R. A. Graham

Shock compression of solids

Abstract This review contains a brief, comprehensive, critical assessment of the status of investigations concerning the response of solids to shock compression. Mechanical, metallurgical, electrical, optical and other phenomena occurring in substances subjected to shock pressures covering the range from about 0.1 to 6000 GPa are considered. Emphasis is placed on physical interpretation of observations peculiar to the shock environment and on the relationships among observations in the various areas of investigation.

Piezoelectric Current from Shock‐Loaded Quartz—A Submicrosecond Stress Gauge

Current from X‐cut quartz disks may be used to detect stress‐time profiles induced by shock loading. The current amplitude and its time dependence are functions of the dielectric, piezoelectric, and mechanical properties of quartz under shock‐loading conditions. The results of an extensive experimental study of the current from shock‐loaded quartz disks are reported for shock stress up to 50 kbar. The experiment is performed by impacting precisely aligned X‐cut quartz disks upon each other at various measured velocities and observing the current in one of the disks during the first wave transit. Within the low signal range, the piezoelectric stress constant e11 is found to be 0.174 C‐m−2. The coefficient relating current jump to stress jump in one‐dimensional strain is found to be 2.04×10−8 C‐cm−2‐kbar−1 up to 6 kbar and 2.15×10−8 C‐cm−2‐kbar−1 from 9 to 18 kbar. The wave velocity was determined to be constant to 25 kbar. The observed current waveform could be fully interpreted in terms of rate‐independen...

Shock-induced chemical reactions in titanium-silicon powder mixtures of different morphologies: Time-resolved pressure measurements and materials analysis

The response of porous titanium (Ti) and silicon (Si) powder mixtures with small, medium, and coarse particle morphologies is studied under high-pressure shock loading, employing postshock materials analysis as well as nanosecond, time-resolved pressure measurements. The objective of the work was to provide an experimental basis for development of models describing shock-induced solid-state chemistry. The time-resolved measurements of stress pulses obtained with piezoelectric polymer (poly-vinyl-di-flouride) pressure gauges provided extraordinary sensitivity for determination of rate-dependent shock processes. Both techniques showed clear evidence for shock-induced chemical reactions in medium-morphology powders, while fine and coarse powders showed no evidence for reaction. It was observed that the medium-morphology mixtures experience simultaneous plastic deformation of both Ti and Si particles. Fine morphology powders show particle agglomeration, while coarse Si powders undergo extensive fracture and entrapment within the plastically deformed Ti; such processes decrease the propensity for initiation of shock-induced reactions. The change of deformation mode between fracture and plastic deformation in Si powders of different morphologies is a particularly critical observation. Such a behavior reveals the overriding influence of the shock-induced, viscoplastic deformation and fracture response, which controls the mechanochemical nature of shock-induced solid-state chemistry. The present work in conjunction with our prior studies, demonstrates that the initiation of chemical reactions in shock compression of powders is controlled by solid-state mechanochemical processes, and cannot be qualitatively or quantitatively described by thermochemical models.

Crystal defects and the dissolution kinetics of rutile

The dissolution rate of rutile in hydrofluoric acid was measured to examine the importance of line and point defects on the reaction rate. Well-annealed rutile was shocked with an explosive charge to induce a high density of dislocations (4 × 1011cm−2), paramagnetic point defects (≈2 × 1019 cm−3), and lattice strain as measured by X-ray line broadening (≈ 2 × 10−3). Subsamples of the shocked material were then thermally annealed in order to prepare samples with a wide variation in dislocation density and point defect concentration. The unshocked starting material had a dislocation density of about 106 cm−2, no detectable lattice strain (<10−5), and no detectable point defects as measured by electron spin resonance (< ≈1 × 1016cm−3). In spite of this large variation in dislocations and point defect concentrations, we observed only a factor of two variation in the reaction rate for shocked and annealed material. Existing theories suggest that etch pits nucleate and grow at the outcrop of a dislocation on the crystal surface. Assuming that the measured dislocation densities can be used to estimate the density of surface outcrops, and that each outcrop dissolves to form an etch pit, the relation between dissolution rates and dislocations can be interpreted in terms of a mean rate of etch pit growth. The mean rate of etch pit growth in shocked samples is less than 9 × 10−27cm3s−1. In experiments with single rutile crystals, however, observable etch pits grow at rates on the order of 1 × 10−19cm3s−. This discrepancy suggests either that: (i) the observed etch pits grow much more rapidly than the mean rate; or (ii) bulk dislocation density is not a useful measure of potential sites for etch pit growth on rutile crystal surfaces.

