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In this study, the effects of random laminate misalignment on the macroscopic and microscopic elastic/viscoplastic behaviors of ultrafine plate–fin structures are statistically investigated adopting Monte Carlo simulation. To this end, a multiscale method that analyzes the elastic–viscoplastic behavior of ultrafine plate–fin structures with random laminate misalignment both macroscopically and microscopically is proposed based on the homogenization theory for nonlinear time-dependent materials combined with the substructure method. Using the method, Monte Carlo simulations for elastic and elastic–viscoplastic behaviors of ultrafine plate–fin structures subjected to uniaxial tension or simple shear are performed for many cases of random laminate misalignment. The obtained results reveal that the random laminate misalignment affects the microscopic behavior of ultrafine plate–fin structures more than the macroscopic behavior; microscopic stress and viscoplastic strain exhibit considerable variability depending on the laminate misalignment, and their maximum values can become about 30–50% higher than those in the case without laminate misalignment. This suggests the importance of considering random laminate misalignment in the design and strength/life prediction of ultrafine plate–fin structures.

It has been proposed that a plastic strain surface is reset to a point and re-evolves every cycle to correctly evaluate the plastic strain range under cyclic loading (Ohno et al., 2018b). This resetting scheme has the advantage of providing a definite value for the evolution parameter irrespective of the amounts of cyclic hardening, pre-straining, and ratcheting. In the present study, the resetting scheme was experimentally verified by performing the following three types of uniaxial cyclic tests of 316 stainless steel at 600 °C: constant strain range, gradual decrease, and step decrease tests. The gradual decrease tests, a new type of cyclic tests, had gradual strain range reduction with increasing number of cycles in the absence and presence of ratcheting such as found at notch roots. Thus, the effect of the strain range history on cyclic hardening was observed to be weaker than that due to stepwise decreasing the strain range. Using a constitutive model with the resetting scheme enabled good simulation of the cyclic hardening behavior in the gradual decrease tests. Cyclic softening after stepwise decreasing the strain range was also simulated well by extending the evolution equation of cyclic hardening.

In this study, a through-the-thickness negative Poisson's ratio of an angle-ply carbon fiber-reinforced plastic (CFRP) laminate is experimentally investigated using a 3D digital scanning method. For this, an image-based measurement method using a 3D digital scanner is developed to obtain the thickness change of CFRP laminates. The thickness change is used to calculate the through-the-thickness Poisson's ratio of CFRP laminates. Then, a tensile test of a [±θ°] angle-ply CFRP laminate is performed, and the through-the-thickness Poisson's ratio is measured based on the developed method. The results obtained suggest that the through-the-thickness Poisson's ratio exhibits negative values which become increasingly negative as (visco)plastic deformation progresses in the laminate, as demonstrated in our previous analysis.

Thermo-mechanical cyclic experiments on 304 stainless steel were performed at several temperature ranges with Tmin (minimum temperature) of 150 °C and Tmax (maximum temperature) ranging from 350 °C to 1000 °C. Corresponding isothermal cyclic experiments were also performed at several temperatures. Temperature-history dependent cyclic hardening was thus observed to significantly occur under thermo-mechanical cyclic loading when Tmax was around 600 °C. In contrast, almost no cyclic hardening occurred when Tmax was 1000 °C. The observed, thermo-mechanical cyclic hardening behavior was then simulated using a cyclic viscoplastic constitutive model with a cyclic hardening parameter. The simulation focused on the saturated state of cyclic hardening, leading to the following findings. The saturated thermo-mechanical cyclic hysteresis loops were not predicted well by simply taking into account temperature dependence in the cyclic hardening parameter. Then, by assuming the cyclic hardening parameter to be dependent on Tmax, the saturated thermo-mechanical hysteresis loops were simulated well. These mean that the cyclic hardening parameter of 304 stainless steel should not change with temperature but depend on Tmax in the saturated state of cyclic hardening under thermo-mechanical cyclic loading.

