Skip to main content
Erschienen in: Continuum Mechanics and Thermodynamics 4/2021

15.10.2020 | Original Article

Nonlinear hybrid continuum–discrete dynamic model of influence of hydrogen concentration on strength of materials

verfasst von: A. V. Porubov, A. K. Belyaev, V. A. Polyanskiy

Erschienen in: Continuum Mechanics and Thermodynamics | Ausgabe 4/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

A new nonlinear lattice model for an influence of the hydrogen concentration on the elastic constants of the lattice model of a material is developed. A weakly nonlinear long-wavelength continuum model is considered, and a model nonlinear equation for the dynamics of concentration of hydrogen is obtained asymptotically. The model predicts a decrease in the stiffness coefficient as well as a light local moving increase due to the localized nonlinear concentration wave propagation.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Troiano, A.R.: The role of hydrogen and other interstitials in the mechanical behavior of metals. Trans. ASM. 52, 54–80 (1960) Troiano, A.R.: The role of hydrogen and other interstitials in the mechanical behavior of metals. Trans. ASM. 52, 54–80 (1960)
2.
Zurück zum Zitat Oriani, R.A.: A mechanistic theory of hydrogen embrittlement of steels. Berichte der Bunsengesellschaft für physikalische Chemie 76, 848–857 (1972) Oriani, R.A.: A mechanistic theory of hydrogen embrittlement of steels. Berichte der Bunsengesellschaft für physikalische Chemie 76, 848–857 (1972)
3.
Zurück zum Zitat Jemblie, L., Olden, V., Akselsen, O.M.: A review of cohesive zone modelling as an approach for numerically assessing hydrogen embrittlement of steel structures. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 375, 20160411 (2017)ADSCrossRef Jemblie, L., Olden, V., Akselsen, O.M.: A review of cohesive zone modelling as an approach for numerically assessing hydrogen embrittlement of steel structures. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 375, 20160411 (2017)ADSCrossRef
4.
Zurück zum Zitat Birnbaum, H.K., Sofronis, P.: Hydrogen-enhanced localized plasticity - a mechanism for hydrogen-related fracture. Mater. Sci. Eng., A 176, 191–202 (1994)CrossRef Birnbaum, H.K., Sofronis, P.: Hydrogen-enhanced localized plasticity - a mechanism for hydrogen-related fracture. Mater. Sci. Eng., A 176, 191–202 (1994)CrossRef
5.
Zurück zum Zitat Sofronis, P., Birnbaum, H.K.: Mechanics of the hydrogen-dislocation-impurity interactions I. Increasing shear modulus. J. Mech. Phys. Solid. 43, 49–90 (1995)ADSCrossRef Sofronis, P., Birnbaum, H.K.: Mechanics of the hydrogen-dislocation-impurity interactions I. Increasing shear modulus. J. Mech. Phys. Solid. 43, 49–90 (1995)ADSCrossRef
6.
Zurück zum Zitat Lynch, S.: Hydrogen embrittlement phenomena and mechanisms. Corros. Rev. 30, 105–123 (2012) Lynch, S.: Hydrogen embrittlement phenomena and mechanisms. Corros. Rev. 30, 105–123 (2012)
7.
Zurück zum Zitat Djukic, M.B., et al.: The synergistic action and interplay of hydrogen embrittlement mechanisms in steels and iron: localized plasticity and decohesion. Eng. Fract. Mech. 216, 106528 (2019)CrossRef Djukic, M.B., et al.: The synergistic action and interplay of hydrogen embrittlement mechanisms in steels and iron: localized plasticity and decohesion. Eng. Fract. Mech. 216, 106528 (2019)CrossRef
8.
Zurück zum Zitat Sofronis, P., Liang, Y., Aravas, N.: Hydrogen induced shear localization of the plastic flow in metals and alloys. Eur. J. Mech. A. Solids 20, 857–872 (2001)CrossRef Sofronis, P., Liang, Y., Aravas, N.: Hydrogen induced shear localization of the plastic flow in metals and alloys. Eur. J. Mech. A. Solids 20, 857–872 (2001)CrossRef
9.
