Advertisement

Determination of Hugoniots and Expansion Isentropes

  • M.V. Zhernokletov
Chapter
Part of the Shock Wave and High Pressure Phenomena book series (SHOCKWAVE)

Abstract

Equations (1.21) or (1.26), expressing the laws of conservation of mass, momentum, and energy at a shock discontinuity reveal that for known initial conditions, the problem of finding all five unknown shock front field variables (P, V, D, u, E) reduces to experimentally recording any two of them. These two are subsequently sufficient for construction of the Hugoniot. Straightforward and accurate measurements of compressed condensed matter pressure and density are dificult to perform. The methods most commonly applied, therefore, involve construction of the Hugoniot in terms of the kinematic parameters D and u.

Keywords

Shock Wave Shock Front Sound Speed Base Plate Rarefaction Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    1. Altshuler, L.V., Krupnikov, K.K., Ledenev, B.N., Zhuchikhin, V.I., and Brazhnik, M.I., “Dynamic Compressibility and Equation of State of Iron Under High Pressure,” Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, Vol. 34, No. 4, 1958, pp. 874–885, [English trans., Soviet Physics JETP, Vol. 7, No. 4, 1958, pp. 606–614].Google Scholar
  2. 2.
    2. Rice, M.N., McQueen, R.G., and Walsh, J.M., “Compression of Solids by Strong Shock Waves,” Solid State Physics - Advances in Research and Applications, Vol. 6, 1958, pp. 1–63.Google Scholar
  3. 3.
    3. McQueen, R.G., and Marsh, S.P., “Equation of State for Nineteen Metallic Elements from Shock-Wave Measurements to Two Megabars,” Journal of Applied Physics, Vol. 31, No. 7, 1960, pp. 1253–1269.CrossRefGoogle Scholar
  4. 4.
    4. Zeldovich, Ya.B., and Raizer, Yu.P., Physics of Shock Waves and High- Temperature Hydrodynamic Phenomena, Nauka Publ., Moscow, 1966, [English trans. Academic Press, NY, Vol. 1 (1966), Vol. 2 (1967); Reprinted in a single volume by Dover Publ., Mineola, NY 2002].Google Scholar
  5. 5.
    5. Zhernokletov, M.V., Simakov, G.V., Sutulov, Yu.N., and Trunin, R.F., “Expansion Isentropes of Aluminum, Iron, Molybdenum, Lead, and Tantalum, Teplofizika Vysokikh Temperatur, Vol. 33, No. 1, 1995, pp. 40–43, [English trans., High Temperature, Vol. 33, No. 1, 1995, pp. 36–39].Google Scholar
  6. 6.
    6. Altshuler, L.V., Krupnikov, K.K., and Brazhnik, M.I., “Dynamic Compressibility of Metals Under Pressures From 400,000 to 4,000,000 Atmospheres,” Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, Vol. 34, No. 4, 1958, pp. 886–893, [English trans., Soviet Physics JETP, Vol. 7, No. 4, 1958, pp. 614–619].Google Scholar
  7. 7.
    7. Bugaeva, V.A., Evstigneev, A.A., and Trunin, R.F., “Analysis of Calculation Data on the Adiabats of Expansion for Copper, Iron, and Aluminum,” Teplofizika Vysokikh Temperatur, Vol. 34, No. 5, 1996, pp. 684–690, [English trans., High Temperature, Vol. 34, No. 5, 1996, pp. 674–680].Google Scholar
  8. 8.
    8. Altshuler, L.V., Trunin, R.F., Krupnikov, K.K., and Panov, N.V., “Explosive Laboratory Devices for Studying Material Compression in Shock Waves,” Uspekhi Fizicheskikh Nauk, Vol. 166, No. 5, 1996, pp. 575–581.CrossRefGoogle Scholar
  9. 9.
    9. Altshuler, L.V., and Petrunin, A.P., “An X-Ray Investigation of the Compressibility of Light Materials Under the Action of Shock-Wave Impacts,” Zhurnal Tekhnicheskoi Fiziki, Vol. 31, No. 6, 1961, pp. 717–725, [English trans., Soviet Physics - Technical Physics, Vol. 6, No. 6, 1961, pp. 516–522].Google Scholar
