Skip to main content
Log in

Calculation of elasto-plastic strains and stresses in notches under multiaxial loading

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

Abstract

A method for calculating elasto-plastic notch tip strains and stresses in bodies subjected to multiaxial loading has been presented. The method has been formulated in terms of strain energy density relationships. Two approximate formulae are derived based on the analysis of strain energy density in the notch tip region. The two formulae represent the lower and upper limits of the band within which the actual elasto-plastic notch tip strains can be found. All necessary relationships are derived for a general multiaxial stress state. The calculated notch tip strain and stress components are compared with experimental and finite element data obtained for a variety of loading conditions and materials. This method may be particularly useful for stress/strain analysis of notched components subjected to lengthy multiaxial cyclic loading histories.

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. R.M. Wetzel (ed.), Fatigue Under Complex Loading: Analyses and Experiments, Society of Automotive Engineers, Warrendale, PA (1977).

    Google Scholar 

  2. H. Neuber, Journal of Applied Mechanics, ASME 26: 4 (1961) 544–550.

    Google Scholar 

  3. T.H. Topper, R.M. Wetzel and J. Morrow, Journal of Materials 4: 1 (1969) 200–209.

    Google Scholar 

  4. A. Conle and H. Nowack, Experimental Mechanics 17: 2 (1977) 53–63.

    Google Scholar 

  5. K. Molski and G. Glinka, Materials Science and Engineering 50: 2 (1981) 93–100.

    Google Scholar 

  6. G. Glinka, Engineering Fracture Mechanics 22: 5 (1986) 839–854.

    Google Scholar 

  7. A.E. Gemma, Engineering Fracture Mechanics 21: 3 (1985) 495–501.

    Google Scholar 

  8. N. Dowling, W.R. Brose and W.K. Wilson, in Fatigue under Complex Loading, Vol. 6, Advances in Engineering, R.M. Wetzel (ed.), Society of Automotive Engineers, Warrendale, PA (1977).

    Google Scholar 

  9. M. Hoffman and T. Seeger, ASME Journal of Engineering Materials and Technology 107: 4 (1985) 250–260.

    Google Scholar 

  10. L. Lemaitre and J.L. Chaboche, Mechanics of Solid Materials, Cambridge University Press, Cambridge, U.K. (1990).

    Google Scholar 

  11. G. Glinka, Engineering Fracture Mechanics 22: 3 (1985) 485–508.

    Google Scholar 

  12. A. Moftakhar, Calculation of Time Independent and Time Dependent Strains and Stresses in Notches, Ph.D. dissertation, University of Waterloo, Ontario, Canada (1994).

    Google Scholar 

  13. W.N. Sharp, C.H. Yang and R.L. Tregoning, Journal of Applied Mechanics, ASME 59: 2 (1992) S50-S56.

    Google Scholar 

  14. M. Hoffman and T. Seeger, The Use of Hencky's Equations for the Estimation of Multiaxial Elastic-Plastic Notch Stresses and Strains, Report No. FB-3/1986, Technische Hochschule Darmstadt (1986).

  15. T. Seeger and M. Hoffman, Kerbbeanspruchungen I, Vorhaben No. 71, Forschungshefte, Forschungskuratorium Maschinenbau e.V., FKM, Heft 115, Germany (1985).

    Google Scholar 

  16. H.D. Hibbit, B.I. Karlsson and P.E. Sorenson, ABAQUS Theory Manual, Version 4.8 (1989).

  17. A. Moftakhar, A. Buczynski and G. Glinka, in Conference Proceedings Fatigue 93, J.P. Bailon and J.I. Dickson (eds.), Engineering Materials Advisory Services Ltd., U.K. (1994).

    Google Scholar 

  18. MAPLE—Waterloo Maple Software, University of Waterloo, Waterloo, ON, Canada (1992).

Download references

Author information

Authors and Affiliations

Authors

Additional information

On leave from Warsaw University of Technology.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moftakhar, A., Buczynski, A. & Glinka, G. Calculation of elasto-plastic strains and stresses in notches under multiaxial loading. Int J Fract 70, 357–373 (1994). https://doi.org/10.1007/BF00032453

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00032453

Keywords

Navigation