The physical meanings of two incremental-J-integral-based fracture criteria for crack growth in elastic-plastic materials

Abstract

According to a previous paper (Lu LK, Liu ZL, Zhuang Z. Eng Frac Mech. 2021, 254: 107907), the Rice J-integral can be generalized into two incremental J-integrals for crack growth in elastic-plastic materials: one is based on free energy density, and the other is based on internal energy density. This paper aims at providing the physical meanings of these two criteria. The fracture criterion of incremental-J-integral based on free energy corresponds to a direct generalization of the classic Griffith equilibrium condition. This fracture criterion means no net change in total energy during the quasi-static crack growth in an elastic-plastic solid. For a small crack extension, the body’s potential energy is reduced by a value, which can be balanced by the increment of plastic dissipation work plus an extra energy term. The crack growth could happen if this extra energy term equals the energy required for forming these new crack surfaces. For the incremental-J-integral based on the internal energy density, its fracture criterion is a direct result of the first law of thermodynamics of a cracked body containing two independent thermodynamic systems: the volumetric and surface systems. In addition, the cases that a part of crack surfaces has tractions are discussed. If the loaded part of crack surfaces is stationary during crack growth, the results are identical to cases that crack surfaces are traction-free. If the loaded-part of crack surfaces moves with the growing crack tip, the derived fracture criteria become the incremental J-integral criteria in which the integral contour is a boundary of this loaded-part of crack surfaces.