Isentropic Compression Experiments Research Articles

An analytic and complete equation of state for condensed phase materials

Analytic equations of state (EOS) are intended to reproduce theoretical and experimental data in a single phase portion of the thermodynamic space. We devise a complete and thermodynamically consistent model with four distinct features: (1) a reference isotherm that remains thermodynamically stable, (2) a flexible specific heat model based on a fourth-order rational polynomial, (3) a Grüneisen parameter that depends on specific volume and temperature, and (4) pressure and internal energy functions that can be inverted analytically in temperature. The model aims to improve the accuracy of existing equations of state while remaining computationally efficient. To demonstrate its features, we include calibrations for single-crystal pentaerythritol tetranitrate (PETN), liquid nitromethane (NM), and hexagonal close-packed beryllium (Be) metal. The parameter optimization uses the specific heat capacity, Grüneisen parameter, and static compression curves obtained from density functional theory for the crystalline solids and molecular dynamics simulations for liquid NM. We also present a velocity autocorrelation function that yields accurate phonon densities of states for the EOS calibration from the molecular dynamics trajectories. Each of the three calibrations is constrained to enforce the ambient state from experimental measurements and validated against experimental Hugoniot data from multiple sources. We also include one-dimensional hydrodynamic simulations of the isentropic compression experiments for beryllium conducted at the Z facility.

Three-dimensional full-field velocity measurements in shock compression experiments using stereo digital image correlation.

Shock compression plate impact experiments conventionally rely on point-wise velocimetry measurements based on laser-based interferometric techniques. This study presents an experimental methodology to measure the free surface full-field particle velocity in shock compression experiments using high-speed imaging and three-dimensional (3D) digital image correlation (DIC). The experimental setup has a temporal resolution of 100ns with a spatial resolution varying from 90 to 200μm/pixel. Experiments were conducted under three different plate impact configurations to measure spatially resolved free surface velocity and validate the experimental technique. First, a normal impact experiment was conducted on polycarbonate to measure the macroscopic full-field normal free surface velocity. Second, an isentropic compression experiment on Y-cut quartz-tungsten carbide assembly is performed to measure the particle velocity for experiments involving ramp compression waves. To explore the capability of the technique in multiaxial loading conditions, a pressure shear plate impact experiment was conducted to measure both the normal and transverse free surface velocities under combined normal and shear loading. The velocities measured in the experiments using digital image correlation are validated against previous data obtained from laser interferometry. Numerical simulations were also performed using established material models to compare and validate the experimental velocity profiles for these different impact configurations. The novel ability of the employed experimental setup to measure full-field free surface velocities with high spatial resolutions in shock compression experiments is demonstrated for the first time in this work.

Shock-ramp analysis test problem

Quasi-isentropic (ramp) compression is now a well-established experimental method and so are the analysis techniques to give Lagrangian sound speed, pressure, and density along the sample material's isentrope. A shock followed by ramp compression is a natural extension to investigate, for example, shock melt and refreeze on compression, or isentropes of states off the Hugoniot or principal isentrope. In practice, graded-density impactors produce initial shocks, compression by shaped laser pulses may be unable to produce a smooth pressure increase from zero, and incidental perturbations on the drive pulse may also give rise to shocks, so robust shock-ramp analysis methods will be needed. Appropriate analysis methods are needed for shock-ramp experiments, based on those for quasi-isentropic compression, and these require validation. This paper describes three different analyses of a shock-ramp test problem, including an assessment of their estimated errors. The methods tested were based on hydrodynamic characteristics or integration backward in space. All methods gave the known Lagrangian sound speed to within ∼1%, and pressure and volume to within less than 2% and 1%, demonstrating that the analysis methods of isentropic compression experiments can be confidently extended to the analysis of shock and ramp compression.

A fully coupled thermomechanical dislocation model for explosive crystal (β-HMX) subjected to isentropic compression loading

A fully coupled thermomechanical dislocation model is developed to analyze the thermomechanical responses of explosive crystal β-cyclotetramethylene tetranitramine (β-HMX) subjected to isentropic compression loading. The volumetric thermoelastic deformation is considered by a complete equation of state (logarithmic EoS) and the dislocation-based plasticity includes the automatic transition from the low-rate thermally activated to the high-rate drag limited regime. The proposed model is applied for the first time to simulate isentropic compression experiments (ICE) on oriented HMX single crystals. The calculated results can well capture the isentropic elastic limit, stress relaxation and steeper plastic wave speed of the ICE wave profiles. Nonlinear thermoelasticity by both pressure-dependent elasticity tensor and the complete EoS is shown to be responsible for the obvious steepness in wave profiles. The anisotropic elastoviscoplastic response can be distinctly reflected by detailed dislocation activities on seven slip systems instead of phenomenological model just through empirical determination. Pure isentrope is decoupled from quasi-isentrope by subtracting the contribution from deviatoric strain and thermal effect, providing thermodynamically consistent data for complete EoS. Contributions of anisotropic temperature rises by pressure volume work and dislocation-based plasticity work are influenced by loading history. Results provide insights into understanding the transition from isentropic wave to shock wave and ignition behavior of explosives at the mesoscale under complex thermodynamic scenarios.

