Generalized domain-independent interaction integral for solving the stress intensity factors of nonhomogeneous materials

Abstract

The generalized domain-independent interaction integral (DII-integral) is investigated due to its extremely promising application in solving the stress intensity factors (SIFs) of nonhomogeneous materials with complex interfaces. A recent study revealed that the DII-integral, which is domain-independent for material interfaces, can be established by defining an appropriate auxiliary field. Regrettably, the kind of auxiliary field that can be used is not very clear. This work first discusses the conditions that the auxiliary field must satisfy for establishing a DII-integral and provides a framework for designing more applicable auxiliary fields. In this framework, a generalized auxiliary field and the corresponding generalized DII-integral are derived. The generalized auxiliary field contains two free constants and can be expressed as the linear combination of a widely used auxiliary field and a new auxiliary field, which are referred to as the crack face traction-free auxiliary field and the zero mean stress auxiliary field, respectively. The generalized auxiliary field is effective in establishing the DII-integral for purely mechanical loading, and the zero mean stress auxiliary field is also effective in the establishment of the DII-integral for isotropic mismatch strain problems. The generalized DII-integral is the linear function of mode-I and mode-II SIFs and its expression does not involve the free constants in the generalized auxiliary field. Then, a patched extended finite element method (XFEM) is briefly introduced to remove the crack-tip enrichment and instead employ a patched mesh in the modeling. The patched XFEM does not depend on the material constitutive relations and thus has a larger applicable scale than does the traditional XFEM. Finally, the DII-integral combined with the patched XFEM is employed to investigate four representative crack problems. Numerical examples show that the generalized DII-integral exhibits good domain-independence for homogeneous, nonhomogeneous, and discontinuous properties. Although the numerical values of the DII-integral do not remain constant for different values of the free constants due to numerical errors, good numerical precision can be achieved if the free constants do not deviate too much from those used in the crack face traction-free auxiliary field. In addition, the DII-integral using the zero mean stress auxiliary field is demonstrated to be reliable and convenient in solving the SIFs of particulate composites under an initial thermal strain.