Elastic–plastic behavior of steel sheets under in-plane cyclic tension–compression at large strain

Elastic–plastic behavior of two types of steel sheets for press-forming (an aluminum-killed mild steel and a dual-phase high strength steel of 590 MPa ultimate tensile strength) under in-plane cyclic tension–compression at large strain (up to 25% strain for mild steel and 13% for high strength steel) have been investigated. From the experiments, it was found that the cyclic hardening is strongly influenced by cyclic strain range and mean strain. Transient softening and workhardening stagnation due to the Bauschinger effect, as well as the decrease in Young's moduli with increasing prestrain, were also observed during stress reversals. Some important points in constitutive modeling for such large-strain cyclic elasto-plasticity are discussed by comparing the stress–strain responses calculated by typical constitutive models of mixed isotropic–kinematic hardening with the corresponding experimental observations.     

A unified expression of elastic–plastic notch stress–strain calculation in bodies subjected to multiaxial cyclic loading

In this paper, a simplified thermodynamics analysis of cyclic plastic deformation is performed in order to establish an energy transition relation for describing the elastic–plastic stress and strain behavior of the notch-tip material element in bodies subjected to multiaxial cyclic loads. Based on the thermodynamics analysis, it is deduced that in the case of elastic–plastic deformation, Neuber’s rule inevitably overestimates the actual stress and strain at the notch tip, while the equivalent strain energy density (ESED) method tends to underestimate the actual notch-tip stress and strain. According to the actual energy conversion occurring in the notch-tip material element during cyclic plastic deformation, a unified expression for estimating the elastic–plastic notch stress–strain responses in bodies subjected to multiaxial cyclic loads is developed, of which Neuber’s rule and the ESED method become two particular cases, i.e. upper and lower bound limits of the notch stress and strain estimations. This expression is verified experimentally under both proportional and non-proportional multiaxial cyclic loads and a good agreement between the calculated and the measured notch strains has been achieved. It is also shown that in the case of multiaxial cyclic loading, the unified expression distinctly improves the accuracy of the notch-tip stress–strain estimations in comparison with Neuber’s rule and the ESED method. The unified expression of the notch stress–strain calculation developed in this paper can thus provide a more logical approximate approach for estimating the elastic–plastic notch-tip stress and strain responses of components subjected to lengthy multiaxial cyclic loading histories for local strain approach-based fatigue-crack-initiation life prediction.     

Cyclic viscoelastoplasticity and low-cycle fatigue of polymer composites

Observations are reported on a polymer composite (polyamide-6 reinforced with short glass fibers) in tensile relaxation tests with various strains, tensile creep tests with various stresses, and cyclic tests with a stress-controlled program (ratcheting with a fixed maximum stress and various minimum stresses). Constitutive equations are developed in cyclic viscoelastoplasticity of polymer composites. Adjustable parameters in the stress–strain relations are found by fitting observations in relaxation tests and cyclic tests (16 cycles of loading–unloading). It is demonstrated that the model correctly predicts experimental data in creep tests and dependencies of maximum and minimum strains per cycle on number of cycles up to fatigue fracture of specimens. The influence of strain rate and minimum stress on number of cycles to failure is studied numerically.     

Cyclic plasticity modeling with the distribution of non-linear relaxations approach

Motivated by the distribution of non-linear relaxation (DNLR) approach, a phenomenological model is proposed in order to describe the cyclic plasticity behavior of metals under proportional and non-proportional loading paths with strain-controlled conditions. Such a model is based on the generalization of the Gibbs's relationship outside the equilibrium of uniform system and the use of the fluctuation theory to analyze the material dissipation due to its internal reorganization. The non-linear cyclic stress–strain behavior of metals notably under complex loading is of particular interest in this study. Since the hardening effects are described appropriately and implicitly by the model, thus, a host of inelastic behavior of metals under uniaxial and multiaxial cyclic loading paths are successfully predicted such as, Bauschinger, strain memory effects as well as additional hardening. After calibrating the model parameters for two metallic materials, the model has demonstrated obviously its ability to describe the cyclic elastic-inelastic behavior of the nickel base alloy Waspaloy and the stainless steel 316L. The model is then implemented in a commercial finite element code simulating the cyclic stress–strain response of a thin-walled tube specimen. The numerical responses are in good agreement with experimental results.     

