13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- 5.2. A central crack in thin piezoelectric structure When H decreases to a very small value, the plate becomes piezoelectric film. Since the film is thin, the crack length is set to be relatively small. Let L/a=25, 50, normalized stress intensity factor 0 / ( ) IK a is presented versus H/a which is changing from 1 to 6 1 10 . When the ratio is as small as 10-6, it is sufficient for modeling many thin piezoelectric films as used in smart materials and micro-electro-mechanical systems. With the decrease of H, the stress intensity factor keep increasing when the strip is relatively thick, namely H/a is higher than 0.01. But in the interval [0, 0.01], the SIFs become stable. Since the crack is small, the value of 0 / ( ) IK a is not so high. For the straight line element method, the stress intensity factors at H/a= 6 1 10 jump slightly. 0.0 0.2 0.4 0.6 0.8 1.0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 Normalized K1 H/a L/a=50(line) L/a=50(quadratic) L/a=25(line) L/a=25(quadratic) Figure 3. Normalized stress intensity factors versus H/a Dynamic intensity factors are also taken into consideration. For H/a=0.1, L/a=25, Fig. 3 shows the normalized dynamic intensity factors versus dimensionless time tcL/H, where 2 22 22 22 ( / ) / Lc C e . (46) The methods of line element and quadratic element are both used and the results coincide with each other very well. 0 2 4 6 8 1012141618 0.0 0.5 1.0 1.5 2.0 Normalize K1 Dimensionless time line element quadratic element Figure 4. Normalized dynamic stress intensity factors versus dimensionless time
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