Abstract
The problem of electrically charged crack in a piezoelectric material under the action of remote electromechanical load is considered. The material is polarized in the direction orthogonal to the crack faces. Assuming that all fields are independent of the coordinate co-directed with the crack front and using the special presentations of electromechanical quantities via sectionally-analytic function, the problem is reduced to the vector Hilbert problem and solved exactly. All required electromechanical quantities are presented by means of simple formulas. The behavior of stresses, electric field and electric displacement jump are analyzed. It is shown that the electric charge can eliminate the field singularities at one of the two crack tips. The proposed solution, together with the presented table of parameters for some widely used piezoceramics materials, like PZT-4 and many others, can be easily used by the reader for an engineering calculation of the near-crack-tip electromechanical fields in these materials.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Beom H. G., Atluri S. N. (2002) Conducting cracks in dissimilar piezoelectric media. International Journal of Fracture 118: 285–301
Beom H.G. (1999a) Singular behaviour near a crack tip in an electrostrictive material. Journal of the Mechanics and Physics of Solids 47: 1027–1049
Beom H.G. (1999b) Small scale nonlinear analysis of electrostrictive crack problems. Journal of the Mechanics and Physics of Solids 47: 1379–1395
Karapetian E., Kachanov M., Sevostianov I. (2002) The principle of correspondence between elastic and piezoelectric problems. Archive of Applied Mechanics 72: 564–587
Li, Q., Chen, Y. (2008). Solution for a semi-permeable interface crack in elastic dielectric/piezoelectric bimaterials, ASME, J. Appl. Mech., 75: 011010, 1-13.
Loboda V., Lapusta Y., Sheveleva A. (2007) Electro-mechanical pre-fracture zones for an electrically permeable interface crack in a piezoelectric bimaterial. Int. J. Solids Struct. 44: 5538–5553
Loboda V., Lapusta Y., Govorukha V. (2008) Mechanical and electrical yielding for an electrically insulated crack in an interlayer between piezoelectric materials. International Journal of Engineering Science, 46(3): 260–272
Loboda V., Mahnken R. (2011) On investigation of an electrode at the interface of a piezoelectric bimaterial space under remote electromechanical loading. Acta Mech. 221: 327–339
Muskhelishvili N.I. (1963) Some Basic Problems in the Mathematical Theory of Elasticity. Noordhoff, Groningen
Pak Y.E. (1992) Linear electro-elastic fracture mechanics of piezoelectric materials. International Journal of Fracture 54: 79–100
Parton V.Z., Kudryavtsev B.A. (1988) Electromagnetoelasticity. Gordon and Breach Science Publishers, New York
Ru C.Q., Mao X. (1999) Conducting cracks in a piezoelectric ceramic of limited electrical polarization. Journal of the Mechanics and Physics of Solids 47: 2125–2146
Sevostianov, Kachanov (2000) Microcracking in piezoelectrics weakens the electromechanical coupling and changes its directionality. International Journal of Fracture 101: L3–L8
Zhang T.Y., Gao C.F. (2004) Fracture behaviors of piezoelectric materials. Theoretical and Applied Fracture Mechanics 41: 339–379
Suo Z. (1993) Models for breakdown-resistant dielectric and ferroelectric ceramics. Journal of the Mechanics and Physics of Solids 41: 1155–1176
Suo Z., Kuo C.-M., Barnett D.M., Willis J.R. (1992) Fracture mechanics for piezoelectric ceramics. Journal of Mechanics and Physics of Solids 40: 739–765
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Knysh, P., Loboda, V., Labesse-Jied, F. et al. An Electrically Charged Crack in a Piezoelectric Material Under Remote Electromechanical Loading. Int J Fract 175, 87–94 (2012). https://doi.org/10.1007/s10704-012-9704-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-012-9704-4