S30408低温棘轮效应本构描述

S30408奥氏体不锈钢因其优异的力学性能和耐低温性能而被广泛用于制作LNG等低温罐车罐体的内容器。此类罐体的内容器在其支撑部位不但承受内压引起的恒定应力还会承受惯性载荷引起的交变应力,容易发生渐进的塑性应变累积即棘轮效应。但目前还缺乏有效预测S30408低温棘轮效应的本构描述。利用几种较为先进的本构模型对低温S30408奥氏体不锈钢棘轮应变进行模拟,发现这些本构模型存在循环初期过低预测和循环后期过高预测的缺点,并且这种过高预测会随着循环圈数的增加而增大。基于Ohno - Wang II模型,关联形变马氏体含量与各向同性强化与随动强化,并给出马氏体极限含量dL的演化规律,进而提出一种含马氏体相变的循环塑性本构模型。与其它模型相比,该模型能有效改善在循环初期预测值过低和后期预测值过高的情况,同时能够较好地预测循环加载过程中形变马氏体的含量。     

S30408低温棘轮效应本构描述

S30408奥氏体不锈钢因其优异的力学性能和耐低温性能而被广泛用于制作LNG等低温罐车罐体的内容器。此类罐体的内容器在其支撑部位不但承受内压引起的恒定应力还会承受惯性载荷引起的交变应力，容易发生渐进的塑性应变累积即棘轮效应。但目前还缺乏有效预测S30408低温棘轮效应的本构描述。利用几种较为先进的本构模型对低温S30408奥氏体不锈钢棘轮应变进行模拟，发现这些本构模型存在循环初期过低预测和循环后期过高预测的缺点，并且这种过高预测会随着循环圈数的增加而增大。基于Ohno - Wang II模型，关联形变马氏体含量与各向同性强化与随动强化，并给出马氏体极限含量dL的演化规律，进而提出一种含马氏体相变的循环塑性本构模型。与其它模型相比，该模型能有效改善在循环初期预测值过低和后期预测值过高的情况，同时能够较好地预测循环加载过程中形变马氏体的含量。     

Nonlocal gradient-dependent modeling of plasticity with anisotropic hardening

This work addresses the formulation of the thermodynamics of nonlocal plasticity using the gradient theory. The formulation is based on the nonlocality energy residual introduced by Eringen and Edelen (1972). Gradients are introduced for those variables associated with isotropic and kinematic hardening. The formulation applies to small strain gradient plasticity and makes use of the evanescent memory model for kinematic hardening. This is accomplished using the kinematic flux evolution as developed by Zbib and Aifantis (1988). Therefore, the present theory is a four nonlocal parameter-based theory that accounts for the influence of large variations in the plastic strain, accumulated plastic strain, accumulated plastic strain gradients, and the micromechanical evolution of the kinematic flux. Using the principle of virtual power and the laws of thermodynamics, thermodynamically-consistent equations are derived for the nonlocal plasticity yield criterion and associated flow rule. The presence of higher-order gradients in the plastic strain is shown to enhance a corresponding history variable which arises from the accumulation of the plastic strain gradients. Furthermore, anisotropy is introduced by plastic strain gradients in the form of kinematic hardening. Plastic strain gradients can be attributed to the net Burgers vector, while gradients in the accumulation of plastic strain are responsible for the introduction of isotropic hardening. The equilibrium between internal Cauchy stress and the microstresses conjugate to the higher-order gradients frames the yield criterion, which is obtained from the principle of virtual power. Microscopic boundary conditions, associated with plastic flow, are introduced to supplement the macroscopic boundary conditions of classical plasticity. The nonlocal formulation developed here preserves the classical assumption of local plasticity, wherein plastic flow direction is governed by the deviatoric Cauchy stress. The theory is applied to the problems of thin films on both soft and hard substrates. Numerical solutions are presented for bi-axial tension and simple shear loading of thin films on substrates.     

