Effect of closure of collinear cracks on the stress-strain state and the limiting equilibrium of bent shallow shells

  • I. P. ShatskiiEmail author
  • N. V. Makoviichuk


The problem of closure of collinear cracks during bending of a shallow shell is considered within the framework of the Kirchhoff theory. Crack closure is described using the model of contact along a line on one of the shell faces. Strain and moment intensity factors and fracture load are studied as functions of shell curvature and defect location, and the distribution of contact forces along the cracks is investigated.


shell bending crack closure strength 


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  1. 1.
    A. M. Khludnev and V. A. Kovtunenko, Analysis of Cracks in Solids, WIT-Press, Southampton-Boston (2000).Google Scholar
  2. 2.
    I. Shatskii, V. Perepichka, T. A. Dalyak, and A. Shcherbii, “Problems of the theory of plates with interrelated boundary conditions at cuts,” in: Mathematical Problems of the Mechanics of Inhomogeneous Structures [in Ukrainian], Vol. 2, Kamenyar, Lviv (2000), pp. 51–54.Google Scholar
  3. 3.
    A. T. Zehnder and M. J. Viz, “Fracture mechanics of thin plates and shells under combined membrane, bending and twisting loads,” Appl. Mech. Rev., 58, 37–48 (2005).ADSCrossRefGoogle Scholar
  4. 4.
    A. M. Khludnev, “Theory of cracks with possible closure,” Usep. Mekh., 3, No. 4, 41–82 (2005).Google Scholar
  5. 5.
    I. P. Shatskii, “Integral equations of problems of a shallow shell weakened by a cut whose edges are in contact,” Bop. Akad. Nauk Ukr. RSR, Ser. A, No. 2, 26–29 (1991).Google Scholar
  6. 6.
    A. M. Khludnev, “Contact problem for a shallow shell with a crack,” Prikl. Mat. Mekh., 59, No. 2, 318–326 (1995).MathSciNetGoogle Scholar
  7. 7.
    I. P. Shatskii, “Problem of a cut the with contacting faces in a bent shallow shell,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 5, 164–173 (1998).Google Scholar
  8. 8.
    I. P. Shatskii, “Closure of a transverse crack during bending of a shallow cylindrical shell,” Mat. Metod. Fiz.-Mekh. Polya, 43, No. 2, 149–154 (2000).Google Scholar
  9. 9.
    I. P. Shatskii, “Closure of a longitudinal crack in a shallow cylindrical panel in bending,” Fiz.-Khim. Mekh. Mater., 41, No. 2, 45–48 (2005).Google Scholar
  10. 10.
    I. P. Shatskii and N. V. Makoviichuk, “Equilibrium of a shallow spherical shell with a contact of the crack edges under bending,” Teor. Prikl. Mekh., 41, 146–150 (2005).Google Scholar
  11. 11.
    Liu Rong, C. H. Wang, and R. G. Bathgate, “Crack closure in spherical shells,” Int. J. Fract., 99, No. 4, 307–323 (1999).CrossRefGoogle Scholar
  12. 12.
    Liu Rong, Zhang Tie, X. J. Wu, and C. H. Wang, “Crack closure effect on stress intensity factors of an axially and a circumferentially cracked cylindrical shell,” Int. J. Fract., 125, No. 3/4, 227–248 (2004).zbMATHCrossRefGoogle Scholar
  13. 13.
    I. P. Shatskii and M. B. Makoviichuk, “Contact interaction of crack edges in shallow shells in tensile bending,” Fiz.-Khim. Mekh. Mater., 41, No. 4, 45–52 (2005).Google Scholar
  14. 14.
    I. P. Shatskii, “Interaction between collinear cuts with contacting edges in a bent plate,” Fiz.-Khim. Mekh. Mater., 26, No. 3, 70–75 (1990).Google Scholar
  15. 15.
    F. Erdogan and M. Ratwani, “A note on the interference of two collinear crack in a cylindrical shells,” Int. J. Fract, 10, No. 4, 463–465 (1974).CrossRefGoogle Scholar
  16. 16.
    V. A. Osadchuk, Stress-Strain State and Limiting Equilibrium of Shells with Cuts [in Russian], Naukova Dumka, Kiev (1985).Google Scholar
  17. 17.
    A. N. Guz (ed.), Mechanics of Composites, Vol. 7: Stress Concentration, A.S.K., Kiev (1998).Google Scholar

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© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Ivano-Frankovsk Sector of the Podstrigach Institute of Applied Problems of Mechanics and MathematicsNational Academy of Sciences of UkraineIvano-FrankovskUkraine

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