Effect of viscoelasticity in the film‐blowing process

Numerical simulations have been undertaken for the film‐blowing process of viscoelastic fluids under different operating conditions. Viscoelasticity is described by an integral constitutive equation of the K‐BKZ type with a spectrum of relaxation times, which can fit the experimental data well for the shear and extensional viscosities and the normal stresses measured in shear flow. Nonisothermal conditions are considered by applying the Morland–Lee hypothesis, which incorporates the appropriate shift factor and pseudotime into the constitutive equation. The momentum and energy equations are expressed in the machine direction only by using a quasi‐one‐dimensional approach introduced earlier by Pearson and Petrie. The resulting system of differential equations is solved using the finite element method and the Newton‐Raphson iterative scheme. The method of solution was first checked against the Newtonian and Maxwell results for various film characteristics given earlier. The simulations are compared with available experimental data and previous simulations in terms of film shape, velocity, stresses, and temperature. The present results show that the existing modeling of force balances is inadequate for quantitative agreement with the experimental studies. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007     

An experimental investigation of normal and shear stress interaction of an epoxy resin and model predictions

The axial‐torsional interaction of an epoxy resin was investigated by subjecting thin‐walled tubular specimens to combined normal and shear stress components. It is shown that a superimposed normal stress (tensile or compressive) or hydrostatic pressure will influence shear creep behavior. Similarly, a superposed shear stress affects the normal stress response of the resin. The axial‐torsional stress interaction is also observed in transient stress responses under different strain paths, and in the creep deformation with non‐proportional stress histories. Urear viscoelastic constitutive models are unable to predict the aforementioned behaviors. Two typical nonlinear viscoelastic constitutive models are examined with respect to their capabilities to predict the observed response. It Is shown that the predictions of these two models agree only qualitatively but not quantitatively with the experimental results.     

Numerical simulation of viscoelastic two-phase flows using openFOAM

In this work a new solver is developed for the OpenFOAM^® CFD toolbox, which handles viscoelastic two-phase flows. A derivative of the volume-of-fluid (VoF) methodology is used to describe the interface. Established constitutive equations derived from kinetic theory, such as Oldroyd-B, Giesekus, FENE-P and FENE-CR, from network theory of concentrated solutions and melts, such as linear and exponential Phan-Thien–Tanner (PTT), and from reptation theory, such as Pom–Pom and XPP models, as well as multi-mode formulations are implemented in OpenFOAM. Validation of the numerical technique is performed by comparing detailed simulation predictions to data from several experimental studies, numerical studies and analytical models found in the literature. Two well-known viscoelastic free-surface effects, namely the Weissenberg and the Die Swell effect, are simulated. Furthermore, transient and steady-state droplet flow in shear and elongational flows is examined.     

A practical approach to modeling time‐dependent nonlinear creep behavior of polyethylene for structural applications

The purpose of this work is to develop a practical method for constitutive modeling of polyethylene, based on a phenomenological approach, which can be applied for structural analysis. Polyethylene is increasingly used as a structural material, for example, in pipes installed by trenchless methods, where the relatively low stiffness of polyethylene reduces the required installation forces, chemical inertness makes it applicable for corrosive environments, and adequate strength allows its use in sewer, gas, and water lines. Polyethylene exhibits time‐dependent constitutive behavior which is also dependent on the applied stress level resulting in nonlinear stress–strain relationships. Nonlinear viscoelastic theory has been well established and a variety of modeling approaches have been derived from it. To realistically utilize the nonlinear modeling approaches in design, a simple method is needed for finding a constitutive formulation for a specific polyethylene type. This paper presents such a practical approach to nonlinear viscoelastic modeling utilizing both the multi‐Kelvin element theory and the power law functions to model creep compliance. Creep tests are used to determine material parameters and models are generated for four different polyethylene materials. The corroboration of the models is completed by comparisons with results from different tensile creep, step‐loading creep, and load‐rate tests. POLYM. ENG. SCI., 48:159–167, 2008. © 2007 Society of Plastics Engineers     

Non-linear viscoelastic behavior and damping factor of polypropylene/clay nanocomposites

The non-linear viscoelastic properties of pure polypropylene and its clay nanocomposites are studied to establish structure–property relationship in conjunction with clay concentrations. First, flow birefringence is performed through a slit-die to obtain centerline principal stress difference during elongational flow for clay nanocomposites. The centerline stress profile of clay nanocomposite reveals additional viscoelastic nature even at low silicate concentrations, while similar short-time chain relaxation is observed. The effects of higher clay concentrations are further examined during the simple shearing flow to consider damping properties of the clay nanocomposites. The step strain, dynamic shear and steady shear are performed. All the samples show time-strain separable melt flow behavior adequately demonstrated through Wagner’s exponential damping function. The damping coefficient is found to be strongly dependent on clay percentage revealing viscoelastic differences therein. We have also used a time-strain separable Kaye-Bernstein Kearsley Zapas (K-BKