韧性材料裂纹尖端孔洞群体损伤演化的实验和模拟

长期以来，材料的孔洞损伤一直是力学家和材料学家所关注的焦点之一，相应的研究方法很多，所得到的成果也很丰富。但是这些研究大部分是基于单个孔洞或有限个孔洞来考虑的，很少将大量的孔洞损伤作为整体来探讨。本文就是考虑到在韧性金属合金材料的破坏和失效过程中，往往是有大量的孔洞损伤参与其中的。我们试图将这些作为整体来考虑，并着重对初始裂纹钝化扩展过程的裂尖前沿来进行研究和讨论。本文从微孔洞数密度守恒方程出发，讨论了裂尖前沿孔洞损伤数密度群体化的方程以及它的解，探讨了损伤各阶矩的分布形式和演化规律。并且对一个系列低碳合金钢样品的I型初始裂纹的钝化扩展和断口孔洞的观察和统计的结果与计算模拟的结果进行了比较，得到了相同的趋势。计算模拟和试验的结果表明，在裂尖前沿孔洞损伤的群体演化过程中，损伤矩的分布是随着离开裂尖距离增加而减少的，并且这种分布随时间增加而且增加，并且趋于稳定分布。最后根据实验中反映出来的由于材料内部的不均匀等造成的孔洞损伤演化的不均匀性，引入随机涨落的概念导出局域孔洞数密度演化守恒方程来探讨这种不均匀性，通过模拟计算得到平均场理论和局域孔洞数密度守恒理论的差异，并由全场孔洞数密度演化守恒方程的分析来证实这个差异。

An analysis on overall crack-number-density of short-fatigue-cracks

The evolution of dispersed short-fatigue-cracks is analysed based on the equilibrium of crack-number-density (CND). By separating the mean value and the stochastic fluctuation of local CND, the equilibrium equation of overall CND is derived. Comparing with the mean-field equilibrium equation, the equilibrium equation of overall CND has different forms in the expression of crack-nucleation-rate or crack-growth-rate. The simulation results are compared with experimental measurements showing the stochastic analyses provide consistent tendency with experiments. The discrepancy in simulation results between overall CND and mean-field CND is discussed.

Short-term variability of solar wind number density, speed and dynamic pressure as a function of the interplanetary magnetic field components: A survey over two solar cycles

The variability of hourly values of solar wind number density, number density variation, speed, speed variation and dynamic pressure with IMF Bz and magnitude |B| has been examined for the period 1965–1986. We wish to draw attention to a strong correlation in number density and number density fluctuation with IMF Bz characterised by a symmetric increasing trend in these quantities away from Bz = 0 nT. The fluctuation level in solar wind speed is found to be relatively independent of Bz. We infer that number density and number density variability dominate in controlling solar wind dynamic pressure and dynamic pressure variability. It is also found that dynamic pressure is correlated with each component of IMF and that there is evidence of morphological differences between the variation with each component. Finally, we examine the variation of number density, speed, dynamic pressure and fluctuation level in number density and speed with IMF magnitude |B|. Again we find that number density variation dominates over solar wind speed in controlling dynamic pressure.

Effects of stochastic extension in ideal microcrack system

The effects of stochastic extension on the statistical evolution of the ideal microcrack system are discussed. First, a general theoretical formulation and an expression for the transition probability of extension process are presented, then the features of evolution in stochastic model are demonstrated by several numerical results and compared with that in deterministic model.

Evolution and propagation of density waves on galactic disk .1. General evolution equation of wavelet and discussion of its solution

This paper presents a general self-consistent theory of evolution and propagation of wavelets on the galactic disk. A simplified model for this theory, i. e. the thin transition-layer approximation is proposed.There are three types of solutions to the basic equation governing the evolution of wavelets on the disk: (ⅰ) normal propagating type; (ⅱ) swing type; (ⅲ) general evolving type. The results show that the first two types are applicable to a certain domain on the galactic disk and a certain region of the wave number of wavelets. The third is needed to join the other two types and to yield a coherent total picture of the wave motion. From the present theory, it can be seen that the well-known "swing theory" of the G-L sheet model holds only for a certain class of basic states of galaxies.

