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

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 ser ies representations of deformation and stress fields in both the inclusion and the surrounding matrix in the presence of the crack. The interaction be tween 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 influ ence of imperfect bonding at the inclusion-matrix interface on the directio n of crack growth. For example, in the case of an inclusion perfectly bonde d to the surrounding matrix, the SIF at the nearby crack tip is greater tha n that at the distant crack tip only when the inclusion is more compliant t han the matrix. In contrast, the effects of imperfect bonding at the inclus ion-matrix interface allow for the SIF at the nearby crack tip to be greate r than that at the distant crack tip even when the inclusion is stiffer tha n the matrix. In fact, for any given case when the inclusion is stiffer tha n the matrix, we show that there is a corresponding critical value of the i mperfect interface parameter below which a radial matrix crack grows toward s the interface leading eventually to complete debonding. In particular, th is critical value of the imperfect interface parameter tends to a non-zero finite value when the stiffness of the inclusion approaches infinity. To ou r knowledge, these results provide, for the first time, a clear quantitativ e description of the relationship between interface imperfections and the d irection of propagation of radial matrix cracks. (C) 2001 Elsevier Science Ltd. All rights reserved.