A modelling of single crystal plasticity with backstress evolution

A substructure based numerical procedure which contains backstress evolution is proposed in order to depict the complex plasticity behavior of materials such as isotropic hardening, kinematic hardening and crystal orientation. The constitutive equations are based on the works of Asaro (1983), Peirce et al. (1982) and Nemat-Nasser (1983). However, two backstress models are proposed in this work and incorporated into the constitutive equations. These two models are studied for the application of simple shear in order to examine their physical feasibility. Parametric studies are also conducted for these two models. The backstress models are also compared with those of Lamar (1989) and Zbib and Aifantis (1987, 1988). The two dimensional model presented here is to give the physical interpretation of the process of crystal plasticity and a more generalized three dimensional model is to follow-up this work.