Determination of the critical size of a statistical representative volume element (SRVE) for carbon reinforced polymers

Representative volume elements (RVEs) have been extensively used to estimate the elastic properties of fibre-reinforced composites. Most of them rely on the assumption of a periodic distribution of fibres which is not realistic. In order to reproduce damage phenomena, such as matrix cracking, it is necessary for volume element to represent properly the random distribution of fibres (distance to first neighbors, occurrence of clusters of fibres, etc.). Therefore, a statistical RVE (SRVE) should satisfy both mechanical and point pattern criteria. The present work establishes the size of a SRVE for a typical carbon fibre reinforced polymer. It is concluded that the minimum size is δ = L/R = 50 (L the side of the element and R the fibre radius).