ПРИСПОСОБЛЯЕМОСТЬ СОСУДА ПОД ДАВЛЕНИЕМ В УСЛОВИЯХ ДЛИТЕЛЬНОГО ТЕРМОСИЛОВОГО НАГРУЖЕНИЯ
Ключевые слова:
приспособляемость, рэтчетинг, приработка, циклическое нагружение, сосуд под давлением, термоциклические нагрузки, пластические деформации, деформации ползучести, неупругость
Аннотация
Статья посвящена исследованию влияния деформаций ползучести на процесс приспособляемости сосуда под давлением при длительном циклическом нагружении. Основу методологии составляет численный анализ на базе метода конечных элементов с применением верифицированной процедуры построения диаграммы приспособляемости в пространстве нормированных механических и тепловых напряжений. В отличие от классической постановки задачи, предполагающей упруго-идеально-пластическое поведение материала, в статье учитывается кинетика ползучести согласно закону Нортона – Бейли. Параметры определяющего соотношения идентифицируются на основе экспериментальных или нормативных изохронных кривых деформирования с использованием унифицированной идентификационной процедуры. Для оценки предельной накопленной неупругой деформации и ее влияния на положение границы области рэтчетинга применяется аналитический метод упругого ядра. В рамках этого подхода восстановление деформации ползучести выполняется по изохронным кривым материала на основе максимальных напряжений в поперечном сечении. Установлено, что метод упругого ядра обеспечивает удовлетворительное качественное совпадение границ зон диаграммы приспособляемости с результатами прямого численного моделирования, однако количественное определение накопленных неупругих деформаций характеризуется существенными расхождениями. Дополнительно рассмотрено влияние упрочнения материала при циклическом нагружении, моделируемого с помощью механизма изотропно-кинематического упрочнения в рамках классической модели Ишлинского – Новожилова – Шабоша. Показано, что учет смешанного упрочнения в расчетной схеме позволяет расширить область допустимых нагрузок и тем самым повысить ресурс эксплуатационной надежности рассматриваемой конструкции.
Литература
1. Ukaz Prezidenta Rossiyskoy Federatsii №529 ot 18.06.2024 “Ob utverzhdenii prioritetnykh napravleniy nauchno-tekhnologicheskogo razvitiya I perechnya vazhneyshikh naukoemkikh tekhnologiy” [Decree of the President of the Russian Federation No. 529 dated 06/18/2024 “On approval of priority areas of scientific and technological development and the list of the most important high-tech technologies”] (In Russian).
2. Adamov E.O., Kaplienko A.V., Orlov V.V. et al. Bystryy reaktor so svintsovym teplonositelem BREST: ot kontseptsii k realizatsii tekhnologii [BREST fast reactor with lead coolant: from concept to technology implementation]. Atomnaya energiya [Atomic Energy]. 2020. Vol. 129. No 4. P. 185–194 (In Russsian).
3. Shamanin I.V., Gavrilov P.M. Vysokotemperaturnye yadernye energeticheskie tekhnologii [High-temperature nuclear energy technologies]. Izvestiya Tomskogo politekhnicheskogo universiteta [Bulletin of the Tomsk Politechnic University]. 2010. T. 316. №4. P. 5–9 (In Russian).
4. Krasilnikov A.V., Konovalov S.V., Bondarchuk E.N. et al. Tokamak with reactor technologies (TRT): Concept, missions, key distinctive features and expected characteristics. Plasma Physics Reports. 2021. Vol. 47. No 11. P. 1092–1106. DOI: 10.1134/S1063780X21110192.
5. GOST R 59115.10-2021. Obosnovanie prochnosti oborudovaniya i truboprovodov atomnykh energeticheskikh ustanovok. Utochnennyy poverochnyy raschet na stadii proektirovaniya [Substantiation of the strength of equipment and pipelines of nuclear power plants. An updated verification calculation at the design stage]. Natsionalnyy standart RF [The National Standard of the Russian Federation]. 2021. 56 p. (In Russian).
6. ASME BPVC.III.5-2015 (Section III, Rules for Construction of Nuclear Facility Components), Division 5 – High Temperature Reactors. 2015. 500 p.
