Domain integral formulation for stress intensity factor computation along curved three-dimensional interface cracks

Abstract

New 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 (a contour integral surrounding a point on the crack front which is evaluated in the limit as the contour is shrunk onto the crack tip) 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. 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; however, these terms become important when domain integral representations are introduced, because they involve fields which are not asymptotically close to the crack tip. In order to compute the pointwise stress intensity factors along the crack front, the domain integrals are evaluated as a post-processing step in the finite element method. In the numerical results, it is demonstrated that it is crucial to incorporate the terms that arise due to lack of equilibrium and compatibility of the auxiliary fields, especially in regions where the local crack front curvature is high. In the paper, we present two numerical examples. As a benchmark, we first 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 is also considered, and the results are discussed.