I. The structure and properties of closed circular duplex DNA. II. Chemically interacting systems at equilibrium in a buoyant density gradient

I. The binding of the intercalating dye ethidium bromide to closed circular SV 40 DNA causes an unwinding of the duplex structure and a simultaneous and quantitatively equivalent unwinding of the superhelices. The buoyant densities and sedimentation velocities of both intact (I) and singly nicked (II) SV 40 DNAs were measured as a function of free dye concentration. The buoyant density data were used to determine the binding isotherms over a dye concentration range extending from 0 to 600 µg/m1 in 5.8 M CsCl. At high dye concentrations all of the binding sites in II, but not in I, are saturated. At free dye concentrations less than 5.4 µg/ml, I has a greater affinity for dye than II. At a critical amount of dye bound I and II have equal affinities, and at higher dye concentration I has a lower affinity than II. The number of superhelical turns, τ, present in I is calculated at each dye concentration using Fuller and Waring's (1964) estimate of the angle of duplex unwinding per intercalation. The results reveal that SV 40 DNA I contains about -13 superhelical turns in concentrated salt solutions.

The free energy of superhelix formation is calculated as a function of τ from a consideration of the effect of the superhelical turns upon the binding isotherm of ethidium bromide to SV 40 DNA I. The value of the free energy is about 100 kcal/mole DNA in the native molecule. The free energy estimates are used to calculate the pitch and radius of the superhelix as a function of the number of superhelical turns. The pitch and radius of the native I superhelix are 430 Å and 135 Å, respectively.

A buoyant density method for the isolation and detection of closed circular DNA is described. The method is based upon the reduced binding of the intercalating dye, ethidium bromide, by closed circular DNA. In an application of this method it is found that HeLa cells contain in addition to closed circular mitochondrial DNA of mean length 4.81 microns, a heterogeneous group of smaller DNA molecules which vary in size from 0.2 to 3.5 microns and a paucidisperse group of multiples of the mitochondrial length.

II. The general theory is presented for the sedimentation equilibrium of a macromolecule in a concentrated binary solvent in the presence of an additional reacting small molecule. Equations are derived for the calculation of the buoyant density of the complex and for the determination of the binding isotherm of the reagent to the macrospecies. The standard buoyant density, a thermodynamic function, is defined and the density gradients which characterize the four component system are derived. The theory is applied to the specific cases of the binding of ethidium bromide to SV 40 DNA and of the binding of mercury and silver to DNA.

A New theory for evaluating the number density of inclusions in films

A new formulation derived from thermal characters of inclusions and host films for estimating laser induced damage threshold has been deduced. This formulation is applicable for dielectric films when they are irradiated by laser beam with pulse width longer than tens picoseconds. This formulation can interpret the relationship between pulse-width and damage threshold energy density of laser pulse obtained experimentally. Using this formulation, we can analyze which kind of inclusion is the most harmful inclusion. Combining it with fractal distribution of inclusions, we have obtained an equation which describes relationship between number density of inclusions and damage probability. Using this equation, according to damage probability and corresponding laser energy density, we can evaluate the number density and distribution in size dimension of the most harmful inclusions. (c) 2005 Elsevier B.V. All rights reserved.

Application of density functional theory to equilibrium adsorption of argon and nitrogen on amorphous silica surface

We present a new version of non-local density functional theory (NL-DFT) adapted to description of vapor adsorption isotherms on amorphous materials like non-porous silica. The novel feature of this approach is that it accounts for the roughness of adsorbent surface. The solid–fluid interaction is described in the same framework as in the case of fluid–fluid interactions, using the Weeks–Chandler–Andersen (WCA) scheme and the Carnahan–Starling (CS) equation for attractive and repulsive parts of the Helmholtz free energy, respectively. Application to nitrogen and argon adsorption isotherms on non-porous silica LiChrospher Si-1000 at their boiling points, recently published by Jaroniec and co-workers, has shown an excellent correlative ability of our approach over the complete range of pressures, which suggests that the surface roughness is mostly the reason for the observed behavior of adsorption isotherms. From the analysis of these data, we found that in the case of nitrogen adsorption short-range interactions between oxygen atoms on the silica surface and quadrupole of nitrogen molecules play an important role. The approach presented in this paper may be further used in quantitative analysis of adsorption and desorption isotherms in cylindrical pores such as MCM-41 and carbon nanotubes.

