Skip to main content
SpringerLink
Log in

Sufficient criterion of fracture in the case with a complex stress state and non-proportional deformation of the material in the pre-fracture zone

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

A general case of proportional loading with a complex stress state of the material in the pre-fracture zone, which is typical for polycrystalline solids with plastic deformation, is considered. A sufficient criterion of fracture is proposed for the case of a complex stress state with non-proportional deformation of the material in the pre-fracture zone. Critical parameters of fracture (pre-fracture zone length and load) for cracks propagating in quasi-brittle materials are obtained with the use of a modified Leonov-Panasyuk-Dugdale model. The pre-fracture zone width is determined by solving the problem of the plasticity theory in the vicinity of the crack tip. The proposed modification of the Leonov-Panasyuk-Dugdale model makes it possible to estimate the critical opening of the crack and the critical displacement of the crack flanks. Inequalities that describe different mechanisms of material fracture under proportional loading (predominantly shear fracture mechanism and fracture mechanism through cleavage) are derived.

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. V. M. Kornev and V. D. Kurguzov, “Multi-parameter sufficient criterion of quasi-brittle strength for a complex stress state,” Fiz. Mezomekh., 9, No. 5, 43–52 (2006).

    Google Scholar 

  2. V. M. Kornev and V. D. Kurguzov, “Multiparametric sufficient criterion of quasi-brittle fracture for complicated stress state,” Eng. Fract. Mech., 75, No. 5, 1099–1113 (2008).

    Article  Google Scholar 

  3. F. A. McClintock and G. R. Irwin, “Plasticity aspects of fracture mechanics,” in: Fracture Toughness Testing and Its Applications, ASTM, STP 381 (1965), pp. 84–113.

    Chapter  Google Scholar 

  4. V. Z. Parton, Fracture Mechanics: From Theory to Practice [in Russian], Izd. LKI, Moscow (2007).

    Google Scholar 

  5. V. M. Kornev, “Branching and kinking of separation crack paths in polycrystals,” Fiz. Mezomekh., 6, No. 5, 37–46 (2003).

    Google Scholar 

  6. B. D. Annin and V. M. Zhigalkin, Behavior of Materials under Complex Loading [in Russian], Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk (1999).

    Google Scholar 

  7. M. Ya. Leonov and V. V. Panasyuk, “Growth of the smallest cracks in solids,” Prikl. Mekh., 5, No. 4, 391-401 (1959).

  8. D. S. Dugdale, “Yielding of steel sheets containing slits,” J. Mech. Phys. Solids, 8, No. 2, 100–108 (1960).

    Article  ADS  Google Scholar 

  9. V. M. Kornev, “Generalized sufficient strength criteria. Description of the pre-fracture zone,” J. Appl. Mech. Tech. Phys., 43, No. 5, 763-769 (2002).

    Google Scholar 

  10. V. M. Kornev, “Stress distribution and opening of cracks in the pre-fracture zone (Neuber-Novozhilov approach),” Fiz. Mezomekh., 7, No. 3, 53–62 (2004).

    MathSciNet  Google Scholar 

  11. I. M. Kershtein, V. D. Klyushnikov, E. V. Lomakin, and S. A. Shesterikov, Fundamentals of Experimental Fracture Mechanics [in Russian], Izd. Mosk. Univ., Moscow (1989).

    Google Scholar 

  12. J. R. Rice, “Mathematical analysis in the mechanics of fracture,” in: H. Liebowitz (ed.), Fracture, Vol. II, Academic Press, New York (1971), pp. 191–311.

    Google Scholar 

  13. G. I. Barenblatt, “Mathematical theory of equilibrium cracks formed during brittle fracture,” Zh. Prikl. Mekh. Tekh. Fiz., No. 4, 3–56 (1961).

  14. M. P. Savruk, Fracture Mechanics and Strength of Materials, Vol. 2: Stress Intensity Factors in Cracked Solids [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

  15. 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).

    Article  MATH  ADS  Google Scholar 

  16. J. W. Hutchinson, “Singular behaviour at the end of tensile crack in a hardening material,” J. Mech. Phys. Solids, 16, 13–31 (1968).

    Article  MATH  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    V. M. Kornev & V. D. Kurguzov

Authors
  1. V. M. Kornev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. D. Kurguzov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. M. Kornev.

Additional information

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 51, No. 6, pp. 153–163, November–December, 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kornev, V.M., Kurguzov, V.D. Sufficient criterion of fracture in the case with a complex stress state and non-proportional deformation of the material in the pre-fracture zone. J Appl Mech Tech Phy 51, 904–912 (2010). https://doi.org/10.1007/s10808-010-0112-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10808-010-0112-0

Key words

Search

Navigation