. The engineering constants such as moduli and Poisson’s ratios of the MWK composite can be determined from the compliance matrix.If the matrix is assumed to be isotropically elastoplastic material, a plastic flow theory must be applied. Prandtl–Reuss flow theory is adopted in the analysis to treat strain hardening region of the matrix [Sm]=[Sm]e,σem⩽σYm(elasticregion)[Sm]e+[Sm]p,σem>σYm(strainhardenningregion)where [Sm]e, [Sm]p, σYm and σem are the elastic compliance and plastic compliance, yield stress and effective stress of matrix, respectively. [Sm]p is defined as[Sm]p=94MTmσem2σ11′σ11′σ22′σ11′σ33′σ11′2σ23′σ11′2σ13′σ11′2σ12′σ11′σ22′σ22′σ33′σ22′2σ23′σ22′2σ13′σ22′2σ12′σ22′σ33′σ33′2σ23′σ33′2σ13′σ33′2σ12′σ33′4σ23′σ23′4σ13′σ23′4σ12′σ23′4σ13′σ13′4σ12′σ13′symmetry4σ12′σ12′where ET is the hardening tangential modulus. The deviatoric stresses, σ′, is given by following relation:There are some advantages if composites are fabricated with stitched fabrics over tape or woven composites such as reduction of labor cost and fiber crimp, increment of tailorability of individual layer and improvements of damage tolerance.Two types of multi-axial warp knit fabric, Himax (Dong-Il Industrial Co.) fabrics, were used for the fabrication of composite plates with and without stitching for the experiments. These fabrics were stacked to the desired thickness and then stitched with Kevlar threads by a house built stitching machine. Four and eight layers of the unidirectional fabrics (T 800) and longitudinal (0°)-transverse (90°)-double bias (±45°) layers of fiber fabrics (DBLT 850) were used to fabricate the 3 mm and 6 mm thick composite plates, respectively. The bias angle can be arranged from 30° to 60° for Himax. The multi-axial fabrics knitted together by very thin polyester strings to enhance handling during the fabrication of composite materials. The effect of the knitted stings on the behaviors of the composites was neglected. The composite plates for the test specimens were fabricated by VARTM (vacuum assisted resin transfer molding) process. In this process, dry fabrics (DBLT 850 or T 800) with or without stitches were stacked up in the cavity of a base steel mold. Then, they were closed by the upper mold plate using clamping bolts or pressing in a press machine. Upon invoking the vacuum, no-leakage was confirmed. The mixture of resin and hardener was injected into the mold cavity. The epoxy resin (KBR1729) and the hardener (KBH1089) were supplied by Kukdo Chemicals Inc. The mixing ratio was 100:90 by weight. After resin filling throughout the mold cavity, it was put in a curing oven. The resin was cured at 130 °C for 2 hours. After cooling down the mold, the composite plate was ejected. shows the fabricated composite plates. shows the photomicrographs of cross-sections of unidirectional (UD) and double-bias-longitudinal-transverse (DBLT: quadric-axial warp knit) fabric composites with and without stitches. The gaps and fiber misalignments and some fiber damages were observed in regions where stitching threads passed through the fabrics. The fiber misalignments of fibers near the stitching threads occurred when the fibers were forced to spread around stitching threads. When the fibers were forced to spread by stitch threads, the gaps were formed by regions where the fibers were displaced by stitch threads. These gaps were more prevalent at fabric surface. These gaps generated resin rich regions when the gaps were filled with resin during impregnation.The fabricated plates were used to make test specimens with a water cooled thin diamond saw. The test coupons were sanded with 500 grit silicon carbide sand paper and cleaned with acetone. The specimens were sanded with 500 grit silicon carbide sand paper and cleaned with acetone. The tabs made of beveled glass/epoxy were applied at the both ends of the specimen using EA-9330 high strength adhesive (Hysol, Inc.). The tensile and in-plane shear tests were conducted. In-plane shear properties were obtained by means the Iosipescu shear tests. The experiments were conducted in a MTS 810.23 servo-hydraulic testing system. The specimens were instrumented with commercially available strain gages (EA gages from Measurement Group, Inc.). The strain gages were bonded to the specimen with M-Bond 200 (Measurement Group, Inc). Stains were acquired with a dynamic strain amplifier (CAS, Inc.) and recorded by a data acquisition system installed in the MTS Test Star II Control system. The acquired data were transferred to a personal computer and stored on a hard disk.The mechanical properties of constituents used in the analysis are shown in . Tensile tests were conducted on the matrix to obtain full stress–strain curves because they are essential for the predictions of the behaviors of MWK fabric composites. shows the stress–strain curve of the epoxy used for the fabrication of composites. shows the tangential moduli of the epoxy in the stain-hardening regions. The fibers were assumed to be linear elastic materials and their properties were obtained from the literature show the comparisons of elastic properties between the predictions and experimental results. The predictions show reasonable agreement with the experimental results. For the UD fabric composites the elastic modulus in the insertion fiber direction, the longitudinal direction, which is normal to the stitch direction decreased with the presence of stitches from the experimental results. It is believed that presence of stitches in the composite has caused misalignment and spreading of fibers around the stitch threads. This spreads of fibers formed fiber depleted regions. These regions were filled with resin during impregnation, resulting degradation of elastic modulus in the longitudinal direction. In the proposed model, the misalignment and spreading of fibers were not considered but the presence of stitch generated the resin rich regions along the insertion fiber direction as shown in (a). The resin rich regions in the model decreased the elastic modulus in the longitudinal direction. The experimental and predicted results show that the elastic modulus in the transverse direction, the stitch direction, increased notably with stitches. The in-plane shear modulus increased and Poisson’s ratio decreased with stitches. All in-plane elastic moduli are increased with decreasing stitch line space and thickness because either decreasing stitch line space or thickness increase the reinforcing effect of stitch since they decrease the stitch fiber volume ratio in the representative volume. The elastic modulus in the longitudinal direction is least affected whereas elastic modulus in the transverse direction is affected. Also, shear moduli and Poisson’s ratios are affected.The elastic moduli in the x and y directions were the same for the unstitched DBLT fabric composites. However, the elastic modulus in the y-direction, the stitch direction, increased much more than that in the x-direction which is normal to the stitch direction showing pronouncing effect of stitching. The elastic moduli in any directions decreased with stitches for DBLT fabric composites showing less degradation due to presence of misalignments and depleted regions of fibers compared to those of UD fabric composites. Similar to the case of UD fabric composites, the in-plane shear modulus of DBLT fabric composites increased and Poisson’s ratio decreased with stitches. All in-plane elastic moduli are increased with decreasing stitch line space and thickness. The effect of stitches on elastic properties of the DBLT fabric composites is more dominant compared to that on the UD fabric composites.The tensile longitudinal stress–strain curves for the UD fabric composites with various stitch line spaces are shown in . The elastic behaviors of the UD fabric composites in the longitudinal direction are linear because they are fiber dominated behaviors. The longitudinal elastic modulus and strength of the composites are decreased with decreasing stitch line spaces. The predicted results show similar trends but the variations due to the different stitch line spaces are smaller. However, the transverse elastic modulus and strength of the UD fabric composites as shown in are increased with decreasing stitch line spaces. Some strain hardening effects are observed in the transverse direction. The in-plane shear stress–strain curves for UD fabric composites with different stitch line spaces are shown in . Some strain hardening effects are observed in the in-plane shear stress–stain curves and the shear modulus is increased with decreasing stitch line spaces. Some quantitative discrepancies are shown between the experiments and predictions for the transverse and in-plane shear stress–strain behaviors but qualitatively they show similar trends. show the longitudinal and transverse stress–strain curves and in-plane shear stress–strain curves of the UD fabric composites with different thicknesses, respectively. The longitudinal and transverse elastic moduli and strengths decreased slightly with increasing thickness since the stitch fiber volume ratio may decrease with increasing thickness within the representative volume. The in-plane shear modulus and strength also decreased slightly with increasing thickness for the same cause. The stress–strain curves in the x and y directions for the DBLT fabric composites with various stitch line spaces are shown in . The experimental stress–strain behaviors of DBLT fabric composites show strong strain hardening behaviors. However, the predictions show less strain hardening behaviors. The similar characteristics are observed for shear stress–strain behaviors of the DBLT fabric composites as shown in . Similar to the cases of the UD fabric composites, the elastic moduli and strengths are increased with decreasing stitch line spaces. However, the experimental results showed that strain hardening rates of DBLT fabric composites in the x and y directions are decreased and increased with decreasing stitch line space whereas the predictions just show the increase of stain hardening rate with decreasing stitch line space. The elastic modulus in the y-direction is higher than that in the x-direction because stitching is performed in the y-directions. It indicates influence of stitch on the composite materials. The elastic strain hardening rates of the in-plane shear stress–strain behaviors of DBLT fabric composites are simply increased with decreasing stitch line space. It is believed that these discrepancies between the predictions and experiments of stress–stain behaviors for DBLT fabric composites are associated with geometrical effects caused by the rearrangement of fiber orientations and positions during deformation. show the stress–strain curves in the x and y directions with different thicknesses. The elastic moduli and strengths decreased slightly with increasing thickness.The bridging model is extended to predict elastic properties and behaviors of the MWK fabric composites incorporating an appropriate representative volume and geometric characteristics. The geometric limitations, effect of stitch and parameters associated with stitch of the MWK composites are considered in the model. The predictions are compared with experiments. The predicted elastic properties are in reasonably good agreement with experimental values. The in-plane properties in the specific direction and out-of-plane properties are affected by stitching. The transverse and in-plane shear moduli and Poisson’s ratios for UD fabric composites are increased with an increasing effect of stitching such as decreasing stitch line space, increasing the thickness of the UD fabric composites. The longitudinal modulus is decreased with stitching because of fiber misalignment and formation of fiber depleted regions, later filled with resin, by spreading of fibers due to the stitches. For the case of DBLT fabric composites, the improvements of elastic properties are observed especially in the stitching direction. The predicted stress–stain behavior shows good agreement with the experimental results for UD fabric composites. However, some discrepancies of stress–strain behavior are found between predictions and for DBLT fabric composites. It is believed that these discrepancies are associated with geometrical effects caused by the rearrangement of fiber orientations and positions during deformation.Spontaneous-combustion coal gangue aggregate concreteAxial compressive behavior of circular concrete-filled steel tube stub columns prepared with spontaneous-combustion coal gangue aggregateThe compressive behavior of circular concrete-filled steel tube (CFST) stub columns prepared with spontaneous-combustion coal gangue aggregate (SCGA) was investigated to study the effect of SCGA substitution level by experimental test and finite element simulation. The test variables included SCGA replacement ratios (0%, 50% and 100%) and steel ratios (8.3%, 11.6% and 14.2%). The study concerns the failure mode, ultimate compressive strength, elastic stiffness, ductility of the specimens, and the confinement effect of the steel tube. The test results showed that the failure mode of specimens prepared with SCGA was similar to that of reference CFSTs; compressive strength, elastic stiffness and ductility of the specimens were reduced by 2.93–4.81% (8.25–10.18%), −16.17–8.24% (3.01–22.16%) and 7.78–10.61% (11.86–16.34%) respectively with the increasing replacement ratio of SCGA from 0% to 50% (100%). A finite element model was proposed based on ABAQUS software and benchmarked against the test data from this study. The numerical results indicated that the SCGA replacement ratio and the confinement effect were the major factors of the compressive behavior of CFSTs. After comparing the test data with the existing design codes, modified design equations considering replacement ratio and confinement effects was proposed to predict the ultimate compressive strength of the specimens prepared with SCGA. Accuracy of the derived modified equation was evaluated, with the mean value of 0.984 and a standard deviation of 0.076. The study provides an experimental basis of the utilization of SCGA in CFST stub columns.Spontaneous-combustion coal gangue aggregate concreteElastic stiffness obtained by experimentElastic stiffness calculated by finite element methodstrength of concrete prisms cured for 28 daysnominal 28-day strength of concrete cylinderssplitting tensile strength of concrete prisms cured for 28 dayscompressive strength of concrete cubes cured for 28 daysaxial load calculated by finite element methodexperimental ultimate load-carrying capacityultimate axial load-carrying capacity calculated by design methodsultimate load-carrying capacity calculated by finite element methodreplacement ratio of spontaneous-combustion coal gangue aggregateaxial deformation corresponds to 0.85Nu at descending branchCoal gangue is a type of solid waste separated from coal minerals [], approximately accounting for over 15% of the coal production according to the current technological level []. Previous studies have reported that the total amount of the coal gangue produced only in China has reached 4.5 billion tons [] with an annual increase of 0.3 billion tons []. The massive accumulation of coal gangue is a worldwide issue that faced by both developed and developing countries. The coal gangue not only occupies land but also has chemical influence on the soil and groundwater within 3–5 km around the waste hill. In the past two decades, a great number of engineering structures have been constructed and consumed a large amount of natural aggregate (NA) which is limited and non-renewable. Coal gangue will occur spontaneous combustion in the process of accumulation due to its own properties and the influence of the surrounding environment. The spontaneous-combustion coal gangue (SCG) is the main part of the waste hill especially for the ones with a long time. Substituting spontaneous-combustion coal gangue aggregate (SCGA) for NA in structural members may give an opportunity to balance the industrial development and resources as well as the environment.The previous X-ray diffraction (XRD) analysis showed that the silica and alumina of SCG were in the ranges of 55.57–59.34% and 21.00–25.28%, respectively []. The contents of these two oxides were similar to natural coarse aggregate [], in which case the SCG may be used in structural concrete according to JGJ52-2006 []. A 12-storey reinforced concrete frame structure using 100% SCGA concrete was studied [], and it was reported that the frame structure prepared with SCGA had better seismic performance than the concrete frame structure reinforced with NA under same conditions and saved the construction costs by 6.6% []. But the shear strength and bonding property are slightly weaker than normal concrete due to the chemical composition of the SCGA. Then, it was proved that replacing natural coarse aggregate (NCA) with spontaneous-combustion coal gangue aggregate is feasible, and the SCGA is able to mix with normal-strength concrete even at a replacement ratio of 100% []. Using spontaneous-combustion coal gangue coarse aggregate to construct structural members, including slabs, beams, columns, and building partition walls has also been investigated []. The strength of concrete mainly determined by the strength of the cement base, aggregates and cementation capacity between them. The interfacial property of spontaneous-combustion coal gangue aggregate concrete was inferior than that of natural aggregate concrete []. This is because the porosity of SCGA was 15.57% larger than that of natural coarse aggregate [], and the water absorption of SCGA is 8.67–11.90% larger than that of natural coarse aggregate. The SCGA is easy to hydrolyze because of its high porosity and feldspar minerals, SCGA-based concrete is prone to cracking during volume shrinkage []. Despite that the mechanical performances of SCGA concrete were inferior to those of natural aggregate concrete [], the SCGA concrete may be used for practical applications [Composite structure covers the use of steel and concrete at the same time, natural aggregate concrete-filled steel tube (CFST) has increasingly found their applications in the building structures, offshore structures and bridges, etc. The most significant advantage of CFST is to make adequately utilize of steel tube and concrete core, which is confinement effect to improve the strength and plasticity of concrete core and postpone the local buckling of steel tube. The CFST prepared with SCGA is attractive as the beneficial for the saving of natural resources and the environmental preservation. The CFST members have been extensively investigated since 1960s []. Studies and experiments using real structures have proved that CFST members have high stiffness, ductility []. Fiber-reinforced polymer confined concrete [] members have progressed remarkably in recent years. The combined effects of complex loads and conditions [] on CFSTs have also been paid more attention. The advantages of the CFST promote the research on other type of concrete cores are regraded to be alternatives to the original normal concrete which is normal strength and composed of natural raw materials. The high strength concrete has been increasing in the use for high-rise and large-span buildings to reduce self-weight. Portoles et al. [] conducted an experimental study on high-strength concrete-filled circular tubular columns subjected to eccentric loading. The maximum eccentricity is 1.0, and the strength of concrete core ranges from 30.54 to 107.33 MPa. The results showed that the high strength concrete has greater efficiency in stub column but the strength enhancement is not obvious. MX. Xiong et al. [] investigated the particle size grading on compressive behavior of CFST using UHSC. It was found that the axial load capacity would not be affected at the limitation which replacement ratio of UHSC below 38%. The CFST using high strength concrete is an effective way to solve the brittleness of high strength concrete. Some attempts on using new concrete materials which focused on substitution natural aggregate to solid industrial waste materials. Liu et al. [] studied the performances of recycled concrete-filled steel tube in the elastic range based on the theory of damage mechanics. It has been proved that the initial damage would not grow under axial load due to the confinement of steel tube. Ren et al. [] tested the axial behavior of dune sand concrete-filled steel tubular stub column. It was found that the thickness of steel has the most significant influence on compressive behavior. M. Nematzadeh el. al [] conducted an experimental study on the initial elastic modulus, real elastic modulus, secant modulus, yielding point modulus and peak load modulus of rubberized fiber-reinforced concrete-filled steel tubular stub columns and carried out a theoretical study. The volume ratio of fiber is 0–1.5% and the volume percentage of sand substituting by crumb rubber is 0–10%. It was found that increasing the content of rubber reduced all five elastic moduli, but the increasing volume of fibers improve the elastic modulus effectively in the high temperature under 500°C. A. Karimi et al. [] set up a finite element model to investigated the volume ratio of steel fibers, tire rubber content, diameter-to-thickness (D/t) ratio of steel tube and exposure temperature of the mechanical behavior of the CFST under axial load. The results showed that the compressive strength declined with the increasing tire content. And the deterioration of tire at 360°C caused the 2.5%–5% decrease of strength in confined concrete. A. Karimi and M. Nematzadeh [] conducted an experiment to investigate the axial compressive behavior of steel fiber reinforced CFSTs using tire aggregate under post-fire conditions. It was founded that the 10% content of tire aggregate lower the compressive strength by 12%, but the toughness and ductility increased with the ascending steel tube thickness. The confined specimens still had a higher axial compressive bearing capacity of the temperature of 500°C. Compared to normal concrete, the outstanding problem of high-strength concrete is autogenous shrinkage. Most of the new material concrete uses recycled or sustainable aggregate which decreases mechanical properties of concrete core. However, by reviewing the aforementioned studies, the advantages of ductility and confinement effect of the steel tube were fully used to offset the brittleness and weakness of the concrete core. Since the mineral composition and structural features of the spontaneous-combustion coal gangue aggregate is very different to natural aggregate and caused disadvantageous in compressive strength, shrinkage and durability, which limited the application of SCGA in structural members. Meanwhile, core concrete has lower shrinkage and creep due to the hermetic environment provided by the outer steel tube []. According to the beneficial attempt on high-strength or new material concrete-filled steel tube columns, using SCGA concrete as