Pulsed-power generators can produce well-controlled continuous ramp compression of condensed matter for high-pressure equation-of-state studies using the magnetic loading technique. X-ray diffraction (XRD) data from dynamically compressed samples provide direct measurements of the elastic compression of the crystal lattice, onset of plastic flow, strength-strain rate dependence, structural phase transitions, and density of crystal defects, such as dislocations. Here, we present a cost-effective, compact, pulsed x-ray source for XRD measurements on pulsed-power-driven ramp-loaded samples. This combination of magnetically driven ramp compression of materials with a single, short-pulse XRD diagnostic will be a powerful capability for the dynamic materials' community to investigate in situ dynamic phase transitions critical to equation of states. We present results using this new diagnostic to evaluate lattice compression in Zr and Al and to capture signatures of phase transitions in CdS.
Pulsed-power generators using the magnetic loading technique are able to produce well-controlled continuous ramp compression of condensed matter for high-pressure equation-of-state studies. X-ray diffraction (XRD) data from dynamically compressed samples provide direct measurements of the elastic compression of the crystal lattice, onset of plastic flow, strength-strain rate dependence, structural phase transitions, and density of crystal defects such as dislocations. Here, we present a cost effective, compact X-ray source for XRD measurements on pulsed-power-driven ramp-loaded samples. This combination of magnetically-driven ramp compression of materials with single, short-pulse XRD diagnostic will be a powerful capability for the dynamic materials community. The success in fielding this new XRD diagnostic dramatically improves our predictive capability and understanding of rate-dependent behavior at or near phase transition. As Sandia plans the next-generation pulse-power driver platform, a key element needed to deliver new state-of-the-art experiments will be having the necessary diagnostic tools to probe new regimes and phenomena. These diagnostics need to be as versatile, compact, and portable as they are powerful. The development of a platform-independent XRD diagnostic gives Sandia researchers a new window to study the microstructure and phase dynamics of materials under load. This project has paved the way for phase transition research in a variety of materials with mission interest.
Ramp-compression experiments have been performed on the “Z” pulsed-power facility to investigate the strengths of Be and lead-antimony alloy. Yield strength and shear stress near peak pressure were obtained from measurements of the sound speed on release and using the Asay self-consistent method. Two S-65 grade Be samples, from batches that showed a significant difference in yield strength at ambient conditions, were found to have near identical yield strengths, which were also in agreement with similar earlier measurements on S-200 grade Be. Yield strength of the Pb4Sb alloy at ∼120 GPa was 1.35 GPa, while a National Ignition Facility experiment by Krygier et al. [Phys. Rev. Lett. 123, 205701 (2020)] found 3.8 GPa at ∼400 GPa pressure. Our result is intermediate between the ambient value and the one by Krygier et al., but the significantly increased strength is probably not associated with the transition to the high-pressure bcc phase of lead.
Magnetic loading was used to shocklessly compress four different metals to extreme pressures. Velocimetry monitored the behavior of the material as it was loaded to a desired peak state and then decompressed back down to lower pressures. Two distinct analysis methods, including a wave profile analysis and a novel Bayesian calibration approach, were employed to estimate quantitative strength metrics associated with the loading reversal. Specifically, we report for the first time on strength estimates for tantalum, gold, platinum, and iridium under shockless compression at strain rates of ∼ 5 × 10 5/s in the pressure range of ∼ 100–400 GPa. The magnitude of the shear stresses supported by the different metals under these extreme conditions are surprisingly similar, representing a dramatic departure from ambient conditions.
Graded density impactors (GDIs) have long been of interest to provide off-Hugoniot loading capabilities for impact systems. We describe a new technique which utilizes sputter deposition to produce an approximately 40 µm-thick film containing alternating layers of Al and Cu. The thicknesses of the respective layers are adjusted to give an effective density gradient through the film. The GDIs were launched into samples of interest with a 2-stage light gas gun, and the resulting shock-ramp-release velocity profiles were measured over timescales of ~10 ns with a new velocimetry probe. Results are shown for the direct impact of the film onto a LiF window, which allows for the dynamic characterization of the GDI, as well as from impact onto a thin (~40 µm) sputtered Ta sample backed by a LiF window. These measurements were coupled into mesoscale numerical simulations to infer the strength of Ta at the high rate (107 s-1), and high pressure (1 MBar) conditions this unique capability provides. Initial results suggest this is a viable strength platform which fills a critical gap and aids in cross-platform comparisons with other high-pressure strength platforms.
