This study deals with two kinds of crack problems; one is a kinked interfacial crack problem, and the other is a subinterface crack problem.
A new conservation integral consisting of the path and area integral, for an arbitrarily kinked interfacial crack is proposed. The new conservation integral is shown to have the physical meaning of the energy release rate. With the help of a weighting function the domain representation associated with the energy release rate is obtained, which is amenable to the finite element computation. Two numerical examples are presented to verify its usefulness; one is the problem of an interfacial crack with a parabolic-curved kink, and the other is the problem of a circular arc-shaped interfacial crack with a straight kink. Applying the present method, the energy release rate at the onset of crack kinking can be obtained easily by assuming the small kink length, while in some cases such as the crack kinking out of the curved interfaces, it seems to depend strongly on the modelling length of the kink crack. This may be brought to attention when we treat the kink cracks out of the curvilinear cracks.
A new and simple alternating technique for solving subinterface crack problems is proposed. The present method only requires a corresponding solution for an infinite homogeneous medium, so it simplifies the bimaterial problem significantly and therefore, it has the potential applicability when the problem is quite complicated such as the interaction between the curved subinterface crack and the interface in anisotropic bimaterial. A subinterface crack loaded by an antiplane shear or inplane tension is examined to verify the usefulness of the present method. Although the number of the iteration required to get the converged solutions depends on the distance between the interface and the subinterface crack, it usually takes less than 4 steps except for the subinterface crack very close to the interface. The results obtained by the present method are in good agreement with the existing solutions over the wide range of the crack depth.