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A. K. Belyaev, D. E. Mansyrev, V. A. Polyanskiy, A. M. Polyanskiy, D. A. Tretyakov, Yu. A. Yakovlev

BOUNDARY LAYER OF HYDROGEN CONCENTRATION UNDER PLASTIC DEFORMATION

DOI: 10.17804/2410-9908.2017.4.032-043

A new model of instability of uniform plastic deformation with the formation of Lüders bands on the surface of a material being deformed is experimentally confirmed. It has been found that nonuniform plastic deformations correlate with hydrogen concentration during the testing of metal specimens in the atmosphere at room temperature. The presence of additional pores and microcracks formed as a result of plastic deformation is the cause of the correlation between plastic deformations and hydrogen concentrations in aluminum alloys. The effect of the boundary layer in the distribution of hydrogen concentrations has been detected. It reflects the fact that all changes associated with mechanical and thermo-mechanical loading are localized in a thin boundary layer at the surface of a metal specimen. The wave approach to the analysis of the continuum equations and the model of the boundary layer of a bicontinuous medium containing hydrogen are used to describe the observed phenomena. The constructed model makes it possible to describe the development of plastic deformation as a wave process in the boundary layer of a bicontinuous medium.

Keywords: plastic deformation, Lüders bands, dissolved hydrogen, boundary-layer model, wave approach

Bibliography:

