Model for plasticity effects in metals under nonproportional cyclic loading

A possible physical mechanism for additional hardening is proposed on the basis of an analysis of experiments on nonproportional cyclic loading of metals. A model for an elastoplastic polycrystal with a hardening law taking into account the interaction of slip systems is developed. The effect of additional hardening for elliptic strain paths and the shapes of stress paths and hysteresis loops typical of elliptic strain paths are described qualitatively. A violation of the assumption of the local determinacy and orientations of stress paths is considered for the square strain paths taking place in tests of chromium-nickel austenite stainless steels. Perm' State Technical University, Perm', 614600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 144–151, November–December, 1999.     

率无关非比例循环弹塑性本构关系

正确地考虑了塑性应变空间中和非比例加载下的离散记忆特性，提出一种新的率无关非比例循环塑性本构关系，并给出了铜的理论预测值与实验结果的比较．     

非比例循环载荷下塑性模量的讨论

对1Cr18Ni9Ti不锈钢进行菱形应变路径的非比例循环本构实验,根据实验结果及分析,对双面本构模型给出了一个极限面定义,以保证屈服面不与极限面相交,在这个极限面定义及实验结果的基础上,对不同本构模型所定义的距离与塑性模量的相关性进行了讨论,表明Mroz和Chen的距离与塑性模量具有较好的相关性。     

理想正交各向异性弹塑性材料平面应变条件下静止裂纹尖端场

以Hill唯象理论为基础,建立正交各向异性弹塑性材料的本构关系,给出理想正交各向异性弹塑性材料在平面应变条件下混合型静止裂纹尖端的弹塑性场.与J.Pan的解不同,采用自相似假定,可以用解析方法求得不存在应力间断的应力场.对满塑性区条件和应变的奇异性加以讨论,这些为建立断裂准则提供了理论的依据.     

A finite strain elastic-viscoplastic self-consistent model for polycrystalline materials

A large strain elastic-viscoplastic self-consistent (EVPSC) model for polycrystalline materials is developed. At single crystal level, both the rate sensitive slip and twinning are included as the plastic deformation mechanisms, while elastic anisotropy is accounted for in the elastic moduli. The transition from single crystal plasticity to polycrystal plasticity is based on a completely self-consistent approach. It is shown that the differences in the predicted stress-strain curves and texture evolutions based on the EVPSC and the viscoplastic self-consistent (VPSC) model proposed by Lebensohn and Tomé (1993) are negligible at large strains for monotonic loadings. For the deformations involving unloading and strain path changes, the EVPSC predicts a smooth elasto-plastic transition, while the VPSC model gives a discontinuous response due to lack of elastic deformation. It is also demonstrated that the EVPSC model can capture some important experimental features which cannot be simulated by using the VPSC model.     

Modeling the thermoelastic–viscoplastic response of polycrystals using a continuum representation over the orientation space

Conventional methodologies towards polycrystal plasticity use an aggregate of single crystals and this choice of the aggregate affects the response of the polycrystal. In order to address this issue, a continuum approach is presented for the representation of polycrystals through an orientation distribution function over the orientation space. Additionally, a constitutive framework for thermoelastic–viscoplastic response of metals based on polycrystal plasticity is presented along with a coupled macro–micro, fully implicit Lagrangian finite element algorithm. Numerical examples that highlight the accuracy, performance and benefits of the proposed approach are presented.     

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.     

