A CONSTITUTIVE MODEL FOR NONPROPORTIONAL CYCLIC PLASTICITY WITH LOADINGPATH DEPENDENCE
考虑路径相关性的非比例循环塑性本构模型

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]