Liquid silicate equation of state : using shock waves to understand the properties of the deep Earth

The equations of state (EOS) of several geologically important silicate liquids have been constrained via preheated shock wave techniques. Results on molten Fe₂SiO₄ (fayalite), Mg₂SiO₄ (forsterite), CaFeSi₂O₆ (hedenbergite), an equimolar mixture of CaAl₂Si₂O₈-CaFeSi₂O₆ (anorthite-hedenbergite), and an equimolar mixture of CaAl₂Si₂O₈-CaFeSi₂O₆-CaMgSi₂O₆(anorthite-hedenbergite-diopside) are presented. This work represents the first ever direct EOS measurements of an iron-bearing liquid or of a forsterite liquid at pressures relevant to the deep Earth (> 135 GPa). Additionally, revised EOS for molten CaMgSi₂O₆ (diopside), CaAl₂Si₂O₈ (anorthite), and MgSiO₃ (enstatite), which were previously determined by shock wave methods, are also presented.

The liquid EOS are incorporated into a model, which employs linear mixing of volumes to determine the density of compositionally intermediate liquids in the CaO-MgO-Al₂O₃-SiO₂-FeO major element space. Liquid volumes are calculated for temperature and pressure conditions that are currently present at the core-mantle boundary or that may have occurred during differentiation of a fully molten mantle magma ocean.

The most significant implications of our results include: (1) a magma ocean of either chondrite or peridotite composition is less dense than its first crystallizing solid, which is not conducive to the formation of a basal mantle magma ocean, (2) the ambient mantle cannot produce a partial melt and an equilibrium residue sufficiently dense to form an ultralow velocity zone mush, and (3) due to the compositional dependence of Fe2+ coordination, there is a threshold of Fe concentration (molar X_Fe ≤ 0.06) permitted in a liquid for which its density can still be approximated by linear mixing of end-member volumes.

High pressure states in condensed matter: I. High pressure behavior of the iron-sulphur system with applications to the earth's core. II. Empirical equation of state for organic compounds at high pressures

Part I:

The earth's core is generally accepted to be composed primarily of iron, with an admixture of other elements. Because the outer core is observed not to transmit shear waves at seismic frequencies, it is known to be liquid or primarily liquid. A new equation of state is presented for liquid iron, in the form of parameters for the 4th order Birch-Murnaghan and Mie-Grüneisen equations of state. The parameters were constrained by a set of values for numerous properties compiled from the literature. A detailed theoretical model is used to constrain the P-T behavior of the heat capacity, based on recent advances in the understanding of the interatomic potentials for transition metals. At the reference pressure of 10⁵ Pa and temperature of 1811 K (the normal melting point of Fe), the parameters are: ρ = 7037 kg/m³, K_S0 = 110 GPa, K_S' = 4.53, K_S" = -.0337 GPa-1, and γ = 2.8, with γ α ρ^-1.17. Comparison of the properties predicted by this model with the earth model PREM indicates that the outer core is 8 to 10 % less dense than pure liquid Fe at the same conditions. The inner core is also found to be 3 to 5% less dense than pure liquid Fe, supporting the idea of a partially molten inner core. The density deficit of the outer core implies that the elements dissolved in the liquid Fe are predominantly of lower atomic weight than Fe. Of the candidate light elements favored by researchers, only sulfur readily dissolves into Fe at low pressure, which means that this element was almost certainly concentrated in the core at early times. New melting data are presented for FeS and FeS₂ which indicate that the FeS₂ is the S-hearing liquidus solid phase at inner core pressures. Consideration of the requirement that the inner core boundary be observable by seismological means and the freezing behavior of solutions leads to the possibility that the outer core may contain a significant fraction of solid material. It is found that convection in the outer core is not hindered if the solid particles are entrained in the fluid flow. This model for a core of Fe and S admits temperatures in the range 3450K to 4200K at the top of the core. An all liquid Fe-S outer core would require a temperature of about 4900 K at the top of the core.

Part II.

The abundance of uses for organic compounds in the modern world results in many applications in which these materials are subjected to high pressures. This leads to the desire to be able to describe the behavior of these materials under such conditions. Unfortunately, the number of compounds is much greater than the number of experimental data available for many of the important properties. In the past, one approach that has worked well is the calculation of appropriate properties by summing the contributions from the organic functional groups making up molecules of the compounds in question. A new set of group contributions for the molar volume, volume thermal expansivity, heat capacity, and the Rao function is presented for functional groups containing C, H, and O. This set is, in most cases, limited in application to low molecular liquids. A new technique for the calculation of the pressure derivative of the bulk modulus is also presented. Comparison with data indicates that the presented technique works very well for most low molecular hydrocarbon liquids and somewhat less well for oxygen-bearing compounds. A similar comparison of previous results for polymers indicates that the existing tabulations of group contributions for this class of materials is in need of revision. There is also evidence that the Rao function contributions for polymers and low molecular compounds are somewhat different.

