Accurate loading analyses of curved cracks under mixed-mode conditions applying the J-integral

In linear elastic fracture mechanics the path-independent J-integral is a loading quantity equivalent to stress intensity factors (SIF) or the energy release rate. Concerning plane crack problems, $$J_k$$ is a 2-dimensional vector with its components $$J_1$$ and $$J_2$$ . These two parameters can be related to the mode-I and mode-II SIFs $$K_{\mathrm{I}}$$ and $$K_{\mathrm{II}}$$ . To guarantee path-independence for curved crack geometries, an integration path along the crack faces must be considered. This paper deals with problems occurring at the numerical calculation of the J-integral in connection with the FE-method. Two new methods for accurately calculating values of $$J_2$$ for arbitrary cracks are presented.