13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- 0 2 4 6 8 10 12 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 tVs/c Kθθ(t) LD=-0.5 LD=0 LD=+0.5 Fig. 4 shows the effect of electric loading on the variation of normalized dynamic HSIFs at the angle 20 =θ degrees. The electric loading parameter DL affects the initial value and the peak value of the dynamic HSIFs. At the very beginning, a positive electric load leads to a lower initial value of the HSIF than negative electric load, whilst the peak value of the dynamic HSIFs induced by the positive electric load is higher than that for the negative electric load. Figure 4. Dynamic hoop stress intensity factors for different electric loadings DL when 20 =θ degrees and h h c 2 4 1 2 = = 5. Concluding remarks An impermeable crack in a piezoelectric strip under in-plane dynamic mechanical and electric loadings is studied. Fourier transforms are applied to reduce the mixed boundary value problem of the crack to dual integral equations, which are further expressed in terms of singular integral equations. Asymptotic fields near the crack tip are obtained in an explicit form and the corresponding field intensity factors are determined. The crack kinking phenomenon is investigated by applying the maximum hoop stress intensity factor criterion. Numerical results show that the geometry of the strip and the electric loading dominate the singular field distribution around the crack tip, and the hoop stress intensity factors are controlled by the material parameters, the electric loadings and the geometric size ratios. Appendix A The constants in Eqs. (14) and (15) are defined as ) ) ( ( ), ) ( ( 2 33 33 33 33 0 33 0 2 2 33 33 33 33 0 33 0 1 e e P C D C e P e D C + − + Τ = + Τ = λ λ λ (A.1) ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ − − + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + + − + = ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ − 2 2 44 2 33 44 13 1 15 2 33 2 44 13 15 31 2 44 2 2 11 ) ( ξ ρ γ γ γ γ ξ ρ C C p C C e e C C e e C p C b a j j j j j j (A.2)
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