Skip to main content
SpringerLink
Log in

A crack within a half-space of orthotropic elastic material

  • Contributed Papers
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

The dislocation layer method combined with a technique of images is used to study a mode III loaded Griffith-type elastic strip crack situated parallel to the free-surface of a semi-infinite orthotropic crystal. The density function of the proposed distribution of dislocations is shown to satisfy a complex singular integral equation. Its closed-form solution provides a compact expression for an appropriate combination of the resulting stress field components. Some representative numerical results are presented in tabular form and discussed.

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. Zener, C.: Fracturing of metals. Cleveland Symposium: A.S.M. 1948.

  2. Bilby, B. A., Eshelby, J. D.: Fracture (Liebowitz, H., ed.), Vol. 1, p. 99. New York: Academic Press 1968.

    Google Scholar 

  3. Lardner, R. W.: Mathematical theory of dislocations and fracture. University of Toronto Press, 1974.

  4. Sneddon, I. N., Lowengrub, M.: Crack problems in the classical theory of elasticity. New York: Wiley 1969.

    Google Scholar 

  5. Mechanics of Fracture, Vol. 1, Methods of Analysis and Solutions of Crack Problems (Sih, G. C., ed.). Leyden: Noordhoff Int. Pub. 1973.

    Google Scholar 

  6. Tupholme, G. E.: Mode III crack in an isotropic elastic half-space. Int. J. Engng. Sci. To appear.

  7. Chou, Y. T., Sha, G. T.: On the elastic field of a dislocation in an anisotropic crystal. Scrip. Metal5, 551–558 (1971).

    Google Scholar 

  8. Tupholme, G. E.: A study of cracks in orthotropic crystals using dislocation layers. J. Eng. Math.8, 57–69 (1974).

    Google Scholar 

  9. Gakhov, F. D.: Boundary value problems. Oxford: Pergamon 1966.

    Google Scholar 

  10. Muskhelishvili, N. I.: Singular integral equations. Leyden: Noordhoff Int. Pub. 1953.

    Google Scholar 

  11. Mikhlin, S. G.: Integral equations. Oxford: Pergamon 1964.

    Google Scholar 

  12. Chou, Y. T.: Interaction of parallel dislocations in a hexagonal crystal. J. Appl. Phys.33, 2747–2751 (1962).

    Google Scholar 

  13. Hearmon, R. F. S.: The elastic constants of crystals and other anisotropic materials; Landolt-Börnstein. Numerical data and functional relationships in science and technology (New series, Editor in Chief: Hellwege, K.-H.) Group III: Crystal and solid state physics, Vol. 11: Elastic, piezoelectric, pyroelectric, piezooptic, electrooptic constants, and nonlinear dielectric susceptibilities of crystals, pp. 1–78. Berlin-Heidelberg-New York: Springer 1979.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, University of Bradford, BD7 1DP, Bradford, England

    G. E. Tupholme

Authors
  1. G. E. Tupholme
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tupholme, G.E. A crack within a half-space of orthotropic elastic material. Acta Mechanica 79, 143–152 (1989). https://doi.org/10.1007/BF01181484

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01181484

Keywords

Search

Navigation