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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (EL–RK–FV) Method for Scalar Nonlinear Conservation Laws

Abstract We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for the mesh cells to handle intersecting characteristics due to shocks. Following this partitioning, we write the equation in a time-differential form and evolve with Runge–Kutta methods in a method-of-lines fashion. High-resolution methods such as ENO and WENO-AO schemes are used for spatial reconstruction. Extension to higher dimensions is done via dimensional splitting. Numerical experiments demonstrate our scheme’s high-order accuracy and ability to sharply capture post-shock solutions with large time-stepping sizes.

Chen, Jiajie↗
DOE OSTI2022

Effect of Topology on Transient Dynamic and Shock Response of Polymeric Lattice Structures

Architected cellular materials, such as lattice structures, offer potential for tunable mechanical properties for dynamic applications of energy absorption and impact mitigation. In this work, the static and dynamic behavior of polymeric lattice structures was investigated through experiments on octet-truss, Kelvin, and cubic topologies with relative densities around 8%. Here, dynamic testing was conducted via direct impact experiments (25–70 m/s) with high-speed imaging coupled with digital image correlation and a polycarbonate Hopkinson pressure bar. Mechanical properties such as elastic wave speed, deformation modes, failure properties, particle velocities, and stress histories were extracted from experimental results. At low impact velocities, a transient dynamic response was observed which was composed of a compaction front initiating at the impact surface and additional deformation bands whose characteristics matched low strain-rate behavior. For higher impact velocities, shock analysis was carried out using compaction wave velocity and Eulerian Rankine–Hugoniot jump conditions with parameters determined from full-field measurements.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Shock Response of Polymethyl Methacrylate (PMMA) Under Explosive Loading

Abstract The dynamic response of polymethyl methacrylate (PMMA) is well understood for one-dimensional planar impact shocks, but limited research has been performed on the response of PMMA under spherical shock loading. In this work, the shock decay of an explosively-driven shock wave into PMMA was experimentally measured. PMMA cubes of various geometries were explosively loaded with an RP-80 detonator to produce the explosive shock wave. High-speed schlieren imaging was implemented to measure the explosively-driven shock wave velocity throughout the PMMA cubes. Photon Doppler velocimetry (PDV) was used to measure the particle velocity imparted by the shock wave at the surface of the cubes. The material shock response was studied at distances from 21.91 to 133.3 mm from the explosive source. The particle velocity history measured by PDV was compared to the wave profile visualized in the high-speed images. The shock wave pulse amplitude decreased with increased distance from the source. The conducted experiments extend the PMMA shock Hugoniot relating to the lower shock and particle velocity regime.

Torres, S. M. (ORCID:0009000287177206)↗
DOE OSTI2023

Shock-Wave Proprieties of High-Strength Ceramics

The shock and release response of a suite of high-strength ceramics has been investigated with controlled planar impact methods and velocity interferometry diagnostics. The study provides Hugoniot, yield and post-yield compressive strength, phase transformation and tensile spall material properties data for these ceramics.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Dynamic properties of 316l stainless steel repaired using electron beam additive manufacturing

Additive manufacturing has the potential to be used for repair of high-value parts, but the strength and integrity of such repaired parts, especially under dynamic loading, in still unknown. This work presents the results of high strain-rate dynamic testing of additively repaired stainless steel samples. The 316L samples were intentionally damaged and subsequently repaired with 308L stainless steel wire using electron beam additive manufacturing. The repaired samples were subjected to gas-gun impact testing to induce incipient damage and determine the role played by the repaired region in dictating damage and failure. The results show the following: 1) the equation of state of the repaired region is comparable to the original material as shown by the unchanged spall plane location, 2) the deformation behavior is similar to the original material as shown by the similar Hugoniot Elastic limit, 3) the spall strength of the repaired region is slightly higher than the original material due to varying grain size, and 4) the damage morphology in the repaired region is different and involves a high rate of void coalescence. In conclusion, despite these minor differences in the spall strength and the damage morphology, the overall dynamic response of the original material and repaired samples is similar suggesting that AM is a promising approach for repairing high-value components.

