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

A path-independent line integral JA 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 JA from each of the Fourier terms in the nonaxisymmetric problem is shown to be decoupled from each other. Relationships between JA and stress intensity factors are also presented for linear elastic fracture problems. Application of JA 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).