Electro-elastic behavior induced by an external circular crack in a piezoelectric material
Source abstract
Abstract
The electro-elastic problem of a transversely isotropic piezoelectric material with a flat crack occupying the outside of a circle perpendicular to the poling axis is considered in this paper. By using the Hankel transform technique, a mixed boundary value problem associated with the considered problem is solved analytically. The results are presented in closed form both for impermeable crack and for permeable crack. A full field solution is given, i.e., explicit expressions for electro-elastic field at any point in the entire piezoelectric space, as well as field intensity factors near the crack front, are determined. A numerical example for a cracked PZT-5H ceramic is given, and the effects of applied electric fields on elastic and electric behaviors are presented graphically.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Numerical methods in engineering · Ultrasonics and Acoustic Wave Propagation · Structural Health Monitoring Techniques
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (30)
Show source-provided references
1. Chen, W.Q. and Shioya, T. (1999). Fundamental solution for a penny-shaped crack in a piezoelectric medium. Journal of the Mechanics and Physics Solids 47, 1459–1475.10.1016/S0022-5096(98)00114-8 ↗
2. Fabrikant, V.I. (2003). Computation of infinite integrals involving three Bessel functions by introduction of new formalism. ZAMM. 83, 363–374.10.1002/zamm.200310059 ↗
3. Gao, C.-F. and Fan, W.X. (1999). Exact solutions for the plane problem in piezoelectric materials with an elliptic or a crack. International Journal of Solids and Structures 36, 2527–2540.10.1016/S0020-7683(98)00120-6 ↗
4. Gradshteyn, I.S. and Ryzhik, I.M. (1980). Table of Integrals, Series and Products. Academic Press, New York.
5. Hao, T.H. and Shen, Z.Y. (1994). A new electric boundary condition of electric fracture mechanics and its applications. Engineering Fracture Mechanics 47, 793–802.10.1016/0013-7944(94)90243-7 ↗
6. Jiang, L.Z. and Sun, C.T. (2001). Analysis of indentation cracking in piezoceramics. International Journal of Solids and Structures 38, 1903–1918.10.1016/S0020-7683(00)00142-6 ↗
7. Karapetian, E., Sevostianov, I. and Kachanov, M. (2000). Penny-shaped and half-plane cracks in a transversely isotropic piezoelectric solid under arbitrary loading. Archive of Applied Mechanics 70, 201–229.10.1007/s004199900060 ↗
8. Kassir, M.K. and Sih, G.C. (1975). Three-dimensional crack problems. In: Mechanics of Fracture (edited by Sih, G.C.), Vol. 2. Noordhoff International Publishing, Leiden.
9. Kogan, L., Hui, C.Y. and Molcov, V. (1996). Stress and induction field of a spheroidal inclusion of a penny-shaped crack in a transversely isotropic piezoelectric material. International Journal of Solids and Structures 33, 2719–2737.10.1016/0020-7683(95)00182-4 ↗
10. Liu, M. and Hsia, K.J. (2003). Interfacial cracks between piezoelectric and elastic materials under in-plane electric loading. Journal of the Mechanics and Physics Solids 51, 921–944.10.1016/S0022-5096(02)00120-5 ↗
11. McMeeking, R.M. (1999). Crack tip energy release rate for a piezoelectric compact tension specimen. Engineering Fracture Mechanics 64, 217–244.10.1016/S0013-7944(99)00068-5 ↗
12. McMeeking, R.M. (2001). Towards a fracture mechanics for brittle piezoelectric and dielectric materials. International Journal of Fracture 108, 25–41.10.1023/A:1007652001977 ↗
13. Pak, Y.E. (1990). Crack extension force in a piezoelectric material. Journal of Applied Mechanics 57, 647–653.10.1115/1.2897071 ↗
14. Pak, Y.E. (1992). Linear electroelastic fracture mechanics of piezoelectric materials. International Journal of Fracture 54, 79–100.10.1007/BF00040857 ↗
15. Park, S. and Sun, C.T. (1995). Fracture criteria for piezoelectric ceramics. Journal of the American Ceramic Society 78, 1475–1480.10.1111/j.1151-2916.1995.tb08840.x ↗
16. Ru, C.Q. (1999). Electric-field induced crack closure in linear piezoelectric media. Acta Materials 47, 4683–4693.10.1016/S1359-6454(99)00310-9 ↗
17. Shindo, Y., Watanabe, K. and Narita, F. (2000). Electroelastic analysis of a piezoelectric ceramic strip with a central crack. International Journal of Engineering Science 38, 1–19.10.1016/S0020-7225(99)00015-4 ↗
18. Sosa, H. (1992). On the fracture mechanics of piezoelectric solids. International Journal of Solids and Structures 29, 2613–2622.10.1016/0020-7683(92)90225-I ↗
19. Sosa, H. and Khutoryansky, N. (1996). New developments concerning piezoelectric materials with defects. International Journal of Solids and Structures 33, 3399–3414.10.1016/0020-7683(95)00187-5 ↗
20. Suo, Z., Kuo, C.-M., Barnett, D.M. and Willis, J.R. (1992). Fracture mechanics for piezoelectric ceramics. Journal of the Mechanics and Physics Solids 40, 739–765.10.1016/0022-5096(92)90002-J ↗
21. Sneddon, I.N. and Lowengrub, M. (1969). Crack Problems in the Classical Theory of Elasticity. John Wiley and Sons, New York.
22. Wang, B. (1992). Three-dimensional analysis of a flat elliptical crack in a piezoelectric material. International Journal of Engineering Science 30, 781–791.10.1016/0020-7225(92)90107-R ↗
23. Wang, B.L. and Mai, Y.-W. (2003). On the electrical boundary conditions on the crack surfaces in piezoelectric ceramics. International Journal of Engineering Science 41, 633–652.10.1016/S0020-7225(02)00149-0 ↗
24. Wang, Z.-K. and Huang, S.-H. (1995). Fields near elliptical crack tip in piezoelectric ceramics. Engineering Fracture Mechanics 51, 447–456.10.1016/0013-7944(94)00288-S ↗
25. Wang, X.D. and Jiang, L.Y. (2002). Fracture behaviour of cracks in piezoelectric media with electromechanically coupled boundary conditions. Proc. R. Soc. London. A458, 2545–2560.10.1098/rspa.2001.0922 ↗
26. Xu, X.-L. and Rajapakse, R.K.N.D. (2001). On a plane crack in piezoelectric solids. International Journal of Solids and Structures 38, 7643–7658.10.1016/S0020-7683(01)00029-4 ↗
27. Yang, F. and Kao, I. (1999). Crack problem in piezoelectric materials: general anti-plane mechanical loading. Mechanics of Materials 31, 395–406.10.1016/S0167-6636(99)00007-1 ↗
28. Yang, J.H. and Lee, K.Y. (2001). Penny shaped crack in three-dimensional piezoelectric strip under in-plane normal loadings. Acta Mechanics 148, 187–197.10.1007/BF01183677 ↗
29. Yang, J.H. and Lee, K.Y. (2003). Penny shaped crack in a piezoelectric cylinder surrounded by an elastic medium subjected to combined in-plane mechanical and electrical loads. International Journal of Solids and Structures 40, 573–590.10.1016/S0020-7683(02)00620-0 ↗
30. Zhang, T.-Y., Qian, C.-F. and Tong, P. (1998). Linear electroelastic analysis of a cavity or a crack in a piezoelectric material. International Journal of Solids and Structures 35, 2121–2149.10.1016/S0020-7683(97)00168-6 ↗