AN EXACT SOLUTION OF CRACK PROBLEMS IN PIEZOELECTRIC MATERIALS

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 for these solutions that: (i) the stress intensity factor is thesame 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, anti independent of the electric lode. (iii) the field solutions in a piezoelectric material are not related to the dielectric constant of air or vacuum inside the crack.

Key words: piezoelectric material, plane problem, crack, energy release rate, exact solution

Gao Cunfa;Fan Weixun. AN EXACT SOLUTION OF CRACK PROBLEMS IN PIEZOELECTRIC MATERIALS. Applied Mathematics and Mechanics (English Edition), 1999, 20(1): 51-58.

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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 JFracture, 1992,54(1):79～100
[6] Pah 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 JFracture, 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 Solal 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 tipsingularities [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] Du Shanyi, Liang Jun, Han Jiecal. The coupled solution of a rigid line inclusion and a crack in anisotropic piezoelectric solids [J]. Acta Mechanica Sinica, 1995,27(5): 544～550 (in Chinese)
[16] Yang Xiaoxiang, Kuang Zhenbang. The calculation of piezoelectric materials with aabed mode crack [J], Acta Mechancia Sinica, 1997,29(3): 314～322 (in Chinese)
[17] Sosa H A, Khutoryansky N. New developments concerning piezoelectric materials withdefects [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]. IntJ Solids Strictures, 1996, 33 (23): 3343～3361
[19] Suo Z. Singularities. Interfaces and cracks in dissimilar anisotropic media [J]. Proc RSoc loud, 1990, A427: 331～358
[20] Lothe J. Integral formalism for surface waves in piezoelectric crystals: Existence considerations [J]. J Appl Phys, 1976,47(5): 1799～1807
[21] Muskhelishvili N I. Some Basic Problems of Mathematical Theory of Elasticity [M]. Leyden: Noordhoof, 1975
[22] Wangsness R K. Electromagnetic Fields [M]. New York: John Wiley & Sons, 1979.