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The Z accelerator at Sandia National Laboratories was used to measure the compression isentrope of 6061-T6 aluminum to 185GPa. The isentropic compression experimental technique uses a rapidly increasing, planar magnetic field to simultaneously subject multiple planar aluminum samples of different thicknesses to a ramped magnetic stress load. This magnetic stress load causes a ramped compression wave to propagate in the aluminum. Motion histories at the rear surface of each aluminum sample are measured through a LiF window using laser velocity interferometry. Backward and forward integration of the one-dimensional equations of motion are used to analyze the data. Imposing the requirement that each motion history comes from the same magnetic stress load is sufficient to determine both the stress load and the stress-strain behavior of the aluminum. Because of shocks that grow in the LiF, the usual VISAR interferometer analysis was modified. The measured compression curve obtained on different aluminum samples for volumetric strains to 46% agrees to within about 2% of peak stress with an isentrope obtained from the often-used Mie-Gruneisen equation of state that was derived from previous Hugoniot data.

Hugoniot measurements were performed on aluminum (6061-T6) in the stress range of 100–500 GPa (1–5 Mbar) using a magnetically accelerated flyer plate technique. This method of flyer plate launch utilizes the high currents, and resulting magnetic fields produced at the Sandia Z Accelerator to accelerate macroscopic aluminum flyer plates (approximately 12×25 mm in lateral dimension and ∼300 μm in thickness) to velocities in excess of 20 km/s. This technique was used to perform plate-impact shock-wave experiments on aluminum to determine the high-stress equation of state (EOS). Using a near-symmetric impact method, Hugoniot measurements were obtained in the stress range of 100–500 GPa. The results of these experiments are in excellent agreement with previously reported Hugoniot measurements of aluminum in this stress range. The agreement at lower stress, where highly accurate gas gun data exist, establishes the magnetically accelerated flyer plate technique as a suitable method for generating EOS data. Furthermore, the present results exhibit increased accuracy over the previous techniques used to obtain data in the higher-stress range. This improved accuracy enhances our understanding of the response of aluminum to 500 GPa, and lends increased confidence to the use of aluminum as a standard material in future impedance matching experiments.

Isentropic compression experiments (ICE) on Sandia National Laboratories’ Z Accelerator are used to make continuous measurements of the index of refraction in single crystal Z-cut sapphire as the longitudinal stress is gradually increased to 20 GPa (uniaxial strain of about ∼3.9%). A planar, ramp compression wave, generated by a large magnetic field, propagates through a planar copper base plate. Part of the rear surface of the base plate is a free surface and part is covered with a sapphire window. Comparisons are made of velocity histories measured simultaneously at the free surface and at the copper/sapphire interface using a velocity interferometer system for any reflector (VISAR). This is sufficient to determine the index of refraction of the sapphire continuously as a function of density. Perturbations to the compression waves caused by interactions with the free surface and with the sapphire are accounted for by backward or forward solutions to the equations of motion. The effect of the unsteady na...

The intense magnetic field generated by the 20 megaampere Z machine [R. B. Spielman et al., Phys. Plasmas 5, 2105 (1998)] at Sandia National Laboratories is being used as a pressure source for material science studies. An application we have studied in great detail involves using the intense magnetic field to accelerate flyer plates (small metal disks) to very high velocities (>20 km/s) for use in shock loading experiments. We have used two-dimensional (2D) magnetohydrodynamic (MHD) simulation to investigate the physics of accelerating flyer plates using multi-megabar magnetic drive pressures. A typical shock physics load is comprised of conducting electrodes that are highly compressible at multi-megabar pressures. Electrode deformation that occurs during the rise time of the current pulse causes significant inductance increase, which reduces the peak current (drive pressure) relative to a static geometry. This important dynamic effect is modeled self-consistently by driving the MHD simulation with an acc...

