Redefined three-dimensional J-integral as finite strain elastic-plastic crack parameter (Energy release rate and contribution of weakly singular terms)

Abstract

A rigorous three-dimensional J-integral in a domain integral representation is derived and applied to elastic–plastic crack propagation problems. It is called the “redefined J-integral” in this paper. The derivation is based on the power balance of a solid. The difference between the powers of external force and strain energy stored in the solid is the energy release rate at the crack tip while the crack propagates. In the process of deriving the redefined J-integral, weakly singular terms that are related to the change of deformation field in the vicinity of the crack front are found to arise. They play a key role in the elastic–plastic crack propagation phenomenon. However, the weakly singular terms have not been discussed in previous studies on the three-dimensional J-integral. The characteristics of the redefined three-dimensional J-integral are theoretically predicted and are verified through crack propagation problems, especially for the role of the weakly singular terms. At this point the present study is unique especially for the considerations on the weakly singular terms. It is found that the redefined three-dimensional J-integral measures the total of the energy release rate at and the change of deformation energy inside a small but finite volume surrounding the crack tip. Hence, the redefined three-dimensional J-integral can be used as the crack parameter for three-dimensional elastic–plastic solids.