A unified perspective of incremental J-integrals by the generalized Griffith framework

Abstract

The novel point of this paper is that the Griffith framework of elastic materials is explained from two different perspectives, which have produced two statements of the generalized Griffith framework suitable for crack growth in elastic–plastic materials. The two statements have encompassed all of these incremental J-integrals. Four aspects of the crack growth in elastic–plastic materials are explored: 1) an explanation is given on why the unique overall energy rate balance has resulted in two different incremental J-integrals. By generalizing Griffith’s idea into the elastic–plastic materials, this paper has proposed two perspectives of the unique power balance on crack propagation: one is based on the Helmholtz free energy, and the other is based on the internal energy. Two expressions of crack driving force are then derived, from which common incremental J-integrals can be directly obtained. 2) A new viewpoint is provided to explain the weaker singularity of growing crack-tip fields in elastic–plastic materials, starting from the physical meaning of the crack driving force. This weaker singularity is attributed to the discontinuous distribution of plastic strain from the plastic unloading behind the crack tip. 3) The physical meanings of finite-contour incremental J-integrals are presented. Interestingly, only the J-integral based on Helmholtz free energy represents the driving force on a finite contour. 4) To tackle the dilemma that the theoretical analyses of cracked bodies considering fracture process zone (FPZ) are very complex, we have proposed a conventional continuum model of such a cracked body, which has transferred this body to a traditional bi-material model.