Hugoniot, Hugoniot elastic limit, and spall strength of selected braze alloys before and after annealing
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McCoy, Chad August [Sandia National Laboratories (↗
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Ti-6Al-4V to over 1.2 Terapascals: Shock Hugoniot and off-Hugoniot Release Experiments, Ab-initio Calculations and a Broad-Range Multiphase EOS.
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Kalita, Patricia↗
Hugoniot, Hugoniot elastic limit, and spall strength of a 98.9Ag1.0Cu0.1Al representative braze
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McCoy, Chad August [Sandia National Laboratories (↗
Hugoniot, sound speed, and phase transitions of single-crystal sapphire for pressures 0.2–2.1 TPa
Sapphire (Al 2 O 3 ) is a major constituent of the Earth's mantle and has significant contributions to the field of high-pressure physics. Constraining its Hugoniot over a wide pressure range and identifying the location of shock-driven phase transitions allows for development of a multiphase equation of state and enables its use as an impedance-matching standard in shock physics experiments. In this paper we present measurements of the principal Hugoniot and sound velocity from direct impact experiments using magnetically launched flyers on the Z machine at Sandia National Laboratories. The Hugoniot was constrained for pressures from 0.2–2.1 TPa and a four-segment piecewise linear shock-velocity–particle-velocity fit was determined. First-principles molecular dynamics simulations were conducted and agree well with the experimental Hugoniot. Sound-speed measurements identified the onset of melt between 450 and 530 GPa, and the Hugoniot fit refined the onset to 525 ± 13 GPa. A phase diagram which incorporates literature diamond-anvil cell data and melting measurements is presented.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Hugoniot equation of state of anorthite glass and lunar anorthosite
Twenty-one Hugoniot experiments were conducted on an amorphous material of anorthite composition, in the pressure range 8-120 GPa, using both routine and new methods. Two Hugoniot measurements at about 120 GPa were made on lunar gabbroic anorthosite (Apollo 15,418). Theoretical Hugoniots are constructed for both materials assuming they are disproportionate to their component oxides. These accurately predict the P-p behavior of the lunar anorthosite Hugoniot at 120 GPa and the anorthite glass Hugoniot above 50 GPa, but overestimate the shock temperatures of anorthite glass. The mixed oxide model fails to predict the release paths of either material. It is concluded that the mixed oxide model is a good description of the bulk properties of the high-pressure phases of anorthite, but does not represent the actual phases. A significant enrichment of calcic refractory material in the earth's lower mantle is not precluded by the bulk properties of the anorthite high-pressure phases.
Boslough, M. B.↗
Shock Hugoniot calculations using on-the-fly machine learned force fields with ab initio accuracy
We present a framework for computing the shock Hugoniot using on-the-fly machine learned force field (MLFF) molecular dynamics simulations. In particular, we employ an MLFF model based on the kernel method and Bayesian linear regression to compute the free energy, atomic forces, and pressure, in conjunction with a linear regression model between the internal and free energies to compute the internal energy, with all training data generated from Kohn–Sham density functional theory (DFT). We verify the accuracy of the formalism by comparing the Hugoniot for carbon with recent Kohn–Sham DFT results in the literature. In so doing, we demonstrate that Kohn–Sham calculations for the Hugoniot can be accelerated by up to two orders of magnitude, while retaining ab initio accuracy. We apply this framework to calculate the Hugoniots of 14 materials in the FPEOS database, comprising 9 single elements and 5 compounds, between temperatures of 10 kK and 2 MK. We find good agreement with first principles results in the literature while providing tighter error bars. In addition, we confirm that the inter-element interaction in compounds decreases with temperature.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Ti-6Al-4V to over 1.2 TPa: Shock Hugoniot experiments, ab initio calculations, and a broad-range multiphase equation of state