7. Gokhfeld D.A. Nesushchaya sposobnost konstruktsiy v usloviyakh teplosmen [The Bearing Capacity of Structures in Heat Exchange Conditions]. Moscow. Mashinostroenie Publ. 1970. 260 p. (In Russian).
8. Gokhfeld D.A., Chernyavskiy O.F. Nesushchaya sposobnost konstruktsiy pri povtornykh nagruzheniyakh [The Bearing Capacity of Structures in Heat Exchange Conditions]. Moscow. Mashinostroenie Publ. 1979. 263 p. (In Russian).
9. Chernyavsky O.F., Chernyavsky A.O. Predelnye sostoyaniya i koeffitsienty zapasa pri povtornykh nagruzheniyakh [Limit states and safety factors under repeated loading]. Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mekhanika [PNRPU Mechanics Bulletin]. 2020. No 3. P. 125–135 (In Russian).
10. Bree J. Elastic-plastic behaviour of thin tubes subject to internal pressure and intermittent high-heat fluxes with application to fast nuclear reactor fuel elements. Journal of Strain Analysis. 1967. Vol. 2. No 3. P. 226–238. DOI: 10.1243/03093247V023226.
11. O'Donnell W.J., Porowski J. Upper bounds for accumulated strains due to creep ratcheting. J. Press. Vessel Technol. 1974. Vol. 96. Iss. 3. P. 150–154.
12. Bradford R.A.W. The Bree problem with primary load cycling in-phase with the secondary load. Int. J. Pressure Vessels Piping. 2012. Vol. 99-100. P. 44–50. DOI: 10.1016/j.ijpvp. 2012.07.014.
13. Bradford R.A.W. The Bree problem with primary load cycling out-of-phase with the secondary load. Int. J. Pressure Vessels Piping. 2017. Vol. 154. P. 83–94. DOI: 10.1016/j.ijpvp. 2017.06.004.
14. Morozov N.F., Fedorenko R.V., Lukin A.V. Chislennyy metod analiza prisposoblyaemosti uprugo-plasticheskikh tel pri peremennykh nagruzkakh [Computational method for ratcheting analysis of the elastoplastic bodies under cyclic loads]. Kompozity i nanostruktury [Composites and Nanostructures]. 2024. Vol. 16. №1. P. 62–78 (In Russian).
15. Pei X., Dong P., Mei J. The effects of kinematic hardening on thermal ratcheting and Bree diagram boundaries. Thin-Walled Struct. 2021. Vol. 159. Article No 107235. DOI: 10.1016/j.tws.2020.107235.
16. Fedorenko R.V., Lukin A.V., Murtazin I.R. O vliyanii mekhanizma uprochneniya na prisposoblyaemost sosuda pod davleniem v usloviyakh termotsiklicheskogo nagruzheniya [The hardening type influence of pressure vessel ratcheting in case of thermal cyclic loads]. Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mekhanika [PNRPU Mechanics Bulletin]. 2025. No 1. P. 117–128 (In Russian).
17. Bradford R.A.W., Ure J., Chen J.F. The Bree problem with different yield stresses on-load and off-load and application to creep ratcheting. Int. J. Press. Vessels Pip. 2013. Vol. 113. P. 32–39. DOI: 10.1016/j.ijpvp.2013.11.004.
18. Bao H., Shen J., Liu Y., Chen H. Shakedown analysis and assessment method of four-stress parameters Bree-type problems. Int. J. Mech. Sci. 2022. Vol. 229. Article No 107518. DOI: 10.1016/j.ijmecsci.2022.107518.
19. Shi H., Chen G., Wang Y., Chen X. Ratcheting behavior of pressurized elbow pipe with local wall thinning. Int. J. Press. Vessels Pip. 2013. Vol. 102-103. P. 14–23. DOI: 10.12989/scs. 2016.20.4.931.
20. Turkova V.A. Inkrementalnyy analiz dvukhosnogo nagruzheniya plastiny s krugovym otverstiem: prisposoblyaemost, znakoperemennaya plastichnost i ratcheting [Incremental analysis of twoaxial loading of the plate with central circular hole: shakedown (accomodation), alternating plasticity, ratcheting]. Vestnik Samarskogo gosudarstvennogo universiteta [Vestnik SSU]. 2015. No 3(125). P. 106–124 (In Russian).
