Self-organized critical behavior in a deforming metal

It has been shown that the transport of mobile dislocations through blockin g dislocation walls in a deforming metal can be treated by a simple percola tion theory. Two different mechanisms for strain propagation are proposed i n the strain percolation model. In the first case, the strain propagates be tween adjacent dislocation cells by activation of sources within the walls. In the second case, as an additional mechanism, unstable locks can be unzi pped by a nearby dislocation pileup which can lead to a large localized str ain. Previous simulations have shown that both cases belong to the same uni versality class as standard percolation. Further extensive simulations of t he 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 funct ion which explains its critical behavior. Other percolation and critical as pects of the model are also discussed in terms of the initial strain, corre lation length (which is a characteristic length scale), and model parameter s. (C) 2001 Elsevier Science B.V. All rights reserved.