Rheology of molecular liquids and concentrated suspensions by microscopic dynamical simulations

The rheology and the associated changes that arise in sheared molecular and colloidal liquids are investigated by Molecular and Brownian Dynamics Computer Simulation. Significant shear thinning and normal pressure effects occur in all liquids when the shear rate approximately equals an inverse characteristic relaxation time for the material. The shear and bulk moduli, and self-diffusion coefficients increase with shear rate for all liquids and stable dispersions. The importance for rheology of hydrodynamic coupling between macromolecule trajectories at high packing fractions is demonstrated. The infinite frequency moduli depend on the packing fraction to a power which is effectively the same for all materials, i.e. ca. 3.5, above a percolation transition at a packing fraction 0.25. The suspending fluid enhances the degree of shear thinning above that of the corresponding single component fluid consisting of pure macroparticles.     

A physically based correlation for the effects of power law rheology and inclination on slug bubble rise velocity

A study has been made of the motion of long bubbles in inclined pipes containing viscous Newtonian and non-Newtonian liquids. A semi-theoretical expression for the rise velocity of air bubbles in water is derived on the hypothesis that the dominant factor is the momentum exchange of the bubble underflow, i.e. the bubble nose shape. The correlation calls on empirical inputs from established literature on bubble rise speeds at high Reynolds number. The effects of increasing Newtonian viscosity are analysed with reference to the momentum exchange and it is shown how viscosity reduces the inclination dependence of the bubble Froude number. Results from an experimental survey in seven different non-Newtonian liquids in three different diameter pipes are presented. These data are correlated so as to decouple the effects of surface tension and viscosity. An empirical relation is proposed for the effective shear rate in the fluid travelling around the bubble nose. Our correlation is compared to literature data from a broad range of Reynolds numbers with excellent agreement except at shallow angles.     

Ultrasonic wave and moduli changes in a curing epoxy resin

During the cure cycle, thermosetting polymeric resins change in physical character from a viscous liquid to a gel and finally to a hardened solid. Ultrasonic-wave-propagation techniques can be used to monitor both the extent of cure and the development of solid-phase moduli. This paper outlines such a program and presents results for a room-temperature, amine-cured epoxy system. Signal attenuation and wave-speed data are given as a function of cure time for 1.0 MHz longitudinal and shear waves. The behavior observed is first interpreted in terms of linear-viscoelastic wave-propagation theory. Then using the wave speeds, apparent elastic moduli are calculated as a function of cure time. Finally, relations are developed which suggest a mapping between the moduli and a normalized reaction-extent variable. Implicit in these relations is that the moduli themselves can serve or be viewed as reaction-extent variables.     

A method of determining complex moduli of viscoelastic materials

A method is introduced whereby the complex moduli of viscoelastic materials may be determined in a relatively simple and accurate manner by means of calibration of the measuring system using a specimen of known properties. The appropriate data-reduction equations are presented and use of the method is demonstrated for determination of complex moduli for bovine bones over a four-octave frequency range.     

Dilatational plastic constitutive equations and their application to ductile fracture analysis of axisymmetric specimens

In many ductile materials voids nucleate and grow under large strain and triaxial stress, which yield volumetric plastic expansion. A constitutive equation is presented, which accounts for this plastic dilatancy. The plastic moduli involved in this equation can be calibrated by using necking tests of axisymmetric bars, void model analysis and computer simulation. To verify the rationality of such a constitutive equation and adjust the values of plastic moduli, the constitutive equation with its moduli to be determined is applied to analyse the ductile fracture behaviour of axisymmetric bars.     

