Size-dependent yield stress in ultrafine-grained polycrystals: A multiscale discrete dislocation dynamics study

In this study, the effects of grain size and dislocation source properties on the yield stress of ultrafine-grained (UFG) polycrystals were examined using three-dimensional multiscale discrete dislocation dynamics (DDD). A polycrystal model containing multiple grains with randomly distributed orientations was constructed within a multiscale DDD framework. Grain boundaries (GBs) were assumed to be penetrable by dislocations, with two dislocation-GB interaction mechanisms, i.e., dislocation absorption at GBs and dislocation emission from GBs, being considered. The simulation investigated the dislocation source effect and demonstrated a nonmonotonic dependency of flow stress on dislocation source length, where the lowest flow stress corresponds to a Frank-Read (FR) source length of d/4 where d is the grain size. When the length of a FR source in the polycrystalline sample exceeds this value, the simulated yield stress increases owing to the constraining effect of grain boundaries on dislocation movement. The grain size dependence of the yield stress shows deviations from the classical Hall-Petch relationship as the exponent in the Hall-Petch type relation ranges from about 0.91 to about 0.98, depending on the initial dislocation density in the samples. Detailed analysis indicates that the grain size dependence of the yield stress is mainly controlled by the effect of grain boundary constraints on dislocation activation. A secondary effect arises from grain size dependent dislocation accumulation and the resulting Taylor hardening. The activation and operation of FR sources were quantitatively examined to further understand the origins of source length and grain size effects. A theoretical model is proposed to account simultaneously for the effects of source length, grain size, and initial dislocation density on the yield stress of polycrystals in the UFG regime.