An equation of state for anisotropic solids under shock loading

An anisotropic equation of state is proposed for accurate extrapolation of high-pressure shock Hugoniot states to other thermodynamics states for shocked single crystals and polycrystalline alloys. The proposed equation of state represents mathematical and physical generalization of the Mie-Grüneisen equation of state for isotropic material and reduces to this equation in the limit of isotropy. Using an anisotropic nonlinear continuum framework and generalized decomposition of a stress tensor [Int. J. Plasticity 24, 140 (2008)], the shock waves propagation along arbitrary directions in anisotropic solids of any symmetry can be examined. The non-associated strength model includes the distortion effect of the yield surface which can be used to describe the anisotropic strength differential effect. A numerical calculation showed that the general pulse shape, Hugoniot Elastic Limits (HELs), and Hugoniot stress levels for aluminum alloy 7010-T6 agree with the experimental data. The results are presented and discussed, and future studies are outlined.     

Amorphization under shock loading

Abstract

The problem of crystalline to amorphous (c → a) phase transformation, in the context of shock loading, is analyzed. The studies under static pressures show that beyond the stability field of the ambient phase, an amorphous phase may be realized if the kinetic conditions are not favorable to the accessibility of equilibrium phase of higher coordination. The examination of shock results of some of these substances reveals that the so-called “mixed phase” region begins at the pressureswhich are same as that oc c → a transformation in the static experiments. Further the Hugoniot temperatures at these pressures are far lower than required for the realization of the high pressure crystalline phase. From these observations as well as from an understanding gained through static experiments, we infer that these materials amorphize under shock loading. The analysis indicates that the existence of hot-spots is not essential to the formation of diaplectic glass. Instead, it seems to emerge directly from the solid-solid phase transformation, adequately aided by favourable kinetic conditions.     

Mechanisms of deformation under shock loading

Mechanisms of deformation suggested as a means of describing the behavior of crystalline solids under shock loading are analyzed from the following standpoints: a history of the stressed state, experimental data on shock wave profiles, microstructural investigations, and a possible role of different defects. One of the most essential features of deformation under such extreme conditions is the possibility of shear generation in the dislocation-free regions. Computer modelling reveals some peculiarities of this process.     

冲击加载下铝的剪切模量

分别用Steinberg-Cochran-Guinan (SCG)模型、修正的SCG模型和有限应变理论对材料的剪切模量做了数值计算，并与一维平面应变加载下铝的实验结果进行了比较.结果表明，修正的SCG模型与实验结果较为符合.在10—80GPa的压力范围下，剪切模量随冲击压力的增加而逐渐增大，这是由于压力的影响占主要地位，发生了加工硬化.在80—125GPa的压力范围下，剪切模量随冲击压力的增大快速减小，这是因为温度的影响比较严重，发生了高温软化现象.剪切模量最终在冲击压力为125GPa处趋于零，这是由于在该压力点冲击熔化发生，剪切强度消失. 关键词： 剪切模量 Steinberg-Cochran-Guinan模型 有限应变理论 铝     

Superfluid equation of state of dilute composite bosons

We present an exact theory of the BEC-BCS crossover in the Bose-Einstein-condensate (BEC) regime, which treats explicitly dimers as made of two fermions. We apply our framework, at zero temperature, to the calculation of the equation of state. We find that, when expanding the chemical potential in powers of the density n up to the Lee-Huang-Yang order, proportional to n(3/2), the result is identical to the one of elementary bosons in terms of the dimer-dimer scattering length a(M), the composite nature of the dimers appearing only in the next order term proportional to n(2).     

静-动加载相结合的材料状态方程实验平台的研制

根据神光-Ⅱ第九路高功率激光加载的特点,对传统静高压金刚石压砧装置进行了改进和优化设计,研制出了适合高功率激光加载条件下材料宽域状态方程研究的新型静高压靶.在神光-Ⅱ高功率激光装置上建立了基于静高压金刚石压砧和动高压激光相结合的材料宽域状态方程研究平台.利用这一平台开展了超纯水的宽域状态方程实验探索,获得了较好的实验结果.     

冲击加载下孔洞贯通的微观机理研究

利用分子动力学方法计算模拟了沿〈100〉晶向冲击加载下单晶铜中双孔洞的贯通过程.发现孔洞周围发射剪切型位错环是孔洞塌缩和增长的原因.在拉伸阶段,孔洞首先分别独立增长,随后其周围塑性变形区开始交叠和相互作用,最后两个孔洞开始直接贯通.这种贯通模式和实验对延性材料中孔洞贯通过程的显微观察结果一致.对四种不同θ值（θ为两个孔洞中心连线与冲击加载方向之间的夹角）的模型分别进行了计算模拟,发现在相同的冲击加载强度下,θ＝0°和θ＝30°的孔洞之间没有相互贯通; 关键词： 纳米孔洞 分子动力学 冲击加载 贯通     

强激光加载下金属材料微喷回收诊断

金属材料在冲击载荷下的动态响应在许多民用工程、航空航天等领域都有重要的应用背景.而金属材料在冲击载荷下的微喷形成过程,包括微射流、碎裂以及微层裂的物理过程的研究中尚存在许多空白.介绍了国内首次在神光Ⅲ原型激光装置上开展的金属材料微喷回收实验,实现了激光加载下低密度泡沫材料对微喷颗粒的回收,对回收样品进行了X光CT分析,通过图像重建,获得了回收微喷颗粒的三维图像,以及颗粒不同形态分布、颗粒尺寸、颗粒质量等定量结果.     

Dynamic strength behavior of a Zr-based bulk metallic glass under shock loading

Dynamic strength behavior of Zr51Ti5Ni10Cu25Al9 bulk metallic glass(BMG) up to 66 GPa was investigated in a series of plate impact shock-release and shock-reload experiments.Particle velocity profiles measured at the sample/Li F window interface were used to estimate the shear stress,shear modulus,and yield stress in shocked BMG.Beyond confirming the previously reported strain-softening of shear stress during the shock loading process for BMGs,it is also shown that the softened Zr-BMG still has a high shear modulus and can support large yield stress when released or reloaded from the shocked state,and both the shear modulus and the yield stress appear as strain-hardening behaviors.The work provides a much clearer picture of the strength behavior of BMGs under shock loading,which is useful to comprehensively understand the plastic deformation mechanisms of BMGs.     

强激光加载下高压液氘材料的电导率

液氘在高压下有丰富的电学光学性质。利用反射率和相对介电函数关系并从广义极化角度出发初步建立了计算低Z材料电导率的简易模型;在神光-Ⅱ装置上利用第九路激光冲击加载液氘材料并测量了其在强激光冲击下的高压状态参数和反射率。结合上述理论模型和实验,研究了高压下液氘的电离度和电导率。结果表明,液氘在约70 GPa时的电导率约为2.87105 (Wm)-1,已呈现出较为明显的金属电导特性。显然,冲击加载下液氘从绝缘分子态开始电离并向金属氘转变发生在更低的压强。     

强激光加载下高压液氘材料的电导率

液氘在高压下有丰富的电学光学性质。利用反射率和相对介电函数关系并从广义极化角度出发初步建立了计算低Z材料电导率的简易模型;在神光-Ⅱ装置上利用第九路激光冲击加载液氘材料并测量了其在强激光冲击下的高压状态参数和反射率。结合上述理论模型和实验,研究了高压下液氘的电离度和电导率。结果表明,液氘在约70 GPa时的电导率约为2.87105 (Wm)-1,已呈现出较为明显的金属电导特性。显然,冲击加载下液氘从绝缘分子态开始电离并向金属氘转变发生在更低的压强。     

An equation of state for alkali metals

Semi-empirical equations of state based on Lindemann's law have been developed to determine the pressure (P) dependence of the melting temperature (T_m) of Li, K, Rb and Cs. The basic inputs are Grüneisen parameter and the bulk modulus. T_m–P variations exhibit maximum melting temperature with concave downwards. The maximum in T_m for Cs is found to occur at pressure of 2.2 GPa whereas for Li, K and Rb it falls in the range of 7–9.5 GPa. The predicted values of T_m as a function of pressure, based on the present empirical relation, fit quite well with the available experimental data. The empirical relation can also be used to extrapolate T_m at higher pressure from the values available at lower pressures.     

