13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- Figure 2. Schematic representation of the finite element model: (a) Case 1; (b) Case 2 ) ( ( ,0) ( ,0) ) ( ( ,0) ( ,0) ) (0 ( ,0) 0 D x D x W a x W E x E x W a x W x W a x c z z c x x (14) where the superscript c stands for the electric quantity in the void inside the crack. The electric potential is all zero on the symmetry planes inside the crack and ahead of the crack, so the boundary conditions of Eqs. (14) reduce to (x, 0) = 0 (0 x W ). Eqs. (14) are the permeable boundary conditions, and appropriate for a slit crack in piezoelectric ceramics [5]. Note that the fracture mechanics parameters such as energy release rate predicted by the permeable and discharging crack models are not significantly different, using the standard air breakdown field for a critical discharge level within the crack gap. A mechanical load is produced by the application of the prescribed force P, corresponding to the appropriate experimental load, at x = 0, z = 0 along the x-direction. For an electrical load, the electric potential ( 0/2) is applied at the edge 0 x W , z = L0/2, so the condition is ) (0 ( , /2) ( /2) 0 0 x W x L (15) The magnitude of the electric field E0 in the z-direction is −0/L0. Other boundary conditions are
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