Low-parametric equation of state for graphite describing solid and porous samples under shock and unloading waves

R. K. Bel'kheeva

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 90 (2024), pp. 50-63

Résumé

This study is aimed to obtain the parameters of the graphite equation of state represented as the Mie-Grüneisen equation of state. Graphite with metals and the porous graphite are considered as simple thermodynamically equilibrium mixtures. The equilibrium state is determined by the conditions of equal pressure, temperature, and velocity of the components in the mixture. Thus, the motion of the multicomponent medium can be described as the motion of a continuum with a special equation of state that takes into account the properties of the mixture components and their concentration, which significantly reduces the number of equations. For the Grüneisen parameter, a logarithmic dependence on density is used, which adequately describes the variation in the Grüneisen parameter for both normal and anomalous behavior of shock adiabats. The increasing scope of the equation of state is a result of comparing experimental data with calculations for the following: 1) shock-wave loading of porous materials to cover the range of higher temperatures; 2) double compression of the samples to cover the range of increased densities; 3) isentropic expansion of samples to cover the range of low densities; and 4) sound velocities, which characterize the compressibility of matter, slope of the Poisson adiabat on the shock adiabat, and propagation velocity of the weak shock waves and unloading waves through the compressed matter. The comprehensive analysis confirms that the proposed model of the equation of state for graphite is applicable to practical applications.

Détail

Keywords: shock adiabat, unloading isentrope, thermodynamic equilibrium, one-temperature approximation, one-velocity approximation
Mots-clés : Grüneisen parameter.

Bibliographie

[1] Ashkoft N., Mermin N., Fizika tverdogo tela, per. s angl., v. 2, Mir, M., 1979, 422 pp.

[2] Belaschenko D.K., Vorotyagin A.V., Gelchinskii B.R., “Kompyuternoe modelirovanie alyu miniya v oblasti vysokikh davlenii”, Teplofizika vysokikh temperatur, 49:5 (2011), 676–686 | DOI

[3] Molodets A.M., Molodets M.A., “Temperaturnaya zavisimost funktsii Gryunaizena khimiche skikh elementov”, Khimicheskaya fizika, 16:5 (1997), 122–126

[4] Kinelovskii S.A., Maevskii K.K., “Model povedeniya poristykh smesei, vklyuchayuschikh v svoi sostav zhelezo, pri udarno-volnovom nagruzhenii”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 29:3 (2014), 82–93

[5] Belkheeva R.K., “Model koeffitsienta Gryunaizena dlya shirokogo diapazona plotnostei na primere medi”, Teplofizika vysokikh temperatur, 59:4 (2021), 514–519 | DOI

[6] Gordeev D.G., Gudarenko L.F., Kayakin A.A. i dr., “Poluempiricheskaya model uravneniya sostoyaniya metallov s effektivnym uchetom ionizatsii. Ch. 2. Uravnenie sostoyaniya alyuminiya”, Voprosy atomnoi nauki i tekhniki. Ser. Teoreticheskaya i prikladnaya fizika, 2010, no. 3, 26–34

[7] Gordeev D.G., Gudarenko L.F., Kayakin A.A., Kudelkin V.G., “Model uravneniya sostoyaniya metallov s effektivnym uchetom ionizatsii. Uravneniya sostoyaniya Ta, W, Al, Be”, Fizika goreniya i vzryva, 49:1 (2013), 106–120

[8] Lomonosov I.V., Fortova S.V., “Shirokodiapazonnye poluempiricheskie uravneniya sostoyaniya veschestva dlya chislennogo modelirovaniya vysokoenergeticheskikh protsessov”, Teplofizika vysokikh temperatur, 55:4 (2017), 596–626 | DOI

[9] Khishchenko K. V., Fortov V.E., Lomonosov I. V., “Multiphase Equation of State for Carbon over Wide Range of Temperatures and Pressures”, Int. J. Thermophys., 26:2 (2005), 479–491 | DOI

[10] Lomonosov I.V., “Multi-phase Equation of State for Aluminum”, Laser and Particle Beams, 25 (2007), 567–584 | DOI

[11] Nigmatulin R.I., Osnovy mekhaniki geterogennykh sred, Nauka, M., 1978, 336 pp. | MR

[12] Belkheeva R.K., “Postroenie uravneniya sostoyaniya poristoi smesi kondensirovannykh komponentov”, Prikladnaya mekhanika i tekhnicheskaya fizika, 53:4 (2012), 3–15 | Zbl

[13] Belkheeva R.K., “Uravnenie sostoyaniya silnoporistogo veschestva”, Teplofizika vysokikh temperatur, 53:3 (2015), 367–377 | DOI

[14] Belkheeva R.K., “Termodinamicheskoe uravnenie sostoyaniya dlya opisaniya povedeniya poristoi smesi pri bolshikh davleniyakh i temperaturakh”, Prikladnaya mekhanika i tekhnicheskaya fizika, 48:5 (2007), 53–60

[15] Coleburn N.L., “The compressibility of pyrolytic graphyte”, j. Chem. Phys., 40:73 (1964), 71–77 | DOI

[16] Doran D.G., “Hugoniot equation of state of pyrolytic graphite to 300 kbars”, j. Appl. Phys., 34 (1963), 844–850 | DOI

[17] Trunin R.F., Gudarenko L.F., Zhernokletov M.V., Sivkov G.V., Eksperimentalnye dannye po udarno-volnovomu szhatiyu i adiabaticheskomu rasshireniyu kondensirovannykh veschestv, ed. R.F. Trunin, RFYaTs-VNIIEF, Sarov, 2006

[18] S.P. Marsh (ed.), LASL Shock Hugoniot Data, University of California Press, Berkeley, 1980

[19] Gust W.H., “Phase transition and shock-compression parameters to 120 GPa for three types of graphite and amorphous carbon”, Physical Review B, 22:10 (1980), 4744–4756 | DOI

[20] McQueen R.G., Marsh S.P., “Hugoniots of graphytes of various initial densities and the equation of state of carbon”, Behavior of dense media under high dynamic pressures, Proc. of the Symp. on the Behavior of Dense Media under High Dynamic Pressures (Sept. 1967, Paris), Gordon and Breach, New York, 1968, 207–216

[21] Zhuk A.Z., Ivanov A.V., Kannel G.I., “Issledovanie kinetiki fazovogo perekhoda grafit-almaz”, Teplofizika vysokikh temperatur, 29:3 (1991), 486–493

[22] Boade R.R., “Shock compression of Foamed Graphite”, j. Appl. Phys., 39:3 (1968), 1609–1617 | DOI

[23] Staver A.M., “Issledovanie termodinamiki fazovogo perekhoda ugleroda v almaz pri udarnom nagruzhenii smesei uglerod + metall”, Detonatsiya. Kriticheskie yavleniya. Fiziko-khimicheskie prevrascheniya v udarnykh volnakh, OIKhF, Chernogolovka, 1978, 131–136