1 Table of Contents 1890

ICF13A

13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- 0 60 120 180 240 300 360  (degree) -1 -0.5 0 0.5 1 z M/ y   y =5107 N/m 2 Ey =106 V/m e15 M/e 15 I =3 d/r1=10 d/r1=1 d/r1=0.1 d/r1=0.02 d/r1=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/r1=10 d/r1=1 d/r1=0.1 d/r1=0.02 d/r1=0.01 Figure 4(a) Tangential stress distribution for different ratios 1 d r with 3 15 15  I Me e Figure 4(b) Tangential electric field distribution for different ratios 1 d r 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/r1=10 d/r1=1 d/r1=0.1 d/r1=0.02 d/r1=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/r1=10 d/r1=1 d/r1=0.1 d/r1=0.02 d/r1=0.01 Figure 5(a) Tangential stress distribution for different ratios 1 d r with 5 15 15  I Me e Figure 5(b) Tangential electric field distribution for different ratios 1 d r with 5 15 15  I Me e given as 2 10 44 44 3.53 10 N m c c I M    , CVm I M 8 44 44 1.51 10       , 2 15 10 e C m I  . The remote shears are 0  zx , 2 7 5 10 N m zy    and far-field electric fields are given as 0  xE and E V m y 6 10   . All the numerical results are given below by using the 30 terms of eigenfunction (M). In order to examine the generality of the present formulation for the problem containing two elliptical inclusions, the case of an infinite medium with the two circular inclusions ( 1 2 2 r r  ) paralleled to the applied loadings (   90  ) is used to verify the present approach. Figures 4(a) and 4(b), respectively, show the tangential shear stress and tangential electric field distribution in the matrix along the boundary of the smaller inhomogeneity for the ratio of 3 15 15  I Me e . After comparing with the results of Chao and Chang [10] and Chen and Wu [1], it can be found that good agreement is made. By changing the ratio of the piezoelectric constant, Figures 5(a) and 5(b), respectively, show the tangential stress and tangential electric field distribution corresponding to 5 15 15  I Me e . The two figures also show the consistency between the present data and those of Chen and Wu [1].

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