On dislocation–defect interactions and patterning: stochastic discrete dislocation dynamics (SDD)

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