We report the atomic- and nanosecond-scale quantification of kinetics of a shock-driven phase transition in Zr metal. We uniquely make use of a multiple shock-and-release loading pathway to shock Zr into the β phase and to create a quasisteady pressure and temperature state shortly after. Coupling shock loading with in situ time-resolved synchrotron x-ray diffraction, we probe the structural transformation of Zr in the steady state. Our results provide a quantified expression of kinetics of formation of β-Zr phase under shock loading: transition incubation time, completion time, and crystallization rate.
In the presence of model discrepancy, the calibration of physics-based models for physical parameter inference is a challenging problem. Lack of identifiability between calibration parameters and model discrepancy requires additional identifiability constraints to be placed on the model discrepancy to obtain unique physical parameter estimates. If these assumptions are violated, the inference for the calibration parameters can be systematically biased. In many applications, such as in dynamic material property experiments, many of the calibration inputs refer to measurement uncertainties. In this setting, we develop a metric for identifying overfitting of these measurement uncertainties, propose a prior capable of reducing this overfitting, and show how this leads to a diagnostic tool for validation of physical parameter inference. The approach is demonstrated for a benchmark example and applied for a material property application to perform inference on the equation of state parameters of tantalum.
This report outlines the fiscal year (FY) 2019 status of an ongoing multi-year effort to develop a general, microstructurally-aware, continuum-level model for representing the dynamic response of material with complex microstructures. This work has focused on accurately representing the response of both conventionally wrought processed and additively manufactured (AM) 304L stainless steel (SS) as a test case. Additive manufacturing, or 3D printing, is an emerging technology capable of enabling shortened design and certification cycles for stockpile components through rapid prototyping. However, there is not an understanding of how the complex and unique microstructures of AM materials affect their mechanical response at high strain rates. To achieve our project goal, an upscaling technique was developed to bridge the gap between the microstructural and continuum scales to represent AM microstructures on a Finite Element (FE) mesh. This process involves the simulations of the additive process using the Sandia developed kinetic Monte Carlo (KMC) code SPPARKS. These SPPARKS microstructures are characterized using clustering algorithms from machine learning and used to populate the quadrature points of a FE mesh. Additionally, a spall kinetic model (SKM) was developed to more accurately represent the dynamic failure of AM materials. Validation experiments were performed using both pulsed power machines and projectile launchers. These experiments have provided equation of state (EOS) and flow strength measurements of both wrought and AM 304L SS to above Mbar pressures. In some experiments, multi-point interferometry was used to quantify the variation is observed material response of the AM 304L SS. Analysis of these experiments is ongoing, but preliminary comparisons of our upscaling technique and SKM to experimental data were performed as a validation exercise. Moving forward, this project will advance and further validate our computational framework, using advanced theory and additional high-fidelity experiments. ACKNOWLEDGEMENTS The authors greatly appreciate the support of Mike Saavedra in machining the experimental samples. The authors would also like to thank the Dynamic Integrated Compression facility (DICE) staff for executing the Thor experiments: Brian Stoltzfus, Randy Hickman, Keith Hodge, Joshua Usher, Lena Pacheco, and Eric Breden. The authors would also like to thank the staff at the Shock Thermodynamics Applied Research (STAR) facility for executing the plate impact experiments: Scott Alexander, Bill Reinhart, Bernardo Farfan, Rocky Palomino, John Martinez, and Rafael Sanchez. Lastly, the authors would like to acknowledge the development support of Jason Sanchez in ALEGRA to incorporate our upscaling method and Michael Powell for helping with post processing scripts for results analysis.