True stress and strain are necessary to estimate the rupture life under creep-fatigue conditions. Finite element analysis (FEA) is one of the most reliable method to calculate true stress and strain, but the accuracy of the obtained result is often greatly dependent on the constitutive model used. Non-unified constitutive model has been proposed, where inelastic strain is decomposed into creep strain and visco-plastic strain. In this paper, a cyclic hardening effect and a plastic strain range dependency were introduced into the non-unified constitutive model to predict the creep-fatigue damage of 316H stainless steel. This model was implemented in a finite element program and FEA were conducted to develop a life assessment method and calculate the creep-fatigue damage by modified ductile exhaustion method. As a consequence, it was revealed that the predicted creep-fatigue lives showed high correspondence with the experimental results by the modified ductile exhaustion method utilizing the non-unified constitutive model.

This paper verifies fin-homogenization for finite element analysis of heat exchanger cores with stacking of flat tubes and thin wavy fins. A first-order homogenization method is proposed on the assumption that uniform deformation prevails a short distance away from each fin layer in the stacking direction while the wavy fins have periodicity in the in-layer directions. Using this homogenization method, the homogenized elastic stiffness values of outer and inner fin layers in an intercooler are evaluated by considering real and sinusoidal shapes of the wavy fins. The homogenized elastic stiffness values attained are examined by performing fin-homogenization-based (fin-h-based) analyses, full-scale analyses, and experiments of tube-fin layered specimens subjected to compression and bending. It is shown that the fin-h-based and full-scale analyses give good agreements to each other even in the presence of macro-strain gradients in the outer and inner fin layers though the homogenization method is of first-order. Moreover, it is shown that the fin-h-based analyses reproduce well the experiments if the homogenized elastic stiffness values obtained for the real shapes of outer and inner fins are used in the analyses. It is also shown that the Bernoulli-Euler assumption is not satisfied in the homogenized outer fin layers under longitudinal bending because the homogenized elastic shear stiffness responsible for the bending is very low.

We study the ability of two scaling exponents to describe the mechanical properties of swollen elastomers. Swelling effects on the Young's modulus and osmotic pressure of swollen elastomers at equilibrium swelling are investigated using literature data and the Flory–Rehner free energy function. An extended model is developed by introducing two scaling exponents into elastic strain energy functions that are separated into deviatoric and volumetric components. This extended model satisfactorily reproduces the two different swelling effects, and also predicts swelling-induced rupture. The predicted tendency readily explains experimental observations well, i.e., swelling-induced rupture occurs when small extensions are applied in good solvents, and elucidates the mechanism of swelling-induced rupture of elastomers.

We investigate the effect of prestrains on swelling-induced buckling patterns in polymeric films with a square lattice of holes. To reproduce experiments conducted by Zhang et al. (2008), poly(dimethylsiloxane) (PDMS) films are pre-strained in in-plane uniaxial tension in a lattice direction, and subsequently swelled by toluene. Finite element analysis is performed using an inhomogeneous field theory of polymeric gels in equilibrium, and with the aid of artificial damping. Periodic units consisting of 2 × 2 and 10 × 10 unit cells are analyzed under a generalized plane strain assumption. Analysis of the 10 × 10 unit cell shows that the resulting buckling pattern depends on the increase in prestrain of e = 0, 0.2, 0.4 and 0.6, evolving as a diamond plate pattern (e = 0), a slightly distorted diamond plate pattern (e = 0.2), a binary pattern of circles and lines (e = 0.4), and a monotonous pattern of ellipses (e = 0.6). These predictions are in very good agreement with experiments. The 2 × 2 unit cell reveals that these different patterns appear continuously as transitional states during transformation into diamond plate patterns; prestrains in uniaxial tension delay the onset of the pattern transformation and equilibrium swelling interrupts the progress of the transformation. Parametric studies demonstrate that the pattern dependence on prestrains originates from intrinsic swelling features, and is a consequence of a particular combination of the selected polymer and solvent.

