Theory and Calculation of the J-Integral for Coupled Chemo-Mechanical Fracture Mechanics

In this paper, by introducing a chemical field, the J-integral formulation is presented for the chemo-mechanical coupled medium based on the laws of thermodynamics. A finite element implementation of the J-integral was performed to study the mode I chemo-mechanical coupled fracture problem. For derivation of the coupled J-integral, the equivalent domain integral (EDI) method was applied to obtain the mode I J-integral, with expression of the area integrals based on constitutive relationships of a linear elastic small deformation for chemo-mechanical coupling, instead of the finite deformation problem. A finite element procedure is developed to compute the mode I J-integral, and numerical simulation of the y-direction stress field is studied by a subroutine UEL (User defined element) developed in ABAQUS software. Accuracy of the numerical results obtained using the mode I J-integral was verified by comparing them to a well-established model based on linear elastic fracture mechanics (LEFM). Furthermore, a numerical example was presented to illustrate path-independence of the formulated J-integral for a chemo-mechanical coupled specimen under different boundary conditions, showing a high accuracy and reliability of the present method. The variation laws of J-integral and the y-direction stress field with external chemical, mechanical loading and time are revealed. The J-integral value increases with larger external concentration loading in the same integral domain. The extent of diffusion is much greater with larger concentration, which leads to a stronger coupling effect due to the chemical field. This work provides new insights into the fracture mechanics for the chemo-mechanical coupled medium.