Elastic precursor

At loading stresses between the HEL and the strong shock threshold, a two-wave structure is observed with an elastic precursor followed by a viscoplastic wave. The region between the two waves is in transition between the elastic and the viscoplastic states. The risetime of the trailing wave is strongly dependent on the loading stress amplitude [5]. 

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 The dashed lines represent the expected free surface velocity based on impedance-match calculation [Duffy and Ahrens, unpublished].

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)... 

The decaying elastic precursor is also studied in a number of single crystals... 

Asay and Gupta [25] measure elastic precursor amplitudes as functions of propagation distance for two different divalent impurity concentrations in <100)-loaded LiF. It is shown that not only does the presence of divalent ions affect the precursor amplitude, but also that the state of the dispersion plays an important part. It is concluded that, for a given concentration of defects, the rate of precursor attenuation is reduced if the defects are clustered. 

Introduction of the surface-nucleation mechanism in numerical computation of elastic-plastic wave evolution leads to enhanced precursor attenuation in thin specimens, but not in thicker ones. Inclusion of dislocation nucleation at subgrain boundaries indicates that a relatively low concentration of subgrain boundaries ( 2/mm) and nucleation density (10"-10 m ) is sufficient to obtain predicted precursor decay rates which are comparable to those obtained from the experiments. These experiments are only slightly above the threshold necessary to produce enhanced elastic-precursor decay. 

These techniques have very important applications to some of the micro-structural effects discussed previously in this chapter. For example, time-resolved measurements of the actual lattice strain at the impact surface will give direct information on rate of departure from ideal elastic impact conditions. Recall that the stress tensor depends on the elastic (lattice) strains (7.4). Measurements of the type described above give stress relaxation directly, without all of the interpretational assumptions required of elastic-precursor-decay studies. 

Show that the relaxation function F can be obtained from elastic precursor measurements of D,u and u according to... 

J.R. Asay and Y.M. Gupta, Effect of Impurity Clustering on Elastic Precursor Decay in LiF, J. Appl. Phys. 43, 2220-2223 (1972). 

Y. Partom, Elastic Precursor Decay Calculation, J. Appl. Phys. 59, 2716-2727 (1986). 

Meyers, M.A., A Model for Elastic Precursor Waves in the Shock Loading of Polycrystalline Metals, Mater. Sci. Engrg. 30, 99-111 (1977). 

Fig. 2.7. Elastic precursor decay in which elastic waves are observed to decrease in amplitude with propagation distance is a typical behavior. The data of this figure describe the behavior of crystalline LiF samples of different yield strengths (after Asay et al. [72A02]).

Fujima, T., Frusawa, H., Minamikawa, H., Ito, K. and Shimizu, T. (2006) Elastic precursor of the transformation from glycolipid nanotube to vesicle, Journal of Physics Condensed Matter, 18, 3089—3096. Kameta, N., Minamikawa, H., Masuda, M., Mizuno, G. and Shimizu, T. (2008) Controllable biomolecule release from self-assembled organic nanotubes with asymmetric surfaces pH and temperature dependence. Soft Matter, 4 (8), 1681-1688. Weiss R.G. and Terech P. (eds.) (2006) Molecular Gels Materials with Self-Assembled Fibrillar Networks, Springer, Dordrecht. 

This method also permits one to observe directly on the film the discontinuous aspect of shock phenomenon and it can be used to observe elastic precursors in weak shocks, to analyze changes of state, and to investigate the causes of shock-wave doubling... 

The formation and evolution of multiple waves becomes more complicated when chemical reactions or phase transitions occur. Volume decreasing phase transformations cause the pressure at point B in Figure 2 and Figure 7 to decrease with time. This common phenomenon is known as elastic precursor decay in elastic-plastic wave system. [9] The timescale for this pressure decay depends primarily on the timescale for the chemical reaction or phase transition that gives rise to the 2" wave. 

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