A Physical Model of the Structure and Attenuation of Shock Waves in Metals

Duan Zhou-ping

Volume 2 Issue 2

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1981 > 2(2): 145-165

Duan Zhou-ping. A Physical Model of the Structure and Attenuation of Shock Waves in Metals[J]. Applied Mathematics and Mechanics, 1981, 2(2): 145-165.

Citation:

Duan Zhou-ping. A Physical Model of the Structure and Attenuation of Shock Waves in Metals[J]. Applied Mathematics and Mechanics, 1981, 2(2): 145-165.

Citation:

Duan Zhou-ping. A Physical Model of the Structure and Attenuation of Shock Waves in Metals[J]. Applied Mathematics and Mechanics, 1981, 2(2): 145-165.

PDF( 1316 KB)

A Physical Model of the Structure and Attenuation of Shock Waves in Metals

Duan Zhou-ping

Institute of Mechanics, Academia Sinica, Beijing

Received Date: 1980-05-01
Publish Date: 1981-04-15

Abstract

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 Hugo-niot 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.

FullText(HTML)

References(29)

References

[1]	Rice,M.H.,McQueen,R.G.and walsh,J.M.,Solid State Phys.,6(1958),1-63.
[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).
[3]	Taylor,J.W.,Dislocation dynamics and dynamic yielding,J.Appl.Phys.,36(1965),3146-50.
[4]	Gilman,J,J.,Dislocation dynamics and the response of materials to impact,Appl.Mech Rev.21(1968),767.
[5]	Gilman,J.J.,Symp.Mechanical behavior of materials under dynamic loads,San Antonio,Texas(1967).
[6]	Johnson,J.N.and Barker,L.M.,Dislocation and steady plastic wave profiles in 6061-T6aluminum,J.Appl.Phys.40(1969),4321.
[7]	Herrmann,W.,Nonlinear stress waves in metals,Wave Propagation in Solids,Ed.by Miklowitz,J.,ASME(1969).
[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).
[9]	Lee,E.H.,Elastic-plastic deformation at finite strain.J.Appl.Mech.,36(1969),1-6.
[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).
[11]	Clifton,R.J.,On the analysis of elastic/visco-plastic waves of finite uniaxial strain.Id.,New York(1971).
[12]	Clifton R.J.,Plastic waves:theory and experiment,Mechanics Today,1,Ed.by Nemat-Nasser,S.,Pergamon Press,Inc.(1972).
[13]	范良藻,段祝平,固体中的激波构造,力学2 (1976) 103-109,科学出版社.
[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).
[15]	Herrmann,W.,Some recent results in elastic-plastic wave propagation.Propagation of Shock Waves in Solids,Ed.by Varley E.ASME(1976).
[16]	Farren,W.S.and Taylor,G.I.,The heat developed during plastic extension of metals,Proc.Roy.Soc.(London),A107(1925),422-51.
[17]	Quinney,H.and Taylor,G.I.,The latent energy remaining in a metal after co1d working,Proc.Roy.Soc.(London),A143(1934),307-26.
[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).
[19]	Bridgman,P.W.,The Physics of High Pressure,Printed in Great Britain by Strangeways Press,Ltd.(1952).
[20]	Broberg.K.B.Shock Waves in Elastic and Elastic-Plastic Media,Stockholm(1956).
[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.
[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.
[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).
[24]	Lindholm,U.S.,Mechanical properties at high rates of strain,Proc.Conf.on Mech.Prop.Mat.at High Rates of strain.(1974),Oxford.
[25]	Gillis,P.P.,Gilman,J.J.and Taylor,J.W.,Stress dependence of dislocation,Phil.Mag.,20(1969),279-89.
[26]	段祝平粘塑性材料的本构方程与一维波理论,中国科学院,力学所研究报告(1976)的待发表
[27]	Chen,P.J.Selected Topics in Wave Propagation,Noordhoff Int.Pub.,Leyden(1976).
[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).
[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).

