Development, validation and analysis of an efficient micro-scale representative volume element for unidirectional composites

Abstract

In the present work, a simple procedure to build periodic representative volume elements (RVE) is developed for UD composite laminae. The procedure is based on the alteration of an initially regular fibre distribution, and includes the possibility to start from different fibre configurations, to use of non-uniform fibre diameter, and for fibres to cross the RVE edges.The obtained RVEs were found to differ from a theoretical hard-core process in terms of Voronoi equivalent radius distribution and nearest neighbour distribution, for which a novel analytical method is proposed. The fibre distributions were instead in good agreement with real microstructures in terms of both short- and long-range morphological indexes, especially when the actual fibre diameter distribution is used. A novel short-range index, called neighbour distance diagram, is also proposed to represent the distances of all the fibre neighbours.The RVEs were then compared to real microstructures in terms of stress distributions. The Cumulative Distribution Function (CDF) of Local Maximum Principal Stress (LMPS) and the Local Hydrostatic Stress (LHS) in the matrix are calculated under transverse, shear and longitudinal stresses and under a temperature gradient, validating the RVE also under a mechanical point of view. Using uniform fibre diameter was found not to have a significant influence on the stress distributions.Eventually, a parametric analysis was carried out to analyse the influence of the fibre volume fraction on LMPS and LHS CDF, under both mechanical and thermal loading conditions.