Dynamics of Polymeric Fluids: Part II The Molecular Theory of Die Swell: Correlation of Ultimate Die Swelling Effect to the Molecular Parameters and the Operational Variables

A general expression for the correlation of the simple shear (tan(?)) to the molecular parameters and the shear rate (γ) was deduced. It shows that the simple shear (tan(?)) may be resolved into free recoil (recoverable strain) and viscous heating (unrecoverable strain). The magnitudes of the simple shears for recoil (tan(?)E) and (tan(?)V) for viscous heating not only depended on the molecular parameters and the operational variables, but also on the exponential fractions of the recoverable (1-Wγ) and unrecoverable (W-γ) conformations for recoil and viscous heating. Therefore the magnitudes of the simple shears (tan(?)E) for recoil and (tan(?)V) for viscous heating are, respectively, expressed as the partition function to the (1-Wγ)th power and the partition function to the (Wγ)th power. Thus correlations of the total recoil and the ultimately recoverable strains to the molecular parameters [n', a,η0, GN0 and (1-Wγ)] and the operational variables (γ, (L/D) and tr) were deduced respectively, which show that at very different shear rates (0≤γ≤∞) the polymeric liquids may exhibit a very different viscoelastic behaviors. After introducing the uniform two-dimensional extension, the definition of swelling ratio and the ratio of L to D [De=(L/D)], two expressions for the ultimate die swelling effect and the ultimate extrudate swelling ratio BEVT5 to the molecular parameters [n', a,η0, GN0 and (1-Wγ)] and the operational variables (γ, (L/D) and tr) were obtained. The two correlation expressions were verified by the experimental data of high-density polyethylene (HDPE) which shows that the two correlation expressions can be used to predict the correlations of the ultimate extrudate swelling behaviors of polymeric liquids to the molecular parameters and the operational variables.     

Dynamics of Polymeric Fluids: Part Ⅱ The Molecular Theory of Die Swell: Correlation of Ultimate Die Swelling Effect to the Molecular Parameters and the Operational Variables

A general expression for the correlation of the simple shear(tanφ)to the molecular parameters and the shear rate(γ)was deduced. It shows that the simple shear(tanφ)may be resolved into free recoil(recoverable strain)and viscous heating(unrecoverable strain). The magnitudes of the simple shears for recoil(tanφE)and(tanφv)for viscous heating not only depended on the molecular parameters and the operational variables,but also on the exponential fractions of the recoverable(1-(W)γ)and unrecoverable((W)γ)conformations for recoil and viscous heating. Therefore the magnitudes of the simple shears(tanφE)for recoil and(tanφv)for viscous heating are, respectively, expressed as the partition function to the(1-(W)γ)th power and the partition function to the(-(W)γ)th power. Thus correlations of the total recoil and the ultimately recoverable strains to the molecular parameters [n', a, η0, G0NN and(1--(W)γ)] and the operational variables(·γ, (L/D)and tr)were deduced respectively, which show that at very different shear rates(0≤·γ≤∞)the polymeric liquids may exhibit a very different viscoelastic behaviors. After introducing the uniform two-dimensional extension, the definition of swelling ratio and the ratio of L to D [De=(L/D)], two expressions for the ultimate die swelling effect and the ultimate extrudate swelling ratio BEVT5 to the molecular parameters [n', a, η0, G0N and(1--(W)·γ)] and the operational variables(·γ,(L/D)and tr)were obtained. The two correlation expressions were verified by the experimental data of high-density polyethylene (HDPE) which shows that the two correlation expressions can be used to predict the correlations of the ultimate extrudate swelling behaviors of polymeric liquids to the molecular parameters and the operational variables.     

Dynamics of Polymeric Fluids：Part Ⅱ The Molecular Theory of Die Swell： Correlation of Ultimate Die Swelling Effect to the Molecular Parameters and the Operational Variables

A general expression for the correlation of the simple shear (tan ) to the molecular parameters and the shear rate ( ) was deduced. It shows that the simple shear (tan ) may be resolved into free recoil (recoverable strain) and viscous heating (unrecoverable strain). The magnitudes of the simple shears for recoil (tan E) and (tan V) for viscous heating not only depended on the molecular parameters and the operational variables, but also on the exponential fractions of the recoverable (1- ) and unrecoverable ( ) conformations for recoil and viscous heating. Therefore the magnitudes of the simple shears (tan E) for recoil and (tan V) for viscous heating are, respectively, expressed as the partition function to the (1- )th power and the partition function to the ( )th power. Thus correlations of the total recoil and the ultimately recoverable strains to the molecular parameters [ , a, η0, GN0 and (1- )] and the operational variables ( ), (L=D) and tr) were deduced respectively, which show that at very different shear rates ( ) the polymeric liquids may exhibit a very different viscoelastic behaviors. After introducing the uniform two-dimensional extension, the definition of swelling ratio and the ratio of L to D [De=(L/D)], two expressions for the ultimate die swelling effect and the ultimate extrudate swelling ratio BEVT5 to the molecular parameters [ , a, η0, GN0 and (1- )] and the operational variables ( , (L/D) and tr) were obtained. The two correlation expressions were verified by the experimental data of high-density polyethylene (HDPE) which shows that the two correlation expressions can be used to predict the correlations of the ultimate extrudate swelling behaviors of polymeric liquids to the molecular parameters and the operational variables.     

Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅱ: Material Function with Nagai Chain Constraints and Determination of Their Parameters from Flow Curves

An integral constitutive equation and a set of material functions for describing the strain history of polymer melts were formulated in terms of the Cauchy-Green and Finger tensors. A simple memory function and the dependence of ηo and τt on M3.4 were derived from the theory of non-linear viscoelasticity with constraints of entanglements for polymer melts and substituted into the Oldroye-Walters-Fredickson constitutive equation. An integral constitutive equation for polymer melts was consequently obtained. Some material functions of the constitutive equation related to certain "test flow" are examined as follows : (1) simple steady shear flow; (2) steady elongation flow; (3) small-amplitude oscillatory shear flow; (4) stress growth upon the inception of steady shear elongation flow; (5) stress relaxation (modulus and compllance). These theoretical relations for simple steady shear flow were compared with experimental data from our laboratory and references for various polymer melts and concentrated solutions. A good agreement between the theory and experiment was achieved.     

Mechanical Properties, Damage and Fracture Mechanisms of Bulk Metallic Glass Materials

The deformation, damage, fracture, plasticity and melting phenomenon induced by shear fracture were investigated and summarized for Zr-, Cu-, Ti- and Mg-based bulk metallic glasses （BMGs） and their composites. The shear fracture angles of these BMG materials often display obvious differences under compression and tension, and follow either the Mohr-Coulomb criterion or the unified tensile fracture criterion. The compressive plasticity of the composites is always higher than the tensile plasticity, leading to a significant inconsistency. The enhanced plasticity of BMG composites containing ductile dendrites compared to monolithic glasses strongly depends on the details of the microstructure of the composites. A deformation and damage mechanism of pseudo-plasticity, related to local cracking, is proposed to explain the inconsistency of plastic deformation under tension and compression. Besides, significant melting on the shear fracture surfaces was observed. It is suggested that melting is a common phenomenon in these materials with high strength and high elastic energy, as it is typical for BMGs and their composites failing under shear fracture. The melting mechanism can be explained by a combined effect of a significant temperature rise in the shear bands and the instantaneous release of the large amount of elastic energy stored in the material.     

Effect of Y2O3 and Total Oxide Addition on Mechanical Properties of Pressureless Sintered β-SiC

The effect of Y2O3 and the total oxide volume fraction (Y2O3 Al2O3) on density and mechanical properties of low temperature (1770～1940℃) pressureless sintered β-SiC ceramics were presented. The optimum temperature for pressureless sintering of β-SiC was found to be～1850℃ and the optimum content of Y2O3 in the oxides was found to be between 40 and 57 wt pct. The highest sintered density was achieved by adding oxides at 14 vol. pct. Both of the highest strength and fracture toughness were achieved at～14 vol. pct oxide addition and yttria concentrations between 40 and 57 wt pct in the oxides. Hardness, on the other hand, was found to be the highest for samples with 14 vol. pct oxide addition and ～64 wt pct Y2O3 in oxides.     

Effects of Mechanical Milling and Sintering Temperature on the Densification,Microstructure and Tensile Properties of the Fe–Mn–Si Powder Compacts

This work reported on the effects of mechanical milling and sintering temperature on the densification,microstructure and mechanical properties of the Fe–28Mn–3Si(wt%) alloy. Elemental Fe, Mn and Si powders were used as the starting materials, and two batches of powder mixture were prepared: one was blended elemental(BE) powder mixture; the other was mechanically milled(MM) powder mixture milled for5 h using planetary ball milling. Both powder mixtures were pressed under a uniaxial pressure of 400 MPa,and subsequently sintered in a high vacuum furnace for 3 h at 1000, 1100, 1200 and 1300 °C. It was found that Mn depletion region(MDR) was formed on the surface of all the sintered samples. The sintered BE compacts had a low density(68.2%) at all temperatures, while the density of the sintered MM compacts increased drastically from ~65% at 1000 °C to ~91% at 1300 °C. All the sintered MM compacts were composed of a predominant γ-austenite and minor ε-martensite. In comparison, additional(Fe, Mn)3Si phase was observed in the BE alloys sintered at 1000 °C, and a single α-Fe phase was identified in the BE compact sintered at 1300 °C. The tensile properties of the sintered MM compacts increased significantly with the temperature and were significantly higher than those of their BE counterparts.     

