13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- in which the constants 0 0 0 0 0 , , , , j ij j j j g q f Y γ are defined in Appendix A. Note that by setting the angle θ equal to zero and using the relations in Eqs. (30), the common expressions for the Mode-I and Mode-II stress intensity factors can be obtained. The dynamic hoop and shear stress intensity factors can be obtained by performing the Laplace inverse transform to Eqs. (28) and (29) as ∫ ∫ = = Br r r Br K p pt dp i t K p pt dp K i t K ) ( , )exp( 2 1 ( , ) ) , ( , )exp( 2 1 ( , ) * * θ π θ θ π θ θ θ θθ θθ (31) where " " Br stands for the Bromwich path of integration. Different criteria have been proposed to predict the direction of crack branching [14]. Here we use the maximum hoop stress intensity factor criterion to predict crack kinking. 4. Numerical results and discussions To study the effect of electro-elastic interaction on the stress field near the crack tip, the electric loading parameter ( ) 33 0 33 0 L e D P D λ = is introduced. The material constants of PCM-80 [15] are used in the following numerical calculation: 5.5 10 (Kg m ) 68.4 10 (C Nm ) ), 15.6 (C m ), 95.2 10 (C Nm 5.99 (C m ), 13.7 (C m ), 3.05 10 (N m ), 16.5 10 (N m ) 11.5 10 (N m ), 17.0 10 (N m ), 3 3 2 2 10 33 2 2 10 11 2 33 2 31 2 15 2 10 44 2 10 33 2 10 13 2 10 11 = × = × = × = =− = = × = × = × = × − − ρ λ λ e e e C C C C (32) The variation of the normalized dynamic hoop stress intensity factors (HSIFs) P c K t 0 ( ) θθ with normalized time tV c s at different angles θ are displayed in Fig. 2. The shear wave velocity is defined as ρ λ11 2 15 44 e V c s = + . Without loss of generality, the geometric size of the strip is taken to be 5 1, 2 1 = = h c h c , and the applied electric loading parameter 0.5 =+ DL . Fig. 2 shows that the HSIFs increase as time increases, and reach their peak values at about 3.5 = tV c s , and then decrease and oscillate about their static values, until when →∞ tV c s , HSIFs reduce to the static values. The peak values of the HSIF at 20 =θ degrees are bigger than that of 0=θ degrees, which means that the crack tends to deviate from the original crack plane, provided that the material has the same fracture toughness in every direction. Fig. 3 shows the variation of peak values of the dynamic hoop stress intensity factors versus angles θ when 0.5 =+ DL . For the case 2 1h h ≠ , the maximum value of the HSIFs appears at an angle different from the original crack plane, which implies that the crack may kink in this particular direction. When 5 1, 2 1 = = h c h c , the crack kinks at about 20 =+ θ degrees, and in another case 1 5, 2 1 = = h c h c , the crack kinks at about 20 =− θ degrees. It is evident that the
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