The rheology of suspensions of vinylon fibers in polymer liquids. I. Suspensions in silicone oil

Summary The steady shear flow properties of suspensions of vinylon fibers in silicone oil were measured by means of a cone-plate type rheometer. Three kinds of vinylon fibers used had no distributions of length and were more flexible than glass fibers and the like. The content of the fibers ranged from 0 to 7 wt.%. Shear viscosity, the first normal-stress difference, yield stress, and relative viscosity were discussed. Shear viscosity and relative viscosity increased with the fiber concentration and the aspect ratio, and depended upon the shear rate. The applicability of Ziegel's equation of viscosity for fiber suspensions was investigated. The first normal-stress difference increased with the fiber concentration, aspect ratio, and shear rate and its relative increase was much larger than for shear stress and viscosity depending on the properties of the characteristic time, The yield stress could be determined by Casson plots for large aspect ratio fiber suspensions even in low concentration comparing with the suspensions of spherical particles or powder. The influence of the flexibility of the fibers for the rheological properties of the fiber suspensions can not be ignored.With 12 figures and 2 tables     

The rheology of suspensions of vinylon fibers in polymer liquids. II. Suspensions in polymer solutions

Summary The rheological properties of vinylon fiber suspensions in polymer solutions were studied in steady shear flow. Shear viscosity, first normal-stress difference, yield stress, relative viscosity, and other properties were discussed. Three kinds of flexible vinylon fibers of uniform length and three kinds of polymer solutions as mediums which exhibited remarkable non-Newtonian behaviors were employed. The shear viscosity and relative viscosity ( _r ) increased with the fiber content and the aspect ratio, and depended upon the shear rate. Shear rate dependence of _r was found only in the low shear rate region. This result was different from that of vinylon fiber suspensions in Newtonian fluids. The first normal-stress difference increased at first slightly with increasing fiber content but rather decreased and showed lower values for high content suspensions than that of the medium. A yield stress could be determined by using a modified equation of Casson type. The flow properties of the fiber suspensions depended on the viscosity of the medium in the suspensions under consideration.With 16 figures and 1 table     

Rheological properties of long glass fiber filled polypropylene

Long glass fiber-filled polypropylene (PP) composites are produced by pultrusion, and the extrudate is cut at different lengths producing composites containing long fibers of controlled length. The rheological properties of such composites in the molten state have been studied using different rheometers. A capillary rheometer has been constructed and mounted on a molding-injection machine. The shear viscosity of filled PP determined from the capillary rheometer, after corrections for entrance effects, was found to be very close to that of unfilled PP. However, large excess pressure losses at the capillary entrance were observed and these data have been used to obtain an apparent elongational viscosity. The apparent elongational viscosity was shown to be considerably larger than the shear viscosity for PP and filled PP, and it increased markedly with fiber length and fiber content. Rotational rheometers with a parallel-plate geometry were used to investigate the viscoelastic properties of these composites and their behavior was found to be non-linear, exhibiting a yield stress. A model is proposed to describe the shear viscosity from a solid-like behavior at low stresses to fluid-like behavior at high shear stresses taking into account fiber content and orientation. A modified model, proposed for elongational flow, describes relatively well the apparent elongational data.     

Dynamic flow properties of vinylon fibre and glass fiber reinforced polyethylene melts

An experimental study of the dynamic shear flow properties of polyethylene melts filled with glass fibers and vinylon fibers was carried out and comparison with the steady shear flow properties was made. The effects of loading level and the characteristics of the fibers on the rheological properties of the fiber-filled systems is discussed. The rigidity and complex viscosity of the fiber-filled systems is sensitive not only to the quantity of fibers but also to their length, distribution and properties. The Cox-Merz empirical law for complex viscosity and steady shear viscosity, and Roscoe's empirical relation for estimating the normal-stress coefficients are both able to be applied to pure polymer melts but not to fiber-filled systems.     

Orientation distribution of fibers and rheological property in fiber suspensions flowing in a turbulent boundary layer

A model relating the translational and rotational transport of orientation distribution function （ODF） of fibers to the gradient of mean ODF and the dispersion coefficients is proposed to derive the mean equation for the ODE Then the ODF of fibers is predicted by numerically solving the mean equation for the ODF together with the equations of turbulent boundary layer flow. Finally the shear stress and first normal stress difference of fiber suspensions are obtained. The results, some of which agree with the available relevant experimental data, show that the most fibers tend to orient to the flow direction. The fiber aspect ratio and Reynolds number have significant and negligible effects on the orientation dis- tribution of fibers, respectively. The additional normal stress due to the presence of fibers is anisotropic. The shear stress of fiber suspension is larger than that of Newtonian solvent, and the first normal stress difference is much less than the shear stress. Both the additional shear stress and the first normal stress difference increase with increasing the fiber concentration and decreasing fiber aspect ratio.     

