Journal of Mathematical Sciences

, Volume 184, Issue 2, pp 145–152 | Cite as

Influence of hardening of a material on the stressed state of an elastoplastic shell with internal crack

  • K. М. Dovbnya
  • I. V. Dmytrieva

The problem of determination of the stressed state of an elastoplastic isotropic shell of arbitrary curvature with an internal crack is considered with regard for hardening of a material. We obtain a system of singular integral equations and solve it numerically by the method of mechanical quadratures. We investigate the influence of hardening of a material on the basic characteristics of the stressed state.


Cylindrical Shell Plastic Zone Singular Integral Equation Transverse Crack Internal Crack 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. N. Bastun and A. A. Kaminskii, “Applied problems in the mechanics of strain hardening of structural metallic materials,” Prikl. Mekh., 41, No. 10, 12–51 (2005); English translation: Int. Appl. Mech., 41, No. 10, 1092–1129 (2005).CrossRefGoogle Scholar
  2. 2.
    F. D. Gakhov, Boundary-Value Problems [in Russian], Nauka, Moscow (1977).Google Scholar
  3. 3.
    M. M. Hordienko, Stress-Strain State of an Elastoplastic Orthotropic Shell of Arbitrary Curvature with Cracks [in Ukrainian], Author’s Abstract of the Candidate-Degree Thesis (Physics and Mathematics), Donetsk (2009).Google Scholar
  4. 4.
    V. L. Danilov, “On the formulation of the law of strain hardening,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 6, 146–150 (1971).Google Scholar
  5. 5.
    E. N. Dovbnya, V. V. Yartemik, and I. V. Gur’eva, “Stressed state of an elastoplastic isotropic shell with a surface crack with regard for the hardening of the material,” Trudy Inst. Prikl. Mat. Mekh. Nats. Akad. Nauk Ukr., 19, 65–71 (2009).Google Scholar
  6. 6.
    A. Yu. Ishlinskii and D. D. Ivlev, Mathematical Theory of Plasticity [in Russian], Fizmatlit, Moscow (2003).Google Scholar
  7. 7.
    A. A. Kaminskii and G. V. Galatenko, “Investigation of fatigue crack growth in materials with hardening,” Prikl. Mekh., 20, No. 4, 54–60 (1984); English translation: Int. Appl. Mech., 20, No. 4, 346–351 (1984).Google Scholar
  8. 8.
    R. M. Kushnir, M. M. Nykolyshyn, and V. A. Osadchuk, Elastic and Elastoplastic Limit State of Shells with Defects [in Ukrainian], Spolom, Lviv (2003).Google Scholar
  9. 9.
    W. Prager, “Hardening of metal in a complex stressed state,” in: Theory of Plasticity [Russian translation], Izd. Inostrannoi Literatury, Moscow (1948), pp. 325–335.Google Scholar
  10. 10.
    V. P. Shevchenko, E. N. Dovbnya, and V. A. Tsvang, “Orthotropic shells with cracks (notches), in: Mechanics of Composites [in Russian], Vol. 7: A. N. Guz’, A. S. Kosmodamianskii, V. P. Shevchenko, etc., Stress Concentration: A.S.K., Kiev (1998), pp. 212–249.Google Scholar
  11. 11.
    A. Baltov and A. Sawczuk, “A rule of anisotropic hardening,” Acta Mech., 1, No. 2, 81–92 (1965).CrossRefGoogle Scholar
  12. 12.
    V. P. Golub, Yu. M. Kobzar, and P. V. Fernati, “An approach to constructing a rheological model of a strain-hardening medium,” Prikl. Mekh., 40, No. 7, 81–97 (2004); English translation: Int. Appl. Mech., 40, No. 7, 776–784 (2004).CrossRefGoogle Scholar
  13. 13.
    A. Khan, M. Kamili, and G. Jackson, “On the evolution of isotropic and kinematic hardening with finite plastic deformation. Part 1,” Int. J. Plasticity, 15, 1265–1275 (1999).MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  • K. М. Dovbnya
    • 1
  • I. V. Dmytrieva
    • 1
  1. 1.DonetskUkraine

Personalised recommendations