A Exact Solution of Crack Problems in Piezoelectric Materials

Gao Cunfa; Fan Weixun

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(1): 47-54

Gao Cunfa, Fan Weixun. A Exact Solution of Crack Problems in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 1999, 20(1): 47-54.

Citation:

Gao Cunfa, Fan Weixun. A Exact Solution of Crack Problems in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 1999, 20(1): 47-54.

Citation:

Gao Cunfa, Fan Weixun. A Exact Solution of Crack Problems in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 1999, 20(1): 47-54.

PDF( 365 KB)

A Exact Solution of Crack Problems in Piezoelectric Materials

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

Received Date: 1997-09-12
Rev Recd Date: 1998-10-03
Publish Date: 1999-01-15

Abstract

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

FullText(HTML)

References(22)

References

[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.