Dynamic fracture analysis in nonhomogeneous piezoelectric materials with a new domain-independent interaction integral

Abstract

In order to comprehend and forecast the dynamic fracture behaviors of piezoelectric materials, dynamic intensity factors (IFs) are crucial fracture parameters. It is a challenge to effectively calculate the dynamic IFs of the piezoelectric materials containing complicated elastic and/or electric interfaces. For piezoelectric materials with nonhomogeneous properties or even random interfaces, a dynamic domain-independent interaction integral (DII-integral) is established to assess the dynamic stress intensity factors (SIFs) and the dynamic electric displacement intensity factor (EDIF). Furthermore, it is theoretically demonstrated that random interfaces in the integration domain have no effect on the efficiency of the DII-integral and it does not include any derivatives of electromechanical characteristics. The extended finite element method (XFEM) is integrated with the dynamic DII-integral method to study typical cracked piezoelectric specimens exposed to electromechanical impact loads. A wonderful consistency is obtained by evaluating the current results with the relevant literature. Good domain-independence of the proposed dynamic I-integral is verified for nonhomogeneous and discontinuous piezoelectric properties (relative deviation < 1 %). The numerical simulations show the amplitudes of the dynamic SIFs and EDIF are highly affected by the polarization direction. In general, the density has an obvious influence on the peak occurrence time of the dynamic SIF and EDIF. The dielectric permittivity impacts the EDIF evidently, however, the SIF marginally. On the contrary, the piezoelectric coefficient obviously impacts the SIF and EDIF. The elastic stiffness has a considerable impact on the SIF but a minor one on the EDIF.