Critical Behavior of a Strain Percolatin Model for Metals with Unstable Locks
Y Shim, Lyle E. Levine, R M. Thomson, M Savage
Using a strain percolatin 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 which may be broken by the stress field of incident dislocations. The presence of such locks changes dramatically some of characteristic features of the system. One such change is a fractal distribution of broken locks within a strained cluster with a model parameter-dependent critical point. It is shown that this problem is a percolation problem within a percolation problem. 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 that is well explained by two-dimensional standard percolation theory. This random aspect of the model at large scales appears to arise from a self-organizing critical behavior of cells which try to develop a minimun stable strin.
Physica A-Statistical Mechanics and Its Applications
, Levine, L.
, Thomson, R.
and Savage, M.
Critical Behavior of a Strain Percolatin Model for Metals with Unstable Locks, Physica A-Statistical Mechanics and Its Applications
(Accessed November 30, 2021)