Skip to main content
SpringerLink
Log in

Calculation of the Unsteady Thermal Stresses in Elastoplastic Solids

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

The one-dimensional boundary problem of the theory of thermal stresses that simulates the shrink fit assembly of cylindrical parts is used to discuss a computational approach to predicting the evolution of the thermal stresses under piecewise-linear plasticity conditions. The solution of the problem is based on the classical maximum shear stress criterion (Tresca–Saint Venant yield criterion), and the maximum reduced shear stress criterion (Ishlinsky–Ivlev yield criterion) is only used to compare the calculation results. The application of piecewise-linear potentials in the theory of plastic flow is shown to allow equilibrium equations to be integrated in both the region of reversible deformation and various parts of a plastic flow region. The dependences thus obtained are important for a time-step calculation algorithm. This algorithm can trace the site and time of both nucleation and completion of plastic flows at each time step. The calculations demonstrate that, following temperature, the stresses in the assembly element materials can pass from correspondence to a certain face of a loading surface to correspondence to its edge and, then, to another face. This circumstance implies the division of the irreversible deformation region into parts, where a plastic flow obeys different sets of equations, which take into account the assignment of the state of stress to various faces and edges of the loading surface. The computational algorithm also makes it possible to trace the beginning of division of a flow region into parts and the motion of the part boundaries through irreversibly deformed materials, including the times of their coincidence (i.e., the disappearance of the parts of the calculation region). A repeated plastic flow is shown to appear. This flow nucleates when an assembly is cooled, i.e., when the assembly element materials return to reversible deformation conditions due to the evolution of the state of stress. Taking into account the change in plastic flow conditions that is caused by the use of piecewise-linear plastic potentials is found to substantially affect the level and the distribution of residual stresses and the final tightness of the assembly.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Berniker, E.I., Posadka s natyagom v mashinostroenii (Interference Fit in Mechanical Engineering), Leningrad: Mashinostroenie, 1966.

    Google Scholar 

  2. Parkus, H., Instationäre Wärmespannungen (Instationary Thermal Stresses), Wien: Springer, 1959.

    Book  MATH  Google Scholar 

  3. Boley, B.A. and Weiner, J.H., The Theory of Thermal Stresses, New York: Wiley, 1960.

    MATH  Google Scholar 

  4. Gokhfeld, D.A. and Cherniavsky, O.F., Limit Analysis of Structures at Thermal Cycling, The Netherlands: Sijthoff & Noordhoff, 1980.

    Google Scholar 

  5. Dopuski i posadki: Spravochnik (Tolerances and Landing, A Handbook), Myagkov, V.D., Palej, M.A., Romanov, A.B., and Braginskii, V.A., Leningrad: Mashinostroenie, 1982, vol. 1.

  6. Bland, D.R., Elastoplastic thick-walled tubes of work-hardening material subject to internal and external pressures and to temperature gradients, J. Mech. Phys. Solids, 1956, vol. 4, no. 4, pp. 209–229. https://doi.org/10.1016/0022-5096%2856%2990030-8

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Ishlinskii, A.Yu. and Ivlev, D.D., Matematicheskaya teoriya plastichnosti (Mathematical Theory of Plasticity), Moscow: Fizmatlit, 2001.

    MATH  Google Scholar 

  8. Perzyna, P. and Sawczuk, A., Problems of thermoplasticity, Nucl. Eng. Des., 1973, vol. 24, no. 1, pp. 1–55. https://doi.org/10.1016/0029-5493%2873%2990017-4

    Article  Google Scholar 

  9. Ohno, N. and Wang, J.D., Transformation of a nonlinear kinematic hardening rule to a multisurface form under isothermal and nonisothermal conditions, Int. J. Plast., 1991, vol. 7, no. 8, pp. 879–891. https://doi.org/10.1016/0749-6419%2891%2990023-R

    Article  MATH  Google Scholar 

  10. Orçan, Y. and Gamer, U., Elastic-plastic deformation of a centrally heated cylinder, Acta Mech., 1991, vol. 90, no. 1, pp. 61–80. https://doi.org/10.1007/BF01177400

    Article  MATH  Google Scholar 

  11. Chaboche, J.L., Thermodynamically based viscoplastic constitutive equation: theory versus experiment, in Proceedings of the ASME Winter Annual Meeting, Atlanta, GA, 1991, pp. 1–20.

