Skip to main content
SpringerLink
Log in

Statistical criteria of yield for various mechanisms of shear formation

  • Published:
Strength of Materials Aims and scope

Abstract

Statistical criteria of the start of macroyield for various mechanisms of shear formation, including the correlation coefficient of tangential microstresses, which makes it possible to take into consideration the mutual influence of the single crystalline grains, are formulated for a model of a polycrystalline material, a microinhomogeneous medium possessing local anisotropy of mechanical properties and consisting of grains with a cubic type of crystalline lattice. Known criteria of strength are compared and it is shown that they are particular cases of the proposed statistical criteria for certain values of this correlation coefficient.

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

Literature cited

  1. G. J. Taylor, “Plastic strain in metals,” J. Inst. Met.,62, No. 1, 307–324 (1938).

    Google Scholar 

  2. J. F. W. Bishop and R. Hill, “A theoretical derivation of the plastic distortion of a polycrystalline aggregate under combined stress,” Phil. Mag.,42, No. 7, 414–427 (1951).

    Google Scholar 

  3. A. G. Kostyuk, “The initial surface of yield of a polycrystalline material,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 12–17 (1971).

    Google Scholar 

  4. E. Kröner, “Zur plastischen Verformung des Vielkristalls,” Acta Met., No. 9, 155–170 (1961).

    Google Scholar 

  5. O. A. Volokhovskaya and V. V. Podalkov, “The elastoplastic behavior of a material taking micrononuniformity into consideration,” Prikl. Mat. Tekh. Fiz., No. 6, 162–168 (1981).

    Google Scholar 

  6. S. D. Volkov, The Statistical Theory of Strength [in Russian], Mashgiz, Moscow-Sverdlovsk (1960).

    Google Scholar 

  7. I. N. Bogachev, A. A. Vainshtein, and A. A. Volkov, An Introduction to Statistical Metallurgy [in Russian], Metallurgiya, Moscow (1972).

    Google Scholar 

  8. D. M. Mekhontseva, F. P. Rybalko, and S. D. Volkov, “The correlation functions of elastic microdeformations,” Fiz. Met. Metalloved.,22, No. 1, 135–136 (1966).

    Google Scholar 

  9. A. V. Gur'ev, L. V. Kuksa, and Yu. D. Khesin, “Investigation of the microfeatures of deformation of real alloys,” Izv. Akad. Nauk SSSR, Met., No. 2, 122–129 (1967).

    Google Scholar 

  10. A. V. Gur'ev and E. P. Bogdanov, “The rules of transition of microplastic deformation into macroplastic for structurally nonuniform materials,” Probl. Prochn., No. 6, 35–41 (1986).

    Google Scholar 

  11. G. S. Pisarenko and A. A. Lebedev, The Deformation and Strength of Materials in the Complex Stressed Condition [in Russian], Naukova Dumka, Kiev (1986).

    Google Scholar 

  12. A. A. Lebedev, B. I. Koval'chuk, F. F. Giginyak, and V. P. Lamashevskii, The Mechanical Properties of Constructional Materials in the Complex Stressed Condition: A Handbook [in Russian], Naukova Dumka, Kiev (1983).

    Google Scholar 

  13. B. K. Vainshtein (ed.), Modern Crystallography [in Russian], Vol. 4, Nauka, Moscow (1981).

    Google Scholar 

  14. A. V. Gur'ev and V. I. Vodop'yanov, “The mechanism of plastic deformation of polycrystalline solids,” Probl. Prochn., No. 5, 21–25 (1970).

    Google Scholar 

  15. A. A. Ostrovskii, “The direction of local layers of yield in the complex stressed condition,” Prikl. Mekh.,10, No. 2, 112–115 (1974).

    Google Scholar 

  16. S. A. Kotrechko and Yu. Ya. Meshkov, “The influence of the spherical tensor on the yield of iron and carbon steels,” Probl. Prochn., No. 1, 66–68 (1987).

    Google Scholar 

  17. A. V. Gur'ev and E. P. Bogdanov, “The influence of structural stresses on the strength of polycrystalline materials,” Probl. Prochn., No. 1, 68–73 (1984).

    Google Scholar 

  18. A. V. Gur'ev and E. P. Bogdanov, “The conditions of macroyield of a polycrystalline material in the complex stressed condition determined by the statistical rules of distribution of tangential stresses in active slip systems,” in: The Strength of Materials and Structural Elements in the Complex Stressed Condition [in Russian], Inst. Probl. Prochn., Kiev (1984), p. 51.

    Google Scholar 

  19. B. I. Beresnev, E. D. Martynov, K. P. Rodionov, et al., The Plasticity and Strength of Solids at High Pressures [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  20. B. I. Koval'chuk, “The criterion of the limiting condition of casing steels under conditions of the complex stressed conditions at normal and increased temperatures,” Probl. Prochn., No. 5, 14–17 (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Problems of Strength, Academy of Sciences of the Ukrainian SSR, Kiev

    E. P. Bogdanov, V. V. Kosarchuk & S. A. Kotrechko

  2. Volgograd

    E. P. Bogdanov, V. V. Kosarchuk & S. A. Kotrechko

Authors
  1. E. P. Bogdanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. V. Kosarchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. A. Kotrechko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Problemy Prochnosti, No. 3, pp. 46–52, March, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bogdanov, E.P., Kosarchuk, V.V. & Kotrechko, S.A. Statistical criteria of yield for various mechanisms of shear formation. Strength Mater 22, 368–376 (1990). https://doi.org/10.1007/BF00768195

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00768195

Keywords

Search

Navigation