36 MATERIALS SCIENCE↗
DOE OSTI2023

The effect of microstructure on the dynamic shock response of 1045 steel

Herein, the effect of microstructure on the shock response of 1045 steel is investigated via plate impact experiments and postmortem characterization. Three unique microstructures are explored: ferrite-pearlite, martensite, and ferrite with spheroidal cementite (i.e. spheroidized). Two spall recovery experiments, at approximate peak pressures of 3.2 and 3.5 GPa, are conducted to assess the Hugoniot elastic limit (HEL), spall strength, and damage morphology of the various microstructures. The ferrite-pearlite and martensite microstructures exhibit continuous yielding at both quasi-static and dynamic rates, while the spheroidized condition displays discontinuous yielding. Discontinuous yielding of the spheroidized microstructure is attributed to a combined low initial dislocation density coupled with a low dislocation nucleation rate. The spall strength of ferrite-pearlite is consistently lower than the spheroidized microstructure, attributed to elongated cementite that is more susceptible to cracking than more spherical cementite precipitates. Despite a high density of boundaries, martensite exhibits the highest spall strength. A large percentage of the boundaries within the martensite microstructure are found to be low energy (i.e. Σ3 or low angle), and are thus less susceptible to spall damage. Overall, the high spall strength of martensite is likely linked to traditional strengthening mechanisms that limit dislocation motion.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Pressure-induced phase transformations in Nb 2 O 5 from ab initio molecular dynamics simulations

Here, the equations of state for the H-, L- and T-Nb 2 O 5 polymorphs were investigated with density functional theory. The shock Hugoniot curves were predicted from ab initio molecular dynamics simulations along 300–2500 K isotherms. Enthalpies derived from simulations at 300 K show that the H → L transition occurs at 6.2 GPa, in agreement with the measured value of ~5.9 GPa, and is more favorable than the H → T transition. Pressure-induced amorphization (PIA) of L-Nb 2 O 5 is in the range ~18-25 GPa, consistent with experiments reporting PIA above 21.4 GPa. The simulated PIA of T-Nb 2 O 5 between ~16 and 26 GPa reproduces PIA observed above 19.2 GPa.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Dimensionless parameters for ballistic performance evaluation of ceramic-faced bicomponent targets against sharp-nosed projectiles

Two dimensionless parameters are proposed to give first-order approximations for the ballistic performance of ceramic-faced bicomponent armor plates impacted by conical-nosed steel projectiles. The current work collates expansive experimental data from Wilkins and Mayseless covering a broad range of material and mechanical properties, target construction, and projectile dimensions, the data is collapsed using the Hugoniot elastic limit of the ceramic strike face as a strength metric. We find that within datasets where experimental conditions are kept constant, a singular cubic curve can be generated, but variations in experimental conditions for the ballistic limit test between datasets can result in differences in the predictive curve coefficients.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Implicit shock tracking for unsteady flows by the method of lines

Here, a recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws is extended to the unsteady case. Central to the framework is an optimization problem which simultaneously computes a discontinuity-aligned mesh and the corresponding high-order approximation to the flow, which provides nonlinear stabilization and a high-order approximation to the solution. This work extends the implicit shock tracking framework to the case of unsteady conservation laws using a method of lines discretization via a diagonally implicit Runge-Kutta method by “solving a steady problem at each timestep”. We formulate and solve an optimization problem that produces a feature-aligned mesh and solution at each Runge-Kutta stage of each timestep, and advance this solution in time by standard Runge-Kutta update formulas. A Rankine-Hugoniot based prediction of the shock location together with a high-order, untangling mesh smoothing procedure provides a high-quality initial guess for the optimization problem at each time, which results in rapid convergence of the sequential quadratic programing (SQP) optimization solver. This method is shown to deliver highly accurate solutions on coarse, high-order discretizations without nonlinear stabilization and recover the design accuracy of the Runge-Kutta scheme. We demonstrate this framework on a series of inviscid, unsteady conservation laws in both one- and two- dimensions. We also verify that our method is able to recover the design order of accuracy of our time integrator in the presence of a strong discontinuity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Dynamic properties of FeCrMnNi, a high entropy alloy