Negative through-the-thickness Poisson’s ratios are investigated macroscopically and microscopically in the elastic–viscoplastic behavior of angle-ply carbon fiber-reinforced plastic (CFRP) laminates. For this purpose, an analysis method is proposed based on a homogenization theory for nonlinear time-dependent composites with point-symmetric internal structures. This method is able to efficiently analyze both the macroscopic and microscopic elastic–viscoplastic properties of angle-ply CFRP laminates fully modeled with microstructures consisting of fibers and a matrix. Using the proposed method, the elastic–viscoplastic analysis of angle-ply carbon fiber/epoxy laminates with various laminate configurations is performed to investigate their Poisson’s ratios in the viscoplastic region. It is revealed that, for a range of laminate configurations, the through-the-thickness Poisson’s ratios exhibit negative values which become increasingly negative as the viscoplastic deformation progresses in the laminates. The effect of strain rate on this increasing negativity is also demonstrated, and microscopic mechanisms are investigated to explain this trend. It is further shown that the increasing negativity significantly affects microscopic interlaminar stress distributions.

We investigate the homogenized elastic–viscoplastic behavior of plate-fin structures subjected to two pore pressures, p 1 and p 2 . The plate-fin structures considered are assumed to be periodic and composed of metallic materials. Hill's macrohomogeneity equation is used to show three special cases in which one of p 1 , p 2 or p m (the mean of p 1 and p 2 ) entirely affects the homogenized viscoplastic behavior in the steady state. To verify the three special cases, we perform FEH (finite element homogenization) analysis of an ultrafine plate-fin structure subjected to p 1 and p 2 , for which two base metals with different strain-rate sensitivities are considered. It is demonstrated that the three special cases typically occur under uniaxial tension and compression in the stacking direction, depending on the strain-rate sensitivity of the base metals. It is further shown that a macromaterial model reproduces well the homogenized stress–strain relations attained in the FEH analysis if p 1 , p 2 or p m is entered for Terzaghi׳s effective stress in the viscoplastic equation in the macromaterial model.

The generalized stacking fault (GSF) energy surfaces of (110), (101), (121), (001), and(100) planes in -Sn are analyzed using first-principles density functional theory calculations. Fromthe minimum energy paths (MEPs) on the GSF energy surfaces analyzed, energetically preferableslip paths of 13 nonequivalent slip systems in -Sn are investigated. It is found that the MEP of(110)[111]/2, (101)[010], (101)[111]/2, (121)[101], and (121)[111]/2 deviates from the straight linepath and takes a curve line path. The results indicate that perfect dislocations on these five slip systemsdissociate into partial dislocations as in cubic and hexagonal crystals.

The cyclic growth and recovery of warpage were observed in experiments on Si/solder/Cu layered plates subjected to cyclic thermal loading [1]. In the present study, the experiments were analyzed using representative material models for the solder and Cu layers in finite element analysis. The warpage growth/recovery behavior observed was reproduced well in the analysis using the Armstrong-Frederick and Ohno-Wang models for the solder and Cu layers, respectively. Material ratcheting due to non-proportional cyclic loading was found to happen in the solder layer as a consequence of the CTE mismatch, while material ratcheting due to proportional cyclic loading occurred in the Cu layer as a result of the significant temperature dependence of viscoplasticity in the solder layer.

We perform finite element homogenization (FEH) analysis to investigate the effect of strain hardening on the monotonic and cyclic loading behavior of plate-fin structures with two pore pressures. As a typical base metal of plate-fin structures, 316 stainless steel is considered and assumed to be the viscoplastic material that obeys the Ohno-Wang kinematic hardening rule. The plate-fin structures are assumed to be periodic and subjected to uniaxial monotonic and cyclic loadings in the stacking direction. A periodic unit cell is used for FEH analysis. Results are compared with those based on three special cases derived from Hill’s macrohomogeneity equation. It is found that the mean pore pressure entirely affect the homogenized viscoplastic behavior. It is further found that the differential pore pressure causes the remarkable accumulation of ratcheting strain in the periodic unit cell, although this internal ratcheting gives no effect on macroscopic relations, resulting in providing a closed hysteresis loop for the plate-fin structures.

