Understanding dynamic fragmentation in shock-loaded metals and predicting properties of the resulting ejecta are of considerable importance for both basic and applied science. The nature of material ejection has been shown to change drastically when the free surface melts on compression or release. In this work, we present hydrodynamic simulations of laser-driven microjetting from micron-scale grooves on a tin surface. We study microjet formation across a range of shock strengths from drives that leave the target solid after release to drives that induce shock melting in the target. The shock-state particle velocity () varies from 0.3 to 3 km/s and the shock breakout pressure is 3–120 GPa. The microjet tip velocity is 1–8 km/s and the free-surface velocity varies from 0.1 to 5 km/s. Two tin equations of state are examined: a “soft” model (LEOS 501) where the target melts for km/s and a more detailed multiphase model (SESAME 2161) that melts for km/s. We use these two models to examine the influence of phase change and the choice of the material model on microjet formation and evolution. We observe in our computational results that jet formation can be classified into three regimes: a low-energy regime where material strength affects jet formation, a moderate-energy regime dominated by the changing phase of tin material, and a high-energy regime where results are insensitive to the material model and jet formation is described by an idealized steady-jet theory. Using an ensemble of 2D simulations, we show that these trends hold across a wide range of drive energies and groove angles.
REFERENCES
1.
J. R.
Asay
, L. P.
Mix
, and F. C.
Perry
, “Ejection of material from shocked surfaces
,” Appl. Phys. Lett.
29
(5
), 284
–287
(1976
). 2.
J. R.
Asay
, “Material ejection from shock-loaded free surfaces of aluminum and lead,” Technical Report SAND76-0542, October 1976.3.
L.
Berthoud
and J. C.
Mandeville
, “Material damage in space from microparticle impact
,” J. Mater. Sci.
32
(11
), 3043
–3048
(1997
). 4.
D. E.
Gault
and J. A.
Wedekind
, “The destruction of tektites by micrometeoroid impact
,” J. Geophys. Res.
74
(27
), 6780
–6794
, (1969
). 5.
M.
Hassani-Gangaraj
, D.
Veysset
, K. A.
Nelson
, and C. A.
Schuh
, “Melt-driven erosion in microparticle impact
,” Nat. Commun.
9
(1
), 5077
(2018
). 6.
D.
Loison
, T.
de Rességuier
, A.
Dragon
, P.
Mercier
, J.
Benier
, G.
Deloison
, E.
Lescoute
, and A.
Sollier
, “Skew photonic doppler velocimetry to investigate the expansion of a cloud of droplets created by micro-spalling of laser shock-melted metal foils
,” J. Appl. Phys.
112
(11
), 113520
(2012
). 7.
R. E.
Tokheim
, L.
Seaman
, T.
Cooper
, B.
Lew
, D. R.
Curran
, J.
Sanchez
, A.
Anderson
, and M.
Tobin
, “Calculating the shrapnel generation and subsequent damage to first wall and optics components for the national ignition facility
,” Fusion Technol.
30
(3P2A
), 745
–751
(1996
). 8.
W. T.
Buttler
, D.
Renner
, C.
Morris
, R.
Manzanares
, E. K.
Anderson
, J. J.
Goett
, J.
Heidemann
, R. M.
Kalas
, A.
Llobet
, J. I.
Martinez
, P. V.
Medina
, J. R.
Payton
, A.
Saunders
, D. W.
Schmidt
, A. M.
Tainter
, D.
Tupa
, S. W.
Vincent
, and W.
Vogan-McNeil
, “Cavitation bubble interacting with a Richtmyer-Meshkov unstable sheet and spike
,” AIP Conf. Proc.
1979
(1
), 080003
(2018
).9.
T.
Rességuier
, L.
Signor
, A.
Dragon
, and G.
Roy
, “Dynamic fragmentation of laser shock-melted tin: Experiment and modelling
,” Int. J. Fract.
163
(1–2
), 109
–119
(2009
). 10.
D. S.
Sorenson
, R. W.
Minich
, J. L.
