Geodesic
The critical state of an inclined layer in a sheet specimen with negative loading biaxiality coefficient
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 1, pp. 123-129 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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V. L. Dilman; A. N. Dheyab. The critical state of an inclined layer in a sheet specimen with negative loading biaxiality coefficient. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 1, pp. 123-129. http://geodesic.mathdoc.fr/item/VYURU_2016_9_1_a9/

[1] Annin B. D., Zhigalkin V. M., The Behavior of Materials Under Complex Loading, Izdatel'stvo SO RAN, Novosibirsk, 1999 [Б. Д. Аннин, В. М. Жигалкин, Поведение материалов в условиях сложного нагружения, Изд-во СО РАН, 1999, Новосибирск]

[2] Lebedev A. A., Koval'chuk B. I., Giginyak F. F., Lamashevskiy V. P., The Mechanical Properties of Structural Materials Under Complex Stress State, In Yure, Kiev, 2003 (in Russian)

[3] Koval'chuk G. I., “On the Question of Loss of Stability of the Plastic Deformation of Shells”, Strength of Materials, 1983, no. 5, 11–16 (in Russian)

[4] Swift H., “Plastic Instability Under Plane Stress”, Journal of the Mechanics and Physics of Solids, 1952, no. 1, 1–18 | DOI

[5] Dil'man V. L., Eroshkina T. V., Mathematical Modelling of the Critical States of Soft Layers in Heterogeneous Connections, Publ. Center of the South Ural State University, Chelyabinsk, 2011 (in Russian)

[6] Kachanov L. M., “On the Strained State of the Plastic Interlayer”, Izvestiya akademii nauk SSSR. Otdelenie tekhnicheskikh nauk. Mekhanika i mashinostroenie, 1962, no. 5, 63–67 (in Russian) | Zbl

[7] Dil'man V. L., Diyab A. N., “The Stress State of a Strip With a Layer Under Considerable Mechanical Heterogeneity”, Bulletin of the South Ural State University. Series: Mathematics. Mechanics. Physics, 7:4 (2015), 11–19 (in Russian) | DOI | Zbl

[8] Tret'yakov M. P., Vil'deman V. E., “Strain-Softening of Materials in the Plane Stress State Conditions”, PNRPU Mechanics Bulletin, 2012, no. 2, 190–203 (in Russian)