In this study, we investigate the effect of geometrical imperfections on swelling-induced buckling patterns in gel films with a square lattice of holes. Finite element analysis is performed using the inhomogeneous field theory of polymeric gels in equilibrium proposed by Hong et al. (2009) . Periodic units consisting of 2 × 2 and 10 × 10 unit cells are analyzed under a generalized plane strain assumption. Geometrical imperfections are introduced using randomly oriented elliptical holes. The 2 × 2 unit cells show that the resulting buckling patterns are sensitive to imperfections; three different buckling patterns are obtained, and the most dominant one is the diamond plate pattern observed in experiments, which cannot be described using the model without imperfections. The 10 × 10 unit cells reveal that random imperfections are responsible for inducing homogeneous transformation into the diamond plate pattern. Furthermore, domain wall formation is simulated using a 10 × 10 unit cell model containing two elliptic holes.

In this study, we investigate the axial compressive stress–strain relationships and deformation processes of wavy single-walled carbon nanotubes (SWCNTs) with multiple Stone–Wales defects using molecular mechanics simulations with the adaptive intermolecular reactive empirical bond-order potential. The wavelength to amplitude ratios of the wavy SWCNTs modeled in this study are 50, 100, or 200. The wavy models have point-symmetric or asymmetric waveforms with respect to the tube axial center. It is found that the symmetric wavy models exhibit a buckling point during axial compression due to bifurcation of the deformation path and experience nearly the same buckling stresses as their pristine straight counterparts. Our simulations show that, regardless of the waveform, wavelength, and amplitude, the axial compressive strength of wavy SWCNTs is in good agreement with the Euler buckling stress.

Numerical simulation is used to evaluate the fatigue life of aluminum bonding wires encapsulated by silicone gel under random vibration testing. The bending strain on aluminum wires is calculated by conducting a 3D finite element analysis while considering the temperature-dependent viscoelastic behavior of silicone gel. The effects of design parameters on the strain are also estimated. The fatigue life of aluminum wire under random vibration testing is evaluated. The wire strain caused by a relatively high frequency vibration is eliminated because of the damping effect caused by the viscoelastic behavior of silicone gel. Therefore, aluminum wire breakage under random vibration can be prevented by using appropriate design parameters.

An elastoplastic implicit integration algorithm applicable to both plane stress and three-dimensional stress states is developed for a general class of combined nonlinear kinematic-isotropic hardening models. The algorithm is first built for three-dimensional stress states in a general manner using the return mapping procedure and the Newton-Raphson method. The plane stress constraint is then incorporated into the Newton-Raphson iteration loop derived for three-dimensional stress states. The resulting algorithm has a mode patch that makes the algorithm applicable to both plane stress and three-dimensional stress states. The algorithm is specified by assuming an advanced evolution model of multiple back stresses, and is verified by performing numerical tests using plane stress, shell, and brick elements. The numerical tests are finite element analyses of homogeneously deformed plates and a cyclically loaded single-hole plate. It is demonstrated that the developed algorithm provides the quadratic convergence of iterations for implicit stress integration in plane stress, shell, and brick elements. It is also demonstrated that the algorithm is stable even in large incremental steps.

