Stress and Strain Measures for Orthotropic Metals at Large Nonproportional Plastic Strain Histories

This chapter reexamines the definitions of equivalent Mises stress and equivalent plastic strain rate for anisotropic materials. Such an issue is of great importance if plastic strain induced anisotropy of initially isotropic materials (for instance, car body sheets) is considered. It is shown that for nonproportional strain histories with alternating simple tension and simple shear intervals, the traditional Hill’s definition for orthotropic materials contains variable material functions instead of three material constants. It is demonstrated that tensor function representation based on plastic strain and stress tensors is worthwhile to be considered even in the framework of classical concepts.