Application of electrical action to design and analysis of magnetically driven solid liner implosion

As a typical cylindrical-convergent drive technique, magnetically driven solid liner implosion could compress interior substance with a shock or quasi-isentropic manner, which has been widely used to investigate the hydrodynamic behavior, the dynamic characteristics of material and fusion energy and so on. For aspecific facility, the implosion parameters depend on material, radius and thickness of the liner, and the ablation of liner restrict the optional parameters. The concept of electrical action is introduced via thin shell model, which not only is the representation of states for conductive metal, but also indicates the change of liner velocity under the condition of thin shell hypothesis. The result shows that the outer velocity of liner increases linearly with electrical action and is directly proportional to liner thickness but inversely proportional to liner density. The incompressible zero-dimensional model is used to calculate the dynamic parameters of thin shell liner, including the implosion time, the outer interface velocity, the implosion kinetic energy, and the electrical action under the condition of low linear current density. There exist optimal radius and thickness which can achieve the maximum velocity, momentum, and kinetic energy. The aluminum is suitable for reaching higher velocity and the copper can obtain higher pressure according to a proportionality coefficient <i>Q</i><sub>b</sub>/<i>ρ</i> which is an intrinsic quality of metal. A one-dimensional (1D) elastic plastic magnetic hydrodynamic code which is called SOL1D is developed to simulate liner implosion behavior. The modified relationship between resistivity and electrical action is introduced to SOL1D, which can adapt higher hydrodynamic pressure. According to current waves, the 1D code can be used to simulate liner implosion behavior for all kinds of current densities. The 1D simulation liner velocity is in agreement with both the experimental results and the electrical action model for liner implosion experiment on FP-1 facility. The simulation of isentropic compression experiment at ZR facility shows that the magnetic diffusion process is suppressed at extra high current density and hydrodynamic pressure, and the electrical action is larger than the experimental value of wire electrical explosion. The zero-dimensional (0D) and 1D simulation show that estimating the liner velocity and liner phase changing via the electrical action are suitable when thin shell hypothesis and low current density assumption are satisfied.

Modeling and Experimental Study on Multibrick Parallel Discharge Driver Based on PEEC Method

Isentropic compression experiments (ICEs) are an important method to study the dynamic characteristics of materials at pressures, temperatures, and stress or strain rate not attainable in conventional shock experiments. Yet it makes high demands toward the precise current pulse tailoring capability of the source. The China Academy of Engineering Physics is now developing a 20-brick parallel discharge driver and a 256-brick parallel discharge driver (CQ-7) to improve the performance and flexibility of compact magnetic compression devices. The load current of ICEs is tailored by optimizing the switch trigger sequence and the brick charging voltage. This paper establishes the equivalent circuit model of the 20-brick parallel discharge driver, taking the distributed inductance, resistance, and capacitance of transmission plates into account based on the partial-element equivalent circuit method. Besides, the equivalent circuit model of discharge brick based on the switch arc resistance model is also established to study the influence of key structural parameters on the output current. Furthermore, by comparing the simulation and experimental results of simultaneous discharge of 20-brick driver, the accuracy of simulation model is confirmed. This paper is of great significance to the design and optimization of multibrick parallel discharge drivers.

Numerical Study of Magnetically Driven Isentropic Compression Experiments on PTS

The most powerful pulse power generator in China—primary test stand (PTS)—was used to get isentropic compression of aluminum to about 100 GPa. The high performance of synchronization system enables to trigger 24 modules according to a required timing sequence, which makes PTS a good platform for electromagnetically driven high energy density physics experiments. Two shots were used to establish the pulse-shaping capability and test the reliability of a numerical code. The first shot used a stripline load driven by a smooth rising current, while the second one was driven by a current with a weak start followed by a sharp rise. The current profiles, as well as the sample thicknesses, are optimized by a 1-D magneto-hydrodynamic code MADE1D, coupled with a full circuit model for PTS. The experimental setup, physical model, and simulation results are introduced. Comparing with the experimental results, simulated velocities at Al/LiF interface agree well with the measurement. It is shown that the shape of current pulse is one of the most important factors that impact the loading process.

