Skip to main content
Log in

Central crack in a piezoelectric disc

  • Published:
KSME International Journal Aims and scope Submit manuscript

Abstract

This study is concerned with the general solution of the field intensity factors and energy release rate for a Griffith crack in a piezoelectric ceramic of finite radius under combined anti-plane mechanical and in-plane electrical loading. Both electrically continuous and impermeable crack surface conditions are considered. Employing Mellin transforms and Fourier series, the problem is reduced to dual integral forms. The solution to the resulting expressions is expressed in terms of Fredholm integral equation of the second kind. The solutions are provided to study the influence of the crack length, the crack surface boundary conditions on the intensity factors and the energy release rate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Deeg, W. F. J., 1980,Analysis of Dislocation, Crack and Inclusion Problems in Piezoelectric Solids, Ph.D. Dissertation, Stanford University.

  • Gao, C. F. and Fan, W. X., 1999, “A general solution for the crack problem in piezoelectric media with collinear cracks,”International Journal of Engineering Science, Vol. 37, pp. 347–363.

    Article  Google Scholar 

  • Kwon, J. H. and Meguid, S. A., 2002, “Analysis of a Central crack normal to a Piezoelectric-Orthotropic Interface,”International Journal of Solids and Structures, Vol. 39, pp. 841–860.

    Article  Google Scholar 

  • Kwon, S. M. and Lee, K. Y., 2000, “Analysis of stress and electric fields in a rectangular piezoelectric body with a center crack under anti-plane shear loading,”International Journal of Solids and Structures, Vol. 37, pp. 4859–4869.

    Article  MathSciNet  Google Scholar 

  • Kwon, S. M. and Lee, K. Y., 2001, “Eccentric crack in a rectangular piezoelectric medium under electromechanical loading,”Acta Mechanica, Vol. 148, pp. 239–248.

    Article  Google Scholar 

  • Liu, J. X., Liu, Y. L., Wang, B. and Du, S. Y., 1998, “Mode III crack in the piezoelectric layer of two dissimilar materials,”Key Engineering Materials, Vol. 145-149, pp. 1167–1172.

    Article  Google Scholar 

  • Magnus, W., Oberhettinger, F. and Soni, R. P., 1966,Formulas and Theorems for the Special Functions of Mathematical Physics (3rd Ed.). Springer-Verlag New York Inc., p. 2.

    Book  Google Scholar 

  • McMeeking, R. M., 1989, “Electrostrictive stresses near crack-like flaws,”Journal of Applied Mathematics and Physics (ZAMP), Vol. 40, pp. 615–627.

    Article  Google Scholar 

  • Meguid, S. A. and Wang, X. D., 1998, “Dynamic antiplane behaviour of interacting cracks in a piezoelectric medium,”International Journal of Fracture, Vol. 91, pp. 391–403.

    Article  Google Scholar 

  • Narita, F. and Shindo, Y., 1998, “Layered piezoelectric medium with interface crack under anti-plane shear,”Theoretical and Applied Fracture Mechanics, Vol. 30, pp. 119–126.

    Article  Google Scholar 

  • Pak, Y. E., 1990, “Crack extension force in a piezoelectric material,”AS ME Journal of Applied Mechanics, Vol. 57, pp. 647–653.

    Article  Google Scholar 

  • Pak, Y. E. and Goloubeva, E., 1996, “Electroelastic properties of a cracked piezoelectric material under longitudinal shear,”Mechanics of Materials, Vol. 24, pp. 287–303.

    Article  Google Scholar 

  • Park, S. B. and Sun, C. T., 1995, “Effect of electric field on fracture of piezoelectric ceramics,”International Journal of Fracture, Vol. 70, pp. 203–216.

    Article  Google Scholar 

  • Qin, Q. H. and Mai, Y. W., 1999, “A closed crack tip model for interface carcks in thermopiezoelectric materials,”International Journal of Solids and Structures, Vol. 36, pp. 2463–2479.

    Article  Google Scholar 

  • Shindo, Y., Narita, F. and Tanaka, K., 1996, “Electroelastic intensification near anti-plane shear crack in orthotropic piezoelectric ceramic strip,”Theoretical and Applied Fracture Mechanics, Vol. 25, pp. 65–71.

    Article  Google Scholar 

  • Shindo, Y., Tanaka, K. and Narita, F., 1997, “Singular stress and electric fields of a piezoelectric ceramic strip with a finite crack under longitudinal shear,”Acta Mechanica, Vol. 120, pp. 31–45.

    Article  Google Scholar 

  • Sneddon, I. N., 1951,Fourier Transforms (1st Ed.). McGraw-Hill, p. 527.

  • Sosa, H. A., 1991, “Plane problems in piezoelectric media with defects,”International Journal of Solids and Structures, Vol. 28, pp. 491–505.

    Article  Google Scholar 

  • Wang, X. D. and Meguid, S. A., 2001, “Modeling and analysis of dynamic interaction between piezoelectric actuators,”International Journal of Solids and Structures, Vol. 38, pp. 2803–2820.

    Article  Google Scholar 

  • Zhang, T. Y., Qian, C. F. and Tong, P., 1998, “Linear electro-elastic analysis of a cavity or a crack in a piezoelectric material,”International Journal of Solids and Structures, Vol. 35, pp. 2121–2149.

    Article  Google Scholar 

  • Zhao, M. H., Shen, Y. P., Liu, Y. J. and Liu, G. N., 1997, “Isolated cracks in three-dimensional piezoelectric solid. Part II: Stress intensity factors for circular crack,”Theoretical and Applied Fracture Mechanics, Vol. 26, pp. 141–149.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jong Ho Kwon.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kwon, J.H. Central crack in a piezoelectric disc. KSME International Journal 18, 1549–1558 (2004). https://doi.org/10.1007/BF02990369

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02990369

Key words

Navigation