Elastic-plastic J-integral in inhomogeneous materials

An analytical and numerical study of an extended J-type integral for inhomogeneous materials is presented for three-dimensional mode-I-crack configurations. This integral is developed by using the Eshelby's energy moment tensor and consists of two parts, a volume integral enclosing the crack front and a surface integral embracing any inhomogeneities. For numerical calculations, the 3D integral appears to be an attractive approach for obtaining pointwise values of the J-integral along a crack front. Numerical examples are presented for a center cracked body subjected to quasi-static loading.