Theoretical Ejecta Model for Elastic-Plastic Solids Based on Richtmyer-Meshkov Instability

doi:10.19596/j.cnki.1001-246x.7721

Abstract

Abstract: Hydrodynamic simulations are performed to study Richtmyer-Meshkov instability (RMI) and material ejection at a metal-vacuum interface using a 2D multi-component elastic-plastic hydrodynamic Eulerian code. Effect of material strength on instability development of roughened surface is analyzed, and relationship between amount of ejected material and saturated bubble amplitude is revealed. Finally, based on RMI theory for elastic-plastic solids, theoretical models to describe critical condition of ejecta formation, total amount and maximum velocity of ejecta from unmelted metals are established.

Key words: ejecta, elastic-plastic solid, Richtmyer-Meshkov instability

CLC Number:

HE Anmin, LIU Jun, SHAO Jianli, LIU Chao, WANG Pei. Theoretical Ejecta Model for Elastic-Plastic Solids Based on Richtmyer-Meshkov Instability[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(5): 505-514.

References

[1] WALSH J M, SHREFFLER R G, WILLING F J. Limiting conditions for jet formation in high velocity collisions[J]. J Appl Phys, 1953, 24:349-359.
[2] ASAY J R, BERTHOLF L D. Material ejection from shock-loaded free surfaces of aluminum and lead[R].Sandia Report, 1976, SAND76-0542.
[3] SORENSON D S, MINICH R W, ROMERO J L, et al. Ejecta particle size distributions for shock loaded Sn and Al metals[J]. J Appl Phys, 2002, 92(10):5830-5836.
[4] VOGAN W S, ANDERSON W W, GROVER M, et al. Piezoelectric characterization of ejecta from shocked tin surfaces[J]. J Appl Phys, 2005, 98(11):113508.
[5] ZELLNER M B, GROVER M, HAMMERBERG J E, et al. Effects of shock-breakout pressure on ejection of micron-scale material from shocked tin surfaces[J]. J Appl Phys, 2007, 102(1):013522.
[6] ZELLNER M B, MCNEIL W V, HAMMERBERG J E, et al. Probing the underlying physics of ejecta production from shocked Sn samples[J]. J Appl Phys, 2008, 103(12):123502.
[7] BUTTLER W T, ZELLNER M B, OLSON R T, et al. Dynamic comparisons of piezoelectric ejecta diagnostics[J]. J Appl Phys, 2007, 101:063547.
[8] CHEN Y T, HU H B, TANG T G, et al. Experimental study of ejecta from shock melted lead[J]. J Appl Phys, 2012, 111(5):053509.
[9] MONFARED S K, ORO D M, GROVER M, et al. Experimental observations on the links between surface perturbation parameters and shock-induced mass ejection[J]. J Appl Phys, 2014, 116(6):063504.
[10] HAN C S, JING F Q, DING J, et al. Study on the phenomena of the mass ejection from the free surface of aluminum at different dynamic loading rates[J]. Chinese J High Press Phys, 1989, 3(2):97-106.
[11] WANG P, HONG T. Parallel computation of three-dimensional smoothed particle hydrodynamics[J]. Chinese J Comput Phys, 2006, 23(4):431-435.
[12] CHEN J, JING F Q, ZHANG J L, et al. Dynamics simulation of ejection of metal under a shock wave[J]. J Phys:Condens Matter, 2002, 14:10833-10837.
[13] LIU C, FENG Q J, QIN Q S, et al. Maximal penetration depth of micro-jet from void under shock loading[J]. Chinese J Comput Phys, 2014, 31(1):44-50.
[14] WANG P, SHAO J L, QIN C S. Effect of loading-wave-front width on micro-jet from aluminum surface[J]. Acta Phys Sin, 2009, 58(2):1064-1070.
[15] ZHAO X W, LI X Z, WANG X J, et al. Effects of surface groove micro-structure on ejection from shocked metal surface[J]. Acta Physica Sinica, 2015, 64(12):124701.
[16] SHAO J L, WANG P, HE A M, et al. Microscopic simulation on shock-induced micro-jet ejection from metal Al surface[J]. Acta Phys Sin, 2012, 61(18):184701.
