Hydrodynamic modeling of laser-induced shock waves in aluminum in a cylindrically-symmetric formulation

V. V. Shepelev

Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 2, pp. 215-229.

Résumé

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.

Détail

Keywords: mathematical modeling, hydrodynamics, computational methods, Riemann solvers, femtosecond lasers, shock waves, equations of state. .

Bibliographie

[1] A. Y. Vorobyev, C. Guo, “Colorizing metals with femtosecond laser pulses”, Appl. Phys. Lett., 92 (2008), 041914 | DOI

[2] J. Bonse, J. Kruger, S. Hohm, A. Rosenfeld, “Femtosecond laser-induced periodic surface structures”, Laser Appl., 24:4 (2012), 042006 | DOI

[3] C. L.A. Leung, S. Marussi, R. C. Atwood, M. Towrie, P. J. Withers, P. D. Lee, “In situ x-ray imaging of defect and molten pool dynamics in laser additive manufacturing”, Nat. Commun., 9 (2018), 1355 | DOI

[4] U. S. Bertoli, B. E. MacDonald, J. M. Schoenung, “Stability of cellular microstructure in laser powder bed fusion of 316l stainless steel”, Mater. Sci. Engrg.: A, 739 (2019), 109–117 | DOI

[5] E. Stratakis, M. Barberoglou, C. Fotakis, G. Viau, C. Garcia, G. A. Shafeev, “Generation of Al nanoparticles via ablation of bulk Al in liquids with short laser pulses”, Optics Express, 17:15 (2009), 12650–12659 | DOI

[6] D. Zhang, B. Gokce, S. Barcikowski, “Laser synthesis and processing of colloids: Fundamentals and applications”, Chem. Rev, 117:5 (2017), 3990–4103 | DOI

[7] T. Sano, T. Eimura, R. Kashiwabara, T. Matsuda, Y. Isshiki, A. Hirose, S. Tsutsumi, K. Ara-kawa, T. Hashimoto, K. Masaki, Y. Sano, “Femtosecond laser peening of 2024 aluminum alloy without a sacrificial overlay, under atmospheric conditions”, J. Laser Appl., 29:1 (2017), 012005 | DOI

[8] U. Trdan, T. Sano, D. Klobcar, Y. Sano, J. Grum, R. Sturm, “Improvement of corrosion re-sistance of AA2024-T3 using femtosecond laser peening without protective and confining medium”, Corros. Sci, 143 (2018), 46–55 | DOI

[9] LSP Technologies: Introduction to Laser Peening, https://www.lsptechnologies.com/wp-content/uploads/2019/03/Intro-to-Laser-Peening-Webinar.pdf

[10] V. V. Shepelev, N. A. Inogamov, “Two-dimensional turning of thermal flux from normal to lateral propagation in thin metal film irradiated by femtosecond laser pulse”, J. Phys. Conf. Ser., 946 (2018), 012010 | DOI

[11] V. V. Shepelev, N. A. Inogamov, S. V. Fortova, “Thermal and dynamic effects of laser irradiation of thin metal films”, Optical and Quantum Electronics, 52:2 (2020) | DOI

[12] V. V. Shepelev, N. A. Inogamov, S. V. Fortova, P. A. Danilov, S. I. Kudryashov, A. A. Kuchmizhak, O. B. Vitrik, “Action of a femtosecond laser pulse on thin metal film supported by glass substrate”, J. Phys. Conf. Ser., 1128 (2018), 012092 | DOI

[13] V. V. Shepelev, N. A. Inogamov, P. A. Danilov, S. I. Kudryashov, A. A. Kuchmizhak, O. Vitrik, “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., 1147 (2019), 012065 | DOI

[14] V. Shepelev, N. A. Inogamov, S. V. Fortova, “The role of geometry in the generation of a shock wave by a femtosecond laser pulse”, J. Phys. Conf. Ser., 1787 (2021), 012023 | DOI

