CRITICAL LOAD FOR A MODE-1 CRACK REINFORCED BY BRIDGING FIBRES.

MOVCHAN, N. V.; WILLIS, J. R.

A long matrix crack in a unidirectional fibre-reinforced composite, perpendicular to the fibre direction and subjected to Mode-1 loading, is considered. The intact composite material is modelled as homogeneous linearly elastic and the bridging fibres 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 fibres break and to the maximal opening at the ends of the region where fibres are broken, are analysed. 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. This necessitates consideration of new boundary layers in the middle of the crack, even in the case when no fibres have broken.

FIBER-reinforced concrete; BOUNDARY layer (Aerodynamics); FLUID dynamics; INTEGRAL equations; AXIAL stresses; AXIAL loads

Quarterly Journal of Mechanics & Applied Mathematics, 1996, Vol 49, Issue 4, p545

0033-5614

Academic Journal

10.1093/qjmam/49.4.545