Critical behavior of a strain percolation model for metals

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 minimum 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 nonuniversal behavior, 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.