A multi-scale crystal-plasticity finite-element framework coupled with efficient and minimalist continuum dislocation dynamics

Abstract

A long-standing challenge in computational crystal plasticity is to develop models for capturing real-sized stress-strain responses from detailed enough dislocation physics at the meso-scale. In this work, a multiscale crystal-plasticity finite-element, continuous dislocation dynamics (CDD) framework is constructed to meet this objective. In this framework, a finite-element method (FEM) is used to compute the macroscopic stress field at the resolution scale of the macro element, from the imposed boundary displacement and the plastic strain due to dislocation motion. The latter is computed at the CDD level by considering the dynamics of an ‘all-dislocation’ density driven by the FEM-level stress field from the applied loading, and the internal stress field due to mutual dislocation interactions at a mesoscopic resolution scale. Test cases of single- and multiple-element FEM for single- and poly-crystalline models of the face-centered crystal structure are studied under tensile, compressive and shear loading conditions, and the results indicate the expected flow anisotropy, stress concentration and plastic instability in these scenarios. This work is an important step towards building physics-based finite-element crystal plasticity models for simulating real-scale elasto-plasticity in metals and alloys.