Skip to main content
Log in

Multiple cracks on the interface between a piezoelectric layer and an orthotropic substrate

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

In the present work, we investigate the problem of multiple cracks on the interface between a piezoelectric layer and an orthotropic substrate. The method of dislocation simulation and singular integral equation are used to solve the crack problem. The theoretical derivation is verified by the classical result in a special case. Numerical results of the stress intensity factor are obtained, and thereby the effects of geometrical parameters and material orthotropy are surveyed. The optimal stiffness ratio of the orthotropic substrate is suggested for the purpose of interfacial fracture prevention, which is significant for the design and assessment of such a kind of smart structures.

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. Li Y.D., Lee K.Y.: Crack tip shielding and anti-shielding effects of the imperfect interface in a layered piezoelectric sensor. Int. J. Solid. Struct. 46, 1736–1742 (2009)

    Article  Google Scholar 

  2. Ru C.: Electrode-ceramic interfacial cracks in piezoelectric multilayer materials. J. Appl. Mech. 67, 255–261 (2000)

    Article  MATH  Google Scholar 

  3. Govorukha V.B., Loboda V.V.: Contact zone models for an interface crack in a piezoelectric material. Acta Mech. 140, 233–246 (2000)

    Article  MATH  Google Scholar 

  4. Gu B., Yu S.W., Feng X.Q.: Transient response of an interface crack between dissimilar piezoelectric layers under mechanical impacts. Int. J. Solid. Struct. 39, 1743–1756 (2002)

    Article  MATH  Google Scholar 

  5. Guo X.H., Fang D.N.: Simulation of interface cracking in piezoelectric layers. Int. J. Nonl. Sci. Num. Sim. 5, 235–242 (2004)

    Article  MATH  Google Scholar 

  6. Huang G.L., Wang X.D.: On the dynamic behaviour of interfacial cracks between a piezoelectric layer and an elastic substrate. Int. J. Fract. 141, 63–73 (2006)

    Article  MATH  Google Scholar 

  7. Li Q., Chen Y.H.: Analysis of a permeable interface crack in elastic dielectric/piezoelectric bimaterials. Acta Mech. Sin. 23, 681–687 (2007)

    Article  MATH  Google Scholar 

  8. Tian W.Y., Rajapakse R.K.N.D.: Fracture parameters of a penny-shaped crack at the interface of a piezoelectric bi-material system. Int. J. Fract. 141, 37–48 (2006)

    Article  MATH  Google Scholar 

  9. Li Y.D., Lee K.Y.: Fracture analysis on the arc-shaped interface in a layered cylindrical piezoelectric sensor polarized along its axis. Eng. Fract. Mech. 76, 2065–2073 (2009)

    Article  Google Scholar 

  10. Hausler C., Jelitto H., Neumeister P. et al.: Interfacial fracture of piezoelectric multilayer actuators under mechanical and electrical loading. Int. J. Fract. 160, 43–54 (2009)

    Article  Google Scholar 

  11. Shin J.W., Lee Y.S.: A moving interface crack between two dissimilar functionally graded piezoelectric layers under electromechanical loading. Int. J. Solid. Struct. 47, 2706–2713 (2010)

    Article  MATH  Google Scholar 

  12. Loboda V., Lapusta Y., Sheveleva A.: Limited permeable crack in an interlayer between piezoelectric materials with different zones of electrical saturation and mechanical yielding. Int. J. Solid. Struct. 47, 1795–1806 (2010)

    Article  MATH  Google Scholar 

  13. Natroshvili D., Stratis I.G., Zazashvili S.: Interface crack problems for metallic-piezoelectric composite structures. Math. Meth. Appl. Sci. 33, 539–562 (2010)

    MathSciNet  MATH  Google Scholar 

  14. Kwon J.H., Meguid S.A.: Analysis of a central crack normal to a piezoelectric-orthotropic interface. Int. J. Solid. Struct. 39, 841–860 (2002)

    Article  MATH  Google Scholar 

  15. Kwon S.M., Lee K.Y.: Steady state crack propagation in a piezoelectric layer bonded between two orthotropic layers. Mech. Mater. 35, 1077–1088 (2003)

    Article  Google Scholar 

  16. Chen Y.Z., Lin X.Y., Wang Z.X.: Antiplane elasticity crack problem for a strip of functionally graded materials with mixed boundary condition. Mech. Res. Commun. 37, 50–53 (2010)

    Article  Google Scholar 

  17. Li Y.D., Lee K.Y.: Collinear unequal crack series in magnetoelectroelastic materials: mode I case solved via new real fundamental solutions. Eng. Fract. Mech. 77, 2772–2790 (2010)

    Article  Google Scholar 

  18. Li Y.D., Lee K.Y.: Two collinear unequal cracks in a poled piezoelectric plane: Mode I case solved by a new approach of real fundamental solutions. Int. J. Fract. 165, 47–60 (2010)

    Article  Google Scholar 

  19. Liebowitz H.: Fracture, An Advanced Treatise, Vol. 1 Microscopic and Macroscopic Fundamentals. Academic Press, New York (1968)

    Google Scholar 

  20. Yang J.S.: An Introduction to The Theory of Piezoelectricity. Springer Science+Business Media, Inc., Boston (2005)

    MATH  Google Scholar 

  21. Zhong X.C., Liu F., Li X.F.: Transient response of a magnetoelectroelastic solid with two collinear dielectric cracks under impacts. Int. J. Solid. Struct. 46, 2950–2958 (2009)

    Article  MATH  Google Scholar 

  22. Muskhelishvili N.I.: Singular Integral Equations. Noordhoff, Groningen (1953)

    MATH  Google Scholar 

  23. Li Y.D., Lee K.Y.: Effects of magneto-electric loadings and piezomagnetic/piezoelectric stiffening on multiferroic interface fracture. Eng. Fract. Mech. 77, 856–866 (2010)

    Article  Google Scholar 

  24. Li X.F., Lee K.Y.: Closed-form solution for an orthotropic elastic strip with a crack perpendicular to the edges under arbitrary anti-plane shear. ZAMM. Zeit. Fur. Ang. Math. Mech. 89, 370–382 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Matbuly M.S., Nassar M.: Analysis of multiple interfacial cracks in an orthotropic bi-material subjected to anti-plane shear loading. Eng. Fract. Mech. 76, 1658–1666 (2009)

    Article  Google Scholar 

  26. Duan X.Y., Li X.F.: An interfacially-cracked orthotropic rectangular bi-material subjected to antiplane shear loading. Appl. Math. Comp. 174, 1060–1079 (2006)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kang Yong Lee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feng, FX., Lee, K.Y. & Li, YD. Multiple cracks on the interface between a piezoelectric layer and an orthotropic substrate. Acta Mech 221, 297–308 (2011). https://doi.org/10.1007/s00707-011-0506-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-011-0506-y

Keywords

Navigation