New phenomena concerning the effect of imperfect bonding on radial matrix cracking in fiber composites

Abstract

In this paper we study the effects of imperfect bonding on stress intensity factors (SIFs) calculated at a radial matrix crack in a fiber (inclusion) composite subjected to various cases of mechanical loading. We use analytic continuation to adapt and extend the existing series methods to obtain series representations of deformation and stress fields in both the inclusion and the surrounding matrix in the presence of the crack. The interaction between the crack and the inclusion is demonstrated numerically for different elastic materials, geometries and varying degrees of bonding (represented by imperfect interface parameters) at the interface. Some qualitatively new phenomena are predicted for radial matrix cracking, specifically the influence of imperfect bonding at the inclusion–matrix interface on the direction of crack growth. For example, in the case of an inclusion perfectly bonded to the surrounding matrix, the SIF at the nearby crack tip is greater than that at the distant crack tip only when the inclusion is more compliant than the matrix. In contrast, the effects of imperfect bonding at the inclusion–matrix interface allow for the SIF at the nearby crack tip to be greater than that at the distant crack tip even when the inclusion is stiffer than the matrix. In fact, for any given case when the inclusion is stiffer than the matrix, we show that there is a corresponding critical value of the imperfect interface parameter below which a radial matrix crack grows towards the interface leading eventually to complete debonding. In particular, this critical value of the imperfect interface parameter tends to a non-zero finite value when the stiffness of the inclusion approaches infinity. To our knowledge, these results provide, for the first time, a clear quantitative description of the relationship between interface imperfections and the direction of propagation of radial matrix cracks.