The goal of this paper was to assess the dynamic properties of a new class of materials, High entropy alloys (HEAs). Specifically, gas gun experiments coupled with recovery were performed on a specific HEA, FeCrMnNi, to measure its equation of state (EOS) and its spall strength, which is a measure of the stress required to nucleate voids under shock loading conditions. While there has been a plethora of work performed to assess the mechanical properties of these HEAs under uniaxial stress conditions as a function of strain rate, investigation of its properties in dynamic extremes remains rare. The current work fills this gap in knowledge for this novel class of materials. Our results show that the measured EOS for this material at one velocity was in reasonable agreement with an estimated Hugoniot. Furthermore, while the spall strength for this material was found to be ~1.9 GPa, with some variation based on sample location, the main failure mode was brittle. This brittle failure leading to formation of cracks in the material is different than the ductile failure observed in pure iron and its alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Shock-induced phase transitions and stacking fault formation in additively manufactured eutectic high-entropy alloy Ni 40 Co 20 Fe 10 Cr 10 Al 18 W 2

Ni 40 Co 20 Fe 10 Cr 10 Al 18 W 2 additively manufactured using laser powder bed fusion (LPBF) is among the toughest as-built alloys reported and is a promising candidate for use in extreme environments. However, its behavior under multi-megabar pressure regimes remains unexplored. We used femtosecond in situ X-ray diffraction to investigate the shock response of LPBF Ni40Co20Fe10Cr10Al18W2 under laser-driven shock compression and release. Our results reveal that the initial dual-phase face-centered + body-centered structure transforms to a single face-centered phase over a wide pressure range of 84±10 to 277±55 GPa, followed by a transition to a single body-centered phase at 431±48 GPa. We establish the Hugoniot equation-of-state of LPBF Ni 40 Co 20 Fe 10 Cr 10 Al 18 W 2 and compare it to the benchmark alloy AlCoCrFeNi 2.1 , demonstrating the effects of W-doping and increased Al content. High stacking fault probabilities, close to those measured in Au and Ag, are observed upon compression. A portion of the stacking faults are annihilated upon release to ambient pressure.

36 MATERIALS SCIENCE↗
DOE OSTI2026

High Pressure X-ray Diffraction and Equation of State of Hydrazine

Synchrotron X-ray diffraction has been used to investigate the structure and equation of state (EOS) of hydrazine (N 2 H 4 ) up to 54.3 GPa at 298 K. The diffraction patterns could be fit to a monoclinic unit-cell structure and put strong constraints on previously reported phase transitions documented by vibrational spectroscopy over this pressure range. Pressure–volume ( P–V ) data were fit using a Vinet EOS, yielding parameters: V 0 = 45.2 Å 3 /molecule (fixed), K 0 = 11.8(7) GPa, and K 0 ′ = 6.5(2). Previously measured high-pressure vibrational frequency shifts were used to estimate the vibrational free energy and model P–V–T isotherms from 0 to 1200 K. The results of the P–V–T isotherms are compared to existing shock Hugoniot data on hydrazine and 298 K isotherms for assemblages of possible decomposition products. This comparison suggests dissociation at high density under shock loading. Good correspondence was found between the static lattice EOS as calculated by the model and the previously reported EOS as calculated by density functional theory. Finally, these results resolve existing uncertainties about the EOS and crystal symmetry of hydrazine at high pressure and provide valuable baseline information on this important energetic material.

diffraction↗
DOE OSTI2024

Static and Dynamic Thermomechanical Properties of Phase-Separated Epoxy Networks with Tuned Microstructures