a concrete core of a steel tube to construct a CFST column may compensate for the weaknesses for SCGA concrete.Previous study of high-strength and new material CFST member have showed that the content of aggregate and confinement effect of the steel tube are the two major factor that influence the mechanical performance of the specimens under axial load. Very few tests have been conducted under compression loading onto concrete-filled steel tube columns prepared with spontaneous-combustion coal gangue aggregate. In this regard, the compressive behavior of circular concrete-filled steel tube stub columns prepared with spontaneous-combustion coal gangue aggregate under an axial compressive load was investigated herein. This study is part of a series research. In this study, the replacement ratio of the SCGA (0%, 50% and 100%), steel tube thickness (2.75 mm, 3.75 mm and 4.50 mm) was considered as the variables. The failure mode, ultimate compressive load, elastic stiffness, ductility and load-strain curves were investigated. Finite element models of such columns were also developed and verified by the experimental results. Moreover, a parametric study was conducted to analyze the mechanical properties of CFST stub columns with respect to the replacement ratio of the SCGA, the compressive strength of the core concrete, the yield strength of the steel tube, and the diameter of the sections. Further, in order to increase the range of concrete-filled steel tube stub columns contained spontaneous-combustion coal gangue aggregate that might be used, a modified equation was finally proposed to circular concrete-filled steel tube stub columns prepared with SCGA under axial compression.A total of 9 groups of circular CFST stub columns (two identical specimens in each group), the details of the specimens are listed in . The test parameters include (1) steel ratio (α): 7.8%, 11.6% and 14.2%; and (2) replacement ratio (r) of SCGA: 0%, 50% and 100%.In this study, steel ratio is defined as:where As and Ac is the cross-section area of steel and concrete.The main results described later in the discussion section, including the ultimate compressive strength, the elastic stiffness, ductility coefficient, and the vertical strain under ultimate bearing capacity of the columns are also presented herein. As this experiment chiefly focused on the axial compressive behavior of the columns, a stub column with a length-to-diameter (L/D) ratio of 3.0 was selected for all the specimens to reduce the end effects or the slenderness effects as suggested by Zhong [Portland cement strength grade 42.5 N was used in this study, and the fine aggregate used was natural river sand (NFA) with a fineness modulus of 2.58. The natural coarse aggregate (NCA) was natural limestone dried under ambient conditions, and the spontaneous-combustion coal gangue coarse aggregate (SCGA) was in the 70% saturated surface dry conditions before mixing with the concrete. The key parameters of the coarse and fine aggregates, including the particle size, the density, the water absorption, and the index of crushing are tabulated in The mix proportions of the SCGA concrete with the three replacement ratios of the SCGA, namely 0%, 50%, and 100%, are presented in . Since the properties of concrete depend on the mixing criteria and approach []. Because of the large difference in the water absorption resulted in the distinctive characteristics of the SCGA-based concrete compared to the NCA-based concrete and the additional absorbed moisture increased the total water-to-binder ratio (w/b) of the concrete []; hence, in each case, the effective water content and the w/b ratio were maintained constant for both the NCA- and SCGA-based concretes, that is, a net water content of 180 kg/m3 and an effective water-to-binder ratio of 0.45. For each replacement ratio, sets of concrete samples, including three concrete cubes with the dimensions 150 mm × 150 mm × 150 mm and three concrete prisms with the dimensions 100 mm × 100 mm × 300 mm were casted.The concrete cubes and prisms were cured under standard conditions at a temperature of 20 ± 2 °C and relative humidity of lower than or equal to 95% for 28 days to obtain the compressive strength and elastic modulus of the core concrete.The mean value and the coefficient of variation (COV) of the experimental results are summarized in . The equivalent values correspond to the strength of the concrete cylinders (fcm), and the strength of concrete prisms (fc,28 and fc,test) was calculated by the adjustment factors described in standards BS EN206 [The material properties of the steel tubes with a thickness of 2.75, 3.75, and 4.50 mm were analyzed by means of the tensile coupon tests. Each group consisted of three samples. The samples were machined from the steel sections and tested on uniaxial apparatus WDW-100D. The test results included the yield strength (fsy), the ultimate tensile strength (fu), the yield strength ratio, the elastic modulus (Es), and the Poisson’s ratio (μs). The average values of the test results for the three samples are listed in Before casting the NCA- and SCGA-based concrete in the steel tube, all the rust inside the tube was brushed by wire. A square steel plate with a length of 150 mm and a thickness of 10 mm was welded to the bottom end of the steel tube. All the specimens were cast in the same day and vibrated until fully consolidated. At the top end, the concrete core surface was levelled smoothly and tightly wrapped with a plastic film which was fixed at the outer surface of the steel tube by a tape. The small gap between the steel tube and the core concrete at the top end of the specimen due to the autogenous shrinkage were capped with a high strength grouting material. After the top end surface plane was adjusted and smooth, the steel tube and the core concrete would work together in the loading process. A steel plate of the same dimensions as the one welded to the bottom end of the steel tube was also welded to the top end of each specimen.The specimens were tested using a 5000 kN hydraulic testing machine. The uniaxial load was measured with the load cell attached to the bottom of the stub column as shown in . In this study, the diameter of the specimens was showed in . All the specimens adopted the L/D ratio of 3.0 to measure the axial compressive behavior. It is because that when L/D>3.5, the column would occur bending deformation which present overall instability failure; when L/D<3.0, the characteristic of the column in the longitude is not obvious and the end friction constraint effect which has influence on the mechanical performance and lead to unreal results cannot be ignored []. Thus, a standard CFST stub column satisfied the requirement of 3.0≤L/D≤3.5. In this test, the L/D value of 3.0 was selected to save the raw materials. The steel tube is cut to the required length since it is integrally formed, the steel tube with a diameter of 140 mm and thickness of 2.75, 3.75 and 4.50 mm was applied in this test corresponding to the diameter-to-thickness ratio of 51, 37 and 31 to avoid local buckling of the steel tube []. This ensures the steel tube carried axial load until achieving the yield strength. A steel plate with a thickness of 40 mm was placed between the column and the load sensor to convey the load uniformly to the whole cross-section of the specimen. The axial shortening (Δ) was measured by two linear variable differential transformers (LVDTs) at the top of the specimen. The test data from the load cell and the LVDTs were recorded by a spectrum instrument automatically. Eight electrical resistance strain gauges (four in the longitudinal direction and four in the horizontal direction) were also attached to the outer surface of the steel tube at the middle height of the specimens.At the initial loading stage, the strain gauges were monitored carefully to ensure that the load was concentrically applied to the column. During the loading in the elastic range, the specimens were loaded at a rate of 2.0 kN/s. As the loading procedure continued to 0.70 Nuc (Nuc is the predicted ultimate bearing load of the specimens), the load interval was 1/15 Nuc and reduced by 50% compared to that in the elastic stage. The load was sustained for 1 min after stabilizing to record the reading at each load interval. When the load reached higher levels, a continual axial compressive load was applied to obtain the ultimate compressive load of the columns. In the post-peak range, the hydraulic actuator used displacement control at a constant rate of 0.5 mm/min.All 18 specimens, including 12 CFST columns prepared with spontaneous-combustion coal gangue aggregate (SCGA), along with the 6 columns prepared with natural aggregate (NA) were tested to failure under axial compression. It can be seen that the failure process of CFST stub columns prepared with SCGA was basically similar to those of specimens using NA. The absolute and relative axial load (N) versus end shortening (Δ) for all test specimens in group a are presented in , respectively. In order to compare the effect of SCGA replacement ratio on the failure process between the specimens prepared with SCGA and CFST using NA clearly, specimens with different SCGA replacement ratios were presented in presented the effect of steel ratio on the specimens.It can be observed that the complete N-Δ curve consists of (a) an elastic stage, (b) an elastic–plastic stage, and (c) a plastic stage.The axial load N≤0.7Nu (Nu is the ultimate compressive strength of the test specimen) corresponds to the elastic stage, where the specimens showed a linear behavior. At the critical point of 0.7Nu, some small diagonal slip lines began to appear at the end of the steel tubes. When the axial load reached the range of 0.7Nu < N < Nu, the specimens were in the elastic-plastic stage which exhibited a nonlinear behavior. Meanwhile, slip lines continued from propagating to the mid-height, but no local buckling was observed on the steel tubes. When the axial load decreased to approximately 0.9Nu in the descending branch, a slight “cracked” sound could be heard; meanwhile, local buckling occurred at the end and mid-height of the steel tubes. The final failure mode of the specimens was presented in After the experimental tests, the steel tubes were cut and removed to investigate the damage of the concrete cores. It can be observed in that the crushed area in all specimens, where the concrete is black, was largely located at one end and mid-height of the concrete cylinder prepared with the spontaneous-combustion coal gangue aggregate. The connection of a number of diagonal cracks to form the crushed regions of the core concrete indicated that substituting the SCGA for the natural aggregate (NA) in the core concrete had negligible effect on the failure mode of the circular concrete-filled steel tube stub columns. CFST stub columns prepared with the spontaneous-combustion coal gangue aggregate for larger replacement ratios of the SCGA showed more obvious but acceptable damage to the concrete core and greater local buckling wave of the steel tube. Core concrete of CFSTs was under three-dimension compression, which the axial direction of the concrete was subjected to isobaric load and the side direction was restrained by the steel tube to avoid easily deform in the meantime. The pores inside the concrete became dense, the micro-crack closed and improved the mechanical properties of concrete core due to the confinement effect. Thus, all the specimens exhibited similar failure modes irrespective of the incorporation of the SCGA.This study concentrated on the influence of the substitution level of the spontaneous-combustion coal gangue aggregate on the strength of the concrete; as a result, the failure of the core concrete occurred in the interfacial transition zones. This indicated that the local buckling failure of the circular concrete-filled steel tube stub columns prepared with the spontaneous-combustion coal gangue aggregate was chiefly due to the crush of the core concrete, causing its supporting function for the steel tube to be lost. As a result, local buckling occurred in the steel tube, and the whole composite specimen began to lose its efficiency. It is shown that for the specimens with the same steel ratio, the end shortening increased with the increasing replacement ratio of the SCGA, while for the specimens with an increasing steel ratio, the end shortening of the CFST stub columns prepared with the spontaneous-combustion coal gangue aggregate enlarged. It is worth mentioning that the specimen with a SCGA replacement ratio of 50% and a steel ratio of 11.6% has more modest descending trend, which may be related to the confinement effects appearing in the plastic stage [The ultimate compressive load (Nu) of the circular concrete-filled steel tube stub columns prepared with the spontaneous-combustion coal gangue aggregate as a function of the replacement ratio of the SCGA and steel ratio is presented in illustrated that the scatter of ultimate compressive strength of the NA-based CFSTs is 0.38%–4.26%, which is similar to the results obtained in the previous studies []. The scatter of Nu of the CFST stub columns prepared with spontaneous-combustion coal gangue aggregate is 0.97%–3.57%, while that for SCGA-based concrete with the replacement ratio of 50% and 100% is 4.9%–13.2%. The lateral constraint offered by the steel tube is a major factor of such considerable reduction in the scatter of test results. Then, since the steel tube is regarded as an isotropic material which the scatter can be ignored, the ultimate axial load carrying by the steel tube is another main reason for the decreasing in scatter. The effect of 25%, 75% replacement ratio would be studied in future.The ultimate compressive load of the specimens declined as the substitution level of the SCGA rose (see ). Compared with the reference CFST stub column, the ultimate compressive strength of the CFST stub column completely prepared with the SCGA decreased by up to 12.7% in the maximum. While the ultimate compressive strength of the standard cubes with the dimensions 150 mm × 150 mm × 150 mm decreased by 19.4% at the same replacement ratio. The scatter of the SCGA-based concrete decreased by 52.6% due to the restrain of the steel tube. The results showed that the structural effect of the SCGA replacement ratio is not so obvious as the material effect.The effect of the SCGA scatter on the ultimate compressive strength of CFSTs can be reduced by combing the steel tube and SCGA-based core as a composite structure. Thus, the effect of steel tube on the ultimate compressive load should be taken into account. In this study, three different steel tube thicknesses were applied which corresponding to the steel ratio of 8.3%, 11.6% and 14.2%. In , the ultimate compressive load of specimens with three replacement ratios has almost the same changing tendency but with the different value. The ultimate compressive load of the column increased approximately by 6.7%–11.6% and 29.0%–32.2% when the steel ratio enlarged by 11.6% and 14.2% respectively. The variation on specimens with the same steel ratio is smaller than 4.9%, which is much smaller than that of the SCGA-based concrete. With the increasing steel ratio, the effect of the SCGA replacement ratio would reduce. On the premise that the total cross-section area and the strength of raw materials remained unchanged, the area of steel tube increased while the area of concrete core decreased at the same time. According to the superposition theory, the increasing steel tube area distributes more axial load than concrete core, which is more obvious than the change of compressive strength of concrete core due to the replacement ratio. The contribution to the steel tube to the ultimate compressive strength of the composite member was one of the main reasons which are significant. The confinement effects restrain the heterogeneity of the SCGAs, which is responsible for the non-uniformity of the strength of the SCGA concrete; therefore, the variability of the ultimate compressive strength of the CFST stub columns declines.Effects of SCGA replacement ratio and steel ratio on the improvement in the strength of the specimens was presented in . As expected, specimens with higher SCGA replacement ratio have lower compressive enhancement which results in lower restraint. indicates that the compressive strength enhancement of the stub columns has a modest decrease up to 3.06% with the increased replacement ratio of SCGA. It illustrated that the effect of SCGA replacement ratio dose not considerably on the ultimate compressive strength, but still cannot be ignored. The strength enhancement decreased with an increase in the replacement ratio of the SCGA except at a steel ratio of 8.3%. It can be noted that the compressive enhancement increased up to 5.07% with the steel ratio. It suggested that the steel ratio has an effect on the confinement effect.Effects of the SCGA replacement ratio and steel ratio on the elastic stiffness (EA) of the specimens was showed in . In the test, the elastic modulus of the specimens was adopted at the point when axial load achieved 0.45Nu to obtain the elastic stiffness [where Δ0.45 is the axial end shortening correspond to 0.45Nu; L is the length of the specimen. The experimental results in showed that the scatter of the EA values is relatively higher. The maximum difference of the elastic stiffness between the 2 identical columns of each group of natural aggregate (NA) CFSTs is 3.15–8.93%, and that for specimens prepared with 100% SCGA is 1.64–12.99%. However, the CFSTs prepared with the 50% SCGA has the highest scatter which is 3.96–13.65%. Simultaneously analyzing indicates that the effect of replacing the natural aggregate with the SCGA on the elastic stiffness of the stub column somewhat differs from that on the ultimate compressive strength., the elastic stiffness of the specimen with a SCGA replacement ratio of 50% was higher than that of the stub columns with a replacement ratio of 0% and 100% at the steel ratio of 8.3% and 11.6%. The composition of the coarse aggregate of the specimens with a SCGA replacement ratio of either 0% or 100% was the single type, while the coarse aggregate of the specimens with a SCGA replacement ratio of 50% was composed of two types of aggregate. The NA and SCGA took 50% volume of the coarse aggregate, the scatter of coarse aggregate was further increased. In , the density of the SCGA is lower than that of NA, which resulted in the NA distributed at the lower end of the specimen and has a higher stiffness. Although the above problem still exists of the columns with a steel ratio of 14.2%, the EA value decreased with the SCGA replacement ratio. This can be explained by that increasing the steel ratio actually leads to the increased steel tube thickness, which increased the cross-section area of the steel, so the confinement effect in the hoop improved significantly. The ultimate compressive strength of the specimens with the steel ratio of 8.3% and 11.6% presented higher scatter. It is indicated that the confinement effect cannot offset the impact on nonuniform aggregate distribution. Further experiments may be required to investigate specimens with an SCGA replacement ratio of 50% at a wider parameter range.The comparison between the CFST stub columns prepared with the spontaneous-combustion coal gangue aggregate and the SCGA-based concrete demonstrates that, at the same mix proportion, the CFST stub columns experienced a much smaller reduction in the elastic stiffness than the SCGA-based concrete owing to the contribution of the steel tube and the confinement effects. At the same replacement ratio of the SCGA, the elastic stiffness of the circular concrete-filled steel tube stub columns prepared with the SCGA decreased by up to 20.2% when the natural aggregate was totally replaced with the spontaneous-combustion coal gangue aggregate, while that of the SCGA concrete declined by up by 32.2%. It is because the mechanical properties of SCGA are weaker than NA. The chemical component of SCGA is different with NA caused the active reaction. Meanwhile, the SCGA has a complex porosity structure and high porosity, which caused stress concentration. The following reasons cause decreases in the elastic stiffness. Furthermore, the elastic stiffness of the CFST stub column increased with the rising steel ratio of the same SCGA replacement ratio due to the contribution to the steel tube to restrict the core concrete. EA value increased 15.1% and 39.8% of the stub columns at replacement ratios of 0% and 100% corresponding to the steel ratio increasing from 8.3% to 14.2%. It indicated that the confinement effect of the steel tube is important to the improvement on elastic stiffness and result in the higher peak load.A ductility coefficient of the CFST stub column is defined on the basis of the load (N) versus axial end shortening (Δ) curve [where υ is the ductility coefficient; Δ0.85 is the displacement corresponding to 85% of the ultimate compressive load in the descending branch; Δu is the displacement corresponding to the peak load in a. Although the definition of the ductility coefficient is physically clear, as showed in , the descending branch of the specimens is quite modest and even has an upward trend. It is not available in this study as the Δ0.85 value may not be measured. According to Yang et al. [], Δ0.85 adopted the value correspond to the axial strain of 0.04 if the Δ0.85 value can not be obtained.The effect of SCGA replacement ratio and steel ratio was focused and the ductility coefficients of specimens are presented in b. It showed that the υ value of CFSTs prepared with SCGA decreased with the increasing SCGA replacement ratio except for SCGA-100-2.75-a. Since the SCGA has pozzolanic activity, the secondary hydration reaction occurred in the 100% SCGA-based concrete. Hydration products increase the bond among the concrete constitutions, and further cause slower reduction of the load in the descending portion of the N-ε curve. The restraint offered by the steel tube with thickness of 2.75 mm is lower, while the effect of SCGA replacement ratio on the ductility is more obvious. When the steel ratio keeps at the value of 8.3%, 11.6% and 14.2%, the υ value decreased up to 10.9%, 3.2%, and 2.8% for the SCGA replacement ratio of 50%; while the υ value decreased up to 6.9% and 12.2% for the SCGA replacement ratio of 100% (the υ value of SCGA-100-2.75-a was not included here). The ductility of specimens with 50% SCGA replacement ratio changes into a larger range, this may be related to the distribution of the two types of coarse aggregate in the concrete core.Meanwhile, the ductility coefficient increased with the increasing steel ratio. The υ value of 0% SCGA replacement ratio increased by 19.9%, 104.5%; the ductility coefficient of 50% SCGA replacement ratio increased by 30.2%, 123.0% and the υ value of CFST stub columns prepared with 100% SCGA increased by −19.4%, 29.6% with the steel ratio increasing from 8.3% to 11.6% and 