Dislocation Density-Based Plasticity Model from Massive Discrete Dislocation Dynamics Database

TL;DR

This paper develops a dislocation density-based plasticity model for single crystal copper by analyzing extensive discrete dislocation dynamics data, capturing strain hardening behavior and slip system interactions.

Contribution

It introduces a generalized Taylor relation and a modified Kocks-Mecking model derived from DDD data, improving understanding of dislocation interactions during plastic deformation.

Findings

Model captures strain hardening rate dependence on loading orientation.

Logarithmic relation between flow stress and shear strain rate.

Dislocation multiplication depends on coplanar slip system activity.

Abstract

We present a dislocation density-based strain hardening model for single crystal copper through a systematic coarse-graining analysis of more than 200 discrete dislocation dynamics (DDD) simulations of plastic deformation under uniaxial tension. The proposed constitutive model has two components: a generalized Taylor relation connecting resolved shear stresses to dislocation densities on individual slip systems, and a generalized Kocks-Mecking model for dislocation multiplication. The DDD data strongly suggests a logarithmic dependence of flow stress on the plastic shear strain rate on each slip system, and, equivalently, an exponential dependence of the plastic shear strain rate on the resolved shear stress. Hence the proposed generalized Taylor relation subsumes the Orowan relation for plastic flow. The DDD data also calls for a correction to the Kocks-Mecking model of dislocation multiplication to account for the increase of dislocation density on slip systems with negligible plastic shear strain rate. This is accomplished by allowing the multiplication rate on each slip system to include contributions from the plastic strain rates of the two coplanar slip systems. The resulting constitutive model successfully captures the strain hardening rate dependence on the loading orientation as predicted by the DDD simulations, which is also consistent with existing experiments.