Scaling in plasticity-induced cell-boundary microstructure: Fragmentation and rotational diffusion

We develop a simple computational model for cell-boundary evolution in plastic deformation. We study the cell-boundary size distribution and cell-boundary misorientation distribution that experimentally have been found to have scaling forms that are largely material independent. The cell division acts as a source term in the misorientation distribution which significantly alters the scaling form, giving it a linear slope at small misorientation angles as observed in the experiments. We compare the results of our simulation with two closely related exactly solvable models that exhibit scaling behavior at late times: (i) fragmentation theory and (ii) a random walk in rotation space with a source term. We find that the scaling exponents in our simulation agree with those of the theories, and that the scaling collapses obey the same equations, but that the shape of the scaling functions depends upon the methods used to measure sizes and to weight averages and histograms.