Skip to main content
SpringerLink
Log in

Thermo-mechanical stress fields and strain energy associated with a mixed-mode propagating crack

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Thermo-mechanical stress field equations are developed for a mixed-mode crack propagating at constant velocity in homogeneous and isotropic materials using an asymptotic approach along with displacement potentials. Asymptotic temperature field equations are first developed for steady state temperature conditions using insulated crack-face boundary conditions. These temperature field equations are later used to derive the first three terms of thermo-mechanical stress field equations for a steady state propagating mixed-mode crack. Using these thermo-mechanical stress fields, various components of the stresses are developed, and the effects of temperature on these stress components are discussed. Further, strain energy density and the circumferential stress criteria are employed to study the effect of temperature and the crack-tip velocity on crack growth direction.

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. Sih G.C.: On the singular character of thermal stress near a crack tip. ASME J. Appl. Mech. 29, 587–589 (1962)

    MATH  Google Scholar 

  2. Kassir M.K., Bergman A.M.: Thermal stress in a solid containing parallel circular crack. Appl. Res. Sci. 25, 262–280 (1971)

    Article  MATH  Google Scholar 

  3. Wilson W.K., Yu I.W.: The use of the J-integral in the thermal stress crack problems. Int. J. Fract. 15, 377–387 (1979)

    Google Scholar 

  4. Chen T.C., Weng C.I.: Coupled transient thermoelastic response in an edge-cracked plate. Eng. Fract. Mech. 39, 915–925 (1991)

    Article  Google Scholar 

  5. Lee K.Y., Sim K.: Thermal shock stress intensity factor by Bueckner’s weight function method. Eng. Fract. Mech. 37, 799–804 (1990)

    Article  Google Scholar 

  6. Katsareas D.E., Anifantis N.K.: On the computation of mode-I and II thermal shock stress intensity factors using a boundary-only element method. Int. J. Numer. Methods Eng. 38, 4157–4169 (1995)

    Article  MATH  Google Scholar 

  7. Hosseini-Tehrani P., Eslami M.R., Daghyani H.R.: Dynamic crack analysis under coupled thermoelastic assumption. Trans. ASME 68, 584–588 (2001)

    Article  MATH  Google Scholar 

  8. Achenbach J.D.: Bifurcation of a running crack in antiplane strain. Int. J. Solids Struct. 11, 1301–1314 (1975)

    Article  MATH  Google Scholar 

  9. Achenbach J.D., Khetan R.P.: Kinking of a crack under dynamic loading conditions. J. Elast. 9, 113–129 (1979)

    Article  MATH  Google Scholar 

  10. Burgers P.: Dynamic kinking of a crack in plane strain. Int. J. Solids Struct. 19, 735–752 (1983)

    Article  MATH  Google Scholar 

  11. Georgiadis H.G., Theocaris P.S.: On the solution of steady-state elastodynamic crack problems by using complex variable methods. J. Appl. Math. Phys. (ZAMP) 36, 146–165 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  12. Freund L.B.: Dynamic Fracture Mechanics. 1st edn. Cambridge Press, New York (1990)

    Book  MATH  Google Scholar 

  13. Shukla A., Choan R.: The stress field surrounding a rapidly propagating curving crack: an experimental study. ASTM STP 945, 86–89 (1987)

    Google Scholar 

  14. Lui C., Rosakis A.: On the higher order asymptotic analysis of a non-uniformily propagating dynamic crack along an arbitrary path. J. Elast. 35, 27–60 (1994)

    Article  Google Scholar 

  15. Chalivendra V.B.: Asymptotic analysis of transient curved crack in functionally graded materials. Int. J. Soilds Struct. 44, 465–479 (2007)

    Article  MATH  Google Scholar 

  16. Jin Z.H., Noda N.: Crack-tip singular fields in nonhomogeneous materials. J. Appl. Mech. 61, 738–740 (1994)

    Article  MATH  Google Scholar 

  17. Parameswaran V., Shukla A.: Crack-tip stress fields for dynamic fracture in functionally gradient materials. Mech. Mat. 31, 579–596 (1999)

    Article  Google Scholar 

  18. Chalivendra V.B., Shukla A.: Transient elastodynamic crack growth in functionally graded materials. J. Appl. Mech. 72, 237–248 (2005)

    Article  MATH  Google Scholar 

  19. Shukla A., Jain N.: Dynamic damage growth in particle reinforced graded materials. Int. J. Impact Eng. 30, 777–803 (2004)

    Article  Google Scholar 

  20. Jiang C.P., Zou Z.Z., Wang D., Liu Y.W.: A discussion about a class of stress intensity factors and its verification. Int. J. Fract. 49, 141–157 (1991)

    Google Scholar 

  21. Sih G.C.: Strain-energy-density factor applied to mixed mode crack problems. Int. J. Fract. 10, 305–321 (1974)

    Article  Google Scholar 

  22. Erdogan F., Sih G.C.: On the crack extension in plates under plane loading and transverse shear. J. Basic Eng. 85, 519–527 (1963)

    Google Scholar 

  23. Yoffe E.H.: The moving Griffith crack. Philos. Mag. 42, 739–750 (1952)

    MathSciNet  Google Scholar 

  24. Broek D.: Elementary Engineering Fracture Mechanics. Martinus Nishoff, Dordrecht (1978)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate Aeronautical Laboratories, Division of Engineering and Applied Science, California Institute of Technology, 1200 E California Blvd., Mail code 205-45, Pasadena, CA, 91125, USA

    Addis Kidane

  2. Department of Mechanical Engineering, University of Massachusetts, North Dartmouth, MA, 02747, USA

    Vijaya B. Chalivendra

  3. Dynamic Photomechanics Laboratory, Department of Mechanical Engineering & Applied Mechanics, University of Rhode Island, Kingston, RI, 02881, USA

    Arun Shukla

Authors
  1. Addis Kidane
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vijaya B. Chalivendra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Arun Shukla
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Addis Kidane.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kidane, A., Chalivendra, V.B. & Shukla, A. Thermo-mechanical stress fields and strain energy associated with a mixed-mode propagating crack. Acta Mech 215, 57–69 (2010). https://doi.org/10.1007/s00707-010-0305-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-010-0305-x

Keywords

Search

Navigation