Гидродинамическое моделирование индуцированных лазером ударных волн в алюминии в цилиндрически-симметричной постановке

Гидродинамическое моделирование индуцированных лазером ударных волн в алюминии в цилиндрически-симметричной постановке

Шепелев В. В.
Сибирский журнал индустриальной математики, 26, 2(94), 215-229 (2023)
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УДК 51.72 
DOI: 10.33048/SIBJIM.2023.26.217

Аннотация:

С помощью двумерной осесимметричной физико-математической модели и алгоритма проведено численное исследование задачи об облучении объёмной алюминиевой мишени единичным фемтосекундным лазерным импульсом. Задача имеет ряд фундаментальных и практических приложений, связанных с упрочняющим воздействием остаточных пластических деформаций после прохождения индуцированной лазером ударной волны, в частности лазерное ударное упрочнение, также известное в литературе как лазерная ковка, лазерный наклёп или лазерный пининг. Осевая симметрия лазерного пучка позволяет уменьшить размерность задачи с трёхмерной до двумерной и существенно сэкономить вычислительные ресурсы. Использовано полуэмпирическое уравнение состояния алюминия в форме Ми — Грюнайзена с подстройкой параметров по холодной кривой металла и данным ударно-волновых экспериментов. Исследован закон распространения и затухания ударной волны, выделены стадии одномерного, переходного и полусферического распространения ударной волны. Описаны размеры и форма области, на которую может быть осуществлено упрочняющее воздействие единичным фемтосекундным лазерным импульсом.

Литература:
  1. Vorobyev A.Y., Guo C. Colorizing metals with femtosecond laser pulses // Appl. Phys. Lett. 2008. V. 92. Article 041914; DOI: 10.1364/OE.14.002164
     
  2. Bonse J., Kruger J., Hohm S., Rosenfeld A. Femtosecond laser-induced periodic surface structures // Laser Appl. 2012. V. 24, N 4. Article 042006; DOI: 10.2351/1.4712658
     
  3. Leung C.L.A., Marussi S., Atwood R.C., Towrie M., Withers P.J., Lee P.D. In situ x-ray imaging of defect and molten pool dynamics in laser additive manufacturing // Nat. Commun. 2018. V. 9. Article 1355; DOI: 10.1038/s41467-018-03734-7
     
  4. Bertoli U.S., MacDonald B.E., Schoenung J.M. Stability of cellular microstructure in laser powder bed fusion of 316l stainless steel // Mater. Sci. Engrg.: A. 2019. V. 739. P. 109–117; DOI 10.1016/j.msea.2018.10.051
     
  5. Stratakis E., Barberoglou M., Fotakis C., Viau G., Garcia C., Shafeev G.A. Generation of Al nanoparticles via ablation of bulk Al in liquids with short laser pulses // Optics Express. 2009. V. 17, N 15. P. 12650–12659; DOI: 10.1364/OE.17.012650
     
  6. Zhang D., Gokce B., Barcikowski S. Laser synthesis and processing of colloids: Fundamentals and applications // Chem. Rev. 2017. V. 117, N 5. P. 3990–4103; DOI: 10.1021/acs.chemrev.6b00468
     
  7. Sano T., Eimura T., Kashiwabara R., Matsuda T., Isshiki Y., Hirose A., Tsutsumi S., Ara-kawa K., Hashimoto T., Masaki K., Sano Y. Femtosecond laser peening of 2024 aluminum alloy without a sacrificial overlay, under atmospheric conditions // J. Laser Appl. 2017. V. 29, N 1. Article 012005; DOI: 10.2351/1.4967013
     
  8. Trdan U., Sano T., Klobcar D., Sano Y., Grum J., Sturm R. Improvement of corrosion re-sistance of AA2024-T3 using femtosecond laser peening without protective and confining medium // Corros. Sci. 2018. V. 143. P. 46–55; DOI: 10.1016/j.corsci.2018.08.030
     
  9. LSP Technologies: Introduction to Laser Peening // https://www.lsptechnologies.com/wp-content/uploads/2019/03/Intro-to-Laser-Peening-Webinar.pdf
     
  10. Shepelev V.V., Inogamov N.A. Two-dimensional turning of thermal flux from normal to lateral propagation in thin metal film irradiated by femtosecond laser pulse // J. Phys. Conf. Ser. 2018. V. 946. Article 012010.
     
  11.  Shepelev V.V., Inogamov N.A., Fortova S.V. Thermal and dynamic effects of laser irradiation of thin metal films // Optical and Quantum Electronics. 2020. V. 52, N 2. Article 88.
     
  12. Shepelev V.V., Inogamov N.A., Fortova S.V., Danilov P.A., Kudryashov S.I., Kuchmizhak A.A., Vitrik O.B. Action of a femtosecond laser pulse on thin metal film supported by glass substrate // J. Phys. Conf. Ser. 2018. V. 1128. Article 012092.
     
