A phase field model of grain boundary migration and grain rotation under elasto–plastic anisotropies

We propose a phase field framework to model both grain rotation and grain boundary migration in a mechanically loaded elasto–plastic solid. We develop this framework on the grounds of the phase field model of grain boundaries proposed by (Kobayashi et al., Physica D 140 (2000)) by coupling the grain orientation phase field θ with the strain energy of an elasto–plastic solid. The lattice plasticity is described by the phenomenological quadratic Hill yield potential. This coupling permits both grain rotation and grain boundary migration to evolve simultaneously with the bulk lattice plasticity minimizing the total energy of the system. Hence, the presented phase field framework allows the study of a rich set of phenomena that emerge from the interplay between grain boundary mediated and dislocation mediated plasticity under the effects of elastic and plastic anisotropy. We demonstrate the model in two case studies: A) bicrystalline nanopillar and B) multigrain nanocrystalline system. In case A, we study the behaviour of stress driven (curvature free) grain boundaries and evaluate the limits for the grain boundary velocity. In case B, additional grain boundary curvature effects come into play and we analyse the constitutive response for different strain rate regimes.