Shock pulse

Throughout this book, a shock pulse (a steady compression wave followed by an expansion wave) will be represented as a profile, such as in Fig. 2.6. In Fig. 2.8 we show a series of P-x snapshots of pressure versus propagation distance x for an initially square pulse, at a series of times t. For a fluid with... 

We imagine a finite-duration shock pulse arriving at some point in the material. The strain as a function of time is shown as the upper diagram in Fig. 7.11 for elastic-perfectly-plastic response (solid line) and quasi-elastic response generally observed (dash-dot line). The maximum volume strain = 1 - PoIp is designated... 

These observations were the basis for the proposal that polymers, like ionic crystals, exhibit shock-induced polarization due to mechanically induced defects which are forced into polar configurations with the large acceleration forces within the loading portion of the shock pulse. Such a process was termed a mechanically induced, bond-scission model [79G01] and is somewhat supported by independent observations of the propensity of polymers to be damaged by more conventional mechanical deformation processes. As in the ionic crystals, the mechanically induced, bond-scission model is an example of a catastrophic shock compression model. 

Figure 4 shows the final ventilation system protection scheme. It should be noted that even with a blast valve that closes in a few milliseconds there will be some reduced shock pulse that "leaks through" during closure of the valve. The peak value of this shock is a function of losses occurring as the shock passes through the valve and the duration is the valve closure time. The leakage shock was predicted using the blast valve manufacturers test data. 

FIGURE 5a SHOCK PULSE AT INLET SIDE OF BLAST VALVE... 

GENERATION OF CUSHION CURVES FROM ONE SHOCK PULSE... 

SocJ 30, 151-58(1960) (Recent advances in condensed media detonation) 37b) Dunkle s Syllabus (1960-1961), pp 4a 4b (Initiation of shock waves) lOa-lOg (Initiation of deflgrn and deton) p 12a (Frank-Kamenet-skii formulation) p 13b (Initiation by electric discharge) p 13f (Thermal Decomposition and Initiation of Explosives, as discussed by B. Reitzner) pp 17a to 17e (Mechanism of initiation and propagation of detonation in solid explosives) pp 17e 17f [Marlow Skidmore (Ref 31) concluded from their investigations that the problem of shock initiation is somehow related to the temperature distribution in the shock pulse and its effect on the chemical reaction rate. They used an Arrhenius type relationship for the rate increase in the frac-... 

In the words of Poulter Moore of Stanford Research Institute (quoted in Ref 4, p 197) "A normal shock pulse traveling in an inert medium is continuously doing work on the medium thru which it is traveling, and hence is continuously being attenuated and therefore decelerated. A detonation is a true shock pulse, but one in which the energy lost in attenuation. is being replaced by the energy released by the chemical reaction associated with the detonation pro-... 

The difference between a normal shock pulse and the shock front in a detonation is explained under "Detonation (and Explosion), Initiation of Explosives and Shock Processes ... 

Ling on shock pulse 3) V. Josephson, JApplPhys 29, 30-2(1958) (Production of high-velocity shocks) 6) Cook (1958), 322-52 (Shock waves in gaseous and condensed media) 7) J.O. Erkman, "Explosively Induced Nonuniform Oblique Shocks , PoulterLabsTechRept 010-58(1958)... 

For a strong primary shock wave, the reflected rarefaction wave propagates into water that has already been set in motion. Consequently, the rarefaction wave arrives earlier than predicted from the acoustic approximation, which ignores the particle velocity. Thus the pressure cutoff is not instantaneous. This effect typically gives a pulse shape shown by the solid line for Point A of Fig 33. The shallower the point at which pressure measurements are made, the sooner the primary shock pulse is truncated and the shorter its duration (see Fig 33, Point B). At shallow enough locations, the rarefaction wave interacts with the shock front and reduces the peak pressure (see Fig 33, Points C and D). The region in which the peak pressure is reduced is known as the anomalous region ... 

The management of a bleeding ulcer is dictated by the severity of the bleed. Mr B is not particularly old, he is not shocked (pulse rate less than f 00 bpm, systolic blood pressure over 100 mmHg), and active bleeding has not been reported. He had the appropriate fluid replacement (saline, a crystalloid). Blood was not needed as he did not have particular signs of hypovolaemic shock and his haemoglobin is above 10 g/dL. He had no risk factors to suggest that antibacterial prophylaxis was necessary before endoscopy. His enalapril and furosemide were temporarily stopped, and if his blood pressure, hydration state... 

However, often the detonation of the next assembly (upon which the detonator acts in the explosive train) is governed, not by the time integral of a pressure pulse (Figs. 7.24 and 7.25), but by the instantaneous shock pulse. In other words, while the depth of the dent is somewhat proportional to f p dt [N m 2 s = kg nr1 s 1]... 

