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 compression and biaxial compression-shear ramp loading conditions is experimentally characterized. It is observed that an imposed uniaxial magnetic field ramped to approximately 10 T through a period of approximately 2500 μs and held near the peak for about 250 μs before being tested appears to anneal the molybdenum panel. In order to provide a physical basis for model development, a general theoretical framework that incorporates electromagnetic loading and the coupling between the imposed field and the inelasticity of molybdenum was developed. Based on this framework, a multi-axial continuum model for molybdenum under electromagnetic loading is presented. The model reasonably captures all of the material characteristics displayed by the experimental data obtained from various experimental configurations. In addition, data generated from shear loading provide invaluable information not only for validating but also for guiding the development of the material model for multiaxial loadings.
The high-pressure response of cryogenic liquid deuterium (LD{sub 2}) has been studied to pressures of {approx}400GPa and densities of {approx}1.5g/cm{sup 3}. Using intense magnetic pressure produced by the Sandia National Laboratories Z accelerator, macroscopic aluminum or titanium flyer plates, several mm in lateral dimensions and a few hundred microns in thickness, have been launched to velocities in excess of 22 km/s, producing constant pressure drive times of approximately 30 ns in plate impact, shock wave experiments. This flyer plate technique was used to perform shock wave experiments on LD{sub 2} to examine its high-pressure equation of state. Using an impedance matching method, Hugoniot measurements of LD{sub 2} were obtained in the pressure range of {approx}22-100GPa. Results of these experiments indicate a peak compression ratio of approximately 4.3 on the Hugoniot. In contrast, previously reported Hugoniot states inferred from laser-driven experiments indicate a peak compression ratio of approximately 5.5-6 in this same pressure range. The stiff Hugoniot response observed in the present impedance matching experiments was confirmed in simultaneous, independent measurements of the relative transit times of shock waves reverberating within the sample cell, between the front aluminum drive plate and the rear sapphire window. The relative timing was found to be sensitive to the density compression along the principal Hugoniot. Finally, mechanical reshock measurements of LD{sub 2} using sapphire, aluminum, and {alpha}-quartz anvils were made. These results also indicate a stiff response, in agreement with the Hugoniot and reverberating wave measurements. Using simple model-independent arguments based on wave propagation, the principal Hugoniot, reverberating wave, and sapphire anvil reshock measurements are shown to be internally self-consistent, making a strong case for a Hugoniot response with a maximum compression ratio of {approx}4.3-4.5. The trends observed in the present data are in very good agreement with several ab initio models and a recent chemical picture model for LD{sub 2}, but in disagreement with previously reported laser-driven shock results. Due to this disagreement, significant emphasis is placed on the discussion of uncertainties, and the potential systematic errors associated with each measurement.
To address known shortcomings of classical metal plasticity for describing material behavior under shock loading, a model which incorporates a distribution in the deviatoric stress state is developed. This distribution will translate in stress space under loading, and growth of the distribution can be included in the model as well. This proposed model is capable of duplicating the key features of a set of reshock and release experiments on 6061-T6 aluminum, many of which are not captured by classical plasticity. The model is relatively simple, is only moderately more computationally intensive, and requires few additional material parameters.
Using intense magnetic pressure, a method was developed to launch flyer plates to velocities in excess of 20 km s{sup -1}. This technique was used to perform plate-impact, shock wave experiments on cryogenic liquid deuterium (LD{sub 2}) to examine its high-pressure equation of state (EOS). Using an impedance matching method, Hugoniot measurements were obtained in the pressure range of 22--100 GPa. The results of these experiments disagree with the previously reported Hugoniot measurements of LD2 in the pressure range above {approx}40 GPa, but are in good agreement with first principles, ab initio models for hydrogen and its isotopes.
