A Micromechanical Study of Fibre-Reinforced Composites with Uncertainty Quantification and Statically Equivalent Random Fibre Distribution

Abstract

The effects of manufacturing defects creates uncertainty on the mechanical response of unidirectional fibre-reinforced composites. These are studied through modelling of three-dimensional Representative Volume Element (RVE). In this study, an algorithm is developed to generate the microstructure of unidirectional fibre reinforced composite with both regular and random fibre distribution and then analyzed using mathematical theory of homogenization to estimate the homogenized or effective material properties. Here, the RVEs are modelled with random fibre distribution but increasing the number of fibres gradually and also randomly varying their positions. This variation in the randomness of the fibre distribution affects the effective properties. Also, the effect of different loading conditions is investigated. The significance of this structural distribution of heterogeneities on the overall effective behaviour is discussed for random structures and uncertainties that occur in composite materials. The variations in the predicted elastic properties for the given volume fraction of the above mentioned scenarios are compared with the experimental values and good agreement is achieved. There is a significant percentage change in transverse shear moduli, ${G_{23}}$ and $\nu _{23}$, which are 21.87 and 35.20% with respect to the experimental results.