The inverse hall–petch relation in nanocrystalline metals: A discrete dislocation dynamics analysis

When the grain size in polycrystalline materials is reduced to the nanometer length scale (nanocrystallinity), observations from experiments and atomistic simulations suggest that the yield strength decreases (softening) as the grain size is decreased. This is in contrast to the Hall–Petch relation observed in larger sized grains. We incorporated grain boundary (GB) sliding and dislocation emission from GB junctions into the classical DDD framework, and recovered the smaller is weaker relationship observed in nanocrystalline materials. This current model shows that the inverse Hall–Petch behavior can be obtained through a relief of stress buildup at GB junctions from GB sliding by emitting dislocations from the junctions. The yield stress is shown to vary with grain size, d, by a d1/2 relationship when grain sizes are very small. However, pure GB sliding alone without further plastic accomodation by dislocation emission is grain size independent.