Skip to main content
SpringerLink
Log in

Investigation of the dynamic behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces by a new method

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

Abstract

The dynamic behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces subjected to the harmonic waves is investigated by a new method. The cracks are parallel to the interfaces in the mid-plane of the piezoelectric layer. By using the Fourier transform, the problem can be solved with two pairs of triple integral equations. These equations are solved by using Schmidt's method. This process is quite different from that adopted previously. Numerical examples are provided to show the effect of the geometry of cracks, the frequency of the incident wave, the thickness of the piezoelectric layer and the constants of the materials upon the dynamic stress intensity factor of cracks.

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. Deeg W E F. The analysis of dislocation, crack and inclusion problems in piezoelectric solids[D]. Ph D thesis, Stanford University, 1980.

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

    MATH  Google Scholar 

  3. Pak Y E. Linear electro-elastic fracture Mechanics of piezoelectric materials [J].International Journal of Fracture, 1992,54 (1): 79–100.

    Google Scholar 

  4. Sosa H A, Pak Y E. Three-dimensional eigenfunction analysis of a crack in a piezoelectric ceramics [J].International Journal of Solids and Structures, 1990,26 (1): 1–15.

    Article  MATH  Google Scholar 

  5. Sosa H A. Plane problems in piezoelectric media with defects[J].International Journal of Solids and Structures, 1991,28 (4): 491–505.

    Article  MATH  Google Scholar 

  6. Sosa H A. On the fracture mechanics of piezoelectric solids[J].International Journal of Solids and Structures, 1992,29 (8): 2613–2622.

    Article  MATH  Google Scholar 

  7. Suo Z, Kuo C M, Barnett D M, et al. Fracture mechanics for piezoelectric ceramics[J].Journal of Mechanics and Physics of Solids, 1992,40 (5): 739–765.

    Article  MATH  MathSciNet  Google Scholar 

  8. Park S B, Sun C T. Fracture criteria for piezoelectric ceramics[J].Journal of American Ceramics Society, 1995,78 (7): 1475–1480.

    Article  Google Scholar 

  9. Zhang T Y, Tong P. Fracture mechanics for a mode III crack in a piezoelectric material[J].International Journal of Solids and Structures, 1996,33 (5): 343–359.

    MATH  Google Scholar 

  10. Gao H, Zhang T Y, Tong P. Local and global energy rates for an elastically yielded crack in piezo-electric ceramics[J].Journal of Mechanics and Physics of Solids, 1997,45 (4): 491–510.

    Article  Google Scholar 

  11. WANG Biao. Three dimensional analysis of a flat elliptical crack in a piezoelectric materials[J].International Journal of Enginerring 1992,30 (6): 781–791.

    MATH  Google Scholar 

  12. Narita K, Shindo Y. Scattering of Love waves by a surface-breaking crack in piezoelectric layered media[J].JSME International Journal, Series A, 1998,41 (1): 40–52.

    Google Scholar 

  13. Narita K, Shindo Y. Scattering of anti-plane shear waves by a finite crack in piezoelectric laminates [J].Acta Mechanica, 1999,134 (1): 27–43.

    Article  MATH  MathSciNet  Google Scholar 

  14. ZHOU Zhen-gong, WANG Biao, CAO Mao-sheng. Analysis of two collinear cracks in a piezoelectric layer bonded to dissimilar half spaces subjected to anti-plane shear[J].European Journal of Mechanics A/Solids, 2001,20 (2): 213–226.

    Article  Google Scholar 

  15. YU Shou-wen, CHEN Zeng-tiao. Transint response of a cracked infinite piezoelectric strip under anti-plane impact [J].Fatigue and Engineering Materials and Structures, 1998,21 (4): 1381–1388.

    Google Scholar 

  16. CHEN Zeng-tiao, Karihaloo B L. Dynamic response of a cracked piezoelectric ceramic under arbitrary electro-mechanical impact[J].Internatioal Journal of Solids and Structures, 1990,36 (5): 5125–5133.

    Google Scholar 

  17. Paul H S, Nelson V K. Axisymmetric vibration of piezo-composite hollow circular cylinder[J].Acta Mechanica, 1996,116 (5): 213–222.

