System identification and modeling of viscoelastic behavior from capillary melt rheological data

An investigation was conducted to identify and characterize the relaxation spectrum of polymer melts from transient capillary rheological data. System identification techniques using an iterative prediction‐error minimization (PEM) method were applied to isolate the viscoelastic melt response from the apparatus dynamics. Parameters for linear time invariant (LTI) models of varying complexity were estimated using capillary rheology data across a range of temperatures and shear rates using the principle of time‐temperature superposition. Melt capillary rheology data for polystyrene was found to exhibit viscoleastic behavior. Subsequently, three viscoelastic constitutive models were then implemented and their model coefficients directly fit using optimization techniques. The implemented methods provided useful relaxation behavior from melt capillary rheology data while also explaining much of the residual error in the purely viscous response as traditionally fit to the Cross‐WLF model. POLYM. ENG. SCI., 54:2824–2838, 2014. © 2014 Society of Plastics Engineers     

Steady‐state viscoelastic flow simulation of polymer melts in a rotational‐type rheometer

Polymer samples in the jigs begins to protrude when the heat is turned up when we measure the rheological characteristics of polymer melts using rotational‐type rheometers, such as parallel and cone‐and‐plate types. To clarify the effects of this protruding part on the obtained rheological data, we tried to evaluate the rotational‐type rheometer by a non‐isothermal viscoelastic flow simulation using the finite element method. The multiple mode Phan‐Thien Tanner (PTT) model was employed as the constitutive equation. As a result, the shear viscosity in the steady state increases with the size of the protruding part of the polymer melt specimen at the same shear rate in case with a parallel plate and a cone‐and‐plate type rheomters. In contrast, the deviation of the primary normal stress difference between the estimated value from the simulation results and the data from the PTT model is almost independent of the size of the protruding part with the cone‐and‐plate type rheometer. In addition, the deviations of the primary normal stress difference with a parallel plate rheometer increase with the protruding part size. However, these deviations are smaller than those of shear viscosity. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

A novel sliding plate rheometer for molten plastics

A novel sliding plate rheometer has been developed that is suitable for use with molten plastics, concentrated polymer solutions, raw elastomers, and other viscoelastic or thixotropic materials. It can generate steady shear rates from 0.05 to 500 s^?1 and can also be used to measure linear viscoelastic properties. In addition, it can be used to measure a broad spectrum of nonlinear viscoelastic properties such as the nonlinear relaxation modulus and the shear stress growth coefficient. In order to measure these nonlinear properties it is necessary to generate large, uniform, transient deformations Involving high strain rates. Rotational and capillary melt rheometers are not capable of generating this type of deformation, and until now it was not convenient to use sliding plate rheometers for this type of application. However, the recent development of a reliable and robust shear stress transducer makes it very convenient to use the sliding plate geometry to carry out all of these tests. The new rheometer is described, and examples of the types of data it can generate are shown.     

低密度聚乙烯熔体毛细管挤出的数值模拟

借助2种微分型黏弹性本构模型DCPP模型和S-MDCPP模型来描述支化高分子熔体的复杂流变行为,并采用离散的弹性黏性应力分裂方法（DEVSS）/迎风流线方法（SU）解决黏弹性流体流动过程中的对流占优问题以及缺少椭圆算子的问题,进而用基于有限增量微积分（FIC）方法的压力稳定型分步算法求解质量守恒方程、动量守恒方程,对低密度聚乙烯（PE-LD）熔体在毛细管中的流动情况以及挤出胀大过程进行模拟,并把模拟结果和实验结果进行比较。结果表明,在低剪切速率时,模型预测的挤出胀大比和壁面剪切应力与实验结果比较接近;2种模型预测的速度、应力以及主链拉伸的吻合程度较好,说明2种模型均能较好地预测PE?LD熔体在毛细管中的复杂流变行为;同时表明计算S-MDCPP模型时所采用的算法是可靠的。     

Analysis of variance in capillary rheometry

The effect of deformation history (hysteresis) on transient capillary rheometric data was studied compared to conventional assumptions regarding steady state data. The factors studied were: the position instrumentation, the pressure instrumentation, entrance and exit effects, polymer melt compressibility, pressure dependence of the viscosity, and polymer melt viscous heating. Statistical analysis of variance was performed to statistically determine the sources of variance to specific degrees of confidence. The polymer melt compressibility, pressure dependence, and viscous heating were found to be statistically significant contributors of the observed variation at the 95% confidence level; the capillary length and instrumentation were not found to be significant. The results indicate that the transient behavior can vary the modeling of the apparent viscosity in a significant manner such that the model fidelity and model coefficients may vary substantially. Hence, polymer melt compressibility, pressure dependence, and viscous heating should be considered during rheological model fitting to increase model fidelity and predictive accuracy in end‐use. POLYM. ENG. SCI., 56:895–904, 2016. © 2016 Society of Plastics Engineers     

