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Modeling of High-Porosity Copper-Based Mixtures under Shock Loading

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Abstract

A thermodynamically equilibrium model is applied for simulating thermodynamic parameters of shock loading of both pure materials and mixtures of homogeneous and porous materials. The model includes a modified equation of state, which has only one fitting parameter determined on the basis of experimental data. The thermodynamic parameters of shock loading of copper and copper-based mixtures with porosities of 1–10 at pressures above 5 GPa are calculated. The results of these calculations are compared to available experimental data (Hugoniot adiabats, double compression by shock waves, and temperature estimates). The possibility of modeling the compression of the mixture as a whole and each component separately is demonstrated.

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References

  1. L. V. Shurshalov, A. A. Charakh’yan, and K. V. Khishchenko, “Numerous Experiment on Impact Compression of a Mixture of Graphite and Water,” Fiz. Goreniya Vzryva 53 (4), 114–121 (2017) [Combust., Expl., Shock Waves 53 (4), 471–478 (2017)].

    Google Scholar 

  2. B. Nayak and S. V. G. Menon, “Non-Equilibrium Theory Employing Enthalpy-Based Equation of State for Binary Solid and Porous Mixtures,” Shock Waves 28 (2), 141–151 (2018).

    Article  ADS  Google Scholar 

  3. A. B. Medvedev, “Equation of State of Silicon Dioxide with Allowance for Evaporation, Dissociation, and Ionization,” Fiz. Goreniya Vzryva 52 (4), 101–114 (2016) [Combust., Expl., Shock Waves 52 (4), 463–475 (2016)].

    Google Scholar 

  4. A. A. Kayakin, L. F. Gudarenko, and D. G. Gordeev, “Equation of State of Compounds of Lithium Isotopes with Hydrogen Isotopes,” Fiz. Goreniya Vzryva 50 (5), 109–122 (2014) [Combust., Expl., Shock Waves 50 (5), 599–611 (2014)].

    Google Scholar 

  5. I. V. Lomonosov and S. V. Fortova, “Wideband Semi-Empirical Equations of State for Numerical Simulation of High-Energy Processes,” Teplofiz. Vysok. Temp. 55 (4), 596–626 (2017).

    Google Scholar 

  6. E. I. Kraus and I. I. Shabalin, “Calculation of Elastic Modules behind Strong Shock Wave,” J. Phys.: Conf. Ser 774, 012009 (2015).

    Google Scholar 

  7. S. D. Gilev, “Few-Parameter Equation of State of Copper,” Fiz. Goreniya Vzryva 54 (4), 107–122 (2018) [Combust., Expl., Shock Waves 54 (4), 482–495 (2018)].

    Google Scholar 

  8. K. V. Khishchenko, “Equation of State for Magnesium Hydride under Condition of Shock Loading,” Math. Montisnigri 43, 70–77 (2018).

    MathSciNet  Google Scholar 

  9. S. A. Kinelovskii and K. K. Maevskii, “Model of the Behavior of the Mixture with Different Properties of the Species under High Dynamic Loads,” Prikl. Mekh. Tekh. Fiz. 54 (4), 13–21 (2013) [J. Appl. Mech. Tech. Phys. 54 (4), 524–530 (2013)].

    Google Scholar 

  10. S. A. Kinelovskii and K. K. Maevskii, “Model of the Behavior of Aluminum and Its Mixtures under Shock Loading,” Teplofiz. Vysok. Temp. 52 (6), 843–851 (2014).

    Google Scholar 

  11. S. A. Kinelovskii and K. K. Maevskii, “Modeling of Shock Loading of Multi-Component Materials Including Bismuth,” Teplofiz. Vysok. Temp. 54 (5), 716–723 (2016).

    Google Scholar 

  12. S. A. Kinelovskii and K. K. Maevskii, “Simple Model for Calculating Shock Adiabats of Powder Mixtures,” Fiz. Goreniya Vzryva 47 (6), 101–109 (2011) [Combust., Expl., Shock Waves 47 (6), 706–714 (2011)].

    Google Scholar 

  13. V. K. Golubev, “Determination of the Range of Applicability of Equations of State for Metals with a Constant Grüneisen Coefficient,” Khim. Fiz. 21 (10), 30–35 (2002).

    Google Scholar 

  14. S. N. Vaidya and G. C. Kennedy, “Compressibility of 18 Metals to 45 kbar,” J. Phys. Chem. Solids 3, 2329–2345 (1970).

