Computation of elastic moduli of nanocrystalline materials using Voronoi models of representative volume elements

In the present work, a numerical model is developed to predict the Young’s modulus and shear modulus of nanocrystalline materials using a Finite Element Analysis. The model is based on Representative Volume Elements (RVE) in which the microstructure of the material is described using the Voronoi tessellation algorithm. The use of the Voronoi particles was based on the observation of the morphology of nanocrystalline materials by Scanning Electron and Transmission Electron Microscopy. In each RVE, three-dimensional modelling of the grain and grain boundaries as randomly-shaped sub-volumes is performed. The developed model has been applied to pure nanocrystallline copper at grain volume fractions of 80%, 90% and 95% taking also into account the parameters of grain size and grain boundary thickness. The elastic moduli of nanocrystalline copper have been computed by loading the RVE in tension. The numerical results reveal that the elastic moduli of nanocrystalline copper increase with increasing the grain volume fraction. On the other hand, for a given grain volume fraction, the results showed no effect of the grain size. The model predictions have been validated successfully against numerical results from the literature and predictions of the Rule of Mixtures and the Mori-Tanaka analytical model.