expansion rate in air, the incident air shock wave properties are determined: shock wave velocity Us, shock wave Mach number Ms, particle velocityus, and incident shock wave pressurePs. Additionally, the energy per unit area or energy fluence transferred from the detonator to an another possible energetic material can be calculated from the values of shock wave pressure Ps, and time duration td if the properties (Hugoniot) of the material are known. 36.2.1 Air Shock Characterization The present paper reports the shock wave expansion from two types of electric detonators corresponding to two different values of strength: number 6 and number 8. The expansion is measured in two coordinates X and Y, corresponding with the longitudinal and transversal axes of the detonator. This is due to the initial elliptical expansion of the shock wave in the 2D plane produced by the charge geometry. As the shock wave expands, it decays in strength, lengthens in duration, and slows down, both because of the spatial divergence and because of the medium attenuation. Most of the sources of compiled data for air blast waves from high explosives are limited to bare, spherical charges in free air. However, different experiments conducted with alternative charge geometries show how explosive materials tens to drive their energy to the larger area of their outer surface. Esparza [13] presented a spherical equivalency of cylindrical charges in free air where a higher explosive yield is reached at 90 from the longitudinal charge axis. The difference in the shock wave magnitude in the different directions will decrease as the shock expands through the air adopting a final spherical shape. This data is in agreement with the experimental observations presented in this paper where the two detonator studied are cylindrical in shape. This shape will produce an initially ellipsoidal expanding shock wave creating higher overpressure in the plane normal to the charge axis. As the shock wave moves outward, the initial ellipsoid will degenerate into an expanding sphere. The shock wave expansion rate in atmospheric air is experimentally measured by using a retro-reflective shadowgraph technique. This expansion is measured along the longitudinal and transversal axes of the detonator providing two set of data. The measured shock wave expansion rate is then fitted to an empirical equation developed by Dewey [14] and reported by Hargather et al. [15] and Biss (2009). This empirical correlation is as follows: Rs ta ð Þ¼AþBa0ta þCln 1þa0ta ð ÞþD ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifffii ln 1þa0ta ð Þ p ð36:1Þ WhereRs represents distance from the center of the blast, ta represents time of arrival of the shock wave, a0 is the local speed of sound, andA, B, C, andDare the yielding coefficients. For curve fits to data close to the charge center, Bshould be set to 1 to guarantee an asymptote to the speed of sound for large time [14]. The calculation of the parameters A, B, C, and Dwas performed by least-squares curve-fit through a computational code written in MATLAB [15]. Next, a relationship between shock velocities versus time can be obtained by simple derivation of the Eq. (36.1) for longitudinal and transversal directions: dRs ts ð Þ dts ¼ Ba0 þ Ca0 1þa0ts þ Da0 2 1þa0ts ð Þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ln 1þa0ts ð Þ p ð36:2Þ An explosive shock moving with a certain velocity Us into an atmosphere where the sonic or acoustic speed is Ca will produce an associated pressure jump known as overpressure of the explosive shock front. Assuming a constant heat capacity ratio for air of 1.4, Kinney and Graham [17] defined the following equation describing the blast overpressure as a function of the shock Mach number Ms ¼Us/Ca and the atmospheric pressure Pa. Ps ¼ 7 M2 s 1 6 Pa ð36:3Þ As can be deduced from Eq. (36.3), for shock waves generated in an explosion, where intensity of shock diminishes with distance from the center of the explosion, shock overpressure approached zero and shock velocity approached sonic as distance increases. That is, any explosive shock wave ultimately degenerates into a sound wave. Equation (36.3) and some alternative forms presented in [17] have been widely used for indirect computation of overpressures from shock velocity measurements. 36 Shadowgraph Optical Technique for Measuring the Shock Hugoniot from Standard Electric Detonators 281
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