MODELING OF THE INITIATION CONDITIONS OF CRACKS IN A PIPE UNDER PRESSURE OF A HYDROGENOUS MEDIUM

Author details

Tatiana V. Zinovieva
Institute for Problems in Mechanical Engineering, Saint Petersburg, Russian Federation

https://doi.org/10.15593/perm.mech/2023.3.08

An actual problem of modern engineering about destruction of a pipeline as a result of influence of hydrogen contained in the transported products is considered. Hydrogen changes the mechanical properties of metal, affecting the stress-strain state of the pipe, which, in turn, affects the distribution of hydrogen in the pipe. The hypotheses about the nature of this relationship accepted in the paper allowed to explain the reason of circumferential crack formation in the pipe under the influence of hydrogen. An algorithm for iterative calculation of the stress-strain state of a tube containing a hydrogen-containing mixture inside the tube has been developed. The coupled problem of the theory of elasticity and diffusion in the planar axisymmetric formulation is solved. Since the interaction process of hydrogen and metal is very slow, it is considered in sequential static formulations. First, the Lame-type problem for a tube with the modulus of elasticity depending on the radial coordinate is solved. By the finite difference method the stress and strain fields of the pressurized pipe are found. Further, the concentration of free hydrogen in the pipe caused by its content on the pipe surfaces and its stress state is determined. The accepted hypothesis about the condition of hydrogen atoms embedding into the crystal lattice of metal allows to estimate the influence of hydrogen on mechanical properties of the pipe material at the next stage of the calculation. The calculation of stress and concentration fields is repeated again with already modified mechanical properties. The iteration process is stopped when the stresses in the tube reach critical values according to Mises criterion or when the mechanical properties of the pipe material stop changing. The calculations show that at some combination of hydrogen concentration and pressure on the pipe wall, zones of plastic deformation arise in the pipe, which can lead to delamination of the material in the circumferential direction. This result is consistent with known experimental data.

Keywords

influence of hydrogenstresses in pipelinehydrogen diffusionhydrogen cracking.

МОДЕЛИРОВАНИЕ УСЛОВИЙ ВОЗНИКНОВЕНИЯ ТРЕЩИН В ТРУБЕ ПОД ДАВЛЕНИЕМ ВОДОРОДОСОДЕРЖАЩЕЙ СРЕДЫ

Рассматривается актуальная проблема современной техники о разрушении трубопровода в результате воздействия на него водорода, содержащегося в транспортируемом сырье. Водород изменяет механические свойства металла, воздействуя на напряженно-деформированное состояние трубы, которое, в свою очередь, оказывает влияние на распределение водорода в трубе. Принятые в работе гипотезы о характере этой связи позволили объяснить причину зарождения окружной трещины в трубе под воздействием водорода. Разработан алгоритм итерационного расчета напряженно-деформированного состояния трубы, внутри которой содержится водородосодержащая смесь. Решена связанная задача теории упругости и диффузии в плоской осесимметричной постановке. Поскольку процесс взаимодействия водорода и металла очень медленный, он рассмотрен в последовательных статических постановках. Сначала решается задача типа Ламе для трубы с модулем упругости, зависящим от радиальной координаты. Методом конечных разностей найдены поля напряжений и деформаций трубы, находящейся под давлением. Далее определяется концентрация свободного водорода в трубе, обусловленная его содержанием на поверхностях трубы и ее напряженным состоянием. Принятая гипотеза об условии вклинивания атомов водорода в кристаллическую решетку металла позволяет на следующем этапе расчета провести оценку влияния водорода на механические свойства материала трубы. Расчет полей напряжений и концентрации повторяется вновь уже с измененными механическими характеристиками. Итерационный процесс останавливается, когда напряжения в трубе достигают критических значений по критерию Мизеса или когда механические свойства материала трубы перестают изменяться. Расчеты показали, что при некоторых сочетаниях концентрации водорода и давления на стенку трубы в ней возникают зоны пластических деформаций, которые могут привести к расслоению материала в окружном направлении. Этот результат соответствует известным экспериментальным данным.

Ключевые слова

влияние водороданапряжения в трубеводородная диффузияводородное растрескивание.

