Probabilistic aspects of strength of short-fiber composites with planar fibre distribution

The study of the fracture of short-fibre composites must involve statistics as an integral part. Two components of composite strength, each with probabilistic aspects, are described in this paper: fibre crossover reinforcement, and fibre gap bridging before fracture. The fibre crossover density is proposed as a measure of mutual fibre strengthening. and simulations are performed to estimate this density. Several different fibre orientations are proposed which have identical elastic properties but different crossover densities, indicating that more information is required for strength prediction than for elastic property prediction. The crossover density is a random variable whose average increases roughly as a fibre length squared function, and whose coefficient of variation decreases with increasing fibre length. The phenomenon of fibres bridging microcrocks is also examined as a fracture mechanism for fibres whose length well exceeds their critical length. General probabilistic expressions are derived which give the distribution of the number of fibres bridging a gap perpendicular to the applied load. These formulae are applied to the distribution of strength of an aligned fibre system.