13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Pre-kinking analysis of a cracked piezoelectric strip under impact loadings Zengtao Chen1,*, Keqiang Hu1 1 Department of Mechanical Engineering, University of New Brunswick, Fredericton NB E3B 5A3, Canada * Corresponding author: ztchen@unb.ca Abstract An impermeable crack in a piezoelectric strip at arbitrary position under in-plane mechanical and electric impact loadings is considered. Due to the asymmetry of the geometry, this crack problem is a mixed-mode one. Fourier and Laplace transforms are applied to reduce the mixed boundary value problem of the crack to a system of singular integral equations. The asymptotic fields near the crack tip are obtained in explicit form and hoop and shear stress intensity factors are defined. Laplace inversion transforms are applied to get the dynamic hoop stress intensity factors. The crack kinking phenomena is investigated by applying the criterion of maximum hoop stress intensity factors. Numerical results show that the geometry of the cracked strip and the electric loadings have effects on the singular field distributions around the crack tip, and the hoop stress intensity factors are influenced by the material parameters, the electric loading and the geometric size ratios. Keywords Mixed-mode crack, Piezoelectric Strip, Singular integral equations, Crack kinking; Hoop stress intensity factor 1. Introduction Piezoelectric materials can be made into various functional devices, such as sensors and actuators, which are widely used in modern industrial fields. Due to the brittleness and low fracture toughness of piezoelectric materials, dynamic fracture analysis of piezoelectric materials has drawn considerable attentions. Dynamic anti-plane crack propagation in piezoelectric materials has been studied by Li and Mataga [1, 2]. Shindo et al. [3] obtained dynamic stress intensity factors of a cracked piezoelectric medium in a uniform dielectric field. The problem of a Griffith crack moving along the interface of two dissimilar piezoelectric materials was solved by Chen et al. [4] using the integral transform technique and it is shown that the stress and electric displacement are dependent on the speed of the crack and the material coefficients. Chen and Yu [5] investigated a semi-infinite crack in a piezoelectric medium subjected to antiplane impact loading. Mode-I transient response of a piezoelectric strip containing a center-situated crack under in-plane mechanical and electric impacts was investigated by Wang and Yu [6], and it was found that the intrinsic mechanical-electrical coupling plays a significant role in the dynamic fracture response of in-plane problems. Crack kinking is an important phenomenon in the fracture of piezoelectric materials in response to electro-mechanical loading. Zhu and Yang [7] modeled the crack kinking in a piezoelectric solid by continuous distribution of edge dislocations and electric dipoles, and the solution was formulated via the Stroh formalism. The mixed-mode crack initiation in piezoelectric strip was studied by Wang and Noda [8] using the method of Fourier transform and singular integral equations. Hu and Zhong [9] considered a moving mode-III crack in a functionally graded piezoelectric strip. They found that the gradient of the material properties can affect the magnitudes of the stress intensity factors, and a high crack moving velocity can change the propagation orientation of the crack. In this paper, the mixed-mode crack in a piezoelectric strip under in-plane electrical and mechanical impact loadings is studied. Fourier transform is employed to reduce the mixed boundary
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