Skip to main content
Log in

Two-dimensional problem of the fracture of materials in compression along surface cracks

  • Published:
Soviet Applied Mechanics Aims and scope

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. A. Ya. Aleksandrov, “Certain relationships between the solutions of plane and axisymmettric problems of the theory of elasticity and the solution of axisymmetric problems by means of analytic functions”, Dokl. Akad. Nauk SSSR,129, No. 4, 754–757 (1959).

    Google Scholar 

  2. V. M. Aleksandrov, “Solution of one class of paired equations”, Dokl. Akad. Nauk SSSR,210, No. 1, 55–58 (1973).

    Google Scholar 

  3. A. A. Bablovan, “Solution of certain paired integral equations”, Prikl. Mat. Mekh.,28, No. 6, 1015–1023 (1964).

    Google Scholar 

  4. R. Ville, “Calculation of the stress intensity factors for a crack in an elastic halfplane subjected to a dynamic load”, Vestn. Mosk. Univ. Mat. Mekh., No. 1, 53–59 (1984).

    Google Scholar 

  5. A. N. Guz', Stability of Elastic Bodies in Cubic Compression [in Russian], Naukova Dumka, Kiev (1979).

    Google Scholar 

  6. A. N. Guz', “One criterion of fracture of solids in compression along cracks. Plane problem”, Dokl. Akad. Nauk SSSR,259, No. 6, 1315–1318 (1981).

    Google Scholar 

  7. A. N. Guz', Mechanics of Brittle Fracture of Materials with Initial Stresses [in Russian], Naukova Dumka, Kiev (1983).

    Google Scholar 

  8. A. N. Guz', “Construction of principles of the mechanics of brittle fracture of materials with initial stresses”, Prikl. Mekh.,19, No. 4, 3–23 (1983).

    Google Scholar 

  9. A. N. Guz', V. I. Knyukh, and V. M. Nazarenko, “Three-dimensional axisymmetric problem on the fracture of a material with two disk-shaped cracks in compression along the crack”, Prikl. Mekh., No. 11, 20–30 (1984).

    Google Scholar 

  10. A. N. Guz' and V. M. Nazarenko, “Axisymmetric problem on the fracture of a half-space with a disk-shaped surface crack”, Dokl. Akad. Nauk SSSR,274, No. 1, 38–41 (1984).

    Google Scholar 

  11. V. I. Krylov and A. A. Pal'tsev, Tables for Numerical Integration of Functions with Logarithmic and Power Singularities\(\begin{gathered} \int\limits_0^1 {\ln \frac{e}{x}f(x)dx,\int\limits_0^1 {x^\beta \frac{e}{x}\ln \frac{e}{{l - x}}} f(x)dx,} \hfill \\ \int\limits_0^1 {\ln \frac{l}{x}f(x)dx, \int\limits_0^\infty {x^\beta e^{ - x} \ln \left( {1 + \frac{l}{x}} \right)} f(x)dx.} \hfill \\ \end{gathered}\) [in Russian], Nauka i Tekhnika, Minsk (1967).

  12. S. G. Mikhlin and Kh. L. Smolitskii, Approximate Methods of Solving Differential and Integral Equations [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  13. V. V. Panasyuk, A. E. Andreikiv, and M. M. Stadnik, “Three-dimensional problems of crack theory (survey). Part 1. Fundamental mechanical concepts and mathematical models in three-dimensional problems of crack theory”, Fiz. Khim. Mekh. Mater.,15, No. 4, 39–55 (1979).

    Google Scholar 

  14. G. N. Polozhii, Generalization of the Theory of Analytic Functions of a Complex Variable. p-Analytic and (p, q)-Analytic Functions and Some of Their Applications [in Russian], Izd. Kiev Univ. (1965).

  15. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Elementary Functions [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  16. L. I. Sedov, Continuum Mechanics, Vol. 2 [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  17. I. Sneddon, Fourier Transforms [Russian translation], IL, Moscow (1955).

    Google Scholar 

  18. M. Abramowitz and I. Stigan (eds.), Handbook of Special Functions [Russian translation], Nauka, Moscow (1979).

    Google Scholar 

  19. Yu. I. Travkin, “One system of paired integral equations with trigonometric series,” Prikl. Mekh.,14, No. 8, 102–109 (1978).

    Google Scholar 

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

    Google Scholar 

  21. G. P. Cherepanov, Mechanics of Brittle Fracture [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  22. R. W. Fredricks, “Solution of a pair of integral equations from elastostatics,” Proc. Nat. Acad. Sci. USA,44, No. 4, 309–312 (1958).

    Google Scholar 

  23. F. Erdogan and K. Arin, “Penny-shaped interface crack between an elastic layer and a half space”, Int. J. Eng. Sci.,10, No. 2, 115–125 (1972).

    Google Scholar 

  24. C. C. Sih (ed.), Mechanics of Fracture, Vol. 1, Noordhoff International Publishing, Leyden (1973).

    Google Scholar 

  25. C. Weber, “Achsensymmetrische deformation von umdrehungskörpern,” Z. Angew. Math. Mech.,5, No. 6, 466–468 (1925).

    Google Scholar 

Download references

Authors

Additional information

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 22, No. 10, pp. 72–81, October, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nazarenko, V.M. Two-dimensional problem of the fracture of materials in compression along surface cracks. Soviet Applied Mechanics 22, 970–978 (1986). https://doi.org/10.1007/BF01273678

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01273678

Keywords

Navigation