Analysis of an interfacial crack between two nonhomogeneous piezoelectric materials using a new domain-independent interaction integral

Considering the difficulties introduced by piezoelectric material non-homogeneity and discontinuities to interfacial crack analysis, a domain-independent interaction integral (DII-integral) is proposed to derive the stress intensity factors (SIFs) and electric displacement intensity factor (EDIF) of an interfacial crack between nonhomogeneous piezoelectrics. For continuously varying material properties, traditional interaction integral (I-integral) needs to compute the derivatives of material parameters with respect to the x(1) direction of the local coordinate system, while the proposed DII-integral is demonstrated to be unrelated to any derivatives of material parameters. Furthermore, a significant improvement is achieved that the new formulation of I-integral remains valid even when the integration domains include intricate and multiple interfaces, as long as the material interfaces are perfectly bonded. Firstly, the intensity factors (IFs) calculated by the combination of the DII-integral and the extended finite element method are compared with the analytical solutions, and it is found that the relative errors of the IFs are all less than 1.79 % with various crack lengths, which verifies the accuracy of the proposed method. For the piezoelectric bi-material model with continuously nonhomogeneous properties, the calculated IFs match each other well (relative deviation < 1.3 %) for different sizes of integration domains. In addition, for the perfectly bonded interface with discontinuous electromechanical properties, the IFs are almost identical (relative deviation < 0.85 %) whether or not the integration domain contains the material interface, which further numerically verifies the good domain-independence of the established DII-integral. For an interfacial crack near extra interfaces, the differences in elastic stiffness and piezoelectric coefficient between interface sides have an obvious influence on mode-I SIF, but mode-II SIF and EDIF are affected mainly by piezoelectric coefficient and dielectric permittivity.