  13. Shepelev V.V., Inogamov N.A., Danilov P.A., Kudryashov S.I., Kuchmizhak A.A., Vitrik O.B Ultrashort pulse action onto thin film on substrate: Qualitative model of shock propagation in sub-strate explaining phenomenon of fast growth of a hole with increase of absorbed energy // J. Phys. Conf. Ser. 2019. V. 1147. Article 012065.
     
  14. Shepelev V., Inogamov N.A., Fortova S.V. The role of geometry in the generation of a shock wave by a femtosecond laser pulse // J. Phys. Conf. Ser. 2021. V. 1787. Article 012023.
     
  15. Shepelev V.V., Inogamov N.A., Petrov Yu.V., Fortova S.V. Equations of state of the Mie-Gruneisen type as applied to problems of laser hardening of materials // J. Phys. Conf. Ser. (in press).
     
  16. Anisimov S.I., Zhakhovskii V.V., Inogamov N.A., Nishihara K., Petrov Yu.V., Khokhlov V.A. Ablated matter expansion and crater formation under the action of ultrashort laser pulse // J. Experiment. Theor. Phys. 2006. V. 103, N 2. P. 183–197.
     
  17. Анисимов С.И., Жаховский В.В., Иногамов Н.А., Нишихара К., Петров Ю.В., Хохлов В.А. Формирование кратера и откольной оболочки коротким лазерным импульсом // Мат. моделирование. 2006. V. 18, N 8. P. 111–122.
     
  18. Fisher D., Fraenkel M., Henis Z., Moshe E., Eliezer S. Interband and intraband (Drude) contributions to femtosecond laser absorption in aluminum // Phys. Rev. E. 2001. V. 65. Article 016409.
     
  19. Toro E.F. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer-Verl., 1999.
     
  20. Годунов С.К., Забродин А.В., Иванов М.Я., Крайко А.Н., Прокопов Г.П. Численное решение многомерных задач газовой динамики. М.: Наука, 1976.
     
  21. Toro E., Spruce M., Speares W. Restoration of the contact surface in the HLL Riemann solver // Shock Waves. 1994. V. 4. P. 25–34.
     
  22. Harten A., Lax P., van Leer B. On upstream differencing and godunov type methods for hyperbolic conservation Laws // SIAM Rev. 1983. V. 25, N 1. P. 35–61.
     
  23. Roe P. Approximate Riemann solvers, parameter vectors and difference schemes // J. Comput. Phys. 1981. V. 43. P. 357–372.
     
  24. Courant R., Friedrichs K., Lewy H. Uber die partiellen differenzengleichungen der mathematischen ¨ physic. Mathematische Annalen. 1928. V. 100, N 1. P. 32–74; DOI: 10.1007/BF01448839
     
  25. Shu C.-W. Essentially Non-oscillatory and Weighted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws. Berlin; Heidelberg: Springer-Verl., 1998. P. 325–432; DOI: 10.1007/BFb0096355
     
  26. Bushman A.V., Fortov V.E. Model equations of state // Sov. Phys. Usp. 1983. V. 26, N 6. P. 465–496; DOI: 10.1070/pu1983v026n06abeh004419
     
  27. Bushman A.V., Kanel G.I., Ni A.L., Fortov V.E. Thermophysics and Dynamics of Intense Pulse Loadings. London: Taylor&Fransis, 1993.
     
  28. Khishchenko K.V. The equation of state for magnesium at high pressures // Tech. Phys. Lett. 2004. V. 30, N 10. P. 829–831; DOI: 10.1134/1.1813723
     
  29. Lomonosov I.V. Multi-phase equation of state for aluminum // Laser Part. Beams. 2007. V. 25. P. 567–584; DOI: 10.1017/S0263034607000687
     
  30. Rose J.H., Smith J.R., Guinea F., Ferrante J. Universal features of the equation of state of metals // Phys. Rev. B. 1984. V. 29. Article 2963.
     
  31. Zel’dovich Y.B., Raizer Y.P. Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Dover, 2002.
     
  32. Anisimov S.I., Zhakhovsky V.V., Inogamov N.A., Migdal K.P., Petrov Y.V., Khokhlov V.A. High-energy-density physics and laser technologies // J. Experiment. Theor. Phys. 2019. V. 129, N 4. P. 757–782; DOI: 10.1134/S1063776119100169.
     
  33. Zhakhovsky V.V., Budzevich M.M., Inogamov N.A., Oleynik I.I., White C.T. Two-zone elastic-plastic single shock waves in solids // Phys. Rev. Lett. 2011. V. 107, N 13. Article 135502; DOI: 10.1103/PhysRevLett.107.135502.

Работа выполнена в рамках государственного задания ИАП РАН.

