Mesoscale Simulation of Dislocation Microstructures at Internal Interfaces

The need for predicting the behavior of crystalline materials on small-scales has led to the development of physically based descriptions of the motion of dislocations. Several dislocation-based continuum theories have been introduced, but only recently rigorous techniques have been developed for performing meaningful averages over systems of moving, curved dislocations, yielding evolution equations based on a dislocation density tensor. Those evolution equations provide a physically based framework for describing the motion of curved dislocations in three-dimensional systems. However, a meaningful description of internal interfaces and the complex mechanistic interaction of dislocations and interfaces in a dislocation based continuum model is still an open task. In this paper, we address the conflict between the need for a mechanistic modeling of the involved physical mechanisms and a reasonable reduction of model complexity and numerical effort. We apply a dislocation density based continuum formulation to systems which are strongly affected by internal interfaces, i.e. grain boundaries and interfaces in composite materials, and focus on the physical and numerical realization. Particularly, the interplay between physical and numerical accuracy is pointed out and discussed.