The flow behavior of fiber suspensions in Newtonian fluids and polymer solutions.

The main purpose of this study was to examine the viscous and elastic properties and capillary flow of fiber suspensions in Newtonian fluids as well as in polymer solutions. The fillers used were glass, carbon, nylon and vinylon fibers. Glycerin was used as a Newtonian suspending medium and HEC and Separan solutions as viscoelastic suspending media. The viscosity and the first normal-stress difference were measured using a coaxial cylindrical rotating viscometer and a parallel-plate rheogoniometer respectively. The influence of the concentration, aspect ratio, diameter and flexibility of the fibers on the viscous and elastic properties of the fiber suspensions was investigated. Empirical equations were obtained for the relative viscosity and first normal-stress difference for the fiber suspensions in glycerin. The capillary flow of these suspensions is discussed in part II.     

Transient shear flow behavior of concentrated long glass fiber suspensions in a sliding plate rheometer

In order to eventually predict the behavior of long fiber suspensions in complex flows commonly found in processing operations, it is necessary to understand their rheology and its connection to the evolution of fiber orientation and configuration in well defined flows. In this paper we report the transient behavior at the startup of shear flow of a polymer melt containing long glass fibers with a length (L) >1 mm, using a sliding plate rheometer (SPR). The operation of the SPR was confirmed by comparing the transient shear viscosity (η⁺) for a polymer melt and a melt containing short glass fibers (L < 1 mm) with measurements obtained from a cone-and-plate device, using a modified sample geometry that was designed to avoid wall effects. For the long fiber systems, measurements could only be obtained in the SPR because these systems would not stay within the gap of the rotational rheometer. Transient stress growth behavior of the long fiber systems was obtained as a function of shear rate and fiber concentration for samples prepared with three different initial orientations. Results showed that, unlike short fiber systems (with a random planar initial orientation) that usually exhibit a single overshoot peak followed by a steady state, η⁺ of the long fiber suspensions often passed through multiple transient regions, depending on the fiber concentration and applied shear rate. Additionally, η⁺ of the long fiber suspensions was found to be highly dependent on the initial orientation of the sheared samples. Finally, the initial and final fiber orientations of the long glass fiber samples were measured and used to initiate an explanation of the viscosity behavior. The results obtained in this research will be useful for future assessment of a quantitative correlation between transient rheology and the evolution of fiber orientation.     

玻璃纤维增强尼龙1010复合材料的摩擦学性能研究

利用ＷＺＭ－１微型注塑机制备了玻璃纤维增强尼龙复合材料,在环－块摩擦磨损试验机上考察了玻璃纤维含量和试验条件下对其摩擦学性能的影响,并利用扫描电子显微镜对其磨损机理进行了分析。结果表明：在给定试验条件下玻璃纤维含量对复合材料的摩擦学性能有显著影响,玻璃纤维质量分数介于２５％～３０％之间时增强效果较好;复合材料的摩擦系数随载荷的增加而下降,达到最小值后,又随载荷的增加而持续上升;其磨损质量损失则随载荷的增加而持续增大,复合材料的磨损以粘着磨损为主,随载荷的增加转变为以玻璃纤维的破坏和磨平为主。     

Analysis of a high intensity shear zone between overlapping fiber ends in a polymer matrix composite

The formation of high intensity shear zones in a glass fiber reinforced thermoplast is studied numerically. The thermoplast is characterized by a finite strain elastic-viscoplastic constitutive relation and the calculations are carried out using a dynamic finite element program where plane strain conditions are assumed to prevail in the direction of the thickness. Different ratios of the elongation strain and the transverse strain are studied to consider the effect of different levels of stress triaxiality and the effect of these states on the shear zone development and emerging strain and stress concentrations. Comparing a case of embedded infinitely stiff fibers to a case with glass fiber reinforcement shows little difference thus illustrating that the glass fibers act approximately as infinitely stiff. Fiber spacing and fiber width are shown to influence the shear zones and the stress fields that develop as the highly deformed region approaches the limit resulting from network stiffening in the polymer. A simple analysis assuming periodicity is included in order to study the mechanical behaviour of the polymer matrix between fiber ends with long overlap.     