The Formula for Apparent Viscosity of Polymer Melt Extruding Through a Capillary Under a Superimposed Vibration

The apparent viscosity of a polymer melt within a capillary was analyzed based on experimental measuring when a sine vibration of small amplitude was superimposed in a parallel manner on the extruding direction of polymer melt. The theoretical model for apparent viscosity of polymer melt under an superimposed vibration was set up independent of any existing constitutive equations. Meanwhile, the calculating steps for previously apparent viscosity were established by making use of novel rheological measurement equipment that was designed by the author. Through collecting and analyzing the instantaneous data of a polymer melt dynamic extruding through a capillary under definite frequency and amplitude of vibration, the apparent viscosity of a polymer melt within a capillary was then calculated.     

Effects of microstructures on the viscoelastic and rheological properties of metallocene‐catalyzed cyclo‐olefin copolymers: A preliminary study

We characterized metallocene‐catalyzed cyclo‐olefin copolymers (mCOCs) with similar heat distortion temperatures but dramatic differences in melt‐flow indices to understand how the molecular conformation affected their rheological and viscoelastic properties. The mCOC conformations were identified with ¹³C‐NMR, whereas the viscoelastic and rheological properties were measured with cone‐and‐plate and high‐pressure capillary rheometers. Our preliminary results showed that the mCOC rheological and viscoelastic properties might depend strongly on the conformation rather than the norbornene content, molecular weight, and molecular weight distribution. mCOCs containing ‐NNN‐ locks (where N represents norbornene) exhibited stronger molecular entanglements than those having no ‐NNN‐ blocks, as reflected in lower crossover frequencies and higher crossover torque. Furthermore, the existence of larger rigid ‐NNN‐ blocks resulted in higher molten viscosities and flow activation energies. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 3695–3701, 2002     

Constitutive modeling of visco-hyperelastic behavior of double-network hydrogels using long-term memory theory

Double-network hydrogels with viscoelastic behavior are appropriate materials for biomechanical applications. In this article, the standard linear solid (SLS) rheological model for the linear viscoelastic materials is generalized to the viscoelastic materials with large nonlinear deformations. Based on this viewpoint, the constitutive equation is proposed as sum of two parts including the strain-dependent elastic stress, and the viscous stress, which depends on the strain and strain rate. The elastic part of the stress is modeled via considering a hyperelastic strain energy function, while the main core of the viscous stress part requires a time-dependent weight function to satisfy the long-term memory fading principle. In addition, the weight function is proposed such that it can capture the mechanical behavior trend corresponding to the strain and strain rate for a double-network hydrogel in the relaxation test. Finally, to evaluate the performance of the proposed constitutive equation for the mechanical behavior modeling of double-network hydrogels, the tests on these materials have been used, and the material parameters are determined from fitting the experimental results to the theory. The agreement of test and theory results showed that the proposed model is capable to model the mechanical behavior of double-network hydrogels.     

A rheological study of aqueous separan solutions

The concentration dependence of the rheological response of aqueous Separan solutions was measured. The shear and primary normal stress response in steady shearing flow, and the relaxation of shear stress following cessation of steady shear flow, were measured with four different polymer solution concentrations. Two different nonlinear constitutive equations, Bird-Carreau and Meister, were used to analyse the data. The Bird-Carreau model fit the steady shear data very well and the parameters obtained from steady shear data allow reasonable estimates of the stress relaxation of these systems. The Meister model provided a fit of the transient stress relaxation data and could be used to estimate the steady shear response. No quantitative molecular theory was developed in this work. However, the nature of the concentration dependence of the Bird-Carreau parameters suggests that as the polymer concentration of aqueous Separan solutions decreases from 2.0 to 0.05 weight percent the solutions should be modeled less by an entangled network theory and more as slightly overlapping hydrodynamic units. The concentration where this behavior seems to be changing appears to be about 0.25 percent by weight of polymer.     

