Asymptotic behavior of a strain percolation model for a deforming metal

In this paper, we present a recent advance in theoretical understanding of a deforming metal, using a strain percolation model which possibly explains spasmodic, fine slip line burst events occurring in the metal. The model addresses how the additional strain nucleated in a cell propagates through a dislocation cell structure, and predicts that near the critical point, the system exhibits critical power-law behavior. It is found that although the model displays long-transient behavior associated with the initial strain in the model, asymptotically critical behavior observed in the system is well explained by standard percolation theory. The long-transient behavior suggests that finite-size effects could be an important factor for the stress-strain relation in the metal. A detailed study reveals that the universal aspects of the model, i.e., the evolution into an initial condition-independent, critical state, arise from collective behavior of a huge number of self-organizing critical cells that develop the minimum or at least marginally stable strain.