压电材料中两平行对称可导通裂纹断裂性能分析

周振功; 王彪

压电材料中两平行对称可导通裂纹断裂性能分析

周振功,
王彪

哈尔滨工业大学复合材料研究所, 哈尔滨 150001

基金项目: 国家杰出青年基金资助项目(19725209);黑龙江省自然科学研究基金资助项目;黑龙江省博士后基金资助项目

详细信息

作者简介:
周振功(1963- ),男,河南镇平人,教授,博士,博士导师(E-mail:zhouzhg@hope.hit.edu.cn).

中图分类号: O345.51
计量
- 文章访问数: 2841
- HTML全文浏览量: 347
- PDF下载量: 721
- 被引次数: 0
出版历程
- 收稿日期: 2001-07-19
- 修回日期: 2001-04-26
- 刊出日期: 2002-12-15

The Behavior of Two Parallel Symmetric Permeable Cracks in Piezoelectric Materials

P O Box 2147, Center for Composite Materials and Electro-Optics Research Center, Harbin Institute of Technology, Harbin 150001, P R China

摘要

摘要: 采用Schmidt研究了压电材料中对称平行的双可导通裂纹的断裂性能,利用富里叶变换使问题的求解转换为求解两对以裂纹面位移之差为未知变量的对偶积分方程,并采用Schmidt方法来对这两对对偶积分程进行数值求解。结果表明应力强度因子和电位移强度因子与裂纹的几何尺寸有关。与不可导通裂纹有关结果相比,可导通裂纹的电位移强度因子远小于相应问题不可导通裂纹的电位移强度因子。
- 压电材料 /
- 裂纹 /
- Schmidt方法 /
- 对积偶分方程 /
- 应力强度因子
Abstract: The behavior of two parallel symmetric cracks in piezoelectric materials under anti-plane shear loading was studied by the Schmidt method for the permeable crack face conditions. By using the Fourier transform, the problem can be solved with two pairs of dual integral equations in which the unknown variable is the jump of the diplacement across the crack surfaces. These equations were solved using the Schmidt method. The results show that the stress and the electric displacement intensity factors of cracks depend on the geometry of the crack. Contrary to the impermeable crack surface condition solution, it is found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller than the results for the impermeable crack surface conditions.
- piezoelectric material /
- parallel crack /
- Schmidt method /
- dual-integral equation /
- stress and electric displacement

HTML全文

参考文献(34)

