| 压电介质内裂纹问题的精确解 |
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| 引用本文： | 高存法,樊蔚勋.压电介质内裂纹问题的精确解[J].应用数学和力学,1999,20(1):47-54. |
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| 作者姓名： | 高存法 樊蔚勋 |
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| 作者单位： | 南京航空航天大学飞行器系, 南京 210016 |
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| 摘 要： | 在压电介质断裂力学分析中,人们常假定裂纹面上的电位移法向分量为零,可是实验表明,这一假设将导致错误的结果。本文基于精确的电边界条件,并应用Stroh公式的方法,导出了含裂纹压电介质在无限远处均匀外载作用下二维问题的精确解。结果表明:(ⅰ)应力强度因子与各向同性材料相同,而电位移强度因子取决于材料常数和机械载荷,但与电载荷无关;(ⅱ)能量释放率大于纯弹性各向异性材料内的值,即总是正的,且与电载荷无关;(ⅲ)裂纹内所含空气的介电常数对介质内的场强无影响。
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| 关 键 词： | 压电介质 二维问题 裂纹 能量释放率 精确解 |
| 收稿时间： | 1997-09-12 |
A Exact Solution of Crack Problems in Piezoelectric Materials |
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| Gao Cunfa,Fan Weixun.A Exact Solution of Crack Problems in Piezoelectric Materials[J].Applied Mathematics and Mechanics,1999,20(1):47-54. |
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| Authors: | Gao Cunfa Fan Weixun |
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| Affiliation: | Department of Aircraft, Nanjing Universtiy of Aeronautics & Astronautics, Nanjing 210016, P R China |
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| Abstract: | An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from the available experiments that the above assumption will lead to erroneous results. In this paper, the two-dimensional problem of a piezoelectric material with a crack is studied based on the exact electric boundary condition on the crack faces. Stroh formalism is used to obtain the closed-form solutions when the material is subjected to uniform loads at infinity. It is shown from these solutions that:(ⅰ) the stress intensity factor is the same as that of isotropic material, while the intensity factor of the electric displacement depends on both material properties and the mechanical loads, but not on the electric load. (ⅱ) the energy release rate in a piezoelectric material is larger than that in a pure elastic-anisotropic material, i e, it is always positive, and independent of the electric loads. (ⅲ) the field solutions in a piezoelectric material are not related to the dielectric constant of air or vacuum inside the crack. |
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| Keywords: | piezoelectric material plane problem crack energy release rate exact solution |
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