The effect of the interphase on crack-inclusion interactions

The problem of a radial or circumferential matrix crack interacting with a circular inclusion surrounded by an interphase region is investigated. The problem is formulated using Kolosov-Muskhelishvili complex potentials where the crack is modeled as a distribution of dislocations. The complex potent ials for a dislocation interacting with a circular inclusion with an interp hase are first rederived and then used in the crack formulation. The corres ponding Cauchy singular integral equations are then solved using the Lobatt o-Chebyshev quadrature technique. After comparing the current solution with previously published results, the influence of the interphase stiffness an d thickness on a radial or circumferential matrix crack is studied for a gl ass fiber-epoxy composite. From this study it was found that compliant inte rphases increase the Mode I stress intensity factors for radial cracks whil e stiff interphases shield these cracks from the inclusion relative to the no-interphase cases. Additionally, the compliant interphases were found to be more affected by the thickness of the interphase. Results for the circum ferential cracks were not as straightforward. Compliant interphases decreas ed the Mode II stress intensity factors but, depending on the interphase th ickness and distance from the crack, could either shield or enhance the Mod e I stress intensity factors. Stiff interphases increased the Mode II SIF b ut decreased the Mode I SIF as compared to the no-interphase cases.