Grain refinement of non-magnetic austenitic steels during asymmetrical hot rolling process

Asymmetrical hot rolling(ASHR) was proposed to acquire productive grain refinement for Fe-20Mn-4Al-0.3C and Fe-18Cr-18Mn-0.5N non-magnetic austenitic steels. The intensive additional shear deformation caused by ASHR promotes the nucleation of recrystallization and grain refining of steel plates. With the speed ratio of 1.2, the austenitic grains were refined to ~5 m on the surface, the recrystallization fraction was enhanced to ~34.7%, and the thickness of fine-grained surface layer increases to ~450m for Fe-20Mn-4Al-0.3 C steel. The Fe-18Cr-18Mn-0.5N steel also exhibited an effective surface grain refinement with an average size of ~3μm, and the recrystallization fraction reached ~76.9% at the speed ratio of 1.15.     

Rheological Behavior for Polymer Melts and Concentrated Solutions Part VII: A Quantitative Verification for the Molecular Theory of Non-linear Viscoelasticity with Entanglement Constraints in Polymer Melts

Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between η(),ψ10()and shear rate(),and topologically constrained dimension number n＇and a were derived. Linear viscoelastic parameters (η0 and G0N)and topologically constrained dimension number (n＇,a and )as a function of the primary molecular weight(Mn),molecular weight between entanglements (Mc) and the entanglement sites sequence distribution in polymer chain were determined. A new method for determination of viscoelastic parameters (η0,ψ10,G0N and J0e),topologically constrained dimension number(n＇,a and v)and molecularweight (Mn, Mc and Me) from the shear flow measurements was proposed.It was used to determine those parameters and structures of HDPE, making a good agreement between these values and those obtained by other methods. The agreement affords a quantitative verification for the molecular theory of nonlinear viscoelasticity with constrained entanglement in polymer melts.     

Segregation of Liquid Phase in the Extruded Semisolid Metal

The influence of stress and strain on the solid/liquid segregation formed in deformed semisolid metal was studied. The compression experiment at a low constant strain rate was conducted on a Gleeble 1500 thermo-mechanical simulator.The stress and strain fields of the samples were calculated by finite element method. The experiment results and the modeling results prove that the hydrostatic pressure gradient is the driving force for solid/liquid segregation. The segregated liquid phase usually agglomerates in the micropores and shear bands are created by sliding of equiaxed dendrite grains. The sliding among the grains is influenced by the solid fraction and grain size of the semisolid slurry,so as the solid fraction and grain size change, the morphology of the segregated liquid changes.     

Principal angles and principal azimuths of frustrated total internal reflection and optical tunneling by an embedded low-index thin film

The condition for obtaining a differential (or ellipsometric) quarter-wave retardation when p- and s-polarized light of wavelength λ experience frustrated total internal reflection (FTIR) and optical tunneling at angles of incidence ? ≥ the critical angle by a transparent thin film (medium 1) of low refractive index n1 and uniform thickness d, which is embedded in a transparent bulk medium 0 of high refractive index n0 takes the simple form: -tanh2 x = tan δp tan δs, in which x = 2πn1(d/λ)(N2sin2? - 1)(1/2), N = n0/n1, and δp, δs are 01 interface Fresnel reflection phase shifts for the p and s polarizations. From this condition, the ranges of the principal angle and normalized film thickness d/λ are obtained explicitly. At a given principal angle, the associated principal azimuths ψr, ψt in reflection and transmission are determined by tan2ψr = -sin 2δs/sin 2δp and tan2ψt = -tan δp/tan δs, respectively. At a unique principal angle ?e given by sin2?e = 2/(N2 + 1), ψr = ψt = 45° and linear-to-circular polarization conversion is achieved upon FTIR and optical tunneling simultaneously. The intensity transmittances of p- and s-polarized light at any principal angle are given by τp = tan δp/tan (δp - δs) and τs = -tan δs/tan (δp - δs), respectively. The efficiency of linear-to-circular polarization conversion in optical tunneling is maximum at ?e.     