The mechanical properties of single-walled carbon nanotubes with one-dimensional intramolecular junctions (CNT-IMJs) are investigated, using first-principles density functional theory calculations. The effects of pentagon–heptagon (5–7) defects (a pair of five- and seven-membered rings) at a junction on the Young’s modulus, tensile strength, and breaking strain of CNT-IMJs are discussed from the viewpoint of charge density and interatomic distance. Our calculations indicate that the deformation concentration on a seven-membered ring causes the strength and elongation of CNT-IMJs to decrease. It is found that the tensile strength and breaking strain of CNT-IMJs depend on the position of 5–7 defects, while these properties of CNT-IMJs are not significantly affected by the number of 5–7 defects. The applicability of the AIREBO classical interatomic potential in the simulation of the tensile deformation in CNT-IMJs is also discussed.

The homogenized elastic-viscoplastic behavior of thick perforated plates with pore pressure is investigated for macro-material modeling. To this end, homogenized stress-strain relations of a periodic unit cell of pore-pressurized thick perforated plates under uniaxial and multiaxial loadings are analyzed using a finite element method with periodic boundary conditions. It is assumed in the analysis that the base metal of the perforated plates exhibits elastic-viscoplasticity based on Hooke’s law and Norton’s power law and has the material parameters of Mod. 9Cr-1Mo steel at 550 \(^\circ \)C. The resulting homogenized stress-strain relations are simulated using a macro-material model in which the pore-viscoplastic macro-strain rate is represented as an anisotropic power function of Terzaghi’s effective stress. It is demonstrated that this macro-material model suitably represents the macro-anisotropy, macro-volumetric compressibility, and pore pressure effect revealed in the viscoplastic range in the finite element homogenization analysis.

This lecture presents constitutive modeling of the homogenized elastic-viscoplastic behavior of pore-pressurized anisotropic open-porous bodies. The base solids are assumed to be metallic materials at small strains and rotations. First, by describing micro-macro relations relevant to periodic unit cells of anisotropic open-porous bodies with pore pressure, constitutive features are discussed for the viscoplastic macrostrain rate in steady states. Second, on the basis of the constitutive features found, the viscoplastic macrostrain rate is represented as an anisotropic function of Terzaghi’s effective stress. Third, the resulting viscoplastic equation is used to simulate the homogenized elastic-viscoplastic behavior of an ultrafine plate-fin structure and a thick perforated plate subjected to macroscopic loading in the absence and presence of pore pressure. The corresponding FE homogenization analysis is performed for comparison to validate the developed viscoplastic equation.

In this study, homogenised elasto-viscoplastic behaviour of thick perforated plates at high temperature was investigated for macro-material modelling. Homogenised stress–strain relations of a periodic unit cell of thick perforated plates subjected to simple and complex loading were analysed using a homogenisation method for periodic solids. The base metals of perforated plates were assumed to exhibit elasto-viscoplasticity based on Hooke’s law and Norton’s power-law, and the material parameters of modified 9Cr–1Mo steel at 550°C were employed. The resulting homogenised stress–strain relations were simulated using a recently developed elasto-viscoplastic macro-material model based on a general form of the quadratic equivalent stress. It has been shown that this macro-model successfully represents the macro-anisotropy and macro-volumetric compressibility that were revealed by the homogenisation analysis in uniaxial, biaxial and triaxial stress states.

In this study, an implicit iterative finite element scheme is developed for the strain gradient theory of single-crystal plasticity that accounts for the self-energy of geometrically necessary dislocations (GNDs). This strain gradient theory belongs to the Gurtin framework for viscoplastic single-crystals. The self-energy of GNDs gives a specific form of energetic higher-order stresses. An implicit finite element equation is obtained for solving a set of homogenization equations. The developed scheme is employed to analyze a model grain, and is verified by comparison with the analytical estimation derived by Ohno and Okumura (2007) [4] . The computational efficiency of the scheme and the incremental stability are discussed. Furthermore, it is shown that the developed scheme is available and applicable to different types of higher-order stresses including energetic and dissipative terms.

