Spatial distribution of local elastic moduli in nanocrystalline metals

Elastoplastic properties of nanocrystalline metals are nonuniform on the scale of the grain size, and this nonuniformity affects macroscopic quantities as, in these systems, a significant part of the material is at or adjacent to a grain boundary. We use molecular dynamics simulations to study the spatial distributions of local elastic moduli in nanograined pure metals and analyze their dependence on grain size. Calculations are performed for copper and tantalum with grain sizes ranging from 5 to 20 nm. Shear-modulus distributions for grain and grain-boundary atoms were calculated. It is shown that the noncrystalline grain boundary has a wide shear-modulus distribution, which is grain-size independent, while grains have a peaked distribution, which becomes sharper with increasing grain size. Average elastic moduli of the bulk, grains, and grain boundary are calculated as a function of grain size. The atomistic simulations show that the reduction of total elastic moduli with decreasing grain size is mainly due to a resulting larger grain-boundary atoms fraction, and that the total elastic moduli can be approximated by a simple weighted average of larger grain elastic moduli and a lower grain-boundary elastic moduli.