1. A.V.Fedorov, A.L.Mikhailov, S.A.Finyushin, D.V.Nazarov, T.A.Govorunova, D.A.Kalashnikov, E.A.Mikhailov, V.N.Knyazev RFNC-VNIIEF, Sarov DETERMINATION OF LONGITUDINAL AND BULK SOUND VELOCITIES IN NATURAL URANIUM UNDER SHOCK-WAVE LOADING

2. The work contents the choice of the loading range and of flyer’s and sample’s geometry to realize method of overtaking release; registration of particle velocity of contact boundary U-LiF by laser interferometer Fabry-Perot with specific kinks, related with arrivals of elastic and plastic release waves; parameters defining (particle velocity and arrival times) for elastic and plastic waves in LiF; recalculation parametres in uranium, using known Hugoniots; defining longitudinal (c l ) and bulk (c b ) sound velocities using х-t diagrams; evaluations for Poisson’s coefficient  and yielding strength Y g by known relations; comparison with theoretical estimations and other experiments

3. Ideal and real shock-wave profiles Asay, et al., 1972 As already has been found by Asay, that real and ideal profiles of loading and release waves could significantly differ. In natural uranium kink, related with elastic wave arrival, has been registered in all of the experiments, but the kink, related with plastic release wave has been registered only in four experiments of the dozen with the limits of method’s resolution.

4. Coarse-grained (100-200 µm) natural uranium (ρ=18.91 g/cm3) was studied in the paper. A set of 12 experiments was performed, in which a uranium impactor was accelerated through a vacuum gap by the help of HE charge and it loaded the sample made of the same material. Loading amplitude of uranium samples in experiments amounted to 40…72 GPa. The velocity of the U–LiF interface was recorded in experiments. Mirror coating made of aluminum 1 µm thick was applied to LiF. There were 2-3 channels of velocity measuring in each experiment. The authors used Fabry-Perot interferometers having baseline distances (a distance between mirrors) from 50 to 150 mm with errors in measurement from  35 m/s to  12 m/s. The values of mass velocity and arrival times at the U–LiF interface of elastic and plastic release waves were recorded on profiles. The values recorded in LiF on the known shock adiabats were converted to states in uranium. Laser LiF Mirror ImpactorTarget W

5. Registering of contact bounary U-LiF velocity profile Interferogram and velocity profile. During the experiments we registered velocity of the boundary U/LiF. Mirror type cover of aluminum thickness 1  m was placed on the contact surface of LiF. We registered values of particle velocities and moments of elastic and plastic waves arrival to the boundary U-LiF. The registered in LiF values than were recalculated using known Hugoniots to find parametersa in Uranium. c l c b

6. where U LiF и U LiF2 – particle velocity when entering of elastic and plastic release waves occur on the boundary of U-LiF correspondingly U – particle velocity in Uranium W – flyer’s velocity D – shock wave velocity L – sample’s thickness l – flyer’s thickness t 1, t 2 – time between shock wave’s arrival to the boundary and the moment of arrival of elastic and plastic release waves correspondingly This equations define values of sound velocities without taking into account changing of state in uranium occurs in opposite (spreading from the boundary U-LiF) release wave. Values of longitudinal and bulk sound velocities in uranium behind the shock-wave front were recalculated by equations:

7. where  el. – amplitude of elastic release wave, Y g – yield strength,  – Poisson’s coefficient Poisson’s coefficient  and yielding strength Y g were found in equations: For all of the investigated pressure range amplitude of elastic release wave consisted Δσ el. = 5.2-6.8 ГПа, Poisson’s coefficient µ=0.37-0.40, yield strength Y g =1,16±0,2 ГПа.

8. № Exp. Flyer l, мм Sample L, мм t 1,  sec t 2,  sec U 1, km/sec P 1, GPa P 2, GPa D, km/sec С L, km/sec С b, km/sec µΔσ el., GPa Y g, GPa 1903 23,970,584-0,96371,88-3,9645,031---- 1904 23,920,484-0,96472,05-3,9664,881---- 1905 1,993,90,498-0,95671,2-3,9544,805---- 1911 1,983,850,454-0,96371,85-3,9645,015---- 1913 1,983,960,422-0,94370-3,9345,105---- 1954 441,441,720,856154,533,7944,7614,0410,3676,471,356 1962 3,95 1,407-0,87463,27-3,8304,789---- 1965 3,963,981,531,760,8964,8958,093,8544,4563,9220,3986,81,149 1987 23,950,580,7620,64742,5937,273,4864,4353,8580,3885,320,971 1997 461,349-0,65643,46-3,5014,476---- 1998 260,309-0,62240,62-3,4494,534---- 2200 23,90,5250,8010,654337,753,4924,6613,8430,3425,251,261 Experimental results The table presents experimental results, where D, P 1, U 1 – shock wave velocity, pressure and particle velocity in uranium in the moment of elastic release wave arrival; P 2 – pressure of plastic release wave; ∆σ el. – amplitude of elastic release wave; Y g – yield strength, µ – Poisson’s coefficient

9. Values of longitudinal (с l ) and bulk (c b ) sound velocities are presented on the picture taken from Eq. (1,2) where opposite (spreading from the boundary U- LiF) release wave moving from LiF, have not been taken into account, and also с l * considering the influence of release wave. In the range under investigation (40-72 GPa) real sound velocities (curve c l *) appeared to be higher over 380- 520 m/sec in general and consisted to be 4.9-5.5 km/sec. The picture presents dependencies of longitudinal and bulk sound velocities from pressure clcbclcb cl*cl*

10. Conclusion In shock wave experiments using laser interferometer Fabry-Perot measurements of longitudinal and bulk sound velocities in natural uranium were held in the range of pressures 40 ÷ 72 GPa. From the registered particle velocity profiles of contact boundary U-LiF the following parameters of elastic-plastic wave were found: longitudinal sound velocity c l =4.44…5.1 km/sec; bulk sound velocity c b = 3.84…4.04 km/sec; amplitude of elastic release wave ∆σ el =5.3…6.8 GPa; Poisson’s coefficient  =0.34…0.4; yield strengthY g =0.96…1.36 ГПа. Complex elastic-plastic behavior of natural uranium, caused by influence of internal structure, was registered.