Rheological behavior of highly filled ethylene propylene diene rubber compounds

The rheological behavior of highly filled ethylene propylene diene rubber (EPDM) compounds was studied with respect to the effect of curative system, grafted rubber, shear rate, temperature and die swell using a Monsanto Processability Tester (MPT) to gain an understanding of the molecular parameters that control the surface finish. All systems show pseudoplastic behavior. At a particular shear rate, shear viscosity increases with blend ratio. The dependence of flow behavior on extrusion velocity indicates a surface effect. The extrudate die swell and maximum recoverable deformation are related by a linear relationship, which is independent of sulfur/accelerator ratio, extrusion temperature and shear rates and blend ratio. The principal normal stress difference increases nonlinearly with shear stress. Activation energy decreases with shear rate in most cases. The faster relaxing system produces extrudate of better surface quality.     

Studies on wire coating extrusion. I. The rheology of wire coating extrusion

Wire coating extrusion was studied, both experimentally and theoretically, using a pressure-type die. For the experimental study, a wire coating apparatus of laboratory scale was constructed, consisting of a pay-off device, extruder, cross-head and pressure-type die, cooling trough, and take-up device. The materials used were low- and high-density polyethylenes and thermoplastic rubber. The following measurements were taken during the experiments: (1) the axial pressure profiles in the die, (2) melt flow rate, and (3) take-up speed. The measurements were then used to determine the effect of the rheological properties of the polymers on the performance of the wire coating operation. It was found that a reduction in axial pressure gradient and a reduction in the recoverable elastic strain of a molten polymer at the die exit can be realized as the speed of the wire is increased. For the theoretical study, using a power-law model, the equations of motion were solved numerically to predict the volumetric flow rate as functions of the pressure gradient in the die and the rheological properties of the polymer being extruded. Solution of the system equations permitted us to predict the velocity profile and shear stress distributions of a molten polymer inside a pressure-type wire coating die.     

Rheology and wire coating of high atomic number metal-low density polyethylene composites

The rheological properties of high atomic number metal-low density polyethylene composites were investigated. Tungsten, tungsten carbide, and lead powders were studied at concentrations up to 10 volume percent. Viscosity-shear rate, die swell-shear rate, and melt draw down to break data were, determined as functions of filler type, filler concentration, and particulate size at 200°C. The viscosity data were found to fit the Einstein relationship over the range of filler loadings and shear rates investigated. Tanner's equation was used to calculate the first normal stress difference from the die swell data. The effect of the fillers on the predicted first normal stress difference was contrary to previously observed experimental evidence. Melt draw down to break data was found to be very sensitive to filler contamination and correlated quite well with wire coating experiments. During low-speed wire coating runs coating quality was found to be seriously affected by small levels of contamination present in the fillers. Coating duality was determined by surface smoothness and uniformity.     

聚合物多层共挤成型离模膨胀过程的三维黏弹性数值模拟

共挤成型中,聚合物黏弹特性与过程参数波动的耦合作用会产生波动的离模膨胀,使得根据共挤制品的形状设计相应的共挤定型口模在工程上仍是一项技术挑战。基于这一技术问题,通过建立的稳态有限元数值算法,系统研究了过程参数和黏弹性流变性能参数对共挤成型离模膨胀的影响规律和机理。研究结果表明,多层共挤口模芯壳层熔体离模膨胀是由熔体的二次流动引起,主要取决于芯壳层熔体二次流动的方向与强度。熔体二次流动的方向与第二法向应力差的正负号有关,而熔体二次流动的强度则与第二法向应力差大小呈正比。芯层熔体的离模膨胀与口模出口和混合区进口处芯层熔体向外的二次流动强度呈正比,而壳层熔体的离模膨胀取决于壳层熔体内外界面向外的二次流动的相对强度。研究还表明芯、壳层熔体及口模整体的离模膨胀随着壳层熔体黏度的增大而增加,而随着壳层熔体进口流量的增大而减小。     

Shear flow of assemblies of cohesive granular materials under constant applied normal stress

We have studied plane shear flow of nearly homogeneous assemblies of uniformly sized, spherical, cohesive particles in periodic domains under constant applied normal stress. Our focus has been on (a) exploration of the effect of inter-particle attractive forces on the flow behavior manifested by dense assemblies under constant applied normal stress, and (b) comparison of the rheological characteristics observed under constant-applied normal stress and constant-volume conditions. As a model problem, the cohesion resulting from van der Waals force acting between particles is considered. Simulations were performed for different strengths of cohesion, shear rates, and applied stresses. From each simulation, the volume fraction, shear stress and the average coordination number have been extracted. We find that cohesive assemblies sheared under constant applied normal stress shear differently from those sheared at constant volume only in the dynamic sense, while the time-averaged rheological characteristics are essentially indistinguishable. At constant volume, the fluctuations in shear stress are larger than, but have the same dependence on cohesion as under constant applied normal stress. This study has also exposed a pronounced dependence of the apparent coefficient of friction on particle volume fraction in the quasi-static flow regime.     

