Motivation

1. 6 ps Shock-induced instabilities are hard to study by hydrodynamic codes. . . l~36 nm h0(t=0)~36 nm 2 10.2 ps 24.7 ps Cu vacuum 29.2 ps 36.3 ps 1 5 Upist=0.7 Upist=1.0 15.7 ps 25.9 ps piston 3 up h us jetting Up=1.0 Up=0.7 42.6 ps 49.2 ps l Upist=0.6 Upist=0.7 Upist=0.5 23.4 ps 30.9 ps Pictures from W.Rider and J.Kamm, LANL For shocks in solids, an accurate description of the non-equilibrium, anisotropic, and high strain effects is extremely important. Shock through light–to–heavy solid (argon) interface Motivation [110] direction, piston velocity Up= 0.70 [100] direction, piston velocity Up= 0.75 [100] direction,piston velocityUp= 0.75 RM / RT instabilities • are important for NIF experiments on decreasing target compression • provide a unique way to measure the strength of solids under high-strain rate and high stress conditions • evolve into “jets” in heterogeneous materials under shock loading (e.g. composite explosives) • but they are not well understood SW front oscillations <110> shock through the interface of light-to-heavy solids: r1/r2 = 1:4 Box: 28x200x905 ao3, ~20 million atoms Up= 0.70 (MD-units) ~ 0.77 km/s l/h ~ 3 : l=106 nm, h(t=0) =32 nm Shock along <100> through the concave interface of light-to-heavy solids: r1/r2 = 1:4 Box: 20x160x640 ao3 (ao=5.29 Ang for Argon) LJ potential, rcut=2.5s, ~8 million atoms Up= 0.75 (MD-units) ~ 0.81 km/s l/h ~ 3 : l=85 nm, h(t=0) =25 nm Up=0.7 1 2 Oscillations of the shock front after passing the interface … 3 … and lateral flow • No significant growth is observed in [100] direction for Upist< 1.0 • Shock front begins to oscillate after passing the concave interface due to the interference of lateral waves • Emergence of oscillating [100] shock front from the free surface results in “jetting” of the material • Reflected shock from the piston does not increase a growth 4 … result in micro- “jetting” from a free surface No significant “jetting” occur from a free surface for the [110] shock after passing through the interface RT in Al foils, Remington et al., Met. Mat Trans. 35A, 2598 (2004). 5 Shock through heavy–to–light solid (argon) interface Methodology [110]: direction, piston velocity Up= 0.5, 0.6, and 0.7 Vorticity evolution: [110] direction, Up=0.7 Why Molecular Dynamics (MD) simulations ? Rarefaction waves propagate back from the interface and from the free surface,with multiple intersections and reverberations Temperature jump persists quite long in vicinity of the interface Upist=0.5 1 2 Upist=0.6 • RMI of light-to-heavy solid interface: • Growth of perturbation appears above the threshold of Up ~ 0.7 • Reshock of the interface by reflected shock from the piston • Rarefaction wave from open surface of second solid moves back to the interface accelerating the perturbation growth RMI of heavy-to-light solid interface: • Growth of perturbation appears above the threshold of Up ~ 0.6 • Phase inversion of the initial perturbation shape • Asymptotic limit in the perturbation growth Vorticity remains visible during growth of the perturbation 3 Upist=0.7 4 5 Local melting in vicinity of the interface can occur (Tmelt ~ 9 for a light solid) 2 1 2 us2 Up=1.0 Up=0.7 us1 up reflected shock perturbation at interface Simulation of RM instability of copper–vacuum interface shock Shock through light (2 ) to heavy (1 ) interface [110] copper  vacuum interface, Up = 2.0 km/s [110] shock in copper  vacuum, Up = 2.8 km/s [110] shock in copper vacuum, Up = 2.8 km/s • 3D MD shock simulations in solid argon and copper • Concave/convex