    Google Scholar 

  15. A. P. Babichev, N. A. Babushkina, A. M. Bratkovskii, et al., Physical Quantities (Energoatomizdat, Moscow, 1991) [in Russian].

    Google Scholar 

  16. W. J. Nellis, A. C. Mitchell, and D. A. Young, “Equation-of-State Measurements for Aluminum, Copper, and Tantalum in the Pressure Range 80–440 GPa (0.8–4.4 Mbar),” J. Appl. Phys. 93 (1), 304–310 (2003).

    Article  ADS  Google Scholar 

  17. R. F. Trunin, L. F. Gudarenko, M. V. Zhernokletov, and G. V. Simakov, Experimental Data on Shock Compression and Adiabatic Expansion of Condensed Substances (VNIIEF, Sarov, 2006) [in Russian].

    Google Scholar 

  18. Shock Waves and Extreme State of Matter, Ed. by V. E. Fortov, L. V. Altshuler, R. F. Trunin, and A. I. Funtikov (Nauka, Moscow, 2000) [in Russian].

    Google Scholar 

  19. A. B. Medvedev, “Model of the Equation of State with Allowance for Evaporation, Ionization, and Melting,” Vopr. Atom. Nauk Tekh., Ser. Teoret. Prikl. Fiz., No. 1, 12–19 (1992).

  20. S. A. Kinelovskii and K. K. Maevskii, “Estimation of Thermodynamic Parameters of Shock Loading on High-Porosity Heterogeneous Materials,” Zh. Tekh. Fiz. 86 (8), 125–130 (2016).

    Google Scholar 

  21. K. K. Maevskii and S. A. Kinelovskii, “Thermodynamic Parameters of Mixtures with Silicon Nitride under Shock Loading in the Equilibrium Model Concept,” Teplofiz. Vysok. Temp. 56 (6), 932–938 (2018).

    Google Scholar 

  22. P. R. Levashov, K. V. Khishchenko, I. V. Lomonosov, and V. E. Fortov, “Database on Shockwave Experiments and Equations of State Available Via Internet,” in Shock Compression of Condensed Matter-2003, Ed. by M. D. Furnish, Y. M. Gupta, and J. W. Forbes (AIP, Melville-New York, 2004), pp. 87–90.

    Google Scholar 

  23. R. F. Trunin, Investigation of Extreme States of Condensed Substances by the Shock Wave Method Hugoniot Equations (VNIIEF, Sarov, 2006) [in Russian].

    Google Scholar 

  24. Yu. N. Zhugin, K. K. Krupnikov, N. A. Ovechkin, et al., “Some Specific Features of Dynamic Compressibility of Quartz,” Fiz. Zemli, No. 10, 16–22 (1994).

  25. B. L. Glushak, A. P. Zharkov, M. V. Zhernokletov, et al., “Experimental Investigations of Thermodynamics of the Dense Plasma of Metals at High Energy Densities,” Zh. Eksp. Teor. Fiz. 96 (4), 1301–1318 (1989).

    ADS  Google Scholar 

  26. LASL Shock Hugoniot Data, Ed. by S. P. Marsh (Univ. California Press, Berkeley, 1980).

    Google Scholar 

  27. R. F. Trunin, “Shock Compressibility of Condensed Substances in Powerful Shock Waves Generated by Underground Nuclear Explosions,” Usp. Fiz. Nauk 164 (11), 1215–1237 (1994).

    Article  Google Scholar 

  28. Methods of Studying Material Properties under Intense Dynamic Loads, Ed. by M. I. Zhernokletov (VNIIEF, Sarov, 2003) [in Russian].

    Google Scholar 

  29. V. K. Gryaznov, M. V. Zhernokletov, I. L. Iosilevskii, et al., “Shock Wave Compression of Strongly Non-Ideal Metal Plasma and its Thermodynamics,” Zh. Eksp. Teor. Fiz. 114 (4), 1242–1265 (1998).

    Google Scholar 

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Correspondence to K. K. Maevskii.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 60, No. 4, pp. 26–34, July–August, 2019.

Original Russian Text © K.K. Maevskii, S.A. Kinelovskii.

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Maevskii, K.K., Kinelovskii, S.A. Modeling of High-Porosity Copper-Based Mixtures under Shock Loading. J Appl Mech Tech Phy 60, 612–619 (2019). https://doi.org/10.1134/S0021894419040035

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  • DOI: https://doi.org/10.1134/S0021894419040035

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