Plastic flow and dislocation strengthening in a dislocation density based formulation of plasticity

Modeling dislocation interaction on a mesoscopic scale is an important task for the description of flow stress and strain hardening in a continuum model. In dislocation based continuum theories, different flow stress formulations are commonly used in the literature. They are usually based on the average dislocation spacing related to the square root of dislocation density, but differ in their degree of homogenization of dislocation interactions, namely whether only total dislocation density is considered in a Taylor term or whether an interaction matrix is used. We analyze the impact of both terms in different crystal orientations as well as homogeneously and inhomogeneously distributed initial dislocation densities. In the dislocation based continuum formulation used here, both terms act as a short-range stress additionally to the mean field long-range stress field of elastic dislocation interaction. We demonstrate that the simplifying assumption of an average over all possible interaction types is a reasonable reduction of complexity in high symmetry systems with homogeneous density distribution. However, we also demonstrate that under specific boundary conditions and for inhomogeneities between slip systems a significantly different density evolution is obtained on slip systems with similar Schmid-factors, when considering different interaction strengths for different types of dislocation interaction. This is in agreement with findings in discrete dislocation dynamics simulations in the literature.