Dynamic material properties experiments provide access to the most extreme temperatures and pressures attainable in a laboratory setting; the data from these experiments are often used to improve our understanding of material models at these extreme conditions. We apply Bayesian model calibration to dynamic material property applications where the experimental output is a function: velocity over time. This framework can accommodate more uncertainties and facilitate analysis of new types of experiments relative to techniques traditionally used to analyse dynamic material experiments. However, implementation of Bayesian model calibration requires more sophisticated statistical techniques, because of the functional nature of the output as well as parameter and model discrepancy identifiability. We propose a novel Bayesian model calibration process to simplify and improve the estimation of the material property calibration parameters. Specifically, we propose scaling the likelihood function by an effective sample size rather than modelling the auto-correlation function to accommodate the functional output. Additionally, we propose sensitivity analyses by using the notion of 'modularization' to assess the effect of experiment-specific nuisance input parameters on estimates of the physical parameters. The Bayesian model calibration framework proposed is applied to dynamic compression of tantalum to extreme pressures, and we conclude that the procedure results in simple, fast and valid inferences on the material properties for tantalum.
For over a decade, velocimetry based techniques have been used to infer the electrical current delivered to dynamic materials properties experiments on pulsed power drivers such as the Z Machine. Though originally developed for planar load geometries, in recent years, inferring the current delivered to cylindrical coaxial loads has become a valuable diagnostic tool for numerous platforms. Presented is a summary of uncertainties that can propagate through the current inference technique when applied to expanding cylindrical anodes. An equation representing quantitative uncertainty is developed which shows the unfold method to be accurate to a few percent above 10 MA of load current.
Material strength and moduli can be determined from dynamic high-pressure ramp-release experiments using an indirect method of Lagrangian wave profile analysis of surface velocities. This method, termed self-consistent Lagrangian analysis (SCLA), has been difficult to calibrate and corroborate with other experimental methods. Using nonequilibrium molecular dynamics, we validate the SCLA technique by demonstrating that it accurately predicts the same bulk modulus, shear modulus, and strength as those calculated from the full stress tensor data, especially where strain rate induced relaxation effects and wave attenuation are small. We show here that introducing a hold in the loading profile at peak pressure gives improved accuracy in the shear moduli and relaxation-adjusted strength by reducing the effect of wave attenuation. When rate-dependent effects coupled with wave attenuation are large, we find that Lagrangian analysis overpredicts the maximum unload wavespeed, leading to increased error in the measured dynamic shear modulus. These simulations provide insight into the definition of dynamic strength, as well as a plausible explanation for experimental disagreement in reported dynamic strength values.
Mattsson, Thomas M.; Flicker, Dawn G.; Benage, John F.; Battaile, Corbett C.; Brown, Justin L.; Lane, James M.; Lim, Hojun L.; Arsenlis, Thomas A.; Barton, Nathan R.; Park, Hye-Sook P.; Swift, Damian C.; Prisbrey, Shon T.; Austin, Ryan A.; McNabb, Dennis P.; Remington, Bruce A.; Prime, Michael B.; Gray, George T.; Bronkhorst, Curt B.; Shen, Shuh-Rong S.; Luscher, D.J.L.; Scharff, Robert J.; Fensin, Sayu J.; Schraad, Mark W.; Dattelbaum, Dana M.; Brown, Staci L.
Sandia's Z Machine has been used to magnetically drive shockless compression of materials in a planar configuration to multi-megabar pressure levels, allowing accurate measurements of quasi-isentropic mechanical response at relatively low temperatures in the solid phase. This paper details recent improvements to design and analysis of such experiments, including the use of new data on the mechanical and optical response of lithium fluoride windows. Comparison of windowed and free-surface data on copper to 350 GPa lends confidence to the window correction method. Preliminary results are presented on gold to 500 GPa and platinum to 450 GPa; both appear stiffer than existing models.
The Thor pulsed power generator is being developed at Sandia National Laboratories . The design consists of up to 288 decoupled an d transit time isolated ca pacitor - switch units , called "bricks" , that can be individually triggered to achieve a high degree of p ulse tailoring for magnetically - driven isentropic compression experiments (ICE). The connecting transmission lines are impedance matched to the bricks, a llowing the capacitor energy to be efficiently delivered to an ICE strip - line load with pe ak pressures of over 100 GPa . Thor will drive experiments to expl ore equation of state, material strength, and phase transition properties of a wide variety of materi als. 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 itera tive use of complex circuit models to converge to the desired electrical pulse . We describe the optimization procedure for the Thor design and show results for various materials of interest. Also, we discuss the extension of these concepts to the megajoule - class Neptune machine design. Given this design, we are able to design shockless ramp - driven experiments in the 1 TPa range of material pressure.