14.2%. The steel ratio would effectively improve the ductility of the CFST stub columns. The reason may be attributed to the increasing of the thickness of the steel tube, thus leading to the postpone of local buckling of the steel tube and offering more uniform confinement. After peak load, there’s no out of plane deformation appeared due to the effective constrain of the steel tube, which lead to a more ductile behavior of the circular CFST stub columns.To further understand the effect of the spontaneous-combustion coal gangue aggregate replacement ratio on lateral and longitudinal deformation of the circular concrete-filled steel tube stub columns, the variations in the axial load with the vertical strain (εv) and with the transverse strain (εh) of the 18 specimens are presented in , in which a positive value indicates the transverse strain, while a negative value denotes the longitudinal strain. The strain increased linearly at a larger slope, which indicated that the specimens were in the elastic stage for the elastic modulus of the specimen remained constant. Except for specimen SCGA-0-2.75-b, with the increasing axial load, the vertical and transverse strain of the other specimens enlarged notably in the elastic–plastic stage and in the plastic stage. The point of the inflection of SCGA-0-2.75-b in the N-ε curve in a was that the strain gauges pasted at the position where local buckling occurred. Other specimens, the strain slightly changed with the increasing SCGA replacement ratio. The trend of the variations indicated that the CFST specimens offered higher constraints on the transverse deformation due to the decrease in the compressive strength of the core concrete caused by the replacement ratio of the SCGA.The variation in the Poisson’s ratio of the core concrete and the steel tube of all the specimens was delineated in . The Poisson’s ratio of steel reflects the ratio of the horizontal deformation to the vertical deformation for the steel tube subjected to uniaxial loading.It demonstrates that the Poisson’s ratio (μ) of the stub columns continued increasing with the load. In the early elastic stage, the Poisson’s ratio of the specimens was in the range of 0.2–0.3, which was similar to the value of μs listed in . This implied that the steel tube was in a uniaxial state of compression, so the core concrete was not restrained by the steel tube. The confinement effect appeared when μ began to exceed the Poisson’s ratio of the steel tube μs at the same load ratio. In this study, it appeared that the N/Nu was lower than 0.6 for most specimens when the expansion of the concrete core exceeded that of the outer steel tube due to the increasing vertical loading. Therefore, the circumferential compressive stress on the steel tube decreased, and the confinement effect started. In the elastic–plastic stage, the steel tube was subjected to the circumferential tension. In the plastic stage, μ appeared to grow considerably due to an increase in the circumferential tensile stress on the steel tube, as well as a decline in the axial compressive stress, indicating that the core concrete expanded laterally and finally reached the ultimate tensile state in the loading process.It is quite time-consuming and costly to perform full-scale experimental investigation, so the finite element analysis was conducted to investigate the axial compressive behavior of the circular concrete-filled steel tube stub columns prepared with the spontaneous-combustion coal gangue aggregate.Finite element models were established by utilizing ABAQUS software to study the mechanical behavior of the concrete-filled steel tube stub columns prepared with spontaneous-combustion coal gangue aggregate as shown in . Before modeling, three main problems: (a) constitutive model of raw materials; (b) element selection and mesh; (c) boundary condition determination and interaction of the concrete core and steel tube should be solved.The elastic–plastic model was selected to simulate the steel materials. In this study, the steel tube was regard as low carbon mild steel. Further, the von Mises yield criterion and the isotropic hardening rule were used after the steel tube yielded. According to the rules by Han [], a multilinear stress–strain relationship was adopted for the steel tube as follows:σs={Esεsεs≤εspaεs2+3Esεs−σspεsp≤εs≤εsuσsu+bfyln(εs/εsu)εs >εsuwhere parameters a and b are expressed by Eqs. The plastic damage model for the confined concrete given by Guo [] was also modified and adopted for the SCGA-based core concrete. The strain–stress relationship of the SCGA concrete is defined as:y={αax+(3−2αa)x2+(αa−2)x3(x≤1)xαd(x−1)2+x(x>1)εcc=[(1300+12.5fc)+262ξ0.2](1+10.0189r2−1.1967r−6.2784)where εcc is the peak strain of the confined SCGA concrete; fc represents the strength of the concrete prisms; αa and αd denote the ascending and descending parameters of stress–strain curve respectively. The flow potential eccentricity was adopted to 0.1, which is the default value. The dilation angle was selected a constant value of 36°. The ratio tensile meridian to compressive meridian is 0.6667 and ratio of fbo/fc’ is 1.16. Meanwhile, the viscosity parameter was applied a constant value of 0.0005.The steel tube was modeled using four-node 3D shell elements with reduced integration (S4R), and nine integration points were set along the thickness of the shell elements following the Simpson integration rule. The core SCGA-based concrete was modeled using eight-node 3D solid elements with reduced integration (C3D8R) []. Since the mesh method has a great influence on the finite element results [], a mesh sensitivity analysis was carried out before modeling to select the most appropriate element size. On the basis of this, element diameter over the cross-section was chosen as the D/10, and that in the axial (Z) direction was set as the same size as the cross-section as presented in . The whole model was meshed with the “structural” method offered by ABAQUS software [], and a mesh style uniformly distributed over the whole specimen was formed.The boundary conditions of the model of the concrete-filled steel tube stub columns prepared with the spontaneous-combustion coal gangue aggregate were in accordance with the test conditions. The center of the top end and bottom end was selected as RP1 and RP2 and set as rigid body with the two ends herein. Top end and bottom end of the circular CFSTs were fixed except for the freedom degree at reference point 1 (RP1) in the direction of the axial load (U1=U2=0, UR1 = UR2 = UR3 = 0). The axial loading was conducted in a displacement control mode by “STATIC GENERAL METHOD” in the modelling at RP1, the results were similarity to the condition that the axial load applied to the rigid steel plate [The “Surface to surface” contact was applied to simulate the interaction between the concrete core and the steel tube. Concrete core was set as “master surface” while steel tube was set as “slave surface”. The influence of the bonding and friction was taken into account for modeling the interface between the outer steel tube and the inner core concrete. The normal behavior of the interface was simulated with a “Hard Contact”. The tangent behavior of the interface was modeled using Coulomb friction model, and the friction coefficient was set at 0.6 based on the former investigation by Han et al. []. The friction coefficient is defined as a constant which determined by the materials of the two contact surfaces. This study focused on the macro behavior of concrete core and steel tube, the effect of SCGA could be ignored here.The axial load (N) versus axial end shortening (Δ) of all the test CFST stub columns prepared with SCGA and the finite element results are showed in . The FE models provided reasonable predictions, especially for the deviation of the ultimate bearing load and the initial stiffness of 0.4–15.6% and 0.1–12.6%.The ultimate compressive load, elastic stiffness and ductility coefficient of the stub columns calculated by the finite element model with the test results were compared in a–c, where NExp is the axial load obtained from the experiments, and NFE is the one calculated by the finite element model; EAExp is the average elastic stiffness of the test data, and EAFE is the value obtained by FE model; υExp is the average ductility coefficient of the test data, and υFE is the value obtained by the FE model. The mean value of NFE/NExp, EAFE/EAExp and υFE/υExp was 0.953, 1.044 and 1.068with a standard deviation of 0.062, 0.069 and 0.078. These cases in which the finite element results were smaller than the experimental data were owing to the individual experimental deviation.The test and finite element modeling axial load (N)-longitudinal strain (εv) and the axial load (N) -transverse strain (εh) curves of the CFST specimens prepared with SCGA was showed in . It was found that the results calculated by FE models were in good agreement with the experimental test results.It can be seen that the N-εh curves obtained by FE model is in close agreement with the experimental test results in the elastic stage. This indicated that the steel tube and the concrete core of the circular concrete-filled steel tube stub columns worked separately at the initial stage. The FE model predictions of the N-εh curves matches well with the experimental results at the elastic-plastic and post-peak stage especially for the specimens with high steel ratio. This indicates that the surface interaction of the FE model is similar to the test specimens.Clearly, the numerical results generally agree with the test results in N-Δ curve, ultimate compressive strength, elastic stiffness, ductility coefficient, and N-ε curve. These comparisons indicated that the FE model is capability to evaluate the axial behavior of CFSTs prepared with SCGA and also reliable to predict the ultimate compressive strength.A parametric analysis accounting for a wider range of parameters was also conducted to fully understand the axial behavior of the circular CFST stub columns prepared with SCGA. The parameters taken into account included the replacement ratio of the SCGA, the compressive strength of the core concrete, the yield strength of the steel tube, and the diameter of the specimen section. A total of 81 samples were analyzed, and the parameters were set as follows: r = 0%, 50%, and 100%; fcu = 30, 35, and 40 MPa; fy = 235, 345, and 420 MPa; D/t = 37.33, 74.67, and 112. The effects of the selected variables on the axial compressive load and elastic stiffness of the CFST stub columns are presented and discussed below.The variation in the axial load with the replacement ratio of the SCGA for the specimens with an equal strength of the core concrete was depicted in a. The ultimate axial compressive load decreased by up to 4.6%–11.2% and 11.6%–20.0% with increasing the replacement ratio of the SCGA to 50% and 100% respectively, which indicated that the replacement ratio of the SCGA had a significant effect on the ultimate axial compressive load of the CFST stub columns. It is worth noting that ref [] obtained similar experimental results for the SCGA concrete using unequal w/b ratios (accordingly unequal compressive strength), so the influence of the replacement ratio of the SCGA cannot be reflected by a single variable. The finite element model in this paper provides an opportunity to separate the replacement ratio of the SCGA from the other parameters. Meanwhile, the effect of the SCGA replacement ratio on the elastic stiffness of the CFSTs is delineated in b. The elastic stiffness declined by up to 6.8%–8.6% and 10.9%–20.9% as the replacement ratio of the SCGA rose to 50% and 100% respectively. The decrease in the elastic stiffness of the CFST stub columns is chiefly owing to the reduction in the elastic modulus of the core concrete [ showed, the ultimate axial compressive load and elastic stiffness of the stub columns both enlarged with an increase in the steel ratio, implying that the radius-to-thickness ratio of the steel tube had an effect on the axial behavior of the column due to the higher confinement effect by the contribution of the steel area.The effect of the compressive strength of the core concrete (fcu) on the ultimate axial load and elastic stiffness of the stub column is illustrated in . The ultimate axial load decreased with an increase in the replacement ratio of the SCGA at the same compressive strength of the SCGA-based core concrete. Moreover, the descending trends corresponding to the compressive strength of 30, 35, and 40 MPa were almost similar, indicating that the compressive strength of the core concrete had a small influence on the axial bearing capacity of the member and was chiefly reflected by the confinement coefficient. According to b, the elastic stiffness declined by up to 9.4% and 20.6% when the replacement ratio of the SCGA enlarged to 50% and 100% respectively. Compared to the core concrete with the compressive strength of 30 MPa, when the compressive strength of the core concrete increased to 40 MPa, the elastic stiffness enlarged by only 9.8%, 7.5%, and 6.4% at an SCGA replacement ratio of 0%, 50%, and 100% respectively. Because the outer steel tube was considered as an isotropic material with a basically constant elastic modulus, the confinement of the core concrete to the steel tube substantially improved the stiffness of the core concrete in the triaxial compression mode [In this study, the mechanical properties of the steel tube adopted in the test were presented in . It showed that the steel tube with the thickness of 2.75 mm, 3.75 mm and 4.50 mm resulted in an increasing in the yield strength of the steel tube. Thus, the experimental results were impacted by the couple effect of steel ratio and yield strength of steel tube. In order to study the influence of SCGA replacement ratio and yield strength of steel tube on the axial compressive behavior of the CFSTs prepared with SCGA as the independent variables, steel tube thickness was selected the thickness of 3.75 mm. The influence of the steel strength (fy) on the axial behavior of the CFST stub columns was presented in . The ultimate compressive load decreased by 11.1% and 26.8% when the replacement ratio of the SCGA rose to 50% and 100% respectively. Compared to the column with an fy of 420 MPa, the axial compressive strength of the specimens with an fy of 235 MPa declined by approximately 16%. The N–r curves corresponding to the three yield strengths were basically parallel, indicating that the different yield strengths of the steel tube had a similar effect on the ultimate compressive load of the member and were finally reflected by the confinement coefficient. The elastic stiffness of the columns did not exhibit a trend similar to their ultimate compressive load and changed slightly with increasing the yield strength of the steel tube with a maximum reduction of 4.4%. This might be because the axial stiffness was calculated by the combined modulus method in this study [], and the elastic modulus of steel (Es) maintained a constant value, while the elastic modulus of the core concrete (Ec) improved by the confinement effect [This section focuses on the impact of the diameter of the specimens on the mechanical behavior of the CFST stub columns while the other parameters, namely the compressive strength of the core concrete, the yield strength of the steel tube, the steel tube thickness, and the L/D value (which was set at 3.0), remain constant. In particular, the diameter of the section was set at 140, 280, and 420 mm corresponding to the confinement coefficient of 1.20, 0.58, and 0.38 respectively. The reason to select this range of the parameters was that a higher confinement coefficient might inhibit the crack propagation of the core concrete. The relationship between the N-Δ curve of the specimens with different diameters was delineated in a–c. The curves of the columns with a diameter of 280 and 420 mm had an evidently descending tail. With increasing the diameter of the section, the proportion of the concrete core increased, so the confinement coefficient decreased correspondingly. The results showed that the axial compressive strength and elastic stiffness of the columns were substantially enhanced as the section enlarged.d that the ultimate axial compressive load decreased with an increase in the replacement ratio of the SCGA. The maximum axial load of the CFST stub column decreased by up to 11.2% and 20.0% at an SCGA replacement ratio of 50% and 100% respectively. The different diameters of the section had an approximately similar descending trend, indicating that the diameter of the section had an almost similar effect on the maximum compressive capacity of the members. The ultimate compressive load of the specimens with the dimensions 420 mm × 3.75 mm × 1260 mm was 446.6%, 485.4%, and 545.9% times larger than that of the typical column with the dimensions 140 mm × 3.75 mm × 420 mm at an SCGA replacement ratio of 0%, 50%, and 100% respectively. The enhancement of the ultimate compressive strength of the columns was due to the increasing ratio of the diameter of the section more than the confinement effect. However, this effect decreased with increasing the diameter of the section since the decline of the confinement effect was offset by the contribution of the ascending proportion of the SCGA concrete core.The effect of the diameter of the section on the variation in the elastic stiffness of the CFST stub column with the SCGA replacement ratio was presented in e. The elastic stiffness of the member decreased at higher replacement ratios of the SCGA. The elastic stiffness of the specimens with the dimensions 420 mm × 3.75 mm × 1260 mm was 6.54, 6.29, and 5.85 times larger than that of the specimens with the dimensions 140 mm × 3.75 mm × 420 mm at an SCGA replacement ratio of 0%, 50%, and 100% respectively. The effect of the section diameter on the specimens with a lower confinement coefficient was considerable []. This is a basic property of concrete and is caused by the fracture failure of concrete; however, the elastic stiffness is related to the properties of the specimen in the elastic stage. The effect of the section diameter is determined by the area of the core concrete and the steel tube as defined in Ref. []. On the whole, the elastic stiffness of the member increased with raising its diameter.The above discussions on the parametric analysis have proved that the replacement ratio of the SCGA is the major factor impacting the ultimate compressive load and elastic stiffness of the circular concrete-filled steel tube stub columns. The effects of the compressive strength of the core concrete, the yield strength of the steel tube, and the diameter of the column section on the ultimate compressive strength of the stub columns can be indirectly reflected by the confinement effect.The theoretical methods for evaluating the circular concrete-filled steel tube (CFST) stub columns prepared with natural aggregate (NA) are divided into three categories, namely the unified strength theory, the confinement theory, and the superposition theory, the corresponding design codes and limitations of which are listed in . The ultimate compressive load of the specimens prepared with SCGA was calculated according to the design codes, and the results were compared with the experimental data to assess whether the existing design codes are acceptable for circular CFST stub columns prepared with spontaneous-combustion coal gangue aggregate.Considering that the SCGA-based concrete core differs from the NA-based concrete core not only in the material properties [] but also in the mechanical performance [] have some limitations which may make them unsuitable for the spontaneous-combustion coal gangue aggregate concrete core. It should be noted that the formulae presented in EC4 [] are virtually identical. On the basis of the equations listed in , the data on the calculated ultimate axial compressive load of the CFST stub columns prepared with the spontaneous-combustion coal gangue aggregate are tabulated in . These calculated results were used to assess the applicability of existing design codes in calculating the ultimate compressive strength.] all underestimated the Nu value, especially AISC [], which indicates that these models underestimate the effect of the confinement of the core concrete to the steel tube.On the contrary, the design formulae CECS28:90 [] overestimated the ultimate compressive load of the stub columns especially for the specimens with a higher confinement coefficient. A larger replacement ratio of the SCGA led to the lower compressive strength of the SCGA-based concrete, which made the confinement coefficient of the CFST stub columns prepared with the SCGA higher than that of the CFST stub columns prepared with natural aggregate under the same conditions. Hence, using design code CECS28:90 [] to predict the ultimate compressive load of the specimens with higher SCGA replacement ratio may cause serious problems, and the results might be unsafe when the replacement ratio of SCGA is 100%. Therefore, it is necessary to develop an empirical model for predicting the mechanical performance of the circular concrete-filled steel tube stub columns prepared with spontaneous-combustion coal gangue aggregate.The distribution of Nexp/Ncal values at an SCGA replacement ratio of 0%, 50%, and 100% calculated by using the above seven models was illustrated in ; it should be noted that design codes AS5100 [] are the same and presented in one figure. All the ultimate compressive loads calculated by the existing prediction formulae were located within the limit of ±15% except for AISC [] models, which led to a very low degree of accuracy. Design models of GB50936-2014 [] were basically located in a set accuracy district close to the baseline of 1.0, but some prediction values were out of range. Although the results calculated by CECS28:90 model [] were concentrated around the baseline and presented a higher degree of accuracy, more than half of the prediction values were near the lower limitation, which may cause hidden problems in structures.The prediction results of the CFST stub columns prepared with natural aggregate were more stable than those of the circular concrete-filled steel tube stub columns prepared with spontaneous-combustion coal gangue aggregate. The distribution of the predicted values of the CFST stub columns prepared with natural aggregate was relatively denser than that of the CFST stub columns prepared with spontaneous-combustion coal gangue aggregate, which indicates that the existing design codes may not be suitable for predicting the behavior of the circular concrete-filled steel tube stub columns prepared with spontaneous-combustion coal gangue aggregate specimens and need some modifications.] code equations offer the most conservative estimations among the seven codes. Design code GB50936-2014 [] offers the second most conservative predictions on ultimate compressive strength. The AISC [] model offers the third most conservative results. Design