An exact solution of crack problems in piezoelectric materials
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.
Key wordspiezoelectric material plane problem crack energy release rate exact solution
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- Pak Y E. Linear electro-elastic fracture mechanics of piezoelectric materials [J].Int J Fracture, 1992,54 (1): 79–100Google Scholar
- 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, 51–62Google Scholar
- Sosa H A. Crack problems in piezoelectric ceramics [J]. AMD-Vol. 161/MD-Vol. 42,Mechanics of Electromagnetic Materials and Structure, ASME, 1993, 63–75Google Scholar
- 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)Google Scholar
- Yang Xiaoxiang, Kuang Zhenbang. The calculation of piezoelectric materials with a mixed mode crack [J],Acta Mechanicia Sinica, 1997,29 (3): 314–322 (in Chinese)Google Scholar
- Muskhelishvili N I.Some Basic Problems of Mathematical Theory of Elasticity [M]. Leyden: Noordhoof, 1975Google Scholar
- Wangsness R K.Electromagnetic Fields [M]. New York: John Wiley & Sons, 1979Google Scholar