The stressed­strained state of a rod at crystallization considering the mutual influence of temperature and mechanical fields

Authors

DOI:

https://doi.org/10.15587/1729-4061.2020.203330

Keywords:

thermomechanical state, Gibbs variation principle, crystallization front, approximate analytical method

Abstract

This paper reports a solution to the problem of determining the motion law of the crystallization front and the thermomechanical state of a two-phase rod for the case of mutual influence of the temperature and mechanical fields. An approximate analytical method has been used to solve the problem, combined with the method of successive intervals and a Gibbs variation principle. This method should indicate what is "more beneficial" to nature under the assigned external influences ‒ to change the temperature of the fixed element of a body or to transfer this element from one aggregate state to another. It is this approach that has made it possible, through the defined motion law of an interphase boundary, to take into consideration the effect of temperature on the tense-deformed state in the body, and vice versa. The ratios have been obtained to define the motion law of an interphase boundary, the temperature field, and the tense-deformed state in the rod. The results are shown in the form of charts of temperature and stress dependence on time and a coordinate.

An analysis of the results shows that changes in the conditions of heat exchange with the environment and geometric dimensions exert a decisive influence on the crystallization process, and, consequently, on temperature and mechanical fields. The principal result is the constructed approximate analytical method and an algorithm for solving the problem on thermoviscoelasticity for growing bodies (bodies with a moving boundary) in the presence of a phase transition considering the heat exchange with the environment. Based on the method developed, the motion law of an interphase boundary, a temperature field, and the tense-deformed state are determined while solving the so-called quasi-related problem of thermoviscoelasticity. An approximate analytical solution has been obtained, which could be used by research and design organizations in modeling various technological processes in machine building, metallurgy, rocket and space technology, and construction

Author Biographies

Andrii Siasiev, Oles Honchar Dniprо National University Gagarina ave., 72, Dnipro, Ukraine, 49010

PhD, Associate Professor

Department of Differential Equations

Andrii Dreus, Oles Honchar Dniprо National University Gagarina ave., 72, Dnipro, Ukraine, 49010

Doctor of Technical Sciences, Associate Professor

Department of Fluid Mechanics and Energy and Mass Transfer

Svitlana Horbonos, Oles Honchar Dniprо National University Gagarina ave., 72, Dnipro, Ukraine, 49010

PhD

Department of Differential Equations

Irina Balanenko, Oles Honchar Dniprо National University Gagarina ave., 72, Dnipro, Ukraine, 49010

PhD

Department of Differential Equations

Serhii Dziuba, Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine Simferopolska ave, 2a, Dnipro, Ukraine, 49005

