Self-Similar Crack Expansion Method for Three-Dimensional Cracks Under Mixed-Mode Loading Conditions

Three-dimensional planar cracks under mixed-mode loading conditions are investigated by using the selfsimilar crack expansion method with the boundary integral equation technique. For a planar crack under general loading (tensile and shear) conditions, the normal displacement and tangential displacements on the crack surface exhibit uncoupled characteristics. However, the tangential displacements in the two directions are generally coupled. In this paper, two coupled boundary integral equations for a crack subject to shear loading are solved using the analytically numerical method, where the integrals on elements’ are estimated by using the explicit expression of the close form of the integrals. Combination of the self-similar crack expansion method and the analytically numerical method results in good accuracy, with errors in stress intensity factors of penny-shaped cracks and elliptical cracks less than one percent. This numerical analysis is applicable to the analysis of cracks with arbitrary geometry.