Zurück zum Zitat Olden, V., Thaulow, C., Johnsen, R.: Modelling of hydrogen diffusion and hydrogen induced cracking in supermartensitic and duplex stainless steels. Mater. Des. 29, 1934–1948 (2008)CrossRef Olden, V., Thaulow, C., Johnsen, R.: Modelling of hydrogen diffusion and hydrogen induced cracking in supermartensitic and duplex stainless steels. Mater. Des. 29, 1934–1948 (2008)CrossRef
10.
Zurück zum Zitat Belyaev, A.K., et al.: The description of deformation and destruction of materials containing hydrogen by means of rheological model. St. Petersburg Polytechn. Univ. J. Phys. Math. 1, 305–314 (2015) Belyaev, A.K., et al.: The description of deformation and destruction of materials containing hydrogen by means of rheological model. St. Petersburg Polytechn. Univ. J. Phys. Math. 1, 305–314 (2015)
11.
Zurück zum Zitat Belyaev, A.K., et al.: Surface effect of the waves of plastic deformation and hydrogen distribution in metals. In: Proceedings of the International Conference Days on Diffraction 2017, IEEE. pp. 45–50 (2017) Belyaev, A.K., et al.: Surface effect of the waves of plastic deformation and hydrogen distribution in metals. In: Proceedings of the International Conference Days on Diffraction 2017, IEEE. pp. 45–50 (2017)
12.
Zurück zum Zitat Belyaev, A.K., Blekhman, I.I., Polyanskiy, V.A.: Equation for the evolution of trapped hydrogen in an elastic rod subjected to high-frequency harmonic excitation. Acta Mech. 227, 1515–1518 (2016)MathSciNetCrossRef Belyaev, A.K., Blekhman, I.I., Polyanskiy, V.A.: Equation for the evolution of trapped hydrogen in an elastic rod subjected to high-frequency harmonic excitation. Acta Mech. 227, 1515–1518 (2016)MathSciNetCrossRef
13.
Zurück zum Zitat Zhang, Z., Obasi, G., Morana, R., Preuss, M.: Hydrogen assisted crack initiation and propagation in a nickel-based superalloy. Acta Mater. 113, 272–283 (2016)ADSCrossRef Zhang, Z., Obasi, G., Morana, R., Preuss, M.: Hydrogen assisted crack initiation and propagation in a nickel-based superalloy. Acta Mater. 113, 272–283 (2016)ADSCrossRef
14.
Zurück zum Zitat Li, H.F., Wang, S.G., Zhang, P., Qu, R.T., Zhang, Z.F.: Crack propagation mechanisms of AISI 4340 steels with different strength and toughness. Mater. Sci. Eng. A 729, 130–140 (2018)CrossRef Li, H.F., Wang, S.G., Zhang, P., Qu, R.T., Zhang, Z.F.: Crack propagation mechanisms of AISI 4340 steels with different strength and toughness. Mater. Sci. Eng. A 729, 130–140 (2018)CrossRef
15.
Zurück zum Zitat Bai, P.P., Zhou, J., Luo, B.W., Zheng, S.Q., Wang, P.Y., Tian, Y.: Hydrogen embrittlement of \(X80\) pipeline steel in\( H_2 S\) environment: effect of hydrogen charging time, hydrogen-trapped state and hydrogen charging-releasing-recharging cycles. Int. J. Minerals Metall. Mater. 27(1), 63–73 (2020)ADSCrossRef Bai, P.P., Zhou, J., Luo, B.W., Zheng, S.Q., Wang, P.Y., Tian, Y.: Hydrogen embrittlement of \(X80\) pipeline steel in\( H_2 S\) environment: effect of hydrogen charging time, hydrogen-trapped state and hydrogen charging-releasing-recharging cycles. Int. J. Minerals Metall. Mater. 27(1), 63–73 (2020)ADSCrossRef
16.