Bibliography

1.Elboujdaini M. Initiation of Near Neutral pH Environmentally Assisted Cracking in Line Pipe Steel. Proceedings of the 16th European Conference of Fracture. Alexandroupolis, Greece, July 3 – 7, 2006. Scholar
2.Balueva A. Modeling of hydrogen embrittlement cracking in pipe-lines under high pressures. Procedia Materials Science, 2014, Vol. 3, pp. 1310-1315. Scholar
3.Yakovlev Yu.A., Polyanskiy V.A., Sedova Yu.S., Belyaev A.K. Modeli vliianiia vodoroda na mekhanicheskie svoistva metallov i splavov [Models of hydrogen influence on the mechanical properties of metals and alloys]. PNRPU Mechanics Bulletin, 2020, No. 3, pp. 136-160. doi: 10.15593/perm.mech/2020.3.13. Scholar
4.Djukic M.B. et al. Towards a unified and practical industrial model for prediction of hydrogen embrittlement and damage in steels. Procedia Structural Integrity, 2016, Vol. 2, pp. 604–611. Scholar
5.Sergeev N.N., Sergeev A.N., Kutepov S.N., et al. Osnovy povysheniia dolgovechnosti vysokoprochnykh stalei, ekspluatiruemykh v vodorodsoderzhashchikh sredakh [Fundamentals for improving the durability of high-strength steels operated in hydrogen-containing environments]. Moscow, Infra-Inzheneriia, 2021, 352 p. Scholar
6.Stepanov A.V. O prichinah prezhdevremennogo razryva [About the causes of premature bursting]. Izv. AN SSSR. OMEN, 1937, No. 6, pp. 797-813. Scholar
7.Vladimirov V.I. Fizicheskaya priroda razrusheniya metallov [The physical nature of metal failures]. M., Metallurgiya, 1984, 280 p. Scholar
8.Kosevich A.M. Dislokacii v teorii uprugosti [Dislocations in theory of elasticity]. Kiev, Naukova dumka, 1978, 219 p. Scholar
9.Chulkin S.G., Zinovieva T.V. Raschet vlijanija vodoroda na prochnost' morskogo truboprovoda [Calculation of hydrogen influence on the strength of marine pipeline]. Marine Intellectual Technologies, 2019, No. 2 (44), Vol. 1, pp. 31-35. doi: 10.13140/RG.2.2.22027.34088. Scholar
10.Zinovieva T.V. Vliianie kontsentratsii vodoroda na rastreskvianie truby [Effect of hydrogen concentration on pipe cracking]. Sovremennoe mashinostroenie: Nauka i obrazovanie: materialy 9-i Mezhdunarodnoi nauchno-prakticheskoi konferentsii (Modern Mechanical Engineering: Science and Education: Proceedings of the 9th International Scientific and Practical Conference). SPb., 2020, pp.196-206. doi: 10.1872/MMF-2020-15. Scholar
11.Filippenko G.V., Zinovieva T.V. Analysis of axisymmetric vibrations of a hydrogen weakened pipe in a layered shell model. Advances in Mechanical Engineering, LNME. Published by Springer International Publishing Switzerland, 2022, pp. 78–85. doi:10.1007/978-3-030-91553-7_9. Scholar
12.Gorsky W.S. Theorie der ordnungsprozesse und der Diffusion in Mischkristallen von CuAu. Sow. Phys., 1935, Bd. 8, pp. 433-456. Scholar
13.Gorsky W.S. Theorie der elastischen Nachwirkung in ungeordneten Mischkristallen (elastische Nachwirkung zweiter Art). Physikalische Zeitschrift der Sowjetunion, 1935, Bd. 8, pp. 457-471. Scholar
