Planar shock compression

When an isotropic material is subjected to planar shock compression, it experiences a relatively large compressive strain in the direction of the shock propagation, but zero strain in the two lateral directions. Any real planar shock has a limited lateral extent, of course. Nevertheless, the finite lateral dimensions can affect the uniaxial strain nature of a planar shock only after the edge effects have had time to propagate from a lateral boundary to the point in question. Edge effects travel at the speed of sound in the compressed material. Measurements taken before the arrival of edge effects are the same as if the lateral dimensions were infinite, and such early measurements are crucial to shock-compression science. It is the independence of lateral dimensions which so greatly simplifies the translation of planar shock-wave experimental data into fundamental material property information. 

The methods used to generate planar shock compression can be divided roughly into three categories, namely, those that make use of (1) explosives (2) guns and (3) energy deposition. Some examples within each category are discussed below. 

The experimental methods for producing planar shock compression can be divided into three general categories, namely, explosives, guns, and energy deposition. Guns are considered the most versatile of the three. 

To reiterate, the development of these relations, (2.1)-(2.3), expresses conservation of mass, momentum, and energy across a planar shock discontinuity between an initial and a final uniform state. They are frequently called the jump conditions" because the initial values jump to the final values as the idealized shock wave passes by. It should be pointed out that the assumption of a discontinuity was not required to derive them. They are equally valid for any steady compression wave, connecting two uniform states, whose profile does not change with time. It is important to note that the initial and final states achieved through the shock transition must be states of mechanical equilibrium for these relations to be valid. The time required to reach such equilibrium is arbitrary, providing the transition wave is steady. For a more rigorous discussion of steady compression waves, see Courant and Friedrichs (1948). 

Shock-compression science originated during and after World War II when experimental facilities for creating planar shock waves were developed, along with prompt instrumentation techniques enabling shock velocity and particle velocity measurements to be made. The main thrust of shock-compression science is to understand the physics and to measure the material properties which govern the outcome of shock-compression events. Experiments involving planar shock waves are the most useful in shock-compression science. 

Figure 8.6. Stress-particle velocity impedance diagram of the shock-compression and wave-interaction process leading to planar spall.

Zeldovich [9], von Neumann [10], and Ddring [11] independently arrived at a theory for the structure of the detonation wave. TTie ZND theory states that the detonation wave consists of a planar shock that moves at the detonation velocity and leaves heated and compressed gas behind it. After an induction period, the chemical reaction starts and as the reaction progresses, the temperature rises and the density and pressure fall until they reach the Chapman-Jouguet values and the reaction attains equilibrium. A rarefaction wave whose steepness depends on the distance traveled by the wave then sets in. Thus, behind the C-J shock, energy is generated by thermal reaction. 

In most flat-plate impact experiments, the direction of motion of the impacting plate is normal to its surface, such that only a planar compressive shock is introduced into the specimen. Within the last fifteen years, however, techniques have been developed for dynamic pressure-shear loading of specimens (Abou-Sayed et al., 1976 Chhabildas and Swegle, 1980). These involve an oblique impact, as illustrated in Fig. 3.6, in which the impact surface on the... 

Figure 8.3. Wave interactions in planar tensile fracture experiment, (a) Shows the distance-time plot of interacting compression C , rarefaction R , and tension T , waves (b) Shows the corresponding particle-velocity profiles including the initial compressive shock wave (tj, tj), the pull-back signal (tj, tj), and subsequent reflection >h).

For purposes of further analyses of detonation structure, the shock wave may be treated as a discontinuity. Both the viscous interaction between the shock and the reaction region and the molecular transport within the reaction region are small perturbations that do not appear to exert qualitatively significant influences on the wave structure. This conclusion appears to apply not only to steady, planar waves but also to unsteady, three-dimensional structures it affords one helpful simplification in the complicated analyses of transverse wave structures. It also alters the interpretation of a detonation as a deflagration-supported shock the support provided by the chemical reactions is of a nonplanar compressible gasdynamic character with negligible molecular transport. 

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