21. Turkova V.A., Stepanova L.V. Razlichnye rezhimy tsiklicheskogo nagruzheniya neuprugoy plastiny: konechnoelementnyy analiz dvukhosnogo nagruzheniya uprugoplasticheskoy plastiny s ellipticheskim vyrezom [Finite element analysis of biaxial cyclic tensile loading of elastoplastic plate with central elliptical hole]. Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mekhanika [PNRPU Mechanics Bulletin]. 2016. No 3. P. 207–221 (In Russian).
22. Volkov I.A., Igumnov L.A., Kostyukov V.E., Prilutsky M.Kh. Chislennyy analiz dolgovechnosti elementov konstruktsiy pri termotsiklicheskom nagruzhenii [Numerical analysis of the durability of structural elements under thermal cyclic loading]. Problemy prochnosti i plastichnosti [Problems of Strength and Plasticity]. 2023. Vol. 85. No 4. P. 551–564 (In Russian).
23. Rabotnov Yu.N. Mekhanika deformiruemogo tverdogo tela [Mechanics of Solids]. Moscow. Nauka Publ. 1988. 711 p. (In Russian).
24. Sedov L.I. Mekhanika sploshnoy sredy [Continuum Mechanics]. Moscow. Nauka Publ. 1994. Vol. 1. 528 p., Vol. 2. 560 p. (In Russian).
25. Abaqus 2017 Theory Guide. Dassault Systems. 2017. 312 p.
26. Fedorenko R.V., Lukin A.V. Parameter identification of the Norton – Bailey creep model using isochronous curves. Mater. Phys. Mech. 2026. Vol. 54. Iss. 1. P. 118–129.
27. Ishlinskii A.Yu. Obshchaya teoriya plastichnosti s lineynym uprochneniem [Plasticity theory with linear hardening]. Ukrainskiy matematicheskiy zhurnal [Ukrainian Mathematical Journal]. 1954. Vol. 6. No 3. P. 314–324 (In Russian).
28. Kadashevich Yu.I., Novozhilov V.V. Teoriya plastichnosti, uchityvayushchaya effekt Baushingera [The theory of plasticity with the Bauschinger effect taken into account]. Doklady AN SSSR. 1956. Vol. 117. No 4. P. 586–588 (In Russian).
29. Сhaboche J.L. Time-independent constitutive theories for cyclic plasticity. Int. J. Plast. 1986. Vol. 2. P. 149–188. DOI: 10.1016/0749-6419(86)90010-0.
30. Chaboche J.L. A review of some plasticity and viscoplasticity constitutive theories. Int. J. Plast. 2008. №24. P. 1642–1693. DOI: 10.1016/j.ijplas.2008.03.009.
31. Lemaitre J. Mechanics of Solid Materials. Cambridge, UK. Cambridge University Press. 1990. 556 p. DOI: 10.1017/CBO9781139167970.
32. Fedorenko R.V., Lukin A.V. Prisposoblyaemost sosuda pod davleniem v usloviyakh termotsiklicheskogo nagruzheniya [Adaptability of a vessel under pressure and thermocyclic loads]. Kompyuternye metody v mekhanike sploshnoy sredy: Trudy seminara. 2024-2025 gg. Saint Petersburg. Politekhpress. 2025. 220 p. (In Russian).
2. Adamov E.O., Kaplienko A.V., Orlov V.V. et al. Bystryy reaktor so svintsovym teplonositelem BREST: ot kontseptsii k realizatsii tekhnologii [BREST fast reactor with lead coolant: from concept to technology implementation]. Atomnaya energiya [Atomic Energy]. 2020. Vol. 129. No 4. P. 185–194 (In Russsian).
3. Shamanin I.V., Gavrilov P.M. Vysokotemperaturnye yadernye energeticheskie tekhnologii [High-temperature nuclear energy technologies]. Izvestiya Tomskogo politekhnicheskogo universiteta [Bulletin of the Tomsk Politechnic University]. 2010. T. 316. №4. P. 5–9 (In Russian).
4. Krasilnikov A.V., Konovalov S.V., Bondarchuk E.N. et al. Tokamak with reactor technologies (TRT): Concept, missions, key distinctive features and expected characteristics. Plasma Physics Reports. 2021. Vol. 47. No 11. P. 1092–1106. DOI: 10.1134/S1063780X21110192.