14.Ovchinnikov I.I. Issledovanie povedeniia obolochechnykh konstruktsii, ekspluatiruiushchikhsia v sredakh, vyzyvaiushchikh korrozionnoe rastreskvianie [Investigation of the behaviour of shell structures operating in environments causing corrosion cracking]. Internet-zhurnal «Naukovedenie» (The online magazine Naukovodenie), 2012, No. 4, available at: http://naukovedenie.ru/PDF/38tvn412.pdf . Scholar
15.Polyanskiy V.A., Belyaev A.K., Alekseeva E.L., Polyanskiy A.M., Tretyakov D.A., Yakovlev Yu.A. Phenomenon of skin effect in metals due to hydrogen absorption. Continuum Mechanics and Thermodynamics, 2019, Vol. 31, No. 6, pp. 1961-1975. doi: 10.1007/s00161-019-00839-2. Scholar
16.Suranov G.I. Vodovod: razrushenie, iznashivanie, smazka detalei mashin [Hydrogen: Destruction, wear and tear, lubrication of machine parts]. Ukhta, UGTU Publishing House, 2015, 224 p. Scholar
17.Nie Y., Kimura Y., Inoue T., et al. Hydrogen embrittlement of a 1500-MPa tensile strength level steel with an ultrafine elongated grain. Metallurgical and Materials Trans. A., 2012, Vol. 43, No. 5, pp. 1670-1687. Scholar
18.Yagodzinskyy Y., Saukkonen T., Andronova E., Rissanen L., Hanninen H. Hydrogen-Induced Cracking of Metastable Austenitic Stainless and High-Strength Carbon Steels. Effects of Hydrogen on Materials: Proceedings of the 2008 International Hydrogen Conference, ASM International, Materials Park, 2009, pp. 123-130. Scholar
19.Lawrence S. K., Somerday B. P., Ingraham M. D., Bahr D. F. Probing the Effect of Hydrogen on Elastic Properties and Plastic Deformation in Nickel Using Nanoindentation and Ultrasonic Methods. JOM, 2018, 70(7), pp. 1068-1073. doi: 10.1007/s11837-018-2850-z. Scholar
20.Müller C., Zamanzade M., Motz C. The Impact of Hydrogen on Mechanical Properties; A New In Situ Nanoindentation Testing Method. Micromachines, 2019, 10(2), 114. doi: 10.3390/mi10020114. Scholar
21.Ortiz M., Ovejero-Garcia J. Effect of hydrogen on Young's modulus of AISI 1005 and 1070 steels. Journal of Materials Science , 1992, Vol. 27 , pp. 6777-6781. Scholar
22.Fuyu Dong, Mengyuan He, Yue Zhang, Lianshun Luo, Yanqing Su, Binbin Wang, Hongjun Huang, Qingchun Xiang, Xiaoguang Yuan, Xiaojiao Zuo, Baoshuai Han, Yanjin Xu. Effects of hydrogen on the nanomechanical properties of a bulk metallic glass during nanoindentation. International Journal of Hydrogen Energy, 2017, Vol. 42, Issue 40, pp. 25436-25445. Scholar
23.Glagolev K.V., Morozov A.N. Fizicheskaia termodinamika [Physical thermodynamics]. M., Bauman University Publishing House, 2007, 270 p. Scholar
24.Horgan C.O., Chan A.M. The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials. J. Elasticity, 1999, 55, pp. 43-59. Scholar
25.Lomakin V. A. Teoriya uprugosti neodnorodnyh tel [Theory of elasticity of inhomogeneous bodies]. M., Izd-vo Moskovskogo universiteta, 1976, 368 p. Scholar
26.Eliseev V. V. Mehanika uprugih tel [Mechanics of elastic bodies]. SPb., SPbGPU Publishing House, 2003, 336 p. Scholar
