Skip to main content
SpringerLink
Log in

Effect of strain rate on the geometry of the plastic zone near a Mode II crack tip. Parametric analysis

  • Published:
Strength of Materials Aims and scope

Abstract

We present an approximate approach to assessment of the effect of the strain rate (γ) on the size (rp) and shape of the plastic zone near a transverse shear crack tip. The analysis is based on including the parameters of the stress—strain diagram for the material as functions of\(\dot \gamma \) in the quasistatic solution for rp. We propose a two-parameter model for taking into account the effect of the magnitude of the applied shear stresses on the geometry of the plastic zone. For a crack in mild steel, we obtain estimates of the evolution of the plastic zone as the strain rate varies within the range 10−4−103 sec−1.

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. J. R. Klepaczko, “Dynamic crack initiation, some experimental methods and modelling,” in: Crack Dynamics in Metallic Materials, Springer-Verlag (1990), pp. 255–453.

  2. J. R. Klepaczko, “A practical stress—strain rate—temperature constitutive relation of power form,” J. Mech. Working Technol.,15, No. 2, 143–165 (1987).

    Google Scholar 

  3. G. R. Irwin, “Plastic zone near a crack and fracture toughness,” Proceedings, Seventh Sagamore Conference (1960), pp. IV54-63.

  4. D. Broek, Elementary Engineering Fracture Mechanics, 4th rev. ed., Martinus Nijhoff Publ. (1987).

  5. L. Banks-Sills and D. Sherman, “Elasto-plastic analysis of a mode II fracture specimen,” Int. J. Fract.,46, No. 2, 105–122 (1990).

    Google Scholar 

  6. C. F. Shih, “Small scale yielding analysis of mixed mode plane-strain crack problems,” Fract. Analysis: ASTM Spec. Techn. Publ., No. 560 (1974), pp. 187–210.

    Google Scholar 

  7. J. Pan and C. F. Shih, “Elastic—plastic analysis of combined mode II and III crack-tip fields under small-scale yielding conditions,” J. Appl. Mech.,57, No. 2, 259–267 (1990).

    Google Scholar 

  8. N. Aravas and S. M. Sharma, “An elastoplastic analysis of the interface crack with contact zones,” J. Mech. Phys. Solids,39, No. 3, 311–344 (1991).

    Google Scholar 

  9. S. G. Larsson and A. J. Carllsson, “Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials,” J. Mech. Phys. Solids,21, No. 3, 263–277 (1973).

    Google Scholar 

  10. J. R. Rice, “Limitations to the small scale yielding approximation for crack tip plasticity,” J. Mech. Phys. Solids,22, No. 1, 17–26 (1974).

    Google Scholar 

  11. M. F. Kanninen and C. H. Popelar, Advanced Fracture Mechanics, Oxford Univ. Press, Oxford, UK (1985).

    Google Scholar 

  12. H. Tada, P. Paris, and G. R. Irwin, The Stress Analysis of Cracks: Handbook, Del Research Corp., Hellertown (1973).

    Google Scholar 

  13. M. P. Savruk, Stress Intensity Factors in Cracked Solids: Handbook [in Russian], Nauk. Dumka, Kiev (1988).

    Google Scholar 

  14. J. R. Rice and G. F. Rosengren, “Plane strain deformation near a crack tip in a power-law hardening material,” J. Mech. Phys. Solids,16, No. 1, 1–12 (1968).

    Google Scholar 

  15. J. W. Hutchinson, “Singular behaviour at the end of a tensile crack in a hardening material,” J. Mech. Phys. Solids,16, No. 1, 13–31 (1968).

    Google Scholar 

  16. J. W. Hutchinson, “Plastic stress and strain fields at a crack tip,” J. Mech. Phys. Solids,16, No. 4, 337–347 (1968).

    Google Scholar 

  17. Z. Z. Du, C. Betegon, and J. W. Hancock, “J dominance in mixed mode loading, “Int. J. Fract.,52, No. 3, 191–206 (1991).

    Google Scholar 

  18. J. D. Campbell and W. G. Ferguson, “The temperature and strain-rate dependence of the shear strength of mild steel,” Phil. Mag.,21, No. 1, 63–82 (1970).

    Google Scholar 

  19. K. Tanaka and M. Kinoshita, “Compressive strength of mild steel at high strain rates at high temperature,” Bull. JSME,10, 429–440 (1967).

    Google Scholar 

  20. J. R. Klepaczko, “The strain rate behavior of iron in pure shear,” Int. J. Solids Struct.,5, No. 6, 533–548 (1969).

    Google Scholar 

  21. J. F. Kalthoff and S. Winkler, “Failure mode transition at high rates of shear loading,” in: Impact 87: International Conference on Impact Loading and Dynamic Behaviour of Materials, DGM Informationsgesellschaft Verlag, Oberursel (1987), Vol. 1, pp. 185–195.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine

    I. V. Varfolomeev

  2. University of Metz, Metz, France

    J. R. Klepaczko

Authors
  1. I. V. Varfolomeev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. R. Klepaczko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Problemy Prochnosti, No. 3, pp. 46–55, March, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Varfolomeev, I.V., Klepaczko, J.R. Effect of strain rate on the geometry of the plastic zone near a Mode II crack tip. Parametric analysis. Strength Mater 27, 138–145 (1995). https://doi.org/10.1007/BF02209479

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02209479

Keywords

Search

Navigation