Critical behavior of a strain percolation model for metals with unstable locks

Using a strain percolation 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 that may be broken by the stress field of incident dislocations. The presence of such locks changes dramatically some of the characteristic features of the system. One such change is a fractal distribution of broken locks within a strained cluster leading to a model parameter-dependent critical point. 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 well explained by ordinary two-dimensional percolation theory. This random aspect of the model at large scales appears to arise from a self-organizing critical behavior of cells that evolve into a state of a minimum stable strain.