Skip to main content
SpringerLink
Log in

Dynamic behavior of two unequal parallel permeable interface cracks in a piezoelectric layer bonded to two half piezoelectric materials planes

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The dynamic behavior of two unequal parallel permeable interface cracks in a piezoelectric layer bonded to two half-piezoelectric material planes subjected to harmonic anti-plane shear waves is investigated. By using the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables were the jumps of the displacements across the crack surfaces. Numerical results are presented graphically to show the effects of the geometric parameters, the frequency of the incident wave on the dynamic stress intensity factors and the electric displacement intensity factors. Especially, the present problem can be returned to static problem of two parallel permeable interface cracks. Compared with the solutions of impermeable crack surface condition, it is found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Pak Y E. Crack extension force in a piezoelectric material[J].Journal of Applied Mechanics, 1990,57 (4): 647–653.

    MATH  Google Scholar 

  2. Chen Zengtao, Yu Shouwen. Anti-plane vibration of cracked piezoelectric materials[J].Mechanics Research Communications, 1998,25 (2): 321–327.

    Google Scholar 

  3. Meguid S A, Wang X D. Dynamic antiplane behaviour of interacting cracks in a piezoelectric medium[J].International Journal of Solids and Structures, 1998,91 (2): 391–403.

    Google Scholar 

  4. Soh A K, Fang D N, Lee K L. Analysis of a bi-piezoelectric ceramic layer with an interfacial crack subjected to anti-plane shear and in-plane electric loading[J].European Journal of Mechanics A/Solids, 2000,19 (5): 961–977.

    Article  MATH  Google Scholar 

  5. Li X F, Tang G J. Antiplane interface crack between two bonded dissimilar piezoelectric layers[J].European Journal of Mechanics A/Solids, 2003,22 (2): 231–242.

    Article  MATH  Google Scholar 

  6. Narita F, Shindo Y, Watanabe K. Anti-plane shear crack in a piezoelectric layer bonded to dissimilar half spaces[J].JSME International Journal Series A, 1999,42 (1): 66–72.

    Google Scholar 

  7. Zhou Zhengong, Wang Biao. The behavior of two parallel symmetry permeable interface cracks in a piezoelectric layer bonded to two half piezoelectric materials planes[J].International Journal of Solids and Structure, 2002,39 (17): 4485–4500.

    Article  Google Scholar 

  8. Zhou Zhengong, Wang Biao. The behavior of tow parallel symmetric permeable cracks in piezoelectric materials[J].Applied Mathematics and Mechanics (English Edition), 2002,23 (12): 1357–1366.

    Google Scholar 

  9. Morse P M, Feshbach H.Methods of Theoretical Physics[M]. McGraw-Hill, New York, 1958, 828–929.

    Google Scholar 

  10. Yan W F. Axisymmetric slipless indentation of an infinite elastic cylinder[J].SIAM Journal on Applied Mathematics, 1967,15 (2): 219–227.

    Google Scholar 

  11. Gradshteyn I S, Ryzhik I M.Table of Integral, Series and Products[M]. Academic press, New York, 1980, 980–997.

    Google Scholar 

  12. Erdelyi A.Tables of Integral Transforms[M]. McGraw-Hill, New York, 1954, 38.

    Google Scholar 

  13. Itou S. Stress intensity factors around a crack in a non-homogeneous interface layer between two dissimilar elastic half-planes[J].International Journal of Fracture, 2001,110 (1): 123–135.

    Article  Google Scholar 

  14. Zhou Zhengong, Han Jiecai, Du Shanyi. Two collinear Griffith cracks subjected to uniform tension in infinitely long strip[J].International Journal of Solids and Structures, 1999,36 (4): 5597–5609.

    Google Scholar 

  15. Ratwani M, Gupta G D. Interaction between parallel cracks in layered composites[J].International Journal of Solids and Structures, 1974,10 (4): 701–708.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Composite Materials, Harbin Institute of Technology, P. O. Box 1247, 150001, Harbin, P. R. China

    Sun Jian-liang, Zhou Zhen-gong & Wang Biao

Authors
  1. Sun Jian-liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhou Zhen-gong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wang Biao
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Contributed by WANG Biao

Foundation items: the National Natural Science Foundation of China (10172030, 50232030); the Natural Science Foundation of Heilongjiang, P. R. China (A0301); the Science Foundation of Heilongjiang for Outstanding Young Scientists

Biographies: SUN Jian-liang, Doctor; ZHOU Zhen-gong, Professor, Doctor, E-mail: zhouzhg@hit.edu.cn

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jian-liang, S., Zhen-gong, Z. & Biao, W. Dynamic behavior of two unequal parallel permeable interface cracks in a piezoelectric layer bonded to two half piezoelectric materials planes. Appl Math Mech 26, 160–170 (2005). https://doi.org/10.1007/BF02438237

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02438237

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation