Release Waves

Expansion waves are the mechanism by which a material returns to ambient pressure. In the same spirit as Fig. 2.2, a rarefaction is depicted for intuitive appeal in Fig. 2.7. In this case, the bull has a finite mass, and is free to be accelerated by the collision, leading to a free surface. Any finite body containing material at high pressure also has free surfaces, or zero-stress boundaries, which through wave motion must eventually come into equilibrium with the interior. Expansion waves are also known as rarefaction waves, unloading waves, decompression waves, relief waves, and release waves. Material flow is in the same direction as the pressure gradient, which is opposite to the direction of wave propagation. 

The properties required of a material in order for it to support a stable shock wave were listed and discussed. Rarefaction, or release waves were defined and their behavior was described. The useful tool of plotting shocks, rarefactions, and boundaries in the time-distance plane (the x-t diagram) was introduced. The Lagrangian coordinate system was defined and contrasted to the more familiar Eulerian coordinate system. The Lagrangian system was then used to derive conservation equations for continuous flow in one dimension. 

What happens when a shock wave collides head-on with a release wave ... 

Shock Luminescence. Some transparent materials give off copious amounts of light when shocked to a high pressure, and thus they can serve as shock arrival-time indicators. A technique used by McQueen and Fritz (1982) to measure arrival times of release waves is based on the reduction of shock-induced luminescence as the shock pressure is relieved. Bromoform, fused quartz, and a high-density glass have been used for their shock luminescence properties. 

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).

Grady, D.E. (1986), Eligh-Pressure Release-Wave Measurements and Phase Transformation in CaCOj, in Shock Waves in Condensed Matter (edited by Y.M. Gupta), Plenum, New York, pp. 589-594. 

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... 

When we translate these observations into Lagrangian wave speed, the data would look like that shown in the lower diagram of Fig. 7.11. The points e and q represent volume strains at whieh elastie-perfeetly-plastie release (e) and quasi-elastie release (q) would undergo transition to large-seale, reverse plastie flow (reverse yield point). The question is the following What is responsible for quasi-elastie release from the shoeked state, and what do release-wave data tell us about the mieromeehanieal response in the shoeked state ... 

Values of are calculated from (7.48) and (7.49) for a constant release-wave strain rate n = —10 s and appropriate bulk and shear moduli corresponding to peak compression of 0.17. The results are shown in Fig. 7.13. The... 

In this chapter the regimes of mechanical response nonlinear elastic compression stress tensors the Hugoniot elastic limit elastic-plastic deformation hydrodynamic flow phase transformation release waves other mechanical aspects of shock propagation first-order and second-order behaviors. 

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. 

The elastic-shock region is characterized by a single, narrow shock front that carries the material from an initial state to a stress less than the elastic limit. After a quiescent period controlled by the loading and material properties, the unloading wave smoothly reduces the stress to atmospheric pressure over a time controlled by the speeds of release waves at the finite strains of the loading. Even though experiments in shock-compression science are typically... 

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. 

The release wave of fused quartz, thought to be elastic to stresses of... 

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. 

Release waves for the elastic-plastic regime are dominated by the strength effect and the viscoplastic deformations. Here again, quantitative study of the release waves requires the best of measurement capability. The work of Asay et al. on release of aluminum as well as reloading, shown in Fig. 2.11, demonstrates the power of the technique. Early work by Curran [63D03] shows that limited time-resolution detectors can give a first-order description of the existence of elastic-plastic behavior on release. 

Observations of smooth spalls in iron provided an early, dramatic demonstration of the importance of release wave behaviors. In 1956, Dally [61E01] reported the existence of remarkably smooth fracture surfaces in explosively compressed steel. The existence of these smooth spalls was a sensitive function of the sample thickness. Analysis and experiments by Erkman [61E01] confirmed that the smooth spalls were associated with interaction of release-wave shocks and shocks from reduction of pressure at free surfaces. These release shocks are a consequence of differences in compressibility at pressures just below and just above the 13 GPa transformation. 

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... 

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... 

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