线型聚乙烯熔体的剪切弹性行为表征

利用稳态剪切柔量，可回复剪切应变以及熔体挤出胀大比等参数，定量计算和定性表征了４种线型聚乙烯熔体的剪切弹性行为，研究了各表征参数之间及其与分子量，分子量分布等分子参数的关系，讨论了剪切弹性行为对加工性能的影响。     

线性双峰聚乙烯/高压聚乙烯/线性低密度聚乙烯共混物的流变行为与力学性能

研究了线性双峰聚乙烯(LBPE)、高压聚乙烯(LDPE)与线性低密度聚乙烯(LLDPE)共混物熔体的流变行为和力学性能。讨论了共混物的组成、剪切应力和剪切速率对熔体粘度和膨胀比的影响。结果说明,共混物熔体为假塑性流体,LBPE含量为70％时熔体粘度最大,含量高于60％时挤出胀大变小,含量高于40％时力学强度增大。     

Viscoelastic properties of low-viscosity liquids studied with thickness-shear mode resonators

The network analysis method was applied to AT cut quartz blanks (f(0) = 10 MHz), which were loaded with liquids of low and medium viscosity (water, methanol, ethanol, 1-propanol, 1-butanol, glycerol solutions). The shift of the resonance frequency Δf could be separated into a term due to rigidly coupled mass Δf(rig) and a term due to viscous damping Δf - Δf(rig). From the difference Δf - Δf(rig) and the broadening of the resonance curve, the complex shear modulus G = G' + iωη(L) was calculated. The viscosity coefficients η(L) are in good agreement with literature data. As G' > 0, it can be concluded that the examined fluids also reveal elasticity at shear frequencies in the MHz range. For the low-viscosity liquids, elastic contributions resulting from collective interactions of molecules are measurable but small and neglectable in most applications. The medium viscous liquid glycerol (98%) begins to exhibit considerable elasticity, resulting from the relaxation of separate molecules.     

聚合物熔体复合挤出胀大过程的数值模拟及可恢复弹性形变分析

建立了两种聚合物熔体流经矩形流道共挤出的三维数值计算模型,采用有限元方法数值模拟了共挤出成型过程及胀大过程,得到了速度场、压力场、应力场,并利用数值计算方法得到了共挤出流动过程的可恢复弹性形变场,分析了挤出胀大率以及可恢复弹性形变的变化过程。结果表明,在共挤出流动的胀大段,共挤出界面的形状和位置发生了改变;经矩形流道共挤出得到的挤出胀大末端截面形状为不对称的鼓形;在共挤出界面附近可恢复弹性形变值存在极值,运用数值方法计算可恢复弹性形变可以对流动过程中可能存在的缺陷进行预测。     

改性聚乙烯醇的流变行为及其吹塑加工研究

研究了改性PVA体系的流变性能及挤出胀大行为。结果表明,改性PVA熔体为假塑性流体,适合挤出吹塑成型。在相同加工条件下,Ac含量增加,改性PVA体系表观黏度和剪切敏感性下降,温度敏感性升高,且改性体系的挤出胀大比减少。通过优化改性PVA组分和挤吹工艺条件,初步实现了PVA吹塑成型。     

Stratified newtonian flow calculations by the boundary element method

A boundary integral equation formulation is used to model the stratified flow of two Newtonian viscous liquids, in which the geometrical detail of the interface between the layers is not known in advance. The technique is tested by comparing predictions with the results of previous finite element solutions, and found to perform well. Finally, the method is used to examine the two-layer jet theory of Tanner (1980) as a means of simplifying the modelling of complex extrudate swell problems.     

Viscosity measurement of Newtonian liquids using the complex reflection coefficient

This work presents the implementation of the ultrasonic shear reflectance method for viscosity measurement of Newtonian liquids using wave mode conversion from longitudinal to shear waves and vice versa. The method is based on the measurement of the complex reflection coefficient (magnitude and phase) at a solid-liquid interface. The implemented measurement cell is composed of an ultrasonic transducer, a water buffer, an aluminum prism, a PMMA buffer rod, and a sample chamber. Viscosity measurements were made in the range from 1 to 3.5 MHz for olive oil and for automotive oils (SAE 40, 90, and 250) at 15 and 22.5degC, respectively. Moreover, olive oil and corn oil measurements were conducted in the range from 15 to 30degC at 3.5 and 2.25 MHz, respectively. The ultrasonic measurements, in the case of the less viscous liquids, agree with the results provided by a rotational viscometer, showing Newtonian behavior. In the case of the more viscous liquids, a significant difference was obtained, showing a clear non-Newtonian behavior that cannot be described by the Kelvin-Voigt model.     

Measurement of the material properties of viscous liquids using ultrasonic guided waves

The theoretical basis for a testing tool in the form of a circular waveguide for measuring both the dynamic viscosity and the longitudinal bulk velocity of viscous liquids is presented. It is based on the measurements of the attenuation of the fundamental torsional mode, T(0,1), and the fundamental longitudinal mode, L(0,1), of the waveguide when immersed in the liquid. The modeling techniques to extract the shear viscosity and the longitudinal bulk velocity are explained and experimentally verified. Results for two viscous liquids are presented: good agreement between theory and experiment was obtained.