The intense magnetic field generated by the 20 megaampere Z machine [R. B. Spielman et al., Phys. Plasmas 5, 2105 (1998)] at Sandia National Laboratories is being used as a pressure source for material science studies. An application we have studied in great detail involves using the intense magnetic field to accelerate flyer plates (small metal disks) to very high velocities (>20 km/s) for use in shock loading experiments. We have used highly accurate velocity interferometry measurements (error ∼1%) in conjunction with one-dimensional magnetohydrodynamic (MHD) simulation to elucidate details of the flyer dynamics. One-dimensional MHD simulations are able to produce experimental results with a high degree of accuracy, thereby revealing otherwise unobtainable, but useful information about magnetically accelerated flyers on Z. Comparisons of simulation results with time-resolved measurements of velocity from a shock loading experiment involving a 925 μm aluminum flyer are presented. Results show that Joule ...

Magnetically applied pressure-shear (MAPS) is a new experimental technique that provides a platform for direct measurement of material strength at extreme pressures. The technique employs an imposed quasi-static magnetic field and a pulsed power generator that produces an intense current on a planar driver panel, which in turn generates high amplitude magnetically induced longitudinal compression and transverse shear waves into a planar sample mounted on the drive panel. In order to apply sufficiently high shear traction to the test sample, a high strength material must be used for the drive panel. Molybdenum is a potential driver material for the MAPS experiment because of its high yield strength and sufficient electrical conductivity. To properly interpret the results and gain useful information from the experiments, it is critical to have a good understanding and a predictive capability of the mechanical response of the driver. In this work, the inelastic behavior of molybdenum under uniaxial compressi...

A magnetohydrodynamic loading technique was used to shocklessly compress beryllium to peak longitudinal stresses of 19–110 GPa and, subsequently, unload in order to determine both the compressive response and also the shear stress supported upon release. Loading strain rates were on the order of 106 s−1, while the unloading rates were nearly constant at 3 × 105 s−1. Velocimetry was used to monitor the ramp and release behavior of a beryllium/lithium fluoride window interface. After applying window corrections to infer in situ beryllium velocities, a Lagrangian analysis was employed to determine the material response. The Lagrangian wavespeed-particle velocity response is integrated to generate the stress-strain path, average change in shear stress over the elastic unloading, and estimates of the shear modulus at peak compression. These data are used to infer the pressure dependence of the flow strength at the unloading rate. Comparisons to several strength models reveal good agreement to 45 GPa, but the data indicate 20%–30% higher strength near 100 GPa.

A magnetic loading technique was used to study the strength of polycrystalline tantalum ramp compressed to peak stresses between 60 and 250 GPa. Velocimetry was used to monitor the planar ramp compression and release of various tantalum samples. A wave profile analysis was then employed to determine the pressure-dependence of the average shear stress upon unloading at strain rates on the order of 105 s−1. Experimental uncertainties were quantified using a Monte Carlo approach, where values of 5% in the estimated pressure and 9–17% in the shear stress were calculated. The measured deviatoric response was found to be in good agreement with existing lower pressure strength data as well as several strength models. Significant deviations between the experiments and models, however, were observed at higher pressures where shear stresses of up to 5 GPa were measured. Additionally, these data suggest a significant effect of the initial material processing on the high pressure strength. Heavily worked or sputtered samples were found to support up to a 30% higher shear stress upon release than an annealed material.

Unloading from a plastically deformed state has long been recognized as a sensitive measure of a material's deviatoric response. In the case of a ramp compression and unload, time resolved particle velocity measurements of a sample/window interface may be used to gain insight into the sample material's strength. Unfortunately, measurements of this type are often highly perturbed by wave interactions associated with impedance mismatches. Additionally, wave attenuation, the finite pressure range over which the material elastically unloads, and rate effects further complicate the analysis. Here, we present a methodology that overcomes these shortcomings to accurately calculate a mean shear stress near peak compression for experiments of this type. A new interpretation of the self-consistent strength analysis is presented and then validated through the analysis of synthetic data sets on tantalum to 250 GPa. The synthetic analyses suggest that the calculated shear stresses are within 3% of the simulated values obtained using both rate-dependent and rate-independent constitutive models. Window effects are addressed by a new technique referred to as the transfer function approach, where numerical simulations are used to define a mapping to transform the experimental measurements to in situ velocities. The transfer function represents a robust methodology to account for complex wave interactions and a dramatic improvement over the incremental impedance matching methods traditionally used. The technique is validated using experiments performed on both lithium fluoride and tantalum ramp compressed to peak stresses of 10 and 15 GPa, respectively. In each case, various windows of different shock impedance are used to ensure consistency within the transfer function analysis. The data are found to be independent of the window used and in good agreement with previous results.

