The Mathematical Institute, University of Oxford, Eprints Archive

Asymptotic analysis of a pile-up of edge dislocation

Hall, C. L. (2011) Asymptotic analysis of a pile-up of edge dislocation. Materials Science and Engineering A . (Submitted)

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Abstract

The idealised problem of a pile-up of dislocation walls (that is, of planes each containing an infinite number of parallel and identical dislocations) was presented by Roy et al. (Mater. Sci. Eng. A 486:653-661, 2008) as a proto-type for understanding the importance of discrete dislocation interactions in dislocation-based plasticity models. They noted that analytic solutions for the dislocation wall density are available for a pile-up of screw dislocation walls, but that numerical methods seem to be necessary for investigating edge dislocation walls. In this paper, we use the techniques of discrete-to-continuum asymptotic analysis to obtain a detailed description of a pile-up of edge dislocation walls. To leading order, we find that the dislocation wall density is governed by a simple differential equation and that boundary layers are present at both ends of the pile-up.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1391
Deposited By:Peter Hudston
Deposited On:08 Sep 2011 07:49
Last Modified:09 Feb 2012 14:01

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