Self-organized critical behavior in a deforming metal

It has been shown that the transport of mobile dislocations through blocking dislocation walls in a deforming metal can be treated by a simple percolation theory. Two different mechanisms for strain propagation are proposed in the strain percolation model. In the first case, the strain propagates between adjacent dislocation cells by activation of sources within the walls. In the second case, as an additional mechanism, unstable locks can be unzipped by a nearby dislocation pileup which can lead to a large localized strain. Previous simulations have shown that both cases belong to the same universality class as standard percolation. Further extensive simulations of the model have been performed to understand how the geometrical aspects of a strained percolating cluster are related to the strain itself. In our case, the strain is an additional variable not present in standard percolation theory. We find that the total strain and the mean strain per strained cell show power-law behavior in the critical regime, and obtain a scaling function which explains its critical behavior. Other percolation and critical aspects of the model are also discussed in terms of the initial strain, correlation length (which is a characteristic length scale), and model parameters.