On the “Anomalous” hardness of nanocrystalline materials

The present paper is a further contribution on a rule of mixtures approach for the prediction of hardness dependence on grain size for nanocrystalline metals and intermetallics. Different behavior for the “bulk” and the “grain boundary” regions is assumed in order to consider the special features of nanocrystalline materials, such as the arrangement of geometrically necessary dislocations and disclinations. The usual Hall-Peteh (HP) relationship is assumed to describe the hardness dependence for each one of the two regions. A “correction” term is introduced for the HP slope of the boundary region as compared to the grain interior HP slope. An integrated formula for the total hardness H is obtained involving the grain size, the grain boundary width, the hardness characteristics of coarse grain counterparts and an extra parameter describing the arrangement of triple junctions. This formula compares well with a large set of experimental data.