code CECS2012 [] offers the less conservative results. Design code CECS28: 90 [] offers the most accurate but the most unsafe predictions, so a model for predicting the behavior of such columns was developed in this work. Considering both accuracy and reliability of the prediction results, the modified GB50936 [] which belongs to unified strength theory was adopted herein. Since the replacement ratio of SCGA basically reflect in the compressive strength of concrete core, the equations in GB50936 [] considers the compressive strength of concrete while this parameter in CECS2012 [] is just a defined value. On the basis of GB20936-2014 [], the model for predicting the ultimate capacity of the circular concrete-filled steel tube stub columns prepared with spontaneous-combustion coal gangue aggregate subjected to axial loading can be expressed in:where As and Ac stand for the area of the steel tube and the core concrete respectively; B and C are the coefficients of the influence of the section shape on the confinement effect; ξ indicates the confinement coefficient; fc represents the strength of concrete prisms; Ks is the modified coefficient.The effects of the replacement ratio of the SCGA and the confinement coefficient on the ultimate compressive load of the CFST stub columns was presented in a. On the basis of the numerical results of 81 finite element models of the circular concrete-filled steel tube stub columns and by means of nonlinear regression analysis, the modified coefficient Ks can be defined as:where r is the replacement ratio of the spontaneous-combustion coal gangue aggregate; and ξ denotes the coefficient of the confinement effect.The modified coefficient Ks involves the coupling relationship between the replacement ratio of the SCGA and the confinement effect with an R2 of 0.908 as showed in can explain 90.8% of the variations in Ks. The ultimate compressive load calculated by Eqs. with the experimental data was compared in b. The comparison of the predicted ultimate compressive load with the experimental data indicated that the derived formulae had a high degree of accuracy. The average value was 0.984 with a standard deviation of 0.076 and a variable coefficient of 0.077.It can be noticed that the predicted values were largely distributed near the baseline. In addition, most of the errors corresponded to the predicted values was smaller than 10%, which was lower than the limitation of 15% defined in Section . The established model can predict the ultimate compressive load of the circular concrete-filled steel tube stub columns accurately with a high degree of safety. Although the results calculated by the modified model for predicting the ultimate compressive load of the circular concrete-filled steel tube stub columns prepared with spontaneous-combustion coal gangue aggregate are slightly lower than the test results, they are still in the range of the 15% limitation. Nonetheless, the effect of the confinement of the SCGA-based concrete to the steel tube needs further investigation.Mechanical performance of circular concrete-filled steel tube (CFST) stub columns prepared with spontaneous-combustion coal gangue aggregate (SCGA) has been investigated. The axial compressive tests of a total of 18 specimens with different replacement ratio of the spontaneous-combustion coal gangue aggregate, namely 0%, 50% and 100%, and different steel ratio, namely 8.3%, 11.6% and 14.2%, has been undertaken to obtain the failure mode, loading carrying capacity, elastic stiffness and ductility of the columns. According to 81 finite element results, a modified equation to predict the ultimate compressive load of the circular concrete-filled steel tube stub columns prepared with spontaneous-combustion coal gangue aggregate has been proposed. The following results were obtained:The failure mode of the CFSTs prepared with SCGA is similar to that of the NA-based CFST columns, and their failure modes are oblique shear pressure damage. The ultimate compressive strength, elastic stiffness and ductility coefficient of the CFST stub columns prepared with 50% SCGA are 2.93–4.81%, −16.17–8.24% and 2.26–16.00% lower than the CFSTs using NA, respectively; while these indices of the specimens prepared with 100% SCGA are 8.25–10.18%, 3.01–20.16%, 11.86–16.34% lower than those of the members prepared with NA, respectively.The SCGA replacement ratio and steel ratio have coupled influences on the compressive behavior of the CFST stub columns prepared with SCGA. As the steel ratio increased from 8.3% to 14.2%, the effect of SCGA replacement ratio on ultimate compressive strength decreased by 17.8%. The scatter of the SCGA-based concrete decreased by 52.6% via composing the steel tube. As steel ratio increased, the confinement effect of the steel tube restrained the development of the cracks of the SCGA concrete core and increase the elastic stiffness before the peak load.The proposed equations in this study includes two key parameters, i.e. replacement ratio of SCGA and confinement coefficient, following the design code of GB50936-2014 using unified strength theory. Based on the experimental and FE results from this study, the proposed model has proven its reliability and accuracy of the ultimate compressive load with the average value and standard deviation of 0.984 and 0.076 respectively.For structural practice, the proposed model in this study can be used to predict the ultimate compressive load of CFST specimens prepared with SCGA, and the optimal replacement ratio of SCGA could be obtained to satisfy the requirements of structural columns.Zhang Yuzhuo: Writing- Reviewing and Editing.Xu Qian: Investigation, Methodology, Original draft preparation.Wang Qinghe: Conceptualization, Funding acquisition, Writing- Reviewing and Editing.Zhou Mei: Writing- Conceptualization, Original draft preparation.Liu Haiqing: Funding acquisition, Investigation.Guo Haiyang: Experimental investigation.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.Isoparametric spline finite strip methodMaterial and geometric nonlinear isoparametric spline finite strip analysis of perforated thin-walled steel structures—Analytical developmentsThis paper presents the analytical developments of the application of the Isoparametric Spline Finite Strip Method (ISFSM) to the material inelastic and geometric nonlinear analysis of perforated thin-walled steel structures. The general theory of the ISFSM is briefly introduced. The formulations of the kinematics, strain–displacement and constitutive assumptions are presented, and the tangential stiffness matrix is derived by applying the incremental equilibrium condition. The requirements for strip continuity and boundary conditions are also discussed. In particular, the plasticity theory and the methods to integrate the ‘rate equations’ are emphasized, and the related ‘backward Euler return method’ and use of a ‘consistent material modulus’ are highlighted. The present isoparametric spline finite strip analysis is verified against a number of analyses of perforated and non-perforated plates and plate assemblages, as described in the companion paper (Yao and Rasmussen, submitted for publication) ► Theoretical basis of inelastic analysis of thin-walled structures by the ISFSM. ► The displacement functions and strain–displacement relations are presented. ► Elasto-plastic constitutive relations for Mindlin plate problems are established. ► The ‘backward Euler return method’ is used to integrate the ‘rate equations’. ► A ‘consistent material modulus’ is incorporated to accelerate the convergence rate.Isoparametric spline finite strip methodCold-formed thin-walled steel structures are frequently manufactured with perforations in order to satisfy service requirements (wiring, piping, etc.), ease connectivity or achieve higher structural performance/weight ratio. Consequently, the redistribution of stresses introduced by perforations will influence the buckling and post-buckling responses of the structure. Extensive research has been carried out in the last four decades on perforated plates In this context, the research motivation for this paper originates from the need to obtain a deeper understanding of the influence of holes on the structural performance of thin-walled members, i.e. elastic buckling, ultimate strength and post-buckling response. Hence, the present work aims to develop a rigorous and efficient material and geometric nonlinear analysis for perforated thin-walled structures by use of the Isoperimetric Spline Finite Strip Method (ISFSM).The ISFSM, which can be considered as a special form of the Finite Element Method (FEM), is an evolved version of the Finite Strip Method (FSM), which was originally developed by Cheung The ISFSM has been previously applied by Eccher et al. to the linear elastic The paper describes the displacement functions, strain–displacement relations and inelastic constitutive material model, and derives the relevant displacement, strain and constitutive matrices. The geometric mapping algorithm, strip continuity and boundary conditions are presented. The nonlinear equilibrium equation and its incremental form are established, and the explicit form of the tangential stiffness matrix is set out. Subsequently, the methods employed to integrate the ‘rate equations’ for elasto-plastic materials are emphasized, and the related ‘backward Euler return method’ and use of a ‘consistent material modulus’ are detailed. A companion paper As the precursor to the ISFSM, the FSM has been used by researchers for the analyses of a variety of structure types including plates, shells, laminated plates, bridges, tall buildings, etc. To date, the FSM has been applied to the linear elastic, vibration and stability, and nonlinear types of analyses The SFSM enhanced the FSM offering greater flexibility by using B-3 splines in the longitudinal direction, while retaining satisfactory efficiency because of the localized nature of the B-3 spline, which helped to yield narrowly banded matrices in the analysis. Successful areas of application of the SFSM include the linear elastic analysis of arbitrarily shaped plates and shells During the 1990s, the ISFSM came to the fore in the literature after the isoparametric concept was introduced into the SFSM. Extensive research on the ISFSM was carried out by Au and Cheung, who originally applied the ISFSM to Mindlin plate bending, plane stress and plane strain problems The ISFSM was further developed by Eccher Compared to the FEM, the ISFSM features strips with rectangular or curved geometric shapes with the longitudinal dimension much greater than the transverse one. In the context of the ISFSM, the structure is first discretized into a number of strips, and each strip is further longitudinally subdivided into a number of sections. Within the cubic finite strip used for the present analysis, there are four nodal lines along which strip nodes are distributed. The number of nodes depends on the number of the longitudinal sections. As distinct from the finite element, the displacement functions of each strip are expressed as products of cubic B3 spline series in the longitudinal direction and Lagrangian cubic shape functions in the transverse direction.Lagrangian cubic polynomials are used in the transverse direction ξ, i.e.where Li(ξ) is the ith component of Lagrangian polynomials corresponding to the ith nodal line of the strip. shows the graphic representation of the transverse shape functions.B3 splines of unit section length are adopted to define the displacements along nodal lines which are in the longitudinal direction η. Each B3 spline φi(η) has non-zero values over four consecutive sections centered over η=ηi and is defined byϕi(η)=16{0,η<ηj−2(η−ηi−2)3,ηj−2<η<ηj−11+3(η−ηi−1)+3(η−ηi−1)2−3(η−ηi−1)3,ηj−1<η<ηj1+3(ηi+1−η)+3(ηi+1−η)2−3(ηi+1−η)3,ηj<η<ηj+1(ηi+2−η)3,ηj+1<η<ηj+20,η>ηj+2(a) illustrates the shape of a single local B3 spline while (b) shows a complete B3 spline series. A complete B3 spline representation is composed of m+3 local B3 splines and m+3 nodes (among which 2 nodes are laid outside each end of the strip as fictitious extra nodes used to completely define a B3 spline series), where m is the number of longitudinal sections of the strip.At the strip level, the displacements of each strip are defined in the natural coordinate system (ξ, η). Each strip has 3 sections and 4 nodal lines in the transverse direction ξ, and can be arbitrarily partitioned into m sections along the longitudinal direction η.The displacement functions of the strip are given as a product of the B3 splines and Lagrangian functions; the generic formulation is as follows:where δ represents the generalized displacement function and refers to u, v, w, θx and θy for the present analysis. αijδ stands for the generalized coefficients to be solved for at the ith nodal line and at the jth longitudinal node.It is convenient to introduce the matrix form of Eq. δ=δ(ξ,η)=Nα=[N1,N2,N3,N4]⋅[α1δT,α2δT,α3δT,α4δT]Twhere Ni is the vector of shape functions for the ith nodal line, and αiδ the vector of nodal coefficients for the ith nodal line. Their explicit forms are given as follows:, three sets of coordinate systems are utilized in the formulation. The global coordinate system (xˆ, yˆ, zˆ) is used to define the geometry of the structure, the boundary conditions and the degrees of freedom belonging to a nodal line that coincide with a fold of the structure. The local coordinate system (x, y) is defined within each strip and is coplanar with the mid-surface of the strip, its y axis is parallel to the global yˆ axis, and has a clockwise rotation γ with respect to the global coordinate system. Although such systems are depicted in , the origins of the two systems are not necessarily at the same point. The stress and strain components, stiffness matrix and load vector of the strip, as well as the degrees of freedom of the nodal lines that do not coincide with a fold of the structure, are expressed in the local coordinate system. A natural coordinate system (ξ, η) of each strip is constructed, which features (possibly non-orthogonal) axes ξ and η, which follow the natural shape of the strip, with ξ being the transverse direction while η being the longitudinal one. Displacement functions and geometric mapping functions () are defined in the natural coordinates.As the Mindlin plate theory is used for the formulation, each node at the mid-surface has five degrees of freedom in the local coordinate system, including two in-plane displacements u and v, one out-of-plane displacement w, and two out-of-plane rotations θx and θy. Their displacement functions all take the specific form of Eq. . The total number of degrees of freedom for a strip is 5×4×(m+3)=20(m+3) in its local coordinates.All the above functions are with respect to the mid-surface of the strip. According to the Mindlin plate theory, the complete kinematics field in local coordinates, uz, vz and wz at a general point, (x, y, z), within the strip, is given bywhere z is the coordinate axis perpendicular to the mid-surface.Recalling the matrix formulation as in Eqs. , the displacement field at the mid-surface of a strip can be obtained as follows:u=u(ξ,η)={u(ξ,η)v(ξ,η)w(ξ,η)θx(ξ,η)θy(ξ,η)}N=[N10000N20000N30000N400000N10000N20000N30000N400000N10000N20000N30000N400000N10000N20000N30000N400000N10000N20000N30000N4]α=[α1uT,α1vT,α1wT,α1θxT,α1θyT,α2uT,α2vT,α2wT,α2θxT,α2θyT,……,α3uT,α3vT,α3wT,α3θxT,α3θyT,α4uT,α4vT,α4wT,α4θxT,α4θyT]TThe algorithms for the geometric mapping of the ISFSM are documented in detail in The geometry of a generic cubic isoparametric spline finite strip with m longitudinal sections is illustrated in (a) shows its original shape in the local Cartesian coordinate system while (b) shows its mapped shape in the natural coordinate system.The global coordinates of a generic point P(xˆ,yˆ,zˆ) within a strip are expressed in terms of the natural coordinates ξ and η aswhere βijxˆ, βijyˆ and βijzˆ are geometric coefficients to be determined from the geometry. In total, there are 4(m+3) coefficients for each coordinate. However, by carefully choosing the sampled geometric nodes, it is not necessary to determine all these geometric coefficients., in a local coordinate system, for the longitudinal direction, if a constant y-spacing hi is assumed for each nodal line i (i=1,…,4), only the y-coordinate values of the nodes corresponding to η=0 and η=m need to be prescribed. Similarly, for the transverse direction, if a constant x-spacing bj is assumed for each transverse row j (j=0,…,m) of the section knots, only the x-coordinate values of the nodes corresponding to ξ=−1 and ξ=1 need to be prescribed for each transverse row. Extending this idea to the global coordinate system, the above local x and y can be replaced by global xˆ and yˆ, while the treatment for global zˆ-coordinates follows the same procedure as that of the x-coordinate detailed above.Following this geometric sampling rule, the xˆ, yˆ and zˆ coordinate values for all the geometric nodes can be found. At this stage, one can either substitute these values into Eqs. and solve for the geometric coefficients or take the advantage of the above sampling method to first simplify Eqs. xˆ(ξ,η)=∑j=−1m+1ϕj(η)(β1jxˆ+β4jxˆ−β1jxˆ2(ξ+1))zˆ(ξ,η)=∑j=−1m+1ϕj(η)(β1jzˆ+β4jzˆ−β1jzˆ2(ξ+1))where yi0 and yim are the y-coordinates of the starting and ending nodes, respectively, of the ith nodal line. It should be noticed that Eq. is already an equation without unknowns while Eqs. still need to be solved for β1jxˆ, β4jxˆ, β1jzˆ and β4jzˆ. For each of Eqs. , a linear system of 2(m+3) equations is required. By substituting the known xˆ and zˆ coordinates of the nodes along the two boundary nodal lines (1st and 4th nodal line) into Eqs. , respectively, it is possible to produce 2(m+1) equations for each respective coordinate, while the remaining 4 conditions can be obtained by substituting into Eqs. the corresponding global coordinates of two extra fictitious nodes within each nodal line (corresponding to arbitrary values of η). to the local coordinates and taking the derivatives with respect to ξ and η, the Jacobian matrix, J, of the transformation can be obtained as[∂ξ∂x∂η∂x∂ξ∂y∂η∂y]=[∂x∂ξ∂y∂ξ∂x∂η∂y∂η]−1=J−T∂x(ξ,η)∂η=∑j=−1m+1ϕ′j(η)(β1jx+β4jx−β1jx2(ξ+1))As spline coefficients αijδ in the displacement functions do not explicitly represent any displacements or their derivatives, the assembling of longitudinally adjoining strips and the application of any boundary conditions require that some of the spline coefficients αijδ in the displacement functions have to be transformed into physical parameters such as displacements, δ, or their derivatives, ∂δ/∂x, ∂δ/∂y, ∂δ/∂ξ or ∂δ/∂η. Details were presented by Eccher , at the place of a generic perforation, the longitudinal geometry of the structure usually has to be split into more than one set of strips in order to accommodate the discontinuity in geometry. Therefore, it is necessary to assemble longitudinally adjoining strips to ensure the required order of continuity along the transverse edges. It will be shown that in order to achieve continuities along the adjoining transverse edges in displacement δ and its derivatives, i.e. ∂δ/∂x, ∂δ/∂y, ∂δ/∂ξ, ∂δ/∂η, ∂2δ/∂x2, ∂2δ/∂y2, ∂2δ/∂ξ2, ∂2δ/∂η2, etc., only the continuities of some key terms need to be satisfied. Specifically, the following conclusions can be drawn:Group 1: If continuities in δ, ∂δ/∂x, ∂δ/∂y, ∂δ/∂ξ and ∂δ/∂η are to be ensured, only the continuities in δ and ∂δ/∂y( or ∂δ/∂η) need to be satisfied;Group 2: If continuities in δ, ∂δ/∂x, ∂δ/∂y, ∂δ/∂ξ, ∂δ/∂η, ∂2δ/∂x2, ∂2δ/∂y2, ∂2δ/∂ξ2, ∂2δ/∂η2 are to be ensured, only the continuities in δ, ∂δ/∂y(or ∂δ/∂η) and ∂2δ/∂y2(or ∂2δ/∂η2) need to be satisfied.These stated sets of continuities have been proved in Although the compatibility conditions of ‘Group 2’ are theoretically feasible, those in ‘Group 1’ are implemented in the present analysis for its adequacy and simplicity. Therefore, if no boundary conditions are specified along the transverse adjoining edges, the first two (α−1i,α0i) and last two (αmi,αm+1i) spline coefficients for any displacement δ at the ith nodal line can be transformed into the physical displacements and their first derivatives as shown belowα−1i→∂δ0i∂yor∂δ0i∂ηα0i→δ0ior∂δ0i∂ξαmi→∂δmi∂yor∂δmi∂ηαm+1i→δmior∂δmi∂ξBefore the assembling process, any prescribed boundary condition also needs to be treated. Specifically, the coefficients related to the prescribed boundary conditions need to be individually transformed into their physical coefficients at first, then substituted into the actual physical values during the analysis.For the present analysis, in general, it is possible to apply five types of boundary conditions, i.e. δji,∂δji/∂ξ,∂δji/∂η,∂δji/∂x,∂δji/∂y, at the generic nodal line i and the generic section knot j for any type of displacement, i.e. δ=u,v,w,θx,θy.However, it has to be pointed out that the type of boundary conditions that can be imposed on a node of a strip is not arbitrary. Attention has to be paid to ensure that the strip is not over-constrained. For example, it is not allowed to impose boundary conditions for δj1, δj2, δj3, δj4 and ∂δji/∂ξ simultaneously for a node of a strip, since ∂δji/∂ξ is a linear combination of δj1, δj2, δj3 and δj4. Further elaboration of the over-constrained conditions can be found in Moreover, no matter whether or not any boundary condition is to be imposed on a node at a transverse adjoining edge, the continuity and transformation requirement set out in Eq. Based on the ISFSM, a material and geometric nonlinear analysis is developed and implemented in this study, and applied to study the post-buckling response and ultimate strength of thin-walled plates and plate assemblies with perforations. The associated flow rules, specifically the Prandtl-Reuss Holes of arbitrary shape, size and location.Large displacements but small rotations.Arbitrary types of boundary conditions and loadings.Different material stress–strain relations for common metals. For instance, ideal elastic–plastic, linear hardening and nonlinear hardening (Ramberg–Osgood Material yielding through the thickness.In order to capture both the local buckling and distortional buckling deformations, the full second-order strain–displacement relations are utilized. Large displacements but small rotations are assumed in the formulation, thus the curvature–displacement relations are linear.The strains in the local coordinate system at the mid-plane areγxy=∂u∂y+∂v∂x+[∂u∂x∂u∂y+∂v∂x∂v∂y+∂w∂x∂w∂y]γxz=∂u∂z+∂w∂x+[∂u∂x∂u∂z+∂v∂x∂v∂z+∂w∂x∂w∂z]γyz=∂v∂z+∂w∂y+[∂u∂y∂u∂z+∂v∂y∂v∂z+∂w∂y∂w∂z] is actually taken to be zero since the out-of-plane displacement is assumed to be invariant through the thickness for thin-walled plates.Bij,x(ξ,η)=L′i(ξ)ϕj(η)∂ξ∂x+Li(ξ)ϕ′j(η)∂η∂xBij,y(ξ,η)=L′i(ξ)ϕj(η)∂ξ∂y+Li(ξ)ϕ′j(η)∂η∂ythe derivative of the generic displacement δ with respect to x becomes∂δ(ξ,η)∂x=∂δ(ξ,η)∂ξ∂ξ∂x+∂δ(ξ,η)∂η∂η∂x=∑i=14∑j=−1m+1L′i(ξ)ϕj(η)αijδ∂ξ∂x+∑i=14∑j=−1m+1Li(ξ)ϕ′j(η)αijδ∂η∂x=∑i=14∑j=−1m+1(L′i(ξ)ϕj(η)∂ξ∂x+Li(ξ)ϕ′j(η)∂η∂x)αijδ=∑i=14∑j=−1m+1Bij,x(ξ,η)αijδSimilarly, for