Micromechanical modelling of the effect of plastic deformation on the mechanical behaviour in pseudoelastic shape memory alloys

Except for the recoverable strain induced by phase transformation, NiTi alloys are very ductile even in the martensite phase. The purpose of the present paper is to study the influence of permanent deformation, which results from plastic deformation of martensite, on the mechanical behaviour of pseudoelastic NiTi alloys. Based on phenomenological theory of martensitic transformation and crystal plasticity, a new three dimensional micromechanical model is proposed by coupling both the slip and twinning deformation mechanisms. The present model is implemented as User MATerial subroutine (UMAT) into ABAQUS/Standard to study the influences of plastic deformation on the stress and strain fields, and on the evolution of martensite transformation. Results show that with the increasing of plastic deformation the residual strain increases and the phase transformation stress–strain curves from the martensite to austenite become steeper and less obvious. Both characteristics, stabilisation of martensite and impedance of the reverse transformation, due to plastic deformation are captured.     

考虑塑性应变记忆恢复的循环棘轮本构模型研究

在统一粘塑性循环本构理论框架下,以Ohno-Abdel-Karim非线性随动硬化模型为基础,建立了一个循环本构模型。模型通过引入塑性应变幅值记忆效应,并在塑性应变记忆项中加入恢复系数,提高了对循环硬化材料单轴棘轮行为的预言能力。将模型应用于316L不锈钢单轴棘轮行为的描述中,模拟不同平均应力、应力幅值下的棘轮应变,均与实验数据吻合较好,证明本文改进的本构模型能合理地描述循环硬化材料的单轴棘轮行为。     

A thermodynamic based higher-order gradient theory for size dependent plasticity

A physically motivated and thermodynamically consistent formulation of small strain higher-order gradient plasticity theory is presented. Based on dislocation mechanics interpretations, gradients of variables associated with kinematic and isotropic hardenings are introduced. This framework is a two non-local parameter framework that takes into consideration large variations in the plastic strain tensor and large variations in the plasticity history variable; the equivalent (effective) plastic strain. The presence of plastic strain gradients is motivated by the evolution of dislocation density tensor that results from non-vanishing net Burgers vector and, hence, incorporating additional kinematic hardening (anisotropy) effects through lattice incompatibility. The presence of gradients in the effective (scalar) plastic strain is motivated by the accumulation of geometrically necessary dislocations and, hence, incorporating additional isotropic hardening effects (i.e. strengthening). It is demonstrated that the non-local yield condition, flow rule, and non-zero microscopic boundary conditions can be derived directly from the principle of virtual power. It is also shown that the local Clausius–Duhem inequality does not hold for gradient-dependent material and, therefore, a non-local form should be adopted. The non-local Clausius–Duhem inequality has an additional term that results from microstructural long-range energy interchanges between the material points within the body. A detailed discussion on the physics and the application of proper microscopic boundary conditions, either on free surfaces, clamped surfaces, or intermediate constrained surfaces, is presented. It is shown that there is a close connection between interface/surface energy of an interface or free surface and the microscopic boundary conditions in terms of microtraction stresses. Some generalities and utility of this theory are discussed and comparisons with other gradient theories are given. Applications of the proposed theory for size effects in thin films are presented.     

高分子材料平面应变拉伸变形局部化

将基于应变软化玻璃状高分子材料微观特征建立的ＢＰＡ８－链分子网络模型引入ＵｐｄａｔｉｎｇＬａｇｒａｎｇｅ有限元方法，建立了适于变形局部化分析的大变形弹塑性有限元驱动应力法．在此基础上，数值模拟了初始各向同性高分子材料平面应变拉伸变形局部化的传播过程．探讨了ＢＰＡ模型对具有加工硬化特性的结晶性高分子材料变形分析的适应性；分析了局部化传播过程中颈缩截面的非均匀应力三轴效应；最后，讨论了网格尺寸以及初始几何不均匀性对颈缩扩散以及应力三轴效应的影响     

Constitutive modeling of strain range dependent cyclic hardening

In this paper, a new approach for constitutive modeling of strain range dependent cyclic hardening is proposed by extending the kinematic hardening model based on the critical state of dynamic recovery. It is assumed that isotropic, as well as kinematic, hardening consists of several parts, and that each part of isotropic hardening evolves when the corresponding part of kinematic hardening is in the critical state of dynamic recovery. The extended model is capable of simulating the cyclic hardening behavior in which different characteristics of cyclic hardening appear depending on strain range. The model is verified by simulating the relatively large cyclic straining tests of 304 stainless steel at ambient temperature, in which cyclic hardening does not stabilize before rupture if strain range exceeds a certain value. The model is further verified by predicting the history dependence of cyclic hardening under incremental cyclic loading and the maximum plastic strain dependence of strain hardening in cyclic tension.     

