Far Eastern Mathematical Journal

To content of the issue


To the calculation of plane stressed states of the theory of unsteady temperature stresses in elastoplastic bodies


Burenin A.A., Kaing V., Tkacheva A.V.

2018, issue 2, P. 131-146


Abstract
On the example of the solution of the boundary value problem of the theory of temperature stresses about local heating and subsequent cooling of a circular plate made of elastoplastic material, the calculations of unsteady temperature stresses are compared either with or without allowance for the dependence of elastic moduli on temperature. It is shown that under the conditions of the dependence of the yield stress on temperature, the problem of calculating the planar temperature stresses under the condition of plastic flow of maximum tangential stresses turns out to be incorrect in its formulation, but it has a solution when using the conditions of the maximal reduced tangential stresses in the formulation and calculations. The conditions for the appearance of repeated plastic currents are noted and residual stresses are calculated.

Keywords:
elasticity, plasticity, thermal stresses, residual deformations, residual stresses

Download the article (PDF-file)

References

[1] B. Boli, Dzh. Ueyner, Teoriya temperaturnykh napryazheniy, Mir, M., 1964.
[2]. G. Parkus, Neustanovivshiyesya temperaturnyye naryazheniya, Mir, M., 1969.
[3] P. Perzyna, A. Sawezuk, “Problems of thermoplasticity”, Nuclear engineering and design., 1979, 94–201.
[4] YU.N. SHevchenko, Termoplastichnost’ pri peremennykh nagruzheniyakh, Nukova dumka, Kiyev, 1970.
[5] A.A. Pozdeyev, YU.I. Nyashin, P.V. Trusov, Ostatochnyye napryazheniya: teoriya i prilozheniya, Nauka, M., 1982.
[6] A.A. Burenin, L.V. Kovtanyuk, Bol’shiye neobratimyye deformatsii i uprugoye posledeystviye, Dal’nauka, Vladivostok, 2013.
[7] J.L. Chaboche, “Thermodynamically based viscoplastic constitutive equation: theory versus experiment”, ASME Winter Annual Meeting, 1991, 1–20.
[8] N. Ohno, J. Wang, “Transformation of a nonlinear kinematic hardening rule toamultisurface formunder isothermal and nonisothermal conditions”, Int. J. Plasticity., 7, (1992), 879–891.
[9] L.V. Kovtanyuk, “Modelirovaniye bol’shikh uprugoplasticheskikh deformatsiy v neizotermicheskom sluchaye”, Dal’nevost. mat.zhurnal., 5:1, (2004), 110–120.
[10] V.S. Bondar’, V.V. Danshin, A.A. Kondratenko, “Variant teorii termoplastichnosti”, Vestnik PNIPU. Seriya «Mekhanika», 2, (2015), 21–35.
[11] U. Gamer, “A concise treatment of the shrink fit withelastic plastic hab”, Int. J. Solids. Struct., 29, (1992), 2463–2469.
[12] W. Mack, “Thermal assembly of an elastic–plastic hub and a solid shaft”, Arch. Appl. Mech., 63, (1993), 42–50.
[13] A. Kovacs, “Residual Stresses in Thermally Loaded Shrink Fits Periodica Polytechnica”, Ser. Mech. Eng., 40:2, (1996), 103–112.
[14] S.E. Aleksandrov, N.N. CHikanova, “Uprugoplasticheskoye napryazhenno-deformirovannoye sostoyaniye v plastine s zapressovannym vklyucheniyem pod deystviyem temperaturnogo polya”, Izv. RAN MTT, 2000, № 4, 149–158.
[15] S.E. Aleksandrov, E.V. Lomakin, Y.-R. Dzeng, “Resheniye termouprugoplasticheskoy zadachi dlya tonkogo diska iz plasticheski szhimayemogo materiala, podverzhennogo termicheskomu nagruzheniyu”, DAN, 443:3, (2012), 310–312.
[16] S.E. Aleksandrov, E.A. Lyamina, O.V. Novozhilova, “Vliyaniye zavisimosti predela tekuchesti ot temperatury na napryazhennoye sostoyaniye v tonkom polom diske”, Problemy mashinostroyeniya i nadezhnost’ mashin, 2013, № 3, 43–48.
[17] E.P. Dats, A.V. Tkacheva, R.V. SHport, “Sborka konstruktsii «kol’tso v kol’tse» sposobom goryachey posadki”, Vestnik CHGPU im. I.YA. YAkovleva, seriya: mekhanika predel’nogo sostoyaniya, 2014, № 4(22), 204–213.
[18] E.P. Dats, A.V. Tkacheva, “Tekhnologicheskiye temperaturnyye napryazheniya v protsessakh goryachey posadki tsilindricheskikh tel pri uchete plasticheskikh techeniy”, PMTF, 57:3 (337), (2016), 208–216.
[19] A.A. Burenin, A.V. Tkacheva, G.A. SHCHerbatyuk, “K raschetu neustoyavshikhsya temperaturnykh napryazheniy v uprugoplasticheskikh telakh”, Vychislitel’naya mekhanika sploshnykh sred, 10:3, (2017), 245–259.
[20] E.P. Dats, E.V. Murashkin, A.V. Tkacheva, G.A. SHCHerbatyuk, “Temperaturnyye napryazheniya v uprugoplasticheskoy trube v zavisimosti ot vybora usloviya plastichnosti”, Mekhanika tverdogo tela, 1, (2018), 32–43.
[21] YU.N. SHevchenko, P.A. Steblyanko, A.D. Petrov, “CHislennyye metody v nestatsionarnykh zadachakh teorii termoplastichnosti”, Problemy vychislitel’noy mekhaniki i prochnosti konstruktsiy, 22, (2014), 250–264.
[22] D.R. Bland, “Elastoplastic thick-walled tubes of work-hardening material subject to internal and external pressures and to temperature gradients”, J. of the Mechanics and Physics of Solids, 4, (1956), 209-229.
[23] A.A. Burenin, L.V. Kovtanyuk, M.V. Polonik, “Vozmozhnost’ povtornogo plasticheskogo techeniya pri obshchey razgruzki uprugoplasticheskoy sredy”, DAN, 375:6, (2000), 767–769.
[24] G.I. Bykovtsev, D.D. Ivlev, Teoriya plastichnosti, Dal’nauka, Vladivostok, 1998.
[25] A.YU. Ishlinskiy, D.D. Ivlev, Matematicheskaya teoriya plastichnosti, Fizmatlit, M., 2001.
[26] A. Nadai, Plastichnost’ i razrusheniye tverdykh tel., t. 2, Mir, M:, 1969.
[27] M.A. Grinfel’d, Metody mekhaniki sploshnykh sred v torii fazovykh prevrashcheniy, Nauka, M., 1990.

To content of the issue