Plasticity in multi-phase solids with incoherent interfaces and junctions

Boundaries and junctions (both internal and external) can contribute significantly to the plastic deformation of metallic solids, especially when the average size of the grains (phases) is less than hundred nanometres or when the size of the solid itself is of the order of microns. The overall permanent deformation of the solid is a result of a coupling between bulk plasticity with moving interfaces/junctions/edges and intrinsic plasticity of internal and external surfaces. We use a novel continuum thermodynamic theory of plastic evolution, with incoherent interfaces and non-splitting junctions, to derive flow rules for bulk and surface plasticity in addition to kinetic relations for interface, edge, and junction motion, all coupled to each other. We assume rate-independent associative isotropic plastic response with bulk flow stress dependent on accumulated plastic strain and an appropriate measure of inhomogeneity. The resulting theory has two internal length scales: one given by the average grain size and another associated with the material inhomogeneity.