Critical Load for a Mode{1 Crack Reinforced by Bridging Fibres

A long matrix crack in a unidirectional bre{reinforced composite, perpendicular to the bre direction and subjected to Mode{I loading, is considered. The intact composite material is modelled as homogeneous linearly elastic and the bridging bres are replaced by restraining tractions acting on the crack surfaces. The problem is formulated in terms of a hypersingular integral equation with respect to the relative crack{face separation and contains a small parameter multiplying the integral term. Two limiting cases, related to the maximal opening in the middle of the crack before bres break and to the maximal opening at the ends of the region where bres are broken, are analyzed. The asymptotic solution of the problem is constructed with the use of a matched expansions technique. The values of applied load, corresponding to these two limiting situations, are estimated.