Sandia is investigating the shock response of single-crystal diamond up to several Mbar pressure in a collaborative effort with the Institute for Shock Physics (ISP) at Washington State University (WSU). This is project intended to determine (i) the usefulness of diamond as a window material for high pressure velocity interferometry measurements, (ii) the maximum stress level at which diamond remains transparent in the visible region, (iii) if a two-wave structure can be detected and analyzed, and if so, (iv) the Hugoniot elastic limit (HEL) for the [110] orientation of diamond. To this end experiments have been designed and performed, scoping the shock response in diamond in the 2-3 Mbar pressure range using conventional velocity interferometry techniques (conventional VISAR diagnostic). In order to perform more detailed and highly resolved measurements, an improved line-imaging VISAR has been developed and experiments using this technique have been designed. Prior to performing these more detailed experiments, additional scoping experiments are being performed using conventional techniques at WSU to refine the experimental design.
Recently an innovative technique known as the Isentropic Compression Experiment (ICE) was developed that allows the dynamic compressibility curve of a material to be measured in a single experiment. Hence, ICE significantly reduces the cost and time required for generating and validating theoretical models of dynamic material response. ICE has been successfully demonstrated on several materials using the 20 MA Z accelerator, resulting in a large demand for its use. The present project has demonstrated its use on another accelerator, Saturn. In the course of this study, Saturn was tailored to produce a satisfactory drive time structure, and instrumented to produce velocity data. Pressure limits are observed to be approximately 10-15 GPa (''LP'' configuration) or 40-50 GPa (''HP'' configuration), depending on sample material. Drive reproducibility (panel to panel within a shot and between shots) is adequate for useful experimentation, but alignment fixturing problems make it difficult to achieve the same precision as is possible at Z. Other highlights included the useful comparison of slightly different PZT and ALOX compositions (neutron generator materials), temperature measurement using optical pyrometry, and the development of a new technique for preheating samples. 28 ICE tests have been conducted at Saturn to date, including the experiments described herein.
Using intense magnetic pressure, a method was developed to launch flyer plates to velocities in excess of 20 km/s. This technique was used to perform plate-impact, shock wave experiments on cryogenic liquid deuterium (LD{sub 2}) to examine its high-pressure equation of state (EOS). Using an impedance matching method, Hugoniot measurements were obtained in the pressure range of 30-70 GPa. The results of these experiments disagree with previously reported Hugoniot measurements of LD{sub 2} in the pressure range above {approx}40 GPa, but are in good agreement with first principles, ab-initio models for hydrogen and its isotopes.
In order to provide real-time data for validation of three dimensional numerical simulations of heterogeneous materials subjected to impact loading, an optically recording velocity interferometer system (ORVIS) has been adapted to a line-imaging instrument capable of generating precise mesoscopic scale measurements of spatially resolved velocity variations during dynamic deformation. Combining independently variable target magnification and interferometer fringe spacing, this instrument can probe a velocity field along line segments up to 15 mm in length. In high magnification operation, spatial resolution better than 10 {micro}m can be achieved. For events appropriate to short recording times, streak camera recording can provide temporal resolution better than 0.2 ns. A robust method for extracting spatially resolved velocity-time profiles from streak camera image data has been developed and incorporated into a computer program that utilizes a standard VISAR analysis platform. The use of line-imaging ORVIS to obtain measurements of the mesoscopic scale dynamic response of shocked samples has been demonstrated on several different classes of heterogeneous materials. Studies have focused on pressed, granular sugar as a simulant material for the widely used explosive HMX. For low-density (65% theoretical maximum density) pressings of sugar, material response has been investigated as a function of both impact velocity and changes in particle size distribution. The experimental results provide a consistent picture of the dispersive nature of the wave transmitted through these samples and reveal both transverse and longitudinal wave structures on mesoscopic scales. This observed behavior is consistent with the highly structured mesoscopic response predicted by 3-D simulations. Preliminary line-imaging ORVIS measurements on HMX as well as other heterogeneous materials such as foam and glass-reinforced polyester are also discussed.
In conjunction with ongoing high-current experiments on Sandia National Laboratories' Z accelerator, the authors have revisited a problem first described in detail by Heinz Knoepfel. Unlike the 1-Tesla MITLs of pulsed power accelerators used to produce intense particle beams, Z's disc transmission line (downstream of the current addition) is in a 100--1,200 Tesla regime, so its conductors cannot be modeled simply as static infinite conductivity boundaries. Using the MHD code MACH2 they have been investigating the conductor hydrodynamics, characterizing the joule heating, magnetic field diffusion, and material deformation, pressure, and velocity over a range of current densities, current rise-times, and conductor materials. Three purposes of this work are (1) to quantify power flow losses owing to ultra-high magnetic fields, (2) to model the response of VISAR diagnostic samples in various configurations on Z, and (3) to incorporate the most appropriate equation of state and conductivity models into the MHD computations. Certain features are strongly dependent on the details of the conductivity model.