Multi-cycle deformation of silicone elastomer: observations and constitutive modeling with finite strains

Observations are reported on a medical grade of silicone elastomer in uniaxial tensile tests up to breakage of specimens, short-term relaxation tests, and cyclic tests with monotonically increasing maximum elongation ratios. Experimental data in cyclic tests demonstrate the fading memory phenomenon: stress–strain diagrams for two specimens with different deformation histories along the first n?1 cycles and coinciding loading programs for the other cycles become identical starting from the nth cycle. A constitutive model is developed in cyclic viscoplasticity of elastomers with finite strains, and its adjustable parameters are found by fitting the experimental data. Ability of the stress–strain relations to predict the mechanical response in cyclic tests with various deformation programs is confirmed by numerical simulation.     

Multi-cycle deformation of semicrystalline polymers: Observations and constitutive modeling

Experimental data are reported on isotactic polypropylene in multi-cycle uniaxial tensile tests where a specimen is stretched up to some maximum strain and retracted down to the zero minimum stress, while maximum strains increase with number of cycles. Fading memory of deformation history is observed: when two samples are subjected to loading programs that differ along the first n − 1 cycles only, their stress–strain diagrams coincide starting from the nth cycle. Constitutive equations are developed in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers, and adjustable parameters in the stress–strain relations are found by fitting the experimental data. Results of numerical simulation demonstrate that the model predicts the fading memory effect quantitatively. To confirm that the observed phenomenon is typical of semicrystalline polymers, experimental data are presented in tensile cyclic tests with large strains on low density polyethylene and compressive cyclic tests on poly(oxymethylene).     

Cyclic stress-softening model for the Mullins effect in compression

This paper models the cyclic stress softening of an elastomer in compression. After the initial compression the material is described as being transversely isotropic. We derive non-linear transversely isotropic constitutive equations for the elastic response, stress relaxation, residual strain, and creep of residual strain in order to model accurately the inelastic features associated with cyclic stress softening. These equations are combined with a transversely isotropic version of the Arruda–Boyce eight-chain model to develop a constitutive relation that is capable of accurately representing the Mullins effect during cyclic stress softening for a transversely isotropic, hyperelastic material, in particular a carbon-filled rubber vulcanizate. To establish the validity of the model we compare it with two test samples, one for filled vulcanized styrene–butadiene rubber and the other for filled vulcanized natural rubber. The model is found to fit this experimental data extremely well.     

Cyclic stress-strain behaviour of alloy AA6060 T4, part II: Biaxial experiments and modelling

Laboratory tests have been conducted to investigate the inelastic behaviour of aluminium alloy AA6060 T4 subjected to non-proportional cyclic loading. The results of four tests with variable strain path shapes and strain amplitudes are reported in this paper. The tests were carried out by applying combined axial force and torque to thin-walled tubular specimens, using effective strain amplitudes in the range 0.4–0.8%. Major emphasis has been put on the two important material properties: plastic anisotropy and influence of strain range and strain path shapes on cyclic hardening. A constitutive model for cyclic plasticity is used to predict the stress response of the alloy for the non-proportional strain paths applied in the experiments. The model adopts a quadratic yield function and multi-component non-linear isotropic and kinematic hardening rules to describe plastic anisotropy, the shape of the hysteresis loops and the evolution of cyclic hardening. Good agreement is obtained between the physical and correlated stress response of the alloy.     

DEM investigation of strain behaviour and force chain evolution of gravel–sand mixtures subjected to cyclic loading

The strain characteristic and load transmission of mixed granular matter are different from those of homogeneous granular matter. Cyclic loading renders the mechanical behaviours of mixed granular matter more complex. To investigate the dynamic responses of gravel–sand mixtures, the discrete element method (DEM) was used to simulate the cyclic loading of gravel–sand mixtures with low fines contents. Macroscopically, the evolution of the axial strain and volumetric strain was investigated. Mesoscopically, the coordination number and contact force anisotropy were studied, and the evolution of strong and weak contacts was explored from two dimensions of loading time and local space. The simulation results show that increasing fines content can accelerate the development of the axial strain and volumetric strain but has little effect on the evolution of contact forces. Strong contacts tend to develop along the loading boundary, presenting the spatial difference. Weak contacts are firstly controlled by confining pressure and then controlled by axial stress, while strong contacts are mainly controlled by axial stress throughout the whole cyclic loading. Once compression failure occurs, the release of axial stress causes the reduction of strong contact proportion in all local regions. These findings are helpful to understand the dynamic responses of gravel–sand mixtures, especially in deformation behaviours and the Spatio-temporal evolution of contact forces.     

