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 potentials for a dislocation interacting with a circular inclusion with an interphase are first rederived and then used in the crack formulation. The corresponding Cauchy singular integral equations are then solved using the Lobatto-Chebyshev quadrature technique. After comparing the current solution with previously published results, the influence of the interphase stiffness and thickness on a radial or circumferential matrix crack is studied for a glass fiber-epoxy composite. From this study it was found that compliant interphases increase the Mode I stress intensity factors for radial cracks while 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 circumferential cracks were not as straightforward. Compliant interphases decreased the Mode II stress intensity factors but, depending on the interphase thickness and distance from the crack, could either shield or enhance the Mode I stress intensity factors. Stiff interphases increased the Mode II SIF but decreased the Mode I SIF as compared to the no-interphase cases.