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Estimation of Metal Strength at Very High Rates Using Free-Surface Richtmyer–Meshkov Instabilities

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Abstract

Recently, Richtmyer–Meshkov Instabilities (RMI) have been proposed for studying the average strength at strain rates up to at least 107/s. RMI experiments involve shocking a metal interface that has initial sinusoidal perturbations. The perturbations invert and grow subsequent to shock and may arrest because of strength effects. In this work we present new RMI experiments and data on a copper target that had five regions with different perturbation amplitudes on the free surface opposite the shock. We estimate the high-rate, low-pressure copper strength by comparing experimental data with Lagrangian numerical simulations. From a detailed computational study we find that mesh convergence must be carefully addressed to accurately compare with experiments, and numerical viscosity has a strong influence on convergence. We also find that modeling the as-built perturbation geometry rather than the nominal makes a significant difference. Because of the confounding effect of tensile damage on total spike growth, which has previously been used as the metric for estimating strength, we instead use a new strength metric: the peak velocity during spike growth. This new metric also allows us to analyze a broader set of experimental results that are sensitive to strength because some larger initial perturbations grow unstably to failure and so do not have a finite total spike growth.

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Notes

  1. Buttler et al. [9] estimated the time and spatially averaged plastic strain rate in a spike with η 0 k = 0.35 at 1.5 × 107/s, and also give much higher estimates of plastic strain and temperature. Those estimates were based on the equations of Piriz [6] and used and a value of 1/3 for the constant α. A value of 3/2 matches the numerical simulations here, and is consistent with more recent work [56] [57]. Switching to α = 3/2 in the equations in Buttler reduces the strain rate and strain estimates by about one order of magnitude [58].

References

  1. Barnes JF, Blewett PJ, McQueen RG, Meyer KA, Venable D (1974) Taylor instability in solids. J Appl Phys 45(2):727–732. doi:10.1063/1.1663310

    Article  Google Scholar 

  2. Colvin JD, Legrand M, Remington BA, Schurtz G, Weber SV (2003) A model for instability growth in accelerated solid metals. J Appl Phys 93(9):5287–5301. doi:10.1063/1.1565188

    Article  Google Scholar 

  3. Lebedev AI, Nizovtsev PN, Rayevsky VA, Solovyov VP (1996) Rayleigh–Taylor Instability in Strong Media, Experimental Study. In: Young R, Glimm J, Boston B (eds) Proceedings of the Fifth International Workshop on Compressible Turbulent Mixing, Stony Brook, 1996

  4. Barton NR, Bernier JV, Becker R, Arsenlis A, Cavallo R, Marian J, Rhee M, Park H-S, Remington BA, Olson RT (2011) A multiscale strength model for extreme loading conditions. J Appl Phys 109(7):073501. doi:10.1063/1.3553718

    Article  Google Scholar 

  5. Smith RF, Eggert JH, Rudd RE, Swift DC, Bolme CA, Collins GW (2011) High strain-rate plastic flow in Al and Fe. J Appl Phys 110(12):123515. doi:10.1063/1.3670001

    Article  Google Scholar 

  6. Piriz AR, Cela JJL, Tahir NA, Hoffmann DHH (2008) Richtmyer-Meshkov instability in elastic-plastic media. Phys Rev E 78(5):056401

    Article  Google Scholar 

  7. Piriz AR, Cela JJL, Tahir NA (2009) Richtmyer–Meshkov instability as a tool for evaluating material strength under extreme conditions. Nucl Instrum Methods Phys 606 (1):139–141

    Article  Google Scholar 

  8. Dimonte G, Terrones G, Cherne FJ, Germann TC, Dupont V, Kadau K, Buttler WT, Oro DM, Morris C, Preston DL (2011) Use of the Richtmyer-Meshkov instability to infer yield stress at high-energy densities. Phys Rev Lett 107(26):264502

    Article  Google Scholar 

  9. Buttler WT, Oró DM, Preston DL, Mikaelian KO, Cherne FJ, Hixson RS, Mariam FG, Morris C, Stone JB, Terrones G, Tupa D (2012) Unstable Richtmyer-Meshkov growth of solid and liquid metals in vacuum. J Fluid Mech 703:60–84

    Article  Google Scholar 

  10. López Ortega A, Lombardini M, Pullin DI, Meiron DI (2014) Numerical simulations of the Richtmyer-Meshkov instability in solid-vacuum interfaces using calibrated plasticity laws. Phys Rev E 89(3):033018

