Skip to main content
SpringerLink
Log in

Analysis of electric boundary condition effects on crack propagation in piezoelectric ceramics

  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

There are three types of cracks: impermeable crack, permeable crack and conducting crack, with different electric boundary conditions on faces of cracks in piezoelectric ceramics, which poses difficulties in the analysis of piezoelectric fracture problems. In this paper, in contrast to our previous FEM formulation, the numerical analysis is based on the used of exact electric boundary conditions at the crack faces, thus the common assumption of electric impermeability in the FEM analysis is avoided. The crack behavior and elasto-electric fields near a crack tip in a PZT-5 piezoelectric ceramic under mechanical, electrical and coupled mechanical-electrical loads with different electric boundary conditions on crack faces are investigated. It is found that the dielectric medium between the crack faces will reduce the singularity of stress and electric displacement. Furthermore, when the permittivity of the dielectric medium in the crack gap is of the same order as that of the piezoelectric ceramic, the crack becomes a conducting crack, the applied electric field has no effect on the crack propagation.

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

Access this article

Log in via an institution

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. Parton Y E. Fracture mechanics of piezoelectric materials.Acta Astronautica, 1976, 3: 671–683

    Article  MATH  Google Scholar 

  2. Deeg W F. The analysis of dislocation, crack and inclusion problems in piezoelectric solids. Ph D Thesis. Standford University. CA, USA. 1980

    Google Scholar 

  3. Park Y E, hermann G. Conservation laws and the material momentum tensor for the elastic dielectric.Int J Engng Sci, 1986, 24: 1365–1374

    Article  Google Scholar 

  4. Park Y E. Crack extension force in a piezoelectric material.J Appl Mech, 1990, 57: 647–653

    Google Scholar 

  5. Sosa H, Pak Y. Three dimensional eigenfunction analysis of a crack in a piezoelectric material.Int J Solid Struct, 1990, 26: 1–15

    Article  MATH  Google Scholar 

  6. McMeeking R M. Electrostrictive forces near crack-like flaws.J Appl Math Phys, 1989, 40: 615–627

    Article  MATH  Google Scholar 

  7. McMeeking R M. A J-integral for the analysis of electrically induced mechanical stress at cracks in elastic dielectrics.Int J Engng Sci, 1990, 28: 605–613

    Article  MATH  Google Scholar 

  8. Wang B. Three-dimensional analysis of a flat elliptical crack in a piezoelectric material.Int J Eng Sci, 1992, 6: 781–791

    Article  MATH  Google Scholar 

  9. Suo Z, Kuo C M, Barnet D M, Willis J R. Fracture mechanics for piezoelectric ceramics.J Mech Phys Solids, 1992, 40: 739–765

    Article  MATH  MathSciNet  Google Scholar 

  10. Dunn M L. The effects of crack face boundary conditions on the fracture mechanics.Engng Fract Mech, 1994, 48: 25–39

    Article  Google Scholar 

  11. Hao T H, Shen Z Y. A new electric boundary condition of electric fracture mechanics and its applications.Engng Fract Mech, 1994, 47: 793–802

    Article  Google Scholar 

  12. Park S B, Sun C T. Effect of electric field on fracture of piezoelectric ceramics.Int J Fract, 1995, 70: 302–316

    Google Scholar 

  13. Sosa H, Khutoryansky N. New developments concerning piezoelectric materials with defects.Int J Solids Struct, 1996, 33: 3399–3414

    Article  MATH  MathSciNet  Google Scholar 

  14. Zhang T Y, Tong P. Fracture mechanics for a mode III crack in a piezoelectric material.Int J Solids Struct, 1996, 33: 343–359

    Article  MATH  Google Scholar 

  15. Kumar S, Singh R N. Crack propagation in piezoelectric materials under combined mechanical and electrical loading.Acta Mater, 1996, 44: 173–200

    Article  Google Scholar 

  16. Gao H J, Zhang T Y, Tong P. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic.J Mech Phys Solids, 1997, 45: 491–510

    Article  Google Scholar 

  17. Tobin A G, Pak Y E. Effect of electric fields on fracture behavior of PZT ceramics.Proc SPIE, Smart Struct Mater, 1993, SPIE1916: 78–86

  18. Park S B, Sun C T. Fracture criteria for piezoelectric ceramics.J Am Ceram Soc, 1995, 78: 1475–1480

    Article  Google Scholar 

  19. Kumar S, Singh R N. Crack propagation in piezoelectric materials under combined mechanical and electricla loading: an experimental study. In: Adaptive Materials Systems. ASME, 1995AMD-Vol. 206/MD-Vol. 58: 69–83. American Society of Mechanical Engineering, New York, 1995

    Google Scholar 

  20. Anderson T L. Fracture Mechanics: Fundamentals and Applications. Boston: CRC Press, 1991

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Tsinghua University, 100084, Beijing, China

    Qi Hang, Fang Daining & Yao Zhenhan

Authors
  1. Qi Hang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fang Daining
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yao Zhenhan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The project supported by the National Natural Science Foundation of China (19672026, 19891180)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hang, Q., Daining, F. & Zhenhan, Y. Analysis of electric boundary condition effects on crack propagation in piezoelectric ceramics. Acta Mech Sinica 17, 59–70 (2001). https://doi.org/10.1007/BF02487770

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02487770

Key Words

Search

Navigation