27.Rabotnov Yu. N. Soprotivlenie materialov [Strength of materials]. M., Lenand, 2019, 456 p. Scholar
28.Chapra S.C., Canale R.P. Numerical Methods for Engineers. McGraw-Hill Education, New York, 2014, 992 p. Scholar
29.Bakhvalov N.S., Zhidkov N.P., Kobelkov G.M. Chislennye metody [Numerical methods]. Moscow, Binom. Laboratoriya znanij, 2011, 640 p. Scholar
30.Zinovieva T.V. Calculation of shells of revolution with arbitrary meridian oscillations. Advances in Mechanical Engineering, LNME. Published by Springer International Publishing Switzerland, 2017, pp. 165-176. doi:10.1007/978-3-319-53363-6_17. Scholar
31.Belyaev A.K., Kudinova N.R., Polyanskiy V.A., Yakovlev Yu.A. Opisanie deformatsii i razrusheniia materialov, soderzhashchikh vodorod, s pomoshch'iu reologicheskoi modeli [The Description of deformation and destruction of materials containing hydrogen by means of rheological model]. Nauchno-tekhnicheskie vedomosti SPbGPU. Fiziko-matematicheskie nauki (St. Petersburg Polytechnical University Journal: Physics and Mathematics), 2015, № 3(225), pp. 134-149. Scholar
32.Belyaev A.K., Polyanskiy V.A., Yakovlev Y.A. Stresses in a pipeline affected by hydrogen. Acta Mechanica, 2012, 223(8), pp. 1611-1619. Scholar
33.Ovchinnikov I.I. Modeli deformirovaniia i zamedlennogo razrusheniia materialov v vodorodosoderzhashchei srede [Models for deformation and delayed fracture of materials in hydrogen-containing media]. Vestnik SGTU (SGTU Bulletin), 2013, № 2 (70), issue 1, pp. 178-183. Scholar
34.Belyaev A.K., Polyanskiy A.M., Polyanskiy V.A., Yakovlev Y.A. An approach to modeling structural materials with low hydrogen concentration. Dynamical Processes in Generalized Continua and Structures, Springer, Cham, 2019, pp. 63-87. Scholar
35.Bekman I. N. Matematika diffuzii [The mathematics of diffusion]. Moscow, OntoPrint, 2016, 400 p. Scholar
36.Kolachev B. A. Vodorodnaia khrupkost' metallov [Hydrogen embrittlement of metals]. Moscow, Metallurgiia, 1985, 216 p. Scholar
37.Turnbull A. Hydrogen diffusion and trapping in metals. Gaseous hydrogen embrittlement of materials in energy technologies. Philadelphia: Woodhead Publishing Limited, 2012, pp. 89-128. Scholar
38.Eeckhout E., Baere I., Depover T., Verbeken K. The effect of a constant tensile load on the hydrogen diffusivity in dual phase steel by electrochemical permeation experiments. Materials Science and Engineering: A, 2020, Vol. 773, article 138872. Scholar
39.Zhao W., Zhang T., He Z., Sun J., Wang Y. Determination of the Critical Plastic Strain-Induced Stress of X80 Steel through an Electrochemical Hydrogen Permeation Method. Electrochimica Acta, 2016, Vol. 214, pp. 336-344. Scholar
40.Borwein J.M., Skerritt M.B. An introduction to modern mathematical computing: with Mathematica. Springer, 2012, Vol. XVI, 224 p. Scholar
41.API SPEC 5L Specification for Line Pipe, Forty-sixth Edition (04/01/2018). Scholar
42.ISO 12213-3:2006 "Natural gas – Calculation of compression factor – Part 3: Calculation using physical properties". Scholar

