Shock data

In this chapter we define what is meant by a shock-wave equation of state, and how it is related to other types of equations of state. We also discuss the properties of shock-compressed matter on a microscopic scale, as well as discuss how shock-wave properties are measured. Shock data for standard materials are presented. The effects of phase changes are discussed, the measurements of shock temperatures, and sound velocities of shock materials are also described. We also describe the application of shock-compression data for porous media. 

In 1963, McQueen, Fritz, and Marsh (J. Geophys. Res. 68, p. 2319) suggested that the high-pressure shock-wave data for fused quartz (Table 1) and the data for crystal quartz pg = 2.65 g/cm, Co = 1.74 km/s and s = 1.70, both described the shock-induced high-pressure phase of SiOj, stishovite pg = 4.35 g/cm ), above 50 GPa. Assume Ej-j, = 1.5 kJ/g show that these shock data are consistent with a constant value of y = 0.9 in the 50-100 GPa range. 

Fig. 2.3. Experimental determination of shock-stress versus volume compression from propagating shock waves is accomplished by a series of experiments carried out at different loading pressures. In the figure, the solid lines connect individual pressure-volume points with the initial condition. These solid straight lines are Rayleigh lines. The dashed line indicates an extrapolation into an uninvestigated low pressure region. Such extrapolation is typical of much of the strong shock data.

These shock data are the limiting elastic compression just prior to a polymorphic phase... 

In the perfectly elastic, perfectly plastic models, the high pressure compressibility can be approximated from static high pressure experiments or from high-order elastic constant measurements. Based on an estimate of strength, the stress-volume relation under uniaxial strain conditions appropriate for shock compression can be constructed. Inversely, and more typically, strength corrections can be applied to shock data to remove the shear strength component. The stress-volume relation is composed of the isotropic (hydrostatic) stress to which a component of shear stress appropriate to the... 

Fig. 2.9. The measured stress-volume relation of shock-loaded sapphire reveals a substantial reduction in strength, but a small finite strength is retained. The reduction in strength is indicated by the small high pressure offset between the static and shock data, and from extrapolation of high pressure shock data to atmospheric pressure conditions (Graham and Brooks [71G01]).

Optical devices or optical systems have provided most of the available strong shock data and were the primary tools used in the early shock-compression investigations. They are still the most widely used systems in fundamental studies of high explosives. The earliest systems, the flash gap and mirror systems on samples, provided discrete or continuous measurements of displacement versus time. 

Fig. 5.10. The pressure dependence of saturation magnetization for iron-nickel alloys shows a strong pressure dependence in the neighborhood of the Invar alloys (28.5 to 40-at. % nickel in the fee phase). The shock data shown are in excellent agreement with the static high pressure data (after Wayne [69W01]).

This is based on a particular model of the interactions among protons and electrons in dense liquid hydrogen, wherein the free energy is minimized to identify the preferred phases. An alternative model that assumes that the PPT is replaced by a continuous transition from molecular to metallic hydrogen can better ht much of the shock data (Ross, 1998). However, this theory is ad hoc and some of the data it does ht have been called into question (Hubbard et al., 1999). 

In most cases, interactions between unlike molecules are treated with Lorentz-Berthelot combination rules [28]. Non-additive pair interactions have been used for N2 and O2 [18]. The resulting N2 model accurately matches double shock data, but is not accurate at lower temperatures and densities [22]. A combination of experiments on mixtures and theoretical developments is needed to develop reliable unlike-pair interaction potentials. 

There is more shock data available on chlorocarbons than the fluorocarbons. This allows for more extensive testing of the validity of the present model. We note that Dremov and Modestov[53] have reported effective exponential-6 parameters for chlorinated methanes. We find their parameters to be inaccurate when used within the current modeling framework, which uses the recently developed HMSA/MC equation of state[22], and a product set including hydrocarbons and condensed carbon. Parameters for fluid CCL were matched to the shock Hugoniot of liquid CCI4. 

Fig. 9.10. Pressure-volume relationship for rare earth metals deduced from shock data. The position of the kinks in the 17, - I7p relationship is indicated by an arrow. The 0 K isotherm is also shown (from Gust and Royce, 1973). Pressure in mega bar.

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