    Article  Google Scholar 

  11. Mikaelian KO (2013) Shock-induced interface instability in viscous fluids and metals. Phys Rev E 87(3):031003

    Article  Google Scholar 

  12. Plohr JN, Plohr BJ (2005) Linearized analysis of Richtmyer-Meshkov flow for elastic materials. J Fluid Mech 537:55–89

    Article  Google Scholar 

  13. Prime MB, Vaughan DE, Preston DL, Buttler WT, Chen SR, Oró DM, Pack C (2014) Using growth and arrest of Richtmyer-Meshkov instabilities and Lagrangian simulations to study high-rate material strength. J Phys Conf Ser 500(11):112051

    Article  Google Scholar 

  14. Opie S, Gautam S, Fortin E, Lynch J, Peralta P, Loomis E (2016) Behaviour of rippled shocks from ablatively-driven Richtmyer-Meshkov in metals accounting for strength. J Phys Conf Ser 717(1):012075

    Article  Google Scholar 

  15. John KK (2014) Strength of tantalum at high pressures through Richtmyer-Meshkov laser compression experiments and simulations. Ph. D. Dissertation. California Institute of Technology, Pasadena, CA

    Google Scholar 

  16. Sternberger Z, Ravichandran R, Wehrenberg C, Remington B, Maddox B, Opachich K, Randall G, Farrell M (2015) A comparative study of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in 2D and 3D in tantalum. In: APS Shock Compression of Condensed Matter Conference Proceedings, p 4003

  17. Buttler WT, Oro DM, Preston D, Mikaelian KO, Cherne FJ, Hixson RS, Mariam FG, Morris CL, Stone JB, Terrones G, Tupa D (2012) The study of high-speed surface dynamics using a pulsed proton beam. AIP Conf Proc 1426 (1):999–1002. doi:10.1063/1.3686446

    Article  Google Scholar 

  18. Jensen BJ, Cherne FJ, Prime MB, Fezzaa K, Iverson AJ, Carlson CA, Yeager JD, Ramos KJ, Hooks DE, Cooley JC, Dimonte G (2015) Jet formation in cerium metal to examine material strength. J Appl Phys 118(19):195903. doi:10.1063/1.4935879

    Article  Google Scholar 

  19. Asay JR, Mix LP, Perry FC (1976) Ejection of material from shocked surfaces. Appl Phys Lett 29(5):284–287. doi:10.1063/1.89066

    Article  Google Scholar 

  20. Germann TC, Hammerberg JE, Holian BL (2004) Large-scale molecular dynamics simulations of ejecta formation in copper. AIP Conf Proc 706 (1):285–288. doi:10.1063/1.1780236

    Article  Google Scholar 

  21. Zellner MB, Buttler WT (2008) Exploring Richtmyer–Meshkov instability phenomena and ejecta cloud physics. Appl Phys Lett 93(11):114102. doi:10.1063/1.2982421

    Article  Google Scholar 

  22. Zellner MB, Dimonte G, Germann TC, Hammerberg JE, Rigg PA, Stevens GD, Turley WD, Buttler WT (2009) Influence of shockwave profile on ejecta. AIP Conf Proc 1195 (1):1047–1050. doi:10.1063/1.3294980

    Article  Google Scholar 

  23. Dimonte G, Terrones G, Cherne FJ, Ramaprabhu P (2013) Ejecta source model based on the nonlinear Richtmyer-Meshkov instability. J Appl Phys 113(2):024905. doi:10.1063/1.4773575

    Article  Google Scholar 

  24. Prime MB, Buttler WT, Sjue SK, Jensen BJ, Mariam FG, Oró DM, Pack CL, Stone JB, Tupa D, Vogan-McNeil W (2016) Using Richtmyer–Meshkov instabilities to estimate metal strength at very high rates. In: Song B, Lamberson L, Casem D, Kimberley J (eds) Dynamic Behavior of Materials. Conference Proceedings of the Society for Experimental Mechanics Series, vol 1. Springer, pp 191–197. doi:10.1007/978-3-319-22452-7_27

  25. King NSP, Ables E, Adams K, Alrick KR, Amann JF, Balzar S, Barnes Jr PD, Crow ML, Cushing SB, Eddleman JC (1999) An 800-MeV proton radiography facility for dynamic experiments. Nucl Instrum Methods Phys 424 (1):84–91

    Article  Google Scholar 

  26. Holtkamp DB (2006) Survey of optical velocimetry experiments-applications of PDV, a heterodyne velocimeter. In: Kiuttu GF, Turchi PJ, Reinovsky RE (eds) International Conference on Megagauss Magnetic Field Generation and Related Topics, Santa Fe, NM, 2006. IEEE, pp 119–128. doi:10.1109/MEGAGUSS.2006.4530668

