A First Experiment at Interfacing Crystal Plasticity and Continuum Dislocation Dynamics

Abstract

A computational approach has been developed for the analysis of the properties of 3D dislocation substructures generated by the vector density continuum dislocation dynamics (CDD), within the framework of crystal plasticity. In the CDD framework, the dislocation density on the individual slip systems is represented by vector fields with a unique dislocation line direction at each point in space. The evolution of these density fields is governed by a set of transport-reaction equations coupled with crystal mechanics. This detailed picture of the dislocation system enables mesoscale plasticity simulations based on dislocation properties at the lattice level. In the current work, a computational approach based on streamline construction is proposed to obtain the statistical properties of the dislocation substructures generated by CDD. Streamlines are obtained by travelling along the tangent of the vector density and velocity fields of the dislocation system, which enables us to construct the dislocation lines and their paths in the deformed crystal in 3D. The streamlines are computed by numerical integration of a set of partial differential equations for the parameterized tangent fields. Here, we use this approach to extract microstructure parameters from the CDD simulations that are relevant to substructure-sensitive crystal plasticity models. These parameters include the mean free path and average mobile dislocation segment length, as well as the dislocation wall volume fraction, together with the corresponding distributions. The results show that, past a short initial rise during monotonic loading, both the mobile dislocation segment length and dislocation mean free path decrease with the applied strain, which is consistent with the models used in the crystal plasticity literature.