13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- Figure 1. Failure curve and experimental results (PIC-151) [10] obtained in [11]. The crack is perpendicular to the poling direction. was calculated to be 0.89 N/m. In Eq. (12), experiment cG is the experimental value or the point plotted in Fig. 1, l theoretica cG is the value on the curve of cG for the experimental value of ψ as calculated from Eq. (11) and N is the number of tests. As a result of the coupling between the first and fourth modes of fracture, which is expressed by the second term in parentheses of the right hand side of Eq. (11), the fracture curve in Fig. 1 is not symmetric with respect to 0 ψ= . Furthermore, it should be emphasized that the apparent fracture toughness Ic G should not be used to predict catastrophic failure. Only the mixed mode fracture curve presented in Eq. (11) and Fig. 1 should be used to predict failure. To interpret the failure curve for a structure fabricated from the same material and containing a crack perpendicular to the poling direction, values of cG below the curve are considered safe; for those above it, failure may be expected. Of course, a probabilistic analysis should be carried out. Next, a fracture criterion for tests carried out in [12] on four-point bend specimens fabricated from PZT-5H (Morgan Electro Ceramics, Wrexham, UK) with poling parallel to the crack faces is presented. In that study, modes I, II and IV were present. Since poling is parallel to the crack faces, 0 2 1 = = a a in Eq. (7). Hence, the fracture criterion in Eq. (6) becomes ( ). tan tan 1 2 tan tan 2 5 2 4 3 φ = + ψ φ+ ψ+a a a Ic cG G (13) Note that during the tests, the electric field was applied perpendicular to the crack faces. The value of Ic G was found to be 20.3 N/m. In Fig. 2, the three-dimensional failure surface in Eq. (13) is plotted. The points shown are the experimental values obtained by analyzing the results from the four-point bend tests. In order to have a better view of the scatter, the phase angle φ in the criterion of Eq. (13) was assumed zero resulting in ( ). 1 tan2 4 = + ψ a Ic cG G (14)
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