A simple, mixtures-based model for the grain size dependence of strength in nanophase metals

A model is presented for the strength of nanophase metals. The model assumes that polycrystalline metals consist of two phases: the “bulk” intragranular regions, and the “grain boundaries”. The boundary phase is treated as a glassy, but not highly rate-dependent material with a constant strength equal to that of the amorphous metal. The crystalline phase is assumed to follow a Hall-Petch equation for the grain-size dependence of strength. Treating the material as a composite, with a rule of mixtures approach, predicts a change in the Hall-Petch slope at small grain sizes, as has been observed. Grain size softening is predicted, but not until sizes below 5 nm. The model is compared to data in the literature.