Zurück zum Zitat Taha, A., Sofronis, P.: A micromechanics approach to the study of hydrogen transport and embrittlement. Eng. Fract. Mech. 68(6), 803–837 (2001)CrossRef Taha, A., Sofronis, P.: A micromechanics approach to the study of hydrogen transport and embrittlement. Eng. Fract. Mech. 68(6), 803–837 (2001)CrossRef
17.
Zurück zum Zitat 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)ADSCrossRef 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)ADSCrossRef
18.
Zurück zum Zitat Barrer, O., et al.: Understanding and mitigating hydrogen embrittlement of steels: a review of experimental, modelling and design progress from atomistic to continuum. J. Mater. Sci. 53, 6251–6290 (2018)ADSCrossRef Barrer, O., et al.: Understanding and mitigating hydrogen embrittlement of steels: a review of experimental, modelling and design progress from atomistic to continuum. J. Mater. Sci. 53, 6251–6290 (2018)ADSCrossRef
19.
Zurück zum Zitat Lilin, Lu, et al.: Hydrogen embrittlement and improved resistance of Al addition in twinning-induced plasticity steel: first-principles study. Materials 12, 1341 (2019)ADSCrossRef Lilin, Lu, et al.: Hydrogen embrittlement and improved resistance of Al addition in twinning-induced plasticity steel: first-principles study. Materials 12, 1341 (2019)ADSCrossRef
20.
Zurück zum Zitat Krawczyk, J., Owczarek, A.L., Prellberg, T.: Semi-flexible hydrogen-bonded and non-hydrogen bonded lattice polymers. Phys. A 388, 104–112 (2009)CrossRef Krawczyk, J., Owczarek, A.L., Prellberg, T.: Semi-flexible hydrogen-bonded and non-hydrogen bonded lattice polymers. Phys. A 388, 104–112 (2009)CrossRef
21.
Zurück zum Zitat Fallahmohammadi, E., Bolzoni, F., Lazzari, L.: Measurement of lattice and apparent diffusion coefficient of hydrogen in \(X65\) and \(F22\) pipeline steels. Int. J. Hydrogen Energy 38, 2531–2543 (2013)CrossRef Fallahmohammadi, E., Bolzoni, F., Lazzari, L.: Measurement of lattice and apparent diffusion coefficient of hydrogen in \(X65\) and \(F22\) pipeline steels. Int. J. Hydrogen Energy 38, 2531–2543 (2013)CrossRef
22.
Zurück zum Zitat Mazzolai, F.M., Birnbaum, H.K.: Elastic constants and ultrasonic attenuation of the \(\alpha \)-\(\alpha \)’ phase of the \(Nb-H(D)\) system. I: Results. J. Phys. F Met. Phys. 15, 507–524 (1985)ADSCrossRef Mazzolai, F.M., Birnbaum, H.K.: Elastic constants and ultrasonic attenuation of the \(\alpha \)-\(\alpha \)’ phase of the \(Nb-H(D)\) system. I: Results. J. Phys. F Met. Phys. 15, 507–524 (1985)ADSCrossRef
24.
Zurück zum Zitat Indeitsev, D., Semenov, B.: About a model of structural-phase transformations under hydrogen influence. Acta Mech. 195(1–4), 295–304 (2008)CrossRef Indeitsev, D., Semenov, B.: About a model of structural-phase transformations under hydrogen influence. Acta Mech. 195(1–4), 295–304 (2008)CrossRef
25.
Zurück zum Zitat Porubov, A.V., Belyaev, A.K., Polyanskiy, V.A.: Nonlinear modeling of dynamics of hydrogen concentration in alloys. Commun. Nonlinear Sci. Numer. Simulat. 90, 10540 (2020)MathSciNetCrossRef Porubov, A.V., Belyaev, A.K., Polyanskiy, V.A.: Nonlinear modeling of dynamics of hydrogen concentration in alloys. Commun. Nonlinear Sci. Numer. Simulat. 90, 10540 (2020)MathSciNetCrossRef
26.
