Acta Mechanica Solida Sinica

, Volume 25, Issue 1, pp 90–99 | Cite as

Elastodynamic Analysis of a Functionally Graded Half-Plane with Multiple Sub-Surface Cracks

  • Rasul Bagheri
  • Mojtaba Ayatollahi
  • Alibakhsh Kasaeian


The stress fields are obtained for a functionally graded half-plane containing a Volterra screw dislocation. The elastic shear modulus of the medium is considered to vary exponentially. The dislocation solution is utilized to formulate integral equations for the half-plane weakened by multiple smooth cracks under anti-plane deformation. The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically. Several examples are solved and the stress intensity factors are obtained.

Key words

functionally graded materials half-plane multiple cracks screw dislocation 


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  1. [1]
    Maue, A.W., Die beuguhg elastischer wellen a der halbebene. ZAMM, 1953, 33: 1–10.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Loeber, J.F. and Sih, G.C., Diffraction of anti-plane shear waves by a finite crack. Journal of Acoustical Society of America, 1968, 44: 90–98.CrossRefGoogle Scholar
  3. [3]
    Luong, W.C., Keer, L.M. and Achenbach, J.D. Elastodynamic stress intensity factors of a crack near an interface. International Journal of Solids and Structures, 1975, 11: 919–925.CrossRefGoogle Scholar
  4. [4]
    Lin, W., Keer, L.M. and Achenbach, J.D., Dynamic stress intensity factors for an inclined subsurface crack. Journal of Applied Mechanics, 1984, 51: 51–773.CrossRefGoogle Scholar
  5. [5]
    Mendelsohn, D.A., Achenbach, J.D. and Keer, L.M., Scattering of elastic waves by a surface-breaking crack. Wave Motion, 1980, 2: 277–292.CrossRefGoogle Scholar
  6. [6]
    Doyum, A.B. and Erdogan, F., A harmonically excited elastic half-plane containing a rigid flat inclusion. Journal of Sound and Vibration, 1994, 171: 97–117.CrossRefGoogle Scholar
  7. [7]
    Ma, L., Wu, L.Z. and Zhou, Z.G., Dynamic stress intensity factors around two parallel cracks in functionally graded layer bonded to dissimilar half-plane subjected to anti-plane incident harmonic stress wave. International Journal of Engineering Science, 2004, 42: 187–202.CrossRefGoogle Scholar
  8. [8]
    Ma, L, Wu, L.Z., Zhou, Z.G, Chung, L and Shi, L.P., Scattering of harmonic anti-plane shear waves by two collinear cracks in functionally graded piezoelectric materials. European Journal of Mechanics A/Solids, 2004, 23: 633–643.CrossRefGoogle Scholar
  9. [9]
    Moharrami, A. and Ayatollahi, M., Anti-plane elastodynamic analysis of orthotropic planes weakened by several cracks. Applied mathematical modeling, 2011, 35: 50–60.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Weertman, J. and Weertman, J.R., Elementary Dislocation Theory. New York: Oxford University Press, 1992.zbMATHGoogle Scholar
  11. [11]
    Achenbach, J.D., Wave Propagation in Elastic Solids. Amsterdam: North-Holland, 1976.zbMATHGoogle Scholar
  12. [12]
    Abramowitz, M. and Stegun, I.A., Handbook of Mathematical Functions. New York: Dover, 1972.zbMATHGoogle Scholar
  13. [13]
    Erdogan, F., Gupta, G.D. and Cook, T.S., Numerical Solution of Singular Integral Equations, Method of Analysis and Solution of Crack Problems. Edited by Sih, G.C., Holland: Noordhoof, Leyden, 1973.CrossRefGoogle Scholar
  14. [14]
    Erdogan, F., The crack problem for bonded non-homogeneous materials under anti-plane shear loading. Transactions ASME. Journal of Applied Mechanics, 1985, 52: 823C828.CrossRefGoogle Scholar
  15. [15]
    Liebowitz, H., Fracture Mechanics. New York: Academic Press, 1968.zbMATHGoogle Scholar
  16. [16]
    Ayatollahi, M., Fariborz, S.J. and Ahmadi Najafabadi, M., Anti-plane elastodynamic analysis of planes with multiple defects. Applied mathematical modeling, 2009, 33: 663–676.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2012

Authors and Affiliations

  • Rasul Bagheri
    • 1
  • Mojtaba Ayatollahi
    • 1
  • Alibakhsh Kasaeian
    • 2
  1. 1.Faculty of EngineeringZanjan UniversityZanjanIran
  2. 2.Faculty of New Sciences and TechnologiesUniversity of TehranTehranIran

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