Numerical Computation of Material Properties of Nanocrystalline Materials Utilizing Three-Dimensional Voronoi Models

Nanocrystalline metals have been the cause of substantial intrigue over the past two decades due to their high strength, which is highly sensitive to their microstructure. The aim of the present project is to develop a finite element two-phase model that is able to predict the elastic moduli and the yield strength of nanostructured material as functions of their microstructure. The numerical methodology uses representative volume elements (RVEs) in which the material microstructure, i.e., the grains and grain boundaries, is presented utilizing the three-dimensional (3D) Voronoi algorithm. The implementation of the 3D Voronoi particles was performed on the nanostructure investigation of ultrafine materials by SEM and TEM. Proper material properties for the grain interiors (GI) and grain boundaries (GB) were computed using the Hall-Petch equation and a dislocation-based analytical approach, respectively. The numerical outcomes show that the Young’s Modulus of nanostructured copper increased by increasing the crystallite volume fraction, while the yield strength increased by decreasing the grain size. The numerical predictions were strongly confirmed in opposition to finite element outcomes, experimental results from the open literature, and predictions from the rule of mixtures and the Mori-Tanaka analytical models.