    Google Scholar 

  12. Lippmann, H., The effect of a temperature cycle on the stress distribution in a shrink fit, Int. J. Plast., 1992, vol. 8, no. 5, pp. 567–582. https://doi.org/10.1016/0749-6419%2892%2990031-7

    Article  Google Scholar 

  13. Gamer, U., A concise treatment of the shrink fit with elastic-plastic hub, Int. J. Solids Struct., 1992, vol. 29, no. 20, pp. 2463–2469. https://doi.org/10.1016/0020-7683%2892%2990003-C

    Article  MATH  Google Scholar 

  14. Mack, W., Thermal assembly of an elastic-plastic hub and a solid shaft, Arch. Appl. Mech., 1993, vol. 63, no. 1, pp. 42–50. https://doi.org/10.1007/BF00787908

    Article  ADS  MATH  Google Scholar 

  15. Knyazeva, A.G., Teplofizicheskie osnovy sovremennykh vysokotemperaturnykh tekhnologii (Thermophysical Fundamentals of Modern High-Temperature Technologies), Tomsk: Tomsk Politekh. Univ., 2009.

    Google Scholar 

  16. Bondar, V.S., Danshin, V.V., and Kondratenko, A.A., Version of the thermoplasticity theory, Vestn. PNIPU, Mekh., 2015, no. 2, pp. 21–35. https://doi.org/10.15593/perm.mech/2015.2.02

    Google Scholar 

  17. Kovtanuk, L.V., The modelling of finite elastic-plastic deformation in non-isothermal case, Dal’nevost. Mat. Zh., 2004, vol. 5, no. 1, pp. 110–120.

    Google Scholar 

  18. Rogovoi, A.A., Constitutive relations for finite elastic-plastic strains, J. Appl. Mech. Tech. Phys., 2005, vol. 46, no. 5, pp. 730–739.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Burenin, A.A. and Kovtanyuk, L.V., Bol’shie neobratimye deformatsii i uprugoe posledejstvie (Large Irreversible Deformations and Elastic Aftereffects), Vladivostok: Dalnauka, 2013.

    Google Scholar 

  20. Alexandrov, S.E. and Chikanova, N.N., Elastic-plastic stress-strain state in a plate with a pressed insertion under the action of a temperature field, Mech. Solids, 2000, vol. 35, no. 4, pp. 125–132.

    Google Scholar 

  21. Alexandrov, S. and Alexandrova, N., Thermal effects on the development of plastic zones in thin axisummetric plates, J. Strain Anal. Eng., 2001, vol. 36, no. 2, pp. 169–175. https://doi.org/10.1243/0309324011512720

    Article  Google Scholar 

  22. Shevchenko, Yu.N. and Steblyanko, P.A., Computing methods in stationary and non-stationary problems of theory thermal-plasticity, Probl. Obchisl. Mekh. Mitsnosti Konstrukts., 2012, no. 18, pp. 211–226.

    Google Scholar 

  23. Shevchenko, Yu.N., Steblyanko, P.A., and Petrov, A.D., Computing methods in non-stationary problems of theory thermal-plasticity, Probl. Obchisl. Mekh. Mitsnosti Konstrukts., 2014, no. 22, pp. 251–264.

    Google Scholar 

  24. Gorshkov, S.A., Dats, E.P., and Murashkin, E.V., Calculation of plane stress field under plastic flow and unloading, Vestn. ChGPU Yakovleva, Ser.: Mekh. Predel’n. Sost., 2014, no. 3 (21), pp. 169–175.