Shock-wave compression of x-cut quartz as determined by electrical response measurements*

Abstract The mechanical response of x -cut quartz in the vicinity of the Hugoniot elastic limit is determined from measurements of the piezoelectric current from samples impact loaded from 26 to 130 kbar. The Hugoniot elastic limit is determined to be 60 −1·5 +3 kbar at a compression of 0·066 −0·002 +0·004 This Hugoniot elastic limit corresponds to a shear strength of 5·5 per cent of the C 44 shear modulus. For stresses well above the Hugoniot elastic limit the electrical current measurements show that the material exhibits a substantial reduction of shear strength. The pressure derivative of the bulk modulus is determined to be 4·5, substantially less than the ultrasonic value. The experimental records show evidence for a time delay for reduction of shear strength which varies from about 10 −7 sec immediately above the 60 kbar Hugoniot elastic limit to about 10 −8 sec for stresses well above the Hugoniot elastic limit. The measurements also show stress relaxation below the Hugoniot elastic limit between 40 and 60 kbar.

Second‐ and third‐order piezoelectric stress constants of lithium niobate as determined by the impact‐loading technique

Determination of the e22, e33, and e15 second‐order piezoelectric stress constants, several third‐order piezoelectric stress constants, and the cD11 and cD33 elastic stiffness constants are reported for lithium niobate from experiments with input strains from 7×10−4 to 8×10−3 produced by the elastic impact‐loading method. Measurements of the e33 constant were made on a large number of samples to establish sample uniformity. The differences were found to be less than 1%. The present value of e33 is higher than that reported in previous work and appears to call for a revision of the accepted value along with that of the elastic constant cE33. The third‐order piezoelectric stress constants are readily detectable, but the values determined in the present investigation are limited in accuracy due to the relatively low strains which could be applied to the samples before conductivity became excessive.

Piezoelectric current from shunted and shorted guard‐ring quartz gauges

Current from quartz disks in guard‐ring configurations is widely used to sense stress pulse profiles resulting from impact or explosive loading. Normally, the guard ring is loaded with a low‐impedance resistive shunt selected to maintain voltage balance between electrodes. A similar configuration in which the guard ring is electrically shorted to the ground electrode with a vapor‐plated metallic conductor along the periphery of the disk has also been used to sense stress pulses. An experimental investigation of the current pulses produced when these shorted guard‐ring quartz gauges are subjected to impact loading has been conducted to compare the responses of shorted and shunted guard‐ring quartz gauges. Gauge configurations with guard‐ring widths which vary from 0.5 to 3.0 times the thickness of the disk were investigated. It is found that, unlike the behavior of the shunted gauges, shorted gauges do not exhibit a universal response characteristic, i.e., each shorted gauge configuration has a different r...

Shock‐Wave Compression of 30% Ni‐70% Fe Alloys: The Pressure‐Induced Magnetic Transition

The compressibility of 30% Ni‐70% Fe (wt %) in the fcc phase is investigated from atmospheric pressure to 40 kbar with shock‐wave loading techniques. The experiments are accomplished utilizing projectile impact techniques with stress profile measurements by the quartz gauge. A sharp change in compressibility indicates a second‐order ferromagnetic Curie point transition at a stress of 25 kbar and a volume of 0.9807 V0. The coefficient of Curie temperature change with pressure is found to be −5.8±0.3°C kbar−1. The agreement of this value with previous magnetic measurements, along with the anomalously large compressibility below the transition and the large decrease in compressibility at an elevated temperature, clearly indicates that this transition is a ferromagnetic to paramagnetic transition. Values for the change of thermal expansion and specific heat at the transition are computed from the Ehrenfest relations. These values are consistent with the magnetic character of the transition and give a complete...

Dielectric Breakdown and Recovery of X‐Cut Quartz under Shock‐Wave Compression

While a shock wave is traversing a disk of X‐cut quartz, a piezoelectric current flows in an external circuit connected across the faces of the disk. In this paper measurements of this current are used to study dielectric breakdown and subsequent recovery which occurs in quartz. Quartz specimen disks were impacted at various stress levels in such a way as to produce shock waves that propagated along the X axis either in the direction of or opposite to that of the pressure‐induced polarization. In the latter case, short‐circuit current measurements show that breakdown occurs at a threshold stress greater than 10 and less than 13 kbar. Since the impact experiment produced one‐dimensional electrical and mechanical conditions in the specimen disk, it was possible to formulate a mathematical model that permitted solutions for internal electrical fields and resistivity in terms of the measured current. Computations with this model show that the field in the stressed portion of the disk at breakdown is about 7.0...

Piezoeletric Current from x‐Cut Quartz Subjected to Short‐Duration Shock‐Wave Loading

When an x‐cut quartz disk is subjected to an impulsive load, the piezoelectric current in an external short circuit is ordinarily an accurate time‐resolved replica of the stress history at the input electrode. Recently, it has been observed that stress pulses whose durations are less than the shock‐wave transit time through the disk sometimes produce anomalous current‐vs‐time responses. In the present work, x‐cut quartz disks are subjected to stress pulses of six different durations and with amplitudes from 9 to 29 kbar. Carefully controlled accurately known pulses are applied to the samples by the impact of projectile‐mounted quartz disks of various thicknesses. The piezoelectric current accompanying each stress pulse is continuously monitored as the pulse propagates through the sample disk. It is found that the anomalous current is a consequence of shock‐induced conductivity in the region of the quartz disk that has been shock loaded and subsequently unloaded to a lower stress value. The threshold for c...