Scaling in Plasticity-Induced Microstructure: Cell Boundary Misorientation Distributions

We study the scaling form for the cell boundary misorientation angle distribution of Hughes and co-workers. By formulating the problem in terms of random walks in rotation space, we are able to incorporate the new cell boundaries formed during cell refinement with increasing deformation ǫ. The simplest form for the corresponding diffusion equation yields a good fit to the experimental scaling curve for the incidental boundaries, including the ǫ scaling of the average angle and the linear slope at small angles. We consider effects of crystalline anisotropy and strain gradients, and show that they also allow scaling collapses but change the form of the scaling function – yielding scaling but not universality. Existing theories formulated in terms of uncorrelated random dislocation motion exhibit the experimental scaling of average angle only if cell refinement is ignored.