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.
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References
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.
Fabrikant, V.I. (2003). Computation of infinite integrals involving three Bessel functions by introduction of new formalism. ZAMM. 83, 363–374.
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.
Gradshteyn, I.S. and Ryzhik, I.M. (1980). Table of Integrals, Series and Products. Academic Press, New York.
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.
Jiang, L.Z. and Sun, C.T. (2001). Analysis of indentation cracking in piezoceramics. International Journal of Solids and Structures 38, 1903–1918.
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.
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.
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.
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.
McMeeking, R.M. (1999). Crack tip energy release rate for a piezoelectric compact tension specimen. Engineering Fracture Mechanics 64, 217–244.
McMeeking, R.M. (2001). Towards a fracture mechanics for brittle piezoelectric and dielectric materials. International Journal of Fracture 108, 25–41.
Pak, Y.E. (1990). Crack extension force in a piezoelectric material. Journal of Applied Mechanics 57, 647–653.
Pak, Y.E. (1992). Linear electroelastic fracture mechanics of piezoelectric materials. International Journal of Fracture 54, 79–100.
Park, S. and Sun, C.T. (1995). Fracture criteria for piezoelectric ceramics. Journal of the American Ceramic Society 78, 1475–1480.
Ru, C.Q. (1999). Electric-field induced crack closure in linear piezoelectric media. Acta Materials 47, 4683–4693.
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.
Sosa, H. (1992). On the fracture mechanics of piezoelectric solids. International Journal of Solids and Structures 29, 2613–2622.
Sosa, H. and Khutoryansky, N. (1996). New developments concerning piezoelectric materials with defects. International Journal of Solids and Structures 33, 3399–3414.
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.
Sneddon, I.N. and Lowengrub, M. (1969). Crack Problems in the Classical Theory of Elasticity. John Wiley and Sons, New York.
Wang, B. (1992). Three-dimensional analysis of a flat elliptical crack in a piezoelectric material. International Journal of Engineering Science 30, 781–791.
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.
Wang, Z.-K. and Huang, S.-H. (1995). Fields near elliptical crack tip in piezoelectric ceramics. Engineering Fracture Mechanics 51, 447–456.
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.
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.
Yang, F. and Kao, I. (1999). Crack problem in piezoelectric materials: general anti-plane mechanical loading. Mechanics of Materials 31, 395–406.
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.
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.
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.
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Li, XF., Lee, K.Y. Electro-elastic behavior induced by an external circular crack in a piezoelectric material. International Journal of Fracture 126, 17–38 (2004). https://doi.org/10.1023/B:frac.0000025299.07167.60
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DOI: https://doi.org/10.1023/B:frac.0000025299.07167.60