Strain gradient plasticity modeling of the cyclic behavior of laminate microstructures

Two recently proposed Helmholtz free energy potentials including the full dislocation density tensor as an argument within the framework of strain gradient plasticity are used to predict the cyclic elastoplastic response of periodic laminate microstructures. First, a rank-one defect energy is considered, allowing for a size-effect on the overall yield strength of micro-heterogeneous materials. As a second candidate, a logarithmic defect energy is investigated, which is motivated by the work of Groma et al. (2003). The properties of the back-stress arising from both energies are investigated in the case of a laminate microstructure for which analytical as well as numerical solutions are derived. In this context, a new regularization technique for the numerical treatment of the rank-one potential is presented based on an incremental potential involving Lagrange multipliers. The results illustrate the effect of the two energies on the macroscopic size-dependent stress–strain response in monotonic and cyclic shear loading, as well as the arising pile-up distributions. Under cyclic loading, stress–strain hysteresis loops with inflections are predicted by both models. The logarithmic potential is shown to provide a continuum formulation of Asaro's type III kinematic hardening model. Experimental evidence in the literature of such loops with inflections in two-phased FFC alloys is provided, showing that the proposed strain gradient models reflect the occurrence of reversible plasticity phenomena under reverse loading.     

Cyclic thermo-viscoplasticity of high density polyethylene

Observations are reported in uniaxial cyclic tensile tests (loading–unloading with various maximum strains) on high density polyethylene at temperatures ranging from room temperature up to 90 °C. It is demonstrated that the maximum stress per cycle and an apparent residual strain (measured at the instant when the tensile force vanishes under retraction) strongly decrease with temperature. The latter seems unexpected as the interval of temperatures covers the α-relaxation temperature, which is conventionally associated with activation of additional mechanisms for inelastic flow. A model is developed that captures the decrease in residual strain with temperature. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. The effects of temperature and maximum strain per cycle on residual strains are studied numerically.     

Hysteretic behavior of rectangular tube (box) sections based on Preisach model

In the present paper, the Preisach model of hysteresis is applied to model cyclic behavior of elasto-plastic material. Rate of loading and viscous effects will not be considered. The problem of axial loading of rectangular cross-section and cyclic bending of rectangular tube (box) will be studied in details. Hysteretic stress–strain loop for prescribed history of stress change is plotted for material modeled by series connection of three unite element. Also moment–curvature hysteretic loop is obtained for a prescribed curvature change of rectangular tube (box). All obtained results clearly show advantages of the Preisach model for describing cyclic behavior of elasto-plastic material.     

Ratchetting of viscoplastic material with cyclic softening,part 1: experiments on modified 9Cr–1Mo steel

Uniaxial and multiaxial ratchetting tests were conducted at temperatures between 200 and 600 °C on modified 9Cr–1Mo steel, which exhibits both viscoplastic and cyclic softening behavior. Anomalous behavior was observed in the stress-controlled uniaxial ratchetting tests; the material exhibited outstanding ratchetting in the tensile direction under zero mean stress. Under the uniaxial conditions, the ratchetting deformation significantly depended on the loading rate and hold time in addition to parameters such as the maximum stress and stress ratio. The uniaxial ratchetting was also accelerated to a great extent when cyclic deformation was given before the ratchetting tests. Under the multiaxial conditions, the ratchetting depended on the steady stress, cyclic strain range and strain rate. The ratchetting progressed faster as the steady stress or strain range became larger, or the strain rate became smaller, as expected. Monotonic compression tests were carried out to investigate the reason for the rachetting under no mean stress. Strain range change tests were also conducted to investigate the effect of strain range on the cyclic softening behavior of the material in detail.     

Cyclic multiaxial and shear finite deformation response of OFHC: Part I,experimental results

A series of experiments has been conducted on oxygen free high conductivity (OFHC) copper hollow cylinders under cyclic free-end torsion and biaxial tension–torsion at large strains. In addition, equations are developed to account for the finite rotation and strains in electrical resistance strain gages. In free-end cyclic torsion experiments with shear strain range equal to 23%, a significant strain in the axial direction is observed and it accumulates with a constant rate cycle by cycle. In the biaxial tension–torsion (multiaxial ratchetting) experiments, in which the primary (constant) axial stress is larger than the initial yield stress of the material, the loading conditions are varied to determine the influence of primary axial stress, cyclic shear strain range, pre-cyclic hardening and loading sequence on multiaxial ratchetting. Some important experimental features are high-lighted and recommended to help modeling efforts later.     

