A simplified evaluation of the mechanical energy release rate of kinked cracks in piezoelectric materials using the boundary element method

Based on the concept of the hoop field intensity factors of an initial crack prior to any kink, an apparent hoop mechanical (strain) energy release rate (MERR) is defined to approximate the MERR of a piezoelectric crack with an infinitesimal kink at any arbitrary angle. The validity and the efficiency of the simplified approximation are examined by numerical examples using the boundary element method (BEM). The generalized crack-opening-displacements or displacement jumps are computed by the traction boundary integral equations (BIEs). By using the displacement extrapolation method, the crack-tip field intensity factors of any arbitrarily kinked crack in linear piezoelectric materials are obtained and the BEM results are validated by comparing them with the available reference analytical results. Then, the differences between the conventional field intensity factors and MERR of an infinitesimally kinked crack and the hoop field intensity factors and hoop MERR of the main crack prior to any kink are numerically analyzed. Finally, the crack propagation in an infinite linear piezoelectric material is numerically simulated. The paths of the crack growth are predicted by adopting four different fracture criteria, namely, the maximum hoop stress intensity factor (SIF) and MERR fracture criteria for the main crack-tip before the next propagation, and the maximum KI and MERR fracture criteria for the kinked tip of the main crack with an infinitesimal branch at an arbitrary kinking angle evaluated by using a trial crack extension technique. The comparisons among these results show that the present simplified approximation can efficiently provide a sufficient accuracy for numerical simulation of crack growth in linear piezoelectric materials.