Critical Behavior of a Strain Percolatin Model for Metals with Unstable Locks

Published

October 12, 2021

Author(s)

Y Shim, Lyle E. Levine, R M. Thomson, M Savage

Abstract

Using a strain percolatin model proposed for the transport of mobile dislocations through a dislocation cell structure in a deforming metal, we have further explored the critical behavior of the model when there are some unstable locks present in the system which may be broken by the stress field of incident dislocations. The presence of such locks changes dramatically some of characteristic features of the system. One such change is a fractal distribution of broken locks within a strained cluster with a model parameter-dependent critical point. It is shown that this problem is a percolation problem within a percolation problem. In the critical regime, growth of a strained cluster as well as the distribution of broken locks within the cluster exhibits universal power-law behavior that is well explained by two-dimensional standard percolation theory. This random aspect of the model at large scales appears to arise from a self-organizing critical behavior of cells which try to develop a minimun stable strin.

Citation

Physica A-Statistical Mechanics and Its Applications

Pub Type

Journals

Keywords

dislocations, percolation, self-organizing criticality

Citation

Shim, Y. , Levine, L. , Thomson, R. and Savage, M. (2021), Critical Behavior of a Strain Percolatin Model for Metals with Unstable Locks, Physica A-Statistical Mechanics and Its Applications (Accessed January 30, 2025)