A.V.Fedorov, A.L.Mikhailov, S.A.Finyushin , D.V.Nazarov , T.A.Govorunova , D.A.Kalashnikov , E.A . Mikhailov , V.N.Kn

1. DETERMINATION OF LONGITUDINAL AND BULK SOUND VELOCITIES IN NATURAL URANIUM UNDER SHOCK-WAVE LOADING 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

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 witharrivals of elastic and plastic release waves; • parameters defining (particle velocity andarrival times) for elastic and plastic waves in LiF; • recalculation parametres in uranium, using known Hugoniots; • defininglongitudinal (cl) andbulk (cb) sound velocitiesusing х-tdiagrams; • evaluations for Poisson’s coefficient andyielding strengthYg by known relations; • comparison with theoretical estimations and other experiments

3. Idealandreal shock-waveprofiles 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 wavearrival, 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. Impactor Target Mirror LiF Laser W 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.

5. cl cb cl cb Registering of contact bounary U-LiF velocity profile Interferogramand 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.

6. Values of longitudinal and bulk sound velocities in uranium behind the shock-wave front were recalculated by equations: whereULiF и ULiF2– 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 t1, t2 – 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 changingof state in uranium occurs in opposite (spreading from the boundary U-LiF) releasewave.

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

8. Experimental results The table presents experimental results, where D, P1, U1 – shock wave velocity, pressureandparticle velocity in uranium in the moment of elastic release wave arrival; P2 – pressure of plastic release wave; ∆σel. – amplitude of elastic release wave; Yg – yield strength, µ – Poisson’s coefficient

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

10. Conclusion In shock wave experimentsusing 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 cl=4.44…5.1 km/sec; • bulk sound velocity cb= 3.84…4.04 km/sec; • amplitude of elastic release wave ∆σel=5.3…6.8 GPa; • Poisson’s coefficient=0.34…0.4; • yield strength Yg =0.96…1.36 ГПа. Complex elastic-plastic behavior of natural uranium, caused by influence of internal structure, was registered.