Zurück zum Zitat Pyun, S.-I., et al.: Electrochemistry of Insertion Materials for Hydrogen and Lithium, Monographs in Electrochemistry. Springer, Berlin (2012)CrossRef Pyun, S.-I., et al.: Electrochemistry of Insertion Materials for Hydrogen and Lithium, Monographs in Electrochemistry. Springer, Berlin (2012)CrossRef
27.
Zurück zum Zitat Krom, A.H.M., Bakker, A.D.: Hydrogen Trapping Models in Steel. Metall. Mater. Trans. 31B, 1475 (2000)CrossRef Krom, A.H.M., Bakker, A.D.: Hydrogen Trapping Models in Steel. Metall. Mater. Trans. 31B, 1475 (2000)CrossRef
28.
Zurück zum Zitat Mazzolai, F.M., Birnbaum, H.K.: Elastic constants and ultrasonic attenuation of the \(a-a^{\prime }\) phase of the Nb-H(D) system 11. : interpretation of results. J. Phys. F: Met. Phys. 15, 525–542 (1985)ADSCrossRef Mazzolai, F.M., Birnbaum, H.K.: Elastic constants and ultrasonic attenuation of the \(a-a^{\prime }\) phase of the Nb-H(D) system 11. : interpretation of results. J. Phys. F: Met. Phys. 15, 525–542 (1985)ADSCrossRef
29.
Zurück zum Zitat Mazzolai, G.: Recent progresses in the understanding of the elastic and anelastic properties of H-free, H-doped and H-contaminated NiTi based alloys. AIP Adv. 1, 040701 (2011)ADSCrossRef Mazzolai, G.: Recent progresses in the understanding of the elastic and anelastic properties of H-free, H-doped and H-contaminated NiTi based alloys. AIP Adv. 1, 040701 (2011)ADSCrossRef
30.
Zurück zum Zitat Coluzzi, B., Costa, C., Marzola, P., Mazzolai, F.M.: Elastic constants of a \(Pd_{85}Pt_{15}\) single crystal containing hydrogen. J. Phys. Condens. Matter 1, 6335–6342 (1989)ADSCrossRef Coluzzi, B., Costa, C., Marzola, P., Mazzolai, F.M.: Elastic constants of a \(Pd_{85}Pt_{15}\) single crystal containing hydrogen. J. Phys. Condens. Matter 1, 6335–6342 (1989)ADSCrossRef
31.
Zurück zum Zitat Mirzoev, FKh, Panchenko, V.Ya., Shelepin, L.A.: X’Laser Control of Processes in Solids. Physics- Uspekhi 39, 1–29 (1996)ADSCrossRef Mirzoev, FKh, Panchenko, V.Ya., Shelepin, L.A.: X’Laser Control of Processes in Solids. Physics- Uspekhi 39, 1–29 (1996)ADSCrossRef
32.
Zurück zum Zitat Mirzoev, FKh, Shelepin, L.A.: Nonlinear strain waves and densities of defects in metal plates induced by external energy fluxes’. Tech. Phys. 46, 952–955 (2001)CrossRef Mirzoev, FKh, Shelepin, L.A.: Nonlinear strain waves and densities of defects in metal plates induced by external energy fluxes’. Tech. Phys. 46, 952–955 (2001)CrossRef
33.
Zurück zum Zitat Ablowitz, M.J., Segur, H.: Solitons and the Inverse Scattering Transform. SIAM, Philadelphia (1981)CrossRef Ablowitz, M.J., Segur, H.: Solitons and the Inverse Scattering Transform. SIAM, Philadelphia (1981)CrossRef
34.