考虑微裂纹相互作用的的岩石微观力学弹塑性损伤模型研究

本文建立基于微裂纹扩展的岩石弹塑性损伤微观力学模型。用自洽方法考虑裂隙间相互影响,压缩载荷下微裂纹尖端翼裂纹稳定扩展表征岩石的微观损伤,基于应变能密度准则用Newton迭代法求复合型断裂的翼裂纹扩展长度,并采用微裂隙统计的二参数Weibull函数模型反映绝对体积应变对微裂纹分布数目影响,进而用翼裂纹扩展所表征的应力释放体积和微裂纹数目来表示含有微裂隙的岩石损伤演化变量;宏观塑性屈服函数采用Voyiadjis等的等效塑性应变的硬化函数,反映塑性内变量对硬化函数的影响;建立岩石的弹塑性损伤本构关系及其数值算法,并用回映隐式积分算法编制了弹塑性损伤模型的程序。从围压和微裂隙长度等因素分析弹塑性损伤模型的岩石的损伤和宏观塑性特性。     

考虑尺寸效应的多晶金属循环塑性分析

本文采用多晶塑性分析方法,设材料点包含一定数量的各向异性单晶晶粒并考虑晶粒尺寸的影响,计算材料点的应力和应变时利用了Taylor假设。模型引入考虑尺寸效应的晶体滑移硬化函数,同时针对晶体滑移引入背应力及其方向性硬化的描述,以反映不同晶粒尺寸材料在循环加载条件下的力学行为。利用该模型,本文第一作者采用显式格式编制了与ABAQUS商用有限元软件接口的用户材料子程序（VUMAT）,实例计算证实该模型可以反映和描述多晶金属材料在材料反复加载条件下的循环塑性行为与尺寸效应。     

Elastoplastic modeling of circular fiber-reinforced ductile matrix composites considering a finite RVE

A micromechanical elastoplastic damage model considering a finite RVE is proposed to predict the overall elastoplastic damage behavior of circular fiber-reinforced ductile (matrix) composites. The constitutive damage model proposed in our preceding work (Kim and Lee, 2009) considering a finite Eshelby’s tensor (Li et al., 2005, Wang et al., 2005) is extended to accommodate the elastoplastic behavior of the composites. On the basis of the exterior-point Eshelby’s tensor for circular inclusions and the ensemble-averaged effective yield criterion, a micromechanical framework for predicting the effective elastoplastic damage behavior of ductile composites is derived. A series of numerical simulations are carried out to illustrate stress–strain response of the proposed micromechanical framework and to examine the influence of a Weibull parameter on the elastoplastic behavior of the composites. Furthermore, comparisons between the present predictions and experimental data available in the literature are made to further assess the predictive capability of the proposed model.     

Strain gradient near interface of coaxial cylinders in torsion

Classical elastoplastic theory predicts that the rotation angle near an interface between two mismatched materials is discontinuous under shear. The strain gradient effects, however, can be significant within a narrow region near the interface. This can be shown by application of the strain gradient plasticity. The matching expansion method was used to obtain asymptotic results. Comparison is then made with those found numerically for the interface torsion problem of a two-layered cylindrical tube. The strain gradient plasticity theory solution differs from that of the classical elastoplastic theory solution, depending on the properties aside from the interface behavior and the loading mode. A failure criterion is also proposed that accounts for the strain gradients.     

Numerical and experimental study of elastoplastic tension-torsion processes in axisymmetric bodies under large deformations

We consider a numerical solution technique for generalized axisymmetric problems with torsion for elastoplastic bodies of revolution of arbitrary shape under large strains, as well as simple or complex loading, and the conditions of inhomogeneous stress-strain state. The processes of elastoplastic deformation, strain localization, and fracture of solid axisymmetric steel samples of variable thickness are studied experimentally and numerically for the cases of proportional and nonproportional kinematic torsional and/or tensile loading until failure. The mutual influence of torsion and tension on the deformation and failure under large strains is estimated.     

Micro–macro approach for the rock salt behaviour

Rock salt is considered as a pure aggregate of halite (mineral NaCl) crystals and its behaviour is investigated by a micro–macro approach. The behaviour of the polycrystalline aggregate is deduced from the properties of the constituent halite crystals. A model for the elastoplastic behaviour of halite crystal has been deduced from experimental data available in the literature. The basic equations of the micro–macro model for the polycrystalline medium and the calculation method are then presented and the elastoplastic behaviour of rock salt is investigated by this method. The hardening effects obtained for the polycrystal are found to be very different from those obtained for FCC metal polycrystals. The differences are explained as a consequence of differences of families of glide systems in these crystals. Finally, the internal stresses in the polycrystal are studied in order to elucidate the origin of cracking and damage of the rock salt.     