Canonical moduli and general solution of equations of a two-dimensional static problem of anisotropic elasticity

Equations of a two-dimensional static problem of anisotropic elasticity are brought to a simple form with the use of orthogonal and affine transformations of coordinates and corresponding transformations of mechanical quantities. It is proved that an arbitrary matrix of elasticity moduli containing six independent components can be always converted by a congruent transformation to a matrix with two independent components, which are called the canonical moduli. Depending on the relations between the canonical moduli, the determinant of the matrix of operators of equations in displacements is presented as a product of various quadratic terms. A general presentation of the solution of equations in displacements in the form of a linear combination of the first derivatives of two quasi-harmonic functions satisfying two independent equations is given. A symmetry operator (i.e., a formula of production of new solutions) is found to correspond to each presentation. In a three-dimensional case, the matrix of elasticity moduli with 21 independent components is congruent to a matrix with 12 independent canonical moduli.     

含椭圆夹杂正交各向异性体的界面应力研究

本文研究了远场作用反平面载荷时含椭圆夹杂正交各向异性体的界面应力分布规律．利用解析函数边值问题理论和共形映射技术,推导了反平面载荷下含椭圆夹杂正交异性体的精确解,获得了夹杂和基体内应力场的闭合解,并通过有限元结果验证了本文解析解的有效性．研究表明：基体材料主方向弹性模量比C55/C44和夹杂形状比 对界面应力影响显著;基体材料主方向模量比C55/C44对界面应力的影响受夹杂/基体模量比Cf/C44的限制．     

On the quasistatic effective elastic moduli for elastic waves in three-dimensional phononic crystals

Effective elastic moduli for 3D solid–solid phononic crystals of arbitrary anisotropy and oblique lattice structure are formulated analytically using the plane-wave expansion (PWE) method and the recently proposed monodromy-matrix (MM) method. The latter approach employs Fourier series in two dimensions with direct numerical integration along the third direction. As a result, the MM method converges much quicker to the exact moduli in comparison with the PWE as the number of Fourier coefficients increases. The MM method yields a more explicit formula than previous results, enabling a closed-form upper bound on the effective Christoffel tensor. The MM approach significantly improves the efficiency and accuracy of evaluating effective wave speeds for high-contrast composites and for configurations of closely spaced inclusions, as demonstrated by three-dimensional examples.     

The spatial development of transient couette flow and shear wave propagation in polymeric liquids by flow birefringence

In this paper the method of polarization modulated flow birefringence is us used to analyze the spatial and temporal dependence of the inception and cessation of Couette flow of polymeric liquids. Data are presented for both a Newtonian but birefringent polybutene oil and two solutions of poly(oxyethylene). The stress-optical rule is used to obtain the corresponding 'shear and normal stresses as functions of both time and space. The data for the Newtonian fluid are compared with analytical solutions to the momentum equations and are found to accurately follow the theoretical predictions. The polymer solutions, on the other hand, show a complex response with evidence for shear stress propagation as a wave of finite, constant speed. The measured wave speeds agree well with recent data reported by Joseph. Riccius and Arney [JFM 171(1986)309] on the same polymer solutions.     

Experimental and theoretical aspects of the two-roll mill problem

Experiments are described in which two cylinders of the same radii-rotate with identical speeds in a bath of Newtonian or non-Newtonian liquid. The torque on one of the cylinders is measured as a function of rotational speed for various values of the cylinder separation and the flow patterns are observed by a dye-injection technique.The observed experimental results for a Newtonian liquid correlate well with the theoretical predictions but a similar correlation in the case of elastic liquids is made difficult by the strongly three-dimensional nature of the flow in this case and the difficulty in estimating the amount of liquid passing through the rollers. The possibility of flow reversal effects due to the high Trouton ratios in the case of the elastic liquids is investigated both experimentally and theoretically.     

The deformation and fracture of balloons

Inflation of balloons provides a straightforward way of achieving large biaxial deformations. Previous studies have shown that when a balloon bursts, crack propagation occurs at very high speed – much higher than would be expected from the low strain modulus and elastic wave velocity of the rubber. The present paper is concerned with studies of the deformation and fracture of cylindrical balloons. On inflation, the deformations of such a balloon pass through an unstable region but subsequently increase monotonically with pressure. In this relatively high pressure region, the ratio of the longitudinal and circumferential extension ratios is broadly in accord with expectations from high-strain elasticity theory when the ratio of the corresponding stresses is taken into account. On bursting, crack speeds up to around 300 m/s in this region. It is shown that these speeds are in accord with large increase in incremental moduli for the highly-strained rubber. Marked changes in crack tip profile observed at very high crack speeds are consistent with control of the rate of growth by inertia rather than by the viscoelastic properties of the rubber (as is believed to be the case at lower speeds). Consistent with this, various elastomers having different glass transition temperatures show similar crack growth behaviour in the very high speed region.     

