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Discussion of fracture paper #34 - The Physics of Hydrogen Embrittlement

ESIS's picture

Hydrogen embrittlement causes problems that probably will become apparent to an increasing extent as hydrogen is taken into general use for energy storage and as a fuel for heating and electricity production. According to Wikipedia, the phenomenon has been known since at least 1875. The subject of this blog 

"The synergistic action and interplay of hydrogen embrittlement mechanisms in steels and iron: Localized plasticity and decohesion", by Milos B. Djukic, Gordana M. Bakic, Vera Sijacki Zeravcic, Aleksandar Sedmak, and Bratislav Rajicic Engineering Fracture Mechanics 216 (2019) 106528, pp. 1-33

is an in-depth and comprehensive review article that deservedly is frequently cited. It deals with the progress made over the past 50 years. For those who want to get into the subject, the paper is an excellent starting point with 243 references and nice descriptions of known mechanisms and methods used for risk assessments. The paper is not open access yet but will be that within a couple of days with courtesy from EFM.

The presumable outdated observations by William Johnson from 1875 are not mentioned in the review article. I assume that not much happened before the second half of the 20th century. Johnson's findings were published in "Proceedings of the Royal Society of London" on New Year's Eve 1875. He conducted measurements of the strength of conventional tensile test specimens. The strength, after bathing the sample in an acid, dropped by up to 20%. As the classically trained experimental physicist Johnson was, he did not stop at strength but also measured the effect of hydrogen on electrical conductivity and on the diffusion rate of the hydrogen. In the latter case, the distribution of hydrogen in the test rod revealed itself as bubbles forming on the fracture surfaces of the test rod. During the test, the rod was dipped to different depths in the acid bath. When the fracture occurred in a part below the surface of the acid bath, the entire cross-section was covered with bubbles from leaking hydrogen and when the fracture occurred at a distance equal to the specimen radius above the bath, only the two thirds closest to the centre of the fracture surface were covered with hydrogen bubbles. The observation gives a wonderful picture of how the diffusion of hydrogen deviates towards the free outer surfaces. Brilliant results with the simple scarce experimental resources of the time.

I traditionally have an inquiry for the authors or any reader regarding something that puzzles me. This time it strikes me that in the review article nothing is mentioned about other affected material properties. I know that the review article focuses on the embrittlement of steel. However, since it is rightly regretted that too little is known to facilitate a formulation of a theory that can provide reliable models for prediction, perhaps observations of other things such as diffusion rates and electrical conductivity may provide more light to the underlying physics. Any suggestions?

All comments, opinions, thoughts regarding the paper, or anything related are encouraged. If you belong to the unfortunate that do not have an iMechanica account, please email me at and I will see what can be done.

Per Ståhle 


Emilio Martínez Pañeda's picture

Dear Per,

Thanks for bringing this to the attention of the iMechanica community, as hydrogen embrittlement is indeed a very interesting topic, both fundamentally challenging and of notable technological importance. Moreover, the problem has very much come to the fore recent years due to the higher susceptibility of high strength alloys and the need to urgently deploy a hydrogen energy infrastructure. 

Milos’ review is a very comprehensive one and, in my opinion, with the right approach (the embrittlement is, at the end of the day, the most important effect). Those new to the discipline are also directed to Gangloff’s chapter [1] or Gangloff and Somerday’s book [2]. In there, other aspects such as diffusivity are also covered. And diffusivity is of course very important to understand rate effects (see, e.g., Fig. 10 in [3]) or the influence of frequency in fatigue (see, e.g., Ref. [4]).

While many questions remain unanswered, I disagree with the statement regarding the lack of "reliable models for prediction". Models capable of quantitatively predicting relevant experimental data such as stress intensity factor threshold and crack growth rates have been presented by several groups, going back to at least the work of Michael Ortiz and co-workers [5]. On our side, we have tried to contribute by developing phase field formulations for hydrogen assisted cracking, which can accommodate any mechanistic interpretation and are currently being used by industry to safely design components for hydrogen storage and transport (see, e.g., [6-8] and Refs. therein). 

Regarding the question on what would be useful to explore to bring light into the underlying physics - I wish I knew!