В. В. Шепелев
  1. Институт автоматизации проектирования РАН, 
    ул. 2-я Брестская, 19/18, г. Москва 123056, Россия

E-mail: vadim.aries@gmail.com

Статья поступила 14.10.2022 г.
После доработки — 14.10.2022 г.
Принята к публикации 12.01.2023 г.

Abstract:

Using two-dimensional cylindrically-symmetric physical and mathematical model and an algorithm, a numerical investigation of the problem of irradiating a volumetric aluminum target with a single femtosecond laser pulse is carried out. The problem has a number of fundamental and practical applications related to the hardening effect of residual plastic deformations after the passage of a laser-induced shock wave, in particular, laser shock hardening technology, also known in the literature as laser forging, laser riveting or laser peening. Axial symmetry of laser beam makes it possible to reduce the dimension of the problem from three-dimensional to two-dimensional and significantly save computational resources. Semi-empirical equation of the state of aluminum in the form of a Mi—Gruneisen with the adjustment of parameters according to the cold curve of the metal and the data of shock-wave experiments was used. The law of shock wave propagation and attenuation is investigated, the stages of (1) single, (2) transient and (3) hemispherical shock wave propagation are identified. The size and shape of the area on which the strengthening effect can be carried out by a single femtosecond laser pulse are described.

References:
  1. Vorobyev A.Y., Guo C. Colorizing metals with femtosecond laser pulses. Appl. Phys. Lett., 2008, Vol. 92, article 041914; DOI: 10.1364/OE.14.002164
     
  2. Bonse J., Kruger J., Hohm S., Rosenfeld A. Femtosecond laser-induced periodic surface structures. Laser Appl., 2012, Vol. 24, No. 4, article 042006; DOI: 10.2351/1.4712658
     
  3. Leung C.L.A., Marussi S., Atwood R.C., Towrie M., Withers P.J., Lee P.D. In situ x-ray imaging of defect and molten pool dynamics in laser additive manufacturing. Nat. Commun., 2018, Vol. 9, article 1355; DOI: 10.1038/s41467-018-03734-7
     
  4. Bertoli U.S., MacDonald B.E., Schoenung J.M. Stability of cellular microstructure in laser powder bed fusion of 316l stainless steel. Mater. Sci. Engrg.: A, 2019, Vol. 739, pp. 109–117; DOI: 10.1016/j.msea.2018.10.051
     
  5. Stratakis E., Barberoglou M., Fotakis C., Viau G., Garcia C., Shafeev G.A. Generation of Al nanoparticles via ablation of bulk Al in liquids with short laser pulses. Optics Express, 2009, Vol. 17, No. 15, pp. 12650–12659; DOI: 10.1364/OE.17.012650
     
  6. Zhang D., Gokce B., Barcikowski S. Laser synthesis and processing of colloids: Fundamentals and applications. Chem. Rev., 2017, Vol. 117, No. 5, pp. 3990–4103; DOI: 10.1021/acs.chemrev.6b00468
     
  7. Sano T., Eimura T., Kashiwabara R., Matsuda T., Isshiki Y., Hirose A., Tsutsumi S., Ara-kawa K., Hashimoto T., Masaki K., Sano Y. Femtosecond laser peening of 2024 aluminum alloy without a sacrificial overlay, under atmospheric conditions. J. Laser Appl., 2017, Vol. 29, No. 1, article 012005; DOI: 10.2351/1.4967013
     
  8. Trdan U., Sano T., Klobcar D., Sano Y., Grum J., Sturm R. Improvement of corrosion re-sistance of AA2024-T3 using femtosecond laser peening without protective and confining medium. Corros. Sci., 2018, Vol. 143, pp. 46–55; DOI: 10.1016/j.corsci.2018.08.030
     
  9. LSP Technologies: Introduction to Laser Peening. https://www.lsptechnologies.com/wp-content/uploads/2019/03/Intro-to-Laser-Peening-Webinar.pdf
     
  10. Shepelev V.V., Inogamov N.A. Two-dimensional turning of thermal flux from normal to lat-eral propagation in thin metal film irradiated by femtosecond laser pulse. J. Phys. Conf. Ser., 2018, Vol. 946, article 012010.
     
  11. Shepelev V.V., Inogamov N.A., Fortova S.V. Thermal and dynamic effects of laser irradiation of thin metal films. Optical and Quantum Electronics, 2020, Vol. 52, No. 2, article 88.
     
  12. Shepelev V.V., Inogamov N.A., Fortova S.V., Danilov P.A., Kudryashov S.I., Kuchmizhak A.A., Vitrik O.B. Action of a femtosecond laser pulse on thin metal film supported by glass substrate. J. Phys. Conf. Ser., 2018, Vol. 1128, article 012092.
     