Zurück zum Zitat Ostoja-Starzewski, M.: Lattice models in micromechanics. Appl. Mech. Rev. 55, 35–60 (2002)ADSCrossRef Ostoja-Starzewski, M.: Lattice models in micromechanics. Appl. Mech. Rev. 55, 35–60 (2002)ADSCrossRef
36.
Zurück zum Zitat Porubov, A.V., Krivtsov, A.M., Osokina, A.E.: Two-dimensional waves in extended square lattice. Int. J. Non-Linear Mech. 99, 281–287 (2018)ADSCrossRef Porubov, A.V., Krivtsov, A.M., Osokina, A.E.: Two-dimensional waves in extended square lattice. Int. J. Non-Linear Mech. 99, 281–287 (2018)ADSCrossRef
37.
Zurück zum Zitat Andrianov, I.V., Danishevskyy, V.V., Rogerson, G.: Vibrations of nonlinear elastic lattices: low- and high-frequency dynamic models, internal resonances and modes coupling. Proc. R. Soc. A 476, 20190532 (2020)ADSMathSciNetCrossRef Andrianov, I.V., Danishevskyy, V.V., Rogerson, G.: Vibrations of nonlinear elastic lattices: low- and high-frequency dynamic models, internal resonances and modes coupling. Proc. R. Soc. A 476, 20190532 (2020)ADSMathSciNetCrossRef
38.
Zurück zum Zitat Frolova, K., Polyanskiy, V., Tretyakov, D., Yakovlev, Y.: Identification of zones of local hydrogen embrittlement of metals by the acoustoelastic effect. In: Altenbach, H., Eremeyev, V., Pavlov, I., Porubov, A. (eds.) Nonlinear Wave Dynamics of Materials and Structures. Advanced Structured Materials, vol. 122, pp. 495–503. Springer, Cham (2020) Frolova, K., Polyanskiy, V., Tretyakov, D., Yakovlev, Y.: Identification of zones of local hydrogen embrittlement of metals by the acoustoelastic effect. In: Altenbach, H., Eremeyev, V., Pavlov, I., Porubov, A. (eds.) Nonlinear Wave Dynamics of Materials and Structures. Advanced Structured Materials, vol. 122, pp. 495–503. Springer, Cham (2020)
39.
Zurück zum Zitat Tretyakov, D., Belyaev, A., Polyanskiy, V., Stepanov, A., Yakovlev, Y.: Correlation of acoustoelasticity with hydrogen saturation during destruction. E3S Web Conf. EDP Sci. 121, 01016 (2019)CrossRef Tretyakov, D., Belyaev, A., Polyanskiy, V., Stepanov, A., Yakovlev, Y.: Correlation of acoustoelasticity with hydrogen saturation during destruction. E3S Web Conf. EDP Sci. 121, 01016 (2019)CrossRef
40.
Zurück zum Zitat Tretyakov, D., Belyaev, A., Galyautdinova, A., Polyanskiy, V., Strekalovskaya, D.: Investigation of the corrosion process and destruction of metals by using acoustodamage method. E3S Web Conf. EDP Sci. 121, 01017 (2019)CrossRef Tretyakov, D., Belyaev, A., Galyautdinova, A., Polyanskiy, V., Strekalovskaya, D.: Investigation of the corrosion process and destruction of metals by using acoustodamage method. E3S Web Conf. EDP Sci. 121, 01017 (2019)CrossRef
Metadaten
Titel
Nonlinear hybrid continuum–discrete dynamic model of influence of hydrogen concentration on strength of materials
verfasst von
A. V. Porubov
A. K. Belyaev
V. A. Polyanskiy
Publikationsdatum
15.10.2020
Verlag
Springer Berlin Heidelberg
Erschienen in
Continuum Mechanics and Thermodynamics / Ausgabe 4/2021
Print ISSN: 0935-1175
Elektronische ISSN: 1432-0959
DOI
https://doi.org/10.1007/s00161-020-00936-7

Weitere Artikel der Ausgabe 4/2021

Continuum Mechanics and Thermodynamics 4/2021 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.