It was nice seeing you in Madeira for ECF23

Kind regards,

Emilio Martínez-Pañeda

[1] R. P. Gangloff. Gangloff R.P. Hydrogen-assisted cracking. In Milne I., Ritchie R., Karihaloo B. (Eds.), Comprehensive Structural Integrity, Vol.6, Elsevier Science, New York, NY (2003), pp. 31-101
[2] R.P. Gangloff, B.P. Somerday. Gaseous Hydrogen Embrittlement of Materials in Energy Technologies. Woodhead Publishing Limited (2012)
[3] P.K. Kristensen, C.F. Niordson, E. Martínez-Pañeda. A phase field model for elastic-gradient-plastic solids undergoing hydrogen embrittlement. Journal of the Mechanics and Physics of Solids 143, 104093 (2020)
[4] R. Fernández-Sousa, C. Betegón, E. Martínez-Pañeda. Analysis of the influence of microstructural traps on hydrogen assisted fatigue. Acta Materialia 199, 253-263 (2020)
[5] S. Serebrinsky, E. A. Carter, M. Ortiz. A quantum-mechanically informed continuum model of hydrogen embrittlement. J. Mech. Phys. Solids, 52 (2004), pp. 2403-2430
[6] E. Martínez-Pañeda, A. Golahmar, C.F. Niordson. A phase field formulation for hydrogen assisted cracking. Computer Methods in Applied Mechanics and Engineering 342, pp. 742-761 (2018)
[7] P.K. Kristensen, C.F. Niordson, E. Martínez-Pañeda. Applications of phase field fracture in modelling hydrogen assisted failures. Theoretical and Applied Fracture Mechanics 110, 102837 (2020)
[8] A. Golahmar, P.K. Kristensen, C.F. Niordson, E. Martínez-Pañeda. A phase field model for hydrogen-assisted fatigue. International Journal of Fatigue 154, 106521 (2022)

ESIS's picture

Dear Emilio,

Thanks for your interest in the ESIS blog. You are definitely right about the importance of hydrogen embrittlement and the excellent review paper by Milos Djucik et al. 

In the blog, I think I should have put more emphasis on the thoughts forwarded in the paper about the synergy effects of HELP and HEDE, i.e. the hydrogen-enhanced local plasticity and the hydrogen-enhanced decoction mechanisms. Their discussion, mainly based on data and the reasoning that relies on the authors' profound expertise and long involvement in the subject, is very interesting. It opened my eyes. 

Both mechanisms, as I understand it, are connected to the effect that hydrogen has on dislocation mobility and that the hydrogen is driven along the hydrostatic stress gradients. The latter of course implies that the metal expands with increasing hydrogen concentration. 

With the material expansion and the yield stress given as functions of the hydrogen concentration, and the fracture toughness at pure cleavage,  the coupled governing PDEs for hydrogen concentration resp. displacements may be derived and used for both analytical and numerical analyses. The elastic material properties and the diffusion constant for hydrogen I assume are already known.

Regards, Per 

Dear Per,

Thank you for your post about the physics of hydrogen embrittlement and our review paper in the Engineering Fracture Mechanics journal from 2019. We intended to emphasize recent important fundamental and multidisciplinary scientific research in hydrogen embrittlement (HE). These efforts aimed to provide a better understanding of still insufficiently researched physics of hydrogen embrittlement phenomena in metallic materials on different scales, including atomic/nano, meso, and macro scales.  

Thank you for pointing out the synergy effects of HELP and HEDE, i.e. the hydrogen-enhanced local plasticity and the hydrogen-enhanced decohesion mechanisms. It seems that the validity of our HELP+HEDE model, originally proposed for hydrogen embrittlement in steel in 2014/2015 [1], further developed in 2016 [2,3], 2018 [4], and 2020 [5], and finally summarized in this critical review paper from 2019 [6], was recently (2015-2021) comprehensively confirmed through experiments and models in numerous metallic materials. These include different types of steel and iron (see [6], and references therein), nickel, Ni-based alloys, and Al alloys. Another review paper about the current state of the art in understanding the synergistic action of HE mechanisms with an overview of recent experimental and modeling pieces of evidence of the HELP+HEDE model of HE in various metallic alloys is in the preparation.

The HELP+HEDE model for HE defined that the previous HELP mechanism activity is not always necessary for the activation and the observed complete predominance of the HEDE mechanism (“non-HELP mediated decohesion” process activation) at high local/global hydrogen concentrations in steels [1-7]. According to the HELP+HEDE model, the degree and nature of decreases in material’s resistance to the crack propagation (steady-state linear decrease or the sudden drop) in steel are strictly related to the local/global hydrogen concentration in metals. Therefore, the synergistic effects of HE mechanisms are reflected through the corresponding predominance of HELP (at lower hydrogen concentration) or HEDE mechanism (at higher hydrogen concentration after reaching the critical local/global concentration) of hydrogen embrittlement [1-7].

In our recent attempt to provide further progress in understanding the HE mechanisms synergy, we proposed the unified HELP+HEDE model in 2021 [7]. Accordingly, the "local HEDE micro-incidents" (grain boundary decohesion, fissures, and initial IG micro-cracks) as discrete micro-scale incidents, appear at a high local hydrogen concentration, but at still moderate global concentration, lower than the critical [7]. In such a case, the HELP mechanism is still predominant (HELP+HEDE, HELP>HEDE), macroscopically speaking. According to the unified HELP+HEDE model, for the full macro HEDE mechanism manifestation (sharp drop in macro-mechanical properties and crack propagation resistance) and its dominance (HELP+HEDE, HEDE>>HELP), the necessary prerequisite is “the macro-volume effects” of HEDE [7]. This means the appearance and accumulation of a large enough number of local HEDE micro incidents in a small volume. The new "local HEDE micro-incidents" concept [7] at the local hydrogen concentration above the critical one, tries to bridge the gap between the various scales (macro, micro-meso, and nano-atomic) in the understanding of the physics of HE [5]. It is important to make distinctions between the critical hydrogen concentration as (i) a global (total)/average hydrogen concentration in the specimen; (ii) local hydrogen concentration at the trap site that causes cracking; or (ii) local hydrogen concentration at a crack tip or a notch root. In all cases, the critical hydrogen concentration depends strongly on the material system, experimental conditions, as well as stress/strain level [8-10].

