Applied Mathematics and Mechanics

, Volume 2, Issue 2, pp 155–182 | Cite as

A physical model of the structure and attenuation of shock waves in metals

  • Duan Zhou-ping


In this paper, a physical model of the structure and attenuation of shock waves in metals is presented. In order to establish the constitutive equations of materials under high velocity deformation and to study the structure of transition zone of shock wave, two independent approaches are involved. Firstly, the specific internal energy is decomposed into the elastic compression energy and elastic deformation energy, and the later is represented by an expansion to third-order terms in elastic strain and entropy, including the coupling effect of heat and mechanical energy. Secondly, a plastic relaxation function describing the behaviour of plastic flow under high temperature and high pressure is suggested from the viewpoint of dislocation dynamics. In addition, a group of ordinary differential equations has been built to determine the thermo-mechanical state variables in the transition zone of a steady shock wave and the thickness of the high pressure shock wave, and an analytical solution of the equations can be found provided that the entropy change across the shock is assumed to be negligible and Hugoniot compression modulus is used instead of the isentropic compression modulus. A quite approximate method for solving the attenuation of shock wave front has been proposed for the flat-plate symmetric impact problem.


Shock Wave Compression Modulus Shock Wave Front Pressure Shock Dislocation Dynamic 
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  1. 1.
    Rice, M. H., McQueen, R. G. and walsh, J. M.,Solid State Phys., 6 (1958), 1–63.Google Scholar
  2. 2.
    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, Ed. by Kinslow, R., Academic Press Inc. New York (1970).Google Scholar
  3. 3.
    Taylor, J. W., Dislocation dynamics and dynamic yielding,J. Appl. Phys., 36 (1965), 3146–50.Google Scholar
  4. 4.
    Gilman, J. J., Dislocation dynamics and the response of materials to impact,Appl. Mech Rev. 21 (1968), 767.Google Scholar
  5. 5.
    Gilman, J. J., Symp. Mechanical behavior of materials under dynamic loads, San Antonio, Texas (1967).Google Scholar
  6. 6.
    Johnson, J. N. and Barker, L. M., Dislocation and steady plastic wave profiles in 6061-T6 aluminum,J. Appl. Phys. 40 (1969), 4321.Google Scholar
  7. 7.
    Herrmann, W., Nonlinear stress waves in metals,Wave Propagation in Solids, Ed. by Miklowitz, J., ASME (1969).Google Scholar
  8. 8.
    Herrmann, W., Hick, D. L. and Young, E. G., Attenuation of elastic-plastic stress waves,Shock Waves and the Mechanical properties of Solids. Ed. by Burke, J. J., and Weiss. V., Syracuse University Press (1971).Google Scholar
  9. 9.
    Lee, E. H., Elastic-plastic deformation at finite strain.J. Appl. Mech., 36 (1969), 1–6.Google Scholar
  10. 10.
    Lee, E. H., Plastic wave propagation analsyis and elastic-plastic theory at finite deformation,Shock Wave and the Mechanical Properties of Solids, Ed. by Burke, J. J. and Weiss. V., Syracuse University, Press (1971).Google Scholar
  11. 11.
    Clifton, R. J., On the analysis of elastic/visco-plastic waves of finite uniaxial strain. Id., New York (1971).Google Scholar
  12. 12.
    Clifton R. J., Plastic waves: theory and experiment,Mechanics Today, 1, Ed. by Nemat-Nasser, S., Pergamon Press, Inc. (1972).Google Scholar
  13. 13.
    Fan, L. Z. and Duan, Z. P. On the structure of shock wave in solids,Mechanics, 2 (1976), 103–109, Sci. Pub. House Press, China.Google Scholar
  14. 14.
    Gilman, J. J., Physical nature of plastic flow and fracture, in Plasticity, Proc. 2nd Symp. on Naval St. Mech., Ed. by Lee, E. H. and Symonds, P. C., Pergamon Press Inc. (1960).Google Scholar
  15. 15.
    Herrmann, W., Some recent results in elastic-plastic wave propagation,Propagation of Shock Waves in Solids, Ed. by Varley E. ASME (1976).Google Scholar
  16. 16.
    Farren, W. S. and Taylor, G. I., The heat developed during plastic extension of metals,Proc. Roy. Soc. (London), A107 (1925), 422–51.Google Scholar
  17. 17.
    Quinney, H. and Taylor, G. I., The latent energy remaining in a metal after cold working,Proc. Roy. Soc. (London), A143 (1934), 307–26.Google Scholar
  18. 18.
    Wilkins, M. L.,Calculation of Elastic-plastic Flow in Method in Computational Physics, Ed. by Alder, B., Fernbachs, S. and Rotenberg, M., Vol. 3. Academic Press, New York (1964).Google Scholar
  19. 19.
    Bridgman, P. W.,The Physics of High Pressure, Printed in Great Britain by Strangeways Press, Ltd., (1952).Google Scholar
  20. 20.
    Broberg, K. B.,Shock Waves in Elastic and Elastic-Plastic Media, Stockholm (1956).Google Scholar
  21. 21.
    Thurston, R. A. and Bernstein, B., Third-order constants and the velocity of small amplitude elastic waves in homogeneously stressed media,Phys. Rev., A133 (1964), 1604–10.Google Scholar
  22. 22.
    Smith, R. T., Stern, R. and Stephens, R. W. B., Third-order elastic moduli of polycrystalline metals from ultrasonic velocity measuremenst,Acoust. Soc. Am. J., 40 (1966), 1002–08.Google Scholar
  23. 23.
    Duvall, G. E., Shock wave and equations of state,Dynamic Response of Materials to Instense Impulsive Loading, Ed. by Chou, P. C. and Hopkins, A. K., Printed in U. S. A. (1972).Google Scholar
  24. 24.
    Lindholm, U. S., Mechanical properties at high rates of strain, Proc. Conf. on Mech. Prop. Mat. at High Rates of strain, (1974), Oxford.Google Scholar
  25. 25.
    Gillis, P. P., Gilman, J. J. and Taylor, J. W., Stress dependence of dislocation,Phil. Mag., 20 (1969), 279–89.Google Scholar
  26. 26.
    Duan Z. P., The Constitutive Equation of Visco-Plastic Materials and One Dimensional Wave Theory, (to be published) Research Report (1979) Institute of Mechanics, Academia. Sinica.Google Scholar
  27. 27.
    Chen, P. J., Selected Topics in Wave Propagation, Noordhoff Int. Pub., Leyden (1976).Google Scholar
  28. 28.
    Herrmann, W. and Nunziato, J. W., Nonlinear constitutive equation,Dynamic Response of Materials to Instense Impulsive Loading, Ed. by Chou, P. C. and Hopkins, A. K. (1972).Google Scholar
  29. 29.
    Nunziato, J. W., Walsh, E. K., Schuler, K. W., and Barker, L. M., Wave propagation in nonlinear viscoelastic solids,Handbuch der Physik Vol. Vla/4 (1974).Google Scholar

Copyright information

© Techmodern Business Promotion Centre 1981

Authors and Affiliations

  • Duan Zhou-ping
    • 1
  1. 1.Institute of MechanicsAcademia SinicaBeijing

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