We present simulations of the dissociation of perfect dislocations into extended partial dislocations in aluminum, palladium, and nickel using a phase field dislocation dynamics (PFDD) theory that incorporates the $\gamma$ surface. As expected from dislocation theory, the simulations show that increasing the intrinsic stacking fault energy, normalized by the product of the shear modulus and Burgers vector, decreases the equilibrium stacking fault width. Significantly, it is also found that increasing the unstable stacking fault energy has the same effect when the intrinsic stacking fault energy is held constant. Furthermore, our results show that the equilibrium configurations cannot be described only by the ratio between the intrinsic and unstable stacking fault energies as previously suggested but rather by their product.

In this paper, we discuss the formulation, recent developments and findings obtained from a mesoscale mechanics technique called phase field dislocation dynamics (PFDD). We begin by presenting recent advancements made in modelling face-centred cubic materials, such as integration with atomic-scale simulations to account for partial dislocations. We discuss calculations that help in understanding grain size effects on transitions from full to partial dislocation-mediated slip behaviour and deformation twinning. Finally, we present recent extensions of the PFDD framework to alternative crystal structures, such as body-centred cubic metals, and two-phase materials, including free surfaces, voids and bi-metallic crystals. With several examples we demonstrate that the PFDD model is a powerful and versatile method that can bridge the length and time scales between atomistic and continuum-scale methods, providing a much needed understanding of deformation mechanisms in the mesoscale regime.

Using a density functional theory-phase field dislocation dynamics model, we reveal a strong inverse relationship between the dislocation equilibrium core width and the normalized intrinsic stacking fault energy for nine face centered cubic (fcc) metals, in quantitative agreement with experiments but not with conventional continuum models. In addition, we show that due to an anomalous feature in its γ-surface, platinum has a fundamentally different core structure and a much wider equilibrium core width than expected. Based on ab initio electronic structure calculations, we attribute this anomaly to distinct differences in the directionality of charge transfer in platinum.