The effects of grain size and dislocation source density on the strengthening behaviour of polycrystals: a two-dimensional discrete dislocation simulation

In this study, the evolution of the flow stress for grain sizes ranging from about 11 to 1 µm under shear deformation was examined using two-dimensional discrete dislocation dynamics. The grain boundaries were assumed to be both the only sources for nucleation of the dislocations and also the only obstacles to the dislocation motion. The analyses were confined to a single-slip system within each grain, with various orientations with respect to the slip system of neighbouring grains. The simulations were carried out for two sets of system sizes. In the first set of simulations the grain morphology was kept constant and the simulation unit cell size varied from 25 µm × 25 µm to 2.5 µm × 2.5 µm. In the second set of simulations the simulation unit-cell size was kept at 25 µm × 25 µm and the grain size was varied. For the grain-size ranges considered, an inverse relationship between the grain size and 0.2% offset flow stress in the form of the Hall–Petch relationship with a d −1/2 dependence was observed, although there is some uncertainty in the exponent. The evolution of flow stress follows a narrow band when expressed as a function of dislocation density divided by the dislocation source density and hence suggests a scaling with the grain size, as seen in an earlier study.