Capillary flow of low‐density polyethylene

The capillary flow of a commercial low‐density polyethylene (LDPE) melt was studied both experimentally and numerically. The excess pressure drop due to entry (Bagley correction), the compressibility, the effect of pressure on viscosity, and the possible slip effects on the capillary data analysis have been examined. Using a series of capillary dies having different diameters, D, and length‐to‐diameter L/D ratios, a full rheological characterization has been carried out, and the experimental data have been fitted both with a viscous model (Carreau‐Yasuda) and a viscoelastic one (the Kaye—Bernstein, Kearsley, Zapas/Papanastasiou, Scriven, Macosko, or K‐BKZ/PSM model). Particular emphasis has been given on the pressure‐dependence of viscosity, with a pressure‐dependent coefficient β_p. For the viscous model, the viscosity is a function of both temperature and pressure. For the viscoelastic K‐BKZ model, the time‐temperature shifting concept has been used for the non‐isothermal calculations, while the time–pressure shifting concept has been used to shift the relaxation moduli for the pressure‐dependence effect. It was found that only the viscoelastic simulations were capable of reproducing the experimental data well, while any viscous modeling always underestimates the pressures, especially at the higher apparent shear rates and L/D ratios. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Mechanical behavior of a semicrystalline polymer before necking. Part II: Modeling of uniaxial behavior

Based on the experimental mechanical characterization presented in Part I of this paper, a model allowing the prediction of the behavior of the studied semicrystalline polymer in the pre‐necking domain was constructed. The modeling of the viscoelastoplastic behavior of polypropylene (PP) was described by partitioning the total strain into a viscoelastic strain and a viscoplastic strain. After being improved with experimental observations, the rheological model of Zener was used to model the viscoelastic behavior of PP. As for viscoplastic behavior modeling, it was based on the characterization of the mechanical behavior performed in the first part of the study. Attention was focused on the strain reversal in order to predict the unloading path. Experimental data from the performed mechanical tests were employed to determine the parameters of the viscoelastoplastic model.     

Boron nitride as a processing aid for the extrusion of polyolefins and fluoropolymers

The influence of a new processing additive (fine particles of boron nitride) on the processability of polyolefins and fluoropolymers in extrusion is studied. The equipment used includes an Instron capillary rheometer with two types of dies, namely capillary dies and special annular dies (Nokia Maillefer wire coating crosshead) attached to the rheometer, and an extruder. Two metallocene polyethylenes and several Teflon® fluoropolymers were tested using these two pieces of equipment. The additive had a significant effect on the extrudate appearance of polyethylene and fluoropolymer particularly in the crosshead dies. It was found to eliminate surface melt fracture and to postpone the critical shear rate for the onset of gross melt fracture to significantly higher values depending on resin type, temperature, and additive concentration (typically 0.005% to 0.5%). To explain the possible mechanism for the effect of the additive on the processability of the resins, rheological measurements using both parallel‐plate and sliding‐plate rheometers were carried out. The rheology of the resins did not seem to change significantly with the addition of boron nitride except for the low‐shear‐rate (low‐frequency) range, where the behavior of the filled resin was found to be similar to that of a crosslinked polymer or a phase‐separated entangled blend. Practical wire coating and tubing extrusion studies for these resins were also carried out.     

Rheological characterization of unsaturated polyester resin sheet molding compound

This paper presents a theoretical and experimental analysis of the rheological behavior of sheet molding compound (SMC). The work analyses the squeeze flow in a parallel plate plastometer of SMC discs which contain 25 percent of fiber glass by weight. This method of flow characterization gives a good insight into the basic rheological behavior of SMC for the compression molding process when producing flat parts. The theoretical analysis applies to thickened and matured SMC at room temperature. The analysis treats SMC as a viscoelastic material having an equation of state with viscous, elastic and yield elements. The time variation of compressive force when squeezing SMC discs between two parallel plates (one fixed and one mobile) has been derived from the equation of state. The values of the viscous, elastic and yield parameters were determined by using a least squares method of curve fitting to the experimental results. There are two aspects to the reported experimental work. One aspect is concerned with showing that the three element model for the equation of state provides a realistic mathematical basis for characterizing the rheological behavior of SMC at room temperature. The other shows how the parallel plate plastometer can be used to give data which characterize SMC flow behavior under conditions similar to those of the actual compression molding process.     

由聚丙烯熔体的流变行为测定其分子量分布

研究了Ｚ３０Ｓ等４种聚丙烯（ＰＰ）切片的流变行为，分别用毛细管流变仪和平板流变仪进行稳态和动态流变特性的测试，测得流变曲线、动态模量及复数粘度。讨论了温度、剪切速率、角频率、分子量（ＭＷ）和分子量分布（ＭＷＤ）对流变行为的影响。研究表明，从稳态和动态测得的流变曲线求得的４种ＰＰ切片的分子量及其分布指数是同落球粘度法与熔融指数法相结合求得的分子量分布指数相吻合的。     

多孔SiC中黏弹性流体的流变性数值研究

为研究黏弹性流体在多孔SiC中流变行为,将多孔SiC的骨架建成十四面体结构单元的阵列,利用POLYFLOW计算流体力学软件,黏弹性流体的本构方程采用PTT模型,主要研究黏弹性流体流经多孔SiC的法向应力及剪切应力随松弛时间、多孔介质孔径以及流速变化规律,以及剪切速率的分布特点。黏弹性流体弹性越强,孔道结构对其作用的应力越大,从而使聚合物分子链发生断裂的几率越大。     

