MATHEMATICAL MODELS OF MECHANISMS FOR ROLLED PRODUCTS ACCELERATED COOLING

The tasks of increasing strength of heat-strengthened rolled products require thorough search for technical solutions, determined by level of understanding of processes occurring in thermal strengthening devices, of which the main is the process of water interaction with hot rolled product. This complex set of phenomena includes movement of water flows relative to moving rolled metal, emergence of vapor gap between water and rolled metal, generation of nanosized droplets and their movement through the layer of vapor, the droplets impact on surface, excitation of elastic waves in rolled material. Analysis of previously derived dispersion equation for Kelvin-Helmholtz instability of vapor-water interface was carried out. It is shown that for 30–60  m/s difference in velocities of liquid and vapor layers, the maximum increment in nanoscale range of wavelengths is observed. Average size of generated drops is determined by wavelength at which the maximum increment dependence is reached. Thus, mechanism of accelerated cooling of rolled steel proposed earlier is confirmed by quantitative calculations. Drops, reaching rolled metal, excite thermoelastic wave which being distributed along its section promotes increase in impact strength. To reveal regularities of propagation of elastic waves created by drops in rolled metal, problem of theory of thermoelasticity in cooling was solved by method of Fourier and Laplace integral transformations. It turned out that the problem posed is analogous to the problem of heating the surface with triangular temperature profile. Evolution of stress waves was investigated. At initial moments, the front of wave appeared to be a stretching wave. When reflected from the free end, the wave becomes a compression wave with stresses leading to cracks closure, and thus it leads to increase in toughness. Obtained results can be used in search for optimal modes of heat treatment of rolled products, providing high mechanical properties.

1. Yur’ev A.B. Uprochnenie stroitel’noi armatury i prokatnykh valkov[Strengthening of building fittings and rolling rolls]. Novosibirsk:  Nauka, 2006, 227 p. (In Russ.). 

2. Liska S., Wozniak J. Model vyvoje structury a mechanich vlastnosti  oceli pri valcovani za tepla. Kovove materialy (Bratislava). 1982,  vol. 20, no. 5, pp. 562–572.

3. Rudskoi A.I., Kolbasnikov N.G. Control of the structure and properties of steels during hot deformation. Zagotovitel’nye proizvodstva v mashinostroenii. 2012, no. 10, pp. 22–30. (In Russ.).

4. Platov S.I., Yaroslavtsev A.V., Tumbasov K.S. Improving the quality of hot-rolled bars made of low- and medium-carbon steel through  the selection of optimal thermomechanical processing modes. Proizvodstvo prokata. 2016, no. 10, pp. 21–25. (In Russ.). 

5. Nogovitsyn A.V., Bogacheva A.V., Evsyukov N.F., Loshkarev D.V. Prediction of structure formation during cooling of rolled metal using mathematical model. Metallurgicheskaya i gornorudnaya pro-myshlennost’. 1999, no. 5, pp. 75–78. (In Russ.).

6. Sarychev  V.D.,  Gromov  V.E.,  Granovskii  A.Yu.,  Shlyapnikov  S.S.,  Il’yashchenko  A.V.  Mathematical  model  of  calculation  of  temperature  fields  at  intermittent  cooling  of  rolled  products.  Fundamental’nye problemy sovremennogo materialovedeniya.  2016, no. 3, pp. 339–342. (In Russ.).

7. Gubinskii V.I., Minaev A.N., Goncharov Yu.V. Umen’shenie okalinoobrazovaniya pri proizvodstve prokata [Reduction  of  scale formation in production of rolled products]. Kiev: Tekhnika, 1981,  135  p. (In Russ.).

8. Sarychev  V.D.,  Nevskii  S.A.,  Il’yashchenko A.V.  On  accelerated cooling mechanisms in thermal hardening of rolled metal. Izvestiya VUZov. Chernaya metallurgiya = Izvestiya. Ferrous Metallurgy.  2017, vol. 60, no. 12, pp. 1005–1007. (In Russ.). 

9. Sarychev V.D., Nevskii S.A., Sarycheva E.V., Konovalov S.V., Gromov V.E. Viscous flow analysis of the Kelvin–Helmholtz instability for short waves. AIP Conference Proceedings. 2016, vol. 1783,  pp. 020198.

10. Mikheev M.A., Mikheeva I.M. Osnovy teploperedachi [Fundamentals of heat transfer]. Moscow: Energiya, 1977, 344 p. (In Russ.).

