An extended homogenous yield function based anisotropic hardening model for description of anisotropic hardening behavior of materials

Except for the Bauschinger effect and permanent softening, work hardening stagnation and cross-effect are often observed deformation behaviors for sheet metals subjected to strain path changes. These complex deformation behaviors are assumed to have great effect on the sheet forming process and the following spring back. To constitutively, and more precisely model these plastic behaviors, extensive models have been successfully developed. Particularly, the combined isotropic-kinematic hardening model is powerful to capture the plastic behavior of sheet metals during forward and reverse loading. However, there is strong coupling between anisotropic yielding and anisotropic hardening with the kinematic hardening. Recently, Barlat et al. (2011) [61] proposed a homogenous yield function based anisotropic hardening model to describe the Bauschinger effect, which is not formulated with the kinematic hardening rule. In the present work, the original anisotropic hardening model is extended to capture the often observed cross-effect during multi-stage loading and work hardening stagnation during reverse loading. Although only four coefficients are newly introduced in the extended model, it can capture well the main trends of work hardening stagnation and cross-effect. The capability of this extended model is demonstrated with applications to two materials, namely, high strength steel and mild steel DC06.