A core-shell mean-field model with shell moduli calibrated to atomistic simulations reproduces the grain-size dependence of elastic moduli for eight cubic metals; the sign of that dependence flips with the Zener factor.
Gleiter, Nanostructured materials: basic concepts and microstructure, Acta Materialia 48 (1) (2000) 1 – 29
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Atomistic and mean-field estimates of effective stiffness tensor of nanocrystalline materials of cubic symmetry
A core-shell mean-field model with shell moduli calibrated to atomistic simulations reproduces the grain-size dependence of elastic moduli for eight cubic metals; the sign of that dependence flips with the Zener factor.