The problem of dislocation patterning and interaction of threading dislocations with immobile dislocation loops and defects was investigated analytically and computationally based upon a statistical analysis and a recently developed model of discrete stochastic dislocation dynamics, respectively. The statistical analysis was based upon the Friedel–Kocks model and showed the validity of the Friedel relation for the critical resolved stress while a power law with different stress dependence was obtained for the average pinning distance on a stable dislocation array. The difference of the stress dependence was attributed to each model assumptions, such as stable dislocation configurations in athermal system or meta-stable configurations in thermally activated system. The stochastic dislocation dynamics computational study includes thermal and strain fluctuation, predicting non-trivial fractal instability of the plastic strain. The height difference correlations of the plastic strain showed that the external load caused a multifractality, and enhances the instability at higher order moments.

On Dislocation-Defect Interactions and Patterning - Stochastic Discrete Dislocation Dynamics. M.Hiratani, H.M.Zbib: Journal of Nuclear Materials, 2003, 323[2-3], 290-303