Skip to main content
SpringerLink
Log in

Fracture of a body with a periodic set of coaxial cracks under forces directed along them: an axisymmetric problem

  • Published:
International Applied Mechanics Aims and scope

Linearized solid mechanics is used to solve an axisymmetric problem for an infinite body with a periodic set of coaxial cracks. Two nonclassical fracture mechanisms are considered: fracture of a body with initial stresses acting in parallel to crack planes and fracture of materials compressed along cracks. Numerical results are obtained for highly elastic materials described by the Bartenev–Khazanovich, Treloar, and harmonic elastic potentials. The dependence of the fracture parameters on the loading conditions, the physical and mechanical characteristics of the material, and the geometrical parameters is analyzed

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. G. N. Bartenev and T. N. Khazanovich, “On the law governing the hyperelastic deformation of cross-linked polymers,” Vysokomolekulyarn. Soed., 32, No. 3, 21–28 (1960).

    Google Scholar 

  2. A. N. Guz, “A note on the linearized theory of brittle fracture of prestressed bodies,” Dokl. AN SSSR, 252, No. 5, 1085–1088 (1980).

    Google Scholar 

  3. A. N. Guz, “A failure criterion for solids compressed along cracks: A three-dimensional problem,” Dokl. AN SSSR, 261, No. 1, 42–45 (1981).

    Google Scholar 

  4. A. N. Guz, Mechanics of Brittle Fracture of Prestressed Materials [in Russian], Naukova Dumka, Kyiv (1983).

    Google Scholar 

  5. A. N. Guz, Brittle Fracture of Prestressed Materials, Vol. 2 of the five-volume series Nonclassical Problems of Fracture Mechanics [in Russian], Naukova Dumka, Kyiv (1991).

    Google Scholar 

  6. A. N. Guz, “Dynamic Problems of the mechanics of the brittle fracture of materials with initial stresses for moving cracks. 1. Problem statement and general relationships,” Int. Appl. Mech., 34, No. 12, 1175–1186 (1998).

    Article  MathSciNet  Google Scholar 

  7. A. N. Guz, M. Sh. Dyshel’, and V. M. Nazarenko, Fracture and Stability of Materials with Cracks, Vol. 4 of the five-volume series Nonclassical Problems of Fracture Mechanics [in Russian], Naukova Dumka, Kyiv (1992).

    Google Scholar 

  8. A. N. Guz, “Description and study of some nonclassical problems of fracture mechanics and related mechanisms,” Int. Appl. Mech., 36, No. 12, 1537–1564 (2000).

    Article  Google Scholar 

  9. Ya. S. Uflyand, Method of Dual Equations in Problems of Mathematical Physics [in Russian], Nauka, Leningrad (1977).

    MATH  Google Scholar 

  10. M. V. Khai and I. P. Laushnik, “Interaction in a periodic set of penny-shaped cracks,” in: Physical and Mechanical Fields in Deformable Media [in Russian], Naukova Dumka, Kyiv (1978), pp. 65–73.

    Google Scholar 

  11. S. Yu. Babich, Yu. P. Glukhov, and A. N. Guz, “Dynamics of a prestressed incompressible layered half-space under moving load,” Int. Appl. Mech., 44, No. 3, 268–285 (2008).

    Article  Google Scholar 

  12. V. L. Bogdanov, A. N. Guz, and V. M. Nazarenko, “Nonaxisymmetric compressive failure of a circular crack parallel to a surface of halfspace,” Theor. Appl. Frac. Mech., 22, 239–247 (1995).

    Article  MathSciNet  Google Scholar 

  13. A. N. Guz, “On the development of brittle-fracture mechanics of materials with initial stress,” Int. Appl. Mech., 32, No. 4, 316–323 (1996).

    Article  MATH  Google Scholar 

  14. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin (1999).

    MATH  Google Scholar 

  15. A. N. Guz, “Constructing the three-dimensional theory of stability of deformable bodies,” Int. Appl. Mech., 37, No. 1, 1–37 (2001).

    Article  Google Scholar 

  16. A. N. Guz, “On some nonclassical problems of fracture mechanics taking into account the stresses along cracks,” Int. Appl. Mech., 40, No. 8, 937–941 (2004).

    Article  MathSciNet  Google Scholar 

  17. A. N. Guz, “Pascal medals lecture (written presentation),” Int. Appl. Mech., 44, No. 1, 3–7 (2008).

    Article  Google Scholar 

  18. A. N. Guz, M. Sh. Dyshel’, and V. M. Nazarenko, “Fracture and stability of materials and structural members with cracks: Approaches and results,” Int. Appl. Mech., 40, No. 12, 1323–1359 (2004).

    Article  Google Scholar 

  19. I. A. Guz and A. N. Guz, “Stability of two different half-planes in compression along interfacial cracks: Analytical solutions,” Int. Appl. Mech., 37, No. 7, 906–912 (2001).

    Article  MathSciNet  Google Scholar 

  20. A. N. Guz, V. M. Nazarenko, and V. L. Bogdanov, “Fracture under initial stresses acting along cracks: Approach, concept and results,” Theor. Appl. Fract. Mech., 48, 285–303 (2007).

    Article  Google Scholar 

  21. F. John, “Plane strain problems for a perfectly elastic material of harmonic type,” Commun. Pure Appl. Math., 13, No. 2, 239–296 (1960).

    Article  MATH  Google Scholar 

  22. M. K. Kassir and G. C. Sih, Mechanics of Fracture. 2. Three Dimensional Crack Problems, Noordhoff, Leyden (1975).

    Google Scholar 

  23. I. Yu. Khoma and O. A. Kondratenko, “Stress distribution around a circular cylindrical cavity in a prestressed plate,” Int. Appl. Mech., 44, No. 1, 23–33 (2008).

    Article  Google Scholar 

  24. V. M. Nazarenko, V. L. Bogdanov, and H. Altenbach, “Influence of initial stress on fracture of a halfspace containing a penny-shaped crack under radial shear,” Int. J. Frac., 104, 275–289 (2000).

    Article  Google Scholar 

  25. L. R. C. Treloar, “Large elastic deformations in rubber-like materials,” in: Proc. IUTAM Colloq., Madrid (1955), pp. 208–217.

  26. Ya. A. Zhuk and I. A. Guz, “Features of plane wave propagation along the layers of a prestrained nanocomposite,” Int. Appl. Mech., 43, No. 4, 361–379 (2007).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine, 03057

    V. L. Bogdanov, A. N. Guz & V. M. Nazarenko

Authors
  1. V. L. Bogdanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. N. Guz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. M. Nazarenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. L. Bogdanov.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 3–18, February 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bogdanov, V.L., Guz, A.N. & Nazarenko, V.M. Fracture of a body with a periodic set of coaxial cracks under forces directed along them: an axisymmetric problem. Int Appl Mech 45, 111–124 (2009). https://doi.org/10.1007/s10778-009-0178-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-009-0178-7

Keywords

Search

Navigation