Titanium alloys are used in a large array of applications. In this work we focus our attention on the most used alloy, Ti-6Al-4V (Ti64), which has excellent mechanical and biocompatibility properties with applications in aerospace, defense, biomedical, and other fields. Here we present high-fidelity experimental shock compression data measured on Sandia’s Z machine. We extend the principal shock Hugoniot for Ti64 to more than threefold compression, up to over 1.2 TPa. We use the data to validate our ab initio molecular dynamics simulations and to develop a highly reliable, multiphase equation of state (EOS) for Ti64, spanning a broad range of temperature and pressures. The first-principles simulations show very good agreement with Z data and with previous three-stage gas gun data from Sandia’s STAR facility. The resulting principal Hugoniot and the broad-range EOS and phase diagram up to 10 TPa and 10 5 K are suitable for use in shock experiments and in hydrodynamic simulations. The high-precision experimental results and high-fidelity simulations demonstrate that the Hugoniot of the Ti64 alloy is stiffer than that of pure Ti and reveal that Ti64 melts on the Hugoniot at a significantly lower pressure and temperature than previously modeled.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Shock compression of cemented tungsten carbides to 100 GPa: Structure of shock waves, Hugoniot relations, and strength
Plate impact experiments are conducted on cemented tungsten carbides (WC) with a 3.7 and 6.0 wt. % cobalt binder to better understand their dynamic, high-pressure response to 100 GPa. The measured wave profiles show propagation of steady structured waves. Standard impedance matching procedures are used to determine the Hugoniot relations in the shock velocity–particle velocity (U s –v p ) and Hugoniot stress–specific volume (P–V/V o ) planes. The Hugoniot elastic limit of the samples is controlled by ductility of the Co binder and is determined to be 4.45 ± 0.29 GPa for cemented WC with 3.7 wt. % cobalt and 3.72 ± 0.24 GPa for a 6.0 wt. % cobalt binder. Both grades show a non-linear U s –v p relationship depending on whether the particle velocity is in the strength dominated or hydrodynamic regime. In the strength dominated regime, a non-linear decrease in U s is observed as v p increases from ambient to the material’s hydrodynamic limit. In the hydrodynamic regime, the U s –v p Hugoniot is linear and is determined to be U s = 4.97(±0.006)+1.446(±0.018)v p km/s for WC with 3.7 wt. % Co and U s = 4.93(±0.006)+1.463(±0.017)v p km/s for 6 wt. % Co. Both WC grades indicate shear-stress hardening with mean stress immediately after yield, followed by pressure softening, and then a sharp fall in stress carrying capacity as the mean stress is increased to ≈70 GPa (hydrodynamic limit) and beyond. This behavior is in contrast to pure WC ceramics, which show continued shear-stress hardening with mean stress to ≈80 GPa.
36 MATERIALS SCIENCE↗
Hugoniot and Dynamic Strength in Polyurea
Polyurea is of interest for blast mitigation of structures, which requires a good understanding of the dynamic properties including the shock Hugoniot and dynamic spall and shear strength. In this study, reverse impact experiments were used to determine the shock Hugoniot, direct impact experiments were used to determine the spall strength, and lateral manganin gauge experiments were used to determine the dynamic shear strength. Reverse impact experiments revealed that the Hugoniot has a linear fit at low pressures and appears to be undergoing a reaction at higher pressures. The spall strength experiments in this study in combination with the literature data showed that the spall strength increases as a function of pressure, which is unusual in polymers and may be attributed to polyurea transforming to a glassy phase. In the shear strength experiments, the shear stress was shown to increase with increasing longitudinal stress in polyurea, similar to estane, another elastomer.
36 MATERIALS SCIENCE↗
Measurement of the Hugoniot and shock-induced phase transition stress in wrought 17-4 PH H1025 stainless steel
Uniaxial strain, reverse-ballistic impact experiments were performed on wrought 17-4 PH H1025 stainless steel, and the resulting Hugoniot was determined to a peak stress of 25 GPa through impedance matching to known standard materials. The measured Hugoniot showed evidence of a solid–solid phase transition, consistent with other martensitic Fe-alloys. The phase transition stress in the wrought 17-4 PH H1025 stainless steel was measured in a uniaxial strain, forward-ballistic impact experiment to be 11.4 GPa. Linear fits to the Hugoniot for both the low and high pressure phase are presented with corresponding uncertainty. The low pressure martensitic phase exhibits a shock velocity that is weakly dependent on the particle velocity, consistent with other martensitic Fe-alloys.
36 MATERIALS SCIENCE↗
A parametric study of slow shock Rankine-Hugoniot solutions and critical Mach numbers
The relationship between Rankine-Hugoniot solutions and critical Mach numbers is studied. The range of upstream parameters for which the resistivity or thermal conduction provide all the dissipation required by the slow shock Rankine-Hugoniot relations are evaluated. The calculation of the critical Mach number by analyzing the flux of shock catching ions is examined. It is observed that the properties of slow shocks depend on shock normal angle, and the ratio of the sound and Alfven speeds upstream. The Rankine-Hugoniot solutions are applicable to the analysis of spacecraft observations of slow shocks.