  1. Von Gerstner F.A. Ueber die Festigkeit der Körper. Annalen der Physik, 1832, vol. 102, iss. 10, pp. 269–279. DOI: 10.1002/andp.18321021005
  2. Savart F. Recherches sur les vibrations longitudinales. Ann. Chim. Phys., 1837, vol. 65, pp. 337–402.
  3. Portevin A., Le Chatelier F. Sur unphenomene observe lorsdel’essai de traction d’alliagesencours de transformation. Compt. Rend. Acad. Sci., Paris, 1923, vol. 176, pp. 507–510.
  4. Penning P. Mathematics of the Portevin-Le Chatelier effect. Acta Metallurgica, 1972, vol. 20, no. 10, pp. 1169–1175. DOI: 10.1016/0001-6160(72)90165-4
  5. Lebyodkin M., Brechetz Y., Estrin Y., Kubin L. Statistical behaviour and strain localization patterns in the Portevin-Le Chatelier effect. Acta Materialia, 1996, vol. 44, no. 11, pp. 4531–4541. DOI: 10.1016/1359-6454(96)00076-6
  6. McCormiсk P.G. A model for the Portevin-Le Chatelier effect in substitutional alloys. Acta Metallurgica, 1972, vol. 20, no. 3, pp. 351–354. DOI: 10.1016/0001-6160(72)90028-4
  7. Kalk A., Nortmann A., Schwink C. Dynamic strain ageing and the boundaries of stable plastic deformation in Cu-Mn single crystals. Philosophical Magazine A, 1995, vol. 72, no. 5, pp. 1239–1259. DOI: 10.1080/01418619508236253.
  8. Leoni F., Zapperi S. Dislocation mutual interactions mediated by mobile impurities and the conditions for plastic instabilities. Physical Review E, 2014, vol. 89, no. 2, pp. 022403. DOI: 10.1103/PhysRevE.89.022403
  9. Kudinova N.R., Polyanskiy V.A., Polyanskiy A.M., Yakovlev Yu.A. Contribution of Surface Tension Energy during Plastic Deformation of Nanomaterials. Doklady Physics, 2016, vol. 61, no. 10, pp. 514–516. DOI: 10.1134/S1028335816100104
  10. Phillips A., Brick R.M. Effect of Quenching Strains on Lattice Parameter and Hardness Values of High Purity Aluminum-copper Alloys. Metals Technol., Tech. Paper., 1934, vol. 563, pp. 94–112.
  11. Grishchenko A.I., Modestov V.S., Polyanskiy V.A., Tretyakov D.A., Shtukin L.V. Experimental investigation of the acoustic anisotropy field in the sample with a stress concentrator. St. Petersburg Polytechnical University Journal: Physics and Mathematics, 2017, vol. 3, iss. 1, pp. 77–82. DOI: 10.1016/j.spjpm.2017.02.005
  12. Belyaev A.K., Polyanskiy V.A., Lobachev A.M., Modestov V.S., Semenov A.S., Grishchenko A.I., Yakovlev Y.A., Shtukin L.V., Tretyakov D.A. Propagation of sound waves in stressed elasto-plastic material. In: Days on Diffraction 2016: Proceedings of the International Conference, St. Petersburg, 2016, pp. 56–61. DOI: 10.1109/DD.2016.7756813
  13. 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., 2016, vol. 227, pp. 1515–1518. DOI: 10.1007/s00707-015-1505-1
  14. Belyaev A.K., Polyanskiy V.A., Grishchenko A.I., Lobachev A.M., Mansyrev D.I., Modestov V.S., Pivkov A.V., Semenov A.S., Shtukin L.V., Tretyakov D.A., Yakovlev Yu.A. Application of the acoustic anisotropy approach for technical diagnostics of structures with large plastic deformations. In: AIP Conference Proceedings, AIP Publishing, 2016, vol. 1785, no. 1, pp. 030004. DOI: 10.1063/1.4967025
  15. Polyanskiy V.A., Belyaev A.K., Arseniev D.G., Yakovlev Yu.A., Polyanskiy A.M., Stoschka M. Measurement of dissolved hydrogen distributions after ultrasonic peening of heataffected zone of welded joint. AIP Conference Proceedings, AIP Publishing, 2016, vol. 1785, no. 1, pp. 030022-1–030022-4. DOI: 10.1063/1.4967043
  16. Belyaev A.K., Polyanskiy A.M., Polyanskiy V.A., Sommitsch Ch., Yakovlev Yu.A. Multichannel diffusion vs TDS model on example of energy spectra of bound hydrogen in 34CrNiMo6 steel after a typical heat treatment. International Journal of Hydrogen Energy, 2016, vol. 41, iss. 20, pp. 8627–8634. DOI: 10.1016/j.ijhydene.2016.03.198
  17. Belyaev A.K., Lobachev A.M., Modestov V.S., Pivkov A.V., Polyanskii V.A., Semenov A.S., Tret’yakov D.A., Shtukin L.V. Estimating the plastic strain with the use of acoustic anisotropy. Mechanics of Solids, 2016, vol. 51, iss. 5, pp. 606–611. DOI: 10.3103/S0025654416050149
  18. Hirao M., Pao Y.H. Dependence of acoustoelastic birefringence on plastic strains in a beam. The Journal of the Acoustical Society of America, 1985, vol. 77, no. 5, pp. 1659–1664. DOI: 10.1121/1.391964
  19. Pao Y.H. Theory of acoustoelasticity and acoustoplasticity. In: Solid mechanics research for quantitative non-destructive evaluation, Springer, Netherlands, 1987, pp. 257–273
  20. Pao Y.H., Wu T.T., Gamer U. Acoustoelastic Birefringences in Plastically Deformed Solids: Part I. Theory. Journal of Applied Mechanics, 1991, vol. 58, no. 1, pp. 11–17. DOI: 10.1115/1.2897137
  21. Alekseeva E.L., Alhimenko A.A., Belyaev A.K., Lobachev A.M., Polyanskiy V.A., Rostovykh G.N., Tretyakov D.A., Shtukin L.V., Yakovlev Y.A. Evaluation of stress-strain state and cracking of weatherproof structural steel by acoustoelasticity. Construction of Unique Buildings and Structures, 2016, vol. 12, pp. 33–44. (In Russian). DOI: 10.18720/CUBS.51.3
  22. NACE Standard TM0284–2003. Test Method. Evaluation of Pipeline and Pressure Vessel Steels for Resistance to Hydrogen-Induced Cracking.
  23. Andronov D.Yu., Arseniev D.G., Polyanskiy A.M., Polyanskiy V.A., Yakovlev Yu.A. Application of multichannel diffusion model to analysis of hydrogen measurements in solid. International. Journal of Hydrogen Energy, 2017, vol. 42, iss. 1, pp. 699–710. DOI: 10.1016/j.ijhydene.2016.10.126
  24. Polyanskiy A.M., Polyanskiy V.A., Yakovlev Yu.A. Experimental determination of parameters of multichannel hydrogen diffusion in solid probe. International Journal of Hydrogen Energy, 2014, vol. 39, iss. 30, pp. 17381–17390. DOI: 10.1016/j.ijhydene.2014.07.080
  25. GOST 21132.1–98. Alyuminiy i splavy alyuminievyye. Metod opredeleniya vodoroda v tverdom metalle vakuum-nagrevom [Aluminum and Aluminum Alloys. Methods for the Determination of Hydrogen in Solid Metal by Vacuum Heating]. (In Russian).
  26. Indeitsev D., Semenov В. About a model of structural-phase transformations under hydrogen influence. Acta Mechanica, 2008, vol. 195, pp. 295304. DOI: 10.1007/s00707-007-0568-z
  27. Belyaev A.K., Kudinova N.R., Polyanskiy V.A., Yakovlev Yu.A. The description of deformation and destruction of materials containing hydrogen by means of rheological model. St. Petersburg Polytechnical University Journal: Physics and Mathematics, 2015, vol. 3, pp. 57–65. DOI: 10.5862/JPM.225.14
  28. Gorsky W.S. Theorie des elastichen Nachwirkung in ungeordneten Mischkristallen (elastische Narchwirkung zweiter Art). Phys. Zeitschrift der Sowjetunion, 1935, vol. 8, pp. 457–471.

