Dislocation patterning in a 2D continuum theory of dislocations

TL;DR

This paper develops a systematic 2D continuum dislocation theory derived from microscopic models, highlighting the importance of diffusion-like terms and dislocation mobility in pattern formation during plastic deformation.

Contribution

It introduces a novel continuum model for dislocation patterning derived from microscopic considerations, emphasizing the role of diffusion terms and phase field energy functional.

Findings

Diffusion-like terms are crucial for dislocation pattern length scale selection.

The continuum theory can be derived from an averaged energy functional using phase field methods.

Dislocation mobility functions are essential for instability and pattern formation.

Abstract

Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were proposed, but few of them (if any) are derived from microscopic considerations through systematic and controlled averaging procedures. In this paper we present a 2D continuum theory that is obtained by systematic averaging of the equations of motion of discrete dislocations. It is shown that in the evolution equations of the dislocation densities diffusion like terms neglected in earlier considerations play a crucial role in the length scale selection of the dislocation density fluctuations. It is also shown that the formulated continuum theory can be derived from an averaged energy functional using the framework of phase field theories. However, in order to account for the flow stress one has in that case to introduce a nontrivial dislocation mobility function, which proves to be crucial for the instability leading to patterning.