Unloading wave

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. 

In materials that support shock waves, the sound speed increases with pressure. It is this same property that causes rarefactions to spread out as they progress. In Fig 2.6(b), an unloading wave is shown propagating into a stationary material with some initial pressure Pq. This time, we consider the evolution of two small decompressional disturbances. The first disturbance moves at the local sound speed of a, into its surroundings, which have begun... 

Unsteady wave A loading or unloading wave whose profile changes with time. The jump conditions cannot be rigorously applied to such a wave. 

Recent experiments by Gray et al. [47] have probed the contribution of the Bauschinger effect on real-time unloading wave profiles and postshock... 

Figure 6.17. VISAR wave profiles of copper and silicon bronze at 10 GPa exhibiting differing unloading wave shapes supporting a Bauschinger effect contribution to unloading.

This phenomenon is still under investigation as is the substantial departure of calculated from that measured at volume strains below 0.15 as shown in Fig. 7.13. Details of these calculations are presented in the work of Johnson et al. [47]. The important consideration is that the unloading wave also contains micromechanical information if we only can be clever enough to apply proper interpretation to macroscale measurements. 

J.N. Johnson, P.S. Lomdahl, and J.M. Wills, Analysis of Internal Stress and An-elasticity in the Shock-Compressed State from Unloading Wave Data, Acta Metall 39, 3015-3026 (1991). 

Further, if one considers the distance the tensile unloading wave can propagate over the time to fracture f from (8.46), a lower bound criterion for the fragment size can be established... 

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... 

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. 

Given limits to the time resolution with which wave profiles can be detected and the existence of rate-dependent phenomena, finite sample thicknesses are required. To maintain a state of uniaxial strain, measurements must be completed before unloading waves arrive from lateral surfaces. Accordingly, larger loading diameters permit the use of thicker samples, and smaller loading diameters require the use of measurement devices with short time resolution. 

As the current pulse is largely dominated by the stress differences, a short duration current pulse is observed upon loading with a quiescent period during the time at constant stress. With release of pressure upon arrival of the unloading wave from the stress-free surface behind the impactor, a current pulse of opposite polarity is observed. The amplitude of the release wave current pulse provides a sensitive measure of the elastic nonlinearity of the target material at the peak pressure in question. 

It is impossible for a pressure to exist at M that is greater than that due to the depth producing the flow at M, and so it instantly drops down to the value it would have for zero flow. But the entire pipe is now under an excess pressure, so the water in it is compressed and the pipe walls are stretched. Then some water starts to flow back into the reservoir, and a wave of pressure unloading travels along the pipe from M to N. At the instant this unloading wave reaches N, the entire mass of water will be under the static pressure equal to the pressure initiating flow at M. But the water is still flowing back into the reservoir, and this... 

In the previous sections, we dealt in detail with the properties at the shock front, the jump process that takes material in front of the shock to the state behind the shock. We showed that this is indeed a discontinuous process, and that pressure disturbances cannot outrun the shock (in the strong shock region). We stated, but did not demonstrate, that the rarefaction wave (also called relief, or unloading wave they are all synonymous) is continuous, that it follows a path function, not a jump condition. Let us look into this statement now. 

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