А. К. Беляев, Д. Э. Мансырев, В. А. Полянский, А. М. Полянский, Д. А. Третьяков, Ю. А. Яковлев

ПОГРАНИЧНЫЙ СЛОЙ КОНЦЕНТРАЦИИ ВОДОРОДА ПРИ ПЛАСТИЧЕСКОЙ ДЕФОРМАЦИИ

В статье проведено экспериментальное обоснование новой модели потери устойчивости равномерной пластической деформации, приводящей к появлению полос Людерса на поверхности деформируемого металла. Установлено, что при испытаниях металлических образцов в атмосфере при комнатной температуре неравномерные пластические деформации коррелированны с концентрацией водорода. В алюминиевых сплавах такая корреляция означает наличие дополнительных пор и микротрещин, возникших в результате пластической деформации. Обнаружен эффект пограничного слоя в распределении концентраций водорода, когда все изменения, связанные с механическим и термомеханическим нагружением, локализованы в тонком пограничном слое у поверхности металлической детали. Для описания обнаруженных явлений использована модель пограничного слоя двухконтинуальной сплошной среды, содержащей водород и волновой подход к анализу уравнений сплошной среды. Построенная модель позволяет описать развитие пластической деформации, как волновой процесс в пограничном слое двухконтинуальной сплошной среды.

Благодарности: Исследование выполнено при поддержке РФФИ, проекты No. 15-08-03112-a и 17-08-00783-a

Ключевые слова: пластическая деформация, полосы Людерса, растворенный водород, модель пограничного слоя, волновой подход

Библиография:

