Fiber Stress Enhancement Due to Initial Matrix Cracking

Abstract

The tendency for a bridged matrix crack to induce fiber breakage is studied theoretically. We contemplate a composite which has a single matrix crack bridged by all fibers, and which is subjected to tension parallel to the reinforcement. Of interest in judging whether the fibers will fail is the degree to which the fiber stress deviates from its mean value, and the dependence of this deviation on interface parameters. This issue is pursued here for an idealized two-dimensional composite with widely spaced fibers and with a fiber-matrix interface which is governed by Coulomb friction. It is shown that a stronger interface causes a higher stress concentration at the fiber surface thereby raising the likelihood of premature fiber failure.