Theory of thermal shock in models of dynamic thermoelasticity


Аuthors

Nenakhov E. V.1*, Kartashov E. M.2, 1**

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. MIREA — Russian Technological University (Lomonosov Institute of Fine Chemical Technologies), 78, Vernadsky prospect, Moscow, 119454, Russia

*e-mail: newnew94@mail.ru
**e-mail: professor.kartashov@qmail.com

Abstract

The problem of thermal shock of a solid is studied on the basis of the model of dynamic thermoelasticity. A brief scheme for deriving the compatibility equation in voltages for dynamic problems is proposed, which generalizes the well-known Beltrami-Mitchell relation for quasistatic cases. The proposed relation is convenient for considering numerous special cases in the theory of thermal shock in Cartesian coordinates for both restricted bodies of canonical form and partially limited ones. In the latter case, the obtained analytical solutions of the dynamic problems of the theory of thermal shock lead to visual and convenient for physical analysis functional structures describing the kinetics of thermal stresses.

As for the cylindrical and spherical coordinate systems, for these cases a “compatibility equation” in displacements was proposed, convenient for studying the problem of thermal shock in bodies with a radial heat flow and central symmetry. The class of problems in which the consideration of the geometrical dimensions of the structure investigated for a thermomechanical reaction under conditions of intense heating is mainly concerned with the near-surface layers is highlighted. As the experiments show, it is these layers that absorb the main amount of heat during a time close to the beginning of heating, corresponding to microsecond duration times during which inertial effects are active. The thermal reaction of a massive body when it is heated by a nonstationary heat flux of an exponential and linear type, as well as under the action of an internal heat source – practically important cases in the theory of thermal strength is investigated. Numerical experiments were carried out and the wave nature of the propagation of thermoelastic waves was described. The effect of material relaxation on sudden heating and sudden cooling of its boundary, which has been little studied in thermomechanics, is described. The dependence of the maximum internal temperature stress on the parameters characterizing the elastic and thermophysical properties of materials, as well as the heating time and cooling time, is established.

Keywords:

thermal shock, the mathematical model, dynamic thermoelasticity, relaxation effect

References

  1. Kartashov E.M., Kudinov V.А. Аnaliticheskaya teoriya teploprovodnosti i prikladnoj termouprugosti [Analytical theory of heat conduction and thermoelasticity]. Moscow: URRS, 2013. 656 p. In Russ.

  2. Parkus G. Neustanovivshiesya temperaturnye napryazheniya [Unsteady thermal stresses]. Moscow: Fizmatlit, 1963. 252 p. In Russ.

  3. Boley B.A., Weiner J.H. Theory of Thermal Stresses. Wiley, New York, 1960. 586 p.

  4. Kartashov E.M. Teoriya teplovogo udara na osnove obobshhennoj modeli dinamicheskoj termouprugosti [Theory of thermal shock based on a generalized model of dynamic thermoelasticity]. Vestnik Moskovskogo gosudarstvennogo universiteta tonkikh khimicheskikh tekhnologij im. M.V. Lomonosova – Bulletin of the Moscow State University of Fine Chemical Technologies, 2012, vol. 7, no. 1, pp.69–72. In Russ.

  5. Lykov A.V. Primenenie metodov termodinamiki neobratimykh protsessov k issledovaniyu teplo– i massoobmena [Application of methods of thermodynamics of irreversible processes to the study of heat and mass transfer]. Inzhenerno-fizicheskij zhurnal – Physical Engineering Journal, 1985, vol. 9, no. 3, pp. 287–304. In Russ.

  6. Shashkov A.G., Bubnov V.A., Yanovsky S.Yu. Volnovye yavleniya teploprovodnosti [Heat conduction wave phenomena]. Minsk: Izdatel'stvo Nauka i tekhnika, 1993. 279 p. In Russ.

  7. Kartashov E.M., Nenakhov E.V. Dinamicheskaya termouprugost' v probleme teplovogo udara na osnove obobshhennogo uravneniya energii [Dynamic thermoelasticity in the problem of heat shock based on the general energy equation]. Teplovye protsessy v tekhnike – Thermal processes in engineering, 2018, vol. 10, no. 7-8, pp.3 34-344. In Russ.

