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Formation of the plastic zone in an anisotropic body with a crack

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The influence of the length of a mode I crack on the plastic zone in an anisotropic body under hard loading is studied. The case of a generalized plane stress state is examined. A boundary-value problem is solved numerically to study the behavior of the main plastic zone at the crack tip, the additional plastic zone on the lateral face of the body, and the merged plastic zone

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References

  1. A. A. Il'yushin, “Some issues of plasticity theory,” Prikl. Mat. Mekh., 7, No. 4, 245–272 (1943).

    MathSciNet  Google Scholar 

  2. E. E. Kurchakov, “Stress-strain relation for nonlinear anisotropic medium,” Int. Appl. Mech., 15, No. 9, 803–807 (1979).

    MATH  Google Scholar 

  3. E. E. Kurchakov, Tensor-Linear Constitutive Equations for a Nonlinear Anisotropic Body [in Russian], Manuscript No. 5544-V86 deposited at VINITI July 30, 1986, Kyiv (1986), p. 16.

  4. V. Z. Parton and E. M. Morozov, Elastoplastic Fracture Mechanics [in Russian], Nauka, Moscow (1985), p. 504.

    Google Scholar 

  5. J. R. Rice, “Mathematical analysis in the mechanics of fracture,” in: H. Liebowitz (ed.), Fracture, An Advanced Treatise, Vol. II, Academic Press, New York (1968).

    Google Scholar 

  6. L. I. Slepyan, Crack Mechanics [in Russian], Sudostroenie, Leningrad (1981), p. 296.

    Google Scholar 

  7. I. S. Sokol'nikov, Tensor Analysis [in Russian], Nauka, Moscow (1971), p. 376.

    MATH  Google Scholar 

  8. M. E. Babeshko and Yu. N. Shevchenko, “Plastic incompressibility of anisotropic material,” Int. Appl. Mech., 41, No. 3, 256–263 (2005).

    Article  Google Scholar 

  9. V. N. Bastun and A. A. Kaminsky, “Applied problems in the mechanics of strain hardening of structural metallic materials,” Int. Appl. Mech., 41, No. 10, 1092–1129 (2005).

    Article  Google Scholar 

  10. G. V. Galatenko, O. S. Degtyaryeva, and A. A. Kaminsky, “Elastic-plastic fracture of an orthotropic plate with a crack under biaxial loading,” Int. Appl. Mech., 26, No. 8, 794–798 (1990).

    MATH  Google Scholar 

  11. A. N. Guz and I. A. Guz, “On models in the theory of stability of multiwalled carbon nanotubes in matrix,” Int. Appl. Mech., 42, No. 6, 617–628 (2006).

    Article  MathSciNet  Google Scholar 

  12. H. Hencky, “Zur Theorie der plastische Deformationen,” in: Proc. 1st Int. Congress on Applied Mechanics, Delft (1924), pp. 312–317.

  13. A. A. Kaminskii and G. V. Galatenko, “Two-parameter model of a mode I crack in an elastoplastic body under plane-strain conditions,” Int. Appl. Mech., 41, No. 6, 621–630 (2005).

    Article  Google Scholar 

  14. A. A. Kaminsky, “Analyzing the laws of stable subcritical growth of cracks in polymeric materials on the basis of fracture mesomechanics models. Theory and experiment,” Int. Appl. Mech., 40, No. 8, 829–846 (2004).

    Article  Google Scholar 

  15. A. A. Kaminsky, M. V. Dudik, and L. A. Kipnis, “On the direction of development of a thin fracture process zone at the tip of an interfacial crack between dissimilar media,” Int. Appl. Mech., 42, No. 2, 136–144 (2006).

    Article  Google Scholar 

  16. A. A. Kaminsky, L. A. Kipnis, and M. V. Dudik, “Initial development of the prefracture zone near the tip of a crack reaching the interface between dissimilar media,” Int. Appl. Mech., 40, No. 2, 176–182 (2004).

    Article  Google Scholar 

  17. A. A. Kaminsky, E. E. Kurchakov, and G. V. Gavrilov, “Study of the plastic zone near a crack in an anisotropic body,” Int. Appl. Mech., 42, No. 7, 749–764 (2006).

    Article  Google Scholar 

  18. A. A. Kaminsky, E. E. Kurchakov, and G. V. Gavrilov, “Formation of a plastic zone in an anisotropic body under loads acting along a crack,” Int. Appl. Mech., 43, No. 5, 475–490 (2007).

    Article  Google Scholar 

  19. A. A. Kaminsky and S. B. Nizhnik, “Study of the laws governing the change in the plastic zone at the crack tip and characteristics of the fracture toughness of metallic materials in relation to their structure (survey),” Int. Appl. Mech., 31, No. 10, 777–798 (1995).

    Article  Google Scholar 

  20. R. Mises, “Mechanik der festen Korper im plastisch deformablen Zustand,” in: Nachrichten von der Koniglichen Gesellschaft der Wissenschaften zu Gottingen, matematisch-physikalische Klasse, No. 4, 582–592 (1913).

  21. A. Nadai, Plasticity, McGraw-Hill Book Company, New York-London (1931), p. 186.

    Google Scholar 

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    E. E. Kurchakov & G. V. Gavrilov

Authors
  1. E. E. Kurchakov
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  2. G. V. Gavrilov
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 36–52, September 2008.

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Kurchakov, E.E., Gavrilov, G.V. Formation of the plastic zone in an anisotropic body with a crack. Int Appl Mech 44, 982–997 (2008). https://doi.org/10.1007/s10778-009-0120-z

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  • DOI: https://doi.org/10.1007/s10778-009-0120-z

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