A two-dimensional discrete dislocation simulation of the effect of grain size on strengthening behaviour

In this study, the evolution of the flow stress for grain sizes ranging from about 16 to 2 μm under shear deformation was simulated using two-dimensional discrete dislocation dynamics. The analyses were confined to a single slip system and to the collective behaviour of a large number of edge dislocations, modelled as line defects in elastic medium. A superposition technique, combined with boundary element method, was used to obtain the solution resulting from the dislocation microstructures and kinematic boundary conditions. The long-range interactions of dislocations were fully accounted for with the multi-pole algorithm without introducing an artificial cut-off radius. The dynamic behaviour of the dislocations, including lattice resistance to dislocation motion, dislocation nucleation and annihilation, were described by a set of constitutive rules in the simulation. Flow stress values increased with decreasing grain size and correlated with grain size in the form of classical Hall–Petch relationship (d)^−1/2. However, a similar correlation was also observed between the flow stress and grain size in the form of (d)⁻¹. The flow stress values for different grain sizes unified to a single curve when expressed as a function of the dislocation density normalized by the grain size. It was observed that dislocation pile-ups can both activate neighbouring dislocation sources and also shut down the active dislocation sources.