We present an approach for the spatial and temporal coarse-graining of dislocation dynamics and the development of dislocation-based mesoscale plasticity theory of crystals. The effectiveness of this approach will be demonstrated by predicting (a) the formation of dislocation cell structure under monotonic loading of copper, in conjunction with the famous similitude law for the inverse dependence of average cell size on stress, and (b) the vein structure characteristic of dislocation patterning under cyclic loading. The coarse graining of dislocation dynamics is based on the framework of statistical mechanics, in the spirit of the classical kinetic theory, which leads to transport equations for dislocations coupled with crystal mechanics, plus a closure problem consisting of finding the spatial and temporal correlations of the dislocation system. While our previous work focused on the estimation of the spatial correlations of dislocation systems, we describe in this presentation how to estimate the temporal correlations from time series analysis of cross slip and dislocation reactions in discrete dislocation dynamics. We further show how to use those temporal correlations to coarse grain these events in time, while keeping their stochastic characteristics. The overall approach has been used to obtain a full solution of the deformation problem, which includes the dislocation patterns, plastic deformation pattern and distorted shape, internal elastic fields, and average stress-strain response. This approach also reveals the critical role of cross slip is cell structure formation under monotonic loading, and the relative suppression of this role when cyclic loading is applied. The change in pattern type due to change on loading only (keeping the initial conditions and all physics the same) is a strong indication that the current approach is adequate. The presentation consists of a short review of relevant models, a description of the mathematical framework of dislocation coarse graining, and a 3D solution of the problem of mesoscale plasticity using a novel finite element approach.

This work is performed in collaboration with Shengxu Xia, a doctoral student of Materials Engineering at Purdue University. The work was supported by the U.S. Department of Energy and Purdue University.