Multi-scale plasticity modeling: Coupled discrete dislocation and continuum crystal plasticity

A hierarchical multi-scale model that couples a region of material described by discrete dislocation plasticity to a surrounding region described by conventional crystal plasticity is presented. The coupled model is aimed at capturing non-classical plasticity effects such as the long-range stresses associated with a density of geometrically necessary dislocations and source limited plasticity, while also accounting for plastic flow and the associated energy dissipation at much larger scales where such non-classical effects are absent. The key to the model is the treatment of the interface between the discrete and continuum regions, where continuity of tractions and displacements is maintained in an average sense and the flow of net Burgers vector is managed via “passing” of discrete dislocations. The formulation is used to analyze two plane strain problems: (i) tension of a block and (ii) crack growth under mode I loading with various sizes of the discrete dislocation plasticity region surrounding the crack tip. The computed crack growth resistance curves are nearly independent of the size of the discrete dislocation plasticity region for region sizes ranging from 30μm×30μm to 10μm×5μm. The multi-scale model can reduce the computational time for the mode I crack analysis by a factor of 14 with little or no loss of fidelity in the crack growth predictions.