perturbation at interface with sinusoidal-like shape • Interfaces: solid-to-solid (argon): 2 = 4 1, copper-to-vacuum: 2 = 0 • Perturbation wavelength l ~ 100nm, initial amplitude h~ 0.25 – 0.33 l • ~20 million atoms in solid argon • ~ 6 million atoms in copper (during 20 – 60 ps) • Box: 14x205x603 ao3, Up=2.8 km/s, Us ~ 8.2 km/s, PH ~204 GPa,l/h = 4 :l/4 =h0 ~18.2 nm • Appearance of molten nuclei in the shocked crystal and void nucleation in a spall Box: 14x205x603 ao3, Up=2.8 km/s, Us ~ 8.2 km/s, PH ~204 GPa,l/h = 4 :l/3 =h0 ~18.2 nm • Box: 14x205x603 ao3, Up=2.0 km/s, Us ~7.8 km/s, PH ~125 GPa,l/h =4 :l/4 =h0 ~18.2 nm • Considerable amorphization seen during phase inversion and the spike growth • Significant disorder but no “dislocations”: tension wave leads to significant dislocation structure • Appearance of the voids and incipient spallation RMI simulations in copper Cu [100]  vacuum interface molten nuclei • Box: 10x100x300 ao3 ~ 3.6 x 36.3 x 109 nm • Up= 1 km/s, Us ~ 5.5 km/s, PH ~ 50 GPa • l/h =1:l =h(t=0) ~ 36 nm • Qualitatively: • initial reversal of perturbation: ripple changes phase before growing • amorphization seen both around maximum of perturbation and in the growing spikes • tension wave does not erase dislocation activity, but the microstructure changes us2 1 ur2 11 ps up=0.7 us1 21 ps ur2 • Flat free surface: Vz2 Up. Concave surface  “jetting”. Vz > 3 Up • szz: reflected tension wave interacts with advancing shock wave. Shear stress also displays this interaction. • Shear stress behind the melting front drops to zero. shock us1 rarefaction incipient spall Spike growth at hollow similar to fluid RMI ?? melting front RM instability of heavy-to-light liquid interface Zhakhovskii, IFSA 2001 us1 phase inversion Dislocation flow at shocked copper-vacuum interface local melting ? Shock through heavy (2 ) to light (1 ) interface Conclusions • EAM Cu potential (Mishin et al): lattice constant ao=0.3615 nm • Pressure in the strongest shock (Up=2.8 km/s): Pshock ~ 0.9 – 1.0 Pmelt • Phase inversion of initial perturbation (spike grows from a valley) • Possible local melting or amorphization in the spike and underneath • Appearance of local voids and incipient spall underneath initial perturbation hills • Significant acceleration of the material in the growing spike similar to the ‘jetting’ regime • Large-scale MD can model effectively the growth of RM instability. • Simulations in Cu <100>/vacuum show wave inversion but no growth • Simulations in Cu <110>/vacuum show wave inversion and possible growth but longer simulations are needed. • Simulations in light-to-heavy LJ solids show growth for both <100> and <110> shocks (for a different Up threshold) • Multiple wave intersections results in shock front oscillations • The temperature increases considerably in the vicinity of the interface 39 ps 55 ps Work in progress Box: 10x200x600 ao3 ~3.6 x 72.6 x 218 nm Up=2.5 km/s, Us ~7.8 km/s, PH ~ 175 GPa l/h=4:l/4 =h~ 18.2 nm • Is grain boundary melting important for the growth of RMI? • …for instance, shocks in nanocrystalline Cu samples. • Light to heavy solids: simulations in He/Cu interfaces Atomistic modeling of the Richtmyer-Meshkov instability in shock loaded solids Sergey Zybin 1), Vasily Zhakhovskii2), Eduardo Bringa 3), Snezhana Abarzhi 4), and Bruce Remington 3) 1) Materials and Process Simulation Center, California Institute of Technology 2) Institute for Laser Engineering, Osaka University 3) Lawrence Livermore National Laboratory , 4) FLASH Center, The University of Chicago