Abstract
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.
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References
Rice, M. H., McQueen, R. G. and walsh, J. M.,Solid State Phys., 6 (1958), 1–63.
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).
Taylor, J. W., Dislocation dynamics and dynamic yielding,J. Appl. Phys., 36 (1965), 3146–50.
Gilman, J. J., Dislocation dynamics and the response of materials to impact,Appl. Mech Rev. 21 (1968), 767.
Gilman, J. J., Symp. Mechanical behavior of materials under dynamic loads, San Antonio, Texas (1967).
Johnson, J. N. and Barker, L. M., Dislocation and steady plastic wave profiles in 6061-T6 aluminum,J. Appl. Phys. 40 (1969), 4321.
Herrmann, W., Nonlinear stress waves in metals,Wave Propagation in Solids, Ed. by Miklowitz, J., ASME (1969).
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).
Lee, E. H., Elastic-plastic deformation at finite strain.J. Appl. Mech., 36 (1969), 1–6.
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).
Clifton, R. J., On the analysis of elastic/visco-plastic waves of finite uniaxial strain. Id., New York (1971).
Clifton R. J., Plastic waves: theory and experiment,Mechanics Today, 1, Ed. by Nemat-Nasser, S., Pergamon Press, Inc. (1972).
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.
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).
Herrmann, W., Some recent results in elastic-plastic wave propagation,Propagation of Shock Waves in Solids, Ed. by Varley E. ASME (1976).
Farren, W. S. and Taylor, G. I., The heat developed during plastic extension of metals,Proc. Roy. Soc. (London), A107 (1925), 422–51.
Quinney, H. and Taylor, G. I., The latent energy remaining in a metal after cold working,Proc. Roy. Soc. (London), A143 (1934), 307–26.
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).
Bridgman, P. W.,The Physics of High Pressure, Printed in Great Britain by Strangeways Press, Ltd., (1952).
Broberg, K. B.,Shock Waves in Elastic and Elastic-Plastic Media, Stockholm (1956).
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.
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.
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).
Lindholm, U. S., Mechanical properties at high rates of strain, Proc. Conf. on Mech. Prop. Mat. at High Rates of strain, (1974), Oxford.
Gillis, P. P., Gilman, J. J. and Taylor, J. W., Stress dependence of dislocation,Phil. Mag., 20 (1969), 279–89.
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.
Chen, P. J., Selected Topics in Wave Propagation, Noordhoff Int. Pub., Leyden (1976).
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).
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).
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Zhou-ping, D. A physical model of the structure and attenuation of shock waves in metals. Appl Math Mech 2, 155–182 (1981). https://doi.org/10.1007/BF01876776
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DOI: https://doi.org/10.1007/BF01876776