    Article  MATH  Google Scholar 

  18. Khutoryansky N M, Sosa H. Dynamic representation formulas and fundamental solutions for piezoelectricity[J].International Journal of Solids and Structures, 1995,32 (8): 3307–3325.

    Article  MATH  MathSciNet  Google Scholar 

  19. Shindo Y, Katsura H, Yan W. Dynamic stress intensity factor of a cracked dielectric medium in a uniform electric field[J].Acta Mechanica, 1996,117 (1): 1–10.

    Article  MATH  Google Scholar 

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

    Google Scholar 

  21. Tauchert T R. Cylindrical bending of hybrid laminates under thermo-electro-mechanical loading [J].Journal of Thernal Stresses, 1996,19 (4): 287–296.

    Google Scholar 

  22. Lee J S, Jiang L Z. Exact electro-elastic analysis of piezoelectric laminate via state space approach [J].International Journal of Solids and Structures, 1996,33, (4): 977–985.

    MATH  Google Scholar 

  23. Tang Y Y, Noor A K, Xu K. Assessment of computational models for thermoelectroelastic multilayered plates[J].Computers and Structures, 1996,61 (6): 915–924.

    Article  Google Scholar 

  24. Batra R C, Liang X Q. The vibration of a rectangular laminated elastic plate with embedded piezoelectric sensors and actuators[J].Computer and Structures, 1997,63 (4): 203–212.

    Article  MATH  Google Scholar 

  25. Heyliger P. Exact solutions for simply supported laminated piezoelectric plates[J].ASME Journal of Applied Mechanics, 1997,64 (4): 299–313.

    Article  MATH  Google Scholar 

  26. Shindo Y, Domon W, Narita F. Dynamic bending of a symmetric piezoelectric laminated plate with a through crack[J].Theoretical and Applied Fracture Mechanics, 1998.,28 (2): 175–184.

    Article  Google Scholar 

  27. Morse P M, Feshbach H.Methods of Theoretical Physics[M]. Vol 1. New York: McGraw-Hill, 1958, 828–929.

    Google Scholar 

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

    Google Scholar 

  29. Erdelyi A.Tables of Integral Transforms [M]. Vol 1. New York: McGraw-Hill, 1954, 38–95.

    Google Scholar 

  30. Keer L M, Luong W C. Diffraction of waves and stress intensity factors in a cracked layered composite [J].Journal of the Acoustical Society of America, 1974,56 (5): 1681–1686.

    Article  Google Scholar 

  31. Amemiya A, Taguchi T.Numerical Analysis and Fortran [M]. Tokyo: Maruzen, 1969.

    Google Scholar 

  32. Itou S. Three dimensional waves propagation in a cracked elastic solid[J].ASME Journal of Applied Mechanics, 1978,45 (2): 807–811.

    MATH  Google Scholar 

  33. Itou S. Three dimensional problem of a running crack[J].International Journal of Engineering Science, 1979,17 (7): 59–71.

    Article  MATH  Google Scholar 

  34. ZHOU Zheng-gong, HAN Jie-cai, DU Shan-yi. 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 

  35. ZHOU Zhen-gong, HAN Jie-cai, DU Shan-yi. Investigation of a Griffith crack subject to anti-plane shear by using the non-local theory[J].International Journal of Solids and Structures, 1999,36, (3): 3891–3901.

    MATH  Google Scholar 

  36. ZHOU Zhen-gong, WANG Biao. Investigation of a Griffith crack subjected to uniform tension using the non-local theory by a new method[J].Applied Mathematics and Mechanics (English Edition), 1999,20 (10): 1099–1107.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Composite Materials and Electro-Optics Research Center, Harbin Institute of Technology, 150001, Harbin, China

    Zhou Zhen-gong & Wang Biao

Authors
  1. Zhou Zhen-gong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wang Biao
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Contributed by Wupang Biao

Foundation items: the National Natural Science Foundation of China (10172030); the Key Project of National Natural Science Foundation of China (50232030)

Biography: Zuphou Zhen-gong (1963−), Professor, Dorctor E-mail: zhouzhg@hope.hit.edu.cn

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhen-gong, Z., Biao, W. Investigation of the dynamic behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces by a new method. Appl Math Mech 24, 1–13 (2003). https://doi.org/10.1007/BF02439371

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02439371

Key words

Chinese Library Classification

2000 MR Subject Classification

Search

Navigation