This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to Saved Citations Download to citation manager Request Permissions Request Reprints Add to My Marked Citations Citing Articles Citing Articles via Google Scholar Citing Articles via Scopus Google Scholar Articles by Vinogradov, V. Articles by Willis, J.R. Search for Related Content Social Bookmarking                         What's this?

The Pair Distribution Function for an Array of Screw Dislocations: Implications for Gradient Plasticity

Department of Applied Mathematics and, Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK

J.R. Willis

Department of Applied Mathematics and, Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK

The problem of spatial correlation within an array of dislocations in a two-dimensional crystalline solid is addressed. A system of equations for joint probability densities is derived based on the assumption that the force on each dislocation remains finite. For arrays of screw dislocations moving on several slip planes the equations are consistent with balanced positive and negative dislocations forming dipoles or mutually cancelling, leaving geometrically necessary dislocations to interact and correlate. The resulting pair distribution function for the geometrically necessary screw dislocations is found, and used to demonstrate the strain gradient correction emerging in the case of micro-scale plasticity.

Key Words: Dislocations • pair distribution functions • strain-gradient plasticity

Mathematics and Mechanics of Solids, Vol. 14, No. 1-2, 161-178 (2009)
DOI: 10.1177/1081286508092609


CiteULike    Complore    Connotea    Del.icio.us    Digg    Reddit    Technorati    Twitter    What's this?