Influence of inertia and viscoelasticity in entry flows through an abrupt annular contraction

A numerical simulation of entry flows in an annular die has been undertaken for Newtonian and power-law fluids as well as viscoelastic fluids that exhibit normal stresses in shear flow. Experimentally measured normal stress and viscosity data are included in a simple rheological model. The influence of inertia and viscoelasticity are examined separately as functions of the Reynolds (Re) and Weissenberg (Ws) numbers. It is found that inertia decreases the size of the corner vortices in the reservoir corners which tend to increase rapidly with elasticity level in the absence of inertia. The combined effect of inertia and elastic forces is to first increase the vortex size followed by a decrease at higher Re numbers. The numberical simulations are in qualitative agreement with experimental studies available in the literature.     

Elongational rheology of polymer melts and solutions

Elongational rheological properties of polymer melts and solutions may be measured using nonlubricated flow characteristics through a semihyperbolic converging die. The effects of body forces related to developing orientation in the fluid during converging extensional flow are so strong that the shearing contribution become negligible in comparison, eliminating the need for lubrication to achieve an essentially pure elongational flow. The effective elongational viscosities of polypropylene melts and lyocell solutions correlated with shear-flow determinations were used to estimate the enthalpy and entropy changes as function of processing conditions. The flow of lyocell solutions through a converging die had, as a result, not only phase separation and cellulose crystallization, but also microfibers formation and high orientation. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 69: 2357–2367, 1998     

附加惯性力作用下竖直矩形流道内过冷流动沸腾的数值模拟

摇摆条件下附加惯性力的作用会对两相流动的压降及汽泡受力产生影响。考虑相变能量和质量输运,采用流体体积(VOF)多相流模型对附加惯性力条件下竖直矩形流道内过冷流动沸腾进行了数值模拟。汽液界面位置通过分段线性插值(PLIC)的方法获得。模拟结果获得了孤立汽泡周围压力、速度、温度分布以及二次流动现象,分析了汽泡聚合过程汽泡形态及内部速度矢量的演变过程,模拟结果与文献中结论吻合良好。附加惯性力作用使得流动压降比静止条件下要大,过冷流动沸腾压降由于汽相产生会在单相流动的基础上产生波动,且热通量越大,压降波动幅度越大。摇摆产生的附加惯性力相对汽泡所受的其他力而言可以忽略不计,而摇摆导致的流量波动会改变汽泡受力大小,进而影响沸腾换热。     

Studies on wire coating extrusion. II. The rheology of wire coating coextrusion

An experimental and theoretical study of wire coating coextrusion through a pressure-type die was carried out. For the experimental study, the wire coating apparatus employed was the same as that described in Part I of this series (14), except for the newly constructed coextrusion die. The die was provided with three melt pressure transducers along the axial direction, which permitted us to determine the pressure gradient in the die. It was found that a reduction in pressure gradient was realized when a lower viscosity polymer was coextruded with a high viscosity polymer. The materials used for the coextrusion were combinations of low-density polyethylene, high-density polyethylene, polystyrene, and two different commercially available thermoplastic rubbers (UniRoyal TPR-1900 and Shell Kraton G 2701). The use of a high shrinking (crystalline) polymer inside a low shrinking (amorphous) polymer was found to give rise to distorted coatings (non-circular cross section of the coated wire). The interface between the coextruded layers was examined under a magnifying lens, and it was found that under certain processing conditions, the interface was highly irregular. Experimental correlations were obtained to explain the onset of an unstable interface in terms of the rheological properties of the individual components being coextruded, and of the processing variables. It was found that interfacial instability occurs when the shear stress and the viscosity ratio (also elasticity ratio) of the two components at the interface exceed certain critical values. For the theoretical study, using a power-law model, the equations of motion were solved numerically to predict the volumetric flow rate as functions of the pressure gradient in the die and the rheological properties of the polymers being coextruded. Solution of the system of equations permitted us to predict the velocity profile and shear stress distributions of two molten polymers inside a pressure-type wire coating coextrusion die. Comparisons were made between the experimental and theoretically predicted volumetric flow rates. The comparison was found to be reasonably good with certain systems. The discrepancy between the experimentally obtained and the theoretically predicted volumetric flow rates was attributed to interface migration and interfacial instability.     