  10. 10.
    10. Altshuler, L.V., and Pavlovskii, M.N., “Magnetoelectric Method for Determining the Density Behind the Front of Colliding Shock Waves,” Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, 1971, No. 2, pp. 110–114, [English trans., Journal of Applied Mechanics and Technical Physics, Vol. 12, No. 2, 1971, pp. 268–272].Google Scholar
  11. 11.
    11. Trunin, R.F., Gudarenko, L.F., Zhernokletov, M.V., and Simakov, G.V., Experimental Data on Shock Compression and Adiabatic Expansion of Condensed Materials, RFNC-VNIIEF, Sarov, Russia, 2001.Google Scholar
  12. 12.
    12. Erskine, D.J., “Improved Arrangement of Shock-Detecting Pins in Shock Equation of State Experiments,” Review of Scientific Instruments, Vol. 66, No. 10, 1995, pp. 5032–5036.CrossRefGoogle Scholar
  13. 13.
    13. McQueen, R.G., Marsh, S.P., Taylor, J.W., Fritz, J.N., and Carter, W.J., “The Equation of State of Solids from Shock Wave Studies” in High Velocity Impact Phenomena, Kinslow, R., ed., Academic Press, New York, 1970, pp. 293–417 (with appendices on pp. 515–568), [Russian trans., Nikolayevsky, V.N., ed., Mir Publ., Moscow, 1973, pp. 299–427].Google Scholar
  14. 14.
    14. Mitchell, A.C., and Nellis, W.J., “Shock Compression of Aluminum, Copper, and Tantalum,” Journal of Applied Physics, Vol. 52, No. 5, 1981, pp. 3363–3374.CrossRefGoogle Scholar
  15. 15.
    15. Zhernokletov, M.V., Zubarev, V.N., and Sutulov, Yu.N., “Porous-Specimen Adiabats and Solid-Copper Expansion Isentropes,” Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, 1984, No. 1, pp. 119–123, [English trans., Journal of Applied Mechanics and Technical Physics, Vol. 25, No. 1, 1984, pp. 107–110].Google Scholar
  16. 16.
    16. Altshuler, L.V., Bushman, A.V., Zhernokletov, M.V., Zubarev, V.N., Leontev, A.A., and Fortov, V.E., “Unloading Isentropes and the Equation of State of Metals at High Energy Densities,” Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, Vol. 78, No. 2, 1980, pp. 741–760, [English trans., Soviet Physics JETP, Vol. 51, No. 2, 1980, pp. 373–383].Google Scholar
  17. 17.
    17. Glushak, B.L., Zharkov, A.P., Zhernokletov, M.V., Ternovoi, V.Ya., Filimonov, A.S., and Fortov, V.E., “Experimental Investigation of the Thermodynamics of Dense Plasmas Formed From Metals at High Energy Concentrations,” Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, Vol. 96, No. 4, 1989, pp. 1301–1318, [English trans., Soviet Physics JETP, Vol. 69, No. 4, 1989, pp. 739–749].Google Scholar
  18. 18.
    18. Zhernokletov, M.V., Medvedev, A.V., and Simakov, G.V., “Expansion Isentrope and Equation of State of Molybdenum at High Energy Densities, Khimicheskaya Fizika, Vol. 14, No. 2–3, 1995, pp. 49–55.Google Scholar
  19. 19.
    19. Zhernokletov, M.V., “Shock Compression and Isentropic Expansion of Natural Uranium,” Teplofizika Vysokikh Temperatur, Vol. 36, No. 2, 1998, pp. 231–238, [English trans., High Temperature, Vol. 36, No. 2, 1998, pp. 214–221].Google Scholar
  20. 20.
    20. Gathers, G.R., Shaner, J.W., and Brier, R.L., “Improved Apparatus for Thermophysical Measurements on Liquid Metals up to 8000 K,” Review of Scientific Instruments, Vol. 47, No. 4, 1976, pp. 471–479.CrossRefGoogle Scholar
  21. 21.
