539.3

annealing, cooling, thermomechanical conditions, residual stresses, relaxation, plastic deforming, thermosensitivity, hardening, finite element method, disk.

An approach to investigation of the thermomechanical processes in solids during cooling under high-temperature annealing and following after annealing thermomechanical conditions is proposed. The annealing is oriented on the relaxation of the residual stresses. This approach is based on the non-stationary thermal conductivity problem, on the problem about a thermoelastoplastic stress and strain state of the thermal sensitive hardenable solids in the deforming process and also on the software based on the finite element method (FEM). As an example the evolution of the residual stress state in disk subjected to annealing and following influence of the static loading applied to the disk hole is analyzed. The hole in disk is coaxial and circular. The residual stresses are specific after coupling by butt welding of two ring disks.

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2. Kasatkin B. S., Prokhorenko V. M., Chertov I. M. Napryazheniya i deformatsii pri svarke. Kyiv, Vyshcha shkola, 1987. 246 p. [In Russian].
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4. Kovalchuk Ya., Shynhera N., Chornomaz N. Stress-strain state of a bottom chord of a welded roof truss. Scientific Journal of TNTU. 2019. Vol. 93. No. 1. P. 41–46.
5. Dubyk Ya., Seliverstova I. The local stress state of the pipeline with axial and angular weld misalignment. Scientific Journal of TNTU. 2019. Vol. 94. No. 2. P. 51–57.
6. Alberg H. Material Modelling for Simulation of Heat Treatment: Licentiate thesis. Luleå University of Technology, 2003. 22 p.
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8. Yasnii P. V., Pyndus Yu. I., Glad'o V. B., Okipnyi I. B., Shul'gan I. V. Scientific and technical section FEM prediction of the influence of warm prestressing on fracture toughness of heat-resistant steel. Strength of Materials. 2011. Vol. 43. No. 2. P. 113–121.
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21. Hachkevych O. R., Mykhailyshyn V. S. Matematychne modelyuvannya i doslidzhennya napruzhenoho stanu til v protsesi okholodzhennya pry vysokotemperaturnomu vidpali. Matematychni metody ta fizyko-mekhanichni polya. 2004. Vol. 47. No. 3, p. P. 186–198. [In Ukrainian].
22. Ziegler H. A modification of Prager’s hardening rule. Quart. Appl. Math. 1959. Vol. 17. P. 55–65.
23. Allen D. H., Haisler W. E. A theory for analysis of thermoplastic materials. Comput. & Struct. 1981. Vol. 13. No. 1. P. 129–135.
24. Tyeplotyekhnichyeskij spravochnik / ed. V. N. Yuryenyev, P. D. Lyebyedyev. In 2 vol. Vol. 2. Moskva: Energiya, 1976. 897 p. [In Russian].