For many scientific and programmatic applications, it is necessary to determine the shock compression response of materials to several tens of Mbar. In addition, a complete EOS is often needed in these applications, which requires that shock data be supplemented with other information, such as temperature measurements or by EOS data off the principal Hugoniot. Recent developments in the use of fast pulsed power techniques for EOS studies have been useful in achieving these goals. In particular, the Z accelerator at Sandia National Laboratories, which develops over 20 million amperes of current in 100-200 ns, can be used to produce muM-Mbar shock pressures and to obtain continuous compression data to pressures exceeding 1 Mbar. With this technique, isentropic compression data have been obtained on several materials to pressures of several hundred kbar. The technique has also been used to launch ultra-high velocity flyer plates to a maximum velocity of 14 km/s, which can be used to produce impact pressures of several Mbar in low impedance materials and over 10 Mbar in high impedance materials. The paper will review developments in both of these areas.
Shock loading techniques are often used to determine material response along a specific pressure loading curve referred to as the Hugoniot. However, many technological and scientific applications require accurate determination of dynamic material response that is off-Hugoniot, covering large regions of the equation-of-state surface. Unloading measurements from the shocked state provide off-Hugoniot information, but experimental techniques for measuring compressive off-Hugoniot response have been limited. A new pulsed magnetic loading technique is presented which provides previously unavailable information on isentropic loading of materials to pressures of several hundred kbar. This smoothly increasing pressure loading provides a good approximation to the high-pressure material isentrope centered at ambient conditions. The approach uses high current densities to create ramped magnetic loading to a few hundred kbar over time intervals of 100--200 ns. The method has successfully determined the isentropic mechanical response of copper to about 200 kbar and has been used to evaluate the kinetics of the alpha-epsilon phase transition occurring in iron at 130 kbar. With refinements in progress, the method shows promise for performing isentropic compression experiments to multi-Mbar pressures.
The Z Accelerator is a fast pulse power facility capable of performing high-pressure studies of the dynamic response of materials under loading conditions unachievable with other methods. A variety of advanced laser diagnostics have been implemented on the facility for shock physics experiments. These include multipoint laser velocity interferometry,line and full field velocity interferometry, time-resolved optical and uv spectroscopy, and both active and passive shock breakout.
Relatively straightforward changes in the optical design of a conventional optically recording velocity interferometer system (ORVIS) can be used to produce a line-imaging velocity interferometer wherein both temporal and spatial resolution can be adjusted over a wide range. As a result line-imaging ORVIS can be tailored to a variety of specific applications involving dynamic deformation of heterogeneous materials as required by the characteristic length scale of these materials (ranging from a few {micro}m for ferroelectric ceramics to a few mm for concrete). A line-imaging ORVIS has been successfully interfaced to the target chamber of a compressed gas gun driver and fielded on numerous tests in combination with simultaneous measurements using a dual delay-leg, ''push-pull'' VISAR system. These tests include shock loading of glass-reinforced polyester composites, foam reverberation experiments (measurements at the free surface of a thin aluminum plate impacted by foam), and measurements of dispersive velocity in a shock-loaded explosive simulant (sugar). Comparison of detailed spatially-resolved material response to the spatially averaged VISAR measurements will be discussed.