A magnetic loading technique was used to produce planar ramp loading of [100] and [110] orientations of single crystal tantalum to peak stresses of either ∼18 or ∼86 GPa for applied plastic strain rates of about 2 × 106/s. It was found that the dynamic elastic limit varied only slightly for factor-of-2 changes in the resulting elastic strain rates near 5 × 105/s. For wave propagation in the [100] direction, the dynamic elastic limit varied from 4.18–3.92 GPa for corresponding sample thicknesses of 0.625–1.030 mm and exhibited a slight rate dependence for the strain rate region studied. For [110] compression, the elastic limit was essentially independent of propagation distance, but exhibited a significant sample-to-sample variation; the elastic limit for this orientation varied from 2.49–3.18 GPa over sample thicknesses of 0.702–1.023 mm, with an average and standard deviation for the data of 2.93 ± 0.27 GPa. There was no apparent rate dependence in this case for the strain rates examined.

A new experimental technique to measure material shear strength at high pressures has been developed for use on magnetohydrodynamic (MHD) drive pulsed power platforms. By applying an external static magnetic field to the sample region, the MHD drive directly induces a shear stress wave in addition to the usual longitudinal stress wave. Strength is probed by passing this shear wave through a sample material where the transmissible shear stress is limited to the sample strength. The magnitude of the transmitted shear wave is measured via a transverse velocity interferometer system from which the sample strength is determined.

In a previous study by Asay et al. [J. Appl. Phys. 106, 073515 (2009)], the inelastic response of annealed and cold-rolled pure polycrystalline tantalum at intermediate strain rates was characterized with ramp wave loading to peak longitudinal stresses of 17 GPa. It was found that the annealed Ta at strain rates of about 106/s exhibited pronounced elastic overshoot, followed by rapid stress relaxation and the amplitude of the elastic precursor depicted essentially no dependence on sample thickness for samples with controlled initial properties, in contrast to the precursor attenuation typically observed in shock wave experiments. The precursor for the cold-rolled sample was more dispersive and did not exhibit the characteristics depicted by the annealed samples. A principal objective of the present study was to gain some insights into this behavior and its implication on the deformation mechanisms for tantalum. Another objective was to gain a fundamental understanding of the dynamic inelasticity of polycr...

A magnetic loading technique was used to ramp load single-crystal [100] lithium fluoride specimens to peak stresses of 5–114 GPa. Waveanalysis of in situparticle velocity profiles was used to estimate the compressive strength of LiF at peak stress. It was found that the strength increased with peak stress and showed two distinct regions of hardening; the first is believed to be governed by strain hardening and the second by pressure hardening. The quasielastic strain obtained from the initial part of the unloading was shown to saturate at about 1.3% for peak stresses greater than approximately 30 GPa. Over the studied pressure range, the measured strength of LiF varied from its initial value of 0.08 to about 1.1 GPa at the highest compressed state of 114 GPa. Comparison of the measured strength to results from two strength models showed good agreement. It was demonstrated that the strength of LiF introduces systematic error of about 10% when used as an interferometer window for measurements of material strength in isentropic compression experiments.

A magnetic loading technique was used to study the strength of pure, annealed, and cold-rolled polycrystalline tantalum under planar ramp loading at strain rates of ∼106/s. Both the initial yield strength and the flow strength after compression to peak loading stresses of 18 GPa were determined. For sample thicknesses ranging from 0.5–6.0 mm, it was found that the elastic limit of ∼3.2 GPa, corresponding to a yield strength of 1.6 GPa, for annealed Ta was sharply defined and essentially independent of sample thickness. After elastic yielding, relaxation of the longitudinal stress occurred for sample thicknesses greater than ∼0.5 mm, approaching an asymptotic value of ∼1.6 GPa. Two different purities of annealed Ta showed no difference in initial yield strength. Cold-rolling annealed Ta to 26% plastic strain resulted in a more dispersed elastic precursor with an amplitude of about 1.6 GPa and with no stress relaxation after yielding. Analysis of unloading wave profiles from the peak loading states allowed ...

