A probabilistic theory for the strength of discontinuous fibre composites

Abstract

The strength of discontinuous fibre-reinforced composites is often reduced due to local stress concentrations at large fibre-end-gaps. A theoretical prediction of the strength of unidirectional fibre composites is performed based upon a probabilistic model of the fibre configuration. This work further develops the concepts of Bader, Chou and Quigley, and Fukuda and Chou. A limiting case of the present analysis shows good agreement with the results of Smith. Emphases are placed on the effect of matrix stress transfer properties including matrix plasticity. For a matrix deforming elastically, the strength is reduced as the composite size (N) increases. As compared with the rule-of-mixtures prediction for continuous fibre composites with identical fibre volume fraction, the reduction is shown to be proportional to (In N)−P, with the exponent P being between 0.5 and 1 for two-dimensional composites and between 0.25 and 0.5 for three-dimensional composites. For a matrix deforming plastically, the local stress concentrations are reduced. Based upon the analytical expression of the local load sharing rule for a plastically deformed matrix, the composite strength is shown to approach the modified rule-of-mixtures of Kelly and Tyson as the matrix yield stress decreases.