On the Use of a Path-Independent Line Integral for Axisymmetric Cracks With Nonaxisymmetric Loading

A path-independent line integral J_A is derived for axisymmetric cracks under nonaxisymmetric loading conditions. The nonaxisymmetric crack problem is solved by expressing its boundary conditions as the sum of a Fourier series. Contribution on J_A from each of the Fourier terms in the nonaxisymmetric problem is shown to be decoupled from each other. Relationships between J_A and stress intensity factors are also presented for linear elastic fracture problems. Application of J_A to numerical fracture mechanics analysis is demonstrated by considering two example problems: an infinitely long circular bar with a penny-shaped internal crack at its center, and a circumferentially cracked pipe (both are under remote tension, bending, and torsion).