Session K2: CM.1 Equation of State: Experimental Methods

Optical methods for determining the shock Hugoniot of Solids

Traditionally, the shock Hugoniot is measured on a point-bypoint basis by a series of high-velocity impact experiments. Observations are typically confined to pointwise pressure or velocity measurements at the free-surfaces of the sample. In this work, shock waves are initiated in transparent polyurethane and opaque polyurea samples using exploding bridgewires, aluminum ballistic projectiles, and gram-scale explosive charges. Shock waves and material motion are observed optically by shadowgraphy using a high-speed-digital camera recording at up to $10^6$ frames/s. Ballistic impact, producing a constant-strength shock wave, is combined with these optical techniques to obtain a single shock Hugoniot point per test. A gram-scale explosive charge produces a shock wave in the material sample that is initially strong, but attenuates as it transits the polymer sample. With optical access to the entire sample, multiple shock and particle velocity combinations may be observed in a single test, allowing the measurement of a shock Hugoniot curve in fewer experiments than by traditional methods. These techniques produce data in general agreement with an extrapolation of published Hugoniot data for polyurethane and polyurea.   

Analysis of temperature measurement at lead/LiF interface under shock compression.

Determining temperature in shock physics experiments is of paramount importance to constrain equations of state and related models. In such experiments, a multi-wavelength pyrometer is usually used to detect radiance emitted by a metallic surface glued on a transparent window. If temporal evolution of the radiance is connected to the instantaneous temperature of the metallic surface by Planck's law, some corrections must be taken into account to remove undesirable noise (emission/absorption from glue/windows, interface effects, hot spots, fractoluminescence, \textellipsis ). Here, we proposed to analyze different radiance signals emitted by a lead surface glued on a lithium fluoride (LiF) window in experiments where P$_{\mathrm{shock}}$ is around tens GPa and to estimate corrective terms to be applied on these data to improve the precision of the determination of the ``true'' temperature of the metallic surface.   

An examination of material strength, phase boundaries and hysteresis through continuous measurements of release isentropes

The majority of high-pressure dynamic compression experiments have focused upon measuring the equation of state (EOS) under conditions in which the pressure is always increasing. While techniques have been developed to measure discrete states upon release isentropes (states beginning at high-pressure and evolving to low pressure), little progress has been made in the continuous measurement of release isentropes. In this work, we present a new technique to measure release isentropes of transparent and opaque materials. These measurements are well suited to examine material strength, phase boundaries and hysteresis upon release. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.   

Velocity correction and refractive index changes for [100] lithium fluoride optical windows under isentropic compression

By means of the new techniques of magnetically driven quasi-isentropic compression based on multi-module pulse power generator PTS developed by us, the dynamic compression of [100] lithium fluoride is researched under ramp wave loading. A pressure of 40--60 GPa over 200--300 ns is realized on LiF samples by load configuration optimizing and current pulse shaping of PTS. Loading strain rates vary from 10$^{5}$ s$^{-1}$ to 10$^{6}$ s$^{-1}$ along the thickness of LiF samples. For experiments, the particle velocities of interface between LiF samples and LiF windows, interface between electrode and LiF window, free-surface of electrode are measured to determine material response by a displacement interferometry technique of Doppler pins system (DPS, Laser wavelength 1550nm). The experimental compression isentropes of researched LiF are obtained using the data processing method of backward integration and Lagrangian analysis for quasi-isentropic compression experiments, which are in agreement with the experimental isentropes measured by T. Ao. Additionally, taken order with apparent velocity(Ua) with windows [100] LiF and half of free-surface of electrode panel velocity(Ut) by a new producer, we obtained velocity correction 1$+\Delta $v/v$_{0}$ and refractive index changes n-$\rho $ under magnetically driven quasi-isentropic compression to 50 GPa.   

A new method to study he effective shear modulus of shocked material

Shear modulus is a crucial material parameter for description of mechanical behavior. However, at strong shock compression, it is generally deduced from the longitudinal and bulk sound velocity evaluated by unloading wave profile measurement. Here, a new method called the disturbed amplitude damping method of shock wave is presented, that can directly measure the shear modulus of material. This method relies on the correlation between the shear modulus of shock compressed state and amplitude damping and oscillation of an initial sinusoidal disturbance on shock front in concerned substance. Two important steps are required to determine the shear modulus of material. The first is to measure the damping and oscillation feature of disturbance by the flyer impacted method. The second is to find the quantitative relationship between the disturbed amplitude damping and shear modulus by the finite difference method which is applied to obtain the numerical solutions for disturbance amplitude damping behavior of sinusoidal shock front in flyer impacted flow field. When aluminum shocked to 80GPa is taken as an example, the shape of perturbed shock front and its disturbed amplitude development with propagation distance, are approximately mapped out. The figure shows an oscillatory damping characteristic. At the early stage the perturbation amplitude on the shock front experiences a decaying process until to zero point, then it rises to a maximum but in reverse phase, and then it decays again. Comparing these data with those simulated using the SCG constitutive model, the effective shear modulus for aluminum shocked to 80GPa is determined to be about 90GPa, which is higher than the result given by Yu.   

Versatile target assembly of explosive loading experiments for measuring sound velocity under high pressure: copper and bismuth as examples

High-pressure sound velocities along the Hugoniot are expected to be helpful in understanding shock-induced phase transition. In this paper, two kinds of versatile target assemblies of explosive loading experiments for measuring sound velocity under high pressure are presented. In the first target assembly, the direct-reverse impact technique and overtake technique are combined to obtain sound velocity data at two different shock pressures in one experiment. In the other one, the overtake technique was modified through measuring the shock wave velocity of sample, flyer velocity, and particle velocity at sample/LiF interface simultaneously, by which both sound velocity and shock Hugoniot data can be obtained independently. More important, the precision of sound velocity data is improved because we do not use shock Hugoniot parameters of sample in data processing. Shock wave experiments were performed to obtain sound velocity of copper and bismuth along Hugoniot. The obtained experimental results are compared to the previously published data, further results and implications are also discussed.