[1]	Deeg W E F.The analysis of dislocation,crack and inclusion problems in piezoelectric solids[D].Ph D thesis.Stanford University,1980.
[2]	Pak Y E.Crack extension force in a piezoelectric material[J].Journal of Applied Mechanics,1990,57(4):647-653.
[3]	Pak Y E.Linear electro-elastic fracture mechanics of piezoelectric materials[J].International Journal of Fracture,1992,54(1):79-100.
[4]	Sosa H A,Pak Y E.Three-dimensional eigenfunction analysis of a crack in a piezoelectric ceramics[J].International Journal of Solids and Structures,1990:26(1):1-15.
[5]	Sosa H A.Plane problems in piezoelectric media with defects[J].International Journal of Solids and Structures,1991,28(4):491-505.
[6]	Sosa H.On the fracture mechanics of piezoelectric solids[J].International Journal of Solids and Structures,1992,29(8):2613-2622.
[7]	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(5):739-765.
[8]	Pack S B,Sun C T.Fracture criteria for piezoelectric ceramics[J].Journal of American Ceramics Society,1995,78(7):1475-1480.
[9]	Zhang T Y,Tong P.Fracture mechanics for a mode Ⅲ crack in a piezoelectric material[J].International Journal of Solids and Structures,1996,33(5):343-359.
[10]	Gao H,Zhang T Y,Tong P.Local and global energy rates for an elastically yielded crack in piezoelectric ceramics[J].Journal of Mechanics and Physics of Solids,1997,45(4):491-510.
[11]	WANG Biao.Three dimensional analysis of a flat elliptical crack in a piezoelectric materials [J].International Journal of Engineering Science,1992,30(6):781-791.
[12]	Narita K,Shindo Y.Scattering of Love waves by a surface-breaking crack in piezoelectric layered media[J].JSME International Journal,Series A,1998,41(1):40-52.
[13]	Narita K,Shindo Y.Scattering of anti-plane shear waves by a finite crack in piezoelectric laminates[J].Acta Mechanica,1999,134(1):27-43.
[14]	Zhou Z G,Wang B,Cao M S.Analysis of two collinear cracks in a piezoelectric layer bonded to dissimilar half spaces subjected to anti-plane shear[J].European Journal of Mechanics,A/Solids,2001,20(2):213-226.
[15]	Yu S W,Chen Z T.Transient response of a cracked infinite piezoelectric strip under anti-plane impact[J].Fatigue and Engineering Materials and Structures,1998,21(4):1381-1388.
[16]	Zhang T Y,Hack J E.Mode-Ⅲ cracks in piezoelectric materials[J].Journal of Applied Physics,1992,71(9):5865-5870.
[17]	McMeeking R M.On mechanical stress at cracks in dielectrics with application to dielectric breakdown[J].Journal of Applied Physics,1989,62(11):3116-3122.
[18]	Suo Z.Models for breakdown-resistant dielectric and ferroelectric ceramics[J].Journal of the Mechanics and Physics of Solids,1993,41(6):1155-1176.
[19]	Dunn M L.The effects of crack face boundary conditions on the fracture mechanics of piezoelectric solids[J].Engineering Fracture of Mechanics,1994,48(1):25-39.
[20]	Zhang T Y,Tong P.Fracture mechanics for a mode Ⅲ crack in a piezoelectric material[J].International Journal of Solids and Structures,1996,33(5):343-359.
[21]	Sosa H,Khutoryansky N.Transient dynamic response of piezoelectric bodies subjected to internal electric impulses[J].International Journal of Solids and Structures,1999,36(9):5467-5484.
[22]	Soh A K,Fang D N,Lee K L.Analysis of a bi-piezoelectric ceramic layer with an interfacial crack subjected to anti-plane shear and in-plane electric loading[J].European Journal of Mechanics,A/Solid,2000,19(6):961-977.
[23]	Morse P M,Feshbach H.Methods of Theoretical Physics[M].New York:McGraw-Hill,1958,1,828-930.
[24]	Gradshteyn I S,Ryzhik I M.Table of Integral,Series and Products[M].New York:Academic Press,1980,1035-1037.
[25]	Erdelyi A.Tables of Integral Transforms[M].Vol 1.New York:McGraw-Hill,1954,34-89.
[26]	Amemiya A,Taguchi T.Numerical Analysis and Fortran[M].Tokyo:Maruzen,1969,105-123.
[27]	Itou S.Three dimensional waves propagation in a cracked elastic solid[J].Journal of Applied Mechanics,1978,45(5):807-811.
[28]	Zhou Z G,Bai Y Y,Zhang X W.Scattering of harmonic shear waves by a finite crack by using the non-local theory[J].International Journal of Engineering Science,1999,37(5):609-620.
[29]	Zhou Z G,Bai Y Y,Zhang X W.Two collinear Griffith cracks subjected to uniform tension in infinitely long strip[J].International Journal of Solids and Structures,1999,36(36):5597-5609.
[30]	Zhou Z G,Han J C,Du S Y.Investigation of a Griffith crack subject to anti-plane shear by using the non-local theory[J].International Journal of Solids and Structures,1999,36(26):3891-3901.
[31]	Zhou Z G,Wang B,Du S Y.Scattering of harmonic anti-plane shear waves by a finite crack by using the non-local theory[J].International Journal of Fracture,1998,91(1):13-22.
[32]	Zhou Z G,Zhang X W,Bai Y Y.Investigation of two Griffith cracks subject to uniform tension by using the non-local theory[J].International Journal of Engineering Science,1999,37(13):1709-1722.
[33]	Zhou Z G,Shen Y P.Investigation of the scattering of harmonic shear waves by two collinear cracks using the non-local theory[J].Acta Mechanica,1999,135(3):169-179.
[34]	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.