New insight on physical meaning of fracture criteria for growing cracks

Because plastic unloading is inevitable during crack growth in elastic plastic materials, the J integral is not applicable anymore, and several path-independent integrals are thus proposed by different authors to overcome this limitation. In this paper, we start from the crack tip energy flux. We first derive two important formulas and then find that these path-independent integrals are in fact identical to each other and consistent with the crack tip energy flux. That is, the crack tip energy flux is more essential for growing cracks in elastic plastic materials. In addition, a force such as crack tip parameter, which is conjugated to crack tip velocity, is proposed by us on the perspective that crack tip energy flux can be considered as the power dissipated by crack tip due to crack growth. This parameter is proved to be the absolute value of the projection of the crack tip configurational force vector into the direction of the nominal crack growth direction, and thus, this parameter is the thermodynamic crack driving force. Moreover, this parameter can represent crack tip stress and displacement fields of growing cracks, and thus, a fracture criterion based on this parameter is proposed. The critical value of this parameter corresponds to the rate of energy dissipated in the fracture process zone per unit crack extension.