Non-Local Theory Solution for an Anti-Plane Shear Permeable Crack in Functionally Graded Piezoelectric Materials

被引:0
作者
Zhen-Gong Zhou
Biao Wang
机构
[1] Center for Composite Materials,School of Physics and Engineering
[2] Harbin Institute of Technology,undefined
[3] Sun Yat-Sen University,undefined
来源
Applied Composite Materials | 2006年 / 13卷
关键词
crack; functionally graded piezoelectric materials; mechanics of solids; non-local theory;
D O I
暂无
中图分类号
学科分类号
摘要
In this paper, the non-local theory solution of a Griffith crack in functionally graded piezoelectric materials under the anti-plane shear loading is obtained for the permeable electric boundary conditions, in which the material properties vary exponentially with coordinate parallel to the crack. The present problem can be solved by using the Fourier transform and the technique of dual integral equation, in which the unknown variable is the jump of displacement across the crack surfaces, not the dislocation density function. To solve the dual integral equations, the jump of the displacement across the crack surfaces is directly expanded in a series of Jacobi polynomials. From the solution of the present paper, it is found that no stress and electric displacement singularities are present near the crack tips. The stress fields are finite near the crack tips, thus allows us to use the maximum stress as a fracture criterion. The finite stresses and the electric displacements at the crack tips depend on the crack length, the functionally graded parameter and the lattice parameter of the materials, respectively. On the other hand, the angular variations of the strain energy density function are examined to associate their stationary value with locations of possible fracture initiation.
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页码:345 / 367
页数:22
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