This work has been performed as part of the search for possible ways to utilize the capabilities of laser and particle beams techniques in shock wave and equation of state physics. The peculiarity of these techniques is that we have to deal with micron-thick targets and not well reproducible incident shock wave parameters, so all measurements should be of a high resolution and be done in one shot. Besides the Hugoniots, the experimental basis for creating the equations of state includes isentropes corresponding to unloading of shock-compressed matter. Experimental isentrope data are most important in the region of vaporization. With guns or explosive facilities, the unloading isentrope is recovered from a series of experiments where the shock wave parameters in plates of standard low-impedance materials placed behind the sample are measured [1,2]. The specific internal energy and specific volume are calculated from the measured p(u) release curve which corresponds to the Riemann integral. This way is not quite suitable for experiments with beam techniques where the incident shock waves are not well reproducible. The thick foil method [3] provides a few experimental points on the isentrope in one shot. When a higher shock impedance foil is placed on the surface of the material studied, the release phase occurs by steps, whose durations correspond to that for the shock wave to go back and forth in the foil. The velocity during the different steps, connected with the knowledge of the Hugoniot of the foil, allows us to determine a few points on the isentropic unloading curve. However, the method becomes insensitive when the low pressure range of vaporization is reached in the course of the unloading. The isentrope in this region can be measured by recording the smooth acceleration of a thin witness plate foil. With the mass of the foil known, measurements of the foil acceleration will give us the vapor pressure.
A principal goal of the shock physics program at Sandia is to establish a capability to make accurate equation of state (EOS) measurements on the Z pulsed radiation source. The Z accelerator is a source of intense x-ray radiation, which can be used to drive ablative shocks for EOS studies. With this source, ablative multi shocks can be produced to study materials over the range of interest to both weapons and ICF physics programs. In developing the capability to diagnose these types of studies on Z, techniques commonly used in conventional impact generated experimental were implemented. The primary diagnostic presently being used for this work is velocity interferometry, VISAR, which not only provides Hugoniot particle velocity measurements, but also measurements of non-shock EOS measurements, such as isentropic compression. In addition to VISAR capability, methods for measuring shock velocity have also been developed for shock studies on Z. When used in conjunction with the Rankine- Hugoniot jump conditions, material response at high temperatures and pressures can be inferred. Radiation in the Z accelerator is produced when approximately 18 MA are passed through a cylindrical wire array typically 20 to 50 mm in diameter and 10 to 20 mm in height. 200-300 wires with initial diameters on the order of 8 to 20 micron form, upon application of the current, a plasma shell, which is magnetically imploded until it collapses and stagnates on axis, forming a dense plasma emitter in the shape of a column, referred to as a" z pinch". The initial wire array and subsequent plasma pinch are confined within a metallic can, referred to as a primary hohlraum, which serves as both a current return path and a reflective surface to contain the radiation. Attached to openings in the primary hohlraum wall are smaller tubes referred to as secondaries. Multiple secondaries can be fielded on most experiments, which are the typical location for mounting EOS samples. In this configuration, the secondary S1 contains two separate VISAR probes for making velocity measurements at different material thicknesses. By correlating the resulting velocity profiles in time, a measurement of shock velocity can be determined. In addition, the velocity profiles provide the Hugoniot particle velocity after the records were impedance-matched. Secondaries S2 and S3 provide measurements of shock velocity using laser light reflected from steps. As the shock arrives at each of these surfaces, the surface reflectivity significantly decreases, which causes a sharp drop in return light. The shock velocity can be inferred from shock arrival at different steps The z-pinch technique is particularly useful for producing high amplitude shock waves for EOS applications. An alternative approach for using Z is to produce shockless loading directly with the magnetic pressure in the accelerator.
In this paper, we describe a new technique for using a pulsed power source (Z pinch) to produce planar shock waves for high-pressure equation of state (EOS) studies. Initial EOS experiments conducted with techniques indicate that these sources are effective for shock wave studies in samples with diameters of a few millimeters and thicknesses of a fraction of one millimeter, and thus provide the possibility for achieving accuracy in shock and particle velocity measurements of a few percent. We have used the Z pinch source to produce the first in-situ time-resolve particle velocity profiles obtained with pulsed radiation sources in the Mbar regime. Particle velocity profiles obtained with a VISAR interferometer are compared with I-D numerical simulations performed with a radiation-hydrodynamics code, ALEGRA. Good agreement with experimental results was achieved in the simulations and suggests that Z pinch source should be a valuable tool for high-pressure EOS studies in thermodynamic regimes important to hypervelocity impact.