Incoherence at heterogeneous interfaces

Abstract

To describe the small scale defect structure of incoherent interfaces in an elastic bi-crystal, we consider a multiscale variational model composed of two parts: a bulk energy density W and a nonconvex interfacial energy density ψ that depends on the microscopic lattice mismatch at the grain boundary and the relative crystallographic normal. Mismatch is described using a referential coherence tensor that measures the relative misfit at the grain boundary and serves to couple the bulk elastic deformation of the grains to small scale defect structures at the interface. Minimizing this energy yields predictions for the distribution of defect microstructures at the interface as a function of grain size, elastic stiffness, and lattice mismatch. Calculations for a heterophase (01) / (01) interface in a two-dimensional bi-crystal system are presented.