Numerical implementation of a crystal plasticity model with dislocation transport for high strain rate applications

Abstract

This paper details a numerical implementation of a single crystal plasticity model with dislocation transport for high strain rate applications. Our primary motivation for developing the model is to study the influence of dislocation transport and conservation on the mesoscale response of metallic crystals under extreme thermo-mechanical loading conditions (e.g. shocks). To this end we have developed a single crystal plasticity theory (Luscher et al (2015)) that incorporates finite deformation kinematics, internal stress fields caused by the presence of geometrically necessary dislocation gradients, advection equations to model dislocation density transport and conservation, and constitutive equations appropriate for shock loading (equation of state, drag-limited dislocation velocity, etc). In the following, we outline a coupled finite element–finite volume framework for implementing the model physics, and demonstrate its capabilities in simulating the response of a [1 0 0] copper single crystal during a plate impact test. Additionally, we explore the effect of varying certain model parameters (e.g. mesh density, finite volume update scheme) on the simulation results. Our results demonstrate that the model performs as intended and establishes a baseline of understanding that can be leveraged as we extend the model to incorporate additional and/or refined physics and move toward a multi-dimensional implementation.