A percolation-type fracture criterion for composites with randomly oriented fibres

A fracture model is built up for a solid composed of brittle fibres randomly oriented in the matrix volume. The fracture process includes a stable growth of microcracks caused by fibre breaking under the load and formation of an infinite cluster of the microcracks. Both upper and lower bounds for ultimate stress in a fibre system are found as functions of the fibre volume fraction. The calculation of the ultimate stresses are performed by using the percolation theory and the theory of branching processes. At the present stage of the theory under consideration, only two types of the microcracks are appraised, namely that of a delamination type which corresponds to a weak fibre/matrix interface, and that of a penny shape which corresponds to a strong fibre/matrix interface. A particular solid contains only one type of the microcracks. In both cases, non-linear dependencies of the ultimate composite strength on fibre volume fraction are obtained.