Relative Articles

[1]	K.S.Erduran. An Integrated Numerical Model for Vegetated Surface and Saturated Subsurface Flow Interaction[J]. Applied Mathematics and Mechanics, 2012, 33(7): 828-844. doi: 10.3879/j.issn.1000-0887.2012.07.004
[2]	SUN Zhen-xu, ZHAO Xiao-li, SONG Jing-jing, DU Te-zhuan. Numerical Investigation on a Transition Prediction Model[J]. Applied Mathematics and Mechanics, 2009, 30(12): 1463-1472. doi: 10.3879/j.issn.1000-0887.2009.12.007
[3]	WANG Ping, TANG Shao-qiang. Numerical Study of Dynamic Phase Transitions in Shock Tube[J]. Applied Mathematics and Mechanics, 2007, 28(7): 824-832.
[4]	ZHANG Ding-guo, XIAO Jian-qiang. A Dynamic Model for Rocket Launcher With Coupled Rigid and Flexible Motion[J]. Applied Mathematics and Mechanics, 2005, 26(5): 561-568.
[5]	ZHU Yi-guo, LÜ He-xiang, YANG Da-zhi. A New Model of Shape Memory Alloys[J]. Applied Mathematics and Mechanics, 2002, 23(9): 896-902.
[6]	LI Shu, ZHANG Fang, WANG Bo, ZHANG Xiao-gu. Proper Application of a Kind of Matrix Construction Method in Physical Parameter Identification of Dynamic Model[J]. Applied Mathematics and Mechanics, 2002, 23(5): 541-547.
[7]	Yan Zhenya, Zhang Hongqing. On a New Algorithm of Constructing Solitary Wave Solutions for Systems of Nonlinear Evolution Equations in mathematical Physics[J]. Applied Mathematics and Mechanics, 2000, 21(4): 342-347.
[8]	Zhu Yong. Numerical Study of a Nonlinear Integro-Differential Equation[J]. Applied Mathematics and Mechanics, 1998, 19(11): 980-985.
[9]	Dai Shiqiang, Zang Hongming. A Semi-Inverse Algorithm in Application of Computer Algebra[J]. Applied Mathematics and Mechanics, 1997, 18(2): 105-111.
[10]	Wu Qing-son, Zhu Hong, Xu Yan-hou, Wang Bo-yi. Numerlcal Study of Shock Diffraction in Dusty Gases[J]. Applied Mathematics and Mechanics, 1995, 16(1): 73-79.
[11]	Jin Jun. On the Stability of the Solution to a Gonorrhea Discrete Mathematical Model[J]. Applied Mathematics and Mechanics, 1994, 15(6): 513-518.
[12]	Luo Ji-sheng, Zhou Heng. A Theoretical Model ol the Coherent Structure in the Wall Region of a Turbulent Boundary Layer[J]. Applied Mathematics and Mechanics, 1993, 14(11): 939-947.
[13]	Zhu Yong. Head-on Collision between Two mKdV Solitary Waves in a Two-Layer Fluid System[J]. Applied Mathematics and Mechanics, 1992, 13(5): 389-399.
[14]	Xu Li-gong. The Interaction of a Shock Wave with the Boundary Layer in a Reflected Shock Tunnel[J]. Applied Mathematics and Mechanics, 1989, 10(6): 523-529.
[15]	Hu De-sui. An Application of Ungar’s Differential Transform to Elastodynamics[J]. Applied Mathematics and Mechanics, 1989, 10(7): 645-648.
[16]	Tan Fu-qi. A Simplified Method for the Construction of the Cubic Spline Function[J]. Applied Mathematics and Mechanics, 1985, 6(6): 567-572.
[17]	Liu Cheng-qun. Note on the Critical Variational State in Elasticity Theory[J]. Applied Mathematics and Mechanics, 1984, 5(6): 895-901.
[18]	Z.J. Luo, C. R. Tang, B. Avitzur, C. J. Van Tyne. A Model for Simulation of Friction Phenomenon between Dies and Workpiece[J]. Applied Mathematics and Mechanics, 1984, 5(3): 323-335.
[19]	Ouyang Chang, Lu Mei-zi. On a Micromechanical Model for Cracked Reinforced Composites[J]. Applied Mathematics and Mechanics, 1981, 2(3): 273-280.
[20]	Hu Hai-chang. On An Eigenvalue Problem Related to the Buckling of Sandwich Beams[J]. Applied Mathematics and Mechanics, 1980, 1(1): 55-62.