研究金属中激波构造与衰减的一个物理模型

段祝平

研究金属中激波构造与衰减的一个物理模型

段祝平

北京中国科学院力学研究所

计量
- 文章访问数: 1853
- HTML全文浏览量: 51
- PDF下载量: 616
- 被引次数: 0
出版历程
- 收稿日期: 1980-05-01
- 刊出日期: 1981-04-15

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

Duan Zhou-ping

Institute of Mechanics, Academia Sinica, Beijing

摘要

摘要: 本文给出了研究金属中激波构造与衰减的一个物理模型.为了建立高速形变下材料的本构方程和研究激波过渡带的构造,需要考虑二个独立的理论方面.首先,将比内能分解成弹性压缩能和弹性形变能,而将形变能作为弹性应变和熵的函数展开到三阶项,其中考虑了热与机械能的耦合效应.其次,从位错动力学角度建议了一个塑性松弛函数以便描述高温、高压下塑性流动的特性.另外,本文给出了一个常微分方程组用以计算定态激波过渡带中各状态变量的分布以及激波的厚度.倘若假定在激波上熵的跳跃可以忽略,并用Hugoniot压缩模量代替等熵压缩摸量,可以获得一个分析解.最后,本文还提出了求解平板对称碰撞中激波波头衰减的一个近似方法。

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.

HTML全文

参考文献(29)

[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).