Effect of waviness and orientation of carbon nanotubes on random apparent material properties and RVE size of CNT reinforced composites

A computational procedure is proposed in this paper for the determination of mesoscale random fields and of the representative volume element (RVE) size of carbon nanotube reinforced composites (CNT-RCs). To this purpose, computer-simulated images of composites with specific weight fraction (wt) of randomly scattered CNTs are examined. The cases of randomly oriented and unidirectionally aligned CNTs with random wavy and straight geometry are considered. A stochastic description of the random CNT waviness is adopted based on real measurements. The proposed approach takes into account the local weight fraction variability by processing statistical volume elements (SVEs) extracted directly from the composite images using the moving window technique. Computational homogenization is applied on various SVE finite element models using both kinematic and static uniform boundary conditions. The response statistics of the SVE models are obtained with Monte Carlo simulation. In this way, the statistical characteristics of the upper and lower bounds of the apparent material properties are effectively computed. The RVE size is defined within a prescribed tolerance, by examining the convergence of these two bounds. The effect of waviness and orientation of CNTs on the mechanical responses, mesoscale random fields and RVE size of CNT-RCs is particularly highlighted.