Wave profiles elastic-plastic

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... 

A typical shock-compression wave-profile measurement consists of particle velocity as a function of time at some material point within or on the surface of the sample. These measurements are commonly made by means of laser interferometry as discussed in Chapter 3 of this book. A typical wave profile as a function of position in the sample is shown in Fig. 7.2. Each portion of the wave profile contains information about the microstructure in the form of the product of and v. The decaying elastic wave has been an important source of indirect information on micromechanics of shock-induced plastic deformation. Taylor [9] used measurements of the decaying elastic precursor to determine parameters for polycrystalline Armco iron. He showed that the rate of decay of the elastic precursor in Fig. 7.2 is given by (Appendix)... 

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.

Wave profiles in the elastic-plastic region are often idealized as two distinct shock fronts separated by a region of constant elastic strain. Such an idealized behavior is seldom, if ever, observed. Near the leading elastic wave, relaxations are typical and the profile in front of the inelastic wave typically shows significant changes in stress with time. 

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. 

Figure 4.16. Free-surface velocity profiles measured on 1400° C molybdenum. The free-surface velocity profile is characterized by an 0.05 km/s amplitude elastic precursor, a plastic wave front, and a spall signal (characteristic dip) upon unloading. The dashed lines represent the expected free surface velocity based on impedance-match calculation [Duffy and Ahrens, unpublished].

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]).

Typical stress-time profiles for the various materials (28.5-at. % Ni, fee and bcc) and various stress regions are shown in Fig. 5.12. The leading part of the profile results from the transition from elastic to plastic deformation. The extraordinarily sharp rise in stress for the second wave in Fig. 5.12(a) and the faster arrival time compared with that in Fig. 5.12(b) is that expected if the input stress is above the transition, whereas the slower rise in Fig. 5.12(b) is that expected if the stress input to the sample is below the transition. The profile in Fig. 5.12(c) for the bcc alloy was obtained for an input particle velocity approximately equal to that in Fig. 5.12(a) for the fee alloy. The bcc alloy shows a poorly defined precursor region, but, in any event, much faster arrival times are observed for all stress amplitudes, as is indicative of lower compressibility. 

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