The results of numerical simulations of 2-dimensional polygonization (the simplest example of dislocation patterning) were presented. The simulations were based upon the elastic interactions of straight edge dislocations; assuming a law of motion which combined rapid glide with slow climb. The simulated patterns reproduced quite well the experimental patterns for Fe-Si. The effects of changing the Peierls stress for glide, or of immobilizing some of the dislocations, were considered. It was found that decreasing the Peierls stress and increasing the fraction of mobile dislocations speeded up pattern formation. It was noted that the energy release at short times was dominated by the disorder in walls and, at longer times, by wall-spacing effects. Insight into the dynamics of wall coarsening was provided by the concept of random dislocation walls. The applicability of continuum flow equations was evaluated, and it was found that the description of polygonization in terms of the dislocation configuration tensor was inadequate.

Simulation and Theory of Polygonization in Single Glide. D.B.Barts, A.E.Carlson: Philosophical Magazine A, 1997, 75[2], 541-62