[17] SHAO J L, WANG P, HE A M. Microjetting from a grooved Al surface under supported and unsupported shocks[J]. J Appl Phys, 2014, 116:073501.
[18] HE A M, WANG P, SHAO J L. Molecular dynamics simulations of ejecta size distributions for shock-loaded Cu with a wedged surface groove[J]. Comput Mater Sci, 2015, 98:271.
[19] HE A M, WANG P, SHAO J L. Molecular dynamics simulations of jet breakup and ejecta production from a grooved Cu surface under shock loading[J]. Chinese Phys B, 2014, 23:000001.
[20] CHERNE F J, HAMMERBERG J E, ANDREWS M J, et al. On shock driven jetting of liquid from non-sinusoidal surfaces into a vacuum[J]. J Appl Phys, 2015, 118:185901.
[21] HE A M, WANG P, SHAO J L. Statistically heterogeneous size distribution of ejecta from shock-loaded Cu with a wedged surface groove[J]. Modelling Simul Mater Sci Eng, 2016, 24:025002.
[22] HAN C S. A semi-empirical equation for estimating the micro-jet ejection from shocked free-surface[J]. Chinese J High Press Phys, 1989, 3:234-240.
[23] MEYER K A, BLEWETT P J. Numerical investigation of the stability of a shock accelerated interface between two fluids[J]. Phys Fluids, 1972, 15:753.
[24] FRACHET V, ELIAS P, MARTINEAU J. Matter ejection from shocked material:A physical model to understand the effects of free surface defects[C]. AIP Conf Proc, 1988, s235.
[25] GEORGIEVSKAYA A, RAEVSKY V A. Estimation of spectral characteristics of particles ejected from the free surfaces of metals and liquids uner a shock wave effect[C]//AIP Conf Proc, 2012, 1426:1007-1010.
[26] BUTTLER W T, ORO D M, PRESTON D L, et al. Unstable Richtmyer-Meshkov growth of solid and liquid metals in vacuum[J]. J Fluid Mech, 2012, 703:60.
[27] DIMONTE G, TERRONES G, CHERNE F J, et al. Ejecta source model based the nonlinear Richtmyer-Meshkov instability[J]. J Appl Phys, 2013, 113(2):024905.
[28] HARRISON A K. Survey of ejecta source modeling in FLAG[R]. Los Alamos National Laboratory, 2015, LA-UR-07-6522.
[29] DIMONTE G, TERRONES G, CHERNE F J, et al. Use of the Richtmyer-Meshkov instability to infer yield stress at high-energy densities[J]. Phys Rev Lett, 2011, 107(26):264502.
[30] LIU J, WANG Y J, FENG Q J, et al. Simulation study on effects of material properties of the bulging flyers driven by colliding detonation waves[J]. Chinese J High Press Phys, 2015, 29:63-68.
[31] LIU J, FENG Q J, ZHOU H B. Simulation study of interface instability in metals driven by cylindrical implosion[J]. Acta Phys Sin, 2014, 63:155201.
[32] LI M S, CHEN D Q. A constitutive model for materials under high-temperature and pressure[J]. Chinese J High Press Phys, 2001, 15:24-31.
[33] MIKAELIAN K O. Analytic approach to nonlinear Rayleigh-Taylor and Richtmyer-Meshkov instabilities[J]. Phys Rev Lett,1998, 80(3):508.
[34] PIRIZ A R, CELA J J, TAHIR N A, et al. Richtmyer-Meshkov instability in elastic-plastic media[J]. Phys Rev E, 2008, 78(5):056401.
[35] JENSEN B J, CHERNE F J, PRIME M B, et al. Jet formation in cerium metal to examine material strength[J]. J Appl Phys, 2015, 118(19):195903.
[36] MIKAELIAN K O. Shock-induced interface instability in viscous fluids and metals[J]. Phys Rev B, 2013, 87(3):031003.
[37] RICHTMYER R D. Taylor instability in shock asscceleration of compressible fluids[J]. Commun Pure Appl Math, 1960, 13:297-319.
[38] DIMONTE G, RAMAPRABHU P. Simulations and model of the nonlinear Richtmyer-Meshkov instability[J]. Phys Fluids, 2010, 22(1):014104.