A link between microstructure evolution and macroscopic response in elasto-plasticity: formulation and numerical approximation of the higher-dimensional Continuum Dislocation Dynamics theory

TL;DR

This paper formulates a higher-dimensional continuum dislocation dynamics theory within single-crystal plasticity and develops a numerical scheme to simulate dislocation behavior, revealing key features like fluxes and curvature in small-scale plasticity.

Contribution

It introduces a concise formulation of hdCDD in a general plasticity context and provides a numerical implementation with analysis of boundary conditions and dislocation features.

Findings

Dislocation fluxes significantly influence small-scale plasticity.

Boundary conditions affect dislocation behavior and material response.

Numerical simulations demonstrate the importance of curvature in dislocation dynamics.

Abstract

Micro-plasticity theories and models are suitable to explain and predict mechanical response of devices on length scales where the influence of the carrier of plastic deformation - the dislocations - cannot be neglected or completely averaged out. To consider these effects without resolving each single dislocation a large variety of continuum descriptions has been developed, amongst which the higher-dimensional continuum dislocation dynamics (hdCDD) theory by Hochrainer et al. (Phil. Mag. 87, pp. 1261-1282) takes a different, statistical approach and contains information that are usually only contained in discrete dislocation models. We present a concise formulation of hdCDD in a general single-crystal plasticity context together with a discontinuous Galerkin scheme for the numerical implementation which we evaluate by numerical examples: a thin film under tensile and shear loads. We study the influence of different realistic boundary conditions and demonstrate that dislocation fluxes and their lines' curvature are key features in small-scale plasticity.