  1. Von Gerstner F. A. Ueber die Festigkeit der Körper // Annalen der Physik. – 1832. – Vol. 102, iss. 10. – P. 269–279. – DOI: 10.1002/andp.18321021005
  2. Savart F. Recherches sur les vibrations longitudinales // Ann. Chim. Phys. – 1837. – Vol. 65. – P. 337–402.
  3. Portevin A., Le Chatelier F. Sur un phenomene observe lors del’essai de traction d’alliages en cours de transformation // Compt. Rend. Acad. Sci. – Paris. – 1923. – Vol. 176. – P. 507–510.
  4. Penning P. Mathematics of the Portevin-Le Chatelier effect // Acta Metallurgica. – 1972. – Vol. 20, no. 10. – P. 1169–1175. – DOI: 10.1016/0001-6160(72)90165-4
  5. Lebyodkin M., Brechetz Y., Estrin Y., Kubin L. Statistical behaviour and strain localization patterns in the Portevin-Le Chatelier effect // Acta materialia. – 1996. – Vol. 44, no. 11. – P. 4531– 4541. – DOI: 10.1016/1359-6454(96)00076-6
  6. McCormiсk P. G. A model for the Portevin-Le Chatelier effect in substitutional alloys // Acta Metallurgica. – 1972. – Vol. 20, no. 3. – P. 351–354. – DOI: 10.1016/0001-6160(72)90028-4
  7. Kalk A., Nortmann A., Schwink C. Dynamic strain ageing and the boundaries of stable plastic deformation in Cu-Mn single crystals // Philosophical Magazine A. – 1995. – Vol. 72, no. 5. – P. 1239–1259. – DOI: 10.1080/01418619508236253
  8. Leoni F., Zapperi S. Dislocation mutual interactions mediated by mobile impurities and the conditions for plastic instabilities // Physical Review E. – 2014. – Vol. 89, no. 2. – P. 022403. – DOI: 10.1103/PhysRevE.89.022403
  9. Contribution of Surface Tension Energy during Plastic Deformation of Nanomaterials / N. R. Kudinova, V. A. Polyanskiy, A. M. Polyanskiy, Yu. A. Yakovlev // Doklady Physics. – 2016. – Vol. 61, no. 10. – P. 514–516. – DOI: 10.1134/S1028335816100104
  10. Phillips A., Brick R. M. Effect of Quenching Strains on Lattice Parameter and Hardness Values of High Purity Aluminum-copper Alloys // Metals Technol., Tech. Paper. – 1934. Vol. 563. – P. 94–112.
  11. Experimental investigation of the acoustic anisotropy field in the sample with a stress concentrator / A. I. Grishchenko, V. S. Modestov, V. A. Polyanskiy, D. A. Tretyakov, L. V. Shtukin // St. Petersburg Polytechnical University Journal: Physics and Mathematics. – 2017. – Vol. 3, iss. 1. – P. 77–82. – DOI: 10.1016/j.spjpm.2017.02.005
  12. Propagation of sound waves in stressed elasto-plastic material / A. K. Belyaev, V. A. Polyanskiy, A. M. Lobachev, V. S. Modestov, A. S. Semenov, A. I. Grishchenko, Y. A. Yakovlev, L. V. Shtukin, D. A. Tretyakov // Proceedings of the International Conference: Days on Diffraction 2016. – St. Petersburg, 2016. – P. 56–61. – DOI: 10.1109/DD.2016.7756813
  13. 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. – 2016. – Vol. 227. – P. 1515–1518. – DOI: 10.1007/s00707-015-1505-1
  14. Application of the acoustic anisotropy approach for technical diagnostics of structures with large plastic deformations / A. K. Belyaev, V. A. Polyanskiy, A. I. Grishchenko, A. M. Lobachev, D. I. Mansyrev, V. S. Modestov, A. V. Pivkov, A. S. Semenov, L. V. Shtukin, D. A. Tretyakov, Yu. A. Yakovlev // AIP Conference Proceedings. – AIP Publishing, 2016. – Vol. 1785, no. 1. – P. 030004. – DOI:10.1063/1.4967025
  15. Measurement of dissolved hydrogen distributions after ultrasonic peening of heataffected zone of welded joint / V. A. Polyanskiy, A. K. Belyaev, D. G. Arseniev, Yu. A. Yakovlev, A. M. Polyanskiy, M. Stoschka // AIP Conference Proceedings. – AIP Publishing, 2016. – Vol. 1785, no. 1. – P. 030022-1–030022-4. – DOI: 10.1063/1.4967043