A Study of Large Plastic Deformations in Dual Phase Steel Using Digital Image Correlation and FE Analysis

Large plastic deformation in sheets made of dual phase steel DP800 is studied experimentally and numerically. Shear testing is applied to obtain large plastic strains in sheet metals without strain localisation. In the experiments, full-field displacement measurements are carried out by means of digital image correlation, and based on these measurements the strain field of the deformed specimen is calculated. In the numerical analyses, an elastoplastic constitutive model with isotropic hardening and the Cockcroft–Latham fracture criterion is adopted to predict the observed behaviour. The strain hardening parameters are obtained from a standard uniaxial tensile test for small and moderate strains, while the shear test is used to determine the strain hardening for large strains and to calibrate the fracture criterion. Finite Element (FE) calculations with shell and brick elements are performed using the non-linear FE code LS–DYNA. The local strains in the shear zone and the nominal shear stress-elongation characteristics obtained by experiments and FE simulations are compared, and, in general, good agreement is obtained. It is demonstrated how the strain hardening at large strains and the Cockcroft–Latham fracture criterion can be calibrated from the in-plane shear test with the aid of non-linear FE analyses. An erratum to this article can be found at     

Anisotropic plastic deformation of extruded aluminum alloy tube under axial forces and internal pressure

The anisotropic plastic deformation behavior of extruded 5000 series aluminum alloy tubes, A5154-H112, of 76 mm outer diameter and 3.9 mm wall thickness is investigated, using a servo-controlled tension-internal pressure testing machine. This machine is capable of applying arbitrary stress or strain paths to a tubular specimen using an electrical, closed-loop control system. Detailed measurements were made of the initial yield locus, contours of plastic work for different levels of work-hardening, and the directions of the incremental plastic strain vectors for both linear and combined stress paths. It is found that the measured work contours constructed in the principal stress space are similar in shape, and that the directions of the incremental plastic strain vectors remain almost constant at constant stress ratios. The work-hardening behavior predicted using Hosford's or the Yld2000-2d yield functions under the assumption of isotropic hardening agrees closely with the observations for both linear and combined stress paths. The material is thus found to work-harden almost isotropically. Both yield functions are effective phenomenological plasticity models for predicting the anisotropic plastic deformation behavior of the material.     

Plastic deformation anisotropy and work-hardening of composite materials

An energy-balance method is applied to discuss plastic anisotropy and work-hardening rate of a composite material. It is found that aligned fibers introduce a strongly anisotropic mode of plastic deformation while randomly-oriented inclusions produce isotropic plastic deformation. The hardening rate due to randomly-oriented inclusions is shown to be independent of the inclusion shape, and to be equal to that due to spherical inclusions when the elastic constants of the inclusions are the same as those of the matrix.     

Application of corotational rates of the logarithmic strain in constitutive modeling of hardening materials at finite deformations

In this paper a finite deformation constitutive model for rigid plastic hardening materials based on the logarithmic strain tensor is introduced. The flow rule of this constitutive model relates the corotational rate of the logarithmic strain tensor to the difference of the deviatoric Cauchy stress and the back stress tensors. The evolution equation for the kinematic hardening of this model relates the corotational rate of the back stress tensor to the corotational rate of the logarithmic strain tensor. Using Jaumann, Green–Naghdi, Eulerian and logarithmic corotational rates in the proposed constitutive model, stress–strain responses and subsequent yield surfaces are determined for rigid plastic kinematic and isotropic hardening materials in the simple shear problem at finite deformations.     