    Google Scholar 

  25. Burenin, A.A., Kovtanyuk, L.V., and Panchenko, G.L., Nonisothermal motion of an elastoviscoplastic medium through a pipe under a changing pressure, Dokl. Phys., 2015, vol. 60, no. 9, pp. 419–422. https://doi.org/10.1134/S1028335815090098

    Article  ADS  Google Scholar 

  26. Aleksandrov, S.E., Lomakin, E.V., and Dzeng, Y.-R., Solution of the thermoelasticoplastic problem for a thin disc of plastically compressible material subjected to thermal loading, Dokl. Phys., 2012, vol. 57, no. 3, pp. 136–139. https://doi.org/10.1134/S1028335812030081

    Article  ADS  Google Scholar 

  27. Aleksandrov, S.E., Lyamina, E.A., and Novozhilova, O.V., The influence of the relationship between yield strength and temperature on the stress state in a thin hollow disk, J. Mach. Manuf. Reliab., 2013, vol. 42, no. 3, pp. 214–218. https://doi.org/10.3103/S1052618813020027

    Article  Google Scholar 

  28. Burenin, A.A., Dats, E.P., and Murashkin, E.V., Formation of the residual stress field under local thermal actions, Mech. Solids, 2014, vol. 49, no. 2, pp. 218–224. https://doi.org/10.3103/S0025654414020113

    Article  ADS  Google Scholar 

  29. Pozdeev, A.A., Nyashin, Yu.I., and Trusov, P.V., Ostatochnye napryazheniya: teoriya i prilozheniya (Residual Stresses: Theory and Applications), Moscow: Nauka, 1982.

    Google Scholar 

  30. Bengeri, M. and Mack, W., The influence of the temperature dependence of the yield stress on the stress distribution in a thermally assembled elastic-plastic shrink fit, Acta Mech., 1994, vol. 103, no. 1, pp. 243–257. https://doi.org/10.1007/BF01180229

    Article  MATH  Google Scholar 

  31. Kovács, Á., Residual stresses in thermally loaded shrink fits, Period. Polytech., Ser.: Mech. Eng., 1996, vol. 40, no. 2, pp. 103–112.

    Google Scholar 

  32. Dats, E.P., Tkacheva, A.V., and Shport, R.V., The assemblage of “ring in ring” constructions with shrink fit method, Vestn. ChGPU Yakovleva, Ser.: Mekh. Predel’n. Sost., 2014, no. 4 (22), pp. 225–235.

    Google Scholar 

  33. Burenin, A.A., Dats, E.P., and Tkacheva, A.V., On the modeling of the shrink fit technology, J. Appl. Ind. Math., 2014, vol. 8, no. 4, pp. 493–499. https://doi.org/10.1134/S199047891404005X

    Article  MathSciNet  MATH  Google Scholar 

  34. Bykovtsev, G.I. and Ivlev, D.D., Teoriya plastichnosti (Theory of Plasticity), Vladivostok: Dalnauka, 1998.

    Google Scholar 

  35. Loginov, Yu.N., Med’ i deformiruemye mednye splavy (Copper and Deformable Copper Alloys, The School-Book), Yekaterinburg: Ural’sk. Gos. Politekh. Univ., 2006.

    Google Scholar 

  36. Marochnik stalei i splavov (Database of Steels and Alloys), Zubchenko, A.S., Ed., Moscow: Mashinostroenie, 2003.

Download references

Author information

Authors and Affiliations

  1. Institute of Machinery and Metallurgy, Far East Branch, Russian Academy of Sciences, Komsomolsk-on-Amur, Russia

    A. A. Burenin & A. V. Tkacheva

  2. Komsomolsk-on-Amur State Technical University, Komsomolsk-on-Amur, Russia

    A. A. Burenin & G. A. Shcherbatyuk

Authors
  1. A. A. Burenin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Tkacheva
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. A. Shcherbatyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Burenin.

Additional information

Original Russian Text © A.A. Burenin, A.V. Tkacheva, G.A. Shcherbatyuk, 2018, published in Vychislitel’naya Mekhanika Sploshnykh Sred, 2017, Vol. 10, No. 3, pp. 245–259.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Burenin, A.A., Tkacheva, A.V. & Shcherbatyuk, G.A. Calculation of the Unsteady Thermal Stresses in Elastoplastic Solids. J Appl Mech Tech Phy 59, 1197–1210 (2018). https://doi.org/10.1134/S0021894418070040

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021894418070040

Key words

Search

Navigation