Wave profiles release

For a given amplitude of the quasi-elastic release wave, the more the release wave approaches the ideal elastic-plastic response the greater the strength at pressure of the material. The lack of an ideally elastic-plastic release wave in copper appears to suggest a limited reversal component, however, this is much less than in the silicon bronze. Collectively, the differences in wave profiles between these two materials are consistent with a micro-structurally controlled Bauschinger component as supported by the shock-recovery results. Further study is required to quantify these findings and... 

Figure 8.7. Propagation of wave profile in an elastic-plastic material from the spall plane to the monitoring interface. The wave front propagates at a plastic wave speed whereas the wave release propagates at an elastic wave speed and complicates the analysis of the material spall strength.

The unloading wave itself provides a direct measure of the strength at pressure from the shape of the release wave. Such a measurement requires time-resolved detection of the wave profile, which has not been the usual practice for most strong shock experiments. 

Fig. 2.11. Strength behavior of solids at pressure can be probed with reshock or release measurements. The resulting wave profiles of such measurements on a 6061-T6 aluminum alloy with VISAR instrumentation are shown. Strength behavior indicated on many solids reveals behavior not accurately described by simple materials models (after Lipkin and Asay [77L02]).

Perhaps the most visible technical problems studied and the most data available on shock-compressed solids are focused on the loading portion of wave profiles. Often, the portion of the wave profile corresponding to the release of pressure to atmospheric, but elevated temperature, values is the more descriptive of solids in the high pressure state. 

GPa, is particularly interesting because of the anomalous slope of the compressiblity to 3 GPa. The wave profile with loading and release wave in Fig. 2.17 shows the anomalous loading and the shock on release from the high stress state. 

Given the various release-wave behaviors summarized above, it is clear that release waves may often dominate wave profiles, and failure to consider their influences can lead to incorrect interpretation of observed materials responses, especially those in which samples are preserved for post-shock... 

Fig. 2.17. Fused quartz is known to have an anomalous softening with stress or pressure in both static and shock loading. The time-resolved wave profile measured with a VISAR system shows the typical low pressure ramp followed by a shock at higher pressure. The release to zero pressure is with a shock, in agreement with the shape of the pressure-volume curve (after Setchell [88S01]).

Dynamic tensile failure, called spall, is frequently encountered in shockloading events. Tension is created as compression waves reflect from stress-free surfaces and interact with other unloading waves or release-wave profiles. Spall has been widely studied by authors such as Curran, Ivanov, Dremin, and Davison and there is considerable data. As shown in Fig. 2.19, the wave profiles resulting from spall are characterized by an additional loading pulse after release of pressure. The late pulse is caused by wave reflection from the internal void of the tensile fracture. Analysis of such wave profiles yields appropriate spall stress values. 

Because of the subtle effects on the loading wave profile, many of the melting studies have utilized physical property measurements such as resistivity or optical opacity. Perhaps more direct are the release-wave speed... 

Of the other experimental methods which have been employed to investigate fast chain reactions at high temperatures, combustion studies in premixed gas flames have been the most generally useful. As with shock waves, profiles within the reaction zone of these flames are strongly dependent on the chemical processes governing the rate of energy release. As has been frequently demonstrated in the past, detailed examination of flame structure can yield significant amounts of kinetic information. 

Figure 3.9. Electromagnetic particle velocity profiles in limestone at 12 GPa. Profiles indicate both the arrival of the shock wave and the release wave from the free surface (Murri et al., 1975).

With nanosecond time resolution, sensitive, accurate detectors, studies of these release waves have proven to be particularly revealing. First-order descriptions of release properties were obtained with rudimentary instrumentation from the earliest studies [65A01] it has required the most sophisticated modern instrumentation to provide the necessary detail to obtain a clear picture of the events. Characteristically different profiles are encountered in the strong-shock, elastic, and elastic-plastic regimes. 

Fig. 2.20. The release wave portion of time-resolved velocity profiles in porous aluminum is shown as measured with VISAR instrumentation. At pressures near that required to cause melt, the release changes from that of an elastic wave to that of a bulk plastic wave, indicating the change to a melt condition (after Asay and Hayes [75A01]).

An accurate study of the temperature profile structure in film and capillary samples involves considerable technical difficulties, which accounts for the lack of direct information on the role of the isothermal and nonisothermal mechanisms in the systems considered. However, some features of the structure are evident from the cinegram of Fig. 9. It shows that the wave front traveling in a capillary is noticeably ahead of the zone of intense reaction-heat release, marked by violent boiling of liquid helium in the cryostat. This observation allows the conclusion that here the fore part of the wave front is located in the not yet heated portion of the sample that is, small degrees of... 

Fig. 71. Based on the measured temperature profile data (curve 1), the distribution of conversion along the combustion wave, riix) (curve 2), and the heat release function, (x) (curve 3), have been determined using Eq. (15). The characteristic length of the zones, is given by the size of the domain where < (jc) is nonzero. The preheating zone, xt, is defined as the sample length ahead of the front where...

Longitudinal profiles of shock wave properties in acetylene are shown in Figure 7 for a flyer plate impact speed of 16 km/s and a flyer plate thickness of six unit cells. Profiles for various times up to 1.2 ps after impact are depicted. At early times before the appearance of the release wave, when the mass velocity and density profiles are flat behind the shock front, it is possible to derive the parameters necessary for a Hugoniot analysis. As for methane, it is found that the Rankine-Hugoniot relations are satisfied. The Hugoniot parameters for several of the acetylene and methane simulations are collected in Table 1. Note that for a given flyer plate velocity, the temperature in the reaction zone is much higher for acetylene than for methane due to the exothermicity of the polymerization reactions. 

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