Effect of phase-transformation on mechanical behavior of dual-phase steel plate

The mechanical behavior of dual phase steel plates is affected by internal stresses created during martensite transformation. Analytical modelling of this effect is made by considering a unit cell made of martensite inclusion in a ferrite matrix. A large strain finite element analysis is then performed to obtain the plane stress deformation state. Displayed numerically are the development of the plastic zone and distribution of local state of stress and strain. Studied also are the shape configuration of the martensite (hard-phase) that influences the interfacial condition as related to stress transmission and damage. Internal stresses are found to enhance the global flow stress after yield initiation in the ferrite matrix. Good agreement is obtained between the analytical results and experimental observations.     

Incorporation of yield surface distortion in finite deformation constitutive modeling of rigid-plastic hardening materials based on the Hencky logarithmic strain

In this paper a constitutive model for rigid-plastic hardening materials based on the Hencky logarithmic strain tensor and its corotational rates is introduced. The distortional hardening is incorporated in the model using a distortional yield function. The flow rule of this model relates the corotational rate of the logarithmic strain to the difference of the Cauchy stress and the back stress tensors employing deformation-induced anisotropy tensor. Based on the Armstrong–Fredrick evolution equation the kinematic hardening constitutive equation of the proposed model expresses the corotational rate of the back stress tensor in terms of the same corotational rate of the logarithmic strain. Using logarithmic, Green–Naghdi and Jaumann corotational rates in the proposed constitutive model, the Cauchy and back stress tensors as well as subsequent yield surfaces are determined for rigid-plastic kinematic, isotropic and distortional hardening materials in the simple shear deformation. The ability of the model to properly represent the sign and magnitude of the normal stress in the simple shear deformation as well as the flattening of yield surface at the loading point and its orientation towards the loading direction are investigated. It is shown that among the different cases of using corotational rates and plastic deformation parameters in the constitutive equations, the results of the model based on the logarithmic rate and accumulated logarithmic strain are in good agreement with anticipated response of the simple shear deformation.     

A generalized formulation of the concept of nonhardening region

A stable hysteresis loop is realized under a cyclic loading between fixed strain limits for metals. To describe this phenomenon the idea of memory hypersphere was proposed by Chabocheet al. [1979] and it has been extended by Ohno [1982] as the concept of nonhardening (strain) region, which assumes that an isotropic hardening does not proceed when a plastic strain exists inside a hypersphere in the plastic strain space. A generalized formulation for this concept is presented in this article, which concerns isotropic-kinematic hardening materials, not limited to metals, undergoing a large deformation with a material rotation.     

Constitutive modeling of cyclic plasticity deformation of a pure polycrystalline copper

Cyclic plasticity experiments were conducted on a pure polycrystalline copper and the material was found to display significant cyclic hardening and nonproportional hardening. An effort was made to describe the cyclic plasticity behavior of the material. The model is based on the framework using a yield surface together with the Armstrong–Frederick type kinematic hardening rule. No isotropic hardening is considered and the yield stress is assumed to be a constant. The backstress is decomposed into additive parts with each part following the Armstrong–Frederick type hardening rule. A memory surface in the plastic strain space is used to account for the strain range effect. The Tanaka fourth order tensor is used to characterize nonproportional loading. A set of material parameters in the hardening rules are related to the strain memory surface size and they are used to capture the strain range effect and the dependence of cyclic hardening and nonproportional hardening on the loading magnitude. The constitutive model can describe well the transient behavior during cyclic hardening and nonproportional hardening of the polycrystalline copper. Modeling of long-term ratcheting deformation is a difficult task and further investigations are required.     

Anisotropic hardening and non-associated flow in proportional loading of sheet metals

