Asymptotic analysis of the potential energy difference because of a crack at a V-notch edge in a 3D domain

The difference in the potential energy in an elastic three-dimensional domain with a V-notch with and without a small crack ( δ Π ) under a general mixed mode I + II + III loading is provided as an asymptotic series. It involves the V-notch edge stress intensity functions, the area of the formed crack, and special geometrical functions that can be pre-computed and tabulated. Importantly, the stress intensity functions along the crack front and the solution for the V-notched domain with the presence of the crack are un-necessary. The analytical formulation is verified by finite element methods, demonstrating the accuracy of the obtained expressions.