One-dimensional magneto-hydrodynamic simulation of the magnetic drive isentropic compression experiments on primary test stand

The 10 MA primary test stand (PTS), the most powerful pulse power generator in China, is used to obtain isentropic compression of Al samples under a pressure of about 100 GPa. The high performance of laser-triggered gas switches enables the precise synchronization of the 24 modules according to the required timing sequence. This advantage makes the PTS a very good platform for dynamic material compression with fundamental capability of pulse shaping. Tens of isentropic compression experiments have been conducted on the PTS, among which two distinct loading profiles were designed and used to obtain distinct compression processes. The first current, which is used to obtain a shockless compression, has a relatively smooth rise, and the rise-rate keeps almost constant during the 400 ns-long compression. The second current shape has a mild rise but a sharp ends, which is designed to make an artificial turn-point in the velocity history, which is helpful for the numerical code verification. The current profile, as well as the sample thickness, is optimized by a one-dimensional magneto-hydrodynamic (1D MHD) code MADE1D coupled with a full circuit model for the PTS. The equation of state and conductivity model used here have a wide coverage in the density, temperature and pressure range. The strength of material and its constitution model are also taken into consideration to simulate the elastic and plastic flow of metal at relatively low pressure and temperature. Compared with the experimental results, the simulated velocity at the sample/window interface is found to agree well with the measurement for most of the cases. This suggests that the MHD simulations with the circuit model are able to reflect the main process of the loading history, and help to analyze and elucidate the phenomena contributing to the compression. It shows that the current waveform is one of the most important factors that affect the loading process. For the PTS and strip-line electrodes it uses, a current rise ratio less than 15 kA/ns helps to obtain a smooth off-Hugoniot pressure rise. The temperature rise due to the pdV work is very small, and most of the sample material, except those in the skin layer where current passes through, keeps solid during the compression. However, for a current rises at 40 kA/ns or more, the ramp loading wave could be sharpened into a shock within the sample thicker than 1.2 mm. Based on the PTS flexibility of pulse shaping, a wide range of desired load processes can be gained by designing and controlling the load current and sample thickness precisely.

Optimization of current waveform tailoring for magnetically driven isentropic compression experiments.

The Thor pulsed power generator is being developed at Sandia National Laboratories. The design consists of up to 288 decoupled and transit time isolated capacitor-switch units, called "bricks," that can be individually triggered to achieve a high degree of pulse tailoring for magnetically driven isentropic compression experiments (ICE) [D. B. Reisman et al., Phys. Rev. Spec. Top.-Accel. Beams 18, 090401 (2015)]. The connecting transmission lines are impedance matched to the bricks, allowing the capacitor energy to be efficiently delivered to an ICE strip-line load with peak pressures of over 100 GPa. Thor will drive experiments to explore equation of state, material strength, and phase transition properties of a wide variety of materials. We present an optimization process for producing tailored current pulses, a requirement for many material studies, on the Thor generator. This technique, which is unique to the novel "current-adder" architecture used by Thor, entirely avoids the iterative use of complex circuit models to converge to the desired electrical pulse. We begin with magnetohydrodynamic simulations for a given material to determine its time dependent pressure and thus the desired strip-line load current and voltage. Because the bricks are connected to a central power flow section through transit-time isolated coaxial cables of constant impedance, the brick forward-going pulses are independent of each other. We observe that the desired equivalent forward-going current driving the pulse must be equal to the sum of the individual brick forward-going currents. We find a set of optimal brick delay times by requiring that the L2 norm of the difference between the brick-sum current and the desired forward-going current be a minimum. We describe the optimization procedure for the Thor design and show results for various materials of interest.

Loading Circuit Coupled Magnetohydrodynamic Simulation of Sample Configurations in Isentropic Compression Experiments

Based on the 1-D elastic–plastic reactive hydrodynamic code Simplified Stretch Sin, a magnetohydrodynamic (MHD) version SSS/MHD has been developed. The new code is of multifield coupling, making use of the Resistance-Inductance-Capacitance circuit equations related to loading currents and others. To calculate MHD and circuit variables consistently and simultaneously, on the basis of Faraday’s law, the relations between loading currents and magnetic flux in configuration cavities, variation in total magnetic flux and back electromotive force, and an iteration procedure are employed. The sample configurations in magnetically driven isentropic compression experiments (ICEs) here consist of parallel slabs and cavities, in which the step targets are a pair of slabs symmetrical to loading electrodes and of the same sample material but different in thickness. Self-consistent MHD and circuit calculations for ICE step targets of aluminum, tantalum, and plastic binder explosive is reported in this paper. The results agree with the measured ones well, including loading current profiles and velocity histories on samples’ free surface or optics window interface. Since the input data for this code are geometric sizes, material parameters, and original circuit parameters only, its results are independent of measured or empirical data, and could be helpful in design and prediction of ICE or other experiments.

