Skip to main content
SpringerLink
Log in

Modification of the fracture criterion for V-shaped notches (plane problem). Relationship between toughness and strength and structural parameters

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

Abstract

A fracture criterion of the type of the Neuber-Novozhilov criterion is proposed to describe the fracture in the vicinity of the tip of a V-shaped notch under tensile and shear loading. In the proposed criterion, the limits of averaging of the stresses along the notch axis depend on the presence, location, and size of the initial defects in the material. The crystal lattice parameter of the initial material is chosen for the characteristic linear size. For a V-shaped notch subjected to tension and shear, simple equations are obtained that relate the stress intensity factors for the modified singularity coefficients, the singularity coefficients themselves, and the theoretical tensile and shear strengths of a single crystal of the material taking into account the damage to the material in the vicinity of the notch tip. The equations obtained allow a passage to the limit from a notch to a crack. It is shown that the classical critical stress intensity factor used in the strength analysis of cracked solids is not a material constant.

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. H. Neuber, Kerbspannunglehre: Grunglagen f¨ür Genaue Spannungsrechnung, Springer-Verlag (1937).

  2. V. V. Novozhilov (1969) ArticleTitleNecessary and sufficient criteria of brittle strength Prikl. Mat. Mekh. 33 IssueID2 212–222

    Google Scholar 

  3. V. M. Kornev (1996) ArticleTitleIntegral criteria for the brittle strength of cracked bodies with defects in the presence of vacancies at the tip of a crack. Strength of compacted ceramics-type bodies J. Appl. Mech. Tech. Phys. 37 IssueID5 756–765

    Google Scholar 

  4. V. M. Kornev (2000) ArticleTitleHierarchy of strength criteria of structured brittle media. Satellite initiation of macrocracks J. Appl. Mech. Tech. Phys. 41 IssueID2 367–387

    Google Scholar 

  5. V. M. Kornev (2000) ArticleTitleMultiscale criteria of shear strength of block brittle media. Satellite initiation of micropores Fiz. Tekh. Probl. Razrab. Polezn. Iskop. 40 IssueID5 7–16

    Google Scholar 

  6. R. Thompson (1983) Physics of fracture R. M. Latanision J. R. Pickens (Eds) Atomistics of Fracture Plenum Press New York 167–204

    Google Scholar 

  7. N. H. Macmillan (1983) The ideal strength of solids R. Latanision J. R. Pickens (Eds) Atomistics of Fracture Plenum Press New York 95–164

    Google Scholar 

  8. N. F. Morozov (1988) ArticleTitleBrittle fracture problems and their solution using elasticity methods Mechanics and Progress in Science and Engineering 3 54–63

    Google Scholar 

  9. N. F. Morozov B. N. Semenov (1986) ArticleTitleUsing the Novozhilov criterion of brittle fracture to determine fracture loads for V-shaped notches in complex stressed states Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela 1 122–126

    Google Scholar 

  10. K. Hellan (1984) Introduction to Fracture Mechanics McGraw-Hill New York

    Google Scholar 

  11. V. V. Panasyuk A. E. Andreikiv S. E. Kovchik (1977) ArticleTitleDetermination of the fracture toughness KIc of structural materials from their mechanical characteristics and structural parameters Fiz. Khim. Mekh. Mater. 13 IssueID2 120–122

    Google Scholar 

  12. V. M. Kornev (2002) ArticleTitleGeneralized sufficient strength criteria. Description of the pre-fracture zone J. Appl. Mech. Tech. Phys. 43 IssueID5 128–136

    Google Scholar 

  13. A. Seweryn (1994) ArticleTitleBrittle fracture criterion for structures with sharp notches Eng. Fract. Mech. 47 673–681

    Google Scholar 

  14. A. Seweryn (1996) ArticleTitleElastic stress singularities and corresponding generalized stress intensity factors for angular corners under various boundary conditions Eng. Fract. Mech. 55 529–556

    Google Scholar 

  15. A. Seweryn A. Lukaszewicz (2002) ArticleTitleVerification of brittle fracture criteria for elements with V-shaped notches Eng. Fract. Mech. 69 673–681

    Google Scholar 

  16. A. Carpinteri (1987) ArticleTitleStress singularity and generalized fracture toughness at the vertex of re-entrant corners Eng. Fract. Mech. 26 143–155

    Google Scholar 

  17. M. L. Dunn W. Suwito S. Cunningham C. May (1997) ArticleTitleFracture initiation at sharp notches under mode I, mode II, and mild mixed mode loading Int. J. Fract. 84 367–381

    Google Scholar 

  18. M. L. Dunn W. Suwito S. Cunningham (1997) ArticleTitleFracture initiation at sharp notches: correlation using critical stress intensities Int. J. Solids Struct. 34 3873–3883

    Google Scholar 

  19. V. A. Vinokurov S. A. Kurkin G. A. Nikolaev (1996) Welded Structures. Fracture Mechanics and Working Capacity Criteria Mashinostroenie Moscow

    Google Scholar 

  20. V. M. Kornev (2002) ArticleTitleModified Neuber-Novozhilov criterion of rupture for V-shaped cuts (antiplane problem) J. Appl. Mech. Tech. Phys. 43 IssueID1 128–134

    Google Scholar 

  21. M. P. Savruk (1988) Failure Mechanics and Strength of Materials: Handbook, Part 2: Stress-Intensity Coefficients for Bodies with Cracks Naukova Dumka Kiev

    Google Scholar 

  22. F. A. McClintock and G. R. Irwin, Plasticity Aspects of Fracture Mechanics, ASTM STP (1965).

  23. V. E. Panin, “Physical mesomechanics of materials — a new branch related to physics and solid mechanics,” in: Contemporary Scientific Problems: Proc. Sci. Session (Novosibirsk, Russia, November 25–26, 2003), Novosibirsk (2004), pp. 167–184.

  24. K. G. Schmitt-Thomas, Metallkunde für das Maschinenwesen, Springer-Verlag (1989).

  25. M. Atkinson (1995) ArticleTitleFurther analysis of the size effect in indentation hardness test of some metals J. Mater. Res. 10 IssueID11 2908–2915

    Google Scholar 

  26. S. V. Smirnov, V. K. Smirnov, A. N. Soloshenko, and V. P. Shveikin, “Determination of the coefficients in the strain-resistance functional relation from results of conical indentation tests,” Metally, No. 6, 91–94 (1998).

  27. V. M. Kornev V. D. Kurguzov (1999) ArticleTitleA discrete-integral strength criterion for complicated stress states Fatigue Fract. Eng. Mater. Struct. 22 IssueID11 989–995

    Google Scholar 

  28. I. M. Kershtein V. D. Klyushnikov E. V. Lomakin S. A. Shesterikov (1989) Fundamentals of Experimental Fracture Mechanics Izd. Mosk. Univ. Moscow

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    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

Additional information

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 106–115, January–February, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kornev, V.M., Kurguzov, V.D. Modification of the fracture criterion for V-shaped notches (plane problem). Relationship between toughness and strength and structural parameters. J Appl Mech Tech Phys 46, 85–93 (2005). https://doi.org/10.1007/s10808-005-0043-3

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10808-005-0043-3

Key words

Search

Navigation