Conventional isotropic hardening models constrain the shape of the yield function to remain fixed throughout plastic deformation. However, experiments show that hardening is only approximately isotropic under conditions of proportional loading, giving rise to systematic errors in calculation of stresses based on models that impose the constraint. Five different material data for aluminum and stainless steel alloys are used to calibrate and evaluate five material models, ranging in complexity from a von Mises’ model based on isotropic hardening to a non- associated flow rule (AFR) model based on anisotropic hardening. A new model is described in which four stress–strain functions are explicitly integrated into the yield criterion in closed form definition of the yield condition. The model is based on a non-AFR so that this integration does not affect the accuracy of the plastic strain components defined by the gradient of a separate plastic potential function. The model not only enables the elimination of systematic errors for loading along the four loading conditions, but also leads to a significant reduction of systematic errors in other loading conditions to no higher than 1.5% of the magnitude of the predicted stresses, far less that errors obtained under isotropic hardening, and at a level comparable to experimental uncertainty in the stress measurement. The model is expected to lead to a significant improvement in stress prediction under conditions dominated by proportional loading, and this is expected to directly improve the accuracy of springback, tearing, and earing predictions for these processes. In addition, it is shown that there is no consequence on MK necking localization due to the saturation of the yield surface in pure shear that occurs with the aluminum alloys using the present model.     

Anisotropic finite elastoplasticity with nonlinear kinematic and isotropic hardening and application to sheet metal forming

The paper discusses the derivation and the numerical implementation of a finite strain material model for plastic anisotropy and nonlinear kinematic and isotropic hardening. The model is derived from a thermodynamic framework and is based on the multiplicative split of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong–Frederick kinematic hardening. Introducing the so-called structure tensors as additional tensor-valued arguments, plastic anisotropy can be modelled by representing the yield surface and the plastic flow rule as functions of the structure tensors. The evolution equations are integrated by a new form of the exponential map that preserves plastic incompressibility and uses the spectral decomposition to evaluate the exponential tensor functions in closed form. Finally, the applicability of the model is demonstrated by means of simulations of several deep drawing processes and comparisons with experiments.     

A crystal plasticity model that incorporates stresses and strains due to slip gradients

This work is concerned with incorporating the kinematic and stress effects of excess dislocations in a constitutive model for the elastoplastic behavior of crystalline materials. The foundation of the model is a three term multiplicative decomposition of the deformation gradient in which the two classical terms of plastic and elastic deformation are included along with an additional term for long range strain due to the collective effects of excess dislocations. The long range strain is obtained from an assumed density of Volterra edge dislocations and is directly related to gradients in slip. A new material parameter emerges which is the size the region about a continuum point that contributes to long range strains.Using Hookean elasticity, the stress at a point is linearly related to the sum of the elastic plus the long range strain fields. However, the driving force for slip is postulated to be due only to the elastic stress so that the long range stress is a back stress in the constitutive relationship for plastic deformation. A consistent balance of the total deformation rate with the three proposed mechanisms of deformation leads to a set of differential equations that can be solved for the elastic stress, rotation and pressure which then implicitly defines the material state and equilibrium stress. Results from the simulation of a tapered tensile specimen demonstrate that the constitutive model exhibits isotropic and kinematic type hardening effects as well as changes in the pattern of plastic deformation and necking when compared to a material without slip gradient effects.     

Micromechanics of plastic deformation and phase transformation in a three-phase TRIP-assisted advanced high strength steel: Experiments and modeling

The micromechanics of plastic deformation and phase transformation in a three-phase advanced high strength steel are analyzed both experimentally and by microstructure-based simulations. The steel examined is a three-phase (ferrite, martensite and retained austenite) quenched and partitioned sheet steel with a tensile strength of ~980 MPa. The macroscopic flow behavior and the volume fraction of martensite resulting from the austenite–martensite transformation during deformation were measured. In addition, micropillar compression specimens were extracted from the individual ferrite grains and the martensite particles, and using a flat-punch nanoindenter, stress–strain curves were obtained. Finite element simulations idealize the microstructure as a composite that contains ferrite, martensite and retained austenite. All three phases are discretely modeled using appropriate crystal plasticity based constitutive relations. Material parameters for ferrite and martensite are determined by fitting numerical predictions to the micropillar data. The constitutive relation for retained austenite takes into account contributions to the strain rate from the austenite–martensite transformation, as well as slip in both the untransformed austenite and product martensite. Parameters for the retained austenite are then determined by fitting the predicted flow stress and transformed austenite volume fraction in a 3D microstructure to experimental measurements. Simulations are used to probe the role of the retained austenite in controlling the strain hardening behavior as well as internal stress and strain distributions in the microstructure.