Claude Renero

The equation of state of solids

Abstract An equation of state for solids, in reduced variables, is obtained within the context of a system-independent formulation of the thermodynamics of high pressures. This formulation is valid for materials obeying a linear relationship between shock and particle velocities. An adequate set of scaling factors for pressure, compression, specific energy, and temperature, is first introduced. A modified Mie-Gruneisen equation, as well as many other thermodynamic relationships and coefficients, are then expressed in terms of reduced variables. Explicit expressions for the temperature along the Hugoniot, and for the equation of state, are obtained. It is also shown that when given in their reduced form, each of the two thermodynamic coefficients appearing in the equation of state can be considered as having the same constant value for many different materials. The possibility and convenience of using a “standard material” is discussed. Numerical results obtained using this reduced variables formalism are in good agreement with those computed or measured, by different authors, for various materials over a wide range of pressures. This is a good indication of the “universality” of the reduced equations obtained, and of the usefulness of the formalism.

Experimental facilities for impact physics research at the National University of Mexico

Abstract A gas gun for impact studies is described. The main parameters are 75.4 mm inside diameter and 13 m length. The 20-1 diaphragm breech is designed for a 40 MPa working pressure. The impact chamber is a cylinder, 62 cm in diameter and 51.5 cm in height, with a window to obtain photographic records. A 3 m 3 recuperation tank, pressure sealed to recover the helium, encloses the stopping mechanism. A building (20m×5m) was constructed so that the impact chamber and recuperation tank are inside a concrete room. The barrel and breech recoil freely, except for a couple of shock absorbers. The gun accelerates 1 kg projectiles to 1 km/s when filled with helium at design pressure. The main experimental interests are: (a) on controlled initial temperature targets, to test the previous theoretical work on the equation of state; (b) shock-induced polarization; and (c) the shock-induced phase transition of germanium.

Remarks on the Kumar isothermal equation

Abstract A comparison is made between an equation for room-temperature isotherms recently proposed by Kumar, and a universal system-independent equation of state proposed some years ago by Prieto and Renero. This comparison is made using both equations to obtain room-temperature isotherms for Cu, Pd, K and Mo. It is also shown that by the use of suitable scaling factors for the variables involved in Kumar’s equation, it can be expressed in universal system-independent form.

Comparison of two universal equations of state for solids

A comparison between two of the so-called universal equations of state for solids is made. It is shown that although the Vinet equation and the Prieto-Renero equation are obtained on very different bases, their general form is very similar. Furthermore, the coefficients of the temperature dependent terms in the two equations are identical. This leads to a new relationship between the isothermal bulk modulus and other measurable parameters of the material. Numerical results obtained using both equations are shown to be in good agreement with some reported experimental data for gold, and for sodium chloride. The meaning of universality is different from one equation to the other; however, both of these meanings have been already accepted and used in relation to the scope of validity of equations of state. It is concluded that the use of one or the other equation depends more on the availability of the physical parameters needed than on the reliability of the equation itself.

Design operation and test of a light gas gun in a developing country

A detailed description is given of the light gas gun designed, machined, and operated at the National University of Mexico. Emphasis is made on the difficulties to be faced in a developing country to construct this kind of experimental facility, as well as on the solutions given. In particular, the barrel is made of 15 interlocking sections, each one as long as could be machined and honed in the available lathes in our country. These sections are conically tapered inside to allow the projectile to move from one section to the next without being shaved or deformed. The double diaphragm type breech has a working pressure of 40 MPa, the length of the barrel is 12.7 m and its bore is 75 mm. We indicate how to maximize the bursting cross section of the diaphragms, because this increases the projectile velocity. The projectile mass may be chosen between 0.5 and 2 kg, and the maximum projectile velocity may be as high as 1200 m/s. The gas gun performances are presented and, as a final remark, we comment on what ...

Reduced variables and universality in high pressure physics

There has been recently, in the field of high pressure physics in particular, a large number of publications on various ‘‘universal’’ equations of state, or ‘‘nearly universal’’ expressions. In the present paper we shall show that the resulting proliferation of different scaling factors and reduced expressions may be redundant since most of them can be shown to be equivalent. The mathematical processes developed by the different authors lead in general to some degree of arbitrariness in the choice of scaling factors, preventing the obtention of a consistent set of reduced variables. We shall also show that such a set can be obtained in a straightforward way from similarity considerations.

Shock mach number as a variable in high pressure thermodynamics

Abstract The recent proposal of considering the shock Mach number as an independent variable in the thermodynamics of high pressures is critically discussed. Although this variable has been widely used in the past whenever reduced or scaled variables are introduced in the study of materials at shock pressures, to consider the shock Mach number as an independent variable is new and the implications of this procedure are worth exploring. The advantages of using this independent variable within the context of a universal system-independent formulation of the thermodynamics of high pressures are thoroughly analyzed. The relations between the different mechanical and thermal variables introduced by various authors are exhibited through the comparison of different formalisms when expressed in terms of the shock Mach number as independent variable. Ar empirical relationship between the Hugoniot temperature and this variable is found to be of interest because of its simplicity. As a consequence of this, a very simple form of a high pressure empirical equation of state is also proposed.

Influence of the propellant flow on the performance of diaphragm operated gas guns

Many different properties of matter under shock wave loading can be studied through the use of gas‐gun accelerated projectiles. Knowledge of the motion of the projectile, and in particular of its velocity, is thus of prime importance. This motion depends upon the sudden release of a compressed gas confined in a breech. The corresponding firing mechanism is a geometrical restriction to the flow of the accelerating gas behind the projectile. In this article a theoretical expression is obtained to take into account this restriction, and is applied to the case of the diaphragm type of firing mechanism. Two conditions are imposed to the one dimensional and isentropic flow at the diaphragm zone: the continuity of the fluid flow (density times velocity times cross section) and the continuity of force (pressure times cross section). The theoretical expression obtained can be expressed in term of upper and lower bounds. A comparison with experimental results, obtained in our laboratory, is carried out, showing tha...

A mixing rule for the shock parameters during phase transitions at high pressures

Abstract A study is made of shock-induced phase changes. The transition zone is considered as a mixture of both the initial and the final phases, at any stage of the transition. It is assumed that the material always responds linearly in US − UP. Only transitions at US constant are considered. A mixing rule is introduced by the assumption that the coefficients of the linear relationship during the transition are linear functions of the changing molar fractions of the two phases. This mixing rule is first tested for some mixtures. A few algebraic relations in the P − V and US − UP representations during the phase transitions are obtained. Some of these relations are used to predict the characteristics of reported transitions.