Mechanical properties of single-walled carbon nanotubes with one-dimensional intramolecular junctions (CNT-IMJs) are investigated using first-principles density functional theory calculations. The influence of Stone-Wales (SW) defects (a pair of five- and seven-membered rings) at a junction on the Young's modulus, tensile strength and breaking strain of the CNT-IMJs are discussed from the charge density and interatomic distance. Our calculations reveal that deformation concentration on a seven-membered ring causes the decrease in the strength and elongation of the CNT-IMJs. It is found that the tensile strength and breaking strain of the CNT-IMJs depend on the position of SW defects, while the number of SW defects hardly affects them. The applicability of AIREBO classical interatomic potential to simulate tensile deformation in the CNT-IMJs is also discussed.

Plastic size effect analysis of lamellar composites consisting of elastic and elastic–plastic layers is performed using a discrete dislocation plasticity approach, which is based on applying periodic homogenization to the superposition method for discrete dislocation plasticity. In this approach, the decomposition of displacements into macro and perturbed components circumvents the calculation of superposing displacement fields induced by dislocations in an infinitely homogeneous medium, resulting in two periodic boundary value problems specialized for the analysis of representative volume elements. The present approach is verified by analyzing a model lamellar composite that includes edge dislocations fixed at interfaces. The plastic size effects due to dislocation pile-ups at interfaces are also analyzed. The analysis shows that, strain hardening in elastic–plastic layers arises depending on two factors, namely the thickness and stiffness of elastic layers; and the gap between slip planes in adjacent elastic–plastic layers. In the case where the thickness of elastic layers is several dozen nm, strain hardening in elastic–plastic layers is restrained as the gap of the slip planes decreases. This particular effect is attributed to the long range stress due to pile-ups in adjacent elastic–plastic layers.

In this study, a duplex model is developed as a constitutive model for the homogenized elastic–viscoplastic behavior of a class of plate–fin structures operating at high temperatures. This model consists of plate and fin layers, which are individually ruled by different macro-constitutive models. An anisotropic, compressible power-law equation that was derived in a recent study by the present authors is used to describe the homogenized viscoplastic behavior of the fin layer. On the other hand, an isotropic, incompressible power-law equation is used as the macro-constitutive equation of the plate layer. The duplex model developed is applied to an ultra-fine plate–fin structure made of Hastelloy X. It is shown that the duplex model is more successful under multiaxial loading than the corresponding simplex model in which plates and fins are non-separately homogenized.

Warpage variations of Si/solder/OFHC-Cu layered plates under cyclic thermal loading were investigated as a fundamental subject for inverter power modules. Two different solders, fully annealed and as-received OFHC-Cu plates, and three thickness ratios of the Si and Cu layers were used for the layered plates tested. It was experimentally observed that the initial warpage induced by soldering either grew or recovered with an increase in the number of temperature cycles: the cyclic growth of warpage occurred when the OFHC-Cu layer was fully annealed before soldering and was relatively thick. By performing 3D finite element analysis using available material data, it was then shown that the observed cyclic growth/recovery of warpage can be simulated well if an appropriate constitutive model is employed for the cyclic plastic behavior of OFHC-Cu plates.

In this study, we investigate the influence of closed faces on the compressive strength of open cell metallic foams computationally. To this end, numerical models are developed for a commercial product of open cell aluminium foams (ERG Duocel), and a perfect model for Kelvin open cell foams is extended by introducing a closed face into the cubic unit cell. Finite element analysis using a homogenisation approach is performed for three different closed face models as well as for the perfect model. It is found that the introduction of closed faces into the perfect model hardly increases the compressive strength of Kelvin open cell foams, and mainly causes the increase in relative density. The applicability of the developed closed face model is verified by comparison with semiempirical relations.

