Archive of Applied Mechanics

, Volume 83, Issue 11, pp 1549–1567 | Cite as

Multiple interacting cracks in an orthotropic layer

  • A. M. Baghestani
  • A. R. Fotuhi
  • S. J. Fariborz
Original

Abstract

The stress fields in an orthotropic layer containing climb and glide edge dislocations are obtained by means of the complex Fourier transform. Stress analysis in the intact layer under in-plane point loads is also carried out. These solutions are employed to derive integral equations for the layers weakened by several interacting cracks subject to in-plane deformation. The integral equations are of Cauchy singular type. These equations are solved numerically for the density of dislocations on a crack surface. The dislocation densities are utilized to derive stress intensity factor for cracks. Several examples are solved and the interaction between the two cracks is investigated.

Keywords

Orthotropic layer Edge dislocation Multiple cracks Distributed dislocation technique 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Huang H., Kardomateas G.A.: Stress intensity factors for a mixed mode center crack in an anisotropic strip. Int. J. Fract. 108, 367–381 (2001)CrossRefGoogle Scholar
  2. 2.
    Das S.: Interaction between line cracks in an orthotropic layer. Int. J. Math. Math. Sci. 29, 31–42 (2002)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Li X., Wu Y.: The numerical solutions of the periodic crack problems of anisotropic strip. Int. J. Fract. 118, 41–56 (2002)CrossRefGoogle Scholar
  4. 4.
    Matbuly M.S., Nassar M.: Elastostatic analysis of edge cracked orthotropic strips. Acta Mechanica 165, 17–25 (2003)CrossRefMATHGoogle Scholar
  5. 5.
    Guo L.-C., Wu L.-Z., Zeng T., Ma L.: Mode I crack problem for a functionally graded orthotropic strip. Eur. J. Mech. A/Solids 23, 219–234 (2004)CrossRefMATHGoogle Scholar
  6. 6.
    Liu L., Kardomateas G.A., Holmes J.W.: Mixed-mode stress intensity factors for a crack in an anisotropic bi-material strip. Int. J. Solids Struct. 41, 3095–3107 (2004)CrossRefMATHGoogle Scholar
  7. 7.
    Li X.-F.: Two perfectly bonded dissimilar orthotropic strips with an interfacial crack normal to the boundaries. Appl. Math. Comput. 163, 961–975 (2005)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Caimmi F., Pavan A.: A mode II crack problem with sliding contact in an orthotropic strip. Int. J. Fract. 153, 93–104 (2008)CrossRefMATHGoogle Scholar
  9. 9.
    Das S., Chakraborty S., Srikanth N., Gupta M.: Symmetric edge cracks in an orthotropic strip under normal loading. Int. J. Fract. 153, 77–84 (2008)CrossRefMATHGoogle Scholar
  10. 10.
    Das S., Mukhopadhyay S., Prasad R.: Stress intensity factor of an edge crack in bounded orthotropic materials. Int. J. Fract. 168, 117–123 (2011)CrossRefGoogle Scholar
  11. 11.
    Herakovich C.T.: Mechanics of Fibrous Composites. Wiley, New York (1997)Google Scholar
  12. 12.
    Bueckner H.F.: The propagation of cracks and the energy of elastic deformation. J. Appl. Mech. Trans. ASME 80, 1225–1230 (1958)Google Scholar
  13. 13.
    Fotuhi A.R., Faal R.T., Fariborz S.J.: In-plane analysis of a cracked orthotropic half-plane. Int. J. Solids Struct. 44, 1608–1627 (2006)CrossRefGoogle Scholar
  14. 14.
    Erdogan, F., Gupta, G.D., Cook, T.S.: Numerical solution of integral equations. In: Sih, G.C. (eds) Methods of Analysis and Solution of Crack Problems, Noordhoof, Leyden, Holland (1973)Google Scholar
  15. 15.
    Delale F., Bakirta I., Erdogan F.: The problem of an inclined crack in an orthotropic strip. J. Appl. Mech. Trans. ASME 46, 90–96 (1979)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • A. M. Baghestani
    • 1
  • A. R. Fotuhi
    • 2
  • S. J. Fariborz
    • 1
  1. 1.Department of Mechanical EngineeringAmirkabir University of Technology (Tehran Polytechnic)TehranIran
  2. 2.Department of Mechanical EngineeringYazd UniversityYazdIran

Personalised recommendations