Romero
, T. W.
Tunnell
, and R. M.
Malone
, “Ejecta particle size distributions for shock loaded Sn and Al metals
,” J. Appl. Phys.
92
(10
), 5830
–5836
(2002
). 11.
J.
Xin
, A.
He
, W.
Liu
, G.
Chu
, M.
Yu
, W.
Fan
, Y.
Wu
, T.
Xi
, M.
Shui
, Y.
Zhao
, P.
Wang
, Y.
Gu
, and W.
He
, “X-ray radiography of microjetting from grooved surfaces in tin sample subjected to laser driven shock
,” J. Micromech. Microeng.
29
(9
), 095011
(2019
). 12.
W. T.
Buttler
, D. M.
Oró
, D. L.
Preston
, K. O.
Mikaelian
, F. J.
Cherne
, R. S.
Hixson
, F. G.
Mariam
, C.
Morris
, J. B.
Stone
, G.
Terrones
, and D.
Tupa
, “Unstable Richtmyer–Meshkov growth of solid and liquid metals in vacuum
,” J. Fluid Mech.
703
, 60
–84
(2012
). 13.
T.
de Rességuier
, D.
Loison
, A.
Dragon
, and E.
Lescoute
, “Laser driven compression to investigate shock-induced melting of metals
,” Metals
4
(4
), 490
–502
(2014
). 14.
F. J.
Cherne
, J. E.
Hammerberg
, M. J.
Andrews
, V.
Karkhanis
, and P.
Ramaprabhu
, “On shock driven jetting of liquid from non-sinusoidal surfaces into a vacuum
,” J. Appl. Phys.
118
(18
), 185901
(2015
). 15.
M. B.
Zellner
, W.
Vogan McNeil
, J. E.
Hammerberg
, R. S.
Hixson
, A. W.
Obst
, R. T.
Olson
, J. R.
Payton
, P. A.
Rigg
, N.
Routley
, G. D.
Stevens
, W. D.
Turley
, L.
Veeser
, and W. T.
Buttler
, “Probing the underlying physics of ejecta production from shocked Sn samples
,” J. Appl. Phys.
103
(12
), 123502
(2008
). 16.
T.
de Rességuier
, E.
Lescoute
, A.
Sollier
, G.
Prudhomme
, and P.
Mercier
, “Microjetting from grooved surfaces in metallic samples subjected to laser driven shocks
,” J. Appl. Phys.
115
(4
), 043525
(2014
). 17.
B. A.
Remington
, P.
Allen
, E. M.
Bringa
, J.
Hawreliak
, D.
Ho
, K. T.
Lorenz
, H.
Lorenzana
, J. M.
McNaney
, M. A.
Meyers
, S. W.
Pollaine
, K.
Rosolankova
, B.
Sadik
, M. S.
Schneider
, D.
Swift
, J.
Wark
, and B.
Yaakobi
, “Material dynamics under extreme conditions of pressure and strain rate
,” Mater. Sci. Technol.
22
(4
), 474
–488
(2006
). 18.
H. S.
Park
, B. A.
Remington
, R. C.
Becker
, J. V.
Bernier
, R. M.
Cavallo
, K. T.
Lorenz
, S. M.
Pollaine
, S. T.
Prisbrey
, R. E.
Rudd
, and N. R.
Barton
, “Strong stabilization of the Rayleigh–Taylor instability by material strength at megabar pressures
,” Phys. Plasmas
17
(5
), 056314
(2010
). 19.
M. A.
Meyers
, B. A.
Remington
, B.
Maddox
, and E. M.
Bringa
, “Laser shocking of materials: Toward the national ignition facility
,” JOM
62
(1
), 24
–30
(2010
). 20.
A. M.
Saunders
, S. J.
Ali
, H. S.
Park
, J.
Eggert
, F.
Najjar
, C.
Huntington
, T.
Haxhilmali
, B.
Morgan
, Y.
Ping
, and H. G.
