Finite Element Modelling of Hydrogen Embrittlement by Considering Hydrogen Coverage Boundary Conditions
Dario Gravina
Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, G4 0LZ Glasgow, UK McDermott International, W4 5XT London, UK
Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, G4 0LZ Glasgow, UK
Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, G4 0LZ Glasgow, UK
DOI: https://doi.org/10.36956/sms.v7i4.2617
Received: 10 August 2025 | Revised: 17 November 2025 | Accepted: 24 November 2025 | Published Online: 24 December 2025
Copyright © 2025 Dario Gravina, Selda Oterkus, Erkan Oterkus. Published by Nan Yang Academy of Sciences Pte. Ltd.
This is an open access article under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) License.
Abstract
In this study, an alternative modelling approach for absorbed hydrogen stress corrosion cracking (SCC) is proposed, with hydrogen-enhanced decohesion (HEDE) identified as the key failure mechanism. All analyses have been performed by utilising only ABAQUS standard elements, COH2D4T and CPE4T, already available within the software and without the need to develop external subroutines. The study also tends to highlight the criticality of implementing a correct Traction Separation Law (TSL) curve to simulate the hydrogen diffusion within the specimen and using the concept of dynamic hydrogen penetration by continuously updating the hydrogen concentration boundary conditions as the crack propagates. In conclusion, this study successfully demonstrated that standard software elements (COH2D4T and CPE4T) can effectively model physical problems and crack velocity propagation without custom subroutines. It emphasized that while the specific shape of the Traction-Separation Law (TSL) is less critical, its correct implementation is vital for simulating dynamic hydrogen coverage. Crucially, excluding this dynamic coverage—a common practice—risks significantly underestimating crack propagation speed. Although results incorporating dynamic coverage aligned well with experimental data, minor discrepancies are likely due to unmodeled factors like material property variations, hydrogen trapping, temperature, and granular microstructure, which are proposed for future research.
Keywords: Hydrogen Embrittlement; Finite Element Method; Cohesive Zone Model; Stress Corrosion Cracking; Fracture
References
[1] Veziroǧlu, T.N., Sahin, S., 2008. 21st Century’s energy: Hydrogen energy system. Energy Conversion and Management. 49, 1820–1831
[2] Barreto, L., Makihira, A., Riahi, K., 2003. The hydrogen econeromy in the 21st century: A sustainable development Scenario. International Journal of Hydrogen Energy. 28, 267–284
[3] Witkowski, A., Rusin, A., Majkut, M., et al., 2018. Analysis of compression and transport of the methane/hydrogen mixture in existing natural gas pipelines. International Journal of Pressure Vessels and Piping. 166, 24–34
[4] Edwards, R.L., Font-Palma, C., Howe, J., 2021. The status of hydrogen technologies in the UK: A multi-disciplinary review. Sustainable Energy Technologies and Assessments. 43, 100901. DOI: https://doi.org/10.1016/j.seta.2020.100901
[5] The Oil & Gas Technology Centre, 2021. Phase 1 Project Report: Delivery of an offshore hydrogen supply programme via industrial trials at the Flotta Terminal – HOP Project HS413. Available from: https://assets.publishing.service.gov.uk/media/5e4ab9bf40f0b677ca249fed/Phase_1_-_OGTC_-_Hydrogen_Offshore_Production.pdf (cited 5 August 2025).
[6] Oil & Gas Authority, 2018. UKCS Decommissioning: 2018 Cost Estimate. Available from: https://www.nstauthority.co.uk/media/4925/decommissioning-cost-report-2018.pdf (cited 5 August 2025).
[7] De Meo, D., Diyaroglu, C., Zhu, N., et al., 2016. Modelling of stress-corrosion cracking by using peridynamics. International Journal of Hydrogen Energy. 41(15), 6593–6609.
[8] Lynch, S.P., 2011. Mechanistic and fractographic aspects of stress corrosion cracking (SCC). In: Raja V.S., Shoji T. (Eds.). Stress Corrosion Cracking - Theory and Practice. Woodhead Publishing Limited: Cambridge, UK.
[9] Wang, M., Akiyama, E., Tsuzaki, K., 2006. Determination of the critical hydrogen concentration for delayed fracture of high strength steel by constant load test and numerical calculation. Corrosion Science. 48, 2189–2202.
[10] Yatabe, H., Yamada, K., Rios de Los, E.R., et al., 1995. Formation of hydrogen-assisted intergranular cracks in high strength steels. Fatigue & Fracture of Engineering Materials & Structures. 18, 377–384.