Shockless compression experiments were performed on x-cut quartz single crystals to examine the effect of loading path and rate on the inelastic behavior. The Lagrangian wave velocity and stress were determined from the measured particle velocities and compared to the previously measured elastic values. The data show that x-cut quartz remains essentially elastic up to stresses greater than 10GPa during ramp loading, but that the elastic yield behavior is dependent on the sample thickness. These results indicate that the elastic response of x-cut quartz is dependent on the loading path, rate, and sample thickness.

A magnetic loading technique was used to ramp load pure aluminum and 6061 aluminum alloy to peak stresses of approximately 29GPa. The peak loading rate was approximately 106∕s, followed by unloading from peak stress at a rate of about 105∕s. The pure aluminum samples had impurity levels ranging from about 10ppmto0.5wt% and average grain sizes in the range of 144–454μm. The 6061 alloy was prepared in either the T6 condition with grain sizes of 5–50μm, or in the T0 or T6 heat treatment condition with a grain size of about 40μm. A wave profile technique was used to estimate the compressive strength during unloading. It was found that the compressive strength estimated during unloading increased with peak stress for all materials and that the change in strength was insensitive to initial material properties. This observation is in agreement with previous results obtained from shock loading of the same materials [H. Huang and J. R. Asay, J. Appl. Phys. 98, 033524 (2005)] and suggests that the deformation mecha...

Veloce is a medium-voltage, high-current, compact pulsed power generator developed for isentropic and shock compression experiments. Because of its increased availability and ease of operation, Veloce is well suited for studying isentropic compression experiments (ICE) in much greater detail than previously allowed with larger pulsed power machines such as the Z accelerator. Since the compact pulsed power technology used for dynamic material experiments has not been previously used, it is necessary to examine several key issues to ensure that accurate results are obtained. In the present experiments, issues such as panel and sample preparation, uniformity of loading, and edge effects were extensively examined. In addition, magnetohydrodynamic simulations using the ALEGRA code were performed to interpret the experimental results and to design improved sample/panel configurations. Examples of recent ICE studies on aluminum are presented.

The mesoscopic scale response of low-density pressings of granular sugar (sucrose) to shock loading has been examined in gas-gun impact experiments using both VISAR and a line-imaging, optically recording velocity interferometer system in combination with large-volume-element, high-resolution, three-dimensional numerical simulations of these tests. Time-resolved and spatially resolved measurements of material motion in waves transmitted by these pressings have been made as a function of impact velocity, sample thickness, and sample particle size distribution. Observed wave profiles exhibit a precursor regime arising from elastic stress wave propagation and a dispersive compaction wave with superimposed localized particle velocity fluctuations of varying amplitude. Material motion associated with dynamic stress bridging leads compaction wave arrival by ∼2μs at the lowest impact velocity (0.25kms−1) employed in this study and

The Z accelerator [R. B. Spielman, W. A. Stygar, J. F. Seamen et al., Proceedings of the 11th International Pulsed Power Conference, Baltimore, MD, 1997, edited by G. Cooperstein and I. Vitkovitsky (IEEE, Piscataway, NJ, 1997), Vol. 1, p. 709] at Sandia National Laboratories delivers ∼20MA load currents to create high magnetic fields (>1000T) and high pressures (megabar to gigabar). In a z-pinch configuration, the magnetic pressure (the Lorentz force) supersonically implodes a plasma created from a cylindrical wire array, which at stagnation typically generates a plasma with energy densities of about 10MJ∕cm3 and temperatures >1keV at 0.1% of solid density. These plasmas produce x-ray energies approaching 2MJ at powers >200TW for inertial confinement fusion (ICF) and high energy density physics (HEDP) experiments. In an alternative configuration, the large magnetic pressure directly drives isentropic compression experiments to pressures >3Mbar and accelerates flyer plates to >30km∕s for equation of state ...