Figs. 7.24 and 7.25), the strength of a detonator often corresponds better to an instantaneous shock pulse. 

N.B. A shock pulse (shock or pressure wave) develops when two pieces of moving metal contact each other in an initial impact. This shock pulse is in the ultrasonic frequency range and typically occurs at around 36 kHz. The amplitude of the shock pulse is proportional to the velocity of the impact. 

When impact occurs, a pressure or shock pulse is formed. Slab A continues to press upon slab B, sustaining the pressure. The shock moves into B toward the right, and also into A toward the left. As long as the slabs are in contact, the pressure, as well as the particle velocity on both sides of the interface, must remain the same and equal. This is shown in the x-t diagram in Figure 18.2. 

Look familiar In order to solve for all these parameters, we need an EOS in order to eliminate E and leave us an expression, P = f v). Since we do not have the EOS, we again resort to the Hugoniot. So the rarefaction unloads isentro-pically, and we assume that the isentrope is the same as the values along the Hugoniot. Let us take a look at this process on the P-v plane. To start with. Figure 19.1, a P-x snapshot, shows a square-wave pressure or shock pulse. 

Interaction of a nonsquare shock pulse with a free surface we will see how this can lead to multiple spall or scabbing. 

We now see the entire process of forming a square-wave pulse in a target by collision of a flyer. The pulse starts at G (Figure 19.10) and ends at tz (Figure 19.10) The constant-pressure portion of the shock pulse initially then has a duration of 2 t, and then gets narrower in time due to attenuation. 

Example 19.3 A thick slab of stainless steel has been impacted by a flyer plate. The impact formed a square-wave shock pulse in the steel that traveled to the opposite surface (which was free). The interaction of the shock pulse at the free surface produced a rarefaction wave that is traveling back into the square-wave shock pulse. The shock pressure is 7.5 GPa. When the rarefactions meet they will form a tension. Will the steel spall at this point ... 

We realize now that the square-wave shock pulse does not remain square. As soon as the rear square face of the shock is formed, it immediately begins to tip forward due to the effects we have seen from the rarefaction wave. Shock waves can also be formed that start with a fully sloped back, as when the shock is induced in a materia from detonation of an adjacent explosive. Figure 19.26 shows a sawtoothed wave in the P-x diagram. This is an idealized form of a partially attenuated shock pulse identical to the shock pulse received from an adjacent detonation. 

Let us consider that we shock an explosive with a square-wave pulse shock wave. This shock pulse has an amplitude P, the shock pressure, and a duration... 

Example 22.1 In a previous section we gave an example (section 19.2) of the impact of a polyethylene flyer, 5 mm thick, impacting a piece of PBX9404 at 2.5 km/s. We saw that this formed in the unreacted explosive a square-wave shock pulse with pressure of 7.73 GPa and duration of 1.6 s. Will the PBX9404 detonate promptly from this input ... 

We saw that the rarefaction traveling axially into the rear of the shock pulse in an explosive can attenuate the peak shock pressure, and thereby cause longer than ideal run distance or even cause detonation failure. Rarefactions traveling radially into the sides or edges of the impact shock wave can do the same. 

This effect is seen quite dramatically in data obtained by both Moulard and Wenograd (Ref. 9). In both sets of tests reported, very long shock pulses were used (the flyers were actually cylinders). Therefore, the data are shown only for pressure, not energy fluence. Each data point represents the 50% pressure for detonation versus nondetonation for different diameter flyers. The explosive targets were Composition B, and the flyers were steel. These results are shown plotted in Figure 22.8. 

The pressure duration cannot be significantly varied in this type of high-explosive setup and is mainly determined by the thickness of the projectile. Thinner projectiles yield higher pressures but also shorter pressure pulses. In our experiments with peak pressures of 20 GPa, the length of the shock pulse amounts to 1 ps, whereas, at 100 GPa the pulse is probably no longer than 0.1-0.2 ps [35]. 

In line with the longer shock pulse in the electrical discharge experiment, calcite recovered from this experiment shows a larger damaged area with a diameter of 3790 pm and a depth of 930 pm (Fig. 1.10b). Despite the development... 

Due to the short length of a probe temperature rise (about 1 ps) the measurement stage is shifted to the cooling tail followed by the shock heating pulse.The cooling process is recorded due to relatively low, so-called monitoring current across the probe. The shock pulse may be superimposed on... 

Strain rates < 5xl0 /s consists of irregular dislocation entanglements. As the pulse duration increases, these entanglements become more distinguishable. However, at strain rates S 5x10 /s, the microstructure consists of micro bands. These bands become more defined as the shock pulse duration increases. Within these bands, areas of high dislocation densities, surrounded by relatively lower dislocation density areas were observed. 

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