High-Pressure Shock Compression of Solids

In 1956, Nobel-Prize-Winner-to-Be, P.W. Bridgman published a short paper entitled “High-Pressure Polymorphism of Iron” [1], reporting the results of his measurements of the resistance of iron samples under static high pressures. The work was motivated by the report by Bancroft et al. [2] of a discontinuity in the pressure–volume relation of iron at 13 GPa under high-pressure shock loading, which they interpreted as due to a previously unknown polymorphic phase transformation. Finding no indication of such a transition, Bridgman commented upon the Los Alamos work as:

Shock waves are the ubiquitous result of matter moving at velocities faster than the speed at which adjacent material can move out of the way. Examples range in scale from the shock waves generated by the collapse of microscopic cavitation bubbles to light-year scale “collisionless shocks” in the interstellar medium. The concept of a shock wave is well illustrated by the flow of snow in front of a moving snowplow (Fig. 2.1). When a plow begins moving into fresh, loose snow, a layer of packed snow builds up on the blade. The interface between the fresh snow and packed snow moves out ahead of the blade at a speed greater than that of the plow.

Investigations in the field of shock compression of solid materials were originally performed for military purposes. Specimens such as armor were subjected to either projectile impact or explosive detonation, and the severity and character of the resulting damage constituted the experimental data (see, e.g., Helie, 1840). Investigations of this type continue today, and although they certainly have their place, they are now considered more as engineering experiments than scientific research, inasmuch as they do little to illuminate the basic physics and material properties which determine the results of shock-compression events.

The use of plane shock waves to determine the equations of state of condensed materials to very high pressure began in 1955 with the classic papers of Walsh and Christian (1955) and Bancroft et al. (1956). Walsh and Christian described the use of in-contact explosives to determine dynamic pressure– volume relations for metals and compare these to the then available static compression data. Bancroft et al. described the first polymorphic phase change discovered in a solid, via shock waves—iron. Two years later Soviet workers (Al’tshuler et al., 1958) reported the first data for iron to pressures of several million bars (megabars) actually exceeding the pressure conditions within the center of the Earth. Since that time the equations of state of virtually hundreds of condensed materials have been studied, including elements, compounds, alloys, rocks and minerals, polymers, fluids, and porous media. These studies have employed both conventional and nuclear explosive sources, as well as impactors launched with a range of guns to speeds of approximately 10 km/s. Recently, Avrorin et al. (1986) have reported shock-compression data in lead to a record pressure of 550 Mbar.

While the field of shock-wave physics has provided significant insights into many of the processes related to wave propagation in materials, the exact micromechanisms of deformation during shock loading remain poorly understood. The initial response of a material subjected to explosive or high-velocity impact conditions is to propagate shock waves that rapidly traverse the material. These waves produce dynamic deformations, the extent of strain is dependent on the precise method of loading and the degree to which a hydrostatic stress state is maintained. If we are to develop an understanding of the total response of a material to impact, we must investigate the specific influence of shock waves on microstructure and the corresponding effects on mechanical properties. The severe loading path conditions imposed during a shock induce a high density of defects in most materials, i.e., dislocations, point defects, and/or deformation twins. In addition, during the shock process some materials may undergo a pressure-induced phase transition which will affect the real-time material response. If the phase remains present to ambient conditions (although metastable) the post-mortem substructure and mechanical response will also reflect the high-pressure excursion. Interpretation of the results of shock-wave effects on materials must therefore address all of the details of the shock-induced deformation substructure in light of the operative metallurgical strengthening mechanisms in the material under investigation, and the experimental conditions under which the material was deformed and recovered.

The application of what is commonly known as solid continuum mechanics has been very successful in descriptions of the shock-compression process. It has given us the jump conditions, useful concepts of average quantities such as density and specific internal energy (for example), and constitutive descriptions (including equations of state) involving these average quantities and their time rates of change. Even as we profitably use these ideas, we always have in mind micromechanical concepts such as the crystal lattice, the electronic structure of the crystallographic system, and lattice defects which give rise to important physical phenomena.

The dynamic fracture and fragmentation of a solid body or structure can result from the application of an intense impulsive load. The scale of such events ranges from shaped-charge jet breakup and rock blasting to astro-physical impacts and creation of planetary debris. In rock blasting, for example, specific information on ejecta velocities and fragment size distributions is sought, and methods to control resulting fragment sizes by proper placement and type of explosives are of interest (Grady and Kipp, 1987). In stretching shaped-charge jets, fragmentation characteristics, such as time-to-breakup and particle size are intimately tied to performance (Chou and Carleone, 1977). Ejecta from planetary and meteoric impact provide information on the evolution and dynamics of the solar system (Melosh, 1984). The applications in which solids or structures are subjected to intense dynamic loading and when breakup must be mitigated or controlled are numerous and varied. The need to understand the dynamic fracture mechanisms for such applications has provided the impetus for research in this rich area, and the field is currently quite active. The response of a single crack or void, within a solid body, to both static and impulsive loading has received considerable attention over the past several decades and is reasonably well understood (Freund, 1973; Chen and Sih, 1977; Kipp et al., 1980). The mechanics of a system of cracks or voids under impulsive or stress-wave loading, and how the cooperative response of such a system relates to the transient strength and ultimate failure and fragmentation of a solid body is less well understood, and has been a subject of study over the past decade (Curran et al., 1977; Davison and Graham, 1979; Meyer and Aimone, 1983; Grady and Kipp, 1987; Curran et al., 1987). Experimental studies of fracture under high-rate loading have revealed unusual features associated with the phenomenon, such as enhanced material strength and failure-stress dependence on loading conditions. Although such observations have led to the postulation of rate-dependent material properties, most of the features can be understood through fundamental fracture concepts when considered in terms of a system of interacting cracks or voids.

In this section, we discuss the role of numerical simulations in studying the response of materials and structures to large deformation or shock loading. The methods we consider here are based on solving discrete approximations to the continuum equations of mass, momentum, and energy balance. Such computational techniques have found widespread use for research and engineering applications in government, industry, and academia.

In closing, we would like to re-emphasize our original goal of creating a tutorial, as well as a textbook, for the beginning student of high-pressure shock-compression science. We feel that we have been able to achieve this through the coverage of materials presented in Chapters 1 through 9. Throughout the book, we have tried to provide a perspective of the technological advances that have occurred in the understanding of the dynamic response of materials over the past half-century. As Bob Graham discussed in the first chapter, the field of shock compression grew but of a need to describe the high-pressure response of materials in regimes previously inaccessible by conventional methods. This requirement has led to the development of a rich variety of experimental and theoretical tools that have been indispensable in probing the transitory nature of the shock-compression event. From systematic experimental and theoretical studies, a deep understanding has been obtained of the thermophysical and mechanical properties of condensed materials in extreme pressure and temperature environments.