    Chapter  Google Scholar 

  27. Yeh Y, Cummins HZ (1964) Localized fluid flow measurements with an He–Ne laser spectrometer. Appl Phys Lett 4(10):176–178. doi:10.1063/1.1753925

    Article  Google Scholar 

  28. Foreman JW, George EW, Lewis RD (1965) Measurement of localized flow velocities in gases with a laser Doppler flowmeter. Appl Phys Lett 7(4):77–78. doi:10.1063/1.1754319

    Article  Google Scholar 

  29. Buttler WT, Lamoreaux SK, Omenetto FG, Torgerson JR (2004) Optical Velocimetry. ArXiv Physics e-prints

  30. Strand OT, Goosman DR, Martinez C, Whitworth TL, Kuhlow WW (2006) Compact system for high-speed velocimetry using heterodyne techniques. Rev Sci Instrum 77(8):083108. doi:10.1063/1.2336749

    Article  Google Scholar 

  31. Caramana EJ, Burton DE, Shashkov MJ, Whalen PP (1998) The construction of compatible hydrodynamics algorithms utilizing conservation of total energy. J Comput Phys 146(1):227–262. doi:10.1006/jcph.1998.6029

    Article  Google Scholar 

  32. Burton DE, Carney TC, Morgan NR, Runnels SR, Sambasivan SK, Shashkov MJ (2011) A cell-centered Lagrangian hydrodynamics method for multi-dimensional unstructured grids in curvilinear coordinates with solid constitutive models. Los Alamos National Laboratory Report Report LA-UR-11-04995

  33. Kenamond M, Bement M, Shashkov M (2014) Compatible, total energy conserving and symmetry preserving arbitrary Lagrangian–Eulerian hydrodynamics in 2D rz – Cylindrical coordinates. J Comput Phys 268:154–185. doi:10.1016/j.jcp.2014.02.039

    Article  Google Scholar 

  34. Burton DE (1992) Connectivity structures and differencing techniques for staggered-grid free-Lagrange hydrodynamics. Report Lawrence Livermore National Laboratory, Report No. UCRL–JC–110555

  35. Burton DE (1994) Consistent finite-volume discretization of hydrodynamic conservation laws for unstructured grids. Lawrence Livermore National Laboratory Report UCRL–JC–118788.

  36. Fung J, Harrison AK, Chitanvis S, Margulies J (2013) Ejecta source and transport modeling in the FLAG hydrocode. Computers Fluids 83:177–186. doi:10.1016/j.compfluid.2012.08.011

    Article  Google Scholar 

  37. Sambasivan SK, Shashkov MJ, Burton DE (2013) A finite volume cell-centered Lagrangian hydrodynamics approach for solids in general unstructured grids. Int J Numer Methods Fluids 72 (7):770–810. doi:10.1002/fld.3770

    Article  Google Scholar 

  38. Morgan NR, Kenamond MA, Burton DE, Carney TC, Ingraham DJ (2013) An approach for treating contact surfaces in Lagrangian cell-centered hydrodynamics. J Comput Phys 250:527–554. doi:10.1016/j.jcp.2013.05.015

    Article  Google Scholar 

  39. Denissen NA, Rollin B, Reisner JM, Andrews MJ (2014) The tilted rocket rig: a Rayleigh–Taylor test case for RANS models1. J Fluid Eng 136(9):091301–091301. doi:10.1115/1.4027776

    Article  Google Scholar 

  40. Lipnikov K, Reynolds J, Nelson E (2013) Mimetic discretization of two-dimensional magnetic diffusion equations. J Comput Phys 247:1–16. doi:10.1016/j.jcp.2013.03.050

    Article  Google Scholar 

  41. Simulia Abaqus 6.14 (2014). Dassualt Systems

  42. Landshoff R (1955) A numerical method for treating fluid flow in the presence of shocks. Los Alamos National Laboratory Report LA-1930

  43. VonNeumann J, Richtmyer RD (1950) A Method for the numerical calculation of hydrodynamic shocks. J Appl Phys 21(3):232–237. doi:10.1063/1.1699639

    Article  Google Scholar 

  44. Margolin LG (1988) A centered artificial viscosity for cells with large aspect ratio. Report Lawrence Livermore National Laboratory report UCRL-53882

