Dynamic scaling in a simple one-dimensional model of dislocation activity

Authors: Deslippe, Jack¹; Tedstrom, R.¹; Daw, Murray S.¹; Chrzan, D.²; Neeraj, T.²; Mills, M.²

Source: Philosophical Magazine, Volume 84, Number 23, August 11, 2004 , pp. 2445-2454(10)

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Abstract:

We examine a simple one-dimensional (1D) model of dislocation activity, including a stress-activated source and mutually interacting dislocations. We demonstrate, through numerical and analytical steps, that the dislocations emitted from a 1D stress-activated source evolve towards a distribution which is self-similar in time, and we derive the power-law forms and distribution function. We show that the asymptotic distribution is a step function, and the dislocation front moves out linearly in time. The spacing between dislocations in the asymptotic distribution is uniform and increases logarithmically in time. The number of dislocations increases as t /ln( t ), and the strain increases as t 2 /ln( t ).

Document Type: Research article

DOI: http://dx.doi.org/10.1080/14786430410001690042

Affiliations: 1: Department of Physics and Astronomy Clemson University Clemson South California 29634 USA 2: Department of Materials Science and Engineering The Ohio State University Columbus Ohio 43210 USA

Publication date: 2004-08-01

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