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Combined Action of Bending and Tension of an Isotropic Plate with Through Crack in the Absence of Contact between the Faces and with Regard for the Plastic Zones and Hardening of Material at the Tips

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We study the problem of combined bending and tension of an isotropic plate containing a through crack by distributed bending moments and forces at infinity in the absence of contact between the crack faces and external loads applied to the crack but in the presence of plastic zones at its tips. We also take into account the phenomenon of hardening of the material satisfying the Tresca plasticity conditions in the form of a surface layer or a plastic hinge. By using complex potentials of plane problem and the classical theory of bending of plates, we obtain an analytic solution of the problem in the class of functions bounded at the tips of the plastic zones. We also present the dependences for the lengths of the plastic zones and the opening displacements of the crack faces at the tips. The numerical analysis of these dependences is performed for different parameters of the problem.

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Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine

    V. K. Opanasovych, М. М. Nykolyshyn, M. S. Slobodian, S. O. Alfavitska & O. K. Bilash

Authors
  1. V. K. Opanasovych
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  2. М. М. Nykolyshyn
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  3. M. S. Slobodian
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  4. S. O. Alfavitska
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  5. O. K. Bilash
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Correspondence to S. O. Alfavitska.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 61, No. 3, pp. 11701–110, July–September, 2018.

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Opanasovych, V.K., Nykolyshyn, М.М., Slobodian, M.S. et al. Combined Action of Bending and Tension of an Isotropic Plate with Through Crack in the Absence of Contact between the Faces and with Regard for the Plastic Zones and Hardening of Material at the Tips. J Math Sci 254, 117–128 (2021). https://doi.org/10.1007/s10958-021-05292-8

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