Shear rheometry and visualization of glass fiber suspensions

The nonlinear rheological behavior of short glass fiber suspensions has been investigated in this work by rotational rheometry and flow visualization. A Newtonian and a Boger fluid (BF) were used as suspending media. The suspensions exhibited shear thinning in the semidilute regime and weaker shear thinning in the transition to the concentrated one. Normal stresses and relative viscosity were higher for the BF suspensions than for the Newtonian ones presumably due to enhanced hydrodynamic interactions resulting from BF elasticity. In addition, relative viscosity of the suspensions increased rapidly with fiber content, suggesting that the rheological behavior in the concentrated regime is dominated by mechanical contacts between fibers. Visualization of individual fibers and their interactions under flow allowed the detection of aggregates, which arise from adhesive contacts. The orientation states of the fibers were quantified by a second order tensor and fast Fourier transforms of the flow field images. Fully oriented states occurred for shear rates around 20 s^− 1. Finally, the energy required to orient the fibers was higher in step forward than in reversal flow experiments due to a change in the spatial distribution of fibers, from isotropic to planar oriented, during the forward experiments.     

A model long-discontinuous-fiber filled thermoplastic melt in extensional flow

The shear cell model works for dilute fiber filled systems in extensional flow. This research investigates the suitability of the idea for highly aligned fibers in a concentrated suspension. A model fiber-filled polymer system made from nylon fibers in low-density polyethylene provided a means of controlling the material parameters. Two systems, with fiber aspect ratios of 20 and 100, containing 50% 0.5 mm fibers by volume are investigated. The thickness of the polymer layer, i.e. with fibers this size, allows bulk viscosity data to be compared with the data from the filled fluid. A weaving process created the discontinuous fiber/polyethylene preforms with high alignment of the fibers and with control of the fiber to fiber overlap. Testing the polyethylene in simple shear and extending the nylon/polyethylene provided the data needed to check the micro mechanics. A cone and plate rheometer and a capillary instrument produced the viscosity/strain rate data that characterized the specific polyethylene used in the composite. A furnace inset placed in an Instron hydraulic test machine allowed extension of the filled system at strain rates from 0.002 to 0.4 s⁻¹. The shear experiments show that the low-density polyethylene is a simple shear-thinning melt that provides a good model fluid. The extension of the filled systems shows an increase of the apparent extensional viscosity from that of neat polyethylene. Apparent viscosity rises two to three orders of magnitude for the systems investigated. The micromechanics allowed the conversion of the extensional data from the two filled systems to the shear viscosity of the polymer surrounding the fibers. The calculated polyethylene viscosity compares well with the data from the standard rheometers. The shear cell approach may be applied to highly aligned, high fiber-volume-fraction suspensions when the viscosity of the polymer is known at the scale of the film surrounding each fiber.     

不同温度下2种钨结构增强Zr基非晶合金的动态压缩性能

利用SHPB装置对钨丝增强Zr基非晶复合材料和钨骨架增强Zr基非晶复合材料进行了3种环境温度下多种应变率的动态压缩性能测试。比较了2种材料的动态力学性能,发现二者均具有应变率敏感性和较强的塑性变形能力。但二者承载机制存在较大差异。钨丝增强结构变形主要表现在钨丝的失稳,由数值模拟初步分析了这种局部结构失稳控制的变形以及热失稳现象;钨骨架增强结构变形前期钨骨架起主要承载作用,而不是各成分的共同作用,这导致材料的屈服强度比纯非晶和纯钨的低。     

