13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- value problem of the crack to solving a system of singular integral equations. The asymptotic fields near the crack tip are obtained in an explicit form and the hoop and shear stress intensity factors are then determined. The crack kinking phenomenon is investigated by applying the maximum hoop stress intensity factor criterion. The coupled electro-mechanical effects on the crack-tip fields are investigated and the influence of the geometric feature of the strip on the crack kinking is discussed. 2. Problem statement and method of solution Consider a transversely isotropic, linear piezoelectric material and denote the rectangular coordinates of a point by ( , , ) x y z . The constitutive equations can be written as ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ∂ ∂ ∂ ∂ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ∂ ∂ +∂ ∂ ∂ ∂ ∂ ∂ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ∂ ∂ ∂ ∂ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ + ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ ∂ ∂ +∂ ∂ ∂ ∂ ∂ ∂ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ z x u z u x u z u x e e e D D z x e e e u z u x u z u x C C C C C z x z x z x z x z x xz zz xx φ φ λ λ φ φ σ σ σ 33 11 33 31 15 15 33 31 44 33 13 13 11 0 0 0 0 0 0 0 0 0 0 0 0 (1) where x z u u, are components of the displacement vector and φ is the electric potential, 44 11 13 33, , , C C C C are elastic constants, 15 31 , e e are piezoelectric constants, and 11 33 , λ λ are dielectric permittivities, ijσ and iD ( i j x z, , = ) are components of stress and electric displacement, respectively. Figure 1. A cracked piezoelectric strip under in-plane mechanical and electric impact loadings Studied in this paper is a Griffith crack of length c2 in a piezoelectric strip of width 2 1h h+ , with the poling direction perpendicular to the crack plane, as shown in Fig. 1. Uniform impact D0H(t) P0H(t) x h1 h2 2c z
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