13th International Conference on Fracture June 16–21, 2013, Beijing, China -1The thermal effect of anti-plane anti-plane crack in a functionally functionally graded piezoelectric piezoelectric strip under electric shock XingLi*, Yongyi Long, Pengpeng Pengpeng Shi School of Mathematics and Computer Science, Ningxia University, 750021, China * Corresponding author: email@li_x@nxu.edu.cn Abstract The thermal effect of mode III crack in a functionally graded strip under the electric shock is investigated. This fracture analysis can be expressed through the superposition of two problem solutions. The first solution is the dynamic behaviors of a functionally graded piezoelectric material with central crack subjected to the electric shock. The second solution means the temperature field by calculating the power of point heat source around the crack tip. Based on the Laplace transform and Fourier transform technique, this mixed boundary value problems is reduced to a Cauchy singular integral equation, which is solved numerically by the Cauchy-Chebyshev quadrature technique. Numerical results are presented to show the effects of geometrical of crack and graded quantities of material on the stress intensity factors. Keywords Anti-plane crack, Functionally graded piezoelectric materials, Electric shock, Thermal effect 1. Introduction Piezoelectric materials (PMs) have been widely used as a smart material in electromechanical devices due to the demand of transform from mechanical to electrical loadings, and vice versa. To improve the reliability and durability problems arising largely from high residual and thermal stress, poor interfacial bonding strength, the functionally graded piezoelectric materials (FGPMs) as a new class of advanced composites have been developed. Recently, some researchers start to investigate the fracture behavior in FGPMs. Wang and Node [1] firstly studied the thermo-piezoelectric fracture problem of a functionally graded piezoelectric layer bonded to a metal. They obtained the thermal flow, stress and electric displacement intensity factors and predict the direction of crack extension by using the energy density theory. Wang considered the mode III crack problem in FGPM, where the material properties are assumed in a class of functional form such that an analytic solution is possible. Recently, Li and Lee [2] investigated the fracture behavior of a weak discontinuous interface between two piezoelectric strips under electro-mechanical loads by using the methods of Fourier integral transform and Cauchy singular integral equation. Ding and Li [3] studied the problem of periodic interface cracks in a functionally graded coating-substrate structure. Recently, based on the methods of variable separation and singular integral equation, Ref. [4] investigated the arc-shaped interfacial cracking problem in a hollow cylinder that consists of an inner orthotropic dielectric layer and an outer functionally graded piezoelectric layer. Although a variety of challenging issues related to certain crack problems in the functionally graded piezoelectric materials have been addressed, one of the remaining problems that need to fully understand is that FGPMs belongs to the dielectric material. Research of Bilyk et al [5] revealed that applying high current on the conductor, the temperature of conductor is lager than the temperature just under force load. To the authors' knowledge, few papers considered the solution for the problem of the heating effect of the crack tip in FGPM under electric shock. Then, this paper discusses the heating effect of the crack tip on piezoelectric medium under the high electric shock load.
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