Using Richtmyer–Meshkov Instabilities to Estimate Metal Strength at Very High Rates

  • Michael B. Prime
  • William T. Buttler
  • Sky K. Sjue
  • Brian J. Jensen
  • Fesseha G. Mariam
  • David M. Oró
  • Cora L. Pack
  • Joseph B. Stone
  • Dale Tupa
  • Wendy Vogan-McNeil
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


Recently, Richtmyer–Meshkov instabilities (RMI) have been proposed for studying strength at strain rates up to 107/s. RMI experiments involve shocking a metal interface that has geometrical perturbations that invert and grow subsequent to the shock. As these perturbations grow, their growth may arrest, or they may grow unstably and eventually fail. The experiments observe the growth and arrest to study the specimen’s yield (deviatoric) strength. Along these lines we first review some RMI experimental results on Cu. Next, the paper presents explicit Lagrangian simulations used to help interpret the Cu RMI results and infer the strength, i.e. flow stress, of the target metal. A Preston-Tonks-Wallace (PTW) constitutive model is modified to be more accurate at the strain rates accessed in the experiment. The advantages and disadvantages of RMI, as compared to the Rayleigh–Taylor (shockless) instabilities that are used more commonly to infer strength, are discussed. The advantages of using simple velocimetry measurements in place of radiography are also discussed.


Richtmyer–Meshkov instabilities Shock High strain rate Strength Rayleigh–Taylor 



We acknowledge the support of the pRad team in acquiring these data. In addition, we appreciate contributions to these experiments by members of the LANL MST-7 group where our Cu targets were machined and characterized by F. Garcia, B. Day and D. Schmidt.

This work was performed at Los Alamos National Laboratory, operated by the Los Alamos National Security, LLC for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. By acceptance of this article, the publisher recognizes that the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes.