11. Sarychev V.D., Voloshina M.S., Gromov V.E. Mathematical model of thermoelastic waves generation under the influence of concentrated energy fluxes on materials. Fundamental’nye problemy sovremennogo materialovedeniya.  2011,  vol.  8,  no.  4,  pp.  71–77.  (In  Russ.).

12. Finkel’ V.M. Fizicheskie osnovy tormozheniya razrusheniya [Physical basics of fracture deceleration]. Moscow: Metallurgiya, 1977,  360 p. (In Russ.).

13. Fomin I.M. Zalechivanie treshchin volnami napryazhenii v shchelochno-galoidnykh kristallakh: Avtorefer. dis. … kand. fiz.-mat. nauk [Cracks healing by stress waves in alkali-halide crystals: Extended Abstract of Cand. Sci. Diss.]. Rostov-on-Don, 1984, 20 p.  (In Russ.).

14. Parkus  Heinz.  Instationare Warmespannugen.  Wien:  Springer-Verl., 1959. (Russ.ed.: Parkus H. Neustanovivshiesya temperaturnye napryazheniya. Shapiro G.S. ed. Moscow, GIFML, 1963, 252 p.).

15. Novatskii  V.  Dinamicheskie zadachi termouprugosti [Dynamic problems of thermoelasticity]. Transl. from Polish. Moscow: Mir,  1970, 256 p. (In Russ.).

16. Kovalenko A.D. Termouprugost’ [Thermoelasticity]. Kiev: Vishcha  shkola, 1975, 216 p. (In Russ.).

17. Hetnarski R.B., Eslami M.R. Thermal stresses – advanced theory and applications. Springer, 2009, 579 p.

18. Jordan P.M., Puri P. Revisiting the Danilovskaya problem. Journal of Thermal Stresses. 2006, vol. 29, pp. 865–878. 

19. Youssef H.M., Al-Felali A.S. Generalized thermoelasticity problem  of material subjected to thermal loading due to laser pulse. Appl. Math. 2012, no. 3, pp. 142–146. 

20. Kumar R., Kumar A., Singh D. Thermomechanical interactions due  to laser pulse in microstretch thermoelastic medium. Arch. Mech.  2015, vol. 67, no. 6, pp. 439–456. 

21. Sur  A.,  Kanoria  M.  Three  dimensional  viscoelastic  medium  under  thermal  shock.  Engineering Solid Mechanics.  2016,  vol.  4, pp.  187–200.

22. Nikolarakis A.M., Theotokoglou E.E. Thermal shock problem of a  three-layered functionally graded zirconia/titanium alloy strip based  on a unified generalized thermoelasticity theory. Journal of Thermal Stresses. 2016, vol. 40, no. 5, pp. 583–602. 

23. Wang Y.Z., Liu D., Wang Q., Zhou J. Z. Generalized solutions of transient thermal shock problem with bounded boundaries. Mecca-nica. 2016, vol. 52, no. 8, pp. 1935–1945. 

24. Othman M.I.A., Atwa S.Y., Elwan A.W. Effect of thermal loading  due to laser pulse on 3-D problem of micropolar Thermoelastic solid  with energy dissipation. Mechanics and Mechanical Engineering.  2017, vol. 21, no. 3, pp. 679–701. 

25. Liang W., Huang S., Tan W. S., Wang Y.Z. Asymptotic approach to transient thermal shock problem with variable material properties. Mechanics of Advanced Materials and Structures. 2017, vol.  23, no.  5, pp. 586–592. 

26. Kant S., Mukhopadhyay S. Investigation of a problem of an elastic half space subjected to stochastic temperature distribution at the  boundary. Applied Mathematical Modelling. 2017, vol. 46, no. 6,  pp. 492–518. 

27. Babenkov  M.B.,  Ivanova  E.A. Analysis  of  the  wave  propagation  processes  in  heat  transfer  problems  of  the  hyperbolic  type.  Continuum Mechanics and Thermodynamics.  2014,  vol.  26,  no.  4,  pp.  483–502.

28. Vovnenko N.V., Zimin B.A., Sud’enkov Yu.V. Experimental study  of thermoelastic stresses in heat-conducting and non-heat-conducting solids under submicrosecond laser heating. Technical Physics.  2011, vol. 56, no. 6, pp. 803–808. (In Russ.).

29. Zubko A.E., Samokhin A.A. On the nanosecond photoacoustic effect in absorbing condensed media. Inzhenernaya fizika. 2017, no.  7,  pp. 69–72. (In Russ.).