A Proof of Taylor Scaling for Curvature-Driven Dislocation Motion Through Random Arrays of Obstacles

We prove Taylor scaling for dislocation lines characterized by line-tension and moving curvature under the action of an applied shear stress in a plane containing random array obstacles. Specifically, we show--in sense optimal scaling--that critical yielding, or percolation-like unbounded motion dislocation, scales proportion to square root obstacle density. For sufficiently small densities, dominates linear-scaling that results from purely energetic considerations and, therefore, characterizes dominant rate-limiting mechanism regime.