 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| V. F. Bakirov, "Integral relations for the problem of a crack on a piezoelectric-conductor interface," Mech. Solids. 39 (6), 99-115 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
6 |
Pages |
99-115 |
| Title |
Integral relations for the problem of a crack on a piezoelectric-conductor interface |
| Author(s) |
V. F. Bakirov (Ufa) |
| Abstract |
A plane problem of a crack on an interface between an isotropic elastic conductor and a transversely isotropic piezoelectric is considered. Using the integral Fourier transform, the problem is reduced to a system of three singular integral equations on the interface. These equations relate the normal and tangential stresses and the normal electric-induction component with the normal and tangential components of the crack opening vector and the jump of the electric-field potential on the crack surfaces. The systems of equations for a crack with electric contact between the surfaces and a crack with electrically insulated surfaces are investigated analytically. For both models, integral relations which make it possible to obtain an exact solution as a function of the loadings applied to the crack surfaces are formulated. As an example, analytical solutions of the crack problem, which correspond to some simple loading conditions, are given. |
| References |
| 1. | B. A. Kudryavtsev, V. Z. Parton, and V. I. Rakitin, "Fracture mechanics of piezoelectric materials. A straight tunnel crack on a conductor interface," PMM [Applied Mathematics and Mechanics], Vol. 39, No. 1, pp. 149-159, 1975. |
| 2. | C. M. Kuo and D. M. Barnett, "Stress singularities of interface crack in bonded piezoelectric half-spaces", in J. J. Wu et al. (Editors), Modern Theory of Anisotropic Elasticity and Applications, pp. 33-50, SIAM Proc., Ser. Philadelphia, 1991. |
| 3. | Z. Suo, C. M. Kuo, D. M. Barnett, and J. R. Willis,
"Fracture mechanics for piezoelectric ceramics," J. Mech. and Phys. Solids, Vol. 40, No. 4, pp. 739-765, 1992. |
| 4. | H. G. Beom and S. N. Alturi, "Near-tip filds and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media," Intern. J. Fracture, Vol. 75, No. 2, pp. 163-183, 1996. |
| 5. | D. M. Barnett and J. Lothe, "Dislocations and line charges in anisotropic piezoelectric insulators," Physica Status Solidi (B), Vol. 67, No. 1, pp. 105-111, 1975. |
| 6. | V. B. Govorukha and V. V. Loboda, "Contact zone models for an interface crack in a piezoelectric material," Acta Mech., Vol. 140, No. 3-4, pp. 233-246, 2000. |
| 7. | V. F. Bakirov, Crack on an Interface between
Piezoelectric and Conductor Subjected to Electric and Mechanical Loadings. Preprint N687 [in Russian], In-t Probl. Mekh. RAN, Moscow, 2002. |
| 8. | Y. E. Pak, "Linear electro-elastic fracture mechanics of piezoelectric materials," Intern. J. Fracture, Vol. 54, No. 1, pp. 79-100, 1992. |
| 9. | S. B. Park and C. T. Sun, "Effect of electric field on fracture of piezoelectric ceramics," Intern. Journal of Fracture, Vol. 70, No. 3, pp. 203-216, 1994. |
| 10. | N. I. Muskhelishvili, Some Basic Problems of Mathematical Theory of Elasticity [in Russian], Nauka, Moscow, 1966. |
| 11. | L. I. Slepyan, Crack Mechanics [in Russian],
Sudostroenie, Leningrad, 1981. |
| 12. | R. V. Goldstein and M. N. Perel'muter, "Modeling of bonding at
an infinite crack," Intern. J. Fracture, Vol. 99, No. 1-2, pp. 53-79, 1999. |
| 13. | J. R. Rice and G. C. Sih, "Plane problems of cracks in dissimilar media," Trans. ASME Ser. E J. Appl. Mech., Vol. 32, No. 2, pp. 418-423, 1965. |
| 14. | B. M. Malyshev and R. L. Salganik, "The strentgh of adhesive joints using the theory of cracks," Intern. J. Fract. Mech., Vol. 1, No. 2, pp. 114-128, 1965. |
| 15. | V. Z. Parton and B. A. Kudryavtsev, Electromagnetoelasticity of
Piezoelectric and Electroconductive Bodies [in Russian], Nauka, Moscow, 1988. |
|
| Received |
25 April 2003 |
| << Previous article | Volume 39, Issue 6 / 2004 | Next article >> |
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