A new conservation integral for circular arc crack under multiple loads

In this paper, a path independent integral JF∗ that represents the rate of energy flux at the tip during crack extension in a homogeneous and isotropic material has been derived from the principle of virtual work for a two-dimensional stationary circular arc crack subjected to multiple loads. This integral is an extension of the two-dimensional version of F-integral and includes the presence of the effects of thermal strains, initial strains and body forces, hitherto, unavailable in open literature, to the best of the authors’ knowledge. It has been further demonstrated that Rice’s J  -integral, the J^-integral derived by Kishimoto et al. and the F  -integral proposed by Lorentzon et al. are special cases of the generalized integral JF∗. The integral has been implemented into a finite element post-processing program for examining the path independence behavior under elastic and elastic–plastic deformation subjected to mechanical loads and thermo-elastic analyses under pure thermal loads. Within the limits of numerical accuracy, the application demonstrates that the solutions for the energy release rate on different contours preserve nearly identical values over the computational range.