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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2016, Volume 9, Issue 1, Pages 123–129 (Mi vyuru307)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Notes

The critical state of an inclined layer in a sheet specimen with negative loading biaxiality coefficient

V. L. Dilman, A. N. Dheyab

South Ural State University, Chelyabinsk, Russian Federation

Abstract: We study conditions for the loss of stability in a plastic deformation of a layer of weaker material in a sheet specimen. The layer is not collinear with the exterior forces acting in the sheet plane, which are orthogonal to each other and have opposite signs. The parameters of the problem are: the angle between the layer and the direction of exterior forces; the ratio of stresses due to exterior forces; the ratio of strengths of the layer material and the main material of the sheet specimen; the strengthening law of the layer material; the ratio of thicknesses of the layer and the specimen. Basing on Swift's plastic instability criterion for a deformation of the layer material, we obtain an algorithm for calculating critical stress in the layer and critical exterior loading in dependence on the indicated parameters. When contact strengthening of the layer is absent, our results have explicit analytic expressions. We find conditions under which the layer does not lower the strength of the specimen. We find conditions for the stressed state of the layer to be a pure shear and study this case.

Keywords: inclined plastic layer; plastic instability; stress-strain state; Swift's criterion.

DOI: https://doi.org/10.14529/mmp160110

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Bibliographic databases:

UDC: 539.374
MSC: 35L72, 74C05
Received: 17.11.2015
Language:

Citation: V. L. Dilman, A. N. Dheyab, “The critical state of an inclined layer in a sheet specimen with negative loading biaxiality coefficient”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 9:1 (2016), 123–129

Citation in format AMSBIB
\Bibitem{DilDhe16}
\by V.~L.~Dilman, A.~N.~Dheyab
\paper The critical state of an~inclined layer in a~sheet specimen with negative loading biaxiality coefficient
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2016
\vol 9
\issue 1
\pages 123--129
\mathnet{http://mi.mathnet.ru/vyuru307}
\crossref{https://doi.org/10.14529/mmp160110}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000371348500010}
\elib{http://elibrary.ru/item.asp?id=25717242}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. N. Dheyab, “An effect of the slope layer in sheet sample on a strength for negative coefficient of a biaxial loading factor of a sample”, J. Comp. Eng. Math., 3:1 (2016), 27–36  mathnet  crossref  mathscinet  zmath  elib
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