Edge dislocations in crystal structures considered as traveling waves of discrete models

TL;DR

This paper models edge dislocations in crystal structures as traveling waves within a discrete framework, deriving analytical and numerical insights into their depinning, velocity, and interactions.

Contribution

It introduces a simplified discrete model for edge dislocations and provides analytical descriptions of depinning and collective effects in the strongly overdamped regime.

Findings

Calculated static and dynamic depinning stresses.

Derived dislocation velocity and displacement profiles.

Established conditions for collective depinning of multiple dislocations.

Abstract

The static stress needed to depin a 2D edge dislocation, the lower dynamic stress needed to keep it moving, its velocity and displacement vector profile are calculated from first principles. We use a simplified discrete model whose far field distortion tensor decays algebraically with distance as in the usual elasticity. An analytical description of dislocation depinning in the strongly overdamped case (including the effect of fluctuations) is also given. A set of $N$ parallel edge dislocations whose centers are far from each other can depin a given one provided $N=O(L)$, where $L$ is the average inter-dislocation distance divided by the Burgers vector of a single dislocation. Then a limiting dislocation density can be defined and calculated in simple cases.