the derivative with respect to yFor the derivatives with respect to z, i.e. ∂u/∂z and ∂v/∂z in Eqs. , the mid-surface displacements u and v in Eqs. first need to be treated as the displacements uz and vz through the thickness, then utilizing Eqs. , it is easy to see that ∂u/∂z and ∂v/∂z in Eqs. reduce to the rotations θx and θy, respectively. They can be written aswhere α is the generalized displacement coefficient, which takes the formα=[α1uTα1vTα1wTα1θxTα1θyTα2uTα2vTα2wTα2θxTα2θyT……α3uTα3vTα3wTα3θxTα3θyTα4uTα4vTα4wTα4θxTα4θyT]T, the generic sub-vector αiδ represents the full set of m+3 displacement coefficients referring to the ith nodal line and the generic displacement δ.The basic strain matrices Bδx, Bδy and Bδz are expressed bywhere the generic sub-vectors Bxi, Byi and Bzi refer to the ith nodal line and contain the full set of m+3 functions given in Eqs. Bxi=Bxi(ξ,η)=[Bi−1,x(ξ,η)Bi0,x(ξ,η)Bi1,x(ξ,η)…Bim,x(ξ,η)Bim+1,x(ξ,η)]Byi=Byi(ξ,η)=[Bi−1,y(ξ,η)Bi0,y(ξ,η)Bi1,y(ξ,η)…Bim,y(ξ,η)Bim+1,y(ξ,η)]Bzi=Bzi(ξ,η)=[Bi−1,z(ξ,η)Bi0,z(ξ,η)Bi1,z(ξ,η)…Bim,z(ξ,η)Bim+1,z(ξ,η)] for the strain–displacement relations can be rewritten in the condensed formwhere ε=[εxεyγxyγxzγyzχxχyχxy]T, and BL and B1(α) denote the linear and nonlinear strain matrices respectively. Making use of Eqs. BL=[BuxBvyBuy+BvxBuz+BwxBvz+BwyBθxxBθyxBθxy+Bθyx]while the nonlinear strain matrix B1(α) isB1(α)=12[αTBuxTBux+αTBvxTBvx+αTBwxTBwxαTBuyTBuy+αTBvyTBvy+αTBwyTBwyαTBuxTBuy+αTBuyTBux+αTBvxTBvy+αTBvyTBvx+αTBwxTBwy+αTBwyTBwxαTBuxTBuz+αTBuzTBux+αTBvxTBvz+αTBvzTBvx+αTBwxTBwz+αTBwzTBwxαTBuyTBuz+αTBuzTBuy+αTBvyTBvz+αTBvzTBvy+αTBwyTBwz+αTBwzTBwy000]Note that B1(α) is a linear matrix in terms of α, thus the following equality holdsFor use in the iterative solution procedure, the nonlinear strain matrix B1(α) is approximated by B1(α)≅B1(αprev)=12[u,xBux+v,xBvx+w,xBwxu,yBuy+v,yBvy+w,yBwyu,xBuy+u,yBux+v,xBvy+v,yBvx+w,xBwy+w,yBwxu,xBuz+u,zBux+v,xBvz+v,zBvx+w,xBwz+w,zBwxu,yBuz+u,zBuy+v,yBvz+v,zBvy+w,yBwz+w,zBwy000]where w,z=0 and αprev is the solution of the displacement coefficients obtained from last iteration. u,x, v,x, w,x, u,y, v,y, w,y, θx and θv are the values evaluated at αprev with respect to α, the incremental strain–displacement relation is derived asdε=[BL+B1(α)]dα+dB1(α)dααdα=[BL+2B1(α)]dα=[BL+BN(α)]dα=B¯(α)dα, and BN(α)=2B1(α), which is the nonlinear strain matrix related to the infinitesimal strain increment dε.It should be noticed that in the Mindlin plate theory, the out-of-plane shear strains, γxz and γyz, are considered; however, they and their corresponding shear stresses, τxz and τyz will not be included in the elasto-plastic calculations for the present analysis, which implies that the out-of-plane shear stress and shear strain relations will always remain elastic during the analysis. Although this is not theoretically stringent, it is a generally accepted assumption in the application of Mindlin theory to thin-walled structures because γxz and γyz are usually relatively small for such structures and so the influence of the simplification on the results is negligible.As the Mindlin plate theory is adopted, the stress–strain relations, or the elasto-plastic material modulus Dep for the present Isoparametric Spline Finite Strip (ISFS) analysis, are based on the strains of the mid-surface of the strip, which indicates that Dep is formed by integrating the plane stress material modulus Dep(z) through the thickness.The strains, εx(z), εy(z) and τxy(z), at any point in the local coordinates, can be expressed by the mid-plane strains at the corresponding point aswhere εx, εv, γxv, χx, χv and χxv are mid-surface strains defined in Eqs. ε(z)=[εx(z)εy(z)γxy(z)]=[100z000100z000100z][εxεyγxyχxyχyχxy]=[IzI]ε′In the plane stress state, the incremental stress at any point within the strip can be expressed asdσ(z)=[dσx(z)dσy(z)dτxy(z)]=Dep(z)dε(z)=Dep(z)[IzI]dε′where Dep(z) is the elasto-plastic material modulus for plane stress problems to be derived in By integrating through the thickness, we obtain the stress–strain relations for Mindlin plates as follows:dσ(m)=∫−t/2t/2dσ(z)dz=∫−t/2t/2Dep(z)dε(z)dz=∫−t/2t/2Dep(z)[IzI]dzdε′dσ(b)=∫−t/2t/2dσ(z)zdz=∫−t/2t/2Dep(z)zdε(z)dz=∫−t/2t/2Dep(z)[zIz2I]dzdε′where dσ(m) represents the membrane stress σx, σv and τxv, while dσ(b) refers to the bending stress mx, mv and mxv.where dσ′=[σxσyτxymxmymxy]T, and Dep is the elasto-plastic material modulus for Mindlin plates as follows:where De and Dp are the elastic and plastic material modulus for Mindlin plates, respectively. De is written aswhere De(z) is the material elastic modulus for plane stress problems, which is assumed to be isotropic. Note that the superscript z in De(z) is only used to distinguish De(z) from the De matrix, it does not indicate that De(z) is a function of z,where E is Young’s modulus and v is Poisson’s ratio.After integration, the De matrix in Eq. can be separated into the membrane part DM and flexural part DF as with the out-of-plane shear part DS, we can obtain the complete material elastic modulus for the present analysis or Mindlin plate problems denotes the plastic material modulus for Mindlin plate problems. It can be written asOnce an incremental step has converged, the material of the structure needs to be updated by re-calculating the Dp(z) matrix for all integration points inside the structure and then numerically integrating them through the thickness to obtain Eq. . The calculation of Dp(z) will be introduced in the next section.This section will mainly concentrate on the aspects of plasticity theory related to the calculation of Eq. for the present analysis. In summary, the von Mises yield criterion , for the present analysis, only the plane stress condition is considered for any specific point inside the structure.An initial yield surface is postulated, defining that yielding will occur when the stresses σ satisfy the general yield functionwhere κ0 is the initial value of the strain hardening parameter, which also defines the initial yield stress. The von Mises yield criterion is adopted for the present analysis as it has proven to be suitable for metal plasticity. In the plane stress state, the two dimensional von Mises yield criterion is given byF0=(σx2+σy2−σxσy+3τxy2)1/2−σ0(κ0)=σe−σ0(κ0)=0where σe is the von Mises effective stress and σ0(κ0) is the initial yield stress.Once yielding occurs, the subsequent yield surface or the loading surface becomes depends on the hardening rule. For the present analysis, isotropic strain hardening is assumed. Isotropic hardening for a 2D stress space is shown in , in which the loading surface expands uniformly about the origin in the stress space and maintains its shape and orientation. Isotropic hardening proves to be suitable for the case of monotonic loading, which usually does not result in significant strain reversals and does not display the pronounced Bauschinger effect. The specific loading surface for isotropic strain hardening isF=(σx2+σy2−σxσy+3τxy2)1/2−σ0(κ)=σe−σ0(κ)=0where κ is the strain hardening parameter, which defines the instantaneous position of the loading surface, and is a function of the equivalent plastic strain εps aswhich is accumulated from the equivalent plastic strain ratesε̇ps=23(ε̇px2+ε̇py2+ε̇pxε̇py+14γ̇ps2)1/2F=(σx2+σy2−σxσy+3τxy2)1/2−σ0(εps)=σe−σ0(εps)=0Suppose that under uniaxial tension in the x direction, we have ε̇py=ε̇pz=−0.5ε̇px, which suggests there is no plastic volume change, substituting these values of plastic strain into Eq. gives ε̇ps=ε̇px, and note that σe=σx. Consequently, σ0(εps) can be readily obtained from the stress–strain curve of the uniaxial coupon test. In addition, as shown in , taking linear hardening for example, we can define the plastic modulus or the hardening parameter asThe plastic strain increment ε̇p is related to the stress increment through the flow rulewhere λ̇ is a positive scalar usually referred to as the ‘plastic strain-rate multiplier’, Q is defined as the plastic potential, which is a function of stresses and plastic strains. If the surface given by Q corresponds to the loading surface F, then it is termed associated plasticity, which is commonly suitable for metal plasticity, otherwise it is termed non-associated plasticity, which is more applicable to softening materials like soils.ε̇p=(ε̇pxε̇pyε̇pxy)=λ̇(∂F∂σ)=λ̇φ=λ̇2σe(2σx−σy2σy−σx6τxy)where φ is a stress vector, which is normal to the loading surface as shown in Within the bounds of small strain flow theory, it is usually valid to assume that the strain increment can be separated into an elastic part ε̇e and a plastic part ε̇p, such thatUsing the elastic stress–strain relations, the stress increment can be expressed asσ̇=(σ̇xσ̇yσ̇xy)=De(z)((ε̇xε̇yε̇xy)−(ε̇pxε̇pyε̇pxy))=De(z)(ε̇−ε̇p)=De(z)(ε̇−λ̇φ)where De(z) is the elastic modulus for the plane stress problems as defined in Eq. For plastic flow to occur, the stresses must remain on the loading surface, hence, taking the variation of Eq. gives the tangency condition as follows:Ḟ=∂FT∂σσ̇+∂F∂σ0∂σ0∂εpsε̇ps=φTσ̇−H′ε̇ps=0 by φT, then substituting the product and Eq. from which we obtain the material tangential modulus Dep(z) for plane stress problems asDep(z)=De(z)−Dp(z)=De(z)−De(z)φφTDe(z)φTDe(z)φ+H′Eq. (110) can be substituted back into Eq. , we can obtain the elasto-plastic material tangential modulus Dep for Mindlin plate problems.The present material and geometric nonlinear analysis is to be solved by an incremental/iterative strategy. Iterations are required for each increment of load step, and the structure is only required to be in equilibrium at the end of each increment. The principle of virtual work is used to formulate the total equilibrium equation.At a given displacement α from the last increment or iteration, given the virtual displacement dαT, and making use of Eq. , the internal virtual work can be expressed aswhere V is the volume of the strip, and the stress vector σ(α) is obtained by accumulating all the previous incremental values until the current displacement α, such thatThe incremental stresses σ̇ are calculated by integrating the stress–strain rate equations, as described in dwe=∫V(dδTfe(α))dV=dαT∫V(NTfe(α))dV=dαTf(α)where fe(α) is the external load vector, and f(α) is the equivalent load vector. Equilibrium is achieved by equating dwi with dwe, that isIntroducing the out of balance force vectorIt should be noted that at the end of each iteration, Eq. is used to evaluate if the out of balance force is small enough to conclude that the force convergence criterion can be deemed to be satisfied.In order to obtain the tangential stiffness of the structure at a given displacement α, we take the variation of Ψ(α) asdΨ(α)=d(∫V(B¯(α)Tσ(α))dV−f(α))=∫V(dB¯(α)Tσ(α)+B¯(α)Tdσ(α))dV−df(α)Taking the variation of σ(α) with respect to α, and making use of Eq. dσ(α)=d(∫0αDep(α)dε)=d(∫0αDep(α)B¯(α)dα)=Dep(α)B¯(α)dαwhere Dep(α) denotes the elasto-plastic tangential modulus for Mindlin plate problems at the current displacement α.dΨ(α)=∫V(dBN(α)Tσ(α))dV+∫V(B¯(α)TDep(α)B¯(α))dVdα−df(α)BN(α)=[αTBuxTBux+αTBvxTBvx+αTBwxTBwxαTBuyTBuy+αTBvyTBvy+αTBwyTBwyαTBuxTBuy+αTBuyTBux+αTBvxTBvy+αTBvyTBvx+αTBwxTBwy+αTBwyTBwxαTBuxTBuz+αTBuzTBux+αTBvxTBvz+αTBvzTBvx+αTBwxTBwz+αTBwzTBwxαTBuyTBuz+αTBuzTBuy+αTBvyTBvz+αTBvzTBvy+αTBwyTBwz+αTBwzTBwy000]=αT[BuxTBux+BvxTBvx+BwxTBwxBuyTBuy+BvyTBvy+BwyTBwyBuxTBuy+BuyTBux+BvxTBvy+BvyTBvx+BwxTBwy+BwyTBwxBuxTBuz+BuzTBux+BvxTBvz+BvzTBvx+BwxTBwz+BwzTBwxBuyTBuz+BuzTBuy+BvyTBvz+BvzTBvy+BwyTBwz+BwzTBwy000]dBN(α)=dαT[BuxTBux+BvxTBvx+BwxTBwxBuyTBuy+BvyTBvy+BwyTBwyBuxTBuy+BuyTBux+BvxTBvy+BvyTBvx+BwxTBwy+BwyTBwxBuxTBuz+BuzTBux+BvxTBvz+BvzTBvx+BwxTBwz+BwzTBwxBuyTBuz+BuzTBuy+BvyTBvz+BvzTBvy+BwyTBwz+BwzTBwy000] is accumulated from each increment as defined in Eq. σ(α)=[σ¯x(α)σ¯y(α)τ¯xy(α)τ¯xz(α)τ¯yz(α)m¯x(α)m¯y(α)m¯xy(α)]T, the first term on the right-hand side of Eq. where Kσ is the so-called initial stress matrix given byKσ=∫V[σ¯x(α)(BuxTBux+BvxTBvx+BwxTBwx)+σ¯y(α)(BuyTBuy+BvyTBvy+BwyTBwy)+τ¯xy(α)(BuxTBuy+BuyTBux+BvxTBvy+BvyTBvx+BwxTBwy+BwyTBwx)+τ¯xz(α)(BuxTBuz+BuzTBux+BvxTBvz+BvzTBvx+BwxTBwz+BwzTBwx)+τ¯yz(α)(BuyTBuz+BuzTBuy+BvyTBvz+BvzTBvy+BwyTBwz+BwzTBwy)]dV∫V(B¯(α)TDep(α)B¯(α))dV=∫V([BL+BN(α)]TDep(α)[BL+BN(α)])dV=∫V(BLTDep(α)BL)dV+∫V(BLTDep(α)BN(α))dV+∫V(BN(α)TDep(α)BL)dV+∫V(BN(α)TDep(α)BN(α))dV=KL+KNwhere KL is the conventional small displacement stiffness matrix and KN is the so-called large displacement matrix. They are defined asKN=∫V(BLTDep(α)BN(α))dV+∫V(BN(α)TDep(α)BL)dV+∫V(BN(α)TDep(α)BN(α))dVwhere KT=KL+KN+Kσ is the total tangent stiffness matrix, and the material status in KT is updated once an increment step has converged, i.e. Eq. In order to avoid shear locking problems, a selective reduced Gaussian integration scheme is adopted for the integrations related to the calculations of the tangential stiffness matrix and the out of balance load vector. More details are given in Because of the path dependent nature of material nonlinearity, specifically the flow rules where σn+1 denotes the total stresses at the end of the nth increment, σn the total stresses at the start of the nth increment and Δσn the total incremental stresses in the nth increment, which can be separated into two parts: Δσe,n derived from the elastic strains Δεe,n and Δσep,n derived from the elasto-plastic strains Δεep,n.The incremental stress Δσn corresponds to the total incremental strains Δεn, which further corresponds to the incremental change in displacement coefficients Δαn, which have accumulated in all the previous iterations within the nth increment, i.e.where k is the total number of iterations in the nth increment.Given the instantaneous elasto-plastic tangential modulus Dep(z), the Δσep,n term in Eq. can be obtained by integrating the stress–strain relations or the so-called rate equationsFor simplicity, the superscript z will be dropped hereafter for all D matrices that represent the stress–strain relations for the plane stress condition.As a path dependent material has different responses for loading and unloading, it is important to note that the incremental strains Δεn other than the iterative strains Δεni=Bdαni should be used for the integration of stresses. This is because stresses obtained by iterative strains can lead to spurious unloading during iterations, thus yielding unrealistic stresses at the end of the increment were very small, a simple forward-Euler scheme could be utilized to gain sufficient accuracy in the resulting incremental stresses. However, since the strain changes are not infinitesimally small and neither is the modulus Dep instantaneous, an uncorrected forward-Euler scheme will usually lead to the accumulation of errors and thus a drift away from the loading surface. For this reason, the rate equations have to be integrated numerically in other ways.It is worth noting that the accuracy of a material nonlinear analysis largely depends on the integration strategy used to integrate the rate equations, and previous researchers have proposed various kinds of algorithms for this purpose. These algorithms can be classified into explicit and implicit categories.The explicit methods mainly refer to the forward-Euler scheme The implicit methods generally include the mid-point algorithm and the backward Euler scheme In the present analysis, both explicit and implicit integration schemes have been implemented into the computer program and comparisons have been made between the schemes. An implicit scheme is finally adopted for the present analysis because of its accuracy and numerical stability. Details are given in the following sections.With an explicit strategy, it is necessary to first calculate the intersection point of the elastic stress predictor with the loading surface, then to obtain the corresponding elasto-plastic strains used for the integration of the rate equations.First the total incremental strains for the nth increment are obtained according to the strain–displacement relations, that isThen the elastic stress–strain relations are used to calculate the stress predictor asThe loading function F(σ˜n+1,κn) in Eq. is computed, giving rise to the following three situations distinguished by the value of F(σ˜n+1,κn):If F(σ˜n+1,κn)≤0, the current point is undergoing elastic loading or unloading, and the final stresses are simply the stress predictor, i.e.If F(σ˜n+1,κn)>0 and F(σn,κn)<0, the current point is transiting from the elastic region to the plastic region, and thus the elastic proportion me of the total strains can be obtained by solving the following loading function:The value of me should be in the range of (0, 1).If F(σ˜n+1,κn)>0 and F(σn,κn)=0, the current point is continuing its elasto-plastic loading, thus me=0.For the latter two situations, the elasto-plastic strains are therefore obtained byGiven Δεep,n, any suitable explicit scheme can be used to calculate the integral of the rate equations to obtain the incremental elasto-plastic stresses Δσep,n in the nth increment.The stresses at the end of the increment are finally given bywhere Δσ˜n=DeΔεn. If a direct forward-Euler scheme is used for the integration, the resulting stresses will inevitably lie outside the loading surface. A more precise explicit procedure, based on the Runge–Kutta method, is implemented in the present analysis. A single step forward-Euler integration is first applied for an increment of Δεep,n/2 to obtainΔσep,n1/2=Dep,n0(12Δεep,n)=12Dep,n0Δεep,nwhere Dep,n0 denotes the elasto-plastic tangential modulus at the beginning of the nth increment. It should be noted that before the Runge–Kutta procedure, or more generally, the integration procedure is carried out, Dep,n0 should be re-computed using the current new stresses. This is because, in the case of extreme strain reversals, the strains could unload so rapidly that their elastic stress predictor exceeds the loading surface in the reversed direction, thus the actual Dep,n0 calculated from σn+meΔσ˜n would be much different from the initial Dep,n0, which is calculated from σn. Then the stresses Δσep,n1/2 from Eq. are used to compute Dep,n1/2 corresponding to half of the nth increment. Thus the stresses Δσep,n resulting from the elasto-plastic strains Δεep,n for the nth increment can be estimated byFinally the total stresses can be obtained from Eq. This Runge–Kutta method has second-order accuracy which is superior to the forward-Euler method, which has only first-order accuracy. However, no matter which type of explicit method is used for the integration procedure, the resulting stresses will usually drift away from the loading surface by some margin. In order to reduce the error, one can either introduce correcting algorithms after the explicit procedure is carried out to force the stresses to artificially return to the loading surface, or use the so-called sub-incrementation method to divide the explicit procedure into a number of small domains. The latter can significantly reduce the errors (at the expense of increased computational effort), and is implemented in the present analysis. In this method, the incremental strain Δεn is divided into msub sub-steps, each having a size of Δεep,n/msub, then the above Runge–Kutta procedure is applied for each step.One important issue raised by the sub-incrementation method is the determination of a suitable number of sub-steps. Two methods regarding this are tried in the present analysis, as follows:Angle ψ method. The integer msub is defined by the angle ψ between the deviatoric stresses sij0 corresponding to the beginning of the nth increment and the elastic deviatoric stress predictor sijP corresponding to the end of the nth increment ψ=cos−1[sij0sijP(sij0sij0)1/2(sijPsijP)1/2]where sij is the deviatoric stress tensor, which in the plane stress context is defined aswhere δij is the Kronecker delta. The value of k in Eq. needs to be decided by the required accuracy. Usually k=0.01 ensures that errors are less than 1% Two-step Euler method. The integer msub is defined by a two-step Euler procedure used to estimate the error produced by the forward-Euler procedure σn+1P1=σn+DeΔεe,n+Dep,n0Δεep,n=σn+Δσe,n+Δσep,n1which leads to a new tangential modulus Dep,nP1. Then re-computing the step in Eq. using the averaged tangential modulus yieldsσn+1P2=σn+DeΔεe,n+12(Dep,n0+Dep,nP1)Δεep,n=σn+Δσe,n+12(Δσep,n1+Δσep,n2)Hence, an estimate of the error is given byTo estimate the required number of sub-steps msub, we first find the variation of the loading surface F in Eq. , retaining up to second-order terms with respect to Δσ suggests that the truncated error in the forward-Euler method is proportional to the square of the length of the stress increment Δσ. Assuming that the total error will be roughly 1/m times the error for a single step if m sub-steps are used, Crisfield Therefore, if a tolerance of β in F is to be satisfied, the required number of sub-steps is given byThe current research found that, if a non-smooth material stress–strain curve is used, for instance, an ideal elastic–plastic curve rather than a stress–strain curve with continuous slopes, the explicit scheme will exhibit notable difficulties in staying accurate around the slope discontinuity points of the material curve. In this situation, the ‘angle ψ method’ defined in Eq. yields less accurate results than the ‘two-step Euler method’ described in Eqs. , because the angle ψ between the two sets of deviatoric stresses does not reflect the current properties of the material stress–strain curve, specifically, the curvature of the curve which is closely related to the determination of msub. Therefore, the msub determined by the angle ψ method will usually be substantially underestimated so that the procedure is unable to produce accurate integration around slope discontinuity points. Moreover, the parameter k in the angle ψ method used to determine the value of msub is empirically based.In the present analysis, a backward Euler return method is also implemented for calculating the integral of . The backward Euler return method is based on the equation, we assume that A is the starting point inside or on the loading surface, B is the so-called ‘elastic trial point’, which corresponds to the elastic stress predictor and C is the requested final point on the loading surface. involves the vector φC, which is normal to the loading surface at the final point C, which is on the loading surface. In general, φC cannot be directly calculated from the data at A or B, so an iterative procedure is needed at each Gauss-point to obtain the stresses at the final point C.A starting estimate of φC can be obtained by performing a first-order Taylor expansion about point B of the loading surface FF=FB+(∂FT∂σ)BΔσ+(∂FT∂εps)BΔεps=FB−ΔλφBTDeφB−ΔλH′Bwhere φB=(∂FT/∂σ)B and use has been made of Eqs. , as well as the incremental form of Eq. with Δε=0 because the total strain Δε has already been applied in moving from point A to point B (). Equating the loading function value F to zero givesA vector, r, is introduced to compute the difference between the current stresses σC and the stresses given by Eq. Iterations are performed until r has been reduced to zero