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Simulation of Ce Response to Dynamic Loading

Simulation of Ce Response to Dynamic Loading. A.V.Petrovtsev, V.A.Bychenkov, V.V.Dremov, V.M.Elkin, G.V.Kovalenko, D.M.Shalkovsky, N.Sokolova, D.A.Varfolomeev RFNC-VNIITF, Snezhinsk, Russia.

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Simulation of Ce Response to Dynamic Loading

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  1. Simulation of Ce Response to Dynamic Loading A.V.Petrovtsev, V.A.Bychenkov, V.V.Dremov, V.M.Elkin, G.V.Kovalenko, D.M.Shalkovsky, N.Sokolova, D.A.Varfolomeev RFNC-VNIITF, Snezhinsk, Russia Joint US-Russia Conference on Advances in Material Science Prague, Czech Republic, August 30 - September 4, 2009

  2. LANL – VNIITF projects to study of dynamic properties of structuralmaterials • 1999-2003Dynamic Response of Pure Iron and 30CGSA Steel:Methodical investigation into wave profiles, elastic-plastic behavior, phase transitions and fracture kinetics, and shock- induced changes in their microstructures and properties helped develop realistic phenomenological models now widely used in our theoretical and numerical studies 2003-2008:Phase Transition Kinetics and High-rate Stress-strain Response of Pure Cerium

  3. 1457m/s Wfs, m/s 1079m/s 779m/s 437m/s Black lines – FP measurements 1Color lines - simulation Impactor (Iron) Sample (Iron) t, s 0.75 t, s В FR1 FR1 А  FR2 FR2 x, сm x, сm Simulation of Experiments with Iron Comparison of calculated profiles with the results of Fabry - Perot measurements in spall experiments1 3 A.Petrovtsev, E.Kozlov, V.Dremov et al.,AIP Conf. Proc.955 (2008), 511-514 1 Ch.Voltz, G.Roy,AIP Conf. Proc. 706 (2004), 511-514 Symmetrical plate-impact experiment 2: hi=hs=6.3mm, Wi=848m/s 2 Tang, Z., Zhang, X. et al., AIP Conf. Proc. 845 (2006), 662-665

  4. New Project on Pure Cerium ●Explosive experiments to collect new data on wave profiles in cerium ●Strength at high strain rates and the effect of the - phase transformation ●Shock-induced structural and behavioral changes ●Construction of EOS and models for the description of cerium high strain-rate behaviour The first stage of preparation to the experiments was to select their optimal setup with the help of numerical simulation (2006-2007)

  5. P (-)-phase transition Stable -phase Metastable -phase -phase-based alloy -phase-based alloy Pure -phase Pure phase Phase equilibrium с T Multiphase (, , , L)Equation of State of Ce1,2 ● and: the Aptekar-Ponyatovsky modelof pseudo-binary alloys T G=(1-c)G0+cG0 +c(1-c)Gmix+TR[clnc+(1-c)ln(1-c) , G0-G0+Gmix(1-2c)+RTln[c/(1-c))]=0, -2Gmix+RT[1/c-1/(1-c)]>0,c – fractionof 0 phase 1 V.M.Elkin, E.A.Kozlov, E.V.Kakshina, and Yu.S.Moreva.AIP Conf. Proc. 845 (2006), 77-802 V.M.Elkin, V.N. Mikhaylov, T.Yu. Mikhaylova, F.J.Cherne, Proc. of VIII US-Russia workshop “Fund. Pu. Prop.”, 2008 (to be published in Phys. Rev. B)

  6. F(V,T)=FC(V)+FH(V,T)+FAE(V,T)-StrT EOS Vinet et al. Debye approx. T2 law Multiphase (, , , L)Equation of State of Ce1,2 ● Pure 0, 0,  and L phases: traditional description 1 V.M.Elkin, E.A.Kozlov, E.V.Kakshina, and Yu.S.Moreva.AIP Conf. Proc. 845 (2006), 77-802 V.M.Elkin, V.N. Mikhaylov, T.Yu. Mikhaylova, F.J.Cherne, Proc. of VIII US-Russia workshop “Fund. Pu. Prop.”, 2008 (to be published in Phys. Rev. B)

