Study of yield strength size dependence by three-dimensional, intensive microstructures dislocation-density function dynamics

The smaller-being-stronger size effect of sub-micron to micron scale crystals is studied using a new dislocation-density function dynamics approach and the results are compared to previous micro-pillar experiments. While it is computationally expensive for discrete dislocation dynamics schemes to handle high quantities of dislocations, the new full dynamics approach can simulate dislocation activities in meso-scale samples with high dislocation density. In this scheme dislocations are represented in terms of densities instead of discrete lines of dislocations.

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 and is a realistic description of the interactions between dislocations. In this project, 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. Realistic deformation behaviour of metals can be simulated using this scheme.

This new simulator considers the flux, production due to connectivity, annihilation and the elastic interactions between dislocation densities. A coarse-graining procedure is adopted to capture discrete dislocation events. The three-dimensional specimens used in the simulation have single slip system and can simulate stage I hardening, which is the dominant hardening mode observed in experiments of micro-pillars. The simulation results show that micron scale crystals exhibit a smaller-being-stronger size dependence of yield strength.