利用Schmidt方法研究压电材料Ⅰ-型界面裂纹问题

周振功; 王彪

利用Schmidt方法研究压电材料Ⅰ-型界面裂纹问题

周振功¹,
王彪²

1.
哈尔滨工业大学复合材料研究所,哈尔滨 150001;2.中山大学物理与工程学院,广州 510275

基金项目: 国家自然科学基金资助项目(10572043,10572155);黑龙江省杰出青年基金资助项目(JC04-08)

详细信息

作者简介:
周振功(1963- ),河南省镇平县人,教授,博士,博士生导师(联系人.Tel:+86-451-86402396;Fax:+86-451-86402386;E-mail:zhouzhg@hit.edu.cn).

中图分类号: O346.53
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出版历程
- 收稿日期: 2005-01-06
- 修回日期: 2006-03-21
- 刊出日期: 2006-07-15

Investigation of the Behavior of a Model-Ⅰ Interface Crack in Piezoelectric Materials by Using the Schmidt Method

ZHOU Zhen-gong¹,
WANG Biao²

1.
Center for composite materials, Harbin Institute of Technology, Harbin 150001, P. R. China;

摘要

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．
- 界面裂纹 /
- 应力强度因子 /
- 压电材料
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.
- interface crack /
- intensity factors /
- piezoelectric materials

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参考文献(16)

[1]	England A H. A crack between dissimilar media[J].Journal of Applied Mechanics,1965,32(3):400—402. doi: 10.1115/1.3625813
[2]	Rice J R. Elastic fracture mechanics concept for interface cracks[J].ASME Journal of Applied Mechanics,1988,55(2):98—103. doi: 10.1115/1.3173668
[3]	Comninou M. The interface crack[J].ASME Journal of Applied Mechanics,1977,44(4):631—636. doi: 10.1115/1.3424148
[4]	Comninou M. The interface crack in shear field[J].ASME Journal of Applied Mechanics,1978,45(2):287—290. doi: 10.1115/1.3424289
[5]	Comninou M, Schmueser D.The interface crack in combined tension compression and shear field[J].ASME Journal of Applied Mechanics,1979,46(3):345—348. doi: 10.1115/1.3424553
[6]	Suo Z,Kuo C M, Barnett D M,et al.Fracture mechanics for piezoelectric ceramics[J].Journal of the Mechanics and Physics of Solids,1992,40(4):739—765. doi: 10.1016/0022-5096(92)90002-J
[7]	Herrmann K P, Loboda V V.Fracture mechanical assessment of electrically permeable interface cracks in piezoelectric bimaterials by consideration of various contact zone models[J].Archive of Applied Mechanics,2000,70(1):127—143. doi: 10.1007/s004199900052
[8]	Morse P M, Feshbach H.Methods of Theoretical Physics[M].New York: McGraw-Hill,1958,1:926.
[9]	Erdogan F, Wu B H. Interface crack problems in layered orthotropic materials[J].Journal of the Mechanics and Physics of Solids,1993,41(5):889—917. doi: 10.1016/0022-5096(93)90004-Y
[10]	Ding H J, Chen B, Liang J.General solutions for coupled equations for piezoelectric media[J].International Journal of Solids and Structures,1996,33(16):2283—2296. doi: 10.1016/0020-7683(95)00152-2
[11]	Yang F Q. Fracture mechanics for a Mode Ⅰ crack in piezoelectric materials[J].International Journal of Solids and Structures,2001,38(21):3813—3830. doi: 10.1016/S0020-7683(00)00244-4
[12]	ZHOU Zhen-gong,SUN Jian-liang,WANG Biao.Investigation of the behavior of a crack in a piezoelectric material subjected to a uniform tension loading by use of the non-local theory[J].International Journal of Engineering Science,2004,42(19/20):2041—2063. doi: 10.1016/j.ijengsci.2004.08.004
[13]	Gradshteyn I S, Ryzhik I M.Table of Integrals, Series and Products[M].New York:Academic Press,1980,923—967.
[14]	Erdelyi A.Tables of Integral Transforms[M].New York:McGraw-Hill,1954,68—105.
[15]	周振功，王彪.采用新方法研究非局部理论中Ⅰ-型裂纹的断裂问题[J]. 应用数学和力学,1999,20(10):1025—1032.
[16]	周振功，王彪.采用新方法研究加层压电材料中平行界面共线双裂纹的断裂问题[J]. 应用数学和力学,2003，24(1):1—11.

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利用Schmidt方法研究压电材料Ⅰ-型界面裂纹问题

作者简介:
周振功(1963- ),河南省镇平县人,教授,博士,博士生导师(联系人.Tel:+86-451-86402396;Fax:+86-451-86402386;E-mail:zhouzhg@hit.edu.cn).

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Investigation of the Behavior of a Model-Ⅰ Interface Crack in Piezoelectric Materials by Using the Schmidt Method

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利用Schmidt方法研究压电材料Ⅰ-型界面裂纹问题

作者简介: 周振功(1963- ),河南省镇平县人,教授,博士,博士生导师(联系人.Tel:+86-451-86402396;Fax:+86-451-86402386;E-mail:zhouzhg@hit.edu.cn).

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Investigation of the Behavior of a Model-Ⅰ Interface Crack in Piezoelectric Materials by Using the Schmidt Method

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出版历程

目录

作者简介:
周振功(1963- ),河南省镇平县人,教授,博士,博士生导师(联系人.Tel:+86-451-86402396;Fax:+86-451-86402386;E-mail:zhouzhg@hit.edu.cn).