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The Laser Interferometer Space Antenna (LISA), requires high precision displacement measurement between widely spaced pairs of freely floating test masses. We describe a proposed design for the optical telescopes that form an essential part of the laser heterodyne interferometry measurement system and discuss how the design and implementation will address the unique challenges of this specialized application.
Heterodyne interferometer laser gauges are used in space-based astronomical interferometers to very accurately measure and compensate for variations in starlight pathlength.
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 100 ns with a spatial resolution varying from 90 to 200 μm/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.
Photonic Doppler Velocimetry (PDV) was used to measure the exploding surface of coated metal driven by lineal current density increasing at 3 × 10 15 A/m/s. Here, aluminum-6061 rods were coated with three thicknesses (5, 17, and 41 μm) of Parylene-N and driven to 850 kA in approximately 100 ns, with the metal thicker than the skin depth. According to PDV, the metal surface melts at 85 ± 13 T and expands with a constant acceleration. Then, at surface magnetic field 140-180 T, the metal acceleration begins to increase in time. Later, plasma forms on, and is correlated with PDV signal loss from, uncoated aluminum rods, 5-μm-coated rods, and 17-μm-coated rods, while no evidence suggests plasma forms on 41-μm-coated metal.
TATB (1,3,5-triamino-2,4,6-trinitrobenzene) is a powerful explosive whose dynamical behavior is difficult to study because TATB is so insensitive to initiation by shock waves. We used a tabletop microscope equipped with 0–4.5 km/s laser-launched flyer plates to study shock initiation of TATB, which was fabricated in the form of an array of hundreds of plastic-bonded explosive minicharges (X-TATB = 80% TATB + 20% Sylgard 182 polymer). The 4 ns shocks from the flyer plates were not effective in initiating TATB, but we also developed a two-layer array where flyers first initiated a plastic-bonded PETN (pentaerythritol tetranitrate) charge (X-PETN = 80% PETN + 20% Sylgard), which drove an initiating 25 ns shock into the X-TATB. Thermal emission from shocked X-TATB was used to measure time-dependent temperature profiles with a resolution of 2 ns and to produce high-speed (5 ns) videos. In X-TATB, flyer plates produced 2500–3500 K hot spots and combustion at 2500 K. With X-PETN initiators, X-TATB had 3500–4000 K hot spots and a powerful volume explosion lasting a few nanoseconds. Prospects for producing TATB detonations on a tabletop are discussed.
The performance of energetic materials subjected to dynamic loading significantly depends on their micro- and meso-scale structural morphology. The geometric versatility offered by additive manufacturing opens new pathways to tailor the performance of these materials. Additively manufactured energetic materials (AMEMs) have a wide range of structural characteristics with a hierarchy of length scales and process-inherent heterogeneities, which are hitherto difficult to precisely control. It is important to understand how these features affect AMEMs’ response under dynamic/shock loading. Therefore, temporally and spatially resolved measurements of both macroscopic behavior and micro- and meso-level processes influencing macroscopic behavior are required. In this paper, we analyze the shock compression response of an AMEM simulant loaded under several impact conditions and orientations. Furthermore, x-ray phase contrast imaging (PCI) is used to track features across the observed shock front and determine the linear shock velocity vs particle velocity equation of state, as well as to quantify the interior deformation fields via digital image correlation (DIC) analyses. Photon Doppler velocimetry is simultaneously used to measure the particle velocities of the specimens, which are consistent with those obtained from x-ray PCI. The DIC analyses provide an assessment of the average strain fields inside the material, showing that the average axial strain depends on the loading intensity and reaches as high as 0.23 for impact velocities up to 1.5 km/s. The overall results demonstrate the utility of x-ray PCI for probing “in-material” equation of state and interior strains associated with dynamic shock compression behavior of the AMEM simulant.