  7. Phase states of dynamically compressed Ce1 0.73-1.1GPa: region - transformation on the compression isentrope; above this region the main shock front arises in the wave structure 7.4GPa: dissolution of the three-wave configuration (no phase precursor) 10.7-22.3GPa: region melting on the Hugoniot; liquid states lie above this region No melting at release <17.2GPa – solidification at release>5.4GPa – isentropes run above (in T) the critical point of - equilibrium 1 V.M.Elkin, V.N. Mikhaylov, T.Yu. Mikhaylova, F.J.Cherne, Proc. of VIII US-Russia workshop “Fund. Pu. Prop.”, 2008 (to be published in Phys. Rev. B)

  8. EOS Implementation in Hydrocodes ●EOS for all phases were tabulated ●The difficulty of simulating the - transformation comes from the smallness of the metastability regions for these phases in AP models  EOS for andphases and their mixture is reproduced by unique tabulated relations derived in equilibrium approximation ●The hydrodynamic code VOLNA1 in 1D calculations and the 2D code SPRUT2 in 2D calculations were used ● As a fist approximation, very simple models of elastic-plastic properties were used:- the Prandl-Reiss equation associated with the flow law by Mises - in 1D simulation: Steinberg-like dependencies for the shear modulus and yield stress was assumed independent of strain rate and strain level • in 2D simulation: a constant Poisson’s ratio and pressure dependent yield stress 1 V.F. Kuropatenko, G.V. Kovalenko et al. Issues of Atomic Science and Technologies, series “Mathematical Simulation of Physical Processes”, #2, pp.9-25, 19892 V.A. Bychenkov, V.V. Gadjiyeva. Issues of Atomic Science and Technologies, series “Techniques and Codes for Numerical Solution of Problems in Mathematical Physics”, 1978, Vol.2(2) .

  9. , GPa ● - Voronov et al.1    P, GPa Elastic-plastic model Figures show experimental data and data from calculations with our EP model for shear modulus at T=300K isotherm (left) and sound velocities on Hugoniot (right) CL, CB, km/s L -L  ● (CB), ♦(CL) - Zhernokletov et al.2○ (CB), ◊(CL) - Kovalyov et al.3 - VNIITF EOS - LANL EOS CL CB P, GPa 1 F.F. Voronov, V.A. Goncharova, O.V. Stal’gorova, J. Exp. and Tech. Phys., 1979, Vol.76, #4, pp.1351-1357.2M.V. Zhernokletov, A.E. Kovalyov, V.V. Komissarov, M.G. Novikov, M.A. Zocher , AIP Conf. Proc. 955 (2008), 117-1203A.E. Kovalyov, V.A. Borisyonok,M.V. Zhernokletov et al. Proc. of VIII US-Russia workshop “Fund. Pu. Prop.”, RFNC-VNIITFSnezhinsk, Russia, 2008, pp.105-106

  10. U, mm/s U, mm/s  - VISAR data2 - VNIITF EOS  - LANL EOS1 (D. Hayes)  - VISAR data2 - VNIITF EOS •  - LANL EOS1 (D. Hayes) t, s t, s Impactor Window (LiF) Sample (Се) Shock-wave experiments1,2 that were done at LANL in 2004-2006 to investigate wave profiles in Ce, were numerically simulated Adjusting models in LANL experiments simulation Exp.56-04-15: Impactor – 304 steel plate, hi=7.0mm, Wi=275m/s; hs=2.1mm, H1.8GPa Exp.56-04-23:Impactor – tungsten plate, hi=4.0mm, Wi=828m/s;hs=2.4mm, H7.1GPa EOS and models used adequately describe cerium response to shock 1 Hixson, R.S., Preston, D.L., Gray, G.T. III et al., LANL Report, 2002 2 F.J. Cherne, P.A. Rigg, W.W. Anderson, R.S. Hixson, Presentation LA-UR-06-4898.