1.Elboujdaini M., 2006. Initiation of Near Neutral pH Environmentally Assisted Cracking in Line Pipe Steel // Proceedings of the 16th European Conference of Fracture. – Alexandroupolis, Greece, July 3 – 7, 2006. Scholar
2.Balueva A. Modeling of hydrogen embrittlement cracking in pipe-lines under high pressures // Procedia Materials Science. – 2014. – Vol. 3. – P. 1310–1315. Scholar
3.Модели влияния водорода на механические свойства металлов и сплавов / Ю.А. Яковлев, В.А. Полянский, Ю.С. Седова, А.К. Беляев // Вестник Пермского национального исследовательского политехнического университета. Механика. –2020. – № 3.– С. 136–160. DOI: 10.15593/perm.mech/2020.3.13 Scholar
4.Towards a unified and practical industrial model for prediction of hydrogen embrittlement and damage in steels / M.B. Djukic [et al.] // Procedia Structural Integrity. – 2016. – Vol. 2. – P. 604–611. Scholar
5.Основы повышения долговечности высокопрочных сталей, эксплуатируемых в водородсодержащих средах / Н.Н. Сергеев, А.Н. Сергеев, С.Н. Кутепов [и др.]. – М.: Инфра-Инженерия, 2021. – 352 с. Scholar
6.Степанов А.В. О причинах преждевременного разрыва // Изв. АН СССР. ОМЕН. – 1937. – № 6. – С. 797–813. Scholar
7.Владимиров В.И. Физическая природа разрушения металлов. – М.: Металлургия, 1984. – 280 с. Scholar
8.Косевич А.М. Дислокации в теории упругости. – Киев: Наукова думка, 1978. – 219 с. Scholar
9.Чулкин С.Г., Зиновьева Т.В. Расчет влияния водорода на прочность морского трубопровода // Морские интеллектуальные технологии. – 2019. – № 2 (44). – Т. 1. – С. 31–35. DOI: 10.13140/RG.2.2.22027.34088 Scholar
10.Зиновьева Т.В. Влияние концентрации водорода на растрескивание трубы // Современное машиностроение: Наука и образование: материалы 9-й Международной научно-практической конференции. – СПб., 2020. – С. 196–206. DOI: 10.1872/MMF-2020-15 Scholar
11.Filippenko G.V., Zinovieva T.V. Analysis of axisymmetric vibrations of a hydrogen weakened pipe in a layered shell model // Advances in Mechanical Engineering, LNME. – Published by Springer International Publishing Switzerland, 2022. – P. 78–85. DOI: 10.1007/978-3-030-91553-7_9 Scholar
12.Gorsky W.S. Theorie der ordnungsprozesse und der Diffusion in Mischkristallen von CuAu // Sow. Phys. – 1935. – Bd. 8. – P. 433–456. Scholar
13.Gorsky W.S. Theorie der elastischen Nachwirkung in ungeordneten Mischkristallen (elastische Nachwirkung zweiter Art) // Physikalische Zeitschrift der Sowjetunion. – 1935. – Bd. 8. – P. 457–471. Scholar
14.Овчинников И.И. Исследование поведения оболочечных конструкций, эксплуатирующихся в средах, вызывающих коррозионное растрескивание [Электронный документ] // Науковедение. – 2012. – № 4. – URL: http://naukovedenie.ru/ PDF/38tvn412.pdf. (дата обращения: 21.04.2022). Scholar
15.Phenomenon of skin effect in metals due to hydrogen absorption / V.A. Polyanskiy, A.K. Belyaev, E.L. Alekseeva, A.M. Polyanskiy, D.A. Tretyakov, Yu.A. Yakovlev // Continuum Mechanics and Thermodynamics. – 2019. – Vol. 31, no. 6. – P. 1961–1975. DOI: 10.1007/s00161-019-00839-2 Scholar
16.Суранов Г.И. Водород: разрушение, изнашивание, смазка деталей машин. – Ухта: УГТУ, 2015. – 224 с. Scholar
17.Hydrogen embrittlement of a 1500-MPa tensile strength level steel with an ultrafine elongated grain / Y. Nie, Y. Kimura, T. Inoue [et al.] // Metallurgical and Materials Trans. A. – 2012. – Vol. 43, no. 5. – P. 1670–1687. Scholar
18.Hydrogen-Induced Cracking of Metastable Austenitic Stainless and High-Strength Carbon Steels / Y. Yagodzinskyy, T. Saukkonen, E. Andronova, L. Rissanen, H. Hanninen // Effects of Hydrogen on Materials: Proceedings of the 2008 International Hydrogen Conference. – ASM International, Materials Park, 2009. – P. 123–130. Scholar
19.Probing the Effect of Hydrogen on Elastic Properties and Plastic Deformation in Nickel Using Nanoindentation and Ultrasonic Methods / S.K. Lawrence, B.P. Somerday, M.D. Ingraham, D.F. Bahr // JOM. – 2018. – Vol. 70(7). – P. 1068–1073. DOI: 10.1007/s11837-018-2850-z Scholar