An isothermal equation of state for solids

An isothermal equation of state (EOS) for solids, recently suggested by the authors in the realistic form, V/V₀=f(P), with relative volume as the dependent and the pressure as the independent variable, was shown to have an advantage for some close-packed materials in that it allows B′_∞=(∂B_s/∂P)_s(P→∞) to be fitted, and this is where the usual standard equations fail. In the present study, our EOS is applied to a number of inorganic as well as organic solids, including alloys, glasses, rubbers and plastics; varying widely in their bonding and structural characteristics, as well as in their bulk modulus values. A very good agreement is observed between the data and fits. The results obtained are compared with those from two well-known equations, expressible in the realistic form, proposed by Murnaghan and Luban. Further, the results are also compared with those from the widely used two- and three-parameter EOSs, expressible in the unrealistic form only, P=f(V/V₀), proposed by Birch—and also with those from the EOS model of Keane in which B′_∞ is explicitly expressed as an equation of state parameter. The results obtained from our model compare well to these EOSs. Our EOS, in general, yields the smallest mean-squared deviations between data and fits. The values of B′_∞calculated from our EOS are compared with those from Keane's model. Further, we have studied the variation of B′_∞with temperature using the experimental isotherms of Mo and W at 10 different temperatures ranging from 100 to 1000 K, and observed that the values of B′_∞ yielded by our model and that of Keane vary, as expected, within a narrow range. Furthermore, our EOS is applied to study the stability of the fit parameters with variation in the pressure ranges with reference to the isothermal compression data on Mo and W—and also to study the variation of isothermal bulk modulus with pressure, with reference to the ultrasonic data on NaCl and noted a very good agreement with experiment. In addition, our model is applied, with B₀ and B′₀ constrained to the theoretical values, to the five theoretical isotherms of MgO at 300, 500, 1000, 1500 and 2000 K obtained on the basis of a first principles approach—a good agreement is observed with the predictions, and the values of B′_∞ inferred at different temperatures tend to converge to a constant value.     

混合物质高压状态方程的计算

介绍了在温度相同的条件下,混合物中各组元通过密度-压强迭代法,达到温度和压强平衡,再结合叠加原理,编程计算出混合物质状态方程。为验证该程序,对氘氚与氩按不同比例混合时的状态参量进行了分析。当氘氚中含少量氩时,计算得到的状态方程与纯氘氚符合较好;同样地,氩中含少量氘氚时的状态方程也与纯氩的很接近。这说明该程序是可行的。     

Criterion for existence of shock waves in relativistic magnetohydrodynamics with a general equation of state

Relativistic stationary shock waves in an ideal conducting fluid are studied for the general equation of state. We use small viscosity arguments to obtain a criterion that selects physically admissible shock transitions without any supposition about convexity of the Poisson adiabats. The relations between the magnetosound speeds and the speed of the shock obtained as a consequence of this criterion reveal specific differences between relativistic considerations versus classical ones.     

混合物质高压状态方程的计算

 介绍了在温度相同的条件下,混合物中各组元通过密度-压强迭代法,达到温度和压强平衡,再结合叠加原理,编程计算出混合物质状态方程。为验证该程序,对氘氚与氩按不同比例混合时的状态参量进行了分析。当氘氚中含少量氩时,计算得到的状态方程与纯氘氚符合较好;同样地,氩中含少量氘氚时的状态方程也与纯氩的很接近。这说明该程序是可行的。     

An invariant solution of the Fokker-Planck equation and rheological equation of state of a macromolecular solution

The Fokker-Planck equation is solved for a soft dumbbell in a homogeneous hydrodynamic field invariantly with respect to rheonomous transformations. The equation of state for a soft dumbbell with relaxation time has the form:P ^ab + ^–1 P ^ab =1/2kTG ^ab .P ^ab is the convected derivative of the stress tensorP ^ab andG ^ab the metric tensor. For a more general model-network composed of Hookean springs with constant hydrodynamic interaction (e.g. a model of Gaussian sub-chains) we obtain the equation of state by combining the contributions of the above-mentioned type. Such an equation of state describes linear visco-elastic behaviour with general spectrum of the relaxation times. If convected derivation with respect to time is used in the calculation, the viscosity is Newtonian even if the calculation is performed in a coordinate system rotating with the molecule.     

An equation of state of the Ising systems

In the framework of the spin operators diagram technique the method of taking into account the correlation effects in magnetic system based on the idea of $\text{1}\text{z}$ expansion (z is the number of the nearest neighbours) is proposed. An equation of state of 3-dimensional Ising systems with the arbitrary spin values S in the first order in $\text{1}\text{z}$ is presented which considerably improves the mean field theory (being the zeroth order approximation). For various lattices the calculated values of Tc coinside within 1% with the results of the high-temperature expansions.     

An equation of state for alkali halide crystals

Nonparametric equations of state are obtained for NaBr, KBr, RbCl, and RbBr crystals with B1 and B2 lattices over a wide pressure range. Binding energy, lattice parameters, and free crystal compressibility are calculated together with phase-transition pressures and volume change on transition from B1 to B2 lattice. Calculated results agree well with experimental data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 101–105, January. 1976.