Here, polymerization-induced phase separation is a useful method for the construction of heterogeneous epoxy networks with properties exceeding their homogeneous counterparts. In this work, we examine the static and dynamic thermomechanical properties of phase-separated epoxy networks salient to their application as encapsulants. Three heterogeneous epoxy-amine networks with nano-, meso-, and macro-phase-separated morphologies comprised of hard and soft domains are compared to a rigid, unstructured network. The glass transition profiles of the heterogeneous networks are complex, spanning many decades in the frequency domain. The nanophase-separated morphology leads to higher coefficient of thermal expansion, yet surprisingly is characterized by reduced residual stress. Under both quasi-static and dynamic compression (strain rates of order 10 –3 and 10 3 s –1 , respectively), the nanophase-separated network also exhibits higher modulus and strength. In split-Hopkinson bar experiments, the energy dissipation characteristics of the epoxy networks were nearly identical. Curiously, however, the Hugoniot response of the macro-phase-separated network determined by ballistic shockwave analysis indicates a remarkable ability of this material to mitigate shockwave propagation in comparison to many homogeneous and heterogeneous polymer materials. Collectively, this work reveals several previously unreported phenomena with respect to structure–property relationships in phase-separated epoxy networks, illustrating the potential value of systematically tuned microstructures for optimization of application-specific physical properties.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Shock compression of FeOOH and implications for iron-water interactions in super-earth magma oceans

Iron(Fe)-water reactions in a magma ocean can influence water storage and density of planets. These reactions can form Fe-O-H phases, whose density, melting, and electronic properties at planetary interior conditions are important for informing planetary models. Here, we study natural goethite (α-FeOOH) that is shock-compressed along its principal Hugoniot. Analysis of our velocity interferometer system for any reflector (VISAR) results extends the equation of state to over 800 GPa. X-ray diffraction and VISAR reflectivity results indicate the onset of melting occurs at ~95 GPa with complete melting by 166 GPa, which may be relevant to low seismic velocity anomalies observed above the core-mantle boundary. Analysis of X-ray emission spectroscopy results up to 285 GPa shows the spin crossover of Fe, with dominantly low spin Fe above ~265 GPa in the melt, supporting formation of dense basal magma oceans in terrestrial planets. Using our measured FeOOH densities, we model planetary interiors up to 10 Earth masses. Assuming FeOOH forms via iron-water reactions, the radius decreases by up to 28%, while the density increases by up to 165% compared to the unreacted cases, providing an avenue to investigate water storage and evolution in super-Earths and sub-Neptunes.

Zhang, Yanyao [Stanford Univ., CA (United States)]↗
DOE OSTI2020

A measurement of the equation of state of carbon envelopes of white dwarfs

White dwarfs represent the final state of evolution for most stars. Certain classes of white dwarfs pulsate, leading to observable brightness variations, and analysis of these variations with theoretical stellar models probes their internal structure. Modelling of these pulsating stars provides stringent tests of white dwarf models and a detailed picture of the outcome of the late stages of stellar evolution. However, the high-energy-density states that exist in white dwarfs are extremely difficult to reach and to measure in the laboratory, so theoretical predictions are largely untested at these conditions. In this paper we report measurements of the relationship between pressure and density along the principal shock Hugoniot (equations describing the state of the sample material before and after the passage of the shock derived from conservation laws) of hydrocarbon to within five per cent. The observed maximum compressibility is consistent with theoretical models that include detailed electronic structure. This is relevant for the equation of state of matter at pressures ranging from 100 million to 450 million atmospheres, where the understanding of white dwarf physics is sensitive to the equation of state and where models differ considerably. The measurements test these equation-of-state relations that are used in the modelling of white dwarfs and inertial confinement fusion experiments, and we predict an increase in compressibility due to ionization of the inner-core orbitals of carbon. We also find that a detailed treatment of the electronic structure and the electron degeneracy pressure is required to capture the measured shape of the pressure–density evolution for hydrocarbon before peak compression. Our results illuminate the equation of state of the white dwarf envelope (the region surrounding the stellar core that contains partially ionized and partially degenerate non-ideal plasmas), which is a weak link in the constitutive physics informing the structure and evolution of white dwarf stars.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Evidence of hydrogen-helium immiscibility at Jupiter-interior conditions

