Shock determination

The sensitivity of an energetic material towards accidental stimuli such as fast heating, electrostatic discharge, friction, impact and shock determines its safety characteristic and, hence, decides whether a certain material may be actually used and whether it can be safely transported. Corresponding test methods are described in Test Series 3 of the UN Orange Book [la]. These tests determine the sensitiveness to impact, friction (and impacted friction), thermal stabiUty and response of the substance to fire. 

Under constant pattern conditions the LUB is independent of column length although, of course, it depends on other process variables. The procedure is therefore to determine the LUB in a small laboratory or pilot-scale column packed with the same adsorbent and operated under the same flow conditions. The length of column needed can then be found simply by adding the LUB to the length calculated from equiUbrium considerations, assuming a shock concentration front. 

The properties of high quaUty vitreous sihca that determine its uses iaclude high chemical resistance, low coefficient of thermal expansion (5.5 X 10 /° C), high thermal shock resistance, high electrical resistivity, and high optical transmission, especially ia the ultraviolet. Bulk vitreous sihca is difficult to work because of the absence of network-modifyiag ions present ia common glass formulations. An extensive review of the properties and stmcture of vitreous sihca is available (72). 

Applications. Initial appHcations have been largely in military and aerospace areas. These include hydrauHc seals for military aircraft and fuel seals and diaphragms for both military and civiHan aircraft. Shock mounts for EZ are used on aircraft engines. Large fabric-reinforced boot seals are used in the air intake system on the M-1 tank. The material s useful temperature range, fuel and fatigue resistance, and fire resistance were determining factors in this appHcation. 

Thus, the effluent concentration becomes zero at Ti Tp = 1/R. The position of the leading edge (a shock front ) is determined from Eq. (16-132) ... 

Histamine is the biological amine, playing an important role in living systems, but it can also cause unnatural or toxic effects when it is consumed in lai ge amounts. It can occur with some diseases and with the intake of histamine-contaminated food, such as spoiled fish or fish products, and can lead to undesirable effects as headache, nausea, hypo- or hypertension, cai diac palpitations, and anaphylactic shock syndrome. So, there is a need to determine histamine in biological fluids and food. 

The equation that expresses conservation of energy can also be determined by considering Fig. 2.3. Since the piston moves a distance u At, the work done by the piston on the fluid during this time interval is Pu At. The mass of material accelerated by the shock wave to a velocity u is PqU At. The kinetic energy acquired by this mass element is therefore (pqUu ) At/2. If the specific internal energies of the undisturbed and shocked material are denoted by Eq and E, respectively, the increase in internal energy is ( — o)Po V At per unit mass. The work performed on the system is equal to the sum of kinetic and... 

For interactions in which material at a given point experiences only one shock wave and no other shocks or rarefactions, the principal Hugoniot is all that is required to determine the states achieved. In situations in which a material experiences several shocks or rarefactions, using the principal Hugoniot to approximate subsequently shocked or released states may or may not be a good approximation. In this section, only singly-shocked materials at small strains are considered. 

It is important to note that the state determined by this analysis refers only to the pressure (or normal stress) and particle velocity. The material on either side of the point at which the shock waves collide reach the same pressure-particle velocity state, but other variables may be different from one side to the other. The material on the left-hand side experienced a different loading history than that on the right-hand side. In this example the material on the left-hand side would have a lower final temperature, because the first shock wave was smaller. Such a discontinuity of a variable, other than P or u that arises from a shock wave interaction within a material, is called a contact discontinuity. Contact discontinuities are frequently encountered in the context of inelastic behavior, which will be discussed in Chapter 5. 

Investigations in the field of shoek eompression of solid materials were originally performed for military purposes. Speeimens sueh as armor were subjected to either projectile impact or explosive detonation, and the severity and character of the resulting damage constituted the experimental data (see, e.g., Helie, 1840). Investigations of this type continue today, and although they certainly have their place, they are now considered more as engineering experiments than scientific research, inasmuch as they do little to illuminate the basic physics and material properties which determine the results of shock-compression events. 

The advent of lasers allowed optical interferometry to become a useful and accurate technique to determine surface motion in shocked materials. The two most commonly used interferometric systems are the VISAR (Barker and Hollenbach, 1972) and the Fabry-Perot velocity interferometer (Johnson and Burgess, 1968 Durand et al., 1977). Both systems produce interference fringe shifts which are proportional to the Doppler shift of the laser light reflected from the moving specimen surface. Both can accommodate a speci-... 

Figure 3.11. VISAR fringe record and the velocity profile at the calcite/lithium fluoride interface at about 18 GPa. The excellent time resolution of the interferometer allows an unambiguous determination of the rarefaction shock (d) in calcite (Grady, 1986).

Figure 3.15. Current versus time and charge versus time profile determined by PVFj in sapphire at 12 GPa (Graham and Lee, 1986). Profiles indicate both a shock loading and release profile.

In the simplest case when a single shock state is achieved via a shock front, the Rankine-Hugoniot equations involve six variables U, u, p, Pi, i — Eq, and Pi) thus, measuring three, usually U, m, and p, determines the shock state, pi, , - A- The key assumption underpinning the... 

Understanding such interaction is important both in predicting the amplitudes of shock waves transmitted across interfaces (in the case where the equations of state of all materials are known), and in determining release isentropes or reflected Hugoniots (when measurement of the equation of state is needed). Consider first a shock wave in material A being transmitted to a... 

Another important method of determining the Gruneisen ratio in the shock state is the measurement of sound speed behind the shock front. The techniques employing optical analyzers (McQueen et al., 1982) piezoresistive (Chap-... 

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