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．

A CONSTITUTIVE MODEL FOR NONPROPORTIONAL CYCLIC PLASTICITY WITH LOADINGPATH DEPENDENCE

In order to describe the hardening behavior of metallic materials under nonpropertional cyclic loading, a number of nonproportionality parameters have been proposed10]. For some loading paths, the degree of nonpropertional cyclic hardening can be animated by these parameters. But for the paths containing not only the stress relaxation but also the many times unloading per cycle, they do not work well. For instance, these parameters always predicted a higher stress level for the stair-step loading and a lower one for the double-traingular loading than that observed in experiments12,13,20]. In addition, the effects of nonpropertional cyclic loading on the anisotropic hardening behavior are either ignored or poorly estimated by only introducing a scalar parameter into a constitutive model.In this paper, an appropriate nonproportionality parameter and an anisotropic variable related to nonproportional loading trajectory are presented. Based on the delay and the path-dependent response behavior of metallic material under nonproportional loading, the accumulation of plastic strain in radial direction of the stress trajectory is chosen as a measure of the nonproportionality.Correspondingly, a variable for describing the additional isotropic hardening is proposed. The hardening modulus and rate are prescribed as a function of geometry of the loading path and plastic strain amplitude. To consider the anisotropic hardening due to nonproportional loading, a stress term depending on geometry of the loading path is incorporated into Valanis' endochronic plastic response equations8]. A constitutive model for nonproportional cyclic plasticity is formulated,which is applied to simulate the stress responses of 316 and 304 stainless steels for a variety of typical nonproportional cyclic loading paths. The predictions have a good agreement with the experimental results by BenallaJ et al.18] as well as McDowell et al.22]