We have conducted molecular dynamics (MD) simulations of quasi-isentropic ramp-wave compression to very high pressures over a range of strain rates from 1011 down to 108 1/s. Using scaling methods, we collapse wave profiles from various strain rates to a master profile curve, which shows deviations when material response is strain-rate dependent. Thus, we can show with precision where, and how, strain-rate dependence affects the ramp wave. We find that strain rate affects the stress-strain material response most dramatically at strains below 20%, and that above 30% strain the material response is largely independent of strain rate. We show good overall agreement with experimental stress-strain curves up to approximately 30% strain, above which simulated response is somewhat too stiff. We postulate that this could be due to our interatomic potential or to differences in grain structure and/or size between simulation and experiment. Strength is directly measured from per-atom stress tensor and shows significantly enhanced elastic response at the highest strain rates. This enhanced elastic response is less pronounced at higher pressures and at lower strain rates.
In this work, we develop a tantalum strength model that incorporates effects of temperature, strain rate and pressure. Dislocation kink-pair theory is used to incorporate temperature and strain rate effects while the pressure dependent yield is obtained through the pressure dependent shear modulus. Material constants used in the model are parameterized from tantalum single crystal tests and polycrystalline ramp compression experiments. It is shown that the proposed strength model agrees well with the temperature and strain rate dependent yield obtained from polycrystalline tantalum experiments. Furthermore, the model accurately reproduces the pressure dependent yield stresses up to 250 GPa. The proposed strength model is then used to conduct simulations of a Taylor cylinder impact test and validated with experiments. This approach provides a physically-based multi-scale strength model that is able to predict the plastic deformation of polycrystalline tantalum through a wide range of temperature, strain and pressure regimes.
We report on a new technique for obtaining off-Hugoniot pressure vs. density data for solid metals compressed to extreme pressure by a magnetically driven liner implosion on the Z-machine (Z) at Sandia National Laboratories. In our experiments, the liner comprises inner and outer metal tubes. The inner tube is composed of a sample material (e.g., Ta and Cu) whose compressed state is to be inferred. The outer tube is composed of Al and serves as the current carrying cathode. Another aluminum liner at much larger radius serves as the anode. A shaped current pulse quasi-isentropically compresses the sample as it implodes. The iterative method used to infer pressure vs. density requires two velocity measurements. Photonic Doppler velocimetry probes measure the implosion velocity of the free (inner) surface of the sample material and the explosion velocity of the anode free (outer) surface. These two velocities are used in conjunction with magnetohydrodynamic simulation and mathematical optimization to obtain the current driving the liner implosion, and to infer pressure and density in the sample through maximum compression. This new equation of state calibration technique is illustrated using a simulated experiment with a Cu sample. Monte Carlo uncertainty quantification of synthetic data establishes convergence criteria for experiments. Results are presented from experiments with Al/Ta, Al/Cu, and Al liners. Symmetric liner implosion with quasi-isentropic compression to peak pressure ∼1000 GPa is achieved in all cases. These experiments exhibit unexpectedly softer behavior above 200 GPa, which we conjecture is related to differences in the actual and modeled properties of aluminum.
We have developed the design of Thor: a pulsed power accelerator that delivers a precisely shaped current pulse with a peak value as high as 7 MA to a strip-line load. The peak magnetic pressure achieved within a 1-cm-wide load is as high as 100 GPa. Thor is powered by as many as 288 decoupled and transit-time isolated bricks. Each brick consists of a single switch and two capacitors connected electrically in series. The bricks can be individually triggered to achieve a high degree of current pulse tailoring. Because the accelerator is impedance matched throughout, capacitor energy is delivered to the strip-line load with an efficiency as high as 50%. We used an iterative finite element method (FEM), circuit, and magnetohydrodynamic simulations to develop an optimized accelerator design. When powered by 96 bricks, Thor delivers as much as 4.1 MA to a load, and achieves peak magnetic pressures as high as 65 GPa. When powered by 288 bricks, Thor delivers as much as 6.9 MA to a load, and achieves magnetic pressures as high as 170 GPa. We have developed an algebraic calculational procedure that uses the single brick basis function to determine the brick-triggering sequence necessary to generate a highly tailored current pulse time history for shockless loading of samples. Thor will drive a wide variety of magnetically driven shockless ramp compression, shockless flyer plate, shock-ramp, equation of state, material strength, phase transition, and other advanced material physics experiments.
