13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Anti-Plane Moving Polarization Saturation Crack in Ferroelectric Solids Hao-sen Chen2, Dai-ning Fang1 1 LTCS and College of Engineering, Peking University, Beijing, 100871, China 2Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China * Corresponding author: chenhs09@mails.tsinghua.edu.cn Abstract A moving polarization saturation (PS) model is proposed to study the anti-plane Yoffe-type crack with constant velocity in ferroelectric materials. Based on the extended Stroh formalism, the model is solved using complex function method. The closed-form expressions for the electroelastic fields are obtained in a concise way. Results are shown to converge to known solutions for static PS model and the moving linear piezoelectric model. Keywords Moving polarization saturation model; Ferroelectric materials; anti-plane. 1 Introduction Ferroelectric materials always endure dynamic loads, such as mechanical impact or pulse-like electric loading in application [1]. Since their instinct low fracture toughness, the reliability concerns and optimal design of smart devices using ferroelectrics call for a better understanding of the fracture behavior. Compared with the well developed static piezoelectric fracture mechanics, few investigations on the dynamic fracture mechanics of piezoelectric and ferroelectric materials have been reported. The crack propagation problem is always the popular point of study among the theoretical dynamic fracture mechanics. Freund [2] classified the problems of crack propagation into three classes (1) The first type is the steady state crack growth. Chen and Yu [3] studied the anti-plane moving crack problem in piezoelectric materials. They found that the intensity factors are independent of the velocity of the crack. Soh et al. [4] researched the generalized plane problem of a finite Griffith crack moving with constant velocity in an anisotropic piezoelectric material. (2) The second type is self-similar crack growth. (3) The third type is the crack growth due to time-independent or time-dependent loading. In this case, Li and Mataga [5, 6] obtained the transient closed-form solutions for dynamic stress and electric displacement intensities and dynamic energy release rate of a propagating crack in homogeneous hexagonal piezoelectric materials dynamic anti-plane point loading. To et al. [7] studied propagation of a mode-III interfacial conductive crack along a conductive interface between two piezoelectric materials. Chen et al. [8] researched the problem of dynamic interfacial crack propagation in elastic–piezoelectric bi-materials subjected to uniformly distributed dynamic anti-plane loadings on crack faces. All the aforementioned studies on the problems of crack propagation are mainly about the linear dynamic fracture mechanics. However, when the electrical load is not weak, ferroelectric materials exhibit strong electrical nonlinearity, Gao et al. [9] proposed a strip polar saturation (PS) model of electrical yielding. It is convenient to propose some simplified models or approximate analyses. Shen et al. [10] developed a strip electric saturation and mechanical yielding model for a mode III interfacial crack of Yoffe type between ferroelectric-plastic bi-materials. In this paper, the static PS model is extended to the moving PS model for studying the anti-plane crack propagation problem of ferroelectric materials. The plan of the rest of the paper is
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