# Boundary-layer analysis of a pile-up of walls of edge dislocations at a lock

created by vanmeurs on 08 Sep 2018

[BibTeX]

preprint

Inserted: 8 sep 2018

Year: 2015

ArXiv: 1502.05805 PDF

Abstract:

In this paper we analyse the behaviour of a pile-up of vertically periodic walls of edge dislocations at an obstacle, represented by a locked dislocation wall. Starting from a continuum non-local energy $E_\gamma$ modelling the interactions$-$at a typical length-scale of $1/\gamma$$-$of the walls subjected to a constant shear stress, we derive a first-order approximation of the energy $E_\gamma$ in powers of $1/\gamma$ by $\Gamma$-convergence, in the limit $\gamma\to\infty$. While the zero-order term in the expansion, the $\Gamma$-limit of $E_\gamma$, captures the bulk' profile of the density of dislocation walls in the pile-up domain, the first-order term in the expansion is a boundary-layer' energy that captures the profile of the density in the proximity of the lock. This study is a first step towards a rigorous understanding of the behaviour of dislocations at obstacles, defects, and grain boundaries.

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