Effect of micro-randomness on macroscopic properties and fracture of laminates

Abstract

Composite materials demonstrate a considerable extent of heterogeneity. A non-uniform spatial distribution of reinforcement results in variations of local properties of fibrous laminates. This non-uniformity not only affects effective properties of composite materials but is also a crucial factor in initiation and development of damage and fracture processes that are also spatially non-uniform. Such randomness in microstructure and in failure evolution is responsible for non-uniform distributions of stresses in composite specimens even under externally uniform loading, resulting, for instance, in a random distribution of matrix cracks in cross-ply laminates. The paper deals with statistical features of a distribution of carbon fibres in a transversal cross-sectional area in a unidirectional composite with epoxy matrix, based on various approaches used to quantify its microscopic randomness. A random character of the fibres’ distribution results in fluctuations of local elastic moduli in composites, the bounds of which depend on the characteristic length scale. A lattice model to study damage and fracture evolution in laminates, linking randomness of microstructure with macroscopic properties, is discussed. An example of simulations of matrix cracking in a carbon fibre/epoxy cross-ply laminate is given.