Multiscale polycrystal plasticity

Polycrystal plasticity models are commonly developed with a narrow focus on the grain as the fundamental unit of crystallographic orientation and anisotropic behavior. However, deformation and strengthening mechanisms occur simultaneously at multiple length scales and may lead to bulk deformation behavior of metals that is substantially different from that predicted by simple forms of polycrystal plasticity. The development of dislocation substructure occurs at subgrain scales while, at the same time, geometrically necessary dislocation boundaries (GNBs) are generated that extend over several grain diameters. A framework is presented here for the efficient treatment of multiple, simultaneously evolving strengthening mechanisms. The theory focuses on a macroscale hardening surface representation of the strengthening due to GNB formation. Crystallographic shear flow resistance is determined via a mapping procedure of the macroscale hardening surface to the length scale of grains. Predicted stress-strain curves based on the hardening surface formulation are compared to experimental data and polycrystal plasticity predictions for OFHC Cu. It is demonstrated that the hardening surface model of GNB strengthening mechanisms can provide improved predictive capability of nonproportional nonproportional loading behavior of Cu compared to conventional slip system hardening laws commonly used in polycrystal plasticity applications.