A computationally efficient implementation of continuum dislocation dynamics: Formulation and application to ultrafine-grained Mg polycrystals. (March 2023)

• Record Type: Journal Article
• Authors: Luo, Xi; Zaiser, Michael
• Is Part Of: Journal of the mechanics and physics of solids. Volume 172(2023)
• Publication Date: 2023-03
• Subjects: Continuum dislocation dynamics -- Dislocation transport -- Back stress -- Crystal plasticity; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2022.105166
• Languages: English
• ISSNs: 0022-5096

Abstract

Abstract: Continuum dislocation dynamics (CDD) represents the evolution of systems of curved and connected dislocation lines in terms of density-like field variables which include the volume density of loops (or 'curvature density') as an additional field. Since dislocation curvature represents a spatial derivative of the underlying discrete dislocation density tensor, the curvature field evolution equation of necessity contains numerically inconvenient higher-order derivatives of the density fields. We propose a simple approximation to express curvature in terms of density fields, and demonstrate its application to a benchmark problem in deformation of Mg polycrystals. Highlights: Dislocation curvature is approximately expressed by density fields. Back stress related to spatial derivatives of dislocation densities is considered. High-efficient FFT based spectral method is used to solve the boundary value problem. This CDD model is a promising tool for high-throughput calculations of polycrystals.