Shock Wave Parameters

Fig. 9.1-5 Shock Wave Parameters fora Spherical TNT Surface Explosion at Sea level.

The thermodynamic method has limitations. Since the method ignores the intermediate stages, it cannot be used to determine shock-wave parameters. Furthermore, a shock wave is an irreversible thermodynamic process this fact complicates matters if these energy losses are to be fully included in the analysis. Nevertheless, the thermodynamic approach is a very attractive way to obtain an estimate of explosion energy because it is very easy and can be applied to a wide range of explosions. Therefore, this method has been applied by practically every worker in the field. 

Figure A.3. Positive phase shock wave parameters for a hemispherical TNT explosion on the surface at sea level (Ref. 7).

Snay J.H. Rosenbaum, "Shock Wave Parameters in Fresh Water for Pressures up to 95 Kilobars , NOL Rept NavOrd 2383 (1952)... 

The measurable underwater shock wave parameters, namely peak overpressure, pressure decay and shock velocity were defined in Fig 2. Actual pressure time records are similar to the idealized sketch of Fig 2, but unfortunately they are rarely as neat . Peak overpressures and time constants can be read directly from such records. Impulse (/pdt) and Energy Flux Density (const x /P2dt) require either analytical or graphical integration. Shock velocity is obtained from arrival times, ie, the time between firing of the expl charge and the start of the steeply rising pressure pulse... 

Especially for npnideal explosives charge shape and size should if possible resemble that of the intended application. Deviations from spherical charge shape should, however, not be too large. Length to diameter ratios over 10 should be avoided because shock energy evaluation with only one gage assumes spherical symmetry in shock wave parameters. ... 

For a given series of underwater expin tests, the shock wave parameters relative to a standard expl are determined from lines fitted to the data by the method of least squares. Hence, the slopes of the similitude lines reported in the various references cited vary somewhat. The Equal Weight Ratios about to be presented in Table 5 assume a constant slope for all expls for each of the four parameters shown. This seems to be a reasonable... 

The output of primers includes hot gases, particles, a pressure pulse, and sometimes a shock wave. Parameters which have been measured to characterize the primer include the volume of gas emitted, the impulse imparted to a column of mercury, the light output, the temperature rise of a calorimeter, the pressure, the conductivity between probes, and the functioning time. No general quantitative relationship between the parameters and the initiation of the next explosive in the element or train has yet emerged, although individually they may all have some importance [2,5.6]. 

It is known that shock wave parameters namely peak pressure (strain rate) and pulse duration result in an increase in the mechanical properties of metals. Increasing the peak pressure results in increasing both the plastic strain and strain rate. Murr and Wilsdorf [37] observed that the dislocation density varies as a square root of the applied pressure. The result of the calculated dislocation density histories carried out at different strain rates reveals that the saturated dislocation density and the rate of dislocation multiplication increase with strain rate as illustrated in Fig 11. 

Summary of the calculations is listed in table 2. This table displays the shock wave parameters calculated in the code and the corresponding theoretical values. The values of the axial stress (O33) obtained from our calculations are in a very good agreement with the corresponding theoretical values given by equation 16. However, the speeds of the longitudinal elastic wave are underestimated when compared to their theoretical values. This is attributed to the effect of FE mesh size. In fact when a fine mesh is used, the velocity approaches the theoretical wave speed value as shown in Fig. 19. 

In all the shock wave parameters, if the super pressure of shock wave front is known, all other parameters can be calculated according to the relationship of shock waves. Once the dimension relationship is fixed, the relationship of shock wave parameters and explosive packing is reachable. 

Each point on this plot may be related to a certain point on the pressure-time curve (Figure 4.32). Thus, for instance, the region of the sharp drop of the detonation pressure at low values of the plate thickness corresponds to the influence of the chemical reaction zone on the shock wave parameters in the metal plate. When the metal plate thickness equals zero, the pressure... 

If the curve, presenting the impedance ratios, is plotted for a series of plates made of different materials inp - W coordinates, then the intersection of this curve with the p= p DW line represents the CJ point (Figure 4.40). At that point, the impedance of the metal plate is equal to the impedance of the detonation products. This means that there is neither rarefaction nor slowing down of the detonation products, i.e., the detonation and the shock wave parameters at the explosive/plate interface are equal to the shock wave parameters. The technique described is known as the impedance match technique. 

If the above equations are combined, then different forms of relationships between shock wave parameters may be obtained. However, the most fi-equentiy used relationships are... 

It is evident from the above that, in order to establish the adial tic shock equation for a given medium, at least two shock wave parameters have to be determined experimentally. Modern experimental methods enable direct determination of the shock wave pressure and shock wave firont velocity with good accuracy. This proves to be sufficient for defining the adiabatic shock equation for a given medium. Once the adiabatic shock equation of a material is known, one may predict the behaviour of the material under cfynamic pressure action. 

On the other hand, the determination of the shock wave parameters has significant importance from the practical point of view. Thus, for instance, the study of the shock wave propagation through an explosive is important for the estimation of the initiation mechanism and the sensitivity of the explosives to... 

For the determination of the shock wave parameters in different media, the methods identical to those used for the determination of detonation wave parameters can be applied to a large extent. 

It should also be mentioned that there are a number of empirical expressions (Held, 1983, 1990 Lehmann, 1973) that one can use to calculate, with certain accuracy, the shock wave parameters such as shock wave pressure in different materials, shock wave velocity, pressure positive phase duration, and shock wave impulse. 

Fig. 6 The influence of explosive boiling on the shock wave parameters. Expansion of gas (a) and hot water (b). The time scale is 1 ms per division. The pressure scale (bottom traces) is 0.018 MPa per division. The impulse scale (upper traces) is 110 Pa s per division.

FIGURE 3.3. Shock wave parameters for a spherical TNT explosion on a surface at sea level (Lees, 1996). 

B. D. Lambourn, The Effect of Explosive Properties on the Shock Wave Parameters of Underwater Explosions , Sixth International Symposium on Detonation, ACR-221, 561 (1976). 

B.E. Gelfand, S.A. Gubin, V.N. Mikhalkin, V.A. Shargatov, Calculation of the shock wave parameters from the detonation of combustible gas mixtures of variable composition. Combust. Explos. Shock Waves 21(3), 355-360 (1985)... 

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