On the conversion of K- to J-characterization in linear elastic 3D configurations

An equation for converting characterization of 3D fields in cracked plates in terms of the stress intensity factor to the one in terms of J-integral is developed. It can be used in applications such as finite element codes and identification of the adequate "effective" elastic modulus in the ASTM E1921 standard. We consider standard specimens - plates that can be thin or thick as compared to the in-plane dimension. It is found that the actual specimen compliance lies in-between the ones corresponding to the 2D plane stress and 2D plane strain approximations. However, the near tip field that governs the K to J conversion is predominantly plane strain for the studied cases. Another finding is that the geometrical factor in 2D, f(a/W), for standard specimens is different from the one obtained on the basis of a 3D analysis.