A PERCOLATION-TYPE FRACTURE CRITERION FOR COMPOSITES WITH RANDOMLY ORIENTED FIBERS

A fracture model is built up for a solid composed of brittle fibres ra ndomly oriented in the matrix volume. The fracture process includes a stable growth of microcracks caused by fibre breaking under the load a nd formation of an infinite cluster of the microcracks. Both upper and lower bounds for ultimate stress in a fibre system are found as funct ions of the fibre volume fraction. The calculation of the ultimate str esses are performed by using the percolation theory and the theory of branching processes. At the present stage of the theory under consider ation, only two types of the microcracks are appraised, namely that of a delamination type which corresponds to a weak fibre/matrix interfac e, and that of a penny shape which corresponds to a strong fibre/matri x interface. A particular solid contains only one type of the microcra cks. In both cases, non-linear dependencies of the ultimate composite strength on fibre volume fraction are obtained. (C) 1997 Elsevier Scie nce Ltd.