Response of Shock-Compressed Solids

What are the characteristic mechanical responses of solids to shock loading This question is most clearly addressed through the relation between stress-volume relations and wave structures. 

The characteristic behavior of solids includes a limiting value of elastic 

Introduction to High-Pressure Shock Compression of Solids 5 

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]. 

The complexity of the typical solid deformation response can be further compounded by the presence of one or more polymorphic phase transformations, and a host of other phenomena typical of solids. Table 1.1 lists a number of such phenomena. 

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To develop a terse, broad description of mechanical, physical, and chemical processes in solids, this book is divided into five parts. Part I contains one chapter with introductory material. Part II summarizes aspects of mechanical responses of shock-compressed solids and contains one chapter on materials descriptions and one on experimental procedures. Part III describes certain physical properties of shock-compressed solids with one chapter on such effects under elastic compression and one chapter on effects under elastic-plastic conditions. Part IV describes work on chemical processes in shock-compressed solids and contains three chapters. Finally, Part V summarizes and brings together a description of shock-compressed solids. The information contained in Part II is available in much better detail in other reliable sources. The information in Parts III and IV is perhaps presented best in this book. 

Fig. 2.1. The traditional approach to the study of mechanical responses of shock-compressed solids is to apply a rapid impulsive loading to one surface of a diskshaped sample and measure the resulting wave propagating in the sample. As suggested in the figure, the wave shapes encountered in shock-loaded solids can be complex and may require measurements with time resolutions of a few nanoseconds.

The present book, with contributions from a group of very knowledgable scientists in the field, is an attempt to provide a basis for addressing Bridgman s concerns. The response requires multidisciplinary contributions from solid mechanics, solid-state physics, materials science, and solid-state chemistry. Certainly, advances in theory, experimentation, and numerical simulation are impressive, and many aspects of shock-compressed solids have been studied in detail. At the fundamental level, however, it is certainly appropriate to question how well shock-compression processes are understood. 

The foundation of shock-compression science is based upon observations and analyses of the mechanical responses of solid samples to shock-loading pulses. Although the resulting mechanical framework is necessary, there is no reason to believe that a sufficiently complete scientific picture can be based on mechanical considerations alone. Nevertheless, the base of our knowledge rests here, and it is essential to recognize its characteristics, and critically examine the work. 

This loss of shear strength was confirmed as typical of other strong solids in mechanical response studies of shock-compressed sapphire by Graham and Brooks [71G01]. In this ease there was a substantial reduction, but not... 

Z. P. Tang, Y. Horie, and S.G. Psakhie, in High-Pressure Shock Compression of Solids, IV, Response of Highly Porous Solids to Shock Loading (eds. Lee Davison, Y. Horie, and Mohsen Shahinpoor), Springer-Verlag, New York, pp. 143-176 (1997). 

In shock-compression science the scientific interest is not so much in the study of waves themselves but in the use of the waves as a means to probe solid materials. As inertial responses to the loading, the waves contain detailed information describing the mechanical, physical, and chemical properties and processes in the unusual states encountered. Physical and chemical changes may be probed further with optical, electrical, or magnetic measurements, but the behaviors are intimately intertwined with the mechanical aspects of the waves. 

Uncoupled solutions for current and electric field give simple and explicit descriptions of the response of piezoelectric solids to shock compression, but the neglect of the influence of the electric field on mechanical behavior (i.e., the electromechanical coupling effects) is a troublesome inconsistency. A first step toward an improved solution is a weak-coupling approximation in which it is recognized that the effects of coupling may be relatively small in certain materials and it is assumed that electromechanical effects can be treated as a perturbation on the uncoupled solution. 

In this book those ferroelectric solids that respond to shock compression in a purely piezoelectric mode such as lithium niobate and PVDF are considered piezoelectrics. As was the case for piezoelectrics, the pioneering work in this area was carried out by Neilson [57A01]. Unlike piezoelectrics, our knowledge of the response of ferroelectric solids to shock compression is in sharp contrast to that of piezoelectric solids. The electrical properties of several piezoelectric crystals are known in quantitative detail within the elastic range and semiquantitatively in the high stress range. The electrical responses of ferroelectrics are poorly characterized under shock compression and it is difficult to determine properties as such. It is not certain that the relative contributions of dominant physical phenomena have been correctly identified, and detailed, quantitative materials descriptions are not available. 

Studies of the electrical and mechanical responses of ferroelectric solids under shock compression show this technical problem to be the most complex of any investigated. The combination of rate-dependent mechanical and electrical processes along with strong electromechanical coupling has clouded physical interpretation of the numerous investigations. 

Table 6.2 summarizes the low pressure intercept of observed shock-velocity versus particle-velocity relations for a number of powder samples as a function of initial relative density. The characteristic response of an unusually low wavespeed is universally observed, and is in agreement with considerations of Herrmann s P-a model [69H02] for compression of porous solids. Fits to data of porous iron are shown in Fig. 6.4. The first order features of wave-speed are controlled by density, not material. This material-independent, density-dependent behavior is an extremely important feature of highly porous materials. 

The Gmeneisen parameter is not necessarily constant (except initially, at zero pressure), but decreases with increa g compression. The EOS for this process is not known for the shocked state, even for a homogeneous expl,much less for such a heterogeneous mixt as a solid proplnt The response of composite proplnts to impact was studied phenomenologically by B. Brown (Ref 22). He divided the response into fracture, ignition and detonation regimes. The ignition velocity was found to be only a function of proplnt mass. His data are shown in Fig 4 to which the results of a more recent study were added (Ref 68). He also found that the yield... 

The melting point of a solid and its response to shock waves depends on the form and depth of the interatomic potential. Its compressibility is simply related to the Born repulsion parameter. The mechanical hardness is a function of the bulk modulus (inverse compressibility), which in turn correlates strongly with the volume density of the chemical bonding energy, i.e., the bonding energy per unit volume the smaller the atoms and the stronger the atomic bond, the harder the solid. In the box on p. 34, a simple relation is derived between the bulk modulus and the Bom repulsion parameter. 

Graham RA (1974) Shock-wave compression of x-cut quartz as determined by electrical response measurements. J Phys Chem Solids 35 355... 

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