Motion of grain boundaries incorporating dislocation structure

TL;DR

This paper develops a continuum model for low angle grain boundary motion in 2D, incorporating dislocation interactions and structure evolution, enabling simulation of boundary shape changes and rotations.

Contribution

It introduces a novel continuum model derived from discrete dislocation dynamics that captures both normal and tangential grain boundary motions, including shape changes.

Findings

Model accurately predicts grain boundary dynamics.

Simulations match discrete dislocation dynamics results.

Accounts for boundary shape change and rotation.

Abstract

In this paper, we present a continuum model for the dynamics of low angle grain boundaries in two dimensions based on the motion of constituent dislocations of the grain boundaries. The continuum model consists of an equation for the motion of grain boundaries (i.e., motion of the constituent dislocations in the grain boundary normal direction) and equations for the dislocation structure evolution on the grain boundaries. This model is derived from the discrete dislocation dynamics model. The long-range elastic interaction between dislocations is included in the continuum model, which ensures that the dislocation structure on a grain boundary is consistent with the Frank's formula. These evolution of the grain boundary and its dislocation structure are able to describe both normal motion and tangential translation of the grain boundary and grain rotation due to both coupling and sliding. Since the continuum model is based upon dislocation structure, it naturally accounts for the grain boundary shape change during the motion and rotation of the grain boundary by motion and reaction of the constituent dislocations. Using the derived continuum grain boundary dynamics model, simulations are performed for the dynamics of circular and non-circular two dimensional grain boundaries, and the results are validated by discrete dislocation dynamics simulations.