Skip to main content
Log in

Fracture Analysis of an Annular Crack in a Piezoelectric Layer

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

A flat annular crack in a piezoelectric layer subjected to electroelastic loadings is investigated under electrically impermeable boundary condition on the crack surface. Using Hankel transform technique, the mixed boundary value problem is reduced to a system of singular integral equations. With the aid of Gauss-Chebyshev integration technique, the integral equations are further reduced to a system of algebraic equations. The field intensity factor and energy release rate are determined. Numerical results reveal the effects of electric loadings and crack configuration on crack propagation and growth. The results seem useful for design of the piezoelectric structures and devices of high performance.

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

  1. Sosa, H., On the fracture mechanics of piezoelectric solids. International Journal of Solids and Structures, 1992, 29: 2613–2622.

    Article  Google Scholar 

  2. Suo, Z., Kuo, C.M., Barnett, D.M. and Willis, J.R., Fracture mechanics for piezoelectric ceramics. Journal of the Mechanics and Physics of Solids, 1992, 40: 739–765.

    Article  MathSciNet  Google Scholar 

  3. Zhang, T.Y. and Tong, P., Fracture mechanics for mode-III crack in a piezoelectric materials. International Journal of Solids and Structures, 1996, 33: 343–359.

    Article  Google Scholar 

  4. Li, X.F. and Lee, K.Y., Effects of electric field on crack growth for a penny-shaped dielectric crack in a piezoelectric layer. Journal of the Mechanics and Physics of Solids, 2004, 52: 2079–2100.

    Article  Google Scholar 

  5. Li, Y.D. and Lee, K.Y., Crack tip shielding and anti-shielding effects of the imperfect interface in a layered piezoelectric sensor. International Journal of Solids and Structures, 2009, 46: 1736–1742.

    Article  Google Scholar 

  6. Shibuya, T., Nakahara, I. and Koizumi, T., The axisymmetric distribution of stresses in an infinite elastic solid containing a flat annular crack under internal pressure. ZAMM-Journal of Applied Mathematics and Mechanics, 1975, 55: 395–402.

    Article  Google Scholar 

  7. Mastrojanni, E.N. and Kermanidis, T.B., An approximate solution of the annular crack problem. International Journal for Numerical Methods in Engineering, 1981, 17: 1605–1611.

    Article  Google Scholar 

  8. Shindo, Y., Normal compression waves scattering at a flat annular crack in an infinite elastic solid. Quartly of Applied Mathematics, 1981, 39: 305–315.

    Article  MathSciNet  Google Scholar 

  9. Shindo, Y., Axisymmetric elastodynamic response of a flat annular crack to normal impact waves. Engineering Fracture Mechanics, 1984, 19: 837–848.

    Article  Google Scholar 

  10. Wijeyewickrema, A.C., Keer, L.M., Hirashima, K. and Mura, T., The annular crack surrounding an elastic fiber in a tension field. International Journal of Solids and Structures, 1991, 27: 315–328.

    Article  Google Scholar 

  11. Han, X.L. and Wang, D., The annular crack in a nonhomogeneous matrix surrounding a fiber under torsional loading—I. Inner crack tip away from or terminating at the interface. Engineering Fracture Mechanics, 1996, 53: 457–464.

    Article  Google Scholar 

  12. Han, X.L. and Wang, D., The annular crack in a nonhomogeneous matrix surrounding a fiber under torsional loading—II. The crack going through the bimaterial interface into the fiber. Engineering Fracture Mechanics, 1996, 53: 457–464.

    Article  Google Scholar 

  13. Narita, F., Shindo, Y. and Lin, S., Axially poled solid cylinder under tension with a flat annular crack. ZAMM-Journal of Applied Mathematics and Mechanics, 2007, 87: 278–289.

    Article  Google Scholar 

  14. Shindo, Y., Lin, S. and Narita, F., Electroelastic response of a flat annular crack in a piezoelectric fiber surrounded by an elastic medium. Journal of Engineering Mathematics, 2007, 59: 83–97.

    Article  Google Scholar 

  15. Eskandaria, M., Moeini-Ardakania, S.S. and Shodja, H.M., An energetically consistent annular crack in a piezoelectric medium. Engineering Fracture Mechanics, 2010, 77: 819–831.

    Article  Google Scholar 

  16. Shodja, H.M., Moeini-Ardakani, S.S. and Eskandari, M., Axisymmetric problem of energetically consistent interacting annular and penny-shaped cracks in piezoelectric materials. Journal of Applied Mechanics, 2011, 78: 021010-1-021010-10.

    Article  Google Scholar 

  17. Erdogan, F. and Gupta, G.D., On the numerical solution of singular integral equations. Quartly of Applied Mathematics, 1972, 29: 525–539.

    Article  MathSciNet  Google Scholar 

  18. Tada, H., Paris, P. and Irwin, G., The Stress Analysis of Crack Handbook. Del Research Corporation, 1985.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yansong Li.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11072160 and 11272223) and the Natural Science Foundation of Hebei Province, China (E2013402077).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Y., Wang, W. Fracture Analysis of an Annular Crack in a Piezoelectric Layer. Acta Mech. Solida Sin. 28, 40–49 (2015). https://doi.org/10.1016/S0894-9166(15)60014-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S0894-9166(15)60014-3

Key Words

Navigation