Spatial distribution of local elastic moduli in nanocrystalline metals

Elastoplastic properties of nanocrystalline metals are non-uniform on the scale of the grain size, and this non-uniformity 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 nano-grained pure metals and analyze their dependence on grain size. Calculations are performed for copper and tantalum with grain sizes ranging from 5-20nm. Shear modulus distributions for grain and grain-boundary atoms were calculated. It is shown that the non-crystalline 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 grains elastic moduli and a lower grain-boundary elastic moduli.