    21. Gathers, G.R., Shaner, J.W., and Young, D.A., “Experimental, Very High- Temperature, Liquid-Uranium Equation of State,” Physical Review Letters, Vol. 33, No. 2, 1974, pp. 70–72.CrossRefGoogle Scholar
  22. 22.
    22. Bushman, A.V., and Fortov, V.E., “Model Equations of State,” Uspekhi Fizicheskikh Nauk, Vol. 140, No. 2, 1983, pp. 177–232, [English trans., Soviet Physics Uspekhi, Vol. 26, No. 6, 1983, pp. 465–496].Google Scholar
  23. 23.
    23. Asay, J.R., and Trucano T.G., “Experimental Measurements of Shock-Induced Vaporization in Cadmium and Lead,” Shock Compression of Condensed Matter - 1989, Schmidt, S.C., Johnson, J.N., and Davison, L.W., eds., Elsevier, Amsterdam, 1990, pp. 143–146.Google Scholar
  24. 24.
    24. Asay, J.R., “The Use of Shock-Structure Methods for Evaluating High-Pressure Material Properties,” International Journal of Impact Engineering, Vol. 20, No. 1–5, 1997, pp. 27–61.CrossRefGoogle Scholar
  25. 25.
    25. Zhernokletov, M.V., and Zubarev, V.N., “Determination of Expansion Isentropes After Shock Compression,” in Combustion and Explosion, Nauka Publ., Moscow, 1972, pp. 565–568.Google Scholar
  26. 26.
    26. Altshuler, L.V., Kormer, S.B., Brazhnik, M.I., Vladimirov, L.A., Speranskaya, M.P., and Funtikov, A.I., “The Isentropic Compressibility of Aluminum, Copper, Lead, and Iron at High Pressures,” Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, Vol. 38, No. 4, 1960, pp. 1061–1073, [English trans., Soviet Physics JETP, Vol. 11, No. 4, 1960, pp. 766–775].Google Scholar
  27. 27.
    27. Kormer, S.B., Sinitsyn, M.V., Kirillov, G.A., and Urlin, V.D., “Experimental Determination of Temperature in Shock-Compressed NaCl and KCl and of their Melting Curves at Pressures up to 700 kbar,” Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, Vol. 48, No. 4, 1965, pp. 1033–1049, [English trans., Soviet Physics JETP, Vol. 21, No. 4, 1965, pp. 689–700].Google Scholar
  28. 28.
    28. McQueen, R.G., Hopson, J.W., and Fritz, J.N., “Optical Technique for Determining Rarefaction Wave Velocities at Very High Pressures,” Review of Scientific Instruments, Vol. 53, No. 2, 1982, pp. 245–250.CrossRefGoogle Scholar
  29. 29.
    29. Gogulya, M.F., and Dolgoborodov, A.Yu., “Indicator Method for Study of Shock and Detonation Waves,” Khimicheskaya Fizika, Vol. 13, No. 12, 1994, pp. 118–127.Google Scholar
  30. 30.
    30. Grigorev, F.V., Kormer, S.B., Mikhailova, O.L., Mochalov, M.A., and Urlin, V.D., “Shock Compression and Brightness Temperature of a Shock Wave Front in Argon. Electron Screening of Radiation,” Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, Vol. 88, No. 4, 1985, pp. 1271–1280, [English trans., Soviet Physics JETP, Vol. 61, No. 4, 1985, pp. 751–757].Google Scholar
  31. 31.
    31. Nikolayev, D.N., Pyalling, A.A., Khishchenko, K.V., et al., “Thermodynamic Properties of Bromoform at High Pressures,” Khimicheskaya Fizika, Vol. 19, No. 10, 2000, pp. 98–108.Google Scholar
  32. 32.
    32. Dolgoborodov, A.Yu., and Voskoboinikov, I.M., “Velocities of Wave Perturbations Behind a Shock-Wave Front in Aluminum,” Fizika Goreniya i Vzryva, Vol. 25, No. 1, 1989, pp. 88–93, [English trans., Combustion, Explosion, and Shock Waves, Vol. 25, No. 1, 1989, pp. 80–85].Google Scholar
  33. 33.
    33. Altshuler, L.V., Pavlovskii, M.N., and Drakin, V.P., “Peculiarities of Phase Transitions in Compression and Rarefaction Shock Waves,” Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, Vol. 52, No. 2, 1967, pp. 400–408, [English trans., Soviet Physics JETP, Vol. 25, No. 2, 1967, pp. 260–265].Google Scholar
