Chapter vii – the equation of state of solids from shock wave studies

Shock-wave data have been obtained for the following rocks: one albitite, one anorthosite, two bronzitites, two diabases, two dunites, two eclogites, one granite, and one Jadeite. The experimental pressure range is from slightly over 0.1 to about 1.0 Mb. There is evidence that all rocks investigated exhibit a phase change. It is estimated that the transformations occur at about 0.1 Mb for the low-density rocks and between 0.3 and 0.6 Mb for the high-density rocks. A single-shock Hugoniot consistent with the data has been determined for the high-pressure modification of some of these rocks. These equations of state are compared with similar equations of state derived from geophysical data for the earth. This comparison supports the model of a mantle composed of high-pressure modifications of these basic rocks with an iron content lying somewhere between that of Twin Sisters dunite and Hortonolite dunite. Other thermodynamic quantities have been calculated based on estimates of the specific heat and the Gruneisen parameter.

Hugoniot equation of state of twelve rocks

Shock compression of solids

Nonequilibrium molecular-dynamics simulations of shock waves in three-dimensional 10-million atom face-centered cubic crystals with cross-sectional dimensions of 100 by 100 unit cells show that the system slips along all of the available {111} slip planes, in different places along the nonplanar shock front. Comparison of these simulations with earlier ones on a smaller scale not only eliminates the possibility that the observed slippage is an artifact of transverse periodic boundary conditions, but also reveals the richness of the nanostructure left behind. By introducing a piston face that is no longer perfectly flat, mimicking a line or surface inhomogeneity in the unshocked material, it is shown that for weaker shock waves (below the perfect-crystal yield strength), stacking faults can be nucleated by preexisting extended defects.

https://science.sciencemag.org/content/sci/280/5372/2085.full.pdf

Plasticity Induced by Shock Waves in Nonequilibrium Molecular-Dynamics Simulations

Plate impact experiments producing plane waves of up to 40 GPa (400 kbar) peak stress were performed using Armco iron specimens and impactors. Highly accurate time‐resolved measurements of the resulting free‐surface velocities of the specimens were obtained with the VISAR laser interferometer instrumentation system. The free‐surface velocity profiles provide new information concerning the rate effects associated with the α → e polymorphic phase transition at 13 GPa, the material strength and release wave speeds at 10 and 40 GPa, and the stress level at which the iron reverts back to the α phase on unloading. A strong magnetic field was found to produce no measurable change in the phase‐transition stress. The accuracy of the ``factor‐of‐2'' assumption relating free‐surface velocity to particle velocity in iron was also evaluated experimentally.

Shock wave study of the α ⇄ ε phase transition in iron

The dislocation dynamics of Gilman and Johnston are applied to the problem of elastic—plastic flow in Armco iron at very high strain rates. The dislocation velocity is assumed to follow the law v=v∞ exp(−τ0/τ); experimental data support this form of dependence and are used to determine the value of τ0. This value is in reasonable agreement with other measurements taken from Luders band front velocities. A second quantity which can be evaluated is the initial density of dislocation lines, N0, which is found to be 2.0×108 cm−2.

Dislocation Dynamics and Dynamic Yielding

Smooth bore cannons were used to produce plane collisions between plates of Armco iron. Projectile velocities ranged from 60 to 400 m/sec. Time resolved measurements of the target free‐surface velocities indicate that the dynamic yielding process is time dependent on a submicrosecond time scale. The shape of the Hugoniot curve in the pressure‐volume plane up to 80 kbars shows that true hydrostatic equilibrium has not yet been established behind the elastic wave. On the other hand the substantially constant free‐surface velocities behind the plastic front indicate that the material cannot be far from equilibrium after a short time. Some data on the rarefaction sound speed in the high pressure region are interpreted to imply a value very near 6 km/sec.

Elastic‐Plastic Properties of Iron

A photoelectric technique is described for measuring the residual temperature of strongly shocked metals. Data for copper shocked to pressures ranging from 0.9 to 1.7 Mbars are in good agreement with published calculations of temperatures.

John W. Taylor

Papers

Dislocation Dynamics and Dynamic Yielding

Elastic‐Plastic Properties of Iron

Residual Temperatures of Shocked Copper