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

A hierarchical multiscale model that couples a region of material described by discrete dislocation plasticity1 to a surrounding region described by conventional crystal plasticity is presented. The coupled model captures size-dependent plasticity phenomena, such as dislocation structuring and formation of geometrically necessary dislocations, that can occur at the micron scale while also capturing the plastic flow, and associated energy dissipation, at much larger scales where size-dependent effects are minimal. 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 burgers vector via "passing" of discrete dislocations is managed. The model is validated through uniaxial plane-strain tension tests which show that the coupled model deforms similarly to both single-scale models. The multiscale model is then applied to study crack growth, where both near-tip dislocation structures and far-field plastic dissipation are crucial to the overall toughening. Results show that the toughening is nearly independent of the size of the discrete dislocation plasticity region around the crack tip down to 5um, simultaneously validating the model and identifying the lengths scales over which size dependence plays a role in this problem. The multiscale model reduces the computational burden of discrete dislocation plasticity modeling substantially with little or no loss of fidelity in the predictions of material behavior, thereby greatly extending the range of discrete dislocation modeling. Future work will combine this method with the Coupled Atomistic/Discrete-Dislocation2 model developed by one of the co-authors, leading to a true atom-to-continuum multiscale model for metallic materials.