Investigation of the Behavior of a Model-Ⅰ Interface Crack in Piezoelectric Materials by Using the Schmidt Method
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摘要: 在一定的假设条件下,即不考虑界面裂纹尖端处裂纹面的相互叠入现象,研究了压电材料Ⅰ-型界面裂纹问题.利用Fourier变换使问题的求解转换为求解两对对偶积分方程.进而把裂纹表面位移差展开成Jacobi多项式形式来求解对偶积分方程.结果表明裂纹尖端应力场和电位移场的奇异性与均匀材料裂纹问题的奇异性相同.当上下半平面材料相同时,解可以退化而得到其精确解.Abstract: The behavior of a Mode-Ⅰ interface crack in piezoelectric materials is investigated under the assumptions that the effect of the crack surface overlapping very near the crack tips is negligible. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Contrary to the previous solution of the interface crack in piezoelectric materials, it is found that the stress and the electric displacement singularities of the present interface crack solution are the same as those of the ordinary crack in homogenous materials. The solution can be returned to the exact solution when the upper half plane material is the same as the lower half plane material.
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Key words:
- interface crack /
- intensity factors /
- piezoelectric materials
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