A probabilistic theory for the strength of discontinuous fibre composites

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. 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. 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.