Skip to main content
SpringerLink
Log in

Steady-state thermal stresses in an infinite elastic medium containing an annular crack

  • Published:
Proceedings of the Indian Academy of Sciences - Mathematical Sciences Aims and scope Submit manuscript

Abstract

An axisymmetric steady-state thermoelastic problem of an infinite isotropic medium containing an annular crack is considered. The faces of the crack are exposed to prescribed temperature distribution. The normal components of stress and displacement on the crack plane and the stress-intensity factors at the boundaries of the crack are expressed in power series in terms of the ratio between the radii of the inner and outer boundaries. These are illustrated graphically.

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. Collins W D, On the solution of some axisymmetric boundary value problems by means of integral equations, VIII. Potential problems for a circular annulus,Proc. Edinburgh Math. Soc. 13 (1963) 235–246

    MATH  MathSciNet  Google Scholar 

  2. Cooke J C, Some further triple integral equation solutions,Proc. Edinburgh Math. Soc. 13 (1963) 303–316

    MATH  MathSciNet  Google Scholar 

  3. Clements D L and Love E R, Potential problems involving an annulus,Proc. Cambridge Philos. Soc. 76 (1974) 313

    MATH  MathSciNet  Google Scholar 

  4. Clements D L and Ang W T, Stress intensity factors for the circular annulus crack,Int. J. Eng. Sci. 26 (1988) 325–329

    Article  MATH  Google Scholar 

  5. Das B R, Some axially symmetric thermal stress distributions in elastic solids containing cracks—I. An external crack in an infinite solid,Int. J. Eng. Sci. 9 (1971) 469–478

    Article  MATH  Google Scholar 

  6. Florence A L and Goodier J N, The linear thermoelastic problem of uniform heat flow disturbed by a penny-shaped insulated crack,Int. J. Eng. Sci. l (1963) 533–540

    Article  MathSciNet  Google Scholar 

  7. Goodier J N, On the integration of the thermoelastic equations,Philos. Mag. VII 23 (1937) 1017

    Google Scholar 

  8. Kumar M and Padmshri, Thermal stresses in a thick elastic slab containing an annular crack,Indian J. Pure Appl. Math. 25 (1994) 1001–1015

    MATH  Google Scholar 

  9. Lal M, Some axially symmetric thermal stress distributions in an elastic solid containing an annular crack,Lett. Appl. Eng. Sci. 20 (1982) 1261–1273

    MATH  Google Scholar 

  10. Noble B, The solution of Bessel function dual integral equations by a multiplying-factor method,Proc. Cambridge Philos. Soc. 59 (1963) 351

    MATH  MathSciNet  Google Scholar 

  11. Nowacki W,Thermoelasticity (London: Pergamon Press) (1962)

    Google Scholar 

  12. Olesiak Z and Sneddon I N, The distribution of thermal stress in an infinite elastic solid containing a penny-shaped crack,Arch. Ration. Mech. Anal. 4 (1960) 238–254

    Article  MATH  MathSciNet  Google Scholar 

  13. Shail R, Some steady-state thermoelastic stress distributions in the vicinity of an external crack in an infinite solid,Int. J. Eng. Sci. 6 (1968) 685

    Article  MATH  Google Scholar 

  14. Sneddon I N and Lowengrub M, Crack, problems in the classical theory of elasticity, (New York: John Wiley and Sons) (1969)

    MATH  Google Scholar 

  15. Selvadurai A P S and Singh B M, The annular crack problem for an isotropic elastic solid,Quart J. Mech. Appl. Math. 38 (1985) 233–243

    Article  MATH  Google Scholar 

  16. Williams W E, Integral equation formulation of some three-part boundary value problems,Proc. Edinburgh Math. Soc. 13 (1963) 317–323

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, 700 032, Calcutta, India

    Rina Bhowmick & Bikash Ranjan Das

Authors
  1. Rina Bhowmick
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bikash Ranjan Das
    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

Bhowmick, R., Das, B.R. Steady-state thermal stresses in an infinite elastic medium containing an annular crack. Proc. Indian Acad. Sci. (Math. Sci.) 107, 71–87 (1997). https://doi.org/10.1007/BF02840475

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02840475

Keywords

Search

Navigation