Microstructural Modeling of Banding in Single Crystals: 'Stack of Domains' Model

Abstract

A rigid-plastic rate-independent crystal plasticity based `stack of domains' model of a single crystal is developed to capture local deformation inhomogeneity and sub-structure formation when subjected to macroscopically homogeneous imposed deformation. This model regards the single crystal as a linear stack of domains with planar shaped domain boundaries. The domains of the model single crystal collectively accommodate the imposed deformation and individual domains maintain velocity and traction continuity with its neighbors. The lattice orientation of individual domains perturbed and that perturbation triggers the inhomogeneity of plastic slip amongst domains. Mobility of domain boundaries relative to the material and a differential hardening law that accounts for the orientational instability of individual domains are also considered in the model. The developed model is applied to predict the formation of banding in initially copper (C), rotated cube (RC) and Goss (G) orientated single crystals when subjected to plane strain deformation and the predictions are compared with the experimental literature.