Calculating the equation of state parameters and predicting the spinodal curve of isotactic polypropylene/poly(ethylene-co-octene) blend by molecular dynamics simulations combined with Sanchez-Lacombe lattice fluid theory

Molecular dynamics simulations are adopted to calculate the equation of state characteristic parameters P*, rho*, and T* of isotactic polypropylene (iPP) and poly(ethylene-co-octene) (PEOC), which can be further used in the Sanchez-Lacombe lattice fluid theory (SLLFT) to describe the respective physical properties. The calculated T* is a function of the temperature, which was also found in the literature. To solve this problem, we propose a Boltzmann fitting of the data and obtain T* at the high-temperature limit. With these characteristic parameters, the pressure-volume-temperature (PVT) data of iPP and PEOC are predicted by the SLLFT equation of state. To justify the correctness of our results, we also obtain the PVT data for iPP and PEOC by experiments. Good agreement is found between the two sets of data. By integrating the Euler-Lagrange equation and the Cahn-Hilliard relation, we predict the density profiles and the surface tensions for iPP and PEOC, respectively. Furthermore, a recursive method is proposed to obtain the characteristic interaction energy parameter between iPP and PEOC. This method, which does not require fitting to the experimental phase equilibrium data, suggests an alternative way to predict the phase diagrams that are not easily obtained in experiments.

Density functional and Monte Carlo studies of sulfur. II. Equilibrium polymerization of the liquid phase

The equilibrium polymerization of sulfur is investigated by Monte Carlo simulations. The potential energy model is based on density functional results for the cohesive energy, structural, and vibrational properties as well as reactivity of sulfur rings and chains [Part I, J. Chem. Phys. 118, 9257 (2003)]. Liquid samples of 2048 atoms are simulated at temperatures 450less than or equal toTless than or equal to850 K and P=0 starting from monodisperse S-8 molecular compositions. Thermally activated bond breaking processes lead to an equilibrium population of unsaturated atoms that can change the local pattern of covalent bonds and allow the system to approach equilibrium. The concentration of unsaturated atoms and the kinetics of bond interchanges is determined by the energy DeltaE(b) required to break a covalent bond. Equilibrium with respect to the bond distribution is achieved for 15less than or equal toDeltaE(b)less than or equal to21 kcal/mol over a wide temperature range (Tgreater than or equal to450 K), within which polymerization occurs readily, with entropy from the bond distribution overcompensating the increase in enthalpy. There is a maximum in the polymerized fraction at temperature T-max that depends on DeltaE(b). This fraction decreases at higher temperature because broken bonds and short chains proliferate and, for Tless than or equal toT(max), because entropy is less important than enthalpy. The molecular size distribution is described well by a Zimm-Schulz function, plus an isolated peak for S-8. Large molecules are almost exclusively open chains. Rings tend to have fewer than 24 atoms, and only S-8 is present in significant concentrations at all T. The T dependence of the density and the dependence of polymerization fraction and degree on DeltaE(b) give estimates of the polymerization temperature T-f=450+/-20 K. (C) 2003 American Institute of Physics.

Equilibrium polymerization of cyclic carbonate oligomers. II. Role of multiple active sites

Ring opening polymerization of bisphenol A polycarbonate is studied by Monte Carlo simulations of a model comprising a fixed number of Lennard-Jones particles and harmonic bonds [J. Chem. Phys. 115, 3895 (2001)]. Bond interchanges produced by a low concentration (0.10%less than or equal toc(a)less than or equal to0.36%) of chemically active particles lead to equilibrium polymerization. There is a continuous transition in both 2D and 3D from unpolymerized cyclic oligomers at low density to a system of linear chains at high density, and the polymeric phase is much more stable in three dimensions than in two. The steepness of the polymerization transition increases rapidly as c(a) decreases, suggesting that it is discontinuous in the limit c(a)-->0. The transition is entropy driven, since the average potential energy increases systematically upon polymerization, and there is a steady decline in the degree of polymerization as the temperature is lowered. The mass distribution functions for open chains and for rings are unimodal, with exponentially decaying tails that can be fitted by Zimm-Schulz functions and simpler exponential forms. (C) 2002 American Institute of Physics.