Extensional rheology of concentrated poly(ethylene oxide) solutions

The shear and extensional rheology of three concentrated poly(ethylene oxide) solutions is examined. Shear theology including steady shear viscosity, normal stress difference and linear viscoelastic material functions all collapse onto master curves independent of concentration and temperature. Extensional flow experiments are performed in fiber spinning and opposed nozzles geometries. The concentration dependence of extensional behavior measured using both techniques is presented. The zero-shear viscosity and apparent extensional viscosities measured with both extensional rheometers exhibit a power law dependence with polymer concentration. Strain hardening in the fiber spinning device is found to be of similar magnitude for all test fluids, irrespective of strain rate. The opposed nozzle device measures an apparent extensional viscosity which is one order of magnitude smaller than the value determined with the fiber spinline device. This could be attributed to errors caused by shear, dynamic pressure, and the relatively small strains developed in the opposed nozzle device. This instrument cannot measure local kinematics or stresses, but averages these values over the non-homogenous flow field. These results show that it is not possible to measure the extensional viscosity of non-Newtonian and shear thinning fluids with this device. Fiber spin-line experiments are coupled with a momentum balance and constitutive model to predict stress growth and diameter profiles. A one-mode Giesekus model accurately captures the plateau values of steady and dynamic shear properties, but fails to capture the gradual shear thinning of viscosity. Giesekus model parameters determined from shear rheology are not capable of quantitatively predicting fiber spinline kinematics. However, model parameters fit to a single spinline experiment accurately predict stress growth behavior for different applied spinline tensions.     

Fiber Remodeling During Torsion of a Fiber Reinforced Hyperelastic Cylinder��Unloading Behavior

Previous studies introduced a constitutive theory for fiber reinforced hyperelastic materials that allows the fibers to undergo microstructural changes. In this theory, increasing deformation of the matrix leads to increasing stretch of the fibers that causes their gradual dissolution. The dissolving fibers reassemble in the direction of maximum principal stretch of the matrix. The implications of the constitutive theory were first studied for two homogeneous deformations: uniaxial extension along the fibers and simple shear in the direction normal to the fibers. The constitutive theory was then used in treatment of the non-homogeneous deformation of combined axial stretch and twisting. The emphasis was on the determination of the influence of increasing axial stretch and twist on the spatial distribution of fiber dissolution and reassembly within the cylinder and also on the axial force and torque applied to the end faces of the cylinder. The present work is concerned with another aspect of combined axial stretch and twisting of the cylinder, namely unloading following dissolution and reassembly of some of the fibers. In this case, the cylinder is given an initial twist until there is an inner core of original fiber/matrix material and an outer sheath of remodeled fiber/matrix material. A condition is established that determines the combinations of axial stretch and twist that cause no additional dissolution and reassembly of fibers during unloading. It is also shown that there is a residual axial stretch and twist if the axial force and torque become zero. A numerical example illustrates this for a particular choice of matrix and fiber properties.     

酚醛纤维增强纸基摩擦材料的性能研究

采用湿式成型工艺制备出5种不同酚醛纤维含量的纸基摩擦材料,研究了酚醛纤维含量对纸基摩擦材料各项性能的影响.通过力学试验机测试了材料剪切强度和压缩-回弹性能,利用同步热分析仪和湿式摩擦试验机测试了材料热性能及摩擦磨损性能,通过扫描电镜观察材料摩擦表面和剪切断裂面的微观形貌.结果表明:随着酚醛纤维含量的增加,材料层间剪切强度逐渐提高,而压缩率变化较小,回弹率先增大后减小;材料耐热性随酚醛纤维含量的增加而降低;随着酚醛纤维含量的增加,磨损率逐渐降低,同时摩擦系数保持稳定.     

Rheology of an emulsion of viscoelastic drops in steady shear

Steady shear rheology of a dilute emulsion with viscoelastic inclusions is numerically investigated using direct numerical simulations. Batchelor's formulation for rheology of a viscous emulsion is extended for a viscoelastic system. Viscoelasticity is modeled using the Oldroyd-B constitutive equation. A front-tracking finite difference code is used to numerically determine the drop shape, and solve for the velocity and stress fields. The effective stress of the viscoelastic emulsion has three different components due to interfacial tension, viscosity difference (not considered here) and the drop phase viscoelasticity. The interfacial contributions – first and second normal stress differences and shear stresses – vary with Capillary number in a manner similar to those of a Newtonian system. However the shear viscosity decreases with viscoelasticity at low Capillary numbers, and increases at high Capillary numbers. The first normal stress difference due to interfacial contribution decreases with increasing drop phase viscoelasticity. The first normal stress difference due to the drop phase viscoelasticity is found to have a complex dependence on Capillary and Deborah numbers, in contrast with the linear mixing rule. Drop phase viscoelasticity does not contribute significantly to effective shear viscosity of the emulsion. The total first normal stress difference shows an increase with drop phase viscoelasticity at high Capillary numbers. However at low Capillary numbers, a non-monotonic behavior is observed. The results are explained by examining the stress field and the drop shape.     