[11] Miresmaeili, R., Ogino, M., Nakagawa, T., et al., 2010. A coupled elastoplastic-transient hydrogen diffusion analysis to simulate the onset of necking in tension by using the finite element method. International Journal of Hydrogen Energy. 35, 1506–1514.
[12] Djukic M.B., Zeravcic V.S., Bakic G.M., et al., 2014. Hydrogen embrittlement of low carbon structural steel. Procedia Materials Science. 3, 1167–1172.
[13] Troiano, A., 2016. The role of hydrogen and other interstitials in the mechanical behaviour of metals. Metallography Microstructure and Analysis. 5, 557–569. DOI: https://doi.org/10.1007/s13632-016-0319-4
[14] Guzmán, A.A., Jeon, J., Hartmaier, A., et al., 2020. Hydrogen Embrittlement at Cleavage Planes and Grain Boundaries in Bcc Iron-Revisiting the First-Principles Cohesive Zone Model. Materials.13, 5785. DOI: https://doi.org/10.3390/ma13245785
[15] Robertson, I.M., Sofronis, P., Nagao, A., et al., 2015. Hydrogen embrittlement understood. Metallurgical and Materials Transactions B. 46, 1085–1103. DOI: https://doi.org/10.1007/s11663-015-0325-y
[16] Zhao, Y.K., Seok, M.Y., Choi, I.C., et al., 2015. The role of hydrogen in hardening/softening steel: Influence of the charging process. Scripta Materialia. 107, 46–49.
[17] Liang, Y., Sofronis, P., Aravas, N., 2003. On the effect of hydrogen on plastic instabilities in metals. Acta Materialia. 51, 2717–2730.
[18] Stepanova, E., Grabovetskaya, G., Syrtanov, M., et al., 2020. Effect of Hydrogen on the Deformation Behavior and Localization of Plastic Deformation of the Ultrafine-Grained Zr–1Nb Alloy. Metals. 10, 592. DOI: https://doi.org/10.3390/met10050592
[19] Djukic, M.B., Bakic, G.M., Sijacki Zeravcic, V., et al., 2016. Hydrogen embrittlement of industrial components: prediction, prevention, and models. Corrosion. 72 (7), 943–961.
[20] Djukic, M.B., Bakic, G.M., Sijacki Zeravcic, V.C., et al., 2016. Towards a unified and practical industrial model for prediction of hydrogen embrittlement and damage in steels. Procedia Structural Integrity. 2, 604–611.
[21] Sofronis, P., McMeeking, R.M., 1989. Numerical analysis of hydrogen transport near a blunting crack tip. Journal of the Mechanics and Physics of Solids. 37, 317–350.
[22] Krom, A.H.M., Bakker, A.D., 2000. Hydrogen trapping models in steel. Metallurgical and Materials Transactions B. 31, 1475–1482.
[23] Taha, A., Sofronis, P.A., 2001. A micromechanics approach to the study of hydrogen transport and embrittlement. Engineering Fracture Mechanics. 68, 803–837.
[24] Alvaro, A., Olden, V., Akselsen, O.M., 2013. 3D cohesive modelling of hydrogen embrittlement in the heat affected zone of an X70 pipeline steel. International Journal of Hydrogen Energy. 38, 7539–7549.
[25] Jiang, D.E., Carter, E.A., 2004. First principles assessment of ideal fracture energies of materials with mobile impurities: Implications for hydrogen embrittlement of metals. Acta Materialia. 52, 4801–4807.
[26] Serebrinsky, S., Carter, E.A., Ortiz, M., 2004. A quantum-mechanically informed continuum model of hydrogen embrittlement. Journal of the Mechanics and Physics of Solids. 52, 2403–2430.
[27] Sobhaniaragh, B., Afzalimir, S.H., Ruggieri, C., 2021. Towards the prediction of hydrogen–induced crack growth in high–graded strength steels. Thin-Walled Structures. 159, 107245. DOI: https://doi.org/10.1016/j.tws.2020.107245
[28] Zhang, X., Lu, G., 2015. Multiscale Modelling of hydrogen embrittlement. Department of Physics and Astronomy, California State University Northridge: Northridge, CA, USA.