退火和调质42CrMo合金钢单轴循环塑性行为的实验研究

在室温下对退火和调质42CrMo合金钢进行了单轴应变控制和应力控制的系统循环实验,并对它们的应变循环和应力循环特性进行比较.揭示和分析了应变幅值、平均应变及其历史对材料应变循环特性的影响以及应力幅值、平均应力及其历史对棘轮行为的影响.讨论了应变循环和应力循环间的交互作用以及不同热处理工艺下材料循环变形行为间的区别.研究发现材料的热处理工艺、平均应力和应力幅值及其历史对材料的棘轮行为都有很大的影响.得到了一些有助于进行合理本构描述的结果.     

循环荷载下硅藻土应变和孔压特性

针对嵊州硅藻土的高结构性及地基应力场的复杂多变，应用GDS 动三轴仪进行不同围压和不同循环应力比下的不排水循环加载试验，分析应力-应变滞回曲线演化、应变累积特性、回弹特性及孔压特性．研究表明：循环应力比及围压对原状硅藻土应变和孔压的发展规律影响明显，随着循环应力比的增加，滞回曲线由线性状态转变为非线性状态，且逐渐向x 轴倾斜，累计应变和回弹应变都随着循环应力比的增加而略微增加，但总应变基本小于2 %；残余孔压比随循环应力比增大而增大，范围为0.1~0.5．并且存在一个临界循环应力比，其值随有效围压的增大而减小，范围为0.8~2.2，当循环应力比大于该值时，试样内部产生一个破裂面迅速发生破坏．在相同循环应力比下，试样的应变随着有效围压的增大而增大．     

304不锈钢室温和高温单轴循环塑性的实验研究

对304不锈钢进行了室温和高温单轴应变控制和应力控制下的系统循环试验。揭示和分析了循环应变幅值、平均应变及其历史和温度历史对材料应变循环特性的影响以及应力幅值、平均应力及其历史以及温度对循环棘轮行为的影响。也讨论了应变循环和应力循环间交互作用对材料循环塑性行为的影响。研究表明,无益单轴应变循环特性还是非对称单轴应力循环下的棘轮效应不仅取决于当前温度和加载状态,而且强烈依赖于其加载历史。研究得到了一些有助于304不锈钢室温和高温单轴循环行为本构描述的结果。     

Elastic–plastic behavior of non-woven fibrous mats

Electrospinning is a novel method for creating non-woven polymer mats that have high surface area and high porosity. These attributes make them ideal candidates for multifunctional composites. Understanding the mechanical properties as a function of fiber properties and mat microstructure can aid in designing these composites. Further, a constitutive model which captures the membrane stress–strain behavior as a function of fiber properties and the geometry of the fibrous network would be a powerful design tool. Here, mats electrospun from amorphous polyamide are used as a model system. The elastic–plastic behavior of single fibers are obtained in tensile tests. Uniaxial monotonic and cyclic tensile tests are conducted on non-woven mats. The mat exhibits elastic–plastic stress–strain behavior. The transverse strain behavior provides important complementary data, showing a negligible initial Poisson's ratio followed by a transverse:axial strain ratio greater than ?1:1 after an axial strain of 0.02. A triangulated framework has been developed to emulate the fibrous network structure of the mat. The micromechanically based model incorporates the elastic–plastic behavior of single fibers into a macroscopic membrane model of the mat. This representative volume element based model is shown to capture the uniaxial elastic–plastic response of the mat under monotonic and cyclic loading. The initial modulus and yield stress of the mat are governed by the fiber properties, the network geometry, and the network density. The transverse strain behavior is linked to discrete deformation mechanisms of the fibrous mat structure including fiber alignment, fiber bending, and network consolidation. The model is further validated in comparison to experiments under different constrained axial loading conditions and found to capture the constraint effect on stiffness, yield, post-yield hardening, and post-yield transverse strain behavior. Due to the direct connection between microstructure and macroscopic behavior, this model should be extendable to other electrospun systems and other two dimensional random fibrous networks.