while ensuring the final stresses σC satisfy the loading condition F=0, as follows:With σB being kept fixed, a first-order Taylor expansion about point C can be applied to Eq. σ̇=−(I+ΔλDe(∂φ∂σ)C)−1(rC+λ̇DeφC)=−QC−1rC−λ̇QC−1DeφC, a first-order Taylor expansion about point C of the loading surface F givesF=FC+(∂FT∂σ)Cσ̇+(∂FT∂εps)Cε̇ps=FC−φCTσ̇−λ̇H′C yields the iterative change of the plastic strain-rate multiplier λ̇, the iterative change of the effective plastic strain isHence the total change of the effective plastic strain Δεps is given bywhere j denotes the jth iteration for the backward Euler return procedure. Substituting λ̇ back into Eq. gives the iterative stress change σ̇, hence the stresses at point C are updated by, and another iteration is performed until the loading surface F and the norm of rC are less than a near-zero tolerance value.In general, the explicit methods presented in can produce results of acceptable accuracy if sufficient sub-divisions are used. However, several drawbacks with it are encountered during the analysis. Firstly, although the Runge–Kutta method in the explicit scheme has a second-order accuracy in determining the tangential modulus matrix Dep, the matrix still remains an approximation and therefore, the resulting stresses are bound to drift away from the loading surface by some margin. Secondly, because no yield surface, or loading surface, is needed for the explicit method, it is usually impossible in the explicit scheme to keep stresses on or within the loading surface. Nevertheless, one can additionally introduce the loading surface into the explicit integration procedure to reduce the error. The procedure that the present analysis has tried is to use Eqs. after the explicit procedure to bring the stresses back close to the loading surface. Although significantly improving the results, this complementary stress-correcting algorithm will produce artificial plastic strains, which may not be consistent with the stresses. Moreover, as this correcting algorithm is a non-iterative procedure, the resulting stresses may still not be sufficiently close to the loading surface.In contrast, the implicit scheme, specifically the backward Euler return method described in , uses a specific loading surface and thus can ensure that the errors of the resulting stresses are within a chosen tolerance, and that the stresses stay on the loading surface. Furthermore, this procedure is a general method with regard to the material stress–strain curve, which means no special considerations are needed for material curves with slope discontinuities. Concerning the numerical efficiency, numerical tests have also shown that the number of iterations needed for a backward Euler procedure is much less than the number of sub-incrementations needed for an explicit procedure in order to reach the same level of accuracy. Moreover, the backward Euler return method does not require the computation of the intersection point of the elastic stress predictor with the loading surface and also allows the generation of a ‘consistent tangent material modulus’ (see ), which accelerates the convergence of the overall iterations at the structural level.In conclusion, considering its accuracy and efficiency, the implicit integration scheme, specifically, the back Euler return method, is recommended for the integration of the rate equations and thus is adopted in the present analysis for all subsequent computations.The concept of the consistent tangent modulus was derived by Simo and Taylor corresponds to the current converged displacement α, but the consistent tangent modulus takes into account the amount of change of the plastic strains in the last increment and uses this information to predict the subsequent increment. Although the prediction is an estimate, in general situations, the consistent tangent modulus can improve the convergence rate in solving the global equilibrium equations.The derivation of the consistent tangent modulus also starts with Eq. where the suffix C relating to the current state has been dropped. The suffix B denotes that σB is the elastic stress predictor. Noting that σ̇B=Deε̇ and (Δλ)=λ̇, differentiation of Eq. σ̇=(I+ΔλDe∂φ∂σ)−1De(ε̇−λ̇φ)=Q−1De(ε̇−λ̇φ)=R(ε̇−λ̇φ)where the Q matrix was introduced previously in Eq. Rewriting the tangency condition in Eq. Ḟ=φTσ̇−H′ε̇ps=φTRε̇−λ̇φTRφ−H′ε̇ps=φTRε̇−λ̇φTRφ−H′λ̇=0 for λ̇ and back-substituting the solution into Eq. where Dep is the consistent tangential material modulus, i.e.If Δλ=0, the consistent tangential modulus given by Eq. degenerates to the standard tangential modulus given by Eq. As the formulation of the consistent tangential modulus is similar to that of the backward Euler procedure, it can be easily incorporated into the backward Euler procedure. Numerical tests show that in most cases the consistent tangential modulus accelerates the convergence rate of iterations. However, for the case of material ideal plasticity, or more generally, for materials with no or little strain hardening, faster convergence is achieved by not engaging the consistent tangential modulus. The reason for this is that if the consistent tangential modulus is engaged for this kind of material, the additional plastic flow Δλ associated with it tends to over-predict the loss of the stiffness of the material and thus impedes the convergence of displacements. This phenomenon is also characterized by the emerging negative eigenvalues of the overall stiffness matrix.An analytical study of the application of the ISFSM to the material and geometric nonlinear analysis of perforated thin-walled metal structures has been presented. The general inelastic nonlinear theory has been discussed in detail by describing the kinematics assumptions, the strain–displacement relations, the material constitutive relations and the equilibrium equations. The geometric mapping algorithm, the strip continuity requirements and the application of boundary conditions are also described.Particular emphasis has been put on detailing the plasticity theory for the plane stress condition, elasto-plastic constitutive relations for the Mindlin plate problems and the available methods for integrating the rate equations. The explicit and implicit integration schemes are extensively discussed and compared with each other, leading to the conclusion that the implicit backward Euler return method is superior to the explicit integration scheme in terms of numerical efficiency and reliability. The consistent material modulus is finally derived, which, generally, proves to accelerate the convergence rate of equilibrium iterations at the structural level.The theory presented in this paper had been applied to derive their corresponding matrix formulations for the present isoparametric spline finite strip analysis, which can be readily coded in a computer program, as described in the companion paper A numerical study of beam-to-column joints subjected to impactLimited documentation is concerned with the behaviour of steel joints subjected to severe impulsive loading originating from incidents such as explosions or impact. In this paper, finite element simulations are used to investigate the behaviour of beam-to-column joints with bolted end-plate connections subjected to impact loading. An elastic-thermoviscoplastic material model was employed in the simulations. Good agreement was obtained between the simulations and previously reported tests in terms of both global and local behaviour. In particular, the numerical model successfully reproduced the experienced failure mode of tensile bolt fracture combined with end-plate deformation. The validated model was employed in investigations of three cases, in which the main findings are as follows: (1) reducing the end-plate thickness significantly increased the energy dissipated by the joint; (2) axial forces in the beams only marginally affected the response; and (3) including the additional inertia introduced by the presence of floor slabs may change the failure mode to premature shear failure.In the past 15–20 years, particularly after the attack on the World Trade Center in 2001, there has been increased interest in the behaviour of joints subjected to extreme dynamic loads. The beam-to-column joints in a framed structure should preferably be able to transmit such loads to the surrounding members without failing. This requires that the joints have adequate properties such as energy dissipation capacity, which can be considered as a combined measure of the strength and ability to deform before failure. Similarly, design code UFC 3-340-02: Structures to resist the effects of accidental explosionsDynamic tests on full-scale joints can increase our knowledge of this topic, but such experiments are expensive and challenging to perform in a controlled manner. Compared to quasi-static tests, a well-defined application of the load is more difficult to achieve in the dynamic case, and more advanced instrumentation tools are required. The interaction between the joint and its surrounding structure is also challenging to consider in experiments; therefore, it is common to only perform tests on the joint itself and on a minor part of the adjacent beam and column members. An example of such an interaction is when large deformations of a framed structure induce considerable axial forces in the beams through catenary action. In addition, the interaction with structural components such as floor slabs is impractical to include in experiments. Considering floor slabs is particularly important under severe dynamic load conditions. This is because these members introduce considerable inertia, which may significantly alter the response compared to the quasi-static case. Moreover, it is difficult to accurately investigate parameters such as energy dissipation in the different components of the joints based on experimental data. Such challenges related to the testing of joints can be readily addressed with numerical simulations. A trustworthy numerical investigation requires that the model is validated. This means that the model is able to capture the experienced global as well as local response of the joint at hand, including the correct failure mode.Few reports on numerical analyses of the transient dynamic response of beam-to-column joints can be found in the literature. Sabuwala et al. For some years, researchers at the Nanyang Technological University have performed experiments and FE simulations to investigate the behaviour of various steel connections during a so-called column-loss scenario; see, for instance, Yang and Tan A comprehensive experimental programme commenced a few years ago at the University of Sheffield, where a purpose-built test rig has been used to study the behaviour of single-sided joints subjected to high loading rates; see Tyas et al. The first objective of this paper is to present and validate a three-dimensional FE model of the impact tests reported by Grimsmo et al. How the energy dissipated in the joint region is influenced by minor changes in the design of the joint. This study is limited to varying the end-plate thickness.How axial forces in the beams affect the behaviour of the joint configuration.How the response of the joint configuration is influenced by the inertia of floor slabs attached to the beams. The purpose of this investigation is to provide a qualitative assessment of the inertia effects. of this paper briefly summarizes the laboratory tests in terms of both full-scale component and material tests. Next, Section presents the material model and discusses how the material parameters were identified. The FE model of the impact tests is introduced in Section . The investigations of energy dissipation, axial force, and inertia are presented in Sections , respectively. Finally, concluding remarks are given in Section The experimental programme, including impact tests in a pendulum accelerator, was thoroughly presented by Grimsmo et al. . The specimens consisted of: two HEA 180 sections that served as beams; an HEB 220 section representing the column; an “impact plate” spot welded to the end of the column; two 10 mm web stiffeners welded to the column; two 12 mm extended end-plates that were welded to the beams by fillet welds with throat thicknesses of 5 mm; and a total of twelve partially threaded M16 × 65 bolts of grade 8.8. The H-sections and end-plates were manufactured from grade S355 steel. Additional dimensions relevant to the modelling are provided in the . The test specimen was designed so that several components of the joint experienced plastic deformation, and so that failure occurred by tensile bolt fracture combined with end-plate bending deformation. Thus, a numerical model of the tests may be considered reliable if it can capture this relatively complex deformation mode.A key part of the pendulum accelerator is the trolley (727 kg) illustrated in , which rolled along two rails and impacted the test specimen with a given velocity. Four tests were performed on the specimen geometry in : two with an impact velocity of approximately 8 m/s and two with an impact velocity of nearly 12 m/s. The duration of a test, i.e., from impact to bolt failure, was between 5 and 10 ms, depending on the impact velocity of the trolley.The beams were supported on steel cylinders placed 690 and 686 mm from each end-plate, as observed in . Thus, the joints were mainly loaded by bending moments and shear forces as the column displaced horizontally due to the impact. All tests included a high-speed camera that monitored the deformation and fracture process of the region around the upper end-plate in . Also, the slight difference in distance to the supports increased the likelihood of failure initiating at the part that was captured by the camera.Mechanical properties of the different components were determined by performing quasi-static and dynamic uniaxial tension tests. The specimens used in these tests are displayed in b) were machined from the bolts. Quasi-static tests were conducted on the specimens in a and b in a standard hydraulic machine with a strain rate of the order of 10−4 |
s−1. Digital cameras captured the deformations of the specimens. The specimens were painted with a speckle pattern, which enabled digital image correlation (DIC) analyses. Thus, local strains in the neck and the true stress–strain response up to failure could be determined. Replicate tests were performed, and a good agreement was achieved between the replicates. Some results from these tests are given in Section . Additional results are provided by Grimsmo et al. c depicts the specimens employed in a strain-rate sensitivity investigation. This specimen was machined from the end-plates and bolts. The materials of the beam and column sections were assumed to have the same strain-rate sensitivity as the end-plate material because all these parts were made of S355 steel. Material tests at strain rates of approximately 10−3 and 10−1 |
s−1 were obtained with a standard hydraulic machine, and a split-Hopkinson tension bar was employed for testing at strain rates of the order of 102 |
s−1. The split-Hopkinson tests were conducted with the instrumentation as described by Vilamosa et al. , the results from these tests are provided together with the calibrated strain-rate sensitivity parameters.The materials were modelled with an elastic-thermoviscoplastic constitutive relation that incorporated the following: linear elasticity, the von Mises yield criterion, the associated flow rule, non-linear isotropic hardening, strain-rate hardening, and thermal softening due to adiabatic heating. The equivalent stress σeq was defined byσeq=σyforεp⩽εp,platσy+∑i=12Qi1-exp-θiQi(εp-εp,plat)1+ε̇pε̇refC[1-Thm]forεp>εp,platwhere σy is the yield stress; Qi and θi, i |
= 1, 2, are the hardening constants of the extended Voce hardening rule; ɛp is the equivalent plastic strain; ɛp,plat is the value of ɛp at the end of the yield plateau; ε̇ref is a reference strain rate that, together with the constant C, governs the rate sensitivity; Th is the homologous temperature; and m is a constant. The homologous temperature is defined as Th |
= (T |
− |
Tr)/(Tm |
− |
Tr), where T is the absolute temperature, Tr is the room temperature, and Tm is the melting temperature. Because the duration of the simulations is less than 10 ms, heat conduction effects can be neglected. Adiabatic heating is therefore assumed, and the temperature increment is calculated aswhere χ is the Taylor–Quinney coefficient, ρ is the density, and Cp is the specific heat capacity.Failure was included in the simulations by employing the fracture criterion proposed by Cockcroft and Latham attains a critical value Wcr. Here, σI is the maximum principal stress. This failure criterion is strain-rate sensitive via the principal stress, cfr. Eq. . Furthermore, the criterion is indirectly dependent on stress triaxiality and the Lode angle, as shown by Gruben et al. The material model, including the constitutive relations and the failure criterion, were implemented in the simulations by a user subroutine developed and validated at SIMLab. provides the material parameters deduced from the material tests discussed in Section . These parameters were employed in the simulations of the full-scale joint tests. All four materials (column, beam, plate, and bolt material) were assigned a Young’s modulus of 210 GPa, Poisson’s ratio of 0.3, and density of 7900 kg/m3.From the quasi-static tension tests performed on the specimens in a and b, true stress-plastic strain curves were obtained, and the yield stress σy and the strain ɛp,plat were read directly from representative curves. Initial values of the hardening parameters Qi and θi were acquired by fitting the term in the first square brackets in Eq. to the pre-necking values of the true stress-plastic strain curves. For the plate and bolt material, the hardening parameters were subsequently optimised via inverse modelling of the quasi-static tension tests such that the correct response was also obtained for post-necking strains, giving the result in . Here, the engineering stress is plotted versus the area reduction at the neck. The inverse modelling procedure was not performed for the column and beam material because only pre-necking plastic strains occurred for these two materials in the full-scale joint tests and simulations.The parameters ε̇ref and C were determined by least-square fitting of linear polynomials to the experimental data obtained from the strain-rate sensitivity investigation. Recall that these experimental data were found from tests performed on the end-plate and bolt material used in the full-scale component tests. The results are displayed in . Here, the axes are defined such that the slope of the linear curves corresponds to the value of C when the temperature factor in Eq. is set to unity. The reference strain rate ε̇ref was chosen as 10−3 |
s−1, i.e., approximately the lowest strain rate in the investigation involving the test specimen shown in , the stresses obtained experimentally were acquired at two pre-necking values of the true strain, i.e., 0.09 and 0.16 for the plate material, and 0.04 and 0.07 for the bolt material. The values of C were calculated as the average of the two slopes determined for each of the two materials.All four materials were given the following temperature-related parameters: m |
= 1.0, Tr |
= 293 K, Tm |
= 1800 K, χ |
= 0.9, and Cp |
= 452 J/kg K. These values were adopted from Børvik et al. The fracture parameter Wcr was determined by simulating the quasi-static tension tests using elements of the same size as those used in the full-scale joint simulations because Wcr is known to be strongly mesh dependent. The simulations were therefore run with element sizes of 3.0 mm and 1.0 mm for the plate and bolt material, respectively. The onset of fracture in the tensile test simulations was defined as the instant when the work, i.e., force integrated over displacement, performed on the specimen equalled the work up to fracture determined by the experiments. At this instant, the largest value of the integral W (see Eq. ) in the mesh corresponded to the critical value Wcr. The fracture parameter was not determined for the column and beam material because these did not exhibit fracture during the tests.The impact tests on the column and beam assembly were simulated using the commercial FE software Abaqus/Explicit The FE model of the impact tests is shown in . By exploiting symmetry, one half of the physical specimen was modelled; see a. Two analytical rigid surfaces with cylindrical shape represented the beam supports. The trolley was modelled as a rigid body with a mass equal to that of the physical trolley, except for the nose of the trolley, which was explicitly modelled and located 0.1 mm from the impact plate at the start of the simulation.b provides a detailed view of the end-plate region. The welds were modelled as triangular parts. c shows that the threads of the bolts were not explicitly included in the model because that would require very small elements, which would further lead to impractically small stable time increments in the explicit analyses. The partially threaded bolts were therefore modelled with a smooth shank along the entire length between the head and nut. A representative diameter of 13.9 mm was applied in the threaded portion; see for additional details about the bolt and nut part. This diameter was deduced from quasi-static tension tests performed on M16 bolt and nut assemblies such that the bolt model would reproduce the maximum force registered during these tests. Note that two nuts per bolt were used in the tests to prevent possible thread failure, and the modelled nut was therefore higher than a single regular nut.b and c show the mesh density of the model. Mesh seeds of 3 mm were applied to the end-plates, which gave 4 elements over the thickness. The column and beams were given mesh seeds of 4 mm. Since significant deformation was experienced by the bolt shank, mesh seeds of approximately 1 mm were applied to this region, which gave 14 elements over the smallest diameter. The remainder of the bolt and nut part was given mesh seeds of approximately 3 mm. Inevitably, somewhat inhomogeneous meshes were obtained due to the challenges related to meshing circular and hexagonal geometries; see c. The entire model contained approximately 310,000 elements. The mesh density was considered sufficient because the model produced results that agreed with those obtained from the tests, and because refining the mesh only minimally affected the response. Solid elements with reduced integration (C3D8R) were employed for the entire model, except for the welds, where wedge elements (C3D6) were used.Appropriate boundary conditions ensured that the supports of the beams were fixed in all directions, and that the trolley was only allowed to translate along the column axis. The pre-impact velocity of the trolley measured in the experiments was set as an initial velocity for the trolley in the model.A tightening moment of 80 Nm was applied