Development of an RVE and its stiffness predictions based on mathematical homogenization theory for short fibre composites

Abstract

In this study an attempt is made to generate the microstructure of short fibre composites through representative volume element (RVE) approach and then analyzed using mathematical theory of homogenization with periodic boundary conditions to estimate the homogenized or effective material properties. An algorithm, based on random sequential adsorption technique (RSA), has been developed to generate the RVE for such materials. The goal of the present study is to demonstrate the methodology to generate RVEs which are effective in predicting the stiffness of the short fibre composites with repetitiveness. For this purpose, RVEs for four different scenarios of fibre orientations have been developed using this technique. These four different scenarios are: Fibres are aligned in a direction; fibres are oriented randomly in one plane; fibres are randomly oriented in one plane and partially random oriented in other plane and finally, fibres are completely random oriented. For each case three to four different fibre volume fractions are studied with five different RVEs for each volume fraction. These four cases presented different material behaviour at macroscale due to random location and orientation of fibres. The effective properties obtained from numerical technique are compared with popular non RVE methods like Halpin–Tsai and Mori–Tanaka methods for the case where fibres are aligned in a direction and were found to be in good agreement. The variation in the predicted properties for a given volume fraction of any of the four cases studied is less than 1%, which indicates the efficacy of the algorithm developed for RVE generations in repetitiveness of predicted effective properties. The four cases studied showed gradual change in macroscopic behaviour from transversely isotropic, with respect to a plane, to a nearly isotropic nature.