An equation of state of a carbon-fibre epoxy composite under shock loading

An anisotropic equation of state (EOS) is proposed for the accurate extrapolation of high-pressure shock Hugoniot (anisotropic and isotropic) states to other thermodynamic (anisotropic and isotropic) states for a shocked carbon-fibre epoxy composite (CFC) of any symmetry. The proposed EOS, using a generalised decomposition of a stress tensor [A.A. Lukyanov, Int. J. Plasticity 24, 140 (2008)], represents a mathematical and physical generalisation of the Mie-Grüneisen EOS for isotropic material and reduces to this equation in the limit of isotropy. Although a linear relation between the generalised anisotropic bulk shock velocity U_s ^A and particle velocity u_p was adequate in the through-thickness orientation, damage softening process produces discontinuities both in value and slope in the U_s ^A-u_p relation. Therefore, the two-wave structure (non-linear anisotropic and isotropic elastic waves) that accompanies damage softening process was proposed for describing CFC behaviour under shock loading. The linear relationship U_s ^A-u_p over the range of measurements corresponding to non-linear anisotropic elastic wave shows a value of c₀ ^A (the intercept of the U_s ^A-u_p curve) that is in the range between first and second generalised anisotropic bulk speed of sound [A.A. Lukyanov, Eur. Phys. J. B 64, 159 (2008)]. An analytical calculation showed that Hugoniot Stress Levels (HSLs) in different directions for a CFC composite subject to the two-wave structure (non-linear anisotropic elastic and isotropic elastic waves) agree with experimental measurements at low and at high shock intensities. The results are presented, discussed and future studies are outlined.     

利用多层阻抗梯度飞片产生准等熵压缩的理论解析

基于冲击波理论对多层阻抗梯度飞片击靶过程波系的相互作用做了理论分析，计算表明在多层阻抗梯度飞片的撞击下，样品的压缩线是一组通过不同初始状态点的冲击压缩线的连线, 它位于冲击压缩(hugoniot)线与等熵压缩线之间. 所以通过飞片层数的设计,可获得介于冲击压缩线与等熵线之间的任意状态点,这就为以后偏冲击压缩(off-hugoniot)状态方程的实验研究提供了理论参考. 实验测量的样品/窗口界面速度与理论计算的一致性支持上述结论的可靠性与准确性. 关键词： 准等熵压缩 多层阻抗梯度飞片 理论解析     

凝聚态物质状态方程的一个数值模型

建立了凝聚态物质的一个三项式状态方程：以Faussurier平均原子模型为基础计算电子热压和电子热能;以Cowan模型为基础计算离子热压和离子热能;用基于实验数据的半经验拟合公式计算物质的冷压和冷能。用实验数据检验了用平均原子模型计算的平均电离度。将状态方程与Hugoniot关系式相结合,计算了Be和Al的冲击绝热曲线,结果充分地展现出电子在高温、高密度条件下的壳层结构效应。     

一种适用于各向异性材料的修正PUFF物态方程

给出一种适用于各向异性材料的修正PUFF物态方程,既能体现各向异性材料在压缩和膨胀过程中材料体积变化的非线性特征,又能反映材料的各向异性强度效应.以正交各向异性材料二维碰撞问题和X射线辐照下的二维热击波为例,利用有限元方法编写程序进行数值模拟,对根据传统PUFF物态方程和修正PUFF物态方程计算得到的平均正应力值作对比研究,结果表明,低压和拉伸状态下二者存在明显差异,在高压下二者趋于一致.     

Shock Hugoniot calculations and melting in Pb

Shock Hugoniot calculations are carried out for lead (Pb) using both solid and liquid state theories. The Hugoniots in solid and liquid cases are in mutual agreement within the experimental uncertainties. However, the shock temperatures are quite different as computed from solid and liquid state theories. This fact can perhaps be used to detect melting along the shock Hugoniot provided the shock temperatures are accurately measured.     