Investigation of the rheological properties of short glass fiber-filled polypropylene in extensional flow

The behavior of short glass fiber–polypropylene suspensions in extensional flow was investigated using three different commercial instruments: the SER wind-up drums geometry (Extensional Rheology System) with a strain-controlled rotational rheometer, a Meissner-type rheometer (RME), and the Rheotens. Results from uniaxial tensile testing have been compared with data previously obtained using a planar slit die with a hyperbolic entrance. The effect of three initial fiber orientations was investigated: planar random, fully aligned in the stretching flow direction and perpendicular to it. The elongational viscosity increased with fiber content and was larger for fibers initially oriented in the stretching direction. The behavior at low elongational rates showed differences among the various experimental setups, which are partly explained by preshearing history and nonhomogenous strain rates. However, at moderate and high rates, the results are comparable, and the behavior is strain thinning. Finally, a new constitutive equation for fibers suspended into a fluid obeying the Carreau model is used to predict the elongational viscosity, and the predictions are in good agreement with the experimental data.     

Sliding plate rheometry of planar oriented concentrated fiber suspension

The rheology of concentrated planar fiber suspensions is investigated. A new experimental technique for fiber suspensions based on a sliding plate rheometer incorporating a shear stress transducer is developed. It is shown that this instrument works well for the tested material systems. The rheological behavior in steady shear is subsequently investigated. The results can be largely explained by a combination of frictional and hydrodynamic interaction. Despite this evidence of friction no yield stress could be detected for the investigated shear rates. It was also found that the fiber aspect ratio did not influence the steady shear viscosity.     

Rheological characterization of continuous fiber—reinforced viscous fluid

The present paper describes a micromechanical technique to determine rheological properties of viscous fluid reinforced with unidirectional continuous fibers. Fluid viscosity is described by a shear thinning model and high viscosity is considered for continuous fibers having considerable rigidity compared to net fluid. The microstructure is identified by a representative volume element that is subjected to equivalent macroscopic deformation fields. The energy balance and periodicity conditions are considered to relate deformation and stress in macro and micro-levels. It is shown that response of viscous fluid reinforced with rigid fibers depends on deformation history as well as rate-of-deformation in the transverse intraply shear and transverse squeeze flows. An orthotropic viscous constitutive equation is derived to describe response of such materials. The material viscosities are evaluated for viscous fluid reinforced with different fiber volume fractions during deformation applied in different rates of deformation. The results are used to derive the functions predicting effective anisotropic viscosities of reinforced fluid.     

The normal stress behaviour of suspensions with viscoelastic matrix fluids

 We investigate the variations in the shear stress and the first and second normal stress differences of suspensions formulated with viscoelastic fluids as the suspending medium. The test materials comprise two different silicone oils for the matrix fluids and glass spheres of two different mean diameters spanning a range of volume fractions between 5 and 25%. In agreement with previous investigations, the shear stress–shear rate functions of the viscoelastic suspensions were found to be of the same form as the viscometric functions of their matrix fluids, but progressively shifted along the shear rate axis to lower shear rates with increasing solid fraction. The normal stress differences in all of the suspensions examined can be conveniently represented as functions of the shear stress in the fluid. When plotted in this form, the first normal stress difference, as measured with a cone and plate rheometer, is positive in magnitude but strongly decreases with increasing solid fraction. The contributions of the first and the second normal stress differences are separated by using normal force measurements with parallel plate fixtures in conjunction with the cone-and-plate observations. In this way it is possible for the first time to quantify successfully the variations in the second normal stress difference of viscoelastic suspensions for solid fractions of up to 25 vol.%. In contrast to measurements of the first normal stress difference, the second normal stress difference is negative with a magnitude that increases with increasing solid content. The changes in the first and second normal stress differences are also strongly correlated to each other: The relative increase in the second normal stress difference is equal to the relative decrease of the first normal stress difference at the same solid fraction. The variations of the first as well as of the second normal stress difference are represented by power law functions of the shear stress with an unique power law exponent that is independent of the solid fraction. The well known edge effects that arise in cone-and-plate as well as parallel-plate rheometry and limit the accessible measuring range in highly viscoelastic materials to low shear rates could be partially suppressed by utilizing a custom- designed guard-ring arrangement. A procedure to correct the guard-ring influence on torque and normal force measurements is also presented. Received: 20 December 2000 Accepted: 7 May 2001