5. GOST R 59115.10-2021. Obosnovanie prochnosti oborudovaniya i truboprovodov atomnykh energeticheskikh ustanovok. Utochnennyy poverochnyy raschet na stadii proektirovaniya [Substantiation of the strength of equipment and pipelines of nuclear power plants. An updated verification calculation at the design stage]. Natsionalnyy standart RF [The National Standard of the Russian Federation]. 2021. 56 p. (In Russian).
6. ASME BPVC.III.5-2015 (Section III, Rules for Construction of Nuclear Facility Components), Division 5 – High Temperature Reactors. 2015. 500 p.
7. Gokhfeld D.A. Nesushchaya sposobnost konstruktsiy v usloviyakh teplosmen [The Bearing Capacity of Structures in Heat Exchange Conditions]. Moscow. Mashinostroenie Publ. 1970. 260 p. (In Russian).
8. Gokhfeld D.A., Chernyavskiy O.F. Nesushchaya sposobnost konstruktsiy pri povtornykh nagruzheniyakh [The Bearing Capacity of Structures in Heat Exchange Conditions]. Moscow. Mashinostroenie Publ. 1979. 263 p. (In Russian).
9. Chernyavsky O.F., Chernyavsky A.O. Predelnye sostoyaniya i koeffitsienty zapasa pri povtornykh nagruzheniyakh [Limit states and safety factors under repeated loading]. Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mekhanika [PNRPU Mechanics Bulletin]. 2020. No 3. P. 125–135 (In Russian).
10. Bree J. Elastic-plastic behaviour of thin tubes subject to internal pressure and intermittent high-heat fluxes with application to fast nuclear reactor fuel elements. Journal of Strain Analysis. 1967. Vol. 2. No 3. P. 226–238. DOI: 10.1243/03093247V023226.
11. O'Donnell W.J., Porowski J. Upper bounds for accumulated strains due to creep ratcheting. J. Press. Vessel Technol. 1974. Vol. 96. Iss. 3. P. 150–154.
12. Bradford R.A.W. The Bree problem with primary load cycling in-phase with the secondary load. Int. J. Pressure Vessels Piping. 2012. Vol. 99-100. P. 44–50. DOI: 10.1016/j.ijpvp. 2012.07.014.
13. Bradford R.A.W. The Bree problem with primary load cycling out-of-phase with the secondary load. Int. J. Pressure Vessels Piping. 2017. Vol. 154. P. 83–94. DOI: 10.1016/j.ijpvp. 2017.06.004.
14. Morozov N.F., Fedorenko R.V., Lukin A.V. Chislennyy metod analiza prisposoblyaemosti uprugo-plasticheskikh tel pri peremennykh nagruzkakh [Computational method for ratcheting analysis of the elastoplastic bodies under cyclic loads]. Kompozity i nanostruktury [Composites and Nanostructures]. 2024. Vol. 16. №1. P. 62–78 (In Russian).
15. Pei X., Dong P., Mei J. The effects of kinematic hardening on thermal ratcheting and Bree diagram boundaries. Thin-Walled Struct. 2021. Vol. 159. Article No 107235. DOI: 10.1016/j.tws.2020.107235.
16. Fedorenko R.V., Lukin A.V., Murtazin I.R. O vliyanii mekhanizma uprochneniya na prisposoblyaemost sosuda pod davleniem v usloviyakh termotsiklicheskogo nagruzheniya [The hardening type influence of pressure vessel ratcheting in case of thermal cyclic loads]. Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mekhanika [PNRPU Mechanics Bulletin]. 2025. No 1. P. 117–128 (In Russian).
17. Bradford R.A.W., Ure J., Chen J.F. The Bree problem with different yield stresses on-load and off-load and application to creep ratcheting. Int. J. Press. Vessels Pip. 2013. Vol. 113. P. 32–39. DOI: 10.1016/j.ijpvp.2013.11.004.
18. Bao H., Shen J., Liu Y., Chen H. Shakedown analysis and assessment method of four-stress parameters Bree-type problems. Int. J. Mech. Sci. 2022. Vol. 229. Article No 107518. DOI: 10.1016/j.ijmecsci.2022.107518.
