Attention was focussed on the mathematical and computational modelling of dislocation correlations in the context of the dislocation dynamics modelling of mesoscale plasticity. A hierarchical system of kinetic equations which described the evolution of dislocation densities of various orders was presented in order to illustrate the role played by correlation in dislocation dynamics. This was followed by a mathematical description of the spatial and line-orientation statistics of dislocation systems within the framework of stochastic fibre processes. Within this framework, the pair correlation was related to the second moment measure of the dislocation distribution in the crystal and dislocation line-tangent spaces. The stochastic fibre process description of correlation was used, in conjunction with the method of dislocation dynamics simulation, to compute the pair correlation in both face-centered cubic and body-centered cubic crystals undergoing small homogeneous plastic deformations at a constant rate. An edge correction scheme was used, as part of the methodology, for computing the pair correlation. The main characteristics of correlations, including oscillatory behaviour, anisotropy and symmetry, were studied in detail. The self-correlations and cross-correlations of dislocations of various species were compared.

Mathematical and Computational Modelling of Correlations in Dislocation Dynamics. J.Deng, A.El-Azab: Modelling and Simulation in Materials Science and Engineering, 2009, 17[7], 075010