Interaction of Internal Crack with Interfacial Rigid Inclusion

The problem of a rigid elliptical inclusion at the interface of two bonded isotropic elastic half planes interacting with an internal crack is examined. The problem is tackled by first obtaining the Green's function of a point dislocation located in one of the bonded half planes and interacting with an interfacial rigid elliptical inclusion. Internal crack is then simulated by the method of distributed dislocations and stress intensity factors at internal crack tips are obtained by solving the resulting singular integral equations numerically. Complex variable method in conjunction with conformal mapping technique is employed to derive the complex stress potentials for the point dislocation problem. The mapping of half-plane with an elliptical notch is carried out by means of rational mapping technique. The influences of inclusion shape and its distance from the internal crack on the stress intensity factors (SIF) of the internal crack tips are discussed. Results show decreasing SIF at internal crack tips as its distance from the interfacial inclusion decreases. This trend is seen for all inclusion shapes studied when the applied load is normal to the internal crack. On the other hand, when loading is parallel to the internal crack, positive SIF at the internal crack tips are observed for certain combinations of distance between the internal crack and interfacial inclusion, and crack size. This is unlike a crack ahead of a cavity where load parallel to the crack line has no contribution to the SIF.