to the bolt and nut assemblies in the tests , the material parameters for the column, beams, end-plates, and bolts were presented. The welds were assigned the same material parameters as the beams, whereas the stiffener was given the parameters of the column. Recall that failure is not considered for the beam and column material, and possible failure of the welds is thus not treated in the current study. The impact plate and the nose of the trolley were both machined from high-strength steel, and were assigned the same properties as the bolt material.The numerical model of the impact tests was validated by demonstrating that the deformation and failure mode experienced in corresponding tests and simulations were similar. In addition, the response was compared in terms of global force–displacement and velocity–time curves. It is demonstrated in Section that the model indeed captures both the local response in the part of the joint that fails and the global response the entire joint. Further, a model of a corresponding quasi-static test is evaluated in Section a shows a close-up of the deformed joint observed in a test and simulation 7 ms after the specimen was impacted by the trolley at 12 m/s. The deformation of the end-plate is clearly similar in the test and simulation, and failure occurred by tensile fracture of the centre bolt (row) in both cases. Note that the head of the centre bolt in b, the opening O is plotted versus the displacement D obtained from both DIC analysis and simulation, and a good agreement is observed. The curves in this figure, and all subsequent curves in this paper, are plotted to the instant where bolt fracture was observed in the respective test or simulation. Thus, considering b, the applied fracture parameter WC produced failure at approximately the same displacement D and opening O in the simulation as observed in the test.. Furthermore, at the incipient necking of the bolts in the simulations, the maximum temperature had increased by approximately 45 K, which reduced the equivalent stress by a factor of only 0.97. However, this factor was 0.84 immediately prior to failure because the maximum temperature had increased by approximately 240 K. This thermal softening resulted in failure at a displacement D equal to 50.9 mm rather than 52.3 mm, which was obtained in a simulation that did not include thermal softening. The response, in terms of force–displacement and deformation mode, was practically unaffected by temperature effects otherwise. depicts various curves obtained from the two replicate tests with an impact velocity of 12 m/s and the corresponding simulation. The force P acquired from the tests was measured by the load cell shown in . In the simulation, the force was defined as the contact force between the nose of the trolley and the impact plate. This difference in force measurement, together with the fact that all contact surfaces were perfectly coplanar in the simulation (most likely not the case in the experiments), explains why the force increased more suddenly in the simulation; see a. Moreover, the trolley system was not completely rigid in reality, which may have introduced additional softness to the response in the tests. Nevertheless, the force curve acquired from the simulation agrees reasonably well with the test results. As thoroughly discussed by Grimsmo et al. b. The first impact caused an acceleration of the column, and because the area under the force–displacement curve is larger for the simulation, the column obtained greater velocity than in the tests. Thereafter, the column decelerated during the non-contact period (approximately from 1 to 4 ms) because the joints started to resist the translation of the column. During this period, the simulation and tests yielded the same behaviour in terms of velocity, which indicates that the joints have the same resistance in the model and test. The trolley had a constant velocity in the non-contact period and eventually impacted the specimen again at approximately 4 ms. Thus, the column was accelerated a second time, which was also well captured by the simulation. c displays the velocity Vt of the trolley as a function of time; good agreement is again observed between the simulation and the test. This implies that the correct amount of kinetic energy was transferred from the trolley to the specimen during impact in the simulation.For the purpose of complete validation, the quasi-static tests of the beam-to-column joints were also simulated. These tests are described by Grimsmo et al. compare the results with the experiments. Note that only one of the two replicate quasi-static tests was monitored with cameras. shows that the deformation mode is generally similar in the tests and simulation. As experienced in the tests, the deformation became asymmetric with respect to the centreline of the column after obtaining the maximum force in the simulation. This asymmetrical behaviour can be seen from the difference in deformation of the two end-plates in . Furthermore, tensile fracture of the bolts occurred at one of the connections in both tests and simulation. However, the magnitude of the asymmetrical behaviour was not the same in the simulation as in the test, and the simulated opening O at failure was smaller than the observed opening in the test; see the curves in b shows that the force was generally larger in the simulation than in the two tests. On the other hand, satisfactory agreement is found when considering the maximum force.The ability to absorb energy is an important property of a structure subjected to dynamic loading. Provided that the validation domain is not exceeded, the numerical model presented in Section can be employed to evaluate how various choices with respect to the joint design affect the energy absorption. FE simulations may also serve to explore differences between quasi-static and dynamic responses. Since the intention of this paper is to demonstrate the methodology, the present study is limited to investigate the effect of varying the thickness of the end-plate. In the study, the energy dissipation Ed is taken as the plastic dissipation in the region enclosing the joints, as defined in . Frictional dissipation is neglected here because Abaqus does not support acquiring it from a specific region. shows curves with accumulated energy dissipation Ed versus displacement D of the column obtained from the simulations of an impact test at 12 m/s and a quasi-static test. The maximum value of the displacement D represents the ability of the joints to deform. This ductility measure is another important property of joints. clearly displays that the maximum displacement D obtained for the impact simulation is larger than for the quasi-static simulation. The reason for this significant difference is related to inertia effects, as elaborately discussed by Grimsmo et al. also shows that energies of approximately 14 and 8 kJ were dissipated in the impact and quasi-static simulations, respectively. The difference in energy dissipation is mainly related to the difference in displacement D at fracture for the two load cases. These energy dissipation values acquired from the simulations agree somewhat with the values determined from the experiments, where the dissipated energy was approximately 20 and 8.5 kJ in the impact and quasi-static tests, respectively is the sudden increase in the dissipation at a displacement D of approximately 5 mm, which occurred only for the impact simulation. This was caused by the inertia of the specimen inducing a deformation mode involving greater shearing action than in the quasi-static simulation. More specifically, the column displaced axially relative to the connected end-plates and beams such that the bolts experienced shear deformation and the bolt holes became plastically elongated. This shearing action also occurred in the tests, as discussed by Grimsmo et al. With the script that generates the model, the user can readily explore favourable changes to the design of the joint configuration under impact load conditions. Here, it was chosen to investigate the effect of changing the end-plate thickness from the 12 mm used in the experiments to 9 and 15 mm. Such a considerable variation of the thickness was chosen because it induced a pronounced change in the response, and it does not necessarily represent a favourable design of the joint. The results are presented in . Note that varying the plate thickness implies a corresponding change in the clamp length of the bolt and nut assemblies, which affects the tensile deformation capacity of the bolts. a shows that both the energy dissipation Ed and the displacement D at failure with the 9 mm end-plate is approximately two times greater than with the two other end-plate thicknesses. b depicts that the thinner end-plate experienced significant bending deformation, which allowed for increased displacement D, and thus more energy dissipation Ed, before failure.With 9 mm thick end-plates, fracture occurred in the centre bolt (row) after significant yielding of the end-plates. This behaviour is reasonable because the calculation procedure following NS-EN 1993-1-8: Design of jointsb are similar to those of the validated model; see a. However, recall that possible failure of the welds is not considered in these simulations. Girão Coelho et al. Reducing the end-plate thickness from 12 to 9 mm increased the energy dissipation before failure by 100% because the deformation capacity of the end-plates was better utilized. However, this thickness reduction decreased the static bending moment resistance and initial rotational stiffness by 23% and 21%, respectively. These two properties are important for the static behaviour of the joint. Increasing the thickness to 15 mm enhanced the energy dissipation by 14%, whereas the moment resistance and stiffness increased by 12% and 9%, respectively. Here, the energy dissipation was determined from the curves in a, and the values of the static bending moment resistance and initial rotational stiffness were obtained from the calculation procedure following EC3 As in the tests, the energy dissipated by the joint was higher in the impact simulation than in the quasi-static simulation. Grimsmo et al. The design code NS-EN 1991-1-7: General actions – Accidental actionsThe deformation and failure modes of the specimen were not appreciably affected by the presence of axial forces. In particular, the deformation of the end-plate region upon failure was similar to that observed in a, and failure still occurred by tensile bolt fracture in the centre bolt row. As expected, however, the additional tensile force experienced by the bolts gave fracture at a reduced displacement D of the column as the axial force in the beams was increased. Fracture occurred at displacements of 50.9, 49.3, and 46.6 mm for axial forces of 0, 150, and 300 kN, respectively.a presents force–displacement curves obtained from the axial force study. By observing the first peak in the figure, it is clear that the axial forces did not affect the initial impact. However, the second impact occurred at a larger displacement D when the axial force was increased. This observation can be explained by b, which presents curves of the velocity V of the column versus time. The figure reveals that increasing the axial force produced a slightly lower deceleration of the column during the non-contact period (approximately 1–4 ms). For the second hit, the trolley thus impacted the specimen at a later instant than for the case with no axial force. The reduced deceleration indicates that the moment resistance of the joints decreased due to the axial forces. This is reasonable because the moment resistance is partly governed by the tensile resistance of the bolts, and here, the bolts experience additional tensile forces introduced by the axial force. Thus, the contribution from the bolts to the moment resistance is reduced. Furthermore, the displacement D of the column is not sufficiently large for the axial force to activate any significant geometrical stiffness in the column and beam assembly.In reality, the axial forces in the beams of a framed structure depend on the deformation of the structural members and are therefore not constant. An axial force that varies with deformation might have affected the behaviour of the joints somewhat differently. Furthermore, large compressive axial forces in the beams may also arise under extreme situations. Although not investigated here, compressive axial forces in the beams tend to increase the moment resistance of joints with end-plate connections provides a cross-sectional view of the end-plate region as it deforms together with fringe plots of the Mises stress. Shear fracture of the bolts clearly occurred, in contrast to the previous simulations, where tensile fracture of the bolts took place. This is due to the additional forces required to accelerate the beams with the higher mass, which further caused the bolts to experience larger shear forces. Failure of the joints occurred at a displacement D of the column of approximately 18 mm. This represents a significant reduction of the ductility of the joint compared to the simulation without the additional mass, where the displacement at failure was 51 mm; see Section The effect of the increased inertia is also clearly observed in the force–displacement and velocity–time curves shown in , where the results obtained with the validated model presented in Section are included for comparison. In terms of the force–displacement curves in a, the first impact was virtually unaffected by the additional inertia of the beams. However, the second impact occurred at a significantly smaller column displacement, and the force level was much higher compared to the second impact for the validated model. Considering the velocity–time curves in b, the two models produced a similar response during the first 0.5 ms. At the end of this period, the end-plates and beams were activated. For the model with the larger inertia of the beams, the column was then more rapidly decelerated, leading to the second impact occurring at an earlier stage. The difference in the maximum force level of the second impact is explained by the difference in the relative velocity between the trolley and the column at the time of this impact. For the model with increased inertia of the beams, the velocity V of the column was 2.8 m/s for the second impact (at approx. 1 ms), whereas it was 4.9 m/s (at approx. 4 ms) for the validated model. As for the validated model (see c), the velocity of the trolley during the non-contact period, and thus at the time of the second impact, was approximately 10 m/s in both cases.This investigation is qualitative in the sense that the purpose is only to provide an indication of the effects of considering the inertia of members such as floor slabs. To properly capture the shear fracture of the bolts, a significantly finer mesh is probably required because the thickness of the shear bands of high-strength steels subjected to high strain rates can be approximately 10 μm, as Kane et al. Note that thermal softening was a prerequisite for obtaining shear failure in the current investigation. Although not shown here, increasing the length of the beams together with the distance to the supports does not affect the response because only approximately 250 mm of the beam length from the end-plates was activated prior to bolt failure. Thus, the inertia of the beams only in the vicinity of the joints is important here.FE simulations of impact tests on a double-sided, beam-to-column joint configuration have been performed. The numerical model was developed with three-dimensional elements and an elastic-thermoviscoplastic material model incorporating work-hardening, strain-rate sensitivity, thermal softening, and failure. The simulations captured the deformation and failure mode observed in the tests. Furthermore, the global response in terms of force–displacement and velocity–time curves agreed with the tests. These comparisons of local and global behaviour served as a validation of the numerical model. The validated model allowed investigating issues that are challenging and costly to investigate in physical tests. It was chosen to study the effects of changing the thickness of the end-plate, introducing tensile forces in the beams and increasing the mass of the beams. Essential observations and conclusions from these studies are:Reducing the end-plate thickness allowed greater bending deformation of the end-plate before bolt fracture. Consequently, the energy dissipated by the joint was significantly increased. Thus, using thinner end-plates seems beneficial for impact load conditions.Imposing significant tensile axial forces in the beams barely affected the response of the joint configuration. The displacement to failure, which represents the ductility of the joint, was somewhat reduced with increasing axial force. Nevertheless, the general behaviour, such as the deformation and failure mode, was practically the same as without axial forces. Thus, for the joint configuration at hand, it is not imperative to consider axial forces in the beams.Taking the additional mass from structural elements such as possible floor slabs into account could affect the failure mode. A simulation with increased inertia of the beams was conducted. In this simulation, the failure mode changed from tensile to shear fracture of the bolts, which led to reduced global deformation prior to failure. These observations highlight how inertia effects may significantly alter the dynamic response compared to the quasi-static response.In conclusion, FE simulations with a validated numerical model can be useful for evaluating the behaviour of joints under severe impulsive load conditions.This appendix provides additional information that enable the reader to build the FE models presented in this paper. provides the details of the test specimen, and shows the dimensions of the impact plate.The bolt and nut assembly was modelled as one part in this paper. The dimensions of the part are given in the section drawing in . As observed from the figure, an additional length of the shank of 1.5 mm was included to account for the countersink of the nut. Two nuts were used in the tests to avoid thread stripping, which explains the height of 20 mm of the portion representing the nut.Influence of time on the microstructure of AISI 321 austenitic stainless steel in salt bath nitridingInfluence of nitriding time on the microstructure and microhardness of AISI 321 austenite stainless steel was investigated, using a complex salt bath heat-treatment at low temperature, 430 °C. Experimental results revealed that after salt bath nitriding, a modified layer was formed on the surface of substrate with the thickness ranging from 2 μm to 30 μm with changing treating time. The nitrided layer depth thickened extensively with increasing nitriding time. The growth of the nitrided layer takes place mainly by nitrogen diffusion according to the expected parabolic rate law. Scanning electron microscopy and X-ray diffraction showed that in 321 stainless steel subjected to complex salt bathing nitrided at such temperature for less than 8 hours, the main phase of the nitrided layer was expanded austenite (S phase) by large. When the treatment time is prolonged up to 8 hours and more, S phase is formed and subsequently transforms partially into CrN, and then the secondary CrN phase precipitated. With treating time prolonged, more CrN precipitates formed along the grain boundaries in the outer part. In the inside part between the some CrN and the substrate, there is still a broad single S phase layer. All treatments can effectively improve the surface hardness.► Austenite stainless steel nitrided by an environment-friendly salt bath can get single S phase for proper time at 430 °C. ► Treated time has greatly effect on surface layer depth and microstructure. ► Some CrN transformed along the grain boundaries after longtime treated.Austenitic stainless steel (ASS), with excellent corrosion resistance and high ductility, is attractive in a wide range of applications, such for outdoor machines in the chemical, coal and oil industries. However, a major disadvantage is its low hardness, which leads to very poor tribological properties Salt bath nitriding is developed as an industrial process especially for surface modification of iron-based steels and this process technology has solved environmental problems and can be applied to harden stainless and high alloy steels with high reaction efficiency However, there is insufficient knowledge about the effects of nitriding factor on microstructure and properties when complex salt bath nitriding is done on AISI 321 stainless steel at low temperature. Therefore, the aim of the study is to make an attempt to investigate the influence of processing time on the microstructure, the phase composition and the microhardness in the nitrided layer by using X-ray diffraction, scanning electron microscopy and energy dispersive X-ray.The salt medium for nitrocarburizing AISI 321 ASS sample was mainly composed of M2CO3 (M denotes some elements of halogen), CO(NH2)2 and some trace components. CNO− concentration in the salt was above 40%.The nascent nitrogen utilized for nitriding reaction comes from the dissociation of CNO−: 4CNO− |
→ CO3− 2 |
+ 2CN− |
+ CO + 2[N] The structural changes in the modified layer were investigated using cross-sections for optical microscopy and the Type JSM5910-LV scanning electron microscopy with the Oxford energy dispersive X-ray tester. X-ray diffractometer type Dmax-1400 with Cu K alpha radiation and a nickel filter were used to determine the phases present in the modified layer.It was observed that the microstructure produced during 430 °C salt bath nitriding of AISI 321 ASS changed with the treatment time, as shown in . A typical cross-sectional micrograph of the nitride layer in a and b is exemplified to show a bright white layer. This phenomenon implies that an enhancement in corrosion resistance to the harsh etchants (here is Marble's reagent) of the modified layer was obtained by nitriding. But the substrate does not. So the nitrided layers are distinguished from the substrate due to the different etching degrees. The thicknesses of nitrided layers were increased with the treated time. It can be seen that the depth of the total modified layer is approximately 33 μm after salt bath treatment for 40 hours at 430 °C. After the stainless steel specimen was treated for 40 hours, some of the secondary precipitate transformed along the grains boundaries. The corrosion resistances of precipitate zone became worse. The dark areas can be easily observed under the microscope after reagent etching ( shows the square of the thickness of the nitrided layer, as a function of salt bath time at 430 °C. It can be seen that the thickness of the nitrided layer soars up with prolonged treatment time. It shows a parabolic rate law expressed as the following equation: D2 |
∝ |
