Path independent integral for circular arc crack: FEM-investigation under mechanical and thermal loads

A conservation integral J F * consisting of path and area integrals, derived from the virtual work principle, was proposed for a two-dimensional stationary circular arc crack subjected to multiple loads. As a sequel to this work, an approach to compute this integral in the finite element context is presented here. The invariant property of J F * , computed on various contours for two typical geometries is examined. The first part of the investigation concerns the elastic–plastic analyses under mechanical loads while in the second part; solutions are obtained for thermal loads. Applications of three plasticity models along with different material properties are considered. Numerical results, within the limits of computational accuracy, demonstrate that the path independence is well preserved over the integration contours for both mechanical and thermal loads. Comments are also made on the utility of the integral to practical engineering problems.