piezoelectric and dielectric constants of PZT-4, numerical values of S in eq. (11) can be computed for p × 10-3 = -15, -10, -5, 0, 5, 10 and 15 Vm/N. Plotted in Fig. 4 are the normalized values of S as a function of p. The curve increases monotonically. Figure 3: Enhancement and retardation of crack growth Figure 4: Energy density and crack growth segment variations with positive and negative electric field strength Once S can be computed numerically for situations where E changes sign, eq. (13) can be applied to show whether the inequalities in eqs. (15) would hold or not. The other curve in Fig. 4 corresponds to crack growth segments r normalized to r . The point with coordinates r = 1.0 and p = 0 corresponds to the crack growth segment r with E = 0. Summarized in Table 1 are the numerical values of r and r normalized with reference to r . When E is positive r /ro is always greater than one. ± j o j ± j o j + j − j o j + j j TABLE 1 Normalized crack growth segments r /r and r /r for PZT-4 and different E/σ × 10 + j o j − j o j -3 values (Vm/N) -15 -10 -5 0 5 10 15 0.765 0.814 0.894 1 1.132 1.290 1.474 Moreover, r /r is always less than one when E is negative. This implies that a crack would grow longer for a positive electric field. Shorter crack growth applies to a negative electric field. For comparing the relative magnitudes of and , the results in Table 1 are sufficient to validate the − j o j + jr , o jr − jr
RkJQdWJsaXNoZXIy MjM0NDE=