On the role of dislocation conservation in single-slip crystal plasticity

Abstract

The objective of this paper is to evaluate the relevance of dislocation conservation within the context of dislocation-based crystal plasticity. In advanced crystal plasticity approaches, dislocations play a prominent role. Their presence, nucleation, motion, and interactions enable the explanation and description of physical phenomena such as plastic slip, hardening and size effects. While the conceptual aspects of the evolution and mechanical consequences of dislocations are treated analogously in a wide range of advanced crystal plasticity formulations, these formulations differ significantly with respect to the underlying dislocation conservation properties. This paper identifies and compares two essentially different approaches to model plastic deformations in a single crystal. Both approaches have in common that they rely on the geometrical relation between the plastic slip and the densities of geometrically necessary dislocations. In the first approach, the geometrical relation serves as a balance and is supplemented with an evolution law for the statistically stored dislocations. In the second approach the local conservation of the total number of dislocations is enforced in addition to the first balance instead of the evolution. Considering a single-slip model pile-up problem, the two representative frameworks are elaborated and confronted theoretically and numerically on the basis of a dimensionless finite-element analysis to evaluate the intrinsic role of dislocation conservation for model predictions.