19. Shi H., Chen G., Wang Y., Chen X. Ratcheting behavior of pressurized elbow pipe with local wall thinning. Int. J. Press. Vessels Pip. 2013. Vol. 102-103. P. 14–23. DOI: 10.12989/scs. 2016.20.4.931.
20. Turkova V.A. Inkrementalnyy analiz dvukhosnogo nagruzheniya plastiny s krugovym otverstiem: prisposoblyaemost, znakoperemennaya plastichnost i ratcheting [Incremental analysis of twoaxial loading of the plate with central circular hole: shakedown (accomodation), alternating plasticity, ratcheting]. Vestnik Samarskogo gosudarstvennogo universiteta [Vestnik SSU]. 2015. No 3(125). P. 106–124 (In Russian).
21. Turkova V.A., Stepanova L.V. Razlichnye rezhimy tsiklicheskogo nagruzheniya neuprugoy plastiny: konechnoelementnyy analiz dvukhosnogo nagruzheniya uprugoplasticheskoy plastiny s ellipticheskim vyrezom [Finite element analysis of biaxial cyclic tensile loading of elastoplastic plate with central elliptical hole]. Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mekhanika [PNRPU Mechanics Bulletin]. 2016. No 3. P. 207–221 (In Russian).
22. Volkov I.A., Igumnov L.A., Kostyukov V.E., Prilutsky M.Kh. Chislennyy analiz dolgovechnosti elementov konstruktsiy pri termotsiklicheskom nagruzhenii [Numerical analysis of the durability of structural elements under thermal cyclic loading]. Problemy prochnosti i plastichnosti [Problems of Strength and Plasticity]. 2023. Vol. 85. No 4. P. 551–564 (In Russian).
23. Rabotnov Yu.N. Mekhanika deformiruemogo tverdogo tela [Mechanics of Solids]. Moscow. Nauka Publ. 1988. 711 p. (In Russian).
24. Sedov L.I. Mekhanika sploshnoy sredy [Continuum Mechanics]. Moscow. Nauka Publ. 1994. Vol. 1. 528 p., Vol. 2. 560 p. (In Russian).
25. Abaqus 2017 Theory Guide. Dassault Systems. 2017. 312 p.
26. Fedorenko R.V., Lukin A.V. Parameter identification of the Norton – Bailey creep model using isochronous curves. Mater. Phys. Mech. 2026. Vol. 54. Iss. 1. P. 118–129.
27. Ishlinskii A.Yu. Obshchaya teoriya plastichnosti s lineynym uprochneniem [Plasticity theory with linear hardening]. Ukrainskiy matematicheskiy zhurnal [Ukrainian Mathematical Journal]. 1954. Vol. 6. No 3. P. 314–324 (In Russian).
28. Kadashevich Yu.I., Novozhilov V.V. Teoriya plastichnosti, uchityvayushchaya effekt Baushingera [The theory of plasticity with the Bauschinger effect taken into account]. Doklady AN SSSR. 1956. Vol. 117. No 4. P. 586–588 (In Russian).
29. Сhaboche J.L. Time-independent constitutive theories for cyclic plasticity. Int. J. Plast. 1986. Vol. 2. P. 149–188. DOI: 10.1016/0749-6419(86)90010-0.
30. Chaboche J.L. A review of some plasticity and viscoplasticity constitutive theories. Int. J. Plast. 2008. №24. P. 1642–1693. DOI: 10.1016/j.ijplas.2008.03.009.
31. Lemaitre J. Mechanics of Solid Materials. Cambridge, UK. Cambridge University Press. 1990. 556 p. DOI: 10.1017/CBO9781139167970.
32. Fedorenko R.V., Lukin A.V. Prisposoblyaemost sosuda pod davleniem v usloviyakh termotsiklicheskogo nagruzheniya [Adaptability of a vessel under pressure and thermocyclic loads]. Kompyuternye metody v mekhanike sploshnoy sredy: Trudy seminara. 2024-2025 gg. Saint Petersburg. Politekhpress. 2025. 220 p. (In Russian).
Опубликован
2026-07-02
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Copyright (c) 2026 Р.В. Федоренко, А.В. Лукин
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