[29] Chen, Y.-S., Huang, C., Liu, P.-Y., 2024. Hydrogen trapping and embrittlement in metals — A review. International Journal of Hydrogen Energy. 136, 789–821. DOI: https://doi.org/10.1016/j.ijhydene.2024.04.076
[30] Martínez-Pañeda, E., Golahmar, A., Niordson, C.F., 2020. A phase field formulation for hydrogen assisted cracking. Computer Methods in Applied Mechanics and Engineering. 342, 742–761. DOI: https://doi.org/10.1016/j.cma.2018.07.021
[31] Wu, J.-Y., Mandal, T., Nguyen, V.P., 2020 A phase-field regularized cohesive zone model for hydrogen assisted cracking. Computer Methods in Applied Mechanics and Engineering 358, 112614. DOI: https://doi.org/10.1016/j.cma.2019.112614
[32] Yamde, A.A., Lade, V.G., Bindwal, A.B., 2024. Machine learning approaches for the prediction of hydrogen uptake in metal-organic-frameworks: A comprehensive review. International Journal of Hydrogen Energy. 98, 1131–1154. DOI: https://doi.org/10.1016/j.ijhydene.2024.12.131
[33] Song, J., Curtin, W.A., 2012. Atomic mechanism and prediction of hydrogen embrittlement in iron. Nature Materials. 20(9), 1279–1284. DOI: https://doi.org/10.1038/nmat3479
[34] Di Stefano, D., Mrovec, M., Elsässer, C., 2015. First-principles investigation of hydrogen trapping and diffusion at grain boundaries in nickel. Acta Materialia. 98, 306–312. DOI: https://doi.org/10.1016/j.actamat.2015.07.031
[35] Muth, A., Fischer, C., Oeser, S., 2025. Fully coupled crystal plasticity and hydrogen diffusion modeling of X52 pipeline steel and weld microstructures Computational Materials Science. 258, 114005. DOI: https://doi.org/10.1016/j.commatsci.2025.114005
[36] Díaz, A., Alegre, J.M., Cuesta, I.I., 2016. A review on diffusion modelling in hydrogen related failures of metals. Engineering Failure Analysis. 66, 577–595.
[37] Oriani, R., 1970. The diffusion and trapping of hydrogen in steel. Acta Metallurgica. 18(1), 147–157.
[38] Hirose, Y., Mura, T., 1984. Growth mechanism of stress corrosion cracking in high strength steel. Engineering Fracture Mechanics. 19(6), 1057–1067.
[39] Hirose, Y., Mura, T., 1984. Nucleation mechanism of stress corrosion cracking from notches. Engineering Fracture Mechanics, 19(2), 317–329.
[40] Jadhav, D.N., Maiti, S.K., 2010. Characterization of stable crack growth through AISI 4340 steel using cohesive zone modelling and CTOD/CTOA criterion. Nuclear Engineering and Design. 240(4), 713–721. DOI: https://doi.org/10.1016/j.nucengdes.2009.11.042
[41] Jha, A., Duhan, N., Singh, I.V., et al., 2025. Numerical study of the hydride embrittlement in zirconium alloy using XFEM. International Journal of Structural Stability and Dynamics. 25(2), 2440002. DOI: https://doi.org/10.1142/S0219455424400029
[42] Kim, D.-H., Park, M.J., Chang, Y.S., et al., 2022. Evaluation of fracture properties of two metallic materials under hydrogen gas conditions by using XFEM. Metals. 12(11), 1813. DOI: https://doi.org/10.3390/met12111813
[43] Kim, D.-H., Sim, J.M., Chang, Y.S. and Baek, U.B., 2021. Hydrogen gaseous effects on fracture resistance of API-X70 estimated by XFEM. Journal of Mechanical Science and Technology. 35(9), 3829-3835. DOI: https://doi.org/10.1007/s12206-021-2106-7
[44] Oterkus, E., 2022. Applications of Peridynamics in Marine Structures. Sustainable Marine Structures. 4(1), 13–15. DOI: https://doi.org/10.36956/sms.v4i1.475
[45] Karpenko, O., Oterkus, S., Oterkus, E., 2022. Titanium Alloy Corrosion Fatigue Crack Growth Rates Prediction: Peridynamics Based Numerical Approach. International Journal of Fatigue. 162, 107023. DOI: https://doi.org/10.1016/j.ijfatigue.2022.107023
[46] Chen, Z., Yang, D., Bian, H., 2023. Peridynamic Modeling of Crack Propagation Driven by Hydrogen Embrittlement. Engineering Fracture Mechanics. 293, 109687. DOI: https://doi.org/10.1016/j.engfracmech.2023.109687
[47] Ran, X., Qian, S., Zhou, J., et al., 2022. Crack Propagation Analysis of Hydrogen Embrittlement Based on Peridynamics. International Journal of Hydrogen Energy. 47(14), 9045–9057. DOI: https://doi.org/10.1016/j.ijhydene.2021.11.173
[48] Chen, Z., Yu, X., Yang, D., 2025. A Peridynamic Plastic Model for Hydrogen-Related Casing Pipe Damage of the Underground Hydrogen Storage. Computational Particle Mechanics. 1–26. DOI: https://doi.org/10.1007/s40571-025-00945-w