Convergence acceleration of molecular dynamics methods for shocked materials using velocity scaling

ABSTRACT

In this work, a convergence acceleration method applicable to extended system molecular dynamics techniques for shock simulations of materials is presented. The method uses velocity scaling to reduce the instantaneous value of the Rankine–Hugoniot conservation of energy constraint used in extended system molecular dynamics methods to more rapidly drive the system towards a converged Hugoniot state. When used in conjunction with the constant stress Hugoniostat method, the velocity scaled trajectories show faster convergence to the final Hugoniot state with little difference observed in the converged Hugoniot energy, pressure, volume and temperature. A derivation of the scale factor is presented and the performance of the technique is demonstrated using the boron carbide armour ceramic as a test material. It is shown that simulation of boron carbide Hugoniot states, from 5 to 20 GPa, using both a classical Tersoff potential and an ab initio density functional, are more rapidly convergent when the velocity scaling algorithm is applied. The accelerated convergence afforded by the current algorithm enables more rapid determination of Hugoniot states thus reducing the computational demand of such studies when using expensive ab initio or classical potentials.     

Molecular dynamics study of the micro-spallation

We present a complete molecular dynamics analysis of the micro-spallation, which corresponds to the various events following the reflexion on a free surface of a unsustained shock wave causing the melting of the material. In a first stage the various curves required for a purely thermodynamic analysis (Hugoniot, melting curve and isentropes) are calculated by the mean of both equilibrium and non equilibrium molecular dynamics. Next we define two cases. In the first one the shock pressure is above the melting pressure (SM case). In the second one the melting occurs during the release wave following the shock (RM case). These two configurations provide quite similar results if the melting kinetic of the SM case is slow enough and we observe the formation of a solid micro-spall. In the other SM cases a direct transition from a liquid to a gas is obtained. As other results we found that (i) the melting under shock is a stationary process in the front shock referential and so is supported by the Rayleigh line and (ii) the spall strength of the micro-spallation is negligible.     

Efficient determination of Hugoniot states using classical molecular simulation techniques

We present a methodology for the efficient calculation of the shock Hugoniot using standard molecular simulation techniques. The method is an extension of an equation of state methodology proposed by Erpenbeck [1992, Phys. Rev. A, 46, 6406] and is considered as an alternative to other methods that generate Hugoniot properties. We illustrate the methodology for shocked liquid N₂ using two different simulation methods: (a) the reactive Monte Carlo method for a reactive system; and (b) the molecular dynamics method for a non-reactive system. The method is shown to be accurate, stable and generally independent of the algorithm parameters. We find excellent agreement with results calculated by other previous simulation studies. The results show that the methodology provides a simulation tool capable of determining points on the shock Hugoniot from a single simulation in an efficient, straightforward manner. Further applications and extensions of the method are briefly discussed.     

动高压下拉格朗日声速的测定及其应用

 通过实时记录冲击加载—再加载和冲击加载—卸载波的粒子速度剖面,得到了再加载和卸载波在93W合金中传播的拉格朗日声速。通过拉格朗日声速从准弹性到纯塑性的转化,获得了材料在一次冲击终态时的剪应力、剪切模量以及考虑了剪应力修正后的93W合金的冲击绝热关系。     

Orientation and Rate Dependence of Wave Propagation in Shocked Beta-SiC from Atomistic Simulations

The orientation dependence of planar wave propagation in beta-SiC is studied via the molecular dynamics （MD） method. Simulations are implemented under impact loadings in four main crystal directions, i.e., （lO0）, （llO）, 〈111〉, and 〈112}. The dispersion of stress states in different directions increases with rising impact velocity, which implies the anisotropic characteristic of shock wave propagation for beta-SiC materials. We also obtain the Hugoniot relations between the shock wave velocity and the impact velocity, and find that the shock velocity falls into a plateau above a threshold of impact velocity. The shock velocity of the plateaux is dependent on the shock directions, while 〈111} and 〈112/ can be regarded as equivalent directions as they almost reach the same plateau. A comparison between the atomic stress from MD and the stress from Rankine-Hugoniot jump conditions is also made, and it is found that they agree with each other very well.     

