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Formation of a plastic zone in an anisotropic body under loads acting along a crack

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Abstract

The effects of tension and compression along a crack on the plastic zone in a finite anisotropic body under plane strain are studied. The formation pattern for the plastic zone with increasing load is established by numerically solving a boundary-value problem for each of the cases. In particular, a new plastic zone is revealed. It occurs at the crack face under a compressive load of certain magnitude. How this plastic zone interacts with that at the crack tip is established

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References

  1. A. A. Il’yushin, “Some issues of the theory of plastic strains,” 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, Analysis of Tensor-Linear Constitutive Equations for a Nonlinear Anisotropic Body [in Russian], Manuscript No. 5544-A86_dep. at VINITI 07.30.86, Kyiv (1986).

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

    Google Scholar 

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

    Google Scholar 

  6. J. Rice, “Mathematical methods in fracture mechanics,” in: H. Liebowitz (ed.), Fracture, Vol. 2: Mathematical Fundamentals, Academic Press, New York (1971).

    Google Scholar 

  7. 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, 1192–1029 (2005).

    Article  Google Scholar 

  8. 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 

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

  10. A. A. Kaminsky 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 

  11. A. A. Kaminsky, M. V. Dudyk, 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 

  12. 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 

  13. R. Mises, “Mechanik der festen Korper im plastisch deformablen Zustand,” Nachrichten von der Koniglichen Gesellschaft der Wissenschaften zu Gottingen, Matematisch-Physikalische Klasse, No. 4, 582–592 (1913).

  14. A. Nadai, Plasticity, McGraw-Hill, New York-London (1931).

    Google Scholar 

  15. W. Olszak and W. Urbanowski, “The plastic potential and the generalized distortion energy in the theory of non-homogeneous anisotropic elastic-plastic bodies,” Arch. Mech. Stos., 8, No. 4, 671–694 (1956).

    MATH  MathSciNet  Google Scholar 

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Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 3–19, May 2007.

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Kaminsky, A.A., Kurchakov, E.E. & Gavrilov, G.V. Formation of a plastic zone in an anisotropic body under loads acting along a crack. Int Appl Mech 43, 475–490 (2007). https://doi.org/10.1007/s10778-007-0045-3

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  • DOI: https://doi.org/10.1007/s10778-007-0045-3

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