A unified mechanistic model for Hall–Petch and inverse Hall–Petch relations of nanocrystalline metals based on intragranular dislocation storage

Abstract

Nanocrystalline (NC) metals often show transition from Hall–Petch (HP) strengthening to inverse HP softening as the average grain size decreases below a critical value. Compared to the HP behavior whose mechanism is well understood as the dislocation pile-up at grain boundaries (GBs), several hypotheses have been proposed to explain the veiled inverse HP behavior and no consensus has been reached yet. In this work, we propose a size-dependent model considering the influence of grain size on the intragranular dislocation storage ability and unify the HP and inverse HP relations for NC metals. The reduction of the intragranular dislocation storage ability with decreasing grain size is revealed as the underlying mechanism of the breakdown of the HP behavior in NC. Prediction of the critical grain size of 26.9nm for the HP-inverse HP transition of NC copper agrees well with experimental results. Numerical results suggest that the harmonized deformation of GB and grain interior (GI) dominates the remarkable ductility enhancement of NC metals in the inverse HP region. Moreover, our results suggest that the formation of dimple structures spanning several grains at fracture surfaces of NC metals is attributed to the coalescence of inter- and intra-granular microcracks and microvoids in clustered grains with Goss texture in local shear bands. As the GB strength increases, NC metals show enhancement in yield strength and delay in occurrence of the inverse HP behavior. Our studies give new insight into the contribution of GB sliding to the plastic behaviors of NC metals, and provide valuable guidance for the rational design of NC metals with high ductility and high strength.