An analysis of the pile-up of infinite periodic walls of edge dislocations

TL;DR

This paper investigates the equilibrium configurations of infinite periodic walls of edge dislocations piled against an obstacle, revealing distinct regions with analytical predictions and parameter-dependent length scales.

Contribution

It provides a detailed analysis of dislocation pile-ups, including analytical predictions for density distributions near and far from the obstacle.

Findings

Near the obstacle, classical single slip plane solution applies.

At larger distances, the dislocation density decays linearly.

Characteristic length scales depend differently on problem parameters.

Abstract

We analyse the equilibrium pile-up configurations of infinite periodic walls of edge dislocations which are forced against an impenetrable obstacle by a constant applied shear stress. Numerically generated density distributions exhibit two distinct regions, for each of which we provide an interpretation and an analytical prediction. Near the obstacle, the influence of neighbouring slip planes may be neglected and the classical solution for a single slip plane applies. At a larger distance a linear decay is obtained. The characteristic length scales of the two parts of the pile-up are shown to depend differently on the parameters of the problem.