Session E5: Equation of State IV: Compression, Off-Hugoniot, Off-Isentrope

Effect of shear strength on the Hugoniot-compression curve and EOS of some metals

To derive true equations of state (EOS) of matter, we need the precise Hugoniot data, and must access the strength under shock compression to draw the isothermal hydrostatic compression curve. For this, we have established the high-speed streak camera measurement system consisting of rotating-mirror type streak camera and pulsed dye laser combined with the one-stage powder gun and two-stage light gas gun. We performed the plate-mirror Hugoniot measurement experiments on tungsten (W), copper (Cu), etc. in the pressure range up to \textgreater 200 GPa by symmetric impact method, and measured the Hugoniot data where the effects of tilt and bowing of the impact plate were carefully considered. It was found that the zero-intercept value (C0) of Us-Up relation (Us $=$C0$+$SUp) of W were larger than the bulk sound velocity by 3.1{\%}, which may show the effect of shear strength in plastic region. The hydrostatic-compression curves were drawn by using the shear strength values reported by Sandia National Laboratories group, and the EOS's were discussed. The hypothesized Us-Up Hugoniot curve of the hydrostatic compression curve converged to the bulk sound velocity.   

Radiance Measurement on Ramp Loading -- Implications for Temperature on Quasi-Isentropes

Temperature increases along a quasi-isentropic loading path have the promise to characterize either the approach to constant entropy in the case of a known Gr\"{u}neisen parameter or else to measure the Gr\"{u}neisen parameter once the quality of the isentrope is established. Our group has developed the ability to synthesize graded density impactors able to generate customized multistep loading paths that included ramp loads, dwells, shock jumps and ramp unloads. Here we present a recent measurement of thermal radiance from a ramp-loaded Sn sample. The sample was shocked to approximately 0.5 Mbar, held at a constant pressure for 400 ns, and then ramp loaded to approximately 1.5 Mbar. Dynamic emissivity was not measured along this path, but radiance was monitored at the sample-LiF window interface as a function of time at 7 wavelengths in the visible spectrum with a spectral resolution of 80 nm. We will discuss experimental results and analysis of the relationship between pressure and radiance on the ramp-loading path of Sn with variable initial temperature along the sample. Assumptions employed in this analysis and implications for temperature along the ramp-loading path, for the closeness of approach to isentropic loading, and for the Gr\"{u}neisen parameter of Sn will also be discussed.   

The effect of shear strength on isentropic compression experiments

Isentropic compression experiments (ICE) are a novel way of obtaining equation of state information for metals undergoing violent plastic deformation. In a typical experiment, millimetre thick metal samples are subjected to pressures on the order of $10-10^2$GPa, while the yield strength of the material can be as low as $10^{-1}$GPa. The analysis of such experiments has so far neglected the effect of shear strength, instead treating the highly plasticised metal as an inviscid compressible fluid. However making this approximation belies the basic elastic nature of a solid object. A more accurate method should strive to incorporate the small but measurable effects of shear strength. Here we present a one-dimensional mathematical model for elastoplasticity at high stress which allows for both compressibility and the shear strength of the material. In the limit of zero yield stress this model reproduces the hydrodynamic models currently used to analyse ICEs. We will also show using a systematic asymptotic analysis that entropy changes are universally negligible in the absence of shocks. Numerical solutions of the governing equations will then be presented for problems relevant to ICEs in order to investigate the effects of shear strength over a model based purely on hydrodynamics.   

Forward modeling of shock-ramped tantalum

Dynamic materials experiments on Sandia's 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 recent tantalum experiment which was shock compressed to 40 GPa followed by a ramp to 80 GPa. *Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Mechanical response of metals under dynamic loading off the principal Hugoniot and isentrope

Controlled dynamic loading of materials on phase-space paths off the principal Hugoniot and isentrope provide a stringent test of equation of state models in regions not typically experimentally constrained. Maturation of hardware design and pulse-shaping capabilities for shock-ramp experiments at Sandia's Z Machine have been exploited to test the mechanical response of a wide range of metals on ramp compression initiated from a well-defined Hugoniot state. A range of 1-8 km/s impact velocities are possible before initiating a ramp wave in a test sample. Capabilities and challenges of this type of experiment will be presented along with recent data on platinum, tin, cerium, and tantalum. Results of these experiments will be discussed in relation to existing equation of state data and models, and the future outlook for experimental constraints on material response on controlled off-principal loading paths. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.