The numerical simulation of boger fluids: A viscometric approximation approach

A general-purpose finite element program has been used to simulate the flow of nonshear-thinning, highly elastic polymer solutions (Boger fluids). In particular, the creeping flow through an abrupt 4:1 circular and planar contraction is studied, as well as the flow at the exit of a capillary die for the determination of extrudate swell. Experimentally measured normal stress and viscosity data are included in a simple rheological model, based on the viscometric simplification of the CEF constitutive equation. Vortex size and intensity in the die entry and extrudate swell at the die exit increase rapidly, with elasticity level, in general agreement with experimental findings. It is shown that despite the limitations of the model, the viscometric approximation can be used to study the effect of normal stresses in cases where a main flow direction can unambiguously be defined. In die exit Flows, it can also provide an upper limit for the determination of extrudate swell, while Tanner's theory of elastic recovery provides the lower limit.     

Hydrodynamic analysis of the mechanisms of agglomerate dispersion

Hydrodynamic dispersion of particle agglomerates occurs whenever the applied shear stresses can break the interparticle bonds responsible for the cohesivity of the agglomerate. Various mechanisms of hydrodynamic dispersion have been demonstrated for silica agglomerates infiltrated to different extents by the suspending fluid. In some cases, hydrodynamic forces are sufficient to induce the removal of incompletely infiltrated fragments from the parent agglomerate (dry cohesive failure) or the breakage of wetted fragments from the infiltrated portion of the parent agglomerate (wet cohesive failure). Dispersion can also occur such that a portion of the fracture surface originates at the interface between the infiltrated periphery of the agglomerate and its dry core (adhesive failure). To elucidate the tendencies for dispersion via various modes, a hydrodynamic analysis of the forces acting on and within the agglomerate has been performed for both uninfiltrated and partially infiltrated structures. This analysis reveals that the size of the region on which the hydrodynamic stress bears is sensitive to the degree of infiltration, which is consistent with the observed shifts in dispersion mechanism.     

Finite element modeling of the flow of a rubber compound through an axisymmetric die using the CEF viscoelastic constitutive equation

This work is devoted to the simulation of the flow of a high viscosity NR/SBR rubber compound through the die of a single screw extruder with axisymmetric geometry. An in-house developed computer code based on the use of continuous penalty finite element method was employed. Three constitutive equations including two generalized Newtonian models namely; power-law and Carreau and an explicit viscoelastic model named CEF (Criminale-Ericksen-Fillbey) were used to reflect the rheological behavior of the material. Using the parameters of the rheological models determined by a slit die rheometry technique, the flow of the compound was simulated through the die and results were compared with experimentally measured mass flow rates. It is shown that for high viscosity rubber compounds the use of generalized Newtonian models which do not take the normal stress in simple shear flow into consideration gives rise to significant errors in prediction of mass flow rates. On the other hand, comparing the simulations results using the CEF equation with experimental data revealed that this model is the best compromise between generalized Newtonian and full viscoelastic models which need high computational costs and effort. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

EPDM橡胶的流变特性实验研究

为了研究橡胶熔体流变性能对其加工成型的影响，利用毛细管流变仪对三元乙丙橡胶（EPDM）的流变特性进行了实验研究。实验结果表明：EPDM橡胶在毛细管挤出时，剪切速率对剪切应力、剪切粘度和挤出胀大的影响最大；挤出温度对三者有一定的影响；在长径比相同时，毛细管半径对剪切应力和剪切粘度几乎没有影响，但对挤出胀大影响较大。     

Finite element analysis of wire coating

A general-purpose finite element program has been used to simulate the flow of polymers through wire-coating dies. The analysis includes Newtonian and power-law fluids. The effect of normal stresses was examined through a simple viscoelastic constitutive equation, Nonisothermal wire coating was studied to obtain the temperature field within the melt. The effect of a slip condition at the solid boundaries was also examined. The determination of the coating melt free surface was carried out through an iterative procedure. The finite element solution provides details about the existence and extent of recirculation regions, about hot spots due to viscous dissipation, and also captures the stress singularities present at the impact of the melt with the wire and at the exit from the die. Pressure distribution, maximum temperature rise, haul-off wire tension, maximum wire tension, and stresses at the wire surface and die wall are also presented.     

Elastic Behavior Analysis of Polymer Melt Extruding through Capillary with An Additional Sinusoidal Vibration

Summary A novel rheological measuring apparatus was designed by the authors, which introduced an additional sinusoidal vibration in parallel on the extruding direction of polymer melt and was called as Constant Velocity Dynamic Capillary Rheometer in this article. After introducing different melt extrusion speeds and different intensities of vibration, the rheological measuring experiments for a LDPE melt were done respectively by using above-mentioned apparatus, and a mathematical model for the primary normal stress difference of polymer melt under the action of vibration was set up accordingly. Then, the change laws of die swell ratio and those of the primary normal stress difference under different frequencies and amplitudes of vibration were obtained. Compared with the stable state extrusion, after introducing an additional sinusoidal vibration, the die swell ratio and the primary normal stress difference of polymer melt are all decreased obviously.     

