Publications

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Dynamic materials experiments on the Z-machine are beginning to reach a regime where traditional analysis techniques break down. Time dependent phenomena such as strength and phase transition kinetics often make the data obtained in these experiments difficult to interpret. We present an inverse analysis methodology to infer the equation of state (EOS) from velocimetry data in these types of experiments, building on recent advances in the propagation of uncertain EOS information through a hydrocode simulation. An example is given for a shock-ramp experiment in which tantalum was shock compressed to 40 GPa followed by a ramp to 80 GPa. The results are found to be consistent with isothermal compression and Hugoniot data in this regime.

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.

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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). 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 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.

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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.

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An absolute stress-density path for shocklessly compressed copper is obtained to over 450 GPa. A magnetic pressure drive is temporally tailored to generate shockless compression waves through over 2.5-mm-thick copper samples. The free-surface velocity data is analyzed for Lagrangian sound velocity using the iterative Lagrangian analysis (ILA) technique, which relies upon the method of characteristics. We correct for the effects of strength and plastic work heating to determine an isentropic compression path. By assuming a Debye model for the heat capacity, we can further correct the isentrope to an isotherm. Our determination of the isentrope and isotherm of copper represents a highly accurate pressure standard for copper to over 450 GPa.

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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.

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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.

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