Stability of failure initiation by fracture for fibrous composite with central crack

Abstract

The interaction of a crack with two circular elastic fibers or inclusions is considered. The strain energy density criterion is applied for determining the stability of the composite system. This is accomplished by finding a length parameter “ l” that represents the distance between [( dW dV ) min max] G and [( dW dV ) min max] L . They correspond to the maximum of the minimum strain energy density referred to the fixed global coordinates and local coordinates which are indicated by the points G and L, respectively. Depending on the relative moduli ratio E 2 E 1 of the fiber and matrix, the location G will change while L always coincides with the crack tip. When the crack and inclusion lie on the axis of load symmetry, G lies in between the crack tip and inclusion boundary for E 2< E 1, while G shifts into the inclusion for E 2> E 1. As the inclusions are displaced slightly away from the axis of load symmetry with an eccentricity e, G can be either above or below the crack plane depending on the ratio E 2 E 1 . In general, instability tends to increase as L and G drift apart. It is found that the system behaves more stably for the case of uniform load while the system behaves less stably for the case of concentrated load as both geometry and material properties are kept the same. The effect of the fiber concentration on the local stress intensification is also examined in this study.