The phase behaviour of warm dense hydrogen–helium (H–He) mixtures affects our understanding of the evolution of Jupiter and Saturn and their interior structures. For example, precipitation of He from a H–He atmosphere at about 1–10 megabar and a few thousand kelvin has been invoked to explain both the excess luminosity of Saturn, and the depletion of He and neon (Ne) in Jupiter’s atmosphere as observed by the Galileo probe. But despite its importance, H–He phase behaviour under relevant planetary conditions remains poorly constrained because it is challenging to determine computationally and because the extremes of temperature and pressure are difficult to reach experimentally. Here we report that appropriate temperatures and pressures can be reached through laser-driven shock compression of H 2 –He samples that have been pre-compressed in diamond-anvil cells. This allows us to probe the properties of H–He mixtures under Jovian interior conditions, revealing a region of immiscibility along the Hugoniot. A clear discontinuous change in sample reflectivity indicates that this region ends above 150 gigapascals at 10,200 kelvin and that a more subtle reflectivity change occurs above 93 gigapascals at 4,700 kelvin. Considering pressure–temperature profiles for Jupiter, these experimental immiscibility constraints for a near-protosolar mixture suggest that H–He phase separation affects a large fraction—we estimate about 15 per cent of the radius—of Jupiter’s interior. Furthermore, this finding provides microphysical support for Jupiter models that invoke a layered interior to explain Juno and Galileo spacecraft observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Evidence of shock-compressed stishovite above 300 GPa

SiO 2 is one of the most fundamental constituents in planetary bodies, being an essential building block of major mineral phases in the crust and mantle of terrestrial planets (1–10 M E ). Silica at depths greater than 300 km may be present in the form of the rutile-type, high pressure polymorph stishovite (P4 2 /mnm) and its thermodynamic stability is of great interest for understanding the seismic and dynamic structure of planetary interiors. Previous studies on stishovite via static and dynamic (shock) compression techniques are contradictory and the observed differences in the lattice-level response is still not clearly understood. Here, laser-induced shock compression experiments at the LCLS- and SACLA XFEL light-sources elucidate the high-pressure behavior of stishovite on the lattice-level under in situ conditions on the Hugoniot to pressures above 300 GPa. We find stishovite is still (meta-)stable at these conditions, and does not undergo any phase transitions. This contradicts static experiments showing structural transformations to the CaCl 2 , α-PbO 2 and pyrite-type structures. However, rate-limited kinetic hindrance may explain our observations. These results are important to our understanding into the validity of EOS data from nanosecond experiments for geophysical applications.

58 GEOSCIENCES↗
DOE OSTI2021

Measuring the structure and equation of state of polyethylene terephthalate at megabar pressures

Abstract We present structure and equation of state (EOS) measurements of biaxially orientated polyethylene terephthalate (PET, $$({\hbox {C}}_{10} {\hbox {H}}_8 {\hbox {O}}_4)_n$$ ( C 10 H 8 O 4 ) n , also called mylar) shock-compressed to ( $$155 \pm 20$$ 155 ± 20 ) GPa and ( $$6000 \pm 1000$$ 6000 ± 1000 ) K using in situ X-ray diffraction, Doppler velocimetry, and optical pyrometry. Comparing to density functional theory molecular dynamics (DFT-MD) simulations, we find a highly correlated liquid at conditions differing from predictions by some equations of state tables, which underlines the influence of complex chemical interactions in this regime. EOS calculations from ab initio DFT-MD simulations and shock Hugoniot measurements of density, pressure and temperature confirm the discrepancy to these tables and present an experimentally benchmarked correction to the description of PET as an exemplary material to represent the mixture of light elements at planetary interior conditions.

36 MATERIALS SCIENCE↗