Edmiston, J. P.↗
Hugoniot properties of porous stainless steel: Insights from molecular dynamics simulations
Here, we present a systematic study of Hugoniot properties of porous 316L stainless steel using both a simple interpolation scheme and direct shock simulations in order to probe pore collapse kinetics as well as final thermodynamic states. Both methods indicate that equilibrated Hugoniot properties depend on pore density only and not on the pore distribution or size. We then create a simple porous equation of state model that is shown to be accurate for a range of validation data. This allows us to extend our simulations to make direct comparison to experimental data that have generally significantly larger system sizes and durations. In addition, our direct shock simulations indicate that the relaxation time after hotspot formation is system size dependent and can reach nanosecond timescales for the largest pores investigated in our study, thereby possibly having a measurable effect on fast dynamic loading experiments.
36 MATERIALS SCIENCE↗
Absolute Hugoniot measurements in low-density plastic foams on the NIKE shock compression platform
The propagation of Mbar-range shock waves in low-density foam materials is of interest to target design in all approaches to inertial confinement fusion, high energy density physics, and laboratory astrophysics. We report absolute Hugoniot measurements for CH 1.72 N 0.086 O 0.37 plastic foams with 73 and 94 mg/cm 3 densities in the 32–107 km/s shock velocity range. The experiments were performed on the shock compression platform developed on the NIKE KrF laser facility at the U.S. Naval Research Laboratory. NIKE's 4 or 8-ns long flat-top laser pulses drive steady shock waves into foam targets at the ablative pressures of 1–7 Mbar. The propagation of the ablation and shock fronts is tracked continuously in time using streaked side-on monochromatic x-ray imaging radiography. The straight x−t trajectories of the shock and ablation fronts in the recorded streak images confirmed their steadiness. The SESAME tabulated equation of state predictions generally agrees with our Hugoniot data within a 95% confidence band. The experimental uncertainty of the evaluated shock density compression ratios remains large, indicating the need for more experiments and improved theoretical understanding of the strong shock propagation mechanisms in dry foams.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Measurements of the inert Hugoniot and observation of mechanical ignition in Ni(V) + Al reactive multilayers via x-ray diffraction
This study investigates the inert Hugoniot response, mechanical ignition, and reaction dynamics of Ni(V)+Al multilayers during longitudinal, laser-driven shock compression experiments. Ni(V)+Al multilayers, known for their self-propagating exothermic reactions, were subjected to longitudinal stresses exceeding 50 GPa using the laser shock facility within the Dynamic Compression Sector (DCS) at the Advanced Photon Source (APS). In situ x-ray diffraction (XRD) revealed that Ni(V) and Al were not in equilibrium during compression, with stress discrepancies attributed to twinning, grain structure effects, and/or dislocation density. However, the measured inert Hugoniot closely matched prior experimental and computational studies, confirming the utility of XRD for measuring the equation of state of thin, complex materials. Additionally, reaction was observed at significantly higher stresses than reported previously using laser-launched flyers. This discrepancy suggests a strong influence of externally imposed shear stress on reaction thresholds, which likely arose from deviations in flyer planarity during past experiments. Full reaction of the multilayer occurred within 40 ns after shock-wave passage, evidenced by complete melting of the constituents. Eulerian hydrocode simulations replicated experimental conditions, providing insights into equilibrium dynamics and experimental artifacts. The results highlight how even small shear forces facilitate ignition in Ni(V)+Al multilayers at lower stresses.
Crystallography↗
Shock-induced melting of [100] lithium fluoride: Sound speed and Hugoniot measurements to 230 GPa
Although [100] lithium flouride (LiF) is the most widely used optical window material in dynamic compression experiments, its high stress (>100 GPa) shock compression response, including melting, is not well understood. To address this need, we measured wave profiles in plate impact experiments to determine the Hugoniot states and longitudinal sound speeds in [100] LiF crystals shock compressed to 231 GPa. The measured peak states are fitted well by a linear shock velocity-particle velocity relation, providing an accurate determination of the LiF Hugoniot curve to significantly higher stresses than previous experiments. The longitudinal sound speeds show a near linear increase with density compression to 182 GPa. Between 182 GPa and 195 GPa, the sound speed and the longitudinal modulus decrease abruptly, due to shock-induced melting. The increasing sound speeds and moduli at higher stresses suggest that shock compressed LiF is fully liquid at 195 GPa and above, allowing determination of the Gruneisen parameter for liquid LiF. Here, the melt stress determined here differs from that predicted by current multiphase equations of state for LiF. Our results provide important insight into the high stress solid and liquid states of shock compressed LiF and point to the need for an improved multiphase equation of state at high pressures and high temperatures.