  8. Podstrigach Ya.S., Lomakin V.A., Koliano Yu.M. Termouprugost' tel neodnorodnoj struktury [Thermoelasticity of bodies of non-uniform structure]. Moscow: Nauka, 1984. 368 p. In Russ.

  9. Kolyano Yu.M. Metody teploprovodnosti i termouprugosti neodnorodnogo tela [Methods of thermal conductivity and thermoelasticity of an inhomogeneous body]. Kiev: Naukova Dumka, 1992. 280 p. In Russ.

  10. Kolpashchikov V.L., Yanovsky S.Yu. Uravneniya dinamicheskoj termouprugosti dlya sred s teplovoj pamyat'yu [Dynamic thermoelasticity equations for environments with thermal memory]. Inzhenerno-fizicheskij zhurnal – Physical Engineering Journal, 1984, vol. 47, no. 4, pp. 670–675. In Russ. Obzor rabot po dinamicheskim problemam termouprugosti. Mekhanika (sb. perevodov).

  11. Zarubin V.S., Kuvyrkin G.N. Matematicheskie modeli mekhaniki i ehlektrodinamiki sploshnoj sredy [Mathematical models of mechanics and electrodynamics of continua]. Moscow: Publishing house Bauman, 2008. 512 p. In Russ.

  12. Novatsky V. Obzor rabot po dinamicheskim problemam termouprugosti. Mekhanika (sb. perevodov). [Review of works on dynamic problems of thermoelasticity. Mechanics (collection of translations)]. 1966, no. 6, pp. 101–142. In Russ.

  13. Kolyano Yu.M. Obobshhennaya termomekhanika (obzor) [Generalized thermomechanics (review)]. Matematicheskie metody i fiziko-mekhanicheskie polya – Mathematical methods and physico-mechanical fields, 1975, Iss. 2, pp. 37–42. In Russ.

  14. Kartashov E.M., Bartenev G.M. Dinamicheskie effekty v tverdykh telakh v usloviyakh vzaimodejstviya s intensivnymi potokami energii [Dynamic effects in solids under conditions of interaction with intense energy flows]. Itogi nauki i tekhniki. Seriya: Khimiya i tekhnologiya vysokomolekulyarnykh soedinenij – Results of science and technology. Series: chemistry and technology of high-molecular compounds. Moscow: VINITI, 1988, vol. 25, pp. 3–88. In Russ.

  15. Kartashov EM, Parton V.Z .Dinamicheskaya termouprugost' i problemy termicheskogo udara [Dynamic thermoelasticity and thermal shock problems]. Itogi nauki i tekhniki. Seriya: Mekhanika deformiruemogo tverdogo tela – Results of science and technology Series of mechanics of a deformable solid body. Moscow: VINITI, 1991, vol. 22, pp. 55–127. In Russ.

  16. Novatsky V. Teoriya uprugosti [Theory of elasticity]. Moscow: Mir. 1975. 872 p. In Russ.

  17. Karslou G., Eger D. Teploprovodnost’ tvyordyh tel [Thermal conductivity of solids]. M.: Nauka, 1964. 488 p. In Russ.

  18. Kartashov E.M. Analiticheskie metody v teorii teploprovodnosti tvyordyh tel [Analytical methods in the theory of the thermal conductivity of solids]. M.: Vysshaya shkola, 2001. 552 p. In Russ.

  19. Danilovskaya V.I. Temperaturnye napryazheniya v uprugom poluprostranstve, voznikayushhie vsledstvie vnezapnogo nagreva ego granitsy [Temperature stresses in the elastic half-space resulting from the sudden heating of its boundary]. Prikladnaya matematika i mekhanika – Journal of Applied Mathematics and Mechanics, 1950, vol. 14, no. 3, pp. 317–318. In Russ.

  20. Mura T. Dynamic thermal stresses due to thermal shocks. Res. Rep. Fac. Engng., Meiji. Univ, 1956, vol. 8, pp. 63–73.

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