压电介质内裂纹问题的精确解

高存法; 樊蔚勋

压电介质内裂纹问题的精确解

南京航空航天大学飞行器系, 南京 210016

详细信息

作者简介:
高存法(1962～ ),男,博士,副教授.

中图分类号: O346.1
计量
- 文章访问数: 2376
- HTML全文浏览量: 67
- PDF下载量: 721
- 被引次数: 0
出版历程
- 收稿日期: 1997-09-12
- 修回日期: 1998-10-03
- 刊出日期: 1999-01-15

A Exact Solution of Crack Problems in Piezoelectric Materials

Department of Aircraft, Nanjing Universtiy of Aeronautics & Astronautics, Nanjing 210016, P R China

摘要

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。
- 压电介质 /
- 二维问题 /
- 裂纹 /
- 能量释放率 /
- 精确解
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.
- piezoelectric material /
- plane problem /
- crack /
- energy release rate /
- exact solution

HTML全文

参考文献(22)

[1]	Parton V Z.Fracture mechanics of piezoelectric materials[J].Acta Astronautic,1976,3(9):671～683
[2]	Pak Y E.Crack extension force in a piezoelectric material[J].ASME J Appl Mech,1990,57(3):647～653
[3]	Suo Z,Kuo C M,Barnett D M,Willis J R.Fracture mechanics for piezoelectric ceramics[J].J Mech Phys Solids,1992,40(4):739～765
[4]	Sosa H A.On the fracture mechanics of piezoelectric solids[J].Int J Solids Structures,1992,29(21):2613～2622
[5]	Pak Y E.Linear electro-elastic fracture mechanics of piezoelectric materials[J].Int J Fracture,1992,54(1):79～100
[6]	Pak Y E,Tobin A.On electric field effects in fracture of piezoelectric materials[J].AMD-Vol,161/MD-Vol.42,Mechanics of Electromagnetic Materials and Structure,ASME,1993,51～62
[7]	Sosa H A.Crack problems in piezoelectric ceramics[J].AMD-Vol.161/MD-Vol.42,Mechanics of Electromagnetic Materials and Structure,ASME,1993,63～75
[8]	Dunn M L.The effect of crack face boundary conditions on the fracture mechanics of piezoelectric solids[J].Eng Fracture Mech,1994,48(1):25～39
[9]	Park S B,Sun C T.Effect of electric field on fracture of piezoelectric ceramic[J].Int J Fracture,1995,70(3):203～216
[10]	Beom H G,Atluri S N.Near-tip fields and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media[J].Int J Fracture,1996,75(2):163～183
[11]	Zhang T Y,Tong P.Fracture mechanics for a mode Ⅲ crack in a piezoelectric material[J].Int J Solids Structures,1996,33(3):343～359
[12]	Kogan L,Hui C Y,Molkov V.Stress and induction field of a spheroidal inclusion or a penny-shaped crack in a transversely isotropic piezoelectric material[J].Int J solids Structures,1996,33(19):2719～2737
[13]	Yu S W,Qin Q H.Damage analysis of thermopiezoelectric properties:Part Ⅰ-Crack tip singularities[J].Theor Appl Fract Mech,1996,25(3):263～277
[14]	Qin Q H,Yu S W.An arbitrarily-oriented plane crack terminating at the interface between dissimilar piezoelectric materials[J].Int J Solids Structures,1997,34(5):581～590
[15]	杜善义,梁军,韩杰才.含刚性线夹杂及裂纹的各向异性压电材料耦合场分析[J].力学学报,1995,27(5):544～550
[16]	扬晓翔,匡震邦.刚度微分法计算压电材料平面断裂问题[J],力学学报,1997,29(3):314～322
[17]	Sosa H A,Khutoryansky N.New developments concerning piezoelectric materials with defects[J].Int J Solids Structures,1996,33(23):3399～3414
[18]	Chung M Y,Ting T C T.Piezoelectric solids with an elliptic inclusion or hole[J].Int J Solids Structures,1996,33(23):3343～3361
[19]	Suo Z.Singularities,interfaces and cracks in dissimilar anisotropic media[J].Proc R Soc Lond,1990,A427:331～358
[20]	20 Lothe J.Integral formalism for surfact waves in piezoelectric crystals:Existence considerations[J].J Appl Phys,1976,47(5):1799～1807
[21]	Muskhelishvili N I.Some Basic Proelems of Mathematical Theory of Elasticity[M].Leyden:Noordhoof,1975
[22]	Wangsness R K.Electromagnetic Fields[M].New York:John Wiley & Sons,1979.