Selection of slip systems in confined single crystal gradient plasticity: coupled effects of slip system orientations, latent hardening, and grain boundaries

In crystal plasticity under prescribed deformation, the incremental material response is potentially non-unique owing to slip system redundancy for most of the crystalline structures. Following Petryk, energy minimizing considerations give the way to select one of these solutions and the set of active systems, which depend on their more or less favorable orientation and their mutual interactions (latent hardening). This variational approach is extended here to confined plasticity in a finite volume, simulating a single crystal embedded in an aggregate. A slip gradient enhanced framework and related micro-hard boundary conditions are considered, using two defect energies introduced by Gurtin and coworkers: the first one takes the slip system polar dislocation densities as internal state variables and the second one is a quadratic potential of the dislocation density tensor. In both cases, micro-hard conditions amount to null flow for the two former quantities. For the classical one dimensional case of a strip in simple shear, the two models yield substantially different solutions, the second one coupling the gradients on the different systems. These results emphasize the necessity for a physically motivated modeling of gradient effects in the vicinity of grain boundary interfaces.