A method of studying spatial and orientation statistics of dislocations in deforming crystals was presented. This method was based upon the use of the concept of a stochastic fiber process to model dislocations. Orientation-dependent statistical measures of the dislocation density, velocity and flux were introduced, and the connection between these statistical measures and the dislocation density tensor and rate of plastic distortion in deforming crystals was established. The parallel dislocation simulator code was used to conduct a simulation of dislocation systems in a body-centered cubic crystal and the numerical data of the simulated dislocation systems were used to compute the statistical measures introduced here. The orientation distributions of the density, velocity and flux of dislocations, as well as the dislocation correlations, were computed as functions of strain and strain rate. The results revealed previously unknown features of these distributions, which illustrates the importance of the statistical method introduced here in understanding the collective behavior of dislocation systems and building density-based models of dislocation dynamics.

Statistical Characterization of Dislocation Ensembles. A.El-Azab, J.Deng, M.Tang: Philosophical Magazine, 2007, 87[8-9], 1201-23