  16. Multichannel diffusion vs TDS model on example of energy spectra of bound hydrogen in 34CrNiMo6 steel after a typical heat treatment / A. K. Belyaev, A. M. Polyanskiy, V. A. Polyanskiy, Ch. Sommitsch, Yu. A. Yakovlev // International Journal of Hydrogen Energy. – 2016. – Vol. 41, iss. 20. – P. 8627–8634. – DOI: 10.1016/j.ijhydene.2016.03.198
  17. Estimating the plastic strain with the use of acoustic anisotropy / A. K. Belyaev, A. M. Lobachev, V. S. Modestov, A. V. Pivkov, V. A. Polyanskii, A. S. Semenov, D. A. Tret’yakov, L. V. Shtukin // Mechanics of Solids. – 2016. – Vol. 51, iss. 5. – P. 606–611. – DOI: 10.3103/S0025654416050149
  18. Hirao M., Pao Y. H. Dependence of acoustoelastic birefringence on plastic strains in a beam // The Journal of the Acoustical Society of America. – 1985. – Vol. 77, no. 5. – P. 1659–1664. – DOI: 10.1121/1.391964
  19. Pao Y. H. Theory of acoustoelasticity and acoustoplasticity // Solid mechanics research for quantitative non-destructive evaluation. – Netherlands : Springer, 1987. – P. 257–273.
  20. Pao Y. H., Wu T. T., Gamer U. Acoustoelastic Birefringences in Plastically Deformed Solids: Part I - Theory // Journal of Applied Mechanics. – 1991. – Vol. 58, no. 1. – P. 11–17. – DOI: 10.1115/1.2897137
  21. Evaluation of stress-strain state and cracking of weatherproof structural steel by acoustoelasticity / E. L. Alekseeva, A. A. Alhimenko, A. K. Belyaev, A. M. Lobachev, V. A. Polyanskiy, G. N. Rostovykh, D. A. Tretyakov, L. V. Shtukin, Y. A. Yakovlev // Construction of Unique Buildings and Structures. – 2016. – Vol. 12. – P. 33-44. – DOI: 10.18720/CUBS.51.3
  22. NACE Standard TM0284-2003. Test Method. Evaluation of Pipeline and Pressure Vessel Steels for Resistance to Hydrogen-Induced Cracking.
  23. Application of multichannel diffusion model to analysis of hydrogen measurements in solid / D. Yu. Andronov., D. G. Arseniev, A. M. Polyanskiy, V. A. Polyanskiy, Yu. A. Yakovlev // International Journal of Hydrogen Energy. – 2017. – Vol. 42, iss. 1. – P. 699–710. – DOI: 10.1016/j.ijhydene.2016.10.126
  24. Polyanskiy A. M., Polyanskiy V. A., Yakovlev Yu. A. Experimental determination of parameters of multichannel hydrogen diffusion in solid probe// International Journal of Hydrogen Energy. – 2014. – Vol. 39, iss. 30. – P. 17381–17390. – DOI: 10.1016/j.ijhydene.2014.07.080
  25. GOST 21132.1-98. Aluminium and aluminium alloys. Methods for determination of hydrogen in solid metal by vacuum hot extraction.
  26. Indeitsev D., Semenov В. About a model of structural-phase transformations under hydrogen influence // Acta Mechanica. – 2008. – Vol. 195. – P. 295–304. – DOI: 10.1007/s00707-007-0568-z
  27. The description of deformation and destruction of materials containing hydrogen by means of rheological model / A. K. Belyaev, N. R. Kudinova, V. A. Polyanskiy, Yu. A. Yakovlev // St. Petersburg Polytechnical University Journal. Physics and Mathematics. – 2015. – Vol. 3. – P. 57–65. – DOI: 10.5862/JPM.225.14
  28. Gorsky W. S. Theorie des elastichen Nachwirkung in ungeordneten Mischkristallen (elastische Narchwirkung zweiter Art) // Phys. Zeitschrift der Sowjetunion. – 1935. – Vol. 8. – P. 457–471.
 
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Библиографическая ссылка на статью

Boundary Layer of Hydrogen Concentration under Plastic Deformation / A. K. Belyaev, D. E. Mansyrev, V. A. Polyanskiy, A. M. Polyanskiy, D. A. Tretyakov, Yu. A. Yakovlev // Diagnostics, Resource and Mechanics of materials and structures. - 2017. - Iss. 4. - P. 32-43. -
DOI: 10.17804/2410-9908.2017.4.032-043. -
URL: http://dream-journal.org/issues/content/article_167.html
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