Dislocation Mechanics of High-Rate Deformations

Four topics associated with constitutive equation descriptions of rate-dependent metal plastic deformation behavior are reviewed in honor of previous research accomplished on the same issues by Professor Marc Meyers along with colleagues and students, as follow: (1) increasing strength levels attributed to thermally activated dislocation migration at higher loading rates; (2) inhomogeneous adiabatic shear banding; (3) controlling mechanisms of deformation in shock as compared with shock-less isentropic compression experiments and (4) Hall–Petch-based grain size-dependent strain rate sensitivities exhibited by nanopolycrystalline materials. Experimental results are reviewed on the topics for a wide range of metals.

On the characterisation of the dynamic compressive behaviour of silicon carbides subjected to isentropic compression experiments

Ceramic materials are commonly used as protective materials particularly due to their very high hardness and compressive strength. However, the microstructure of a ceramic has a great influence on its compressive strength and on its ballistic efficiency. To study the influence of microstructural parameters on the dynamic compressive behaviour of silicon carbides, isentropic compression experiments have been performed on two silicon carbide grades using a high pulsed power generator called GEPI. Contrary to plate impact experiments, the use of the GEPI device and of the lagrangian analysis allows determining the whole loading path. The two SiC grades studied present different Hugoniot elastic limit (HEL) due to their different microstructures. For these materials, the experimental technique allowed evaluating the evolution of the equivalent stress during the dynamic compression. It has been observed that these two grades present a work hardening more or less pronounced after the HEL. The densification of the material seems to have more influence on the HEL than the grain size.

Quasi-isentropic experiment based on Shen Guang-III prototype laser facility with laser direct drive illumination

Quasi-isentropic compression technique is very useful for new material, shock wave physics, and earth physics. With shaping pulse laser, the quasi-isentropic compression technique is provided. For the designed experimental condition, the high energy density of shaping lasers can be used to generate shockless loading on the solid material to reach a high compression rate state with low temperature, which cannot be obtained with shock compression and isentropic compression technique. Then a new way to study the material can be provided. In this paper, the isentropic compression experiment with laser direct-drive illumination based on Shen Guang-III prototype laser facility is conducted. The theoretical model, target designing, experimental results, key technique, experimental characteristics and experimental data are analyzed in detail. The compression pressure above 400 GPa on the loading surface is obtained with experimental data and processing program, which is the highest pressure achieved to date. After comparing the apparent particle velocity with the true particle velocity, the dynamic correction curve can be obtained to achieve the real particle velocity, which is more accurate. The improving direction is provided, which will provide the important information. The experimental data and design will give the valuable reference for the study in this field.

Investigation of Switch Designs for the Dynamic Load Current Multiplier Scheme on the SPHYNX Microsecond Linear Transformer Driver

SPHINX is a microsecond linear transformer driver LTD, used essentially for implosion of Z-pinch loads in direct drive mode. It can deliver a 6-MA current pulse within 800 ns into a Z-pinch load. The dynamic load current multiplier concept enables the current pulse to be modified by increasing its amplitude while reducing its rise time before being delivered to the load. This compact system is made up of concentric electrodes (autotransformer), a dynamic flux extruder (cylindrical wire array), a vacuum convolute (eight postholes), and a vacuum closing switch, which is the key component of the system. Several different schemes are investigated for designing a vacuum switch suitable for operating the dynamic load current multiplier on the SPHINX generator for various applications, including isentropic compression experiments and Z-pinch radiation effects studies. In particular, the design of a compact vacuum surface switch and a multichannel vacuum switch, located upstream of the load are studied. Electrostatic simulations supporting the switch designs are presented along with test bed experiments. Initial results from shots on the SPHINX driver are also presented.

