Scaling of dislocation cell structures: Diffusion in orientation space

Abstract

This paper examines the idea that the evolution of self-organizing dislocation cells is dominated by random fluctuations in cell orientation. The development of the dislocation cell misorientation distributions during deformation is treated on the basis that noise causes the cell orientations to random walk in orientation space. We solve the orientation equivalent of Fick's second law to get a time-dependent solution for the orientation distributions, misorientation distributions and the strain dependence of the average misorientation angle. In the low-angle limit, average misorientation is proportional to the square root of the strain, and the misorientation distributions scale with the average misorientation angle, in agreement with the experiment. The analysis predicts an infinite number of possible scaling states and not a universal curve, as seen in practice. This discrepancy is discussed.