Comparison of two models for anisotropic hardening and yield surface evolution in bcc sheet steels

Abstract

Abstract The purpose of the current work is the investigation and comparison of aspects of the material behavior predicted by two models for anisotropic, and in particular cross, hardening in bcc sheet steels subject to non-proportional loading. The first model is the modified form (Wang et al., 2008) of that due to Teodosiu and Hu (1995, 1998). In this (modified) Teodosiu-Hu model (THM), cross hardening is assumed to affect the yield stress and the saturation value of the back stress. The second model is due to Levkovitch and Svendsen (2007) and Noman et al. (2010). In the Levkovitch-Svendsen model (LSM), cross hardening is assumed to affect the flow anisotropy. As clearly demonstrated in a number of works applying the THM (e.g., Boers et al., 2010; Bouvier et al., 2005, 2003; Hiwatashi et al., 1997; Li et al., 2003; Thuillier et al., 2010; Wang et al., 2008) and the LSM (e.g., Clausmeyer et al., 2014, 2011b; Noman et al., 2010), both of these are capable of predicting the effect of cross hardening on the stress-deformation behavior observed experimentally in sheet steels. As shown in the current work, however, these two models differ significantly in other aspects, in particular with respect to the development of the yield stress, the back stress, and the yield surface. For example, the THM predicts no change in the shape of the yield surface upon change of loading path, in contrast to the LSM and crystal plasticity modeling of bcc sheet steels (Peeters et al., 2002). On the other hand, the LSM predicts no hardening stagnation after cross hardening as observed in experiments, in contrast to the THM. Examples are given.