Skip to main content

Advertisement

SpringerLink
Log in

Nonlinear dynamics of hydrogen concentration in high-strength and high-entropy alloys

  • Original Article
  • Published:
Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

Abstract

A new nonlinear governing equation is obtained for the dynamics of hydrogen concentration. Numerical solution of the equation allows us to describe evolution of localized disturbance of the hydrogen concentration and the significant influence of nonlinearity on the shape of localized waves of the hydrogen concentration.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alvaro, A., Olden, V., Akselsen, O.M.: 3D cohesive modelling of hydrogen embrittlement in the heat affected zone of an X70 pipeline steel. Int. J. Hydrog. Energy 38(18), 7539–7549 (2013)

    Article  Google Scholar 

  2. Alvaro, A., Olden, V., Akselsen, O.M.: 3D cohesive modelling of hydrogen embrittlement in the heat affected zone of an X70 pipeline steel. Part II. Int. J. Hydrog. Energy 39(7), 3528–3541 (2014)

    Article  Google Scholar 

  3. Andrianov, I., Awrejcewicz, J., Danishevs’kyy, V., Ivankov, A.: Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions. Wiley, Chichester (2014)

    Book  Google Scholar 

  4. Belyaev, A.K., Polyanskiy, A.M., Polyanskiy, V.A., Yakovlev, Y.A.: Parametric instability in cyclic loading as the cause of fracture of hydrogenous materials. Mech. Solids 47(5), 533–537 (2012)

    Article  ADS  Google Scholar 

  5. Birnbaum, H.K., Sofronis, P.: Hydrogen-enhanced localized plasticity: a mechanism for hydrogen-related fracture. Mater. Sci. Eng. A 176(1–2), 191–202 (1994)

    Article  Google Scholar 

  6. Brouwer, R.C., Jong, E.C.J.N., Mul, L.M., Handel, G.: Modelling Hydrogen Induced Crack Growth: Validation by Comparison with Experiment. NACE International, Houston, TX (1995)

    Google Scholar 

  7. Chen, Y.Y., Duval, T., Hung, U.D., Yeh, J.W., Shih, H.C.: Microstructure and electrochemical properties of high entropy alloys—a comparison with type-304 stainless steel. Corros. Sci. 47(9), 2257–2279 (2005)

    Article  Google Scholar 

  8. Delafosse, D., Magnin, T.: Interfaces in stress corrosion cracking: a case study in duplex stainless steels. In: Solid State Phenomena, vol. 59, pp. 221–250. (Trans Tech Publ) (1998)

    Article  Google Scholar 

  9. Gorsky, W.S.: Theorie der elastischen nachwirkung in ungeordneten mischkristallen von CuAu. Physikalische Zeitschrift der Sowjetunion 8, 443–456 (1935)

    Google Scholar 

  10. Grossbeck, M.L., Birnbaum, H.K.: Low temperature hydrogen embrittlement of niobium II—microscopic observations. Acta Metall. 25(2), 135–147 (1977)

    Article  Google Scholar 

  11. Haferkamp, H., Meier, O., Harley, K.: Laser beam welding of new high strength steels for auto body construction. In: Sheet Metal 2007, Key Engineering Materials, vol. 344, pp. 723–730. (Trans Tech Publications) (2007)

    Article  Google Scholar 

  12. Hirth, J.P.: Effects of hydrogen on the properties of iron and steel. Metall. Trans. A 11(6), 861–890 (1980)

    Article  Google Scholar 

  13. Hsu, C.Y., Yeh, J.W., Chen, S.K., Shun, T.T.: Wear resistance and high-temperature compression strength of Fcc CuCoNiCrAl\(_{0.5}\)Fe alloy with boron addition. Metall. Mater. Trans. A 35(5), 1465–1469 (2004)

    Article  Google Scholar 

  14. Huang, P.K., Yeh, J.W., Shun, T.T., Chen, S.K.: Multi-principal-element alloys with improved oxidation and wear resistance for thermal spray coating. Adv. Eng. Mater. 6(1–2), 74–78 (2004)

    Article  Google Scholar 

  15. Ignatenko, A.V., Pokhodnya, I.K., Paltsevich, A.P., Sinyuk, V.S.: Dislocation model of hydrogen-enhanced localizing of plasticity in metals with BCC latttice. Paton Weld. J. 3, 15–19 (2012)

    Google Scholar 

  16. Indeitsev, D.A., Semenov, B.N.: About a model of structural-phase transformations under hydrogen influence. Acta Mech. 195(1), 295–304 (2008)

    Article  Google Scholar 

  17. Koyama, M., Springer, H., Merzlikin, S.V., Tsuzaki, K., Akiyama, E., Raabe, D.: Hydrogen embrittlement associated with strain localization in a precipitation-hardened Fe–Mn–Al–C light weight austenitic steel. Int. J. Hydrog. Energy 39(9), 4634–4646 (2014)