Photonic Doppler Velocimetry (PDV) is a fiber-based diagnostic for the extreme conditions created by high-speed impact, explosive detonation, electrical pulsed power, and intense laser ablation. PDV is a conceptually simple application of the optical Doppler effect, but measurements above 1 km/s only became practical at the beginning of the twenty-first century. In this work, I discuss the evolution of PDV, its operational details, practical analysis, and outstanding challenges.
Spall fracture is a high strain-rate damage phenomenon associated with shock or impulsive loading events. When a material that has been subjected to shock compression is allowed to release, rarefaction waves propagate into the sample and reduce the internal stress to zero. If multiple rarefaction waves intersect, they generate tension which, if sufficient, can nucleate voids in the material. It has been observed in several works investigating spall fracture that although the shock-wave profiles suggested spall occurred, imaging of the recovered sample revealed no voids or cracks. In this study, we aim to determine whether a second shock event could recompact existing spall damage, and if so, what form does the microstructure at the recompaction interface have? Through a series of gas-gun flyer-plate impact experiments, we demonstrate that modest shock stresses of 2 GPa–3 GPa are enough to both fully compact a damaged copper target back to a state of zero porosity and, furthermore, drive recrystallization of the interface such that there is a new bond formed where the free surfaces were brought together.
Here, we introduce a novel experimental platform for the study of the Richtmyer–Meshkov instability in a cylindrically converging geometry using a magnetically driven cylindrical piston. Magnetically driven solid liner implosions are used to launch a shock into a liquid deuterium working fluid and, ultimately, into an on-axis rod with a pre-imposed perturbation. The shock front trajectory is tracked through the working fluid and up to the point of impacting the rod through the use of on axis photonic Doppler velocimetry. This configuration allows for precise characterization of the shock state as it impacts the perturbed rod interface. Monochromatic x-ray radiography is used to measure the post-shock interface evolution and rod density profile. The ALEGRA MHD model is used to simulate the dynamics of the experiment in one dimension. We show that late in time the perturbation growth becomes non-linear as evidenced by the observation of high-order harmonics, up to n = 5. Two dimensional simulations performed using a combination of the GORGON MHD code and the xRAGE radiation hydrodynamics code suggest that the late time non-linear growth is modified by convergence effects as the bubbles and spikes experience differences in the pressure of the background flow.
With the advent of additive manufacturing (AM) techniques, a new class of shockwave mitigation and structural supports has been realized through the hierarchical assembly of polymer materials. To date, there have been a limited number of studies investigating the role of structure on shockwave localization and whether AM offers a means to tailor shockwave behavior. Of particular interest is whether the mesoscopic structure can be tailored to achieve shockwave properties in one direction of impact vs the other. In this work, we illustrate directional response in engineered polymer foams. In situ time-resolved x-ray phase contrast imaging at the Advanced Photon Source was used to characterize these diode-like structures. This work offers a breakthrough in materials technology for the development of protective structures that require augmentation of shock in one direction while diminishing transmission in the opposite direction.
Here, this paper describes the calibration of the Arrhenius Wescott–Stewart–Davis (AWSD) reactive flow model for the recently developed high explosive PBX 9701, which consists of 97% 3,3'-diamino-4,4'-azoxyfurazan (DAAF) and 3% FK-800 binder by weight. DAAF-based explosive formulations have several desirable qualities as they are relatively insensitive to non-shock insults but have higher performance than triaminotrinitrobenzene based formulations. Equations of state for the explosive reactants and products are calibrated using a combination of existing and new experimental data and theoretical calculations. The AWSD rate law calibration utilizes both one-dimensional shock-to-detonation and multidimensional rate stick experiments to capture the shock initiation and propagating detonation regimes. Validation of the calibrated model is demonstrated through comparison with recent gas-gun experiments.
