Multiscale Theory of Dislocation Plasticity

Motion of dislocations is a common mechanism of plasticity in many materials. Dislocation-mediated deformation is essentially an inhomogeneous process, which is manifest in the formation of slip lines and complicated cell wall structures. An adequate description of these processes is an important goal of Materials Theory, which aims to describe the mechanical properties of materials and their reliability in service. This publication advances the thermodynamically consistent theory of dislocation-mediated plasticity to include the spatial gradients of the independent variables. We conducted the renormalization group scaling analysis of deformation and obtained the low-energy dislocation structures as ordinary solutions of the equilibrium equations without any arbitrary assumptions. We matched the emerging theoretical structures with the experimentally observed and made several predictions regarding possible experiments.