  34. 34.
    34. Pavlovskii, M.N., “Measurements of the Velocity of Sound in Shock-Compressed Quartzite, Dolomite, Anhydrite, Sodium Chloride, Paraffin, Plexiglas, Polyethylene, and Flouroplast-4,” Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, 1976, No. 5, pp. 136–139, [English trans., Journal of Applied Mechanics and Technical Physics, Vol. 17, No. 5, 1976, pp. 709–712].Google Scholar
  35. 35.
    35. Ruo., A.L., “Linear Shock-Velocity-Particle-Velocity Relationship,” Journal of Applied Physics, Vol. 38, No. 13, 1967, pp. 4976–4980.CrossRefGoogle Scholar
  36. 36.
    36. Altshuler, L.V., Bakanova, A.A., and Dudoladov, I.P., “Effect of Electron Structure on the Compressibility of Metals at High Pressure,” Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, Vol. 53, No. 6, 1967, pp. 1967–1977, [English trans., Soviet Physics JETP, Vol. 26, No. 6, 1968, pp. 1115–1120].Google Scholar
  37. 37.
    37. Gust, W.H., and Royce, E.B., “New Electronic Interactions in Rare-Earth Metals at High Pressure,” Physical Review B, Vol. 8, No. 8, 1973, pp. 3595–3609.CrossRefGoogle Scholar
  38. 38.
    38. Altshuler, L.V., Bakanova, A.A., Dudoladov, I.P., Dynin, E.A., Trunin, R.F., and Chekin, B.S., “Shock Adiabatic Curves of Metals. New Data, Statistical Analysis, and General Laws,” Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, 1981, No. 2, pp. 3–34, [English trans., Journal of Applied Mechanics and Technical Physics, Vol. 22, No. 2, 1981, pp. 145–169].Google Scholar
  39. 39.
    39. Altshuler, L.V., Brusnikin, S.E., and Kuzmenkov, E.A., “Isotherms and Gruneisen Functions for 25 Metals,” Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, 1987, No. 1, pp. 134–146, [English trans., Journal of Applied Mechanics and Technical Physics, Vol. 28, No. 1, 1987, pp. 129–141].Google Scholar
  40. 40.
    40. Fortov, V.E., Altshuler, L.V., Trunin, R.F., and Funtikov, A.I., Shock Waves and Extreme States of Matter, Nauka Publ., Moscow, 2000 [see also, Fortov, V.E., Altshuler, L.V., Trunin, R.F., and Funtikov, A.I., High-Pressure Shock Compression of Solids VII, Springer-Verlag, New York, 2004].Google Scholar
  41. 41.
    41. Altshuler, L.V., “Use of ShockWaves in High-Pressure Physics,” Uspekhi Fizicheskikh Nauk, Vol. 85, No. 2, 1965, pp. 197–258, [English trans., Soviet Physics Uspekhi, Vol. 8, No. 1, 1965, pp. 52–91].Google Scholar
  42. 42.
    42. Zababakhin, E.I., Some Problems of the Gasdynamics of Explosions, RFNCVNIITF, Snezhinsk, Russia, 1997, [English trans., RFNC-VNIITF, Snezhinsk, Russia, 2001].Google Scholar
  43. 43.
    43. Glushak, B.L., Gudarenko, L.F., Styazhkin, Yu.M., et al., “Semi-Empirical Equation of State of Metals with Variable Electron Heat Capacity,” Voprosy Atomnoi Nauki i Tekhniki. Seriya: Matematicheskoe Modelirovanie Fizicheskikh Protsessov, 1991, No. 1, pp. 32–37.Google Scholar
  44. 44.
    44. Glushak, B.L., Gudarenko, L.F., Styazhkin, Yu.M., et al., “Semi-Empirical Equation of State of Metals with Variable Nuclei and Electron Heat Capacity,” Voprosy Atomnoi Nauki i Tekhniki. Seriya: Matematicheskoe Modelirovanie Fizicheskikh Protsessov, 1991, No. 2, pp. 57–61.Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • M.V. Zhernokletov

There are no affiliations available

Personalised recommendations