an:01019568
Zbl 0877.73051
Movchan, N. V.; Willis, J. R.
Critical load for a mode-1 crack, reinforced by bridging fibres
EN
Q. J. Mech. Appl. Math. 49, No. 4, 545-564 (1996).
00036312
1996
j
74R99 74E30
unidirectional fibre-reinforced composite; hypersingular integral equation; crack-face separation; small parameter; matched expansions technique
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 analyzed. The asymptotic solution of the problem is constructed with the use of a matched expansions technique.