36 MATERIALS SCIENCE↗
Symmetry Determining Equations of the Rankine-Hugoniot Equations for Variable Velocity Shock Waves
The “constant velocity piston” problem (Fig. 1), also known as the “piston problem,” is a standard model for a one dimensional, in our case linear, symmetric shock wave moving through an inviscid, perfect gas. The model can be divided into two regions - a perturbed section on the left and an unperturbed section on the right - by a moving shock wave moving left to right. Both the perturbed and unperturbed sections, i.e. the shocked and unshocked regions, respectively, obey the Eulerian conservation equations; however, at the exact location of the shock, there is a mathematical discontinuity not satisfied by the Euler equations. To ensure continuity and conservation of certain quantities when crossing between the unshocked and shocked regions, we evoke a series of equations derived from the Eulerian conservation equations, called the Rankine-Hugoniot equations, or “jump” equations as it is often referred to in the literature on the topic. The classical constant-velocity piston problem assumes the piston features a constant driving velocity (among many other willing suspensions of belief required in the pursuit of a first principles equation model); consequent to this assumption is a constant-velocity shock and a constant-velocity shocked flow state. However, using Lie Group Theory (LGT), also known as symmetry analysis, we can attempt to reinterpret the model with a shock wave of variable velocity in time and space. An extension of the model in this way opens up the possibility for obtaining new analytical solutions to the piston problem for certain shock velocity models. In this report, we use LGT to derive the symmetry determining equations (SDEs), whose solutions are Lie groups, which permit analytical solutions. In the future, we can then use the SDEs to define constraint equations on the shock velocity model and what the successive solutions to the Euler equations might be based off such constraints. This report is structured as follows: Section 2 provides a brief derivation of the Rankine-Hugoniot (“jump”) equations; Section 3 gives an overview of Lie group theory; Section 4 derives the SDEs of the jump equations; Section 5 derives the Euler conservation equations for fluids; and Section 6 presents concluding remarks and opportunities for future studies.
42 ENGINEERING↗
The resolved layer of a collisionless, high beta, supercritical, quasi-perpendicular shock wave. I - Rankine-Hugoniot geometry, currents, and stationarity
Data collected by the ISEE dual-spacecraft mission (on November 7, 1977) on a slowly moving, supercritical, high-beta, quasi-perpendicular bow shock are presented, and the local geometry, spatial scales, and stationarity of this shock wave are assessed in a self-consistent Rankine-Hugoniot-constrained frame of reference. Included are spatial profiles of the ac and dc magnetic and electric fields, electron and proton fluid velocities, current densities, electron and proton number densities, temperatures, pressures, and partial densities of the reflected protons. The observed layer profile is shown to be nearly phase standing and one-dimensional in a Rankine-Hugoniot frame, empirically determined by the magnetofluid parameters outside the layer proper.
Scudder, J. D.↗
A generalized version of the Rankine-Hugoniot relations including ionization, dissociation and related phenomena
For purposes of computing shocks in stellars atmospheres and winds we have developed a generalized version of the Rankine-Hugoniot relations including ionization, dissociation, radiation and related phenomena such as excitation, rotation and vibration of molecules. The new equations are given in analytical form. They are valid as long as the internal energy E, the total pressure P, and the first adiabatic coefficient gamma(sub 1) can be evaluated. However, we have not treated shock structures. In the case of non-LTE we have to employ an approximation for gamma(sub 1) because in that case no definition exists. Our new version of the Rankine-Hugoniot relations can easily be used for many purposes including ab-initio modeling. In our derivation we introduce a parameter gamma(sub H), which is definded as the ratio of the enthalpy H (sometimes called heat function w) to the internal energy E (sometimes called U). Using this parameter we solve the equations for changing mu and (d(natural log P)/d(natural log rho))(sub ad) identically equal to gamma(sub 1) on both sides of the shock. Both gamma(sub H) and gamma(sub 1), and also mu are functions of pressure P and temperature T. We present: (1) the derivation, (2) examples of gamma(sub 1) (P,T) and gamma(sub H) (P,T) which include/exclude ionization and radiation, and (3) as an example the differences in post-shock parameters as function of the pre-shock temperature for the case with ionization and without radiation.
Nieuwenhuijzen, H.↗