Second Hugoniot relationship for solids

The term second Hugoniot is used to describe a locus of states directly attainable by shock compression beginning with an initial state that has itself been achieved by shock compression. For many materials the principal Hugoniot is linear in the shock velocity-particle velocity [U_s — u_p] representation. A second Hugoniot for such materials is not linear in this representation, but the nonlinear effects can often be neglected if the compressions are not too great. These results are based on the Mie-Grüneisen equation of state and are more or less independent of the explicit functional dependence of the Grüneisen parameter. A criterion to evaluate the magnitude of nonlinear effects is posed and Mg and Pb are treated as examples. Calculated second Hugoniots are compared with experimental results for regular reflection in Mg, Pb and U. For these materials nonlinear effects are not important from a practical standpoint for final volumetric compressions to roughly two-thirds of the initial volume. Some future experimental work is also suggested.     

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利用能够体现电子壳层结构效应的三项式状态方程,结合Hugoniot关系式,对Al和Ag的冲击压强和冲击温度进行计算,将结果与实验数据和其他代码计算的结果进行比对。然后对Be、Al、Fe、Ag、Au和Pb金属材料沿Hugoniot曲线上的压强、温度、平均电离度、Fermi简并因子和有效绝热指数进行系统地研究,并给出细致的物理分析。最后总结这些特征物理量随质量密度压缩比变化的一般趋势。     

Gold under high pressure

Abstract

First principle predictions for the equation of state of gold using solid and liquid state theories are compared up to combined pressures and temperatures of 600 GPa and 17 000 K with static diamond anvil cell compression, ultrasonic measurements and shock Hugoniot data which include a recent laser driven shock Hugoniot points at 600 GPa. Excellent agreement between theoretical and experimental data is observed. The theoretically estimated 300 K isotherm agrees to within 2 GPa with the isotherm that has been measured to 70 GPa using the diamond anvil cell. The structural energy estimates show that the normal f.c.c. phase remains stable under pressure. The estimate of the shock Hugoniot temperature of gold at 600 GPa based on a liquid state model is consistent with the measurements of laser induced shock luminescence, which in fact provides an experimental determination of the temperature of gold above its Hugoniot melting point. The powerful means provided by theory in the prediction of material properties of gold at ultra high pressures and temperatures is significant because gold is an efficient converter of laser energy into soft X-rays and is a potential candidate as a standard for high pressure, high temperature work.     

C30混凝土冲击绝热关系和Grüneisen型状态方程的实验研究

采用一级气炮加载技术和锰铜压力计测试技术,对含初始空隙的C30混凝土在一维应变条件下的冲击特性进行了实验测量和分析.基于锰铜压力计测量的压力波形,确定了C30混凝土材料的冲击绝热关系,即冲击波速度D与波后粒子速度u之间满足线性关系.再从C30混凝土的冲击绝热数据出发,获得了计及初始空隙度₀影响的多项式形式Grüneisen型状态方程中的各项系数.实测压力波形还显示：不同位置处的压力波形在迅速上升至峰值后均随时间逐渐衰减,而冲击波峰值又随传播 关键词： Grüneisen型状态方程 冲击绝热关系 混凝土     

冲击加载下Zr51Ti5Ni10Cu25Al9金属玻璃的塑性行为

进行了10—27 GPa应力范围内Zr₅₁Ti₅Ni₁₀Cu₂₅Al₉金属玻璃的平面冲击实验以研究其高压-高应变率加载下的塑性行为.由样品自由面粒子速度剖面的分析获得了冲击加载过程的轴向应力,并通过轴向应力与静水压线的比较获得剪应力.实验结果表明,尽管存在明显的松弛效应,但Zr基金属玻璃的Hugoniot弹性极限随着冲击应力的增加而增加.然而,塑性波阵面上的剪应力则显示先硬化而后软化现象,而且软化的幅度随冲击应力的增加而增加.冲击加载下Zr基金属玻璃的上述剪应力变化特征与分子动力学模拟结果比较一致,但与压剪实验结果和一维应力冲击实验结果明显不同.     

