Acta Mechanica Solida Sinica

, Volume 20, Issue 1, pp 75–86 | Cite as

Scattering of harmonic anti-plane shear stress waves by a crack in functionally graded piezoelectric/piezomagnetic materials

  • Jun Liang
Article

Abstract

In this paper, the dynamic behavior of a permeable crack in functionally graded piezoelectric/piezomagnetic materials is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with the coordinate parallel to the crack. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations in which the unknown is the jump of displacements across the crack surfaces. These equations are solved to obtain the relations between the electric filed, the magnetic flux field and the dynamic stress field near the crack tips using the Schmidt method. Numerical examples are provided to show the effect of the functionally graded parameter and the circular frequency of the incident waves upon the stress, the electric displacement and the magnetic flux intensity factors of the crack.

Key words

functionally graded piezoelectric/piezomagnetic materials crack stress wave 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Wu T. L. and Huang J. H., Closed-form solutions for the magnetoelectric coupling coefficients in fibrous composites with piezoelectric and piezomagnetic phases. International Journal of Solids and Structures, 2000, 37: 2981–3009.CrossRefGoogle Scholar
  2. [2]
    Nan C. W., Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Physical Review B, 1994, 50: 6082–6088.CrossRefGoogle Scholar
  3. [3]
    Huang J. H. and Kuo W. S., The analysis of piezoelectric/piezomagnetic composite materials containing ellipsoidal inclusions. Journal of Applied Physics, 1997, 81(3): 1378–1386.CrossRefGoogle Scholar
  4. [4]
    Li J. Y., Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials. International Journal of Engineering Science, 2000, 38: 1993–2011.CrossRefGoogle Scholar
  5. [5]
    Sih G. C. and Song Z. F., Magnetic and electric poling effects associated with crack growth in BaTiO3-CoFe2O4 composite. Theoretical and Applied Fracture Mechanics, 2003, 39: 209–227.CrossRefGoogle Scholar
  6. [6]
    Song Z. F. and Sih G. C., Crack initiation behavior in magnetoelectrioelastic composite under in-plane deformation. Theoretical and Applied Fracture Mechanics, 2003, 39: 189–207.CrossRefGoogle Scholar
  7. [7]
    Wang B L, Mai Y W. Crack tip field in piezoelectric/piezomagnetic media. European Journal of Mechanics, A/Solid, 2003, 22(4): 591–602.CrossRefGoogle Scholar
  8. [8]
    Gao C. F., Tong P. and Zhang T.Y., Interfacial crack problems in magneto-electroelastic solids. International Journal of Engineering Science, 2003, 41(15): 2105–2121.CrossRefGoogle Scholar
  9. [9]
    Gao C. F., Kessler H., Balke H., Crack problems in magnetoelectroelastic solids. Part I: exact solution of a crack. International Journal of Engineering Science, 2003, 41(9): 969–981.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Liu J. X., Liu X. L., Zhao Y. B., Green’s functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack. International Journal of Engineering Science, 2001, 39(9): 1405–1418.MATHGoogle Scholar
  11. [11]
    Zhou Z. G., Wu L. Z. and Wang B., The dynamic behavior of two collinear interface cracks in magnetoelectro-elastic composites. European Journal of Mechanics A/ Solids, 2005, 24(2): 253–262.CrossRefGoogle Scholar
  12. [12]
    Zhou Z. G., Wang B. and Sun Y. G., Two collinear interface cracks in magneto-electro-elastic composites, International Journal of Engineering Science, 2004, 42: 1157–1167.MATHGoogle Scholar
  13. [13]
    Takagi, K., Li, J. F., Yokoyama, S. and Watanabe, R., Fabrication and evaluation of PZT/Pt piezoelectric composites and functionally graded actuators. Journal of the European Ceramic Society, 2003, 10: 1577–1583.CrossRefGoogle Scholar
  14. [14]
    Chen, J., Liu, Z. X. and Zou, Z. Z., Electriomechanical impact of a crack in a functionally graded piezoelectric medium. Theoretical and Applied Fracture Mechanics, 2003, 39: 47–60.CrossRefGoogle Scholar
  15. [15]
    Jin, B. and Zhong, Z., A moving mode-III crack in functionally graded piezoelectric material: permeable problem. Mechanics Research Communications, 2002, 29: 217–224.CrossRefGoogle Scholar
  16. [16]
    Li C. Y. and Weng, G. J., Antiplane crack problem in functionally graded piezoelectric materials. Journal of Applied Mechanics, 2002, 69(4): 481–488.CrossRefGoogle Scholar
  17. [17]
    Sun J. L., Zhou Z. G. and Wang B., Dynamic behavior of a crack in a functionally graded piezoelectric strip bonded to two dissimilar half piezoelectric material planes. Acta Mechanica, 2005, 176(1–2): 45–60.CrossRefGoogle Scholar
  18. [18]
    Zhou Z. G. and Wang B., Two parallel symmetry permeable cracks in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading. International Journal of Solids and Structures, 2004, 41: 4407–4422.CrossRefGoogle Scholar
  19. [19]
    Morse P. M. and Feshbach H., Methods of Theoretical Physics. Vol.1, New York: McGraw-Hill, 1958.MATHGoogle Scholar
  20. [20]
    Soh A.K., Fang D.N. and Lee K.L., Analysis of a bi-piezoelectric ceramic layer with an interfacial crack subjected to anti-plane shear and in-plane electric loading. European Journal of Mechanics. A/Solid, 2000, 19: 961–977.CrossRefGoogle Scholar
  21. [21]
    Delale, F. and Erdogan, F., On the mechanical modeling of the interfacial region in bonded half-planes. ASME Journal of Applied Mechanics, 1988, 55: 317–324.CrossRefGoogle Scholar
  22. [22]
    Fildis, H. and Yahsi, O. S., The axisymmetric crack problem in a non-homogeneous interfacial region between homogeneous half-spaces. International Journal of Fracture, 1996, 78: 139–163.CrossRefGoogle Scholar
  23. [23]
    Gradshteyn, I.S. and Ryzhik, I.M., Table of Integral, Series and Products. New York: Academic Press, 1980.MATHGoogle Scholar
  24. [24]
    Erdelyi, A. (ed), Tables of Integral Transforms. Vol.1, New York: Magraw-Hill, 1954.MATHGoogle Scholar
  25. [25]
    Zhou Z. G., Du S. Y. and Wu L. Z., Investigation of anti-plane shear behavior of a Griffith permeable crack in functionally graded piezoelectric materials by use of the non-local theory. Composite and Structures, 2007, 78(4): 575–583.CrossRefGoogle Scholar
  26. [26]
    Zhou Z. G., Du S. Y. and Wang B., Dynamic behavior of two parallel symmetric permeable cracks in a piezoelectric material strip. Acta Mechanica Solida Sinica, 2002, 15(4): 294–302.Google Scholar
  27. [27]
    Zhou Z. G. and Wang B., Analysis of the dynamic behavior a Griffith permeable crack in piezoelectric materials use of non-local theory. Acta Mechanica Solida Sinica, 2003, 16(1): 52–60.MathSciNetGoogle Scholar
  28. [28]
    Shbeeb, N. I. and Binienda, W. K., Analysis of an interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness. Engineering Fracture Mechanics, 1999, 64(4): 693–720.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2007

Authors and Affiliations

  • Jun Liang
    • 1
  1. 1.Center for Composite MaterialsHarbin Institute of TechnologyHarbinChina

Personalised recommendations