Prediction of mechanical properties of nanocrystalline materials using Voronoi FE models of representative volume elements

Abstract

In the present work, a numerical model is developed to predict the mechanical properties 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 randomlyshaped sub-volumes is performed. The developed model has been applied to pure nanocrystallline copper taking into account the parameters of grain size and grain boundary thickness. The mechanical properties of nanocrystalline copper have been computed by loading the RVE in tension. The numerical results gave a clear evidence of grain size effect and the Hall-Petch relationship, which is a consequence of macroscopic strain being preferentially accumulated at grain boundaries. On the other hand, for a given grain volume fraction, the results for elastic moduli 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.