Interaction integral formulation for computing stress intensity factors along curved bimaterial interface cracks

Domain integrals for extracting mixed-mode stress intensity factors along curved, three-dimensional bimaterial interface cracks are derived. In the derivation, the asymptotic auxiliary fields for the plane problem of a bimaterial interface crack are imposed along a curved crack front. The general crack-tip interaction integral is then expressed in domain form which is more suitable for numerical computation. A consequence of imposing the auxiliary fields along a curved crack front is that the auxiliary stress fields do not satisfy equilibrium, and the auxiliary strain fields do not satisfy compatibility. It turns out that the terms which arise due to the lack of equilibrium and compatibility are not sufficiently singular to contribute to the crack tip interaction integral or to affect its path independence. It is crucial, however, to include them in the domain integral representations because the domain integrals involve fields which are not asymptotically close to the crack-tip. In the paper, we present two numerical examples. As a benchmark, we consider the problem of a penny-shaped interface crack embedded in a cylinder. The results for the complex stress intensity factor and phase angle are found to be in excellent agreement with the analytical solution. The problem of an elliptical crack embedded between two dissimilar isotropic materials, for which an analytical solution is not available, is also considered, and the results are discussed.