  45. Steinberg DJ (1996) Equation of State and Strength Properties of Selected Materials. Lawrence Livermore National Laboratory Report UCRL-MA-106439 Change 1

  46. Tonks D, Zurek A, Thissell W, Vorthman J, Hixson R (2002) The Tonks ductile damage model. Los Alamos National Laboratory Report LA-UR-03-0809

  47. Zurek AK, Thissell WR, Johnson JN, Tonks DL, Hixson R (1996) Micromechanics of spall and damage in tantalum. J Mater Process Technol 60(1–4):261–267. doi:10.1016/0924-0136(96)02340-0

    Article  Google Scholar 

  48. Tonks DL (1994) Percolation wave propagation, and void link-up effects in ductile fracture. Le Journal de Physique IV 4 (C8):C8-665-C668-670

    Article  Google Scholar 

  49. Tonks DL, Zurek AK, Thissell WR (2002) Void coalescence model for ductile damage. AIP Conf Proc 620 (1):611–614. doi:10.1063/1.1483613

    Article  Google Scholar 

  50. Tonks DL, Bronkhorst CA, Bingert JF (2011) Inertial effects in dynamical ductile damage in copper. Los Alamos National Laboratory Report LA-UR-11-05803

  51. Preston DL, Tonks DL, Wallace DC (2003) Model of plastic deformation for extreme loading conditions. J Appl Phys 93(1):211–220

    Article  Google Scholar 

  52. Dobratz BM, Crawford PC (1985) LLNL Explosives Handbook. Properties of chemical explosives and explosive simulants. Lawrence Livermore National Laboratory Report UCRL-52997 Change 2

  53. López Ortega A, Lombardini M, Barton PT, Pullin DI, Meiron DI (2015) Richtmyer–Meshkov instability for elastic–plastic solids in converging geometries. J Mech Phys Solids 76:291–324. doi:10.1016/j.jmps.2014.12.002

    Article  Google Scholar 

  54. Escobedo JP, Dennis-Koller D, Cerreta EK, Patterson BM, Bronkhorst CA, Hansen BL, Tonks D, Lebensohn RA (2011) Effects of grain size and boundary structure on the dynamic tensile response of copper. J Appl Phys 110(3):033513. doi:10.1063/1.3607294

    Article  Google Scholar 

  55. Bodelot L, Escobedo-Diaz JP, Trujillo CP, Martinez DT, Cerreta EK, Gray Iii GT, Ravichandran G (2015) Microstructural changes and in-situ observation of localization in OFHC copper under dynamic loading. Int J Plast 74:58–74. doi:10.1016/j.ijplas.2015.06.002

    Article  Google Scholar 

  56. Piriz AR, Sun YB, Tahir NA (2015) Hydrodynamic instability of elastic-plastic solid plates at the early stage of acceleration. Phys Rev E 91(3):033007

    Article  Google Scholar 

  57. Piriz AR (2016) Private communicaiton, 14 March 2016

  58. Preston DL (2015) Private communication, 1 May 2015

  59. Meyers MA (1994) Dynamic behavior of materials, Wiley, Newyork

    Book  Google Scholar 

  60. Asay JR, Lipkin J (1978) A self-consistent technique for estimating the dynamic yield strength of a shock-loaded material. J Appl Phys 49(7):4242–4247. doi:10.1063/1.325340

    Article  Google Scholar 

  61. Brown JL, Alexander CS, Asay JR, Vogler TJ, Ding JL (2013) Extracting strength from high pressure ramp-release experiments. J Appl Phys 114(22):223518. doi:10.1063/1.4847535

    Article  Google Scholar 

  62. Reinhart WD, Asay JR, Alexander CS, Chhabildas LC, J Jensen B (2015) Flow strength of 6061-T6 aluminum in the solid, mixed phase, liquid regions. J Dyn Behav Mater 1(3):275–289. doi:10.1007/s40870-015-0030-6

    Article  Google Scholar 

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  1. Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Michael B. Prime, William T. Buttler, Miles A. Buechler, Nicholas A. Denissen, Mark A. Kenamond, Fesseha G. Mariam, John I. Martinez, David M. Oró, Derek W. Schmidt, Joseph B. Stone, Dale Tupa & Wendy Vogan-McNeil

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  1. Michael B. Prime
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Prime, M.B., Buttler, W.T., Buechler, M.A. et al. Estimation of Metal Strength at Very High Rates Using Free-Surface Richtmyer–Meshkov Instabilities. J. dynamic behavior mater. 3, 189–202 (2017). https://doi.org/10.1007/s40870-017-0103-9

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