20.Müller C., Zamanzade M., Motz C. The Impact of Hydrogen on Mechanical Properties; A New In Situ Nanoindentation Testing Method // Micromachines. – 2019. – Vol. 10(2). – P. 114. DOI: 10.3390/mi10020114 Scholar
21.Ortiz M., Ovejero-Garcia J. Effect of hydrogen on Young's modulus of AISI 1005 and 1070 steels // Journal of Materials Science. – 1992. – Vol. 27. – P. 6777–6781. Scholar
22.Effects of hydrogen on the nanomechanical properties of a bulk metallic glass during nanoindentation / Fuyu Dong, Mengyuan He, Yue Zhang, Liangshun Luo, Yanqing Su, Binbin Wang, Hongjun Huang, Qingchun Xiang, Xiaoguang Yuan, Xiaojiao Zuo, Baoshuai Han, Yanjin Xu. // International Journal of Hydrogen Energy. – 2017. – Vol. 42, iss. 40. – P. 25436–25445. Scholar
23.Глаголев К.В., Морозов А.Н. Физическая термодинамика. – М.: Изд-во МГТУ им. Н.Э. Баумана, 2007. – 270 с. Scholar
24.Horgan C.O., Chan A.M. The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials // J. Elasticity. – 1999. – Vol. 55. – P. 43–59. Scholar
25.Ломакин В.А. Теория упругости неоднородных тел. – М.: Изд-во Московского университета, 1976. – 368 с. Scholar
26.Елисеев В.В. Механика деформируемого твердого тела. – СПб.: Изд-во Политехн. ун-та, 2006. – 231 с. Scholar
27.Работнов Ю.Н. Сопротивление материалов. – М.: Ленанд, 2019. – 456 с. Scholar
28.Chapra S.C., Canale R.P. Numerical Methods for Engineers. – McGraw-Hill Education, New York, 2014. – p. 992. Scholar
29.Бахвалов Н.С., Жидков Н.П., Кобельков Г.М. Численные методы. – М.: Бином. Лаборатория знаний, 2011. – 640 с. Scholar
30.Zinovieva T.V. Calculation of shells of revolution with arbitrary meridian oscillations // Advances in Mechanical Engineering, LNME. – Published by Springer International Publishing Switzerland, 2017. – P. 165–176. DOI: 10.1007/978-3-319-53363-6_17 Scholar
31.Описание деформации и разрушения материалов, содержащих водород, с помощью реологической модели / А.К. Беляев, Н.Р. Кудинова, В.А. Полянский, Ю.А. Яковлев // Научно-технические ведомости СПбГПУ. Физико-математические науки. – 2015. – № 3(225). – С. 134–149. Scholar
32.Belyaev A.K., Polyanskiy V.A., Yakovlev Y.A. Stresses in a pipeline affected by hydrogen // Acta Mechanica. – 2012. – 223(8). – P. 1611–1619. Scholar
33.Овчинников И.И. Модели деформирования и замедленного разрушения материалов в водородосодержащей среде // Вестник СГТУ. – 2013. – № 2 (70). – Вып. 1. – С. 178-183. Scholar
34.An approach to modeling structural materials with low hydrogen concentration / A.K. Belyaev, A.M. Polyanskiy, V.A. Polyanskiy, Y.A. Yakovlev // Dynamical Processes in Generalized Continua and Structures, Springer, Cham. – 2019. – P. 63–87. Scholar
35.Бекман И.Н. Математика диффузии. – М.: Издательство «ОнтоПринт», 2016. – 400 с. Scholar
36.Колачев Б.А. Водородная хрупкость металлов. – М.: Металлургия, 1985. – 216 с. Scholar
37.Turnbull A. Hydrogen diffusion and trapping in metals // Gaseous hydrogen embrittlement of materials in energy technologies. – Philadelphia: Woodhead Publishing Limited. – 2012. – P. 89–128. Scholar
38.The effect of a constant tensile load on the hydrogen diffusivity in dual phase steel by electrochemical permeation experiments / E. Eeckhout, I. Baere, T. Depover, K. Verbeken // Materials Science and Engineering: A. – 2020. – Vol. 773. – Article 138872. Scholar
39.Determination of the Critical Plastic Strain-Induced Stress of X80 Steel through an Electrochemical Hydrogen Permeation Method / W. Zhao, T. Zhang, Z. He, J. Sun, Y. Wang // Electrochimica Acta. – 2016. – Vol. 214. – P. 336–344. Scholar
40.Borwein J.M., Skerritt M.B. An introduction to modern mathematical computing: with Mathematica. – Springer, 2012. – Vol. XVI. – P. 224. Scholar
41.API SPEC 5L Specification for Line Pipe, Forty-sixth Edition (04/01/2018). Scholar
42.ISO 12213-3:2006 "Natural gas – Calculation of compression factor – Part 3: Calculation using physical properties". Scholar

Article information

Published: 3 July 2023
Issue date: 3 July 2023
Issue: No. 3 (2023)