    Article  Google Scholar 

  18. Leeuwen, H.P.V.: The kinetics of hydrogen embrittlement: a quantitative diffusion model. Eng. Fract. Mech. 6(1), 141–161 (1974)

    Article  Google Scholar 

  19. Lynch, S.: Hydrogen embrittlement phenomena and mechanisms. Corros. Rev. 30(3–4), 105–123 (2012)

    Google Scholar 

  20. McVeigh, C., Vernerey, F., Liu, W.K., Moran, B., Olson, G.: An interactive micro-void shear localization mechanism in high strength steels. J. Mech. Phys. Solids 55(2), 225–244 (2007)

    Article  ADS  Google Scholar 

  21. Nagumo, M.: Function of hydrogen in embrittlement of high-strength steels. ISIJ Int. 41(6), 590–598 (2001)

    Article  Google Scholar 

  22. Pan, Y., Guan, W., Wen, M., Zhang, J., Wang, C., Tan, Z.: Hydrogen embrittlement of Pt\(_3\)Zr compound from first-principles. J. Alloys Compd. 585, 549–554 (2014)

    Article  Google Scholar 

  23. Polyanskiy, A.M., Popov-Diumin, D.B., Polyanskiy, V.A.: Determination of hydrogen binding energy in various materials by means of absolute measurements of its concentration in solid probe. In: Veziroglu, T.N., Zaginaichenko, S.Y., Schur, D.V., Baranowski, B., Shpak, A.P., Skorokhod, V.V., Kale, A. (eds.) Hydrogen Materials Science and Chemistry of Carbon Nanomaterials, pp. 681–692. Springer, Dordrecht (2007)

    Chapter  Google Scholar 

  24. Robertson, I.M., Sofronis, P., Nagao, A., Martin, M.L., Wang, S., Gross, D.W., Nygren, K.E.: Hydrogen embrittlement understood. Metall. Mater. Trans. B 46(3), 1085–1103 (2015)

    Article  Google Scholar 

  25. Sofronis, P., Liang, Y., Aravas, N.: Hydrogen induced shear localization of the plastic flow in metals and alloys. Eur. J. Mech. A Solids 20(6), 857–872 (2001)

    Article  Google Scholar 

  26. Taha, A., Sofronis, P.: A micromechanics approach to the study of hydrogen transport and embrittlement. Eng. Fract. Mech. 68(6), 803–837 (2001)

    Article  Google Scholar 

  27. Tasan, C.C., Deng, Y., Pradeep, K.G., Yao, M.J., Springer, H., Raabe, D.: Composition dependence of phase stability, deformation mechanisms, and mechanical properties of the CoCrFeMnNi high-entropy alloy system. JOM 66(10), 1993–2001 (2014)

    Article  Google Scholar 

  28. Tong, C.J., Chen, M.R., Yeh, J.W., Lin, S.J., Chen, S.K., Shun, T.T., Chang, S.Y.: Mechanical performance of the Al\(_x\)CoCrCuFeNi high-entropy alloy system with multiprincipal elements. Metall. Mater. Trans. A 36(5), 1263–1271 (2005)

    Article  Google Scholar 

  29. Traidia, A., Alfano, M., Lubineau, G., Duval, S., Sherik, A.: An effective finite element model for the prediction of hydrogen induced cracking in steel pipelines. Int. J. Hydrog. Energy 37(21), 16214–16230 (2012)

    Article  Google Scholar 

  30. Varias, A.G., Massih, A.R.: Simulation of hydrogen embrittlement in zirconium alloys under stress and temperature gradients. J. Nucl. Mater. 279(2–3), 273–285 (2000)

    Article  ADS  Google Scholar 

  31. Yeh, J.W., Chen, S.K., Lin, S.J., Gan, J.Y., Chin, T.S., Shun, T.T., Tsau, C.H., Chang, S.Y.: Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes. Adv. Eng. Mater. 6(5), 299–303 (2004)

    Article  Google Scholar 

Download references

Acknowledgements

The work was performed in Peter the Great St. Petersburg Polytechnic University (SPbPU) and is supported solely by the Russian Science Foundation (Grant No.18-19-00413).

Author information

Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University (SPbPU), Polytechnicheskaya st., 29, Saint Petersburg, Russia

    A. K. Belyaev, V. A. Polyanskiy & A. V. Porubov

  2. Institute for Problems in Mechanical Engineering, Bolshoy 61, V.O., Saint Petersburg, Russia

    A. K. Belyaev, V. A. Polyanskiy & A. V. Porubov

Authors
  1. A. K. Belyaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. A. Polyanskiy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. V. Porubov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Porubov.

Additional information

Communicated by Victor Eremeyev and Holm Altenbach.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Belyaev, A.K., Polyanskiy, V.A. & Porubov, A.V. Nonlinear dynamics of hydrogen concentration in high-strength and high-entropy alloys. Continuum Mech. Thermodyn. 31, 1785–1794 (2019). https://doi.org/10.1007/s00161-018-0734-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00161-018-0734-7

Keywords

Search

Navigation