  1. 1.
    Barnes, J.F., Blewett, P.J., McQueen, R.G., Meyer, K.A., Venable, D.: Taylor instability in solids. J. Appl. Phys. 45(2), 727–732 (1974). CrossRefGoogle Scholar
  2. 2.
    Colvin, J.D., Legrand, M., Remington, B.A., Schurtz, G., Weber, S.V.: A model for instability growth in accelerated solid metals. J. Appl. Phys. 93(9), 5287–5301 (2003). CrossRefGoogle Scholar
  3. 3.
    Lebedev, A.I., Nizovtsev, P.N., Rayevsky, V.A., Solovyov, V.P.: 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 (1996)Google Scholar
  4. 4.
    Barton, N.R., Bernier, J.V., Becker, R., Arsenlis, A., Cavallo, R., Marian, J., Rhee, M., Park, H.-S., Remington, B.A., Olson, R.T.: A multiscale strength model for extreme loading conditions. J. Appl. Phys. 109(7), 073501 (2011). CrossRefGoogle Scholar
  5. 5.
    Smith, R.F., Eggert, J.H., Rudd, R.E., Swift, D.C., Bolme, C.A., Collins, G.W.: High strain-rate plastic flow in Al and Fe. J. Appl. Phys. 110(12), 123515 (2011). CrossRefGoogle Scholar
  6. 6.
    Piriz, A.R., Cela, J.J.L., Tahir, N.A., Hoffmann, D.H.H.: Richtmyer-Meshkov instability in elastic-plastic media. Phys. Rev. E 78(5), 056401 (2008)CrossRefGoogle Scholar
  7. 7.
    Piriz, A.R., Cela, J.J.L., Tahir, N.A.: Richtmyer–Meshkov instability as a tool for evaluating material strength under extreme conditions. Nucl. Instrum. Methods Phys. Res., Sect. A 606(1), 139–141 (2009)CrossRefGoogle Scholar
  8. 8.
    Dimonte, G., Terrones, G., Cherne, F.J., Germann, T.C., Dupont, V., Kadau, K., Buttler, W.T., Oro, D.M., Morris, C., Preston, D.L.: Use of the Richtmyer-Meshkov instability to infer yield stress at high-energy densities. Phys. Rev. Lett. 107(26), 264502 (2011)CrossRefGoogle Scholar
  9. 9.
    Buttler, W.T., Oró, D.M., Preston, D.L., Mikaelian, K.O., Cherne, F.J., Hixson, R.S., Mariam, F.G., Morris, C., Stone, J.B., Terrones, G., Tupa, D.: Unstable Richtmyer-Meshkov growth of solid and liquid metals in vacuum. J. Fluid Mech. 703, 60–84 (2012)CrossRefGoogle Scholar
  10. 10.
    López Ortega, A., Lombardini, M., Pullin, D.I., Meiron, D.I.: Numerical simulations of the Richtmyer-Meshkov instability in solid-vacuum interfaces using calibrated plasticity laws. Phys. Rev. E 89(3), 033018 (2014)CrossRefGoogle Scholar
  11. 11.
    Mikaelian, K.O.: Shock-induced interface instability in viscous fluids and metals. Phys. Rev. E 87(3), 031003 (2013)CrossRefGoogle Scholar
  12. 12.
    Plohr, J.N., Plohr, B.J.: Linearized analysis of Richtmyer-Meshkov flow for elastic materials. J. Fluid Mech. 537, 55–89 (2005)CrossRefGoogle Scholar
  13. 13.
    Prime, M.B., Vaughan, D.E., Preston, D.L., Buttler, W.T., Chen, S.R., Oró, D.M., Pack, C.: Using growth and arrest of Richtmyer-Meshkov instabilities and Lagrangian simulations to study high-rate material strength. J. Phys. Conf. Ser. 500(11), 112051 (2014)CrossRefGoogle Scholar
  14. 14.
    Buttler, W.T., Oro, D.M., Preston, D., Mikaelian, K.O., Cherne, F.J., Hixson, R.S., Mariam, F.G., Morris, C.L., Stone, J.B., Terrones, G., Tupa, D.: The study of high-speed surface dynamics using a pulsed proton beam. AIP Conf. Proc. 1426(1), 999–1002 (2012). CrossRefGoogle Scholar
  15. 15.
    Asay, J.R., Mix, L.P., Perry, F.C.: Ejection of material from shocked surfaces. Appl. Phys. Lett. 29(5), 284–287 (1976). CrossRefGoogle Scholar
  16. 16.
    Germann, T.C., Hammerberg, J.E., Holian, B.L.: Large‐scale molecular dynamics simulations of ejecta formation in copper. AIP Conf. Proc. 706(1), 285–288 (2004). CrossRefGoogle Scholar
  17. 17.
    Zellner, M.B., Buttler, W.T.: Exploring Richtmyer–Meshkov instability phenomena and ejecta cloud physics. Appl. Phys. Lett. 93(11), 114102 (2008). CrossRefGoogle Scholar
  18. 18.
