We consider the problem of contact interaction of the lips of collinear cracks in bending of a shallow orthotropic shell of any curvature. The problem is formulated in the two-dimensional statement on the basis of the model of contact along a line on one face of the shell. The solutions of boundary-value problems are constructed by the methods of singular integral equations and mechanical quadratures. We study the influence of curvature of the shell, relative positions of the collinear cracks, and mechanical properties of the material in the vicinity of the crack tips on the moment intensity factors.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. P. Shchats’kyi, “Integral equations of the problem of bending of a shallow shell weakened by a notch with contacting edges,” Dop. Akad. Nauk Ukr. RSR. Ser. А, No. 2, 26–29 (1991).
M. J. Young and T. C. Sun, “Influence of crack on the stress intensity factor in bending plates—A classical plate solution,” Int. J. Fract., 5, 81–91 (1992).
I. P. Shchats’kyi and M. V. Makoviichuk, “Equilibrium of a spherical shallow shell with regard for the closure of collinear cracks in bending,” Fiz.-Mat. Model. Inform. Tekhnol., Issue 12, 189–195 (2010).
V. K. Opanasovych, V. P. Novosad, and R. H. Sil’vestrov, “Taking into account the contact of crack lips in bending of a transversally isotropic plate,” in: О. E. Andreikiv, I. I. Luchka, and V. V. Bozhydarnyk (editors), Fracture Mechanics and Physics of Building Materials and Structures. Collection of Scientific Works [in Ukrainian], Issue 5, Kamenyar, Lviv (2002), pp. 148–153.
R. Liu, T. Zhang, X. J. Wu, and C. H. Wang, “Determination of stress intensity factors for a cracked shell under bending with improved shell theories,” J. Aerospace Eng., 19, 21–28 (2006).
K. M. Dovbnya and Yu. V. Hryhorchuk, “Stressed state of a shell of double curvature containing a crack under bending loading,” Probl. Obchysl. Mekh. Mitsn. Konstr., Issue 19, 112–116 (2012).
A. N. Guz’ (editor), Mechanics of Composites, Vol. 7: A. N. Guz,’ A. S. Kosmodamianskii, V. P. Shevchenko, et al., Stress Concentration [in Russian], A.S.K., Kiev (1998).
A. A. Korneichuk, “Quadrature formulas for singular integrals,” in: Numerical Methods for the Solution of Differential and Integral Equations and Quadrature Formulas [in Russian], Nauka, Moscow (1964), pp. 64–74.
M. P. Savruk, P. N. Osiv, and I. V. Prokopchuk, Numerical Analysis in Plane Problems of the Theory of Cracks [in Russian], Naukova Dumka, Kiev (1989).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 49, No. 6, pp. 36–40, November–December, 2013.
Rights and permissions
About this article
Cite this article
Dovbnya, K.M., Shevtsova, N.A. Two Collinear Cracks with Contacting Lips in an Orthotropic Shell of Any Curvature Under the Conditions of Bending. Mater Sci 49, 743–748 (2014). https://doi.org/10.1007/s11003-014-9669-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11003-014-9669-8