Magnetically-driven, planar shockless-compression experiments to multi-megabar pressures were performed on tantalum samples using a stripline target geometry. Free-surface velocity waveforms were measured in 15 cases; nine of these in a dual-sample configuration with two samples of different thicknesses on opposing electrodes, and six in a single-sample configuration with a bare electrode opposite the sample. Details are given on the application of inverse Lagrangian analysis (ILA) to these data, including potential sources of error. The most significant source of systematic error, particularly for single-sample experiments, was found to arise from the pulse-shape dependent free-surface reflected wave interactions with the deviatoric-stress response of tantalum. This could cause local, possibly temporary, unloading of material from a ramp compressed state, and thus multi-value response in wave speed that invalidates the free-surface to in-material velocity mapping step of ILA. By averaging all 15 data sets, a final result for the principal quasi-isentrope of tantalum in stress-strain was obtained to a peak longitudinal stress of 330GPa with conservative uncertainty bounds of ±4.5% in stress. The result agrees well with a tabular equation of state developed at Los Alamos National Laboratory.
In support of LLNL efforts to develop multiscale models of a variety of materials, we have performed a set of eight gas gun impact experiments on 2169 steel (21% Cr, 6% Ni, 9% Mn, balance predominantly Fe). These experiments provided carefully controlled shock, reshock and release velocimetry data, with initial shock stresses ranging from 10 to 50 GPa (particle velocities from 0.25 to 1.05 km/s). Both windowed and free-surface measurements were included in this experiment set to increase the utility of the data set, as were samples ranging in thickness from 1 to 5 mm. Target physical phenomena included the elastic/plastic transition (Hugoniot elastic limit), the Hugoniot, any phase transition phenomena, and the release path (windowed and free-surface). The Hugoniot was found to be nearly linear, with no indications of the Fe phase transition. Releases were non-hysteretic, and relatively consistent between 3- and 5-mmthick samples (the 3 mm samples giving slightly lower wavespeeds on release). Reshock tests with explosively welded impactors produced clean results; those with glue bonds showed transient releases prior to the arrival of the reshock, reducing their usefulness for deriving strength information. The free-surface samples, which were steps on a single piece of steel, showed lower wavespeeds for thin (1 mm) samples than for thicker (2 or 4 mm) samples. A configuration used for the last three shots allows release information to be determined from these free surface samples. The sample strength appears to increase with stress from ~1 GPa to ~ 3 GPa over this range, consistent with other recent work but about 40% above the Steinberg model.
This study is best characterized as new technology development for implementing new sensors to investigate the optical characteristics of a rapidly expanding debris cloud resulting from hypervelocity impact regimes of 7 to 11 km/s. Our gas guns constitute a unique test bed that match operational conditions relevant to hypervelocity impact encountered in space engagements. We have demonstrated the use of (1) terahertz sensors, (2) silicon diodes for visible regimes, (3) germanium and InGaAs sensors for the near infrared regimes, and (4) the Sandia lightning detectors which are similar to the silicon diodes described in 2. The combination and complementary use of all these techniques has the strong potential of ''thermally'' characterizing the time dependent behavior of the radiating debris cloud. Complementary spectroscopic measurements provide temperature estimates of the impact generated debris by fitting its spectrum to a blackbody radiation function. This debris is time-dependent as its transport/expansion behavior is changing with time. The rapid expansion behavior of the debris cools the cloud rapidly, changing its thermal/temperature characteristics with time. A variety of sensors that span over a wide spectrum, varying from visible regime to THz frequencies, now gives us the potential to cover the impact over a broader temporal regime starting from high pressures (Mbar) high-temperatures (eV) to low pressures (mbar) low temperatures (less than room temperature) as the debris expands and cools.