Adiabatic release measurements were performed on aluminum (6061-T6) from ∼240-to500-GPa(∼2.4–5Mbar) states on the principal Hugoniot. Using a magnetically accelerated flyer plate technique, capable of launching macroscopic aluminum flyer plates (approximately 12×25mm in lateral dimension and ∼300μm in thickness) to velocities in excess of 20km∕s, direct impact experiments were performed on a low shock impedance, 200-mg∕cc silica aerogel to determine the aerogel Hugoniot in the pressure range of ∼30–75GPa. Release experiments were then performed in which the aerogel was mounted onto an aluminum base plate, and the initial shock in the base plate was transmitted to the aerogel sample. Given the measured aerogel shock velocities from the release experiments and the measured aerogel Hugoniot from the direct impact experiments, release states on release adiabats of aluminum were ascertained. The results were compared to several equation of state models for aluminum, and a rigorous statistical analysis was performed. The statistical analysis enabled the suitability of these various models in describing the release response of hot, liquid states to be determined. This study enhances our understanding of the release response of aluminum for high-pressure states on the Hugoniot and lends confidence to the use of aluminum as a standard material in impedance-matching experiments.

Isentropic compression experiments (ICE) have been performed on the Z accelerator facility at Sandia National Laboratory. We describe the experimental design that used large magnetic fields to slowly compress samples to pressures in excess of 400 kbar. Velocity wave profile measurements were analyzed to yield isentropic compression equations of state (EOS). The method can also yield material strength properties. We describe magnetohydronamic simulations and results of experiments that used the “square short” configuration to compress copper and discuss ICE EOS experiments that have been performed with this method on tantalum, molybdenum, and beryllium.

Time‐resolved measurements of shock‐wave rise times have been accomplished for aluminum, copper, and steel to stress levels of 41, 96, and 139 GPa, respectively, using velocity‐interferometer techniques. To within the time resolution of the technique, the shock transition is found to occur within 3 ns in all materials. Based on this upper limit for the transition time, limiting viscosity coefficients of 1000, 3000, and 4000 P are obtained for 6061‐T6 aluminum, OFHC copper, and 4340 steel, respectively, at strain rates above 108 s−1. It is found that the effective viscosity can be expressed as parameters in a Maxwellian relation for an elastic‐plastic solid, in which the viscosity is related to an effective relaxation time. It is also shown that viscosity is inversely proportional to mobile‐dislocation density, which implies that the density of mobile dislocations obtained during shock compression in these materials is well over 109/cm2.

The acoustic velocities in polymethylmethacrylate have been measured with an ultrasonic pulse‐echo technique as functions of frequency, temperature, and pressure. At atmospheric pressure, data on the velocities and attenuation coefficients were obtained for the temperature range of 22°–75°C in the frequency range of 6–30 MHz. For the measurements of velocity and attenuation as a function of frequency, the complex adiabatic bulk modulus was calculated at room temperature and atmospheric pressure for the above frequencies. At temperatures of 25°, 40°, 55°, and 75°C, the pressure dependence of the longitudinal and shear velocity was determined to 150 kpsi at a frequency of 6 MHz. It was found that the measured velocities under increasing pressure conditions were generally lower than those of decreasing pressure by about 0.5% for the longitudinal measurements and about 1% for the shear measurements. However, measurements of the velocities at atmospheric pressure after the specimens had been exposed to 150 kpsi were usually within 0.1% of the initial values. A discussion is presented which compares the continuity of the present data with equation of state determinations in PMMA at elevated pressures.

The relationship of ultrasonic velocities to equations of state is addressed for two homogeneous isotropic plastics, polystyrene and polymethylmethacrylate. Ultrasonic velocities were measured at hydrostatic pressures up to 10 kbar and temperatures from ambient to 75°C at an acoustic frequency of 6 MHz. From these data the pressure and temperature dependence of the elastic moduli are calculated. In particular, the bulk modulus is used to compute an equation of state from models proposed by Birch and Murnaghan. The nonlinearity of the bulk modulus at pressures below 10 kbar favors the Birch model. Comparison with shock data shows that the Birch equation of state, determined ultrasonically, agrees quite well with the shock data to pressures well over an order of magnitude in excess of the 10‐kbar ultrasonic data for both polystyrene and polymethacrylate.