13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- /2) ( ,0) 0 (0 /2) (0 ( , ) 0 0 0 x L x x L xW (28) The magnitude of the electric field E0 in the x-direction is −0/W. Other boundary conditions are summarized below. At x = L/2 (side surface) ( / 2, ) 0 (0 ) xx L z z W (29) ( / 2, ) 0 (0 ) xz L z z W (30) ( / 2, ) 0 (0 ) xD L z z W (31) At z = 0 (top surface) (,0) ( /2) () (0 / 2) zz x P x x L (32) ( ,0) 0 (0 / 2) zx x x L (33) /2) ( ,0) 0 ( /2 0L x L D x z (34) At z = W (bottom surface) ( /2, ) 0 /2), /2, /2 ( , ) 0 (0 x S S x L u S W xW z zz (35) ( , ) 0 (0 / 2) zx xW x L (36) 0 ( , ) 0 ( / 2 / 2) zD xW L x L (37) In the FEA (ANSYS), the energy release rate was computed using the path-independent integral approach. The energy release rate G for Case 1 is given by , , , , 0 ( ){ ( ) ( ) } x xx x x zx z x x zx x x zz z x z x x x z x z p G Hn u u n u u n DE n DE n d (38) where Γ0 is the contour closing the crack tip, Γp is the path embracing that part of phase boundary which in enclosed by Γ0, H is the electrical enthalpy density, and nx, nz are the components of the outer unit normal vector. The energy release rate G for Case 2 is obtained by exchanging x and z in Eq. (38). For the calculation of G, three contours were defined in the finite element mesh. The values of G for each of these contours are practically identical. Four-node element PLANE 13 was used in the model. The finite element mesh had 4400 elements and 4536 nodes. 4. Results and Discussion Table 2 shows the results of average number of cycles to failure (from two data) for PZT ceramics
RkJQdWJsaXNoZXIy MjM0NDE=