[15] V. V. Shepelev, N. A. Inogamov, Yu. V. Petrov, S. V. Fortova, “Equations of state of the Mie-Gruneisen type as applied to problems of laser hardening of materials”, J. Phys. Conf. Ser. (to appear)

[16] S. I. Anisimov, V. V. Zhakhovskii, N. A. Inogamov, K. Nishihara, Yu. V. Petrov, V. A. Khokhlov, “Ablated matter expansion and crater formation under the action of ultrashort laser pulse”, J. Experiment. Theor. Phys., 103:2 (2006), 183–197 | DOI

[17] S. I. Anisimov, V. V. Zhakhovskii, N. A. Inogamov, K. Nishikhara, Yu. V. Petrov, V. A. Khokhlov, “For mirovanie kratera i otkolnoi obolochki korotkim lazernym impulsom”, Mat. modelirovanie, 18:8 (2006), 111–122 | Zbl

[18] D. Fisher, M. Fraenkel, Z. Henis, E. Moshe, S. Eliezer, “Interband and intraband (Drude) contributions to femtosecond laser absorption in aluminum”, Phys. Rev. E, 65 (2001), 016409 | DOI

[19] E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, Springer-Verl, 1999 | MR | Zbl

[20] S. K. Godunov, A. V. Zabrodin, M. Ya. Ivanov, A. N. Kraiko, G. P. Prokopov, Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki, Nauka, M., 1976 | MR

[21] E. Toro, M. Spruce, W. Speares, “Restoration of the contact surface in the HLL Riemann solver”, Shock Waves, 4 (1994), 25–34 | DOI | Zbl

[22] A. Harten, P. Lax, B. van Leer, “On upstream differencing and godunov type methods for hyperbolic conservation Laws”, SIAM Rev, 25:1 (1983), 35–61 | DOI | MR | Zbl

[23] Roe P., “Approximate Riemann solvers, parameter vectors and difference schemes”, J. Comput. Phys., 43 (1981), 357–372 | DOI | MR | Zbl

[24] R. Courant, K. Friedrichs, H. Lewy, “Uber die partiellen differenzengleichungen der mathematischen physic”, Mathematische Annalen, 100:1 (1928), 32–74 | DOI | MR

[25] C. W. Shu, “Essentially Non-oscillatory and Weighted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws”, Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Springer-Verl, Berlin–Heidelberg, 1998, 325–432 | DOI | MR | Zbl

[26] A. V. Bushman, V. E. Fortov, “Model equations of state”, Sov. Phys. Usp, 26:6 (1983), 465–496 | DOI

[27] A. V. Bushman, G. I. Kanel, A. L. Ni, V. E. Fortov, Thermophysics and Dynamics of Intense Pulse Loadings, Taylor Fransis, London, 1993

[28] K. V. Khishchenko, “The equation of state for magnesium at high pressures”, Tech. Phys. Lett, 30:10 (2004), 829–831 | DOI

[29] I. V. Lomonosov, “Multi-phase equation of state for aluminum”, Laser Part. Beams, 25 (2007), 567–584 | DOI

[30] J. H. Rose, J. R. Smith, F. Guinea, J. Ferrante, “Universal features of the equation of state of metals”, Phys. Rev. B, 29 (1984), 2963 | DOI

[31] Y. B. Zel'dovich, Y. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Dover, 2002

[32] S. I. Anisimov, V. V. Zhakhovsky, N. A. Inogamov, K. P. Migdal, Y. V. Petrov, V. A. Khokhlov, “High energy-density physics and laser technologies”, J. Experiment. Theor. Phys, 129:4 (2019), 757–782 | DOI

[33] V. V. Zhakhovsky, M. M. Budzevich, N. A. Inogamov, I. I. Oleynik, C. T. White, “Two-zone elastic-plastic single shock waves in solids”, Phys. Rev. Lett., 107:13 (2011), 135502 | DOI