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

Adriana Garroni, Patrick van Meurs, Mark A Peletier, Lucia Scardia

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
133 Downloads (Pure)

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 modelling the interactions of the walls subjected to a constant shear stress, we derive a first-order approximation of the energy by Γ-convergence. While the first term in the expansion captures the `bulk' profile of the density of dislocation walls in the pile-up domain, the next-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.
Original languageEnglish
Pages (from-to)2735-2768
JournalMathematical Models & Methods in Applied Sciences
Volume26
Issue number14
DOIs
Publication statusPublished - 30 Dec 2016

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