  11. Sample Lid of capsule Initializationzone HE layer ●The goal of studies is to obtain information on kinetics of phase transformations in cerium and cerium strength within a wide strain range. That is why different types of sample loading were considered:- Sliding detonation of HE layers:plastic HE hHE=0.5,1,2 and 3mm and HMX-containing HE hHE=10..20mm;- Normal detonation of HE layers:plastic HE hHE=3,4 and 5mm and HMX-containing HE hHE=5 and 10mm;- Plate impact: SS impactorhi=3.5mm,Wi=800 and 1100m/s; SS lid hc=3,5 and 10mm●Recovery experiments inclusion of the capsule in the system and further analysis of its state. Capsule material and thickness were varied SS lid hc=2,5 and 10mm, Al lid hc=5mm●Problem with normal detonation and plate impact were solved in 1D approximation Simulation of VNIITF experiments1 1 Experiments set-up and results see V.I.Tarzhanov’s presentation on this conference

  12. yy, GPa Y, cm System with stainless steel lid hc=2mm and hHE=2mm Sliding detonation of a thin PHE layer Cross-sections of stress field at t=5s.X0=1.21cm, X=0.3cm t=3.5s ● The detonation wave creates a system of compression and rarefaction waves in the lid and the sample which move with the detonation front. The sliding loading of the lid leads to an “oblique” principal wave which hits the lid-sample interface and travels through the sample. Compression and tension regions in the lid are shifted in space At small HE layer thicknesses a “steady” mode of the flow is quicklyreached. The right figure shows cross-sections of the stress field at t=5s in X=const planes at distance X=0.3cm beginning from X0=1.21cm. One can see that the shock wave in the sample has a three front structure The compression wave generated in the lid overtakes the main plastic wave in the sample and greatly change its attenuation character

  13. yy, GPa hc=2mm, hHE=2mm; t=5s Y, cm hc=5mm, hHE=2mm; t=5s Sliding detonation of a thin PHE layer t=3.5s hc=5mm, hHE=0.5mm; t=5s Cross-sections of stress field at t=5s. X0=1.21cm, X=0.3cm ● At large capsule lid thicknesses, the values of tensile stresses in the lid may be sufficient for its fracture ● At very small HE layer thicknesses, only a smeared phase precursor and an elastic precursor exist in the compression part of the wave. In addition, the shock rarefaction wave exists in the release part

  14. yy, GPa Y, cm System with steel lid hc=5mm and hHE=10mm Sliding detonation of a thick HE layer Cross-sections of stress field at t=5s.X0=1.12cm, X=0.3cm t=4.5s ● The plastic wave in the sample has one- or two-front structure. Its amplitudes attenuate not so greatly as in the case of the thin HE layer and fall into the range from the beginning of  phase melting to the end of the three front dissolution ● The “steady” mode is notreached in this case

  15. Generator of planar wave HE Lid (steel) Sample (Се) PHE layer , hHE=5mm, stainless lid hc=10mm xx,GPa T, K Stress histories in Ce particles x=0.1cm melting line Hugoniot P-T histories in Ce particles x=0.1cm - P, GPa t, 10-5s Normal detonation of thin layer of PHE  Qualitatively the same pattern of Ce deformation is seen in the case of normal detonation  Figures show calculation data for one system with PHE layer thickness hHE=5mm and stainless capsule lid thickness hc=10mm as an example. The two-wave mode of loading implements in the first part (x<6mm) of the sample. The phase precursor shows up in the wave structure later. Deformation of Ce takes place in the solid phase region. At hc=10mm the reflected compression wave does not affect the plastic wave in the sample

  16. max, GPa  - HMX-based HE, - PHE ND, 10mm - HMX-based HE,  - plastic HE ND, 5mm Melting on shock front PI, 0.8, 1.1 mm/s ND, 3, 5 mm SD, 10mm SD, 0.5, 1, 2 mm Three-wave configuration x, mm Summary data on wave amplitudes in Ce hC=5mm • Sliding detonation (SD) hPHE=0.5mm: wave amplitudes max<1GPa, deformation of Ce will mainly run in the  phase, unusual two-wave compression along with rarefaction shock wave in releaseSD hPHE=1 and 2mm: max<4GPa, a three front configuration will be observed Normal detonation (ND) hPHE=3, 5mm: max4…12GPa, deformation of Ce will mainly run in the solid phase, parameters of the elastic precursor and the plastic wave (and the phase precursor only at the end part of the sample) can be recorded ND hHE=5 and 10mm: amplitudes max8…24GPa mainly fall into the region of melting on the shock front with subsequent solidification in release SD hHE=10 or 20mm and PI at Wi=0.8 or 1.1 km/s: range max8…12GPa very close to experiments with ND thin PHE layers • The compression wave formed in the lid may affects the main plastic wave in the sample at small lid thicknesses The regions of tensile stresses are created in the lid. This can result in its fracture at large hC

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