Plastic spin associated with a non-normality theory of plasticity

A plasticity model using a vertex-type plastic flow rule on a smooth yield surface for an anisotropic solid has been proposed recently. This model is here completed by incorporating the effect of plastic spin. Simple shear with a large shear strain is one of the hardest tests on finite strain anisotropic plasticity models, and it is here shown which plastic spin expression is needed to avoid unrealistic oscillatory behavior of the shear stress under large shear strains. The idea of using non-normality with a smooth yield surface originates from a recent proposal of using an abrupt strain path change to determine the subsequent yield surface shape. For this method both polycrystal plasticity calculations and experiments have shown a vertex-type response on the apparently smooth yield surface.     

Evaluation of self-consistent polycrystal plasticity models for magnesium alloy AZ31B sheet

Various self-consistent polycrystal plasticity models for hexagonal close packed (HCP) polycrystals are evaluated by studying the deformation behavior of magnesium alloy AZ31B sheet under different uniaxial strain paths. In all employed polycrystal plasticity models both slip and twinning contribute to plastic deformation. The material parameters for the various models are fitted to experimental uniaxial tension and compression along the rolling direction (RD) and then used to predict uniaxial tension and compression along the traverse direction (TD) and uniaxial compression in the normal direction (ND). An assessment of the predictive capability of the polycrystal plasticity models is made based on comparisons of the predicted and experimental stress responses and R values. It is found that, among the models examined, the self-consistent models with grain interaction stiffness halfway between those of the limiting Secant (stiff) and Tangent (compliant) approximations give the best results. Among the available options, the Affine self-consistent scheme results in the best overall performance. Furthermore, it is demonstrated that the R values under uniaxial tension and compression within the sheet plane show a strong dependence on imposed strain. This suggests that developing anisotropic yield functions using measured R values must account for the strain dependence.     

考虑路径相关性的非比例循环塑性本构模型

根据非比例加载下金属材料响应的延迟特性及加载路径相关性,选取沿应力迹法向的塑性应变的累积量作为非比例加载影响的度量,相应给出反映非比例附加强化的变量,并假设其模量和强化率与加载路径的几何参数相关．为反映由于非比例加载而引起的材料强化的异向效应,在Valanis的塑性内时响应方程中引入与加载路径几何性质有关的应力项,构成非比例循环塑性本构关系．对316和304不锈钢材料在一些典型非比例循环加载路径下的应力响应进行了理论预测,与Benallal等及McDowell的实验结果取得了良好的一致．     

压缩载荷作用下岩石的细观损伤和塑性研究

建立岩石微裂纹扩展的细观力学模型,研究了岩石的细观损伤和塑性性质.压缩载荷下微裂纹尖端翼裂纹稳定扩展表征岩石的细观损伤,采用应变能密度准则求解复合型断裂的翼裂纹扩展长度,微裂隙统计的二参数Weibull函数模型反映绝对体积应变对微裂纹分布数目影响,进而用翼裂纹扩展所表征的应力释放体积和微裂纹数目来表示含有微裂隙的岩石损伤演化变量;宏观塑性屈服函数采用Voyiadjis等的等效塑性应变的硬化函数,反映了塑性内变量对硬化函数的影响;建立岩石模型的本构关系及其数值算法,并用回映隐式积分算法编制了模型的本构程序.分析弹塑性损伤模型的围压对岩石损伤的影响,并从围压和短微裂隙长度等因素分析模型的岩石的损伤和宏观塑性特性.     

