Asymptotic analysis of a pile-up of regular edge dislocation walls

Type
Article

Authors
Hall, Cameron L.

KAUST Grant Number
KUK-C1-013-04

Date
2011-12

Abstract
The idealised problem of a pile-up of regular dislocation walls (that is, of planes each containing an infinite number of parallel, identical and equally spaced dislocations) was presented by Roy et al. [A. Roy, R.H.J. Peerlings, M.G.D. Geers, Y. Kasyanyuk, Materials Science and Engineering A 486 (2008) 653-661] as a prototype 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 regular screw dislocation walls, but that numerical methods seem to be necessary for investigating regular 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 regular 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. © 2011 Elsevier B.V.

Citation
Hall CL (2011) Asymptotic analysis of a pile-up of regular edge dislocation walls. Materials Science and Engineering: A 530: 144–148. Available: http://dx.doi.org/10.1016/j.msea.2011.09.065.

Acknowledgements
This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).

Publisher
Elsevier BV

Journal
Materials Science and Engineering: A

DOI
10.1016/j.msea.2011.09.065

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