Skip to main content
Log in

On stress intensities induced by direct resistance heating

  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

The temperature field and mode I stress intensity caused by resistance heating are calculated for a model problem. The results indicate that, for a constant far-field electric current, the stress intensity is proportional to the crack length to the power 5/2. Consequently, the effect of localized heating becomes especially important as the crack length increases and may, if ignored, cause significant errors during the more severe thermal fatigue tests that utilize direct resistance heating.

Résumé

On calcule pour un problème de modélisation le champ de température et l'intensité de contrainte de Mode I provoqué par un chauffage par résistance. Les résultats indiquent que, pour un courant électrique constant appliqué, l'intensité de contraintes est proportionnelle à la longueur d'une fissure à la puissance 5/2.

En conséquence, l'effet d'un chauffage local devient spécialement important lorsqu'on augmente la longueur de fissure, et peut, s'il est ignoré, induire des erreurs graves au cours d'essais de fatigue thermique de sévérité accrue qui recourent au chauffage direct par effect Joule.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D.A. Wilson and J.R. Warren, 30th International Gas Turbine Conference and Exhibit, ASME Transactions, Paper no. 85-GT-12, (Houston, TX) March 18–21, 1985.

  2. H.H. Johnson, Materials Research and Standards 5 (1965) 442–445.

    Google Scholar 

  3. G. Clark and J.F. Knott, Journal of the Mechanics and Physics of Solids 23 (1975) 215–216.

    Article  Google Scholar 

  4. R.O. Ritchie and K.J. Bathe, International Journal of Fracture 15 (1979) 47–56.

    Google Scholar 

  5. M.A. Hicks and A.C. Pickard, International Journal of Fracture 20 (1982) 91–101.

    Google Scholar 

  6. M. Saka and H. Abe, International Journal of Engineering Science 21 (1983) 1451–1457.

    Article  Google Scholar 

  7. R.M.J. Kemp, International Journal of Fracture 30 (1986) R33-R36.

    Google Scholar 

  8. A.L. Florence and J.N. Goodier, Journal of Applied Mechanics 27 (1960) 635–639.

    Google Scholar 

  9. A.L. Florence and J.N. Goodier, International Journal of Engineering Science 1 (1963) 533–540.

    Article  Google Scholar 

  10. J.N. Goodier and A.L. Florence in Applied Mechanics, Proceedings of the 11th International Congress of Applied Mechanics, Munich 1964, Springer-Verlag (1966) 562–568.

  11. G.C. Sih, Journal of Applied Mechanics 29 (1962) 587–589.

    Google Scholar 

  12. M.N. Bapu Rao, International Journal of Fracture 12 (1976) RCR 777–779.

    Google Scholar 

  13. Y. Konishi and A. Atsumi, International Journal of Engineering Science 11 (1973) 1–7.

    Article  Google Scholar 

  14. H. Sekine, Engineering Fracture Mechanics 9 (1977) 499–507.

    Article  Google Scholar 

  15. H. Sekine, Journal of Applied Mechanics 44 (1977) 637–642.

    Google Scholar 

  16. J. Tweed and S. Lowe, International Journal of Engineering Science 17 (1979) 357–363.

    Article  Google Scholar 

  17. Y.E. Pak and G. Herrmann, ‘Energy Release Rates for Various Defects Disturbing a Uniform Heat Flow’, to be published.

  18. Y.E. Pak and G. Herrmann, ‘Crack Extension Force in a Dielectric Medium’, submitted to International Journal of Engineering Science.

  19. G.R. Doelp, J.F. Abel and F.C. Moon, ‘Experimental and Numerical Analysis of Electric Currents and Electromagnetic Blunting of Cracks in Thin Plates’, Report 84–12, Department of Structural Engineering, Cornell University, Ithaca, NY (1984).

    Google Scholar 

  20. Y.C. Fung, Foundations of Solid Mechanics, Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1965).

    Google Scholar 

  21. G.B. Sinclair, International Journal of Fracture 28 (1985) 3–16.

    Google Scholar 

  22. S.E. Cunningham, ‘An Estimate of the Thermoelastic Stress Field Induced by an Electric Current Flowing Around a Crack’, Report SM 85–16, Department of Mechanical Engineering, Carnegie-Mellon University, Pittsburgh (1985).

    Google Scholar 

  23. F.B. Hildebrand, Advanced Calculus for Applications, Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1976).

    Google Scholar 

  24. J.R. Warren, private communication, April 1985.

  25. S.L. Hoyt (ed.), Metals Properties, ASME Handbook, McGraw-Hill Book Co., Inc. (1954) 371–383.

  26. Monel, Inconel, Nickel and Nickel Alloys, International Nickel Co., Inc. (1947) 14–17.

  27. H.C. Cross and W.F. Simmons, in Symposium on Materials for Gas Turbines, 49th Annual Meeting, ASTM, Buffalo, NY (1947) 3–51.

  28. D.W. Grobecker (ed.) in Metals for Supersonic Aircraft and Missiles, Proceedings of the Conference, Heat Tolerant Metals for Aerodynamic Applications, ASM, Albuquerque, NM (1958) 234–249.

  29. American Society for Metals, Source Book on Industrial Alloy and Engineering Data (1978) 311–337.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cunningham, S.E., Griffin, J.H. & Sinclair, G.B. On stress intensities induced by direct resistance heating. Int J Fract 33, 135–144 (1987). https://doi.org/10.1007/BF00033745

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00033745

Keywords

Navigation