A few-parameter equation of state of the condensed matter

Kraus, E. I.; Shabalin, I. I.

doi:10.1088/1742-6596/774/1/012009

Cited by 18 publications

(8 citation statements)

References 18 publications

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“…The change in porosity is described relations Carroll-Holt [20]. To close the system uses small number of parameters equation of state [21][22][23], which allows you to make calculations of shock-wave processes with a minimal number of physical parameters as initial data. The stress state of the material presented in the form of Johnson-Holmquist [24].…”

Section: Numerical Simulationmentioning

confidence: 99%

The shock wave compaction of ceramic powders

2019

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Joint theoretical and experimental investigations have allowed to realize an approach with use of mathematical and physical modeling of processes of a shock wave compaction of ceramic powders. The aim of this study was to obtain a durable low-porosity compact sample. The explosive compaction technology is used in this problem because ceramic powders such as boron carbide and aluminum oxide is an extremely hard and refractory material. Therefore, its compaction by traditional methods requires special equipment and considerable expenses. In order to better understand the influence of the loading conditions and, in particular, to study the effect of detonation velocity, explosive thickness and explosion pressure on the properties of the final sample, the problem of compaction of the powder in an axisymmetric case using the conditions of the above experiments have been numerically solved. Thus, using the technology of explosive compaction, compact samples of boron carbide and aluminum oxide are obtained. On the basis of experimental and numerical studies of shock waves propagation, the optimum scheme and parameters of dynamic compaction of boron carbide and aluminum oxide are determined in order to maximize the density and the conservation of the samples after dynamic loading.

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Section: Numerical Simulationmentioning

confidence: 99%

The shock wave compaction of ceramic powders

2019

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“…The author's model of the fewparameter equation of state was proposed in [12][13][14]. We consider the three-term Mie-Grüneisen equation of state with the solid-phase free energy being determined as:…”

Section: Equation Of Solid Statementioning

confidence: 99%

“…Kraus and Shabalin in [12] were demonstrated there that the set of semi-empirical relations (1) describes the behavior of thermodynamic properties of solids within 5% in a wide range of pressures and temperatures. For the equation of state to be applied, it is sufficient to know only six parameters…”

Section: Equation Of Solid Statementioning

confidence: 99%

Melting behind the front of the shock wave

Kraus

Shabalin

2019

THERM SCI

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A simple caloric model of the equation of state is proposed to describe thermodynamic properties of solid materials with phase transitions with the minimum number of parameters as initial data. Thermodynamic characteristics are calculated in the wide range of densities and pressures. The equation of state of the solid phase was modified by introducing configurational entropy, which made it possible to describe a liquid medium by the same functional dependence, but with its initial parameters. This allowed us not only to construct the equation of state for the liquid, but also to determine the dependence of the melting point on pressure as the boundary between the phases with the corresponding state. It is shown that the melting process is practically not noticeable on the shock adiabat in the pressurevolume plane; however, sharp adiabatic breaks are observed in the temperaturepressure plane. The calculated position of the melting curve agrees with the experimental data found; although this does not fully justify the conclusion about the accuracy of the calculation of the liquid phase adiabat, but fully confirms the qualitative picture.

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“…where the temperature is expressed in energy units. It is possible [51,52,65,66] to account for the temperature correction to the Grüneisen coefficient. One can take into account the nonharmonic corrections to T ε and T p calculated for a one-component plasma by the Monte-Carlo method [68], thereby generalizing the Mie-Grüneisen model, but below we will not use these corrections.…”

Section: A Model Three-term Eosmentioning

confidence: 99%

“…The electronic contributions to the specific internal energy and pressure can be presented as [45,66]…”

Section: A Model Three-term Eosmentioning

confidence: 99%

Solution of the Noh problem with an arbitrary equation of state

Velikovich

Giuliani

2018

Phys. Rev. E

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The classic self-similar solutions of the nonstationary compressible Euler equations obtained for a blast-wave propagation (Sedov, Taylor, and von Neumann), a shock-wave implosion (Guderley, Landau, and Stanyukovich), or an impulsive loading of a planar target (von Hoerner, Häfele, and Zel'dovich) have all been derived for a polytropic ideal gas. None of them can be generalized for a fluid with an arbitrary equation of state (EOS), such as the van der Waals EOS of a non-ideal-gas or a three-term EOS of a condensed material. We demonstrate here that the Noh accretion-shock problem is an exception. Its self-similar solutions exist in cylindrical and spherical geometry for fluids and materials with an arbitrary EOS. Such solutions for finite accretion-shock strength and nonuniform inflow velocity are constructed semianalytically with a model three-term equation of state that includes cold, thermal ion (lattice), and thermal electron contributions to the pressure and internal energy. Examples are presented for aluminum and copper. Other material- and EOS-specific semianalytic solutions of the Noh problem can be easily constructed using the same method for any material that in the pressure range of interest can be approximated as a dissipation-free fluid with an arbitrary equation of state.

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A few-parameter equation of state of the condensed matter

Cited by 18 publications

References 18 publications

The shock wave compaction of ceramic powders

The shock wave compaction of ceramic powders

Melting behind the front of the shock wave

Solution of the Noh problem with an arbitrary equation of state

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