Model for Compaction of Ceramic Powders

The use of the Coulomb yield criterion to describe the compaction of granular material is proposed. Its use is demonstrated by the numerical solu tion of the stress and displacement equations de scribing the axisymmetric pressing of a cylindrical compact. The model is applied to the pressing of uranium dioxide pellets; to do so, the shear strength of the pellets is measured as a function of normal stress. These measurements showed an increase of shear strength with normal load and permitted assignment of values of cohesion and angle of internal friction to be used in the Coulomb failure condition. The computed re sults of die wall friction, normal force at the die wall, and stress distribution in the compact are compared with measured results.     

钢丝缠绕液压胶管设计优化有限元分析

钢丝缠绕胶管的爆破压力、轴向变形和径向变形与钢丝缠绕角度密切相关,目前的研究和工程实践中主要是基于压力容器薄膜应力理论和经验公式对四层排布角度相同或者相近的软管进行分析和设计。但是由于薄膜理论的假设建立在胶管小变形和材料各向同性的假设条件下,而由于各层钢丝在受力后,会发生耦合作用,工程上已发现四层角度相同的设计,无论在受力,还是轴向位移都不是最佳方案,不能满足优化的目的。因此,本文使用有限元的分析方法,对四层缠绕胶管的排布角度进行独立优化,发现四层钢丝缠绕胶管每层角度的变化对其本层和其他三层的应力分布均有影响,并且有一定的规律性。利用这一规律,可以实现对钢丝缠绕胶管排布角度的优化,使爆破压力和变形都达到符合使用要求的结果。本文分析的结果被证明和工程试验结果有很好的相关性。     

A model viscoelastic fluid

Shear stress and first normal stress difference data are presented for materials which exhibit a constant viscosity and yet at the same time exhibit elasticity levels of the same order as polymer melts. Flow pattern observations in circular die entry flows in conjunction with independent shear and normal stress measurement strongly suggest that these fluids would make excellent model fluids for melt studies. Studies in which the influence of elasticity in the absence of shear thinning and fluid inertia can easily be made. Furthermore it is clearly shown that a realistic solution to the die entry flow problem is not obtained using second order flow theory. In the second order region the secondary cell is observed to be almost identical in size to the cell observed for an inelastic Newtonian fluid in creeping flow. Marked growth in the secondary cell as a function of elasticity is not observed until the shear rates exceed the region of second order behavior. This growth in cell size as a result of elasticity is followed at higher shear rates by a spiraling flow instability like that observed for some polymer melts.     

Plasto-Hydrodynamic Tube Sinking: Effect of the Change in Viscosity in Theoretical Analysis

Plasto-hydrodynamic die-less tube sinking is a relatively new process that eliminates the need for a conventional reduction die. The pulling action of the tube through the viscous fluid gives rise to drag force and generates hydrodynamic pressure, the magnitude of which depends on the type of the fluid pressure medium, working temperature, tube speed, and the geometry of the pressure unit. This hydrodynamic pressure combined with the shear stress initiates the reduction of the tube diameter, avoiding metal-to-metal contact. In previous theoretical works on the hydrodynamic tube sinking process, the change in polymer viscosity within the pressure units and the consequent change in shear stress were not incorporated. In this paper a combined analytical and numerical solution is developed for predicting the reduction in diameter, taking account of the changes in the viscosity of the polymer melt within a stepped parallel bore unit in the tube sinking process.     

熔体挤出速度对共挤吹塑型坯离模膨胀影响的数值模拟

基于三维非等温黏弹性熔体多相分层流动有限元数值模拟技术,模拟研究了熔体挤出速度对多层共挤吹塑成型环坯离模膨胀和初始温度场的影响规律,揭示了型坯离模膨胀的产生机理。结果表明,多层共挤吹塑成型环坯离模膨胀是由熔体的二次流动诱发而产生,与熔体流出机头进入自由膨胀段的二次流动强度成正比,而其二次流动强度随着熔体挤出速度的增大而增强,因而导致环坯离模膨胀随着熔体挤出速度的增加而增大;多层共挤吹塑成型熔体的二次流动强度与其第二法向应力差成正比关联关系,这与Debbaut的试验研究结论完全吻合,表明二次流动是由第二法向应力差驱动而产生。