This paper describes experiments and analysis of the warpage of Si/solder/Cu layered plates subjected to cyclic thermal loading. As received and annealed Cu plates are used as the Cu layer, and three thickness ratios are considered for the Si and Cu layers. It is experimentally shown that the initial warpage caused by soldering either grows or recovers with an increase in the number of temperature cycles and that the cyclic growth of warpage is apparent when the Cu layer is annealed and is relatively thick. Then, by performing a three‐dimensional finite element analysis, it is demonstrated that the cyclic growth and recovery of warpage shown experimentally can be simulated well if an appropriate constitutive model is employed for kinematic hardening in the Cu layer.

This paper develops a gradient theory of single-crystal plasticity based on a system of microscopic force balances, one balance for each slip system, derived from the principle of virtual power, and a mechanical version of the second law that includes, via the microscopic forces, work performed during plastic flow. When combined with thermodynamically consistent constitutive relations the microscopic force balances become nonlocal flow rules for the individual slip systems in the form of partial differential equations requiring boundary conditions. Central ingredients in the theory are densities of (geometrically necessary) edge and screw dislocations, densities that describe the accumulation of dislocations, and densities that characterize forest hardening. The form of the forest densities is based on an explicit kinematical expression for the normal Burgers vector on a slip plane.

Thermal expansion of a Cu/Si 3 N 4 /Cu layered structure was studied by actual measurement and finite element analysis. Thicker Cu and subjecting the samples to cyclic thermal loading increase the thermal expansion of the layered structure. Strain-controlled cyclic tension/compression tests in Cu were performed to obtain the characteristics of cyclic plasticity. A multi-linear kinematic hardening model was applied to represent the elastoplasticity of Cu. Two sets of material parameters were determined: One set from the initial and a second set from the stabilized stress–strain relationship, respectively. It was demonstrated that the determined material parameters allow accurate prediction of the thermal expansion coefficient within 1 ppm/°C for structures subjected and non-subjected to cyclic thermal loading.

In this study, homogenized elastic–viscoplastic behavior of an ultra-fine plate-fin structure fabricated for compact heat exchangers is investigated. First, the homogenized behavior is numerically analyzed using a fully implicit mathematical homogenization scheme of periodic elastic–inelastic solids. A power-law creep relation is assumed to represent the viscoplasticity of base metals at high temperatures. The plate-fin structure is thus shown to exhibit significant anisotropy as well as noticeable compressibility in both the elastic and viscoplastic ranges of the homogenized behavior. Second, a non-linear rate-dependent macroscopic constitutive model is developed using the quadratic yield function proposed for anisotropic compressible plasticity. The resulting constitutive model is shown to be successful for simulating the anisotropy, compressibility, and rate dependency in the homogenized behavior in multi-axial stress states.

Cyclic hardening and stress relaxation experiments of SUS316HTP were performed under creep-fatigue loading with tensile strain holding at 700◦C. Experiments revealed that under strain holding, the slow stress-relaxation stage satisfying Norton’s law with slight cyclic hardening followed a rapid stress-relaxation stage that was noticeably affected by cyclic hardening. This suggests that in the slow stress-relaxation stage, inelastic deformation mechanisms different from that of viscoplasticity occurred. Experiments were simulated using a cyclic viscoplastic-creep model in which the inelastic strain-rate was decomposed into viscoplastic and creep components that were affected differently by cyclic hardening. The simulation accurately reproduced the experiments.

This study analyzes the yield and buckling behavior of Kelvin open-cell foams subjected to uniaxial compression. A homogenization theory of the updated Lagrangian type is applied to cubic unit cells and cell aggregates in the Kelvin foam model. Macroscopic instability and microscopic bifurcation are thus incrementally examined under uniaxial compression. The analysis is performed by taking into account the non-uniformity of strut cross-sectional areas and the strain hardening–softening behavior of struts that were observed in experiments on open-cell 6101-T6 aluminum alloy foams. It is shown that macroscopic instability primarily occurs as a consequence of the strain hardening–softening behavior of struts. It is further shown that the macroscopic instability stress obtained has (3/2)th power dependence on relative density as predicted in the Gibson–Ashby relation.