Regarding the effect of hydrogen on dislocation mobility, the enhanced dislocation mobility, i.e. HELP mechanism activity was detected over a wide range of hydrogen concentrations. The activity of the HELP mechanism or other possible "plasticity-mediated" HE mechanisms can become minor, or negligible with the increase of hydrogen content in the steel. Especially, when the hydrogen content approaches the critical hydrogen concentration or when it is much higher [1,6,7]. The opposite hydrogen-dislocation interaction, i.e. hydrogen-impeded localized plasticity due to the hydrogen-impeded mobility of dislocations, could also lead to the HEDE initiation. In that case, the HEDE can be treated as an independent HE process and predominant (HELP+HEDE, HEDE>>HELP) upon reaching the local critical hydrogen concentration at the crack tip fracture process zone, according to the HELP+HEDE model for HE [1,6,7].

Dear Emilio,

Thank you for your kind words and for pointing out the recent "reliable models for HE prediction" including your important contributions to the development of phase field formulations for hydrogen-assisted cracking. I wish to point out another recent and important HE modeling paper published in Scripta Materialia [11] by Prof. Zhang's group and co-authors from NTNU, Norway. In this paper, a predictive model unifying both HELP and HEDE effects according to the HELP+HEDE model is developed. It is based on the hydrogen-Gurson type model (H-CGM) to account for HELP (hydrogen enhanced plasticity)-promoted void evolution and the newly developed unified H-CGM model (H-CGM+) to allow the decohesion threshold to be degraded by hydrogen, taking into account also the synergistic effects of HEDE mechanism (HELP+HEDE) [11]. 

It was my pleasure to see you both, dear Par and Emilio, during ECF23 in Portugal. Thank you very much for the excellent discussion regarding the fundamental understanding of the physics of the hydrogen embrittlement phenomena.

Kind regards,

Milos B. Djukic

[1] Djukic M.B., Sijacki Zeravcic V., Bakic G., Sedmak A., Rajicic B.: Hydrogen damage of steels: A case study and hydrogen embrittlement model, Engineering Failure Analysis, Vol. 58, 2015, pp. 485-498, 

[2] Djukic M.B., Bakic G.M., Sijacki Zeravcic V., Sedmak A., Rajicic B.: Hydrogen Embrittlement of Industrial Components: Prediction, Prevention, and Models, Corrosion, Vol. 72, No. 7, 2016, pp. 943-961,

[3] Djukic M., Bakic G., Sijacki Zeravcic V., Maslarevic A., Rajicic B., Sedmak A., Mitrovic R., Miskovic Z.: Towards a Unified and Practical Industrial Model for Prediction of Hydrogen Embrittlement and Damage in Steels, Procedia Structural Integrity, Vol. 2, 2016, pp. 604-611,

[4] Popov B.N., Lee J-W., Djukic M.B.: Chapter 7 - Hydrogen Permeation and Hydrogen Induced Cracking, in Handbook of Environmental Degradation of Materials, Third Edition, edited by Myer Kutz, 2018, William Andrew, Elsevier, 2018, pp. 133-162,

[5] Wasim M., Djukic M.B.: Hydrogen embrittlement of low carbon structural steel at macro-, micro- and nano-levels, International Journal of Hydrogen Energy, Vol.. 45, Issue 3, 2020, pp. 2145-2156,

[6] Djukic M.B., Bakic G., Sijacki Zeravcic V., Sedmak A., Rajicic B.: The synergistic action and interplay of hydrogen embrittlement mechanisms in steels and iron: Localized plasticity and decohesion, Engineering Fracture Mechanics, Vol. 216, 2019, p. 106528,

[7] Wasim M., Djukic M.B., Ngo T.D.: Influence of hydrogen-enhanced plasticity and decohesion mechanisms of hydrogen embrittlement on the fracture resistance of steel, Engineering Failure Analysis, Vol. 123, 2021, p. 105312,

[8] Dadfarnia M., Nagao A., Wang S., Martin M.L., Somerday B.P., Sofronis P.: Recent advances on hydrogen embrittlement of structural materials. Int. J. Fracture, 2015;196(1-2):223-43.

[9] Turnbull A.: Perspectives on hydrogen uptake, diffusion and trapping. Int. J. Hydrogen Ene., 2015;40(47):16961-70.

[10] Wang M., Akiyama E., Tsuzaki K.: Determination of the critical hydrogen concentration for delayed fracture of high strength steel by constant load test and numerical calculation. Corros. Sci., 2006;48(8):2189-2202.

[11] Lin M., Yu H., Ding Y., Wang G., Olden V., Alvaro A., He J., Zhang Z.: A predictive model unifying hydrogen enhanced plasticity and decohesion. Scripta Mater., 2022; 215:114707.

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