In this work, a high-throughput experimental setup was used to characterize initiation threshold and growth to detonation in the explosives hexanitrostilbene (HNS) and pentaerythritol tetranitrate (PETN). The experiment sequentially launched an array of laser-driven flyers to shock samples arranged in a 96-well microplate geometry, with photonic Doppler velocimetry diagnostics to characterize flyer velocity and particle velocity at the explosive–substrate interface. Vapor-deposited films of HNS and PETN were used to provide numerous samples with various thicknesses, enabling characterization of the evolution of growth to detonation. One-dimensional hydrocode simulations were performed with reactions disabled to illustrate where the experimental data deviate from the predicted inert response. Prompt initiation was observed in 144 μm thick HNS films at flyer velocities near 3000 m/s and in 125 μm thick PETN films at flyer velocities near 2400 m/s. This experimental setup enables rapid quantification of the growth of reactions in explosive materials that can reach detonation at sub-millimeter length scales. These data can subsequently be used for parameterizing reactive burn models in hydrocode simulations, as discussed in Paper II [D. E. Kittell, R. Knepper, and A. S. Tappan, J. Appl. Phys. 131, 154902 (2022)].
It is well known that spall failure strongly depends on the microstructure of a material. There have been numerous studies to study the effect of grain size on the overall spall strength and the total amount of damage in single element metals like copper. However, such systematic studies remain rare in two-phase materials and alloys. In this work, two incipient spall experiments were performed on a Cu–1%Pb alloy to understand the effect of grain size on the damage and failure in a two-phase material. Overall, these results showed that even though the spall strength did not change as a function of grain size, there were significant differences in the total amount of damage as a function of grain size. A clear increase in the total damage present in the material was seen as the grain size was increased from 32 to either 70 or 75 μm in either of the experiments. Furthermore, this difference was attributed to variations in the void growth rate as the grain size was increased.
A series of six shock initiation experiments have been carried out on low density LX-14 powder in order to simulate a shock insult on the heavily damage polymer bonded explosive, LX-14. Two distinct morphologies were studied (tap density molding powder and machined swarf), both at the same density of 0.942 g/cm 3 , or 50.1% theoretical maximum density. The purpose of these experiments was to provide data to help make an assessment of the effects that damage has on the material sensitivity to a planar shock. This was achieved primarily by providing shock sensitivity data in the form of a Pop plot, and also reactants equation of state data, which aids in the determination of input conditions for both the experiments performed in this work and also future experiments of this material type. The experiments were of a cut-back format, consisting of four sample heights on each shot and diagnosed with optical velocimetry. The experiments were carried out at the Technical Area 40 Chamber 9 gas gun facility at the Los Alamos National Laboratory, where the LX-14 targets were subjected to Al 6061 and Oxygen Free High Conductivity copper impactors launched to velocities up to 2.14 km/s. Time corrected reactive growth wave profiles are presented in this paper along with the derivation of the following Hugoniot parameters for this explosive, where the molding powder and machine swarf are represented by the following linear equations, respectively, U s = 1.64 (±0.64)u p + 2.25 (±0.49) and U s = 0.87 (±.0.60)u p + 4.08 (±0.49). The results show that the steady increase in shock sensitivity with increasing void fraction reaches an inflection point beyond which the shock sensitivity begins to decease. This inflection point lies between 65% and 50% of the theoretical maximum density of the LX-14. In both cases, the damaged LX-14 was not as sensitive as expected, with a relative shock sensitivity of the molding powder being less than the pressed LX-14, and the machined swarf having a shock sensitivity that is comparable to pressed LX-14.
There exists a large body of evidence from experiments and molecular dynamics simulations to suggest the occurrence of phase transitions in soda-lime glass (SLG) and other silica glasses subject to shock compression to pressures above 3 GPa. In light of these findings, the current work investigated the existence of phase transition in SLG using shock and release experiments. The experiments employed symmetric SLG–SLG impact to achieve complete unloading to zero stress after shock compression to stresses in the range of 3–7 GPa. The stress–strain response and the Lagrangian release wave speed behavior of SLG obtained from these experiments are seen to reveal a mismatch between the loading and unloading paths of the pressure–strain curve for the material, which serves as compelling evidence for the occurrence of a shock-induced phase transition in the material at relatively low pressures. Furthermore, the release wave speed vs strain data obtained from experiments were used to construct a methodology for modeling the shock and release behavior of SLG. Lastly, this scheme implemented in numerical simulations was able to capture the release behavior of shock compressed SLG, for which a robust and satisfactory model was previously unavailable.