C t, where D is the thickness of nitriding layer, C is a constant and t is treated time.This result suggests that this chemical nitriding was controlled by a diffusion process. The fitting line intersects with the X axis at about 0.6 hours. One of the reasons for this incubation time is thought to be the influence of the substantial surface oxide film on AISI 304 ASS After gently polishing the surface black oxide films, which were identified as Cr2O3 and magnetite (Fe3O4), the X-ray diffraction patterns at the untreated and nitrided samples were shown in . The conventional diffraction pattern of non-treated sample (labeled ‘00’ in figure) is shown for comparison. According to these patterns, it is obvious that the phase composition of nitrided layers on AISI 321 steel depends on nitriding time. As depicted in the figure, the phases presented in the untreated AISI 321 sample are dominated by austenite. After complex nitriding treatment at 430 °C for 1 hour, the nitrogen diffuses inwards and the f.c.c. grain lattice is supersaturated by nitrogen to such extent that the alpha phase transforms into supersaturation S phase. With the treatment time prolonged, peaks of the expanded austenite were more intensive, and the left shift distance of the diffraction angles of S phase to lower angles were larger, which is in line with the observations by Sun and Bell in low temperature plasma nitriding , which is in line with the microstructure observation in Under the present test condition, trapping of nitrogen by affinity with chromium readily renders the formation of chromium carbides or chromium nitrides shows X-ray diffraction patterns of the structural characterization of layers of nitrided samples as a function of depth after treated 40 hours. In the figure, Cr2O3 and Fe3O4 are observed in the surface of nitrided samples. It is well known that from the thermodynamic point of view Cr-oxides formation is favored due to high negative enthalpy during oxidation. So, chromium nitrides formed in the nitro-carburized specimens are readily oxidized to Cr2O3 when oxidation takes place. It can be observed that there are still diffraction peaks related to Fe3O4 phase at depth of 16 μm. Moreover, the gradual S phase (111) peak shifting towards higher diffraction angles can be observed as distance increasing from depth of 4 μm to 22 μm. Supersaturation of nitrogen in the S phase expands the f.c.c lattice of the substrate, and thus shifts the corresponding X-ray diffraction peaks of the substrate austenite to lower angles. This phenomenon results obviously from the gradual distortion of the cubic symmetry of the lattice gives the estimated lattice parameters and interplanar spacing from Bragg's law as a function of nitriding time. The observation that the lattice parameter becomes larger when nitriding time increases is in good agreement with the results of other authors as the occupancy, yN, i.e., the fraction of the interstitial sublattice occupied by nitrogen atoms, as a function of the nitriding time. Clearly, yN increases with prolonging the nitriding time. In nitriding 16 hours and 40 hours, the peaks of the S phase are shifted to lower angle though some fine CrN transformed. The lattice parameters and yN from d(111) and from d(200), measured by X-ray diffraction (against depth) are shown in according to the cubic lattice constant. reveals clearly the expansion of the austenitic structure as a function of depth. The yN maintains very high value in the outer layer and sharply falls to zero in substrate.The microstructure scanned by scanning electron microscopy and energy dispersive X-ray of nitrided layer of a cross-section of the complex nitrided sample in 430 °C for 16 hours are shown in . From the pictures it can be obviously observed that some tiny zone has discrepant alloy compositions in the nitrided layer after 16 hours. And it can be obviously observed that there is a sub-layer, which mainly containing Cr near the outer surface. Associated with the previous results, it can be identified as Cr2O3.In order to understand conveniently the influence treat time on phase compositions in these samples, the results of scanning electron microscopy and X-ray diffraction analyses of samples are summarized in is schematic cross-sectional illustration of long time nitridation process for AISI 321 stainless steel at 430 °C. From the figure, it can be found that CrN precipitated initiatively transformed along the grain boundaries after 16 hours at 430 °C, which can be observed in c. The enhanced nitrogen migration along grain boundaries is strongly correlated with a precipitation of CrN, even at low temperatures d). Between the middle CrN sublayer and the substrate, there still exists a broad bright layer, which is a single S phase.The microhardness of nitrided layers as a function of nitriding time is shown in where the hardness increased with the increase of nitriding time. The increase in hardness with increasing nitriding time is due to the increase of nitrided layer thickness and high nitrogen content in the layer. The large increase in the measured values of the microhardness with increasing nitriding time can be explained by the known Austenitic stainless steel nitrided at 430 °C for different times has been investigated. A modified layer was formed on the surface with the thickness ranging from 2 μm to 30.5 μm. And the nitrided layer depth was thickened intensively with increasing nitriding time. The growth of the nitride layer takes place mainly by nitrogen diffusion according to the expected parabolic rate law. Scanning electron microscopy and X-ray diffraction showed 321 stainless steel subjected to complex salt bathing was nitrided at such temperature less than 8 hours and the main phase of the nitrided coating layer was the expanded austenite (S phase) generally. When the treatment time was prolonged up to 8 hours or more, S phase is formed and very few subsequently transforms into CrN, and then little secondary CrN phase precipitated. On prolonging the treated time, some CrN precipitate formed along grain boundaries the outer part for treated 40 hours. In the inside part between the outer layer containing some CrN and the substrate, there still exists a broad single S phase. All treatments can effectively improve the surface hardness.Limits to the preparation of superhard nanocomposites: Impurities, deposition and annealing temperatureImpurities, in particularly oxygen, degrade the mechanical properties of superhard nc-TiN/a-Si3N4 nanocomposites. In the present paper we show that relatively small oxygen impurities also hinder the diffusion and already at a level of about ≥ 0.8 at.% apparently stabilize the Ti–Si–N solid solution to a high temperature of about 1000 °C, thus making it impossible to form stable and strong superhard nanocomposites. Therefore, a hardness enhancement to 30–35 GPa, which has been reported in many publications on a variety of Ti–Si–N and other transition metal nitrides with silicon, is likely to be due to a simple refinement of the crystallite size towards the so called “strongest size”. Although the latter mechanism of strengthening is more universal than the design of superhard nanocomposites with strengthened interface, superhard nanocomposites can be prepared in this way only with a limited number of intrinsically very hard materials.► Degradation of superhard nc-TiN/a-Si3N4 nanocomposites by impurities ► Oxygen is hindering Si-diffusion and apparently stabilizes the solid solution. ► Refinement of the crystallite size enables only a limited increase of hardness. ► We discuss the limits to the preparation of superhard nanocomposites.After the first publications on the high hardness of ≥ 60 GPa of “Ti–Si–N” coatings by Li et al. .) Therefore it is highly demanding to clarify which conditions are needed for the preparation of superhard (H ≥ 40 GPa) quasi-binary nc-TiN/a-Si3N4 and ultrahard (H ≥ 80 GPa) quasi-ternary nc-TiN/a-Si3N4/TiSi2 and related nanocomposites, and what determines their long-term stability.Let us first recall that, as shown in our earlier work, hydrogen impurity causes degradation of the hardness when present in the coatings at a concentration of several at.% oxygen bonds are the strongest in the Ti–Si–N system, oxygen impurities also limit the diffusion which is needed for decomposition of the Ti–Si–N solid solution and formation of stable nc-TiN/a-Si3N4 nanostructure. Therefore, relatively low oxygen impurities of 0.8 at.% “stabilize” the Ti–Si–N solid solution up to high temperatures of 1000 °C, where Flink et al. reported its “re-crystallization” Let us emphasize, that high sensitivity of mechanical properties to minor impurities at a level of several hundreds of ppm is well known and documented in the literature for many materials The investigation into the thermal stability of nitride-based coatings is usually done by thermal annealing (TA) at step-wise increasing temperature with subsequent measurement of their hardness and X-ray diffraction pattern (XRD), or using high-resolution transmission electron microscopy (HRTEM). However, the TA and XRD methods have a limited sensitivity as compared to the measurement of internal friction (IF) and HRTEM is too laborious for such systematic studies. The method of internal friction measurement is described in Refs. Here only briefly the fundamentals of the IF method: The principle of IF is the fact that atoms which are weakly bonded in the solid may change their position between neighboring sites upon applied strain. For example low-coordinated atoms in the grain boundaries or hydrogen atoms dissolved in metals, will be “jumping” between such sites when the material is exposed to a periodic strain, as e.g. in vibrating reed The stoichiometric, pure transition metal nitrides (TmN) and Si3N4 are immiscible The results of the internal friction study on the nc-TiN/a-Si3N4 and nc-(Ti1 − xAlx)N/a-Si3N4 nanocomposites prepared by three different deposition techniques are shown in lower left corner of as function of oxygen impurity content, which has been measured by elastic recoil detection , no internal friction peak has been found in as deposited films which means that the decomposition of the solid solution, phase segregation and the formation of stable superhard nanostructure have been completed during the deposition. These coatings had the lowest oxygen impurity content of a few 100 ppm (0.01 at.%), and, upon annealing, the hardness remained constant up to about 1100 °C where coarsening of the TiN nanocrystals and decrease of the hardness have been found (see Fig. 15a in Ref. as “Int. Friction (Vacuum Arc)” corresponds to nc-(Ti1 − xAlx)N/a-Si3N4 coatings deposited by vacuum arc in an industrial coating equipment of the company SHM with x ≈ 0.5 and Si content of about 5–7 at.% Interestingly, the dependence obtained for our nanocomposites extrapolates very well to the point at a temperature of about 1000 °C and oxygen content of 7500 ppm (0.75 at.%) assigned as “Recrystallization (Vacuum arc)”, where Flink et al. reported the recrystallization of the Ti–Si–N solid solution with a silicon content of about 9 at.% A further extrapolation of the dependence to the point assigned as “a-TiSiN with high Si” yields the temperature corresponding to the stability limit due to oxidation of amorphous Ti-Si-N coatings with high content of silicon nitride reported by Musil et al. . Such a stabilization of silicon nitride by a relatively small content of oxygen may be interesting and useful for the preparation of highly stable SiNx coatings deposited by physical vapor deposition (PVD) at relatively low temperatures. clearly show that oxygen is stabilizing the Ti–Si–N solid solution, because in the coating deposited by plasma CVD at 550 °C, which had a low oxygen content of only a few 100 ppm (0.01 at.%), precipitation of nc-TiN within the stoichiometric Si3N4 has been found in as deposited films up to a high silicon content of 23 at.% units which cannot diffuse at the relatively low deposition temperatures of 100 to 500 °C typically used in these papers. Silicon nitride deposited below about 700–800 °C remains amorphous but it crystallizes above about 1100 °C. It has been also reported that about 1 wt.% oxygen is stabilizing the α-Si3N4 phase A relatively low oxygen impurity content of 0.6–0.7 at.% in the glow discharge hydrogen plasma is sufficient to amorphize nanocrystalline silicon deposited from silane diluted with hydrogen at 500–550 °C units strongly influences the valence charge distribution over several next Si-neighbors. This is disturbing the medium-range order as illustrated in Si bond has an angle of about 153 ± 15–20° (see e.g. units with distorted surrounding are not commensurable with the crystalline Si lattice. A simple estimate shows that the disordered cluster extends over a distance of about 1 nm. At a concentration of oxygen atoms of about 3 at.% the average distance between the clusters is less than about 1 nm. Therefore, the nano-crystalline silicon transfers to amorphous as observed experimentally A similar strong effect of oxygen in the Ti–Si–N system is not surprising because, as already mentioned, the SiO bond is by far the strongest one in the system (the bond strengths in kJ/mol are: SiIn the earlier work, Veprek and Reiprich have shown that in the Ti–Si–N system with low oxygen impurity, a deposition temperature of about 550 °C is needed to complete the decomposition of the solid solution and formation of strong nc-TiN/a-Si3N4 nanocomposites with high hardness . With decreasing deposition temperature, the time needed to complete the decomposition and formation of strong nanostructure increases and, at about 350 °C it is of the order of 103 |
s, i.e. the formation of the nanocomposites cannot occur during the deposition.It is obvious, that the diffusion coefficient of large and strongly bonded units in the Ti–Si–N solid solution will be orders of magnitude smaller than that of Si-atoms in a pure Ti–Si–N system. Therefore one can understand why already a low oxygen impurity content, the temperature needed for the completion of the TiN and Si3N4 phase segregation strongly increases, as shown in for the results obtained by the internal friction measurement at oxygen impurity content of < 0.3 at.%. One can also understand the results of Flink et al. There are at least three situations where oxygen impurities hinder the formation of stable nanocomposites with strong interfaces:At temperatures of > 900 °C, SiO is volatile which results in a loss of silicon during the annealing. During annealing in 1 at. pure argon or nitrogen, the oxygen and water impurities released from the walls of the chamber reach a level of the order of 100 ppm which is enough to form volatile SiO and remove Si from the films. Prior to the deposition of epitaxial Si-films, the desorption of SiO is used in the final stage of the in-situ cleaning of Si-wafers, because the native SiO2 reacts with the underlying silicon according to the shift reaction SiO2(s) + Si(s) = 2 SiO(g) (here “s” and “g” stands for solid and gas, respectively). The volatility of SiO formed by the reduction of SiO2 in hydrogen plasma has been used to synthesize bariumsphene BaTiSiO5 in quantities of hundreds of milligrams by reaction of barium titanate with SiO(g) Deposition temperature of ≥ 550 °C is needed to assure sufficiently fast diffusion and segregation of TiN and Si3N4, but too high deposition temperature results in lowering of the hardness. In their early work, Li et al. have deposited the “Ti–Si–N” coatings also at relatively high temperature of about 800 °C. Although the hardness of their coatings deposited at 560 °C exceeded 60 GPa . The lower hardness of the nanocomposites deposited at 800 °C is either due to the high temperature where the formation of sharp interface is hindered due to too fast diffusion and mixing, or to higher oxygen impurities, or combination of both. Because these problems were not sufficiently understood at that time, no further studies have been done to clarify these questions. It is interesting to note that the hardness of the Ti1 − xCxN, which forms stable solid solution (i.e. does not segregate into two immiscible phases like Ti–Si–N) Even the pure and fairly stable nc-TiN/a-Si3N4 nanocomposites undergo coarsening and loss of hardness upon annealing in nitrogen to 1100–1200 °C as reported in the review These three facts show that the superhard nc-TiN/a-Si3N4 nanocomposites can be prepared only when the concentration of oxygen impurities is below about 0.1 to 0.2 at.% (1000–2000 ppm). Even in such case, the hardness will be limited by the impurities as shown earlier . These coatings have been prepared by plasma CVD.Let us emphasize that the superhard quasi-binary nc-TiN/a-Si3N4 nanocomposites are stable over many years, whereas the quasi-ternary nc-TiN/a-Si3N4/TiSi2 nanocomposites lose their high hardness of 80 to ≥ 100 GPa (see ) due to the mechanical instability of the metastable, low-temperature phases of the TiSi2 (for further details see , their long-term instability reported already in lends support that this may be achieved in the future.The system has to decompose by spinodal mechanism in order to form the nanostructure with sharp interface andthere must be some mechanism of the strengthening of that interface as found e.g. via the valence charge transfer in the TiN/SiNx system As mentioned above, the work of Zhang et al. has shown that the stoichiometric TiN–Si3N4 system is spinodal with a very high de-mixing energy of more than 300 kJ/mol, even at the smallest nitrogen pressure used during PVD The Zr–Al–N system should decompose by nucleation and growth Similar conclusion applies also to the Zr–Si–N The Ti1 − xBxN system consisting of stoichiometric TiN and BN should be chemically spinodal, but the frequently reported nitrogen deficient TiBxN1 − x (“TiN + TiBx”) system should decompose by nucleation and growth B bonds in the interface between stoichiometric TiN and BN tissue Promising is the Zr–Al–O system because it is chemically spinodal These examples show that care has to be taken when interpreting hardness enhancement in the Tm–Si–N and related systems to be due to the spinodal mechanism as outlined for the Ti–Si–N one. A lot of work is needed to elucidate the possibilities of other systems. It were demanding to continue the studies of Sheng et al. because the DFT calculations combined with thermodynamical modeling are much faster and cheaper than experimental trial and error approach.Considering all these limits to the formation of the super- and ultrahard nanocomposites due to oxygen impurities, we can also explain the recent report of Tang et al. one clearly sees that in order to achieve a “recrystallization” of the homogeneous solid solution, annealing of the samples at about 1200 °C would be required. Because of the above discussed volatility of SiO and limited thermal stability of even pure nc-TiN/a-Si3N4 nanocomposites, the silicon would be lost and no nc-TiN/a-Si3N4 nanostructure could be formed. Thus, the results of Tang et al. do not “disprove” the model of Veprek et al. as indicated in In the following section we shall briefly discuss the possibilities of the preparation of hard and superhard coatings by formation of nanostructured materials with the “strongest size”, because this mechanism of strengthening is fairly general. This will also explain why some researchers found hardness enhancement in spite of the relatively large oxygen impurity content in their TmN-SiNx films.In the case of the most frequent mechanism of plastic deformation due to multiplication and movement of dislocations (“crystal plasticity” for crystallite size of > 50 nm. (Notice that besides dislocation activity there are also other mechanisms of plastic deformation, e.g. a; also called “grain boundary sliding”), because the volume fraction of the G. B. material strongly increases, particularly below 10 nm, as illustrated in Here fC and (1 |
− |
fC) are the volume fraction of the crystalline material and of the grain boundaries, respectively, H0 is the hardness of coarse grained material and HG.B. is the “hardness” of the grain boundaries. Experimental data showing hardness maximum at this “strongest size” have been published for many materials There are many possibilities to achieve a refinement of the nanostructure and concomitant increase of the hardness in hard coatings by alloying different elements in multicomponent nitrides, carbides, borides and other materials (see e.g. We have shown that oxygen impurities of about 0.1–0.25 at.% (1000–2500 ppm) hinder the decomposition of Ti–Si–N solid solution and the formation of stable and superhard nc-TiN/a-Si3N4 nanocomposites, which require annealing in nitrogen at elevated temperature. Only when the oxygen impurities are in the range of a few 100 ppm the diffusion and phase segregation with the formation of superhard nanocomposites are completed during the deposition at 550 °C. It is therefore demanding to prepare nanocomposites with even lower impurity content in the range of only few 10 ppm. Such materials should achieve hardness close to or may be even higher than 100 GPa and have high resistance against brittle fracture.From the point of view of industrial applications, achieving purity of 100–200 ppm would enable one to decrease the deposition temperature below 530 °C and thus to coat also tools made of high speed steel which softens above about 530–540 °C. This would significantly extend the range of the applications of such advanced coatings. The lowest impurity content of 700 ppm, which has been achieved by company SHM in industrial coating equipment, lends us to hope that this goal can be achieved in the future.Ti–Si–N coatings with oxygen content of ≥ 0.5 at.% cannot form nanocomposites with strong interface and, therefore, are brittle and require toughening by an addition of ductile metals to higher oxygen impurity content explains the high stability of the Ti–Si–N solid solution of Flink et al. The very high hardness of the ultrahard quasi-ternary nc-TiN/a-Si3N4/TiSi2 nanocomposites has been frequently questioned by other workers because no other group succeeded to reproduce it, due to high level of impurities in their coatings or inappropriate deposition conditions used, as discussed in For the convenience of the reader, we briefly explain the difference between the “as measured” and “calibrated” curves as obtained from the early version of Fischerscope H 100. We shall further show one example of the evaluation of hardness of superhard nanocomposite coating by Fischerscope H 100, which had been built before the paper of O. & P. has been published. Therefore it used the method of D. & N. Accordingly, the “as measured” curve obtained with the given maximum applied load L, has been processed by a special function as to yield the “corrected” curve which gave correct hardness of the material used for the calibration, such as Si(100) single crystal over a large range of loads assuming constant hardness. The Vickers hardness HV |
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