Optimization of loading pressure waveforms for piston driven isentropic compression

Smooth ramp loading with higher pressure amplitude is usually preferred in the isentropic compression experiment (ICE) of condensed materials. Optimizing the pressure waveforms of ICE is important in avoiding any shock wave propagating during ramp loading and raising the peak pressure as high as possible. Most reports on shaping ICE waveforms mainly focused on magnetohydrodynamic numerical simulations; a few used the hydrodynamic theory of isentropic flow. However, some points can be improved. Based on one-dimensional planar isentropic flow theory and regarding the ICE loading pressure exerted on the sample's surface as a time-dependent piston boundary condition, a condition for the ramp-to-shock transition as a compression wave propagates in the sample materials, has been derived that forms a necessary condition to avoid such transitions and determines ICE loading pressure waveforms with shorter rise time. A comparison of results is presented for samples of the maximum thickness and for optimized current waveforms obtained in magnetically driven ICEs.

Bertram Hopkinson's pioneering work and the dislocation mechanics of high rate deformations and mechanically induced detonations

Bertram Hopkinson was prescient in writing of the importance of better measuring, albeit better understanding, the nature of high rate deformation of materials in general and, in particular, of the importance of heat in initiating detonation of explosives. This report deals with these subjects in terms of post-Hopkinson crystal dislocation mechanics applied to high rate deformations, including impact tests, Hopkinson pressure bar results, Zerilli-Armstrong-type constitutive relations, shock-induced deformations, isentropic compression experiments, mechanical initiation of explosive crystals and shear banding in metals.

Molecular dynamics simulations of ramp-compressed copper

The compression of solids by a ramped pressure pulse, as opposed to shock compression, affords the potential to create states of solid-state matter at pressures greater than those achievable in diamond anvil cells. A fundamental understanding of this process requires a knowledge of the loading conditions that discriminate between so-called quasi-isentropic (QI) conditions and those pertaining to the higher entropy states produced by shock loading. We present here molecular dynamics simulations of single-crystal copper deformed over a range of strain rates and demonstrate that QI states at high pressure and low temperature can be present even at strain rates in excess of ${10}^{12}$ s${}^{\ensuremath{-}1}$. These states survive long enough to be studied with novel ultrafast techniques, in principle allowing simple, compact, isentropic compression experiments. Our atomistic simulations, with up to 25 million atoms, simulated for ramp durations of up to 300 ps, show how plastic deformation and melting varies with strain rate.

A simple mechanical analysis of the isentropic compression experiment

The uniaxial strain compression test, also referred to as isentropic compression experiment, was analyzed using a simple basically analytical model. It accounts for the compression under prescribed loading rate of a single phase elastic, elastic-perfectly plastic, or elastic-viscoplastic material. In each case, stresses, elastic and plastic strain rates, as well as the kinetic, elastic, and plastic powers, were derived and compared.

Design Improvements to High-Explosive Pulsed-Power Isentropic-Compression Experiments

A series of 1-D isentropic-compression experiments (ICE) has been initiated using the high-explosive pulsed-power (HEPP) system. Accurate high-stress isentropic equation-of-state (EOS) data had been reported using the HEPP-ICE system. A number of important advantages of the system were demonstrated, including higher stresses, higher accuracy, and larger sample sizes than those of other methods. Several potential design improvements have since been identified and tested. The storage inductor was eliminated, and the experiment was performed before the output of the plate flux compression generator could short-circuit itself. This eliminated the loss of current that occurs when the generator plates bounce apart. A new design of explosively formed fuse opening switch was employed with a multipoint initiation system that reduced the explosive mass, significantly reduced the timing jitter by eliminating air gaps, and minimized flux losses. In addition, with this new switch, the resistance-versus-time profile may be adjusted by controlling the initiation times of its four quadrants. Anomalous results were obtained with the new switch. The results of using this switch in an EOS experiment on pure tantalum are reported.

Circuit Model for Driving Three-Dimensional Resistive MHD Wire Array $Z$-Pinch Calculations

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Compact tungsten wire array <formula formulatype="inline"><tex Notation="TeX">$Z$</tex></formula>-pinches imploded on the Z generator at Sandia National Laboratories have proven to be a powerful reproducible X-ray source. Wire arrays have also been used in dynamic hohlraum radiation flow experiments and as an intense K-shell source, while the generator has been used extensively for isentropic compression experiments. A problem shared by all these applications is current loss, preventing the <formula formulatype="inline"><tex Notation="TeX">$\sim$</tex></formula>20-MA drive current from being reliably coupled to the load. This potentially degrades performance, while uncertainties in how this loss is described limit our predictive capability. We present details of a transmission line equivalent circuit model of the Z generator for use in driving 3-D resistive MHD simulations of wire array loads. We describe how power delivery to these loads is affected by multiple current losses and demonstrate how these may be calculated or reconstructed from available electrical data for inclusion in the circuit model. We then demonstrate how the circuit model and MHD load calculation may be combined to infer an additional current loss that has not been directly diagnosed for wire arrays. </para>