1 Table of Contents 1890

ICF13A

13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- However, 0 60 120 180 240 300 360  (degree) -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 z M/ y   y =5107 N/m 2 Ey =106 V/m e15 M/e 15 I =3 d/b=10 d/b=1 d/b=0.1 d/b=0.02 d/b=0.01 0 60 120 180 240 300 360  (degree) -3 -2 -1 0 1 2 3 E M/E y   y =5107 N/m 2 Ey =106 V/m e15 M/e 15 I =3 d/b=10 d/b=1 d/b=0.1 d/b=0.02 d/b=0.01 Figure 6(a) Tangential stress distribution for different ratios d b with 3 15 15  I Me e Figure 6(b) Tangential electric field distribution for different ratios d b with 3 15 15  I Me e 0 60 120 180 240 300 360  (degree) -3 -2 -1 0 1 2 3 z M/ y   y =5107 N/m 2 Ey =106 V/m e15 M/e 15 I =-5 d/b=10 d/b=1 d/b=0.1 d/b=0.02 d/b=0.01 0 60 120 180 240 300 360  (degree) -3 -2 -1 0 1 2 3 E M/E y   y =5107 N/m 2 Ey =106 V/m e15 M/e 15 I =-5 d/b=10 d/b=1 d/b=0.1 d/b=0.02 d/b=0.01 Figure 7(a) Tangential stress distribution for different ratios d b with 5 15 15  I Me e Figure 7(b) Tangential electric field distribution for different ratios d b with 5 15 15  I Me e in the Chao and Chang’s paper [10], it changes very sharply near   90  and is not consistent with our results when two inclusions are very close to each other ( 1 d r =0.01 and 0.02). It is open for discussions why our results are different from those of Chao and Chang near   90  . Case2: An infinite medium with two elliptical inhomogeneities In this case, the two elliptical inhomogeneities arrayed paralleled to the applied loadings (   90  ) are considered. The semi-major (a) and semi-minor (b) axes are 2 and 1 for two inhomogeneities. The tangential stress and tangential electric field in the matrix along the boundary of the lower inhomogeneity for different ratios of d b are plotted in Figures 6(a) and 6(b), respectively. For the different ratio of the piezoelectric constant ( 5 15 15  I Me e ), the tangential stress and tangential electric field in the matrix along the lower inhomogeniety are given in Figures 7(a) and 7(b), respectively. It can be found that the stress concentration in the case of containing the elliptical inhomogeneities is greater than the case of containing circular ones. Since there are few literatures for discussions on the piezoelectricity containing two elliptical inhomogenieties, we used the limiting case as given in Case 1 to verify the validity of our program. Further, we provided a

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