Rinderknecht
, “Development of high power laser platforms to study metal ejecta interactions,” Technical Report LLNL-PROC-783445, Lawrence Livermore National Laboratory (LLNL), Livermore, CA, 2019.21.
E. M.
Pugh
, R. J.
Eichelberger
, and N.
Rostoker
, “Theory of jet formation by charges with lined conical cavities
,” J. Appl. Phys.
23
(5
), 532
–536
(1952
). 22.
R. J.
Eichelberger
, “Re-examination of the nonsteady theory of jet formation by lined cavity charges
,” J. Appl. Phys.
26
(4
), 398
–402
(1955
). 23.
K. O.
Mikaelian
, “Effect of viscosity on Rayleigh-Taylor and Richtmyer-Meshkov instabilities
,” Phys. Rev. E
47
(1
), 375
–383
(1993
). 24.
G.
Birkhoff
, D. P.
MacDougall
, E. M.
Pugh
, and G.
Taylor
, “Explosives with lined cavities
,” J. Appl. Phys.
19
(6
), 563
–582
(1948
). 25.
M. L.
Wilkins
, “Calculation of elastic-plastic flow,” Technical Report No. UCRL-7322, California University Livermore Radiation Lab, 1963.26.
R. M.
Darlington
, T. L.
McAbee
, and G.
Rodrigue
, “A study of ALE simulations of Rayleigh–Taylor instability
,” Comput. Phys. Commun.
135
(1
), 58
–73
(2001
). 27.
T. V.
Kolev
and R. N.
Rieben
, “A tensor artificial viscosity using a finite element approach
,” J. Comput. Phys.
228
(22
), 8336
–8366
(2009
). 28.
R. W.
Sharp, Jr.
and R. T.
Barton
, “Hemp advection model,” Technical Report No. UCID 17809, California University, Livermore, Lawrence Livermore Laboratory, 1981.29.
P. A.
Sterne
, L. X.
Benedict
, S.
Hamel
, A. A.
Correa
, J. L.
Milovich
, M. M.
Marinak
, P. M.
Celliers
, and D. E.
Fratanduono
, “Equations of state for ablator materials in inertial confinement fusion simulations
,” J. Phys.: Conf. Ser.
717
, 012082
(2016
). 30.
D. J.
Steinberg
, S. G.
Cochran
, and M. W.
Guinan
, “A constitutive model for metals applicable at high-strain rate
,” J. Appl. Phys.
51
(3
), 1498
–1504
(1980
). 31.
D. J.
Steinberg
and C. M.
Lund
, “A constitutive model for strain rates from to s
,” J. Appl. Phys.
65
(4
), 1528
–1533
(1989
). 32.
J. N.
Johnson
, “Dynamic fracture and spallation in ductile solids
,” J. Appl. Phys.
52
(4
), 2812
–2825
(1981
). 33.
V. E.
Fortov
, V. V.
Kostin
, and S.
Eliezer
, “Spallation of metals under laser irradiation
,” J. Appl. Phys.
70
(8
), 4524
–4531
(1991
). 34.
L.
Videau
, P.
Combis
, S.
Laffite
, E.
Lescoute
, J. P.
Jadaud
, J. M.
Chevalier
, D.
Raffestin
, F.
Ducasse
, L.
Patissou
, A.
Geille
, and T.
de Resseguier
, “Laser-driven spall experiments in ductile materials in order to characterize Johnson fracture model constants
,” AIP Conf. Proc.
1426
), 1011
–1014
(2012
). 35.
C.
Greeff
, E.
Chisolm
, and D.
George
, “Sesame 2161: An explicit multiphase equation of state for tin,” Technical Report LA-UR-05-9414, Los Alamos National Laboratory, December 2005.36.
K. V.
Khishchenko
, “Equation of state and phase diagram of tin at high pressures
,” J. Phys.: Conf. Ser.
121
(2
), 022025
(2008
). 37.
G. A.
Cox
, “A multi-phase equation of state and strength model for tin
,” AIP Conf. Proc.
845
), 208
–211
(2006
). 38.
R.
Briggs
, M. G.
Gorman
, S.
