Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Propagation of a shear crack in a randomly heterogeneous body

  • 15 Accesses


Propagation of a crack in a randomly heterogeneous body exposed to longitudinal shear is considered (in a Born approximation). It is proved that the stress means at the crack tip have singularities on the order of (r)−1/2. The effective coefficient of stress intensity is introduced. It is known that the propagation of a crack in a homogeneous body is of a local nature, i.e., energy consumption in the growth of the crack is completely determined by the coefficient of stress intensity, which is a local characteristic. The equivalence of the force and energy approaches is mathematically expressed by the Irwin equation [1]. An analog of the Irwin equation is obtained for the case of a randomly heterogeneous body.

This is a preview of subscription content, log in to check access.

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Literature cited

  1. 1.

    I. R. Irwin, “Fracture,” in: Handbuch der Physik, Vol. 6, Springer, Berlin (1958), p. 551.

  2. 2.

    I. L. Sanders, “On the Griffith-Irwin fracture theory,” J. Appl. Mech.,27, No. 2, 352 (1960).

  3. 3.

    G. P. Cherepanov, “Propagation of cracks in a continuum,” Prikl. Mat. Mekh., No. 3 (1967).

  4. 4.

    V. A. Lomakin, Statistical Problems from the Mechanics of Deformatale Solids [in Russian], Nauka, Moscow (1970).

  5. 5.

    A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1966).

  6. 6.

    M. A. Laverent'ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1965).

  7. 7.

    G. C. Sih, “Stress distribution near internal crack tips for longitudinal shear problems,” J. Appl. Mech., No. 1 (1965).

Download references

Author information

Additional information

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 145–148, January–February, 1976.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bortnikova, V.V., Romalis, N.B. Propagation of a shear crack in a randomly heterogeneous body. J Appl Mech Tech Phys 17, 120–123 (1976). https://doi.org/10.1007/BF00857765

Download citation


  • Mathematical Modeling
  • Energy Consumption
  • Mechanical Engineer
  • Stress Intensity
  • Industrial Mathematic