    Zellner, M.B., Dimonte, G., Germann, T.C., Hammerberg, J.E., Rigg, P.A., Stevens, G.D., Turley, W.D., Buttler, W.T.: Influence of shockwave profile on ejecta. AIP Conf. Proc. 1195(1), 1047–1050 (2009). CrossRefGoogle Scholar
  19. 19.
    Dimonte, G., Terrones, G., Cherne, F.J., Ramaprabhu, P.: Ejecta source model based on the nonlinear Richtmyer-Meshkov instability. J. Appl. Phys. 113(2), 024905 (2013). CrossRefGoogle Scholar
  20. 20.
    King, N.S.P., Ables, E., Adams, K., Alrick, K.R., Amann, J.F., Balzar, S., Barnes Jr., P.D., Crow, M.L., Cushing, S.B., Eddleman, J.C.: An 800-MeV proton radiography facility for dynamic experiments. Nucl. Instrum. Methods Phys. Res., Sect. A 424(1), 84–91 (1999)CrossRefGoogle Scholar
  21. 21.
    Holtkamp, D.B.: Survey of optical velocimetry experiments-applications of PDV, a heterodyne velocimeter. In: Kiuttu, G.F., Turchi, P.J., Reinovsky, R.E. (eds.) Proceedings of 2006 International Conference on Megagauss Magnetic Field Generation and Related Topics, pp. 119–128. IEEE, Santa Fe (2006). doi: 10.1109/MEGAGUSS.2006.4530668
  22. 22.
    Caramana, E.J., Burton, D.E., Shashkov, M.J., Whalen, P.P.: The construction of compatible hydrodynamics algorithms utilizing conservation of total energy. J. Comput. Phys. 146(1), 227–262 (1998). CrossRefGoogle Scholar
  23. 23.
    Burton, D.E., Carney, T.C., Morgan, N.R., Runnels, S.R., Sambasivan, S.K., Shashkov, M.J.: A cell-centered Lagrangian hydrodynamics method for multi-dimensional unstructured grids in curvilinear coordinates with solid constitutive models. Los Alamos National Laboratory Report LA-UR-11-04995 (2011)Google Scholar
  24. 24.
    Dobratz, B.M., Crawford, P.C.: LLNL explosives handbook. Properties of chemical explosives and explosive simulants. Lawrence Livermore National Laboratory Report UCRL-52997 Change 2 (1985)Google Scholar
  25. 25.
    Lyon, S.P., Johnson, J.D.: Sesame: the Los Alamos National Laboratory equation of state database. Los Alamos National Laboratory Report LA-UR-92-3407 (1992)Google Scholar
  26. 26.
    Preston, D.L., Tonks, D.L., Wallace, D.C.: Model of plastic deformation for extreme loading conditions. J. Appl. Phys. 93(1), 211–220 (2003)CrossRefGoogle Scholar
  27. 27.
    Tonks, D., Zurek, A., Thissell, W., Vorthman, J., Hixson, R.: The Tonks ductile damage model. Los Alamos National Laboratory Report LA-UR-03-0809 (2002)Google Scholar
  28. 28.
    Zurek, A.K., Thissell, W.R., Johnson, J.N., Tonks, D.L., Hixson, R.: Micromechanics of spall and damage in tantalum. J. Mater. Process. Technol. 60(1–4), 261–267 (1996). CrossRefGoogle Scholar
  29. 29.
    Tonks, D.L.: Percolation wave propagation, and void link-up effects in ductile fracture. J. Phys. IV 4(C8), C8-665–C8-670 (1994)Google Scholar
  30. 30.
    Tonks, D.L., Zurek, A.K., Thissell, W.R.: Void coalescence model for ductile damage. AIP Conf. Proc. 620(1), 611–614 (2002). CrossRefGoogle Scholar
  31. 31.
    Tonks, D.L., Bronkhorst, C.A., Bingert, J.F.: Inertial effects in dynamical ductile damage in copper. Los Alamos National Laboratory Report LA-UR-11-05803 (2011)Google Scholar
  32. 32.
    Park, H.-S., Lorenz, K.T., Cavallo, R.M., Pollaine, S.M., Prisbrey, S.T., Rudd, R.E., Becker, R.C., Bernier, J.V., Remington, B.A.: Viscous Rayleigh-Taylor instability experiments at high pressure and strain rate. Phys. Rev. Lett. 104(13), 135504 (2010)CrossRefGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2016

Authors and Affiliations

  • Michael B. Prime
    • 1
  • William T. Buttler
    • 1
  • Sky K. Sjue
    • 1
  • Brian J. Jensen
    • 1
  • Fesseha G. Mariam
    • 1
  • David M. Oró
    • 1
  • Cora L. Pack
    • 1
  • Joseph B. Stone
    • 1
  • Dale Tupa
    • 1
  • Wendy Vogan-McNeil
    • 1
  1. 1.Los Alamos National LaboratoryLos AlamosUSA

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