PhD, Senior Researcher

Department of Geodynamic Systems and Vibration Technology

References

  1. Dron, M., Dreus, A., Golubek, A., Abramovsky, Y. (2018). Investigation of aerodynamics heating of space debris object at reentry to earth atmosphere. 69th International Astronautical Congress, IAC-18-A6.1.5. Bremen, 7.
  2. Yemets, V., Harkness, P., Dron’, M., Pashkov, A., Worrall, K., Middleton, M. (2018). Autophage Engines: Toward a Throttleable Solid Motor. Journal of Spacecraft and Rockets, 55 (4), 984–992. doi: https://doi.org/10.2514/1.a34153
  3. Yemets, M., Yemets, V., Dron, M., Harkness, P., Worrall, K. (2018). Caseless throttleable solid motor for small Spacecraft. 69th International Astronautical Congress, IAC-18.C4.8-B4.5A.13. Bremen, 10.
  4. Dreus, A. Y., Kozhevnykov, A. A., Liu, B., Sudakova, D. A. (2019). Approximate analytical model of rock thermal cyclical disintegration under convective cooling. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, 4, 42–47. doi: https://doi.org/10.29202/nvngu/2019-4/5
  5. Opitz, F., Treffinger, P., Wöllenstein, J. (2017). Modeling of Radiative Heat Transfer in an Electric Arc Furnace. Metallurgical and Materials Transactions B, 48 (6), 3301–3315. doi: https://doi.org/10.1007/s11663-017-1078-6
  6. Sudakov, А., Dreus, A., Ratov, B., Delikesheva, D. (2018). Theoretical bases of isolation technology for swallowing horizons using thermoplastic materials. News of the National Academy of Sciences of the Republic of Kazakhstan, Series of Geology and Technical Sciences, 2 (428), 72–80.
  7. Syasev, A., Zelenskaya, T. (2015). Lengthwise movement dynamic boundary-value problem for trailing boundary ropes. Metallurgical and Mining Industry, 3, 283–287. Available at: http://www.metaljournal.com.ua/assets/Journal/english-edition/MMI_2015_3/036%20Syasev.pdf
  8. Kravets, E. (2019). Determining the structure of a laminar detachable current in an open cavity. Eastern-European Journal of Enterprise Technologies, 6 (8 (102)), 28–37. doi: https://doi.org/10.15587/1729-4061.2019.183811
  9. Kozhevnikov, A. A., Sudakov, A. K., Dreus, A. Yu., Lysenko, Ye. Ye. (2014). Study of heat transfer in cryogenic gravel filter during its transportation along a drillhole. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, 6, 49–54.
  10. Kulikov, R. G., Kulikova, T. G. (2014). Numerical methods for solving the problem of polymer crystallizing media deformation taking into account finite deformations. Computational Continuum Mechanics, 7 (2), 172–180. doi: https://doi.org/10.7242/1999-6691/2014.7.2.18
  11. Kul'bovskiy, I. K., Karelin, S. V., Ilyushkin, D. A. (2008). Komp'yuternoe modelirovanie protsessa kristallizatsii massivnyh otlivok vtulok tsilindrov sudovyh dizeley. Vestnik BGTU, 2 (18), 16–19.
  12. Tkachuk, A. N. (2008). Issledovaniya termouprugih kontaktnyh zadach elementov press-form dlya lit'ya pod davleniem s uchetom fazovyh prevrashcheniy v otlivke. Vestnik NTU «KhPI», 2, 144–158.
  13. Senchenkov, I. K., Oksenchuk, N. D. (2013). An estimation of effects of thermostructural mechanical coupling under pulse loading of half-space. Bulletin of Taras Shevchenko National University of Kyiv Series: Physics & Mathematics, 3, 217–219.
  14. Bonetti, E., Frémond, M., Lexcellent, C. (2005). Global Existence and Uniqueness for a Thermomechanical Model for Shape Memory Alloys with Partition of the Strain. Mathematics and Mechanics of Solids, 11 (3), 251–275. doi: https://doi.org/10.1177/1081286506040403
  15. Rao, A., Srinivasa, A. R. (2014). A three-species model for simulating torsional response of shape memory alloy components using thermodynamic principles and discrete Preisach models. Mathematics and Mechanics of Solids, 20 (3), 345–372. doi: https://doi.org/10.1177/1081286514545917
  16. Holland, M. A., Kosmata, T., Goriely, A., Kuhl, E. (2013). On the mechanics of thin films and growing surfaces. Mathematics and Mechanics of Solids, 18 (6), 561–575. doi: https://doi.org/10.1177/1081286513485776
  17. Paroni, R., Tomassetti, G. (2017). Linear models for thin plates of polymer gels. Mathematics and Mechanics of Solids, 23 (5), 835–862. doi: https://doi.org/10.1177/1081286517698740
  18. Hossain, M., Chatzigeorgiou, G., Meraghni, F., Steinmann, P. (2015). A multi-scale approach to model the curing process in magneto-sensitive polymeric materials. International Journal of Solids and Structures, 69-70, 34–44. doi: https://doi.org/10.1016/j.ijsolstr.2015.06.011
  19. Carniel, T. A., Muñoz-Rojas, P. A., Vaz, M. (2015). A viscoelastic viscoplastic constitutive model including mechanical degradation: Uniaxial transient finite element formulation at finite strains and application to space truss structures. Applied Mathematical Modelling, 39 (5-6), 1725–1739. doi: https://doi.org/10.1016/j.apm.2014.09.036
  20. Gudramovich, V. S., Gart, É. L., Strunin, K. А. (2017). Modeling of the Behavior of Plane-Deformable Elastic Media with Elongated Elliptic and Rectangular Inclusions. Materials Science, 52 (6), 768–774. doi: https://doi.org/10.1007/s11003-017-0020-z
  21. Hart, E. L., Hudramovich, V. S. (2016). Projection-iterative modification of the method of local variations for problems with a quadratic functional. Journal of Applied Mathematics and Mechanics, 80 (2), 156–163. doi: https://doi.org/10.1016/j.jappmathmech.2016.06.005
  22. Hart, E. L., Hudramovich, V. S. (2014). Projection-Iterative Schemes for the Realization of the Finite-Element Method in Problems of Deformation of Plates with Holes and Inclusions. Journal of Mathematical Sciences, 203 (1), 55–69. doi: https://doi.org/10.1007/s10958-014-2090-x
  23. Lykov, A. V. (1967). Teoriya teploprovodnosti. Moscow: Vysshaya shkola, 560.
  24. Syasev, A. V. (2001). Priblizhenniy analiticheskiy metod rascheta rastushchih tel s uchetom fazovogo perehoda. Visnyk Dnipropetr. un-tu. Seriya: Mekhanika, 1 (5), 125–137.
  25. Karnauhov, V. G. (1982). Svyazannye zadachi termovyazkouprugosti. Kyiv: Naukova dumka, 250.
  26. Lyubov, B. Ya. (1975). Teoriya kristallizatsii v bol'shih obemah. Moscow: Nauka, 256.
  27. Nikitenko, N. I. (1978). Issledovanie protsessov teplo- i massoobmena metodom setok. Kyiv: Naukova dumka, 213.
  28. Arutyunyan, N. H., Drozdov, A. D., Naumov, V. E. (1987). Mehanika rastushchih vyazkouprugoplasticheskih tel. Moscow: Nauka, 472.

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Published

2020-06-30

How to Cite

Siasiev, A., Dreus, A., Horbonos, S., Balanenko, I., & Dziuba, S. (2020). The stressed­strained state of a rod at crystallization considering the mutual influence of temperature and mechanical fields. Eastern-European Journal of Enterprise Technologies, 3(5 (105), 38–49. https://doi.org/10.15587/1729-4061.2020.203330

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Section

Applied physics