Critical Behavior of a Strain Percolation Model for Metals

Published

April 1, 2002

Author(s)

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

Abstract

Extensive simulations of a strain percolation model for a deforming metal have been performed to examine its strain behavior. We find that the total strain exhibits critical power-law behavior that is well explained by two-dimensional percolation theory. Near the critical point, most of the strained cells organize themselves around a state having the minimum or at least marginally stable strain regardless of the initial conditions. A strain much greater than the manimum stable strain generally decays to a lower value when transmitted to an unstrained cell. The universal behavior of the total strain in the system is a consequence of the self-organizing character of the strain in the critical cluster. Although the probability distributions for the total strain and cluster size appear to exhibit non-universal this may merely represent a transient response before crossover to a true asymptotic, universal behavior occurs. Other critical aspects of the model are also discussed.

Citation

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

Volume

65

Issue

No. 4

Pub Type

Journals

Keywords

dislocations, finite-scaling theory, percolation, self-organizing criticality

Citation

Shim, Y. , Levine, L. and Thomson, R. (2002), Critical Behavior of a Strain Percolation Model for Metals, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) (Accessed October 14, 2025)