具有刚性双边裂纹的压电介质中的电荷相互作用分析

胡元太; 李国清; 蒋树农; 胡洪平; 杨嘉实

具有刚性双边裂纹的压电介质中的电荷相互作用分析

1.
中南大学力学与传感技术研究所,长沙 410083;2.华中科技大学力学系,武汉 430074;3.内布拉斯加大学工程力学系,林肯 68588NE,美国

基金项目: 国家自然科学基金资助项目(10172036);教育部留学回国人员科研启动基金资助项目

详细信息

作者简介:
胡元太(1964- ),教授,博士(Fax:+86-731-5571736;E-mail:hudeng@263.net).

中图分类号: O346.1
计量
- 文章访问数: 2784
- HTML全文浏览量: 139
- PDF下载量: 515
- 被引次数: 0
出版历程
- 收稿日期: 2004-08-05
- 修回日期: 2005-04-11
- 刊出日期: 2005-08-15

Interaction of Electric Charges in a Piezoelectric With Rigid External Cracks

1.
Institute of Mechanics and Sensing Technology, Central South University, Changsha 410083, P. R. China;

摘要

摘要: 利用Stroh方法，研究了含双边固定导电裂纹的二维压电体在广义线力作用下的Green函数．首先分析的是因压电性和边界极化电荷所引起的作用在自由电荷上的Coulomb力．然后，再分析了双边裂纹附近的两个奇异点之间的相互作用问题（其中，至少一个奇异点处存在自由电荷）．数值计算表明：当两个或多个奇点互相靠近且奇点中至少存在一个自由电荷时，Coulomb力将明显影响压电介质内的力电场，这时的Coulomb力将不能再被忽略掉．所得结果不仅适用于平面和反平面问题，也适用于面内变形与面外变形相耦合的情况．
- 双边裂纹 /
- 强度因子 /
- Green函数 /
- Coulomb力
Abstract: Using Stroh's formalism simple explicit expressions of Green's functions for a 2D piezoelectric body with two semi-infinite fixed conductor cracks subjected to a generalized line force were given. The Coulomb force acting on the free line charge due to the piezoelectricity and the distributed bo undary polarization charges was discussed at first. Interactions between two singularities with free charge (s) located in aregion with external cracks were studied, too. The numerical results show that the Coulomb force for two or more singularities with one free charge at least will have much influence on the electr omechanical fields in piezoelectric media when these singularities move closely with each other and therefore cannot be over looked again. The solutions obtained are valid not only for plane and anti-plane problems but also for coupled problems between in-plane and out-of-plane deformations.
- external crack /
- intensity factor /
- Green’s function /
- Coulomb force

HTML全文

参考文献(15)

[1]	Barnett D M,Lothe J.Dislocations and line charges in anisotropic piezoelectric insulators[J].Phys Status Solidi,Ser B,1975,67(1):105—111. doi: 10.1002/pssb.2220670108
[2]	Chadwick P,Smith G D.Foundations of the theory of surface waves in anisotropic medium[J].Adv Appl Mech,1977,17:303—377. doi: 10.1016/S0065-2156(08)70223-0
[3]	HU Yuan-tai, HUANG Yu-ying, CHEN Chuan-yao， et al. Green's functions for a piezoelectric semi-infinite body with a fixed conductor surface[J].Mechanics Research Communications,2000,27(3):333—338. doi: 10.1016/S0093-6413(00)00100-2
[4]	胡元太，赵兴华.具有抛物线边界的二维弹性介质的Green函数[J].应用数学和力学，1996,17(5):337—385.
[5]	Hwu C,Yen W J.Green's functions of two-dimensional anisotropic plates containing an elliptic hole[J].International Journal of Solids and Structures,1991,27(13):1785—1791.
[6]	Ting T C T.Image singularities of Green's functions for anisotropic elastic half-spaces and bimaterials[J].Journal of Elasticity,1991,27(2):119—139.
[7]	Ting T C T,HU Yuan-tai,Kirchner H O K.Anisotropic elastic materials with a parabolic or hyperbolic boundary: a classical problem revisited[J].J Appl Mech,2001,68(4):537—542. doi: 10.1115/1.1381393
[8]	Chung M Y,Ting T C T.Piezoelectric solid with an elliptic inclusion or hole[J].International Journal of Solids and Structures,1996,33(23):3343—3361. doi: 10.1016/0020-7683(95)00189-1
[9]	Kuo C M,Barnett D M.Stress singularities of interfacial cracks in bonded piezoelectric half-spaces[A].In:Wu J J,Ting T C T,Barnett D M Eds.Modern Theory of Anisotropic Elasticity and Applications，Philadelphia:SIAM,1990,33—50.
[10]	Park Y E.Linear electro-elastic fracture mechanics of piezoelectric materials[J].International Journal of Fracture,1992,54:79—100. doi: 10.1007/BF00040857
[11]	Park S B,Sun C T.Effect of electric field on fracture of piezoelectric ceramics[J].International Journal of Fracture,1995,70(3):203—216.
[12]	Sosa H，Khutoryansky N.New developments concerning piezoelectric materials with defects[J].International Journal of Solids and Structures,1996,33:3399—3414. doi: 10.1016/0020-7683(95)00187-5
[13]	Suo Z,Kuo C M,Barnett D M,et al.Fracture Mechanics for piezoelectric ceramics[J].Journal of Mechanics and Physics of Solids,1992,40(4):739—765. doi: 10.1016/0022-5096(92)90002-J
[14]	Stroh A N.Dislocations and cracks in anisotropic elasticity[J].Phil Mag,1958,3(30):625—646. doi: 10.1080/14786435808565804
[15]	Stroh A N.Steady state problem in anisotropic elasticity[J].J Math Phys,1962,41(1):77—103.