Zhang
, D.
McGonegle
, A. L.
Coleman
, F.
Coppari
, M. A.
Morales-Silva
, R. F.
Smith
, J. K.
Wicks
, C. A.
Bolme
, A. E.
Gleason
, E.
Cunningham
, H. J.
Lee
, B.
Nagler
, M. I.
McMahon
, J. H.
Eggert
, and D. E.
Fratanduono
, “Coordination changes in liquid tin under shock compression determined using in situ femtosecond x-ray diffraction
,” Appl. Phys. Lett.
115
(26
), 264101
(2019
). 39.
C.
Roland
, T.
de Rességuier
, A.
Sollier
, E.
Lescoute
, L.
Soulard
, and D.
Loison
, “Hydrodynamic simulations of microjetting from shock-loaded grooves
,” AIP Conf. Proc.
1793
(1
), 100027
(2017
).40.
T.
Haxhilmali
, M.
Echeverria
, F.
Najjar
, P.
Tzeferacos
, S.
Ali
, H. S.
Park
, J.
Eggert
, C.
Huntington
, B.
Morgan
, Y.
Ping
, H.
Rinderknecht
, and A.
Saunders
, “Hydrodynamic and atomistic studies in support of high power laser experiments for metal ejecta recollection and interactions,” Technical Report LLNL-PROC-790058, Lawrence Livermore National Laboratory (LLNL), Livermore, CA, 2019.41.
J. L.
Shao
, P.
Wang
, and A. M.
He
, “Microjetting from a grooved Al surface under supported and unsupported shocks
,” J. Appl. Phys.
116
(7
), 073501
(2014
). 42.
M. B.
Zellner
, M.
Grover
, J. E.
Hammerberg
, R. S.
Hixson
, A. J.
Iverson
, G. S.
Macrum
, K. B.
Morley
, A. W.
Obst
, R. T.
Olson
, J. R.
Payton
, P. A.
Rigg
, N.
Routley
, G. D.
Stevens
, W. D.
Turley
, L.
Veeser
, and W. T.
Buttler
, “Effects of shock-breakout pressure on ejection of micron-scale material from shocked tin surfaces
,” J. Appl. Phys.
102
(1
), 013522
(2007
). 43.
M. B.
Zellner
, G.
Dimonte
, T. C.
Germann
, J. E.
Hammerberg
, P. A.
Rigg
, G. D.
Stevens
, W. D.
Turley
, M.
Elert
, M. D.
Furnish
, W. W.
Anderson
, W. G.
Proud
, and W. T.
Butler
, “Influence of shockwave profile on ejecta
,” AIP Conf. Proc.
1195
), 1047
–1050
(2009
). 44.
C. M.
Robinson
, “Modelling of laser spall experiments on aluminium
,” AIP Conf. Proc.
620
), 1359
–1362
(2002
). 45.
G. I.
Kanel
, S. V.
Razorenov
, V. E.
Fortov
, and V. E.
Fortov
, Shock-Wave Phenomena and the Properties of Condensed Matter
(Springer
, New York
, 2004
).46.
S. N.
Luo
, L. B.
Han
, Y.
Xie
, Q.
An
, L.
Zheng
, and K.
Xia
, “The relation between shock-state particle velocity and free surface velocity: A molecular dynamics study on single crystal Cu and silica glass
,” J. Appl. Phys.
103
(9
), 093530
(2008
). 47.
T.
de Rességuier
, G.
Prudhomme
, C.
Roland
, E.
Brambrink
, D.
Loison
, B.
Jodar
, E.
Lescoute
, and A.
Sollier
, “Picosecond x-ray radiography of microjets expanding from laser shock-loaded grooves
,” J. Appl. Phys.
124
(6
), 065106
(2018
). 48.
A. B.
Georgievskaya
and V. A.
Raevsky
, “A model of a source of shock wave metal ejection based on Richtmyer–Meshkov instability theory
,” J. Dyn. Behav. Mater.
3
(2
), 321
–333
(2017
). © 2020 Author(s).
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