13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- and the energy release rate for Case 1 is larger than that for Case 2. Figure 3 shows the energy release rate G versus electric field E0 for SEPB C-91 ceramics with a = 0.5 and 1.5 mm under Pmax = 110 N for Case 1. The dashed line represents the value of G without polarization switching effect, and the solid line represents the G with switching effect. The prediction with switching effect shows that localized polarization switching leads to a decrease in G and then an increase after E0 reaches about -0.3 and -0.27 MV/m for a = 0.5 and 1.5 mm, respectively. In concluding, numbers of cycles to failure under low and high negative electric fields were significantly larger and smaller than that under zero electric field, and correlated with the fracture surfaces. In addition, as the negative electric field increased, the localized polarization switching led to a decrease in the energy release rate, and the energy release rate increased when the negative electric field increased further. References [1] Y.Shindo, F.Narita, M.Hirama, Dynamic fatigue of cracked piezoelectric ceramics under electromechanical loading: Three-point bending test and finite element analysis. J Mech Mater Struct, 4 (2009) 719-729. [2] F.Narita, Y.Shindo, F.Saito, Cyclic Fatigue Crack Growth in Three-Point Bending PZT Ceramics under Electromechanical Loading. J Am Ceram Soc, 90 (2007) 2517-2524. [3] Y.Shindo, F.Narita, T.Matsuda, Electric field dependence of the mode I energy release rate in single-edge cracked piezoelectric ceramics: Effect due to polarization switching/dielectric breakdown. Acta Mech, 219 (2011) 129-143. [4] S.C.Hwang, C.S.Lynch, R.M.McMeeking, Ferroelectric/ferroelastic interactions and a polarization switching model. Acta Metall Mater, 43 (1995) 2073-2084. [5] Y.Shindo, F.Narita, M.Hirama, Effect of the electrical boundary condition at the crack face on the mode I energy release rate in piezoelectric ceramics. Appl Phys Lett, 94 (2009) 081902. [6] Y.Shindo, M.Yoshida, F.Narita, K.Horiguchi, Electroelastic field concentrations ahead of electrodes in multilayer piezoelectric actuators: experiment and finite element simulation. J Mech Phys Solids, 52 (2004) 1109-1124. Appendix A For piezoelectric ceramics which exhibit symmetry of a hexagonal crystal of class 6 mm with respect to principal x1, x2 and x3 axes, the constitutive relations can be written in the following form: r r r r r r E E E d d d d d s s s s s s s s s s s s 12 31 23 33 22 11 3 2 1 15 15 33 31 31 12 31 23 33 22 11 66 44 44 33 13 13 13 11 12 13 12 11 12 31 23 33 22 11 0 0 0 / 2 0 0 / 2 0 0 0 0 0 0 0 0 / 2 0 0 0 0 0 / 2 0 0 0 0 0 0 / 2 0 0 0 0 0 0 0 0 0 0 0 0 0 (A.1)
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