稠密氦气物态方程研究

用二级氢气炮作为冲击压缩加载工具和多通道瞬态辐射高温计作为主要测量系统,测量了冲击压缩氦气等离子体的光辐亮度历史（初始温度293K,初始压力为1.2MPa）。根据实测记录信号波形的有关特征量,计算得到了氦等离子体的Hugoniot物态方程（含冲击温度）。结果发现：实测Hugoniot物态方程可用Saha方程加Debye-Huckel修正物理模型解释。     

非理想性参数在0.9～2.1区的氩等离子体物态方程研究

采用平面冲击压缩方法产生密度和温度都均匀的氩等离子体,根据辐射高温计记录和飞片速度的测定,通过阻抗匹配方法确定了氩等离子体的Hugoniot物态方程,等离子体温度在1.5 eV～2.6 eV范围,压力在0.2～0.8 GPa之间.计算表明,Saha-Debye-Hückel模型不适用于描述该密度区域的氩等离子体.本文采用Gryaznov模型的计算结果,测量值和理论计算结果符合较好.     

A caloric equation of state of a condensed medium derived based on generalized Hugoniot curves

The caloric equation of state, which expresses the internal energy through the volume and pressure is required in analyzing and calculating shock-wave processes in reacting media. The present work develops a method for constructing such an equation for condensed media on the basis of generalized Hugoniot curves. Expressions approximating the dependence of the Grüneisen coefficient and pressure on the volume along the Hugoniot curve. Formulas for calculating detonation Hugoniot curves from the shock Hugoniot curve of the condensed reaction products. The expressions obtained can be applied to approximate calculations of shockwave processes (for example, gasless detonation) in reacting condensed media. If necessary, such calculations can be performed with the use of physical quantities from standard handbooks.     

Effect of radiation on compressibility of hot dense sodium and iron plasma using improved screened hydrogenic model with l splitting

High pressure investigations of matter involve the study of strong shock wave dynamics within the materials which gives rise to many thermal effects leading to dissociation of molecules, ionization of atoms, and radiation emission, etc.The response of materials experiencing a strong shock can be determined by its shock Hugoniot calculations which are frequently applied in numerical and experimental studies in inertial confinement fusion, laboratory astrophysical plasma,etc. These studies involve high energy density plasmas in which the radiation plays an important role in determining the energy deposition and maximum compressibility achieved by the shock within material. In this study, we present an investigation for the effect of radiation pressure on the maximum compressibility of the material using shock Hugoniot calculations. In shock Hugoniot calculations, an equation of state(EOS) is developed in which electronic contributions for EOS calculations are taken from an improved screened hydrogenic model with-l splitting(I-SHML) [High Energy Density Physics(2018) 26 48] under local thermodynamic equilibrium(LTE) conditions. The thermal ionic part calculations are adopted from the state of the art Cowan model while the cold ionic contributions are adopted from the scaled binding energy model. The Shock Hugoniot calculations are carried out for sodium and iron plasmas and our calculated results show excellent agreement with published results obtained by using either sophisticated self-consistent models or the first principle study.     

High dynamic pressures and applications in materials science

Abstract

The high dynamic pressure behaviour of materials is, for many years, of great interest either for scientific studies (equation of state, Hugoniot and off Hugoniot, phase transitions …) or for industrial applications (synthesis of new materials, hardening, welding, powder compaction, jet cutting…

These different aspects are presented and these capabilities certainly will be an important factor in the next future.