The effect of additives on the speed of the crystallization front of xylitol with various degrees of supercooling

Some liquids can be kept in a supercooled or supersaturated metastable state for substantially long periods. Such liquids can be applied as long-term heat storage where the latent heat can be released when needed. As xylitol possesses a relatively high value of latent heat and as it can be easily supercooled, it has promising properties for this application. However, the speed of the crystallization of xylitol is low, leading to a low release rate of latent heat.Several additives have been experimentally tested for the purpose of accelerating the crystallization speed. The effect of the additives on the latent heat, on the melting temperatures, and on the long-term durability of the supercooled state was also measured.The highest speeds of the crystallization front, at a temperature of 22 °C, were achieved with methanol as an additive leading to speeds 33 times higher in vertical experiments and in 170 times higher in horizontal ones than with pure xylitol. The improved speed of the crystallization front is mostly caused by the methanol flow currents generated as a result of the separation of methanol during crystallization, and to a lesser extent, as a result of the increase in the speed of the growth of the crystals.     

最大地面风速的预测研究

为了解决航天发射场极值风速的预测问题,本文提出了用于极值风速预测的一种新方法－－相关系数法,并利用此方法对三种典型的概率分布进行了对比研究,在对比过程中,检验了三组极值风速,假设每组检验样本内的极值风速数据是统计独立的,于是极值风速就可以描述为随机过程,研究表明最适于描述极值风速的概率分布是reverse Weibull分布,与peak-over-threshold法所得出的结论具有良好的一致性。     

Modeling and simulation of martensitic phase transitions with a triple point

A framework for modeling complex global energy landscapes in a piecewise manner is presented. Specifically, a class of strain-dependent energy functions is derived for the triple point of Zirconia (ZrO₂), where tetragonal, orthorhombic (orthoI) and monoclinic phases are stable. A simple two-dimensional framework is presented to deal with this symmetry breaking. An explicit energy is then fitted to the available elastic moduli of Zirconia in this two-dimensional setting. First, we use the orbit space method to deal with symmetry constraints in an easy way. Second, we introduce a modular (piecewise) approach to reproduce or model elastic moduli, energy barriers and other characteristics independently of each other in a sequence of local steps. This allows for more general results than the classical Landau theory (understood in the sense that the energy is a polynomial of invariant polynomials). The class of functions considered here is strictly larger. Finite-element simulations for the energy constructed here demonstrate the pattern formation in Zirconia at the triple point.     

Stability of the interface in two-layer couette flow of upper convected maxwell liquids

The linear stability of a two-layer Couette flow of upper convected Maxwell liquids is considered. The fluids have different densities, viscosities, and elasticities, with surface tension at the interface. At low speeds, the interfacial mode may become unstable, while other modes stay stable. The shortwave asymptotics of the interfacial mode is analyzed. It is found that an elasticity difference can stabilize or destabilize the flow even in the absence of a viscosity difference. As the viscosity difference increases, the range of elasticities for which there is shortwave stability widens. A linearly stable arrangement can be achieved by placing the less viscous fluid in a thin layer to stabilize longwaves and using elasticities to stabilize shortwaves. Such an arrangement can be stable even when the density stratification is adverse.     

