On the grain-size-dependent elastic modulus of nanocrystalline materials with and without grain-boundary sliding

A closed-form model was proposed to evaluate the elastic properties of nanocrystalline materials as a function of grain size. Grain-boundary sliding, present in nanocrystalline materials even at relatively low temperatures, was included in the formulation. The proposed analytical model agrees reasonably well with the experimental results for nanocrystalline copper and palladium.