A new dislocation-density-function dynamics scheme for computational crystal plasticity by explicit consideration of dislocation elastic interactions

• An approach for numerical crystal plasticity by focusing on the dynamics of dislocation density functions is proposed.
• The convective flux movements of dislocation densities, mutual elastic interactions between dislocations, forest hardening, generation, annihilation and cross slip, are considered.
• Numerical implementation by the finite-volume method, which can handle high gradients, is discussed.
• Numerical examples performed for an Al model show typical strength anisotropy behavior comparable to experimental observations.
• For micron-sized crystals, the new approach can capture the well-known power-law relation between strength and size, low dislocation storage and jerky deformation.

Current strategies of computational crystal plasticity that focus on individual atoms or dislocations are impractical for real-scale, large-strain problems even with today’s computing power. Dislocation-density based approaches are a way forward but a critical issue to address is a realistic description of the interactions between dislocations. In this paper, a new scheme for computational dynamics of dislocation-density functions is proposed, which takes full consideration of the mutual elastic interactions between dislocations based on the Hirth–Lothe formulation. Other features considered include (i) the continuity nature of the movements of dislocation densities, (ii) forest hardening, (iii) generation according to high spatial gradients in dislocation densities, and (iv) annihilation. Numerical implementation by the finite-volume method, which is well suited for flow problems with high gradients, is discussed. Numerical examples performed for a single-crystal aluminum model show typical strength anisotropy behavior comparable to experimental observations. Furthermore, a detailed case study on small-scale crystal plasticity successfully captures a number of key experimental features, including power-law relation between strength and size, low dislocation storage and jerky deformation.