A discrete dislocation dynamics framework for modelling plasticity in two-phase polycrystals

Mechanism based discrete dislocation dynamics framework for modelling plasticity in metallic materials with the morphology of the underlying grains resembling an actual microstructure is extended to incorporate a second-phase. The formulation includes mechanisms that account for dislocation self-interactions and interactions with grain boundaries vis-a-vis grain boundary slip transmission. Dislocation interactions within the constituent grains result in the entangling of dislocations, forming locks essential for controlling various hardening phenomena by obstructing dislocation motion or nucleating fresh dislocations. The presence of the second-phase particle on the emergent mechanical response is studied under various conditions. Results depict an increase in strain hardening rate with increasing second-phase volume fraction until a point where the dimensions of the second-phase approach the grain size. Further, the dislocation-grain boundary interactions in the presence of dislocation self-interactions on the strain hardening are also analyzed. Towards the end, the scaling of yield stress with grain size in the presence of the second-phase is also investigated. The analysis is aided by providing spatial distribution of relevant components of stress and geometrically necessary dislocation density, contributing to the essential hardening mechanisms that lead to the observed effects of second-phase on polycrystalline materials.