  13. Shepelev V.V., Inogamov N.A., Danilov P.A., Kudryashov S.I., Kuchmizhak A.A., Vitrik O.B Ultrashort pulse action onto thin film on substrate: Qualitative model of shock propagation in sub-strate explaining phenomenon of fast growth of a hole with increase of absorbed energy. J. Phys. Conf. Ser., 2019, Vol. 1147, article 012065.
     
  14. Shepelev V., Inogamov N.A., Fortova S.V. The role of geometry in the generation of a shock wave by a femtosecond laser pulse. J. Phys. Conf. Ser., 2021, Vol. 1787, article 012023.
     
  15. Shepelev V.V., Inogamov N.A., Petrov Yu.V., Fortova S.V. Equations of state of the Mie-Gruneisen type as applied to problems of laser hardening of materials. J. Phys. Conf. Ser. (in press).
     
  16. Anisimov S.I., Zhakhovskii V.V., Inogamov N.A., Nishihara K., Petrov Yu.V., Khokhlov V.A. Ablated matter expansion and crater formation under the action of ultrashort laser pulse. J. Experiment. Theor. Phys., 2006, Vol. 103, No. 2, pp. 183–197.
     
  17. Anisimov S.I., Zhakhovskii V.V., Inogamov N.A., Nishikhara K., Petrov Yu.V., Khokhlov V.A. Formirovanie kratera i otkol’noi obolochki korotkim lazernym impul’som[Formation of a crater and a split shell by a short laser pulse]. Mat. Model., 2006, Vol. 18, No. 8, pp. 111–122 (in Russian).
     
  18. Fisher D., Fraenkel M., Henis Z., Moshe E., Eliezer S. Interband and intraband (Drude) contributions to femtosecond laser absorption in aluminum. Phys. Rev. E., 2001, Vol. 65, article 016409.
     
  19. Toro E.F. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer-Verl., 1999.
     
  20. Godunov S.K., Zabrodin A.V., Ivanov M.Ya., Kraiko A.N., Prokopov G.P. Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki [Numerical solution of multidimensional problems of gas dynamics]. Moscow: Nauka, 1976 (in Russian).
     
  21. Toro E., Spruce M., Speares W. Restoration of the contact surface in the HLL Riemann solver. Shock Waves, 1994, Vol. 4, pp. 25–34.
     
  22. Harten A., Lax P., van Leer B. On upstream differencing and godunov type methods for hyperbolic conservation laws. SIAM Rev., 1983, Vol. 25, No 1, pp. 35–61.
     
  23. Roe P. Approximate Riemann solvers, parameter vectors and difference schemes. J. Comput. Phys., 1981, Vol. 43, pp. 357–372.
     
  24. Courant R., Friedrichs K., Lewy H. Uber die partiellen differenzengleichungen der mathematischen ¨ physic. Math. Annal., 1928, Vol. 100, No. 1, pp. 32–74; DOI: 10.1007/BF01448839 (in German).
     
  25. Shu C.-W. Essentially Non-oscillatory and Weighted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws. Berlin; Heidelberg: Springer-Verl., 1998, pp. 325–432; DOI: 10.1007/BFb0096355
     
  26. Bushman A.V., Fortov V.E. Model equations of state. Sov. Phys. Usp., 1983, Vol. 26, No. 6, pp. 465–496; DOI: 10.1070/pu1983v026n06abeh004419
     
  27. Bushman A.V., Kanel G.I., Ni A.L., Fortov V.E. Thermophysics and Dynamics of Intense Pulse Loadings. London: Taylor&Fransis, 1993.
     
  28. Khishchenko K.V. The equation of state for magnesium at high pressures. Tech. Phys. Lett., 2004, Vol. 30, No. 10, pp. 829–831; DOI: 10.1134/1.1813723
     
  29. Lomonosov I.V. Multi-phase equation of state for aluminum. Laser Part. Beams, 2007, Vol. 25, pp. 567–584; DOI: 10.1017/S0263034607000687
     
  30. Rose J.H., Smith J.R., Guinea F., Ferrante J. Universal features of the equation of state of metals. Phys. Rev. B., 1984, Vol. 29, article 2963.
     
  31. Zel’dovich Y.B., Raizer Y.P. Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Dover, 2002.
     
  32. Anisimov S.I., Zhakhovsky V.V., Inogamov N.A., Migdal K.P., Petrov Y.V., Khokhlov V.A. High-energy-density physics and laser technologies. J. Experiment. Theor. Phys., 2019, Vol. 129, No. 4, pp. 757–782; DOI: 10.1134/S1063776119100169.
     
  33. Zhakhovsky V.V., Budzevich M.M., Inogamov N.A., Oleynik I.I., White C.T. Two-zone elastic-plastic single shock waves in solids. Phys. Rev. Lett., 2011, Vol. 107, No. 13, article 135502; DOI: 10.1103/PhysRevLett.107.135502