Skip to main content
Log in

Stress State Near a Small-Scale Crack at the Corner Point of the Interface of Media

  • Published:
International Applied Mechanics Aims and scope

The stress state of a piecewise-homogeneous isotropic elastic body near a small-scale mode I crack at the corner point of the interface of media is analyzed. The exact solution of the corresponding elasticity problem is obtained using the Wiener–Hopf method.

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.

Similar content being viewed by others

References

  1. R. D. Bantsuri, “Solving of the first principal elastic problem for a wedge with a finite notch,” Dokl. AN SSSR, 167, No. 6, 1256–1259 (1966).

    Google Scholar 

  2. F. D. Gakhov, Boundary-Value Problems [in Russian], Nauka, Moscow (1977).

    MATH  Google Scholar 

  3. A. A. Kaminsky, M. V. Dudik, and L. A. Kipnis, “Initial kinking of an interface crack between two elastic media,” Int. Appl. Mech., 43, No. 10, 1090–1099 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  4. A. A. Kaminsky, L. A. Kipnis, and V. A. Kolmakova, “Model of a fracture process zone at the tip of a crack reaching the nonsmooth interface between elastic media,” Int. Appl. Mech., 44, No. 10, 1084–1092 (2008).

    Article  ADS  Google Scholar 

  5. A. A. Kaminsky, L. A. Kipnis, and G. A. Khasin, “Analysis of a plastic zone at a corner point by the trident model,” Int. Appl. Mech., 38, No. 5, 611–616 (2002).

    Article  ADS  Google Scholar 

  6. V. D. Kuliev, Yu. N. Rabotnov, and G. P. Cherepanov, “Retardation of the interface crack between different elastic media,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 4, 120–128 (1978).

  7. M. A. Lavrent’ev and B. V. Shabat, Methods of the Theory of a Complex Variable [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  8. V. V. Loboda and A. E. Sheveleva, “Determining prefracture zones at a crack tip between two elastic orthotropic bodies,” Int. Appl. Mech., 39, No. 5, 566–572 (2003).

    Article  ADS  Google Scholar 

  9. V. M. Nazarenko and A. L. Kipnis, “Stress intensity at the tips of interface shear cracks at a corner point between media,” Dop. NAN Ukrainy, No. 8, 58–63 (2015).

  10. E. M. Nekislykh and V. I. Ostrik, “Elastic equilibrium of a wedge with cracks on the symmetry axis,” Izv. RAN, Mekh. Tverd. Tela, No. 5, 111–129 (2010).

  11. B. Noble, Methods Based on the Wiener–Hopf Technique for the Solution of Partial Differential Equations, Pergamon Press, London (1958).

    MATH  Google Scholar 

  12. V. V. Panasyuk, A. E. Andreikiv, and V. Z. Parton, Fundamentals of the Fracture Mechanics of Materials [in Russian], Naukova Dumka, Kyiv (1988).

    Google Scholar 

  13. V. Z. Parton and P. I. Perlin, Methods of Mathematical Elasticity Theory [in Russian], Nauka, Moscow (1981).

    MATH  Google Scholar 

  14. B. I. Smetanin, “Some problems for slits in an elastic wedge and layer,” Izv.ANSSSR, Mekh. Tverd. Tela, No. 2, 115–122 (1968).

  15. B. I. Smetanin, “On a mixed problem of elasticity for a wedge,” PMM, 32, No. 4, 708–714 (1968).

    MATH  Google Scholar 

  16. Ya. S. Uflyand, Integral Transforms in Problems of Elasticity Theory [in Russian], Nauka, Leningrad (1967).

  17. A. A. Khrapkov, “Closed form solutions of problems on the elastic equilibrium of an infinite wedge with nonsymmetric notch at the vertex,” PMM, 35, No. 6, 1062–1069 (1971).

    MATH  Google Scholar 

  18. V. L. Bogdanov, A. N. Guz, and V. M. Nazarenko, “Spatial problems of the fracture of materials loaded along cracks (review),” Int. Appl. Mech., 51, No. 5, 489–560 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  19. J. P. Dempsey and G. B. Sinclair, “On the singular behavior at the vertex of a bi-metal wedge,” J. Elast., 11, No. 3, 317–327 (1981).

    Article  Google Scholar 

  20. H. E. Doran, “The wedge with a symmetric crack at the vertex in plane elastostatics,” J. Inst. Math. Appl., 5, No. 4, 363–372 (1969).

    Article  MathSciNet  Google Scholar 

  21. A. N. Guz and V. A. Dekret, “Finite-fiber model in the three-dimensional theory of stability of composites (review),” Int. Appl. Mech., 52, No. 1, 1–48 (2016).

    Article  ADS  Google Scholar 

  22. S. A. Kaloerov and A. A. Samodurov, “Problem of electromagnetoviscoelasticity for multiply connected plates,” Int. Appl. Mech., 51, No. 6, 623–639 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  23. A. A. Kaminsky and E. E. Kurchakov, “Influence of tension along a mode I crack in an elastic body on the formation of a nonlinear zone,” Int. Appl. Mech., 51, No. 2, 130–148 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  24. L. M. Keer, D. A. Mendelsohn, and J. D. Achenbach, “Crack at the apex of a loaded notch,” Int. J. Solids Struct., 13, No. 7, 615–623 (1977).

    Article  Google Scholar 

  25. F. Ouchterlony, “Symmetric cracking of a wedge by concentrated loads,” Int. J. Eng. Sci., 15, No. 2, 109–116 (1977).

    Article  Google Scholar 

  26. R. P. Srivastav and P. Narain, “Certain two-dimensional problems of stress distribution in wedge-shaped elastic solids under discontinuous loads,” Proc. Camb. Phil. Soc., 61, No. 4, 945–954 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  27. S. F. Stone and R. A. Westmann, “Stress intensity factors for cracked wedges,” Int. J. Solids Struct., 17, No. 3, 345–358 (1981).

    Article  Google Scholar 

  28. P. S. Theocaris and E. E. Gdoutos, “Stress singularities in cracked composite full-planes,” Int. J. Fract., 13, No. 6, 763–773 (1977).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Kaminsky.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 54, No. 5, pp. 20–34, September–October, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kaminsky, A.A., Kipnis, L.A. & Polishchuk, T.V. Stress State Near a Small-Scale Crack at the Corner Point of the Interface of Media. Int Appl Mech 54, 506–518 (2018). https://doi.org/10.1007/s10778-018-0903-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-018-0903-1

Keywords

Navigation