Evaluation of molecular weight distribution from dynamic moduli

A method to evaluate molecular weight distribution (MWD) from dynamic moduli is presented here. It relies on the least-square fitting of the dynamic data to a model whose parameters depend on the MWD. In particular, the analytical solution for the relaxation modulus previously obtained from the double reptation model, with the Tuminello step relaxation function and the Generalized Exponential Function (GEX) describing the MWD (Nobile and Cocchini 2000), has been used. A Finite Element Approximation (FEA) has been applied to calculate dynamic moduli from the relaxation modulus as a function of MWD. The sensitiveness of the GEX-double reptation dynamic moduli on the model parameters has also been investigated and the results show that large changes of the M_w/M_n ratio weakly affect the dynamic moduli, while small changes of the M_z/M_w ratio significantly deform the dynamic moduli curves. The use of rheological data to obtain MWD, by the model used in this paper, will, therefore, be able to give rather well defined M_z/M_w ratios, while more uncertainty will be presented in the M_w/M_n results. The so-called GEX-rheological model for the dynamic moduli was applied to fit the experimental data of different polymers in order to obtain the best-fit parameters of the MWD of these polymers, without the need for the inversion of the double reptation integral equation. The stability of the results has been confirmed through the evaluation of the 90% confidence intervals for the first molecular weight averages. Finally, concerning the M_w and M_z values, the predictions obtained from the dynamic moduli measurements differ by less than 10% from those obtained from GPC measurements while, as expected, more uncertainty is present in the M_n predictions. Received: 6 February 2000 Accepted: 22 August 2000     

聚氨酯泡沫塑料压缩杨氏模量的理论预测

通过微分法导出了泡沫塑料剪切模量和体积模量所满足的微分方程组，再利用联系泡沫塑料泊松比和孔隙比的Ｋｅｒｎｅｒ－Ｒｕｓｃｈ经验关系及泡沫塑料弹性常数间满足足的关系，在基体材料不可压缩的假设下，确定了泡沫塑料的杨氏模量。本文针对几种密度的泡沫塑料，分别对它们的杨氏模量进行了理论预测和实验测定，结果表明：理论预测的模量在较高密度下与实验符合的很好，在低密度下也给出相当好的近似值。此外，本文的结果同其他理     

The boundaries of the effective elastic moduli for inhomogeneous solids

The calculation of the effective elastic moduli of inhomogeneous solids, which connect the stresses and strains averaged for the material, is accompanied by certain mathematical difficulties owing to correlation relationships of arbitrary orders. Neglect of correlation relationships leads to average elastic moduli, where averaging according to Voigt and Reuss establishes boundaries containing the effective elastic moduli [1]. Approximate values of the latter can be found by taking into account the correlation relationships of the second order in both calculation schemes [2, 3]. Another method of evaluating the true moduli consists of narrowing the boundaries of Voigt and Reuss on the basis of model representations [4-6]. The approximate effective elastic moduli for a series of polycrystals with various common-angle values are presented in [7]. An analysis of the effect of the correlation relationships between the grains of a mechanical mixture of isotropic components on the effective elastic moduli is carried out in [8], although in all the papers just mentioned the use of correlative corrections to narrow the range of elastic moduli is not investigated. Below it is shown that the calculation of the correlation corrections in the second approximation allows the range for the effective moduli to be narrowed.     

On interacting longitudinal-shear waves in large elastic deformation of a composite cylindrical laminate

We consider a large deformation of a cylindrical layer. Through the process of homogenization and the theory of effective moduli this heterogeneous medium is converted to a homogeneous but anisotropic medium. On the basis of John’s semilinear material, an energy function is identified and equations of motion obtained. Using the method of characteristics the speeds of propagating linear longitudinal and non-linear shear cylindrical waves are obtained: these “p-wave” and “s-wave” do interact, contrary to the known view, of the small deformation theory.     

A Rheological comparison of three gloss paints

Summary Using aWeissenberg Rheogoniometer, three gloss paints were tested in rotation, using cone and plate geometry, at shear rates from 1.0 to 2.0×10⁴ secs^–1. The moduli of viscosity and elasticity are calculated. A practical method of correcting the reduction of normal stress measurements due to secondary flows at high platen speeds in described.Presented at the Joint Meeting of the British Society of Rheology and Research Association of British Paint, Colour and Varnish Manufacturers at Teddington, April 29, 1964.