Rheological characterization of controlled-rheology polypropylenes using integral constitutive equations

Controlled-rheology polypropylene melts were prepared via molecular modification of a commercial polypropylene resin. A peroxide-initiated degradation was performed, resulting in materials with different molecular weight distributions. These resins were subjected to rheological characterization, and an integral constitutive equation of the K-BKZ type was used to study the effect of molecular weight characteristics on their rheological properties. Data for the linear viscoelastic spectrum and shear viscosities was used to obtain the model constants. The same constitutive equation has been used to predict the stress and Trouton ratios for simple shear and simple elongational flows, thus giving a quantitative assessment of the viscoelastic character of the melts. The results show the effect of the molecular modification on the rheological behavior of the melts. Polymers produced at higher peroxide concentrations exhibit reduced viscoelasticity manifested in less shear-and strain-thinning behavior. The present work clearly shows the potential of integral constitutive equations in fitting and interpreting experimental data and, thus, giving a much better understanding of the rheological behavior of commercial polymers. © 1996 John Wiley & Sons, Inc.     

The role of the interface in melt linear viscoelastic properties of LLDPE/LDPE blends: Effect of the molecular architecture of the matrix

The rheological properties of blends consisting of a long chain branched low‐density polyethylene (LDPE) and two linear low‐density polyethylenes (LLDPE) are studied in detail. The weight fractions of the LDPE used in the blends are 5 and 15%. The linear viscoelastic characterization is performed at different temperatures for all the blends to check thermorheological behavior and miscibility in the melt state. Blends containing metallocene LLDPE as the matrix display thermorheologically complex behavior and show evidences of immiscibility in the melt state. The linear viscoelastic response exhibits the typical additional relaxation ascribed to the form deformation mechanism of dispersed phase droplets (LDPE). The Palierne model satisfactorily describes the behavior of these blends in the whole frequency range explored. However, those blends with Ziegler‐Natta LLDPE as the matrix fulfill the time‐temperature superposition, but exhibit a broad linear viscoelastic response, further than the expected for an immiscible system with a sharp interface. The rheological analysis reveals that, in addition to the droplets form relaxation, another mechanism at lower frequencies exists. The broad linear response of the blends with the Ziegler‐Natta LLDPE can be explained by hypothesizing a strong interaction between the high molecular weight linear fraction of the LLDPE and the low molecular weight (almost linear) chains of the LDPE phase, forming a thick interface with its own viscoelastic properties. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Rheological analysis of polyvinyl butyral near the glass transition temperature

In many polymer manufacturing operations, the material is processed near the glass transition temperature (T_g). Examples are thermoforming, blow molding, film blowing, hot embossing, forging, plastic welding, and de‐airing in safety glass lamination. In these processes, solid‐like behaviors such as strain hardening and yielding play important roles. These material properties cause the material to flow (or deform) in a way that substantially differs from a polymer melt. In order to understand the flow behavior near the T_g, polyvinyl butyral (PVB), a rubbery polymer used in safety glass lamination, was studied in this work. The flow properties of the polymer above the T_g were characterized by using both shear and elongational rheometers, and a tensile tester. The measured flow properties were described by a viscoelastic constitutive model.     

Using multiple‐mode models for fitting and predicting the rheological properties of polymeric melts. II. Single and double step‐strain flows

Several classes of multiple‐mode rheological constitutive equations are examined for predicting the viscoelastic flow properties of a typical polymer melt in single and double step‐strain flows. The phenomenological parameters appearing in these models have been obtained by the fitting of experimental data taken in small‐amplitude oscillatory shear and steady shear flows. The performance of the models for predicting the experimental data in the step‐strain experiments is examined in detail. Specifically, we examine whether or not mode coupling is necessary to describe the experimental behavior under step‐strain flows. Furthermore, it is demonstrated that the reversing double step‐strain experiment is a very powerful tool for testing viscoelastic constitutive equations. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Shear modification of low density polyethylene

A single screw extruder was used to impose different shear histories on a low density polyethylene with broad molecular weight distribution and high molecular weight tail that had very little long chain branching. This polymer exhibits relatively high melt elasticity and the viscoelastic properties of its melt are strongly affected by preshearing. Such changes are accomplished without significant changes in molecular weight distribution or chemical structure. Measured viscous and elastic properties of the melt are different from piston-driven and screw extruder capillary rheometers. Shear modification effects in single screw extruders are enhanced by decreasing melt temperature, increased screw rotation speeds, and higher screw compression ratios. Melt elasticity can be cycled between high and relatively low values, for the particular polymer, by annealing or shearing the polymer melt.