Simulation and theory of polygonization in single glide

We present the results of numerical simulations of two-dimensional polygonization, the simplest example of dislocation patterning. The simulations are based on the elastic interactions of straight edge dislocations, with a law of motion that combines fast glide with slow climb. The simulated patterns reproduce experimental patterns for Fe-Si quite well. The effects of changing the Peierls stress for glide processes, or immobilizing some of the dislocations, are addressed. Decreasing the Peierls stress and increasing the fraction of mobile dislocations speeds up the pattern formation process. The energy release at short times is dominated by the disorder in walls, and at longer times by wall-spacing effects. We provide insight into the dynamics of wall coarsening via the concept of random dislocation walls. The applicability of continuum flow equations is evaluated. We find that description of the polygonization process in terms of the dislocation configuration tensor is inadequate.