Macro versus micro-scale constitutive models in simulating proportional and nonproportional cyclic and ratcheting responses of stainless steel 304

A recent study by Hassan et al. [Hassan, T., Taleb, L., Krishna, S., 2008. Influences of nonproportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plasticity, 24, 1863–1889.] demonstrated that some of the nonproportional ratcheting responses under stress-controlled loading histories cannot be simulated reasonably by two recent cyclic plasticity models. Two major drawbacks of the models identified were: (i) the stainless steel 304 demonstrated cyclic hardening under strain-controlled loading whereas cyclic softening under stress-controlled loading, which depends on the strain-range and which the existing models cannot describe; (ii) the change in biaxial ratcheting responses due to the change in the degree of nonproportionality were not simulated well by the models. Motivated by these findings, two modified cyclic plasticity models are evaluated in predicting a broad set of cyclic and ratcheting response of stainless steel 304. The experimental responses used in evaluating the modified models included both proportional (uniaxial) and nonproportional (biaxial) loading responses from Hassan and Kyriakides [Hassan, T., Kyriakides, S., 1994a. Ratcheting of cyclically hardening and softening materials. Part I: uniaxial behavior. Int. J. Plasticity, 10, 149–184; Hassan, T., Kyriakides, S., 1994b. Ratcheting of cyclically hardening and softening materials. Part II: multiaxial behavior. Int. J. Plasticity, 10, 185–212.] and Hassan et al. [Hassan, T., Taleb, L., Krishna, S., 2008. Influences of nonproportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plasticity, 24, 1863–1889.] The first model studied is a macro-scale, phenomenological, constitutive model originally proposed by Chaboche et al. [Chaboche, J.L., Dang-Van, K., Cordier, G., 1979. Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. In: Proceedings of the Fifth International Conference on SMiRT, Div. L, Berlin, Germany, L11/3.]. This model was systematically modified for incorporating strain-range dependent cyclic hardening–softening, and proportional and nonproportional loading memory parameters. The second model evaluated is a polycrystalline model originally proposed by Cailletaud [Cailletaud, G., 1992. A micromechanical approach to inelastic behavior of metals. Int. J. Plasticity, 8, 55–73.] based on crystalline slip mechanisms. These two models are scrutinized against simulating hysteresis loop shape, cyclic hardening–softening, cross-effect, cyclic relaxation, subsequent cyclic softening and finally a broad set of ratcheting responses under uniaxial and biaxial loading histories. The modeling features which improved simulations for these responses are elaborated in the paper. In addition, a novel technique for simulating both the monotonic and cyclic responses with one set of model parameters is developed and validated.     

Benchmark experiments and characteristic cyclic plasticity deformation

Key issues in cyclic plasticity modeling are discussed based upon representative experimental observations on several commonly used engineering materials. Cyclic plasticity is characterized by the Bauschinger effect, cyclic hardening/softening, strain range effect, nonproporitonal hardening, and strain ratcheting. Additional hardening is identified to associate with ratcheting rate decay. Proper modeling requires a clear distinction among different types of cyclic plasticity behavior. Cyclic hardening/softening sustains dependent on the loading amplitude and loading history. Strain range effect is common for most engineering metallic materials. Often, nonproportional hardening is accompanied by cyclic hardening, as being observed on stainless steels and pure copper. A clarification of the two types of material behavior can be made through benchmark experiments and modeling technique. Ratcheting rate decay is a common observation on a number of materials and it often follows a power law relationship with the number of loading cycles under the constant amplitude stress controlled condition. Benchmark experiments can be used to explore the different cyclic plasticity properties of the materials. Discussions about proper modeling are based on the typical cyclic plasticity phenomena obtained from testing several engineering materials under various uniaxial and multiaxial cyclic loading conditions. Sufficient experimental evidence points to the unambiguous conclusion that none of the hardening phenomena (cyclic hardening/softening, strain range effect, nonproportional hardening, and strain hardening associated with ratcheting rate decay) is isotropic in nature. None of the hardening behavior can be properly modeled with a change in the yield stress.