1. Vinokurov V. A. Otpusk svarnykh konstruktsij dlya cnizheniya napryazhenij. Moskva, Mashynostroyeniye, 1973. 213 p. [In Russian].
2. Kasatkin B. S., Prokhorenko V. M., Chertov I. M. Napryazheniya i deformatsii pri svarke. Kyiv, Vyshcha shkola, 1987. 246 p. [In Russian].
3. Nyedosyeka A. Ya. Osnovy raschyota i diagnostiki svarnykh konstruktsij. Izdatel’stvo “Indprom”, 1998. 640 p. [In Russian].
4. Kovalchuk Ya., Shynhera N., Chornomaz N. Stress-strain state of a bottom chord of a welded roof truss. Scientific Journal of TNTU. 2019. Vol. 93. No. 1. P. 41–46.
5. Dubyk Ya., Seliverstova I. The local stress state of the pipeline with axial and angular weld misalignment. Scientific Journal of TNTU. 2019. Vol. 94. No. 2. P. 51–57.
6. Alberg H. Material Modelling for Simulation of Heat Treatment: Licentiate thesis. Luleå University of Technology, 2003. 22 p.
7. Yefimenko M. H., Radzivilova N. O. Metaloznavstvo i termichna obrobka zvarnykh zyednan’: pidruchnyk. Kharkiv, 2003. 488 p. [In Ukrainian].
8. Yasnii P. V., Pyndus Yu. I., Glad'o V. B., Okipnyi I. B., Shul'gan I. V. Scientific and technical section FEM prediction of the influence of warm prestressing on fracture toughness of heat-resistant steel. Strength of Materials. 2011. Vol. 43. No. 2. P. 113–121.
9. Pidhurs’kyj I. M., Okipnyj I. B., Stashkiv M. Ya., Kens I. V. Porivnyal’nyj analiz KIN ta kinetyky formy poverkhnevykh piveliptychnykh trishchyn v odnoridnomu poli napruzhen’ ta v zoni koncentratoriv. Proceedings of the V International Conference “In-Service Damage of Materials, its Diagnostics and Prediction” (Ternopil, September 19–20, 2017.). Ternopil: TNTU, 2017. Р. 111–113. [In Ukrainian].
10. Hachkevych O., Mykhailyshyn V., Ravs’ka-Skotnichna A. Chyslova metodyka rozvyazuvannya zadach termomekhaniky til u razi okholodzhennya v protsesi vysokotemperaturnoho vidpalyuvannya. Visnyk L’vivs’koho universytetu. Seriya prykladna matematyka ta informatyka. 2007. Issue 12. Р. 78–92. [In Ukrainian].
11. Budz S. F., Drobenko B. D., Mykhailyshyn V. S. Kompyuternoye modelirovaniye termouprugo­plasticheskogo povedeniya mekhanicheskich sistem. Lvov: In-t prikl. problyem myekhaniki i matyematiki AN Ukrainy, 1992. 60 p. (Preprint AN Ukrainy, In-t prikl. problyem myekhaniki i matyematiki, 34–89). [In Russian].
12. Mykhailyshyn V. S. Iteratsijni procedury v zadachakh neizotermichnoyi pruzhnoplastychnosti z izotropno-kinematychnym zmitsnennyam. Fizyko-khimichna mekhanika materialiv. 1999. Vol. 35. No. 4. Р. 102–112. [In Ukraunian]. (Mykhailyshyn V. S. Iterative Procedures for Problems of Nonisothermal Elastoplasticity with Isotropic Kinematic Hardening. Materials Science. 1999. Vol. 35. No 4. P. 561–571).
13. Emre H. E., Kacar R. Effect of Post Weld Heat Treatment Process on Microstructure and Properties of Friction Welded Dissimilar Drill Pipe. Materials Research. 2015. Vol. 18. No. 3. P. 503–508.
14. Liu P., Sun S., Xu S., Cao M., Feng K. Influence of holding time of annealing treatment on microstructure and properties of TIG welded joint for P91 heat-resistant steel tube. Kovove Mater. 2018. Vol. 56.
    P. 245–252.
15. Fedosov O. V. Zastosuvannya elektronnoho promenya dlya vidpalu zvarnykh zyednan’ tytanovoho splavu VT23. Aviatsionno-kosmicheskaya tyekhnika i tyekhnologiya. 2015 Vol. 123. No 6. P. 52–57. [In Ukrainian].
16. Lobanov L. M. (ed.), Yermolayev H. V., Kvasnyts’kyj V. V., Makhnenko O. V., Yehorov H. V., Labartkava A. V. Napruzhennya ta deformatsiyi pry zvaryuvanni i payanni: pidruchnyk. Mykolayiv: NUK, 2016. 246 p. [In Ukrainian].
17. Kovalenko A. D. Tyermouprugost’. Kyiv: Vyshcha shkola, 1975. 216 p. [In Russian].
18. Vasidzu K. Variatsionnye metody v teorii uprugosti i plastichnosti. Moskva: Mir, 1987. 542 p. [In Russian].
19. Sakharov A. S., Al’tenbakh I. Metod konyechnykh elementov v mekhanike tvyordykh tel. Kyiv: Vyshcha shkola, 1982. 480 p. [In Russian].
20. Morozov Ye. M., Nikishkov G. P., Chernysh T. A. Neizotermicheskaya model’ uprugoplasticheskogo tela i yeyo primyenyeniye dlya MKE-raschyota tel s treshchinami. Analiticheskiye i chislennyye metody resheniya krayevykh zadach plastichnosti i vyazkouprugosti. Svyerdlovsk: AN SSSR, Ural’sk. nauchn. tsentr, 1986. Р. 87–94. [In Russian].
21. Hachkevych O. R., Mykhailyshyn V. S. Matematychne modelyuvannya i doslidzhennya napruzhenoho stanu til v protsesi okholodzhennya pry vysokotemperaturnomu vidpali. Matematychni metody ta fizyko-mekhanichni polya. 2004. Vol. 47. No. 3, p. P. 186–198. [In Ukrainian].
22. Ziegler H. A modification of Prager’s hardening rule. Quart. Appl. Math. 1959. Vol. 17. P. 55–65.
23. Allen D. H., Haisler W. E. A theory for analysis of thermoplastic materials. Comput. & Struct. 1981. Vol. 13. No. 1. P. 129–135.
24. Tyeplotyekhnichyeskij spravochnik / ed. V. N. Yuryenyev, P. D. Lyebyedyev. In 2 vol. Vol. 2. Moskva: Energiya, 1976. 897 p. [In Russian].