Here, we perform a gas gun experiment by shock loading tantalum samples of varying grain structures to assess the suitability of a numerical model for simulating spall behavior. The observed differences in spall strength, as well spallation and re-compression history, are not captured in uncalibrated hydrodynamic simulations. An optimization is performed on the Johnson spall model to determine the best parameters that fit the observed trends. Linear stability analysis is employed to motivate bounds on those parameters. Herein, optimized simulations agree well with the experimental results, reproducing pullback depth and recompression timescales across the different samples tested. Further, the observed pullback time of the single crystal sample was found to imply, via the stability analysis, a percolation threshold in good agreement with the theoretical value for a body centered cubic lattice. Therefore, the combined linear stability and percolation analysis shows promise and may be applied to other materials with diverse microstructures. Collectively, the findings demonstrate that the model is suitable for reproducing spall-induced free surface behavior across various microstructures, but also points to caution in using model coefficients for uncalibrated microstructures.
The study of shock-driven ejecta production has focused on Richtmyer–Meshkov instability (RMI) growth from geometric features of the material surface. Extensive study of this mechanism under both single- and multiple-shock conditions has found that the ejected mass tends to be closely associated with the shocked surface phase, and its temperature is not dramatically greater than the hydrodynamic shock temperature of the bulk. In this work, we propose and demonstrate a new ejecta production mechanism that can occur under multiple-shock conditions based on the collapse of bubbles near the free surface of the material. This mechanism produces ejected mass that is much greater in quantity than observed in the RMI case. The particles are much hotter than predicted by the shock Hugoniot state, and the ejected mass does not appear to be strongly dependent upon initial surface finish. The ejecta source extends into the material with no clear remaining free surface. We name this mechanism Shallow Bubble Collapse (SBC) and discuss the conditions under which it activates. We demonstrate resolved modeling methods that enable the calculation, design, and study of SBC as a mechanism and perform a series of experiments to compare with the models. Under some multiple-shock conditions, SBC ejection produces ten times more ejected mass than RMI growth.
The fracture response of geologic materials is of interest for applications, including geothermal energy harnessing and containment of underground explosions. To better understand the explosively induced fracture response of geomaterials, polymethyl methacrylate (PMMA) was used as a transparent rock surrogate to allow imaging of internal shock propagation and fracture growth processes. Experiments were conducted using high-speed shadowgraphy and photon Doppler velocimetry (PDV), which were compared to numerical simulations. Experiments measured fractures produced in 304.8mm × 304.8mm × 304.8mm PMMA cubes with two simultaneously initiated detonators. The cubes were subjected to varying amounts and directions of externally applied uniaxial stresses, including no stress, 2 MPa stress, and 20 MPa stress. The fracture radius as a function of time was extracted from the high-speed videos. Post-test images of the PMMA cubes aided in the determination of three-dimensional effects not directly imaged by the cameras. The surface velocity history and the shock response captured in PDV and the high-speed videos were compared to the simulated explosive-induced shock response. The simulation results indicate that the shock drives the fracture for the first 20 μs corresponding to a fracture radius of approximately 15 mm in the experiments. The gas-driven fracture extent was estimated analytically using an equilibrium stress distribution calculated after the shock wave propagation through the sample. Reduction in the gas pressure due to the leakage of the explosive products through the crack as a function of time was accounted for. In conclusion, the estimated fracture lengths were in agreement with the experimentally observed fracture lengths.