Mode decomposition of three-dimensional mixed-mode cracks via two-state integrals

A numerical scheme is proposed to obtain the individual stress intensity factors in an axisymmetric crack and in a three-dimensional mixed-mode crack. The procedures presented here are based on the path independence of J and M integrals and mutual or two-state conservation integrals, which involve two elastic fields. A useful method to decompose the stress intensity factors along curved three-dimensional cracks under mixed mode is derived by using appropriate auxiliary fields for the plane problems. The choice of the auxiliary fields available is critical to success of the present scheme, and in this study it is made of not only the asymptotic plane-strain solution, which requires some remedy in application of the two-state integral due to the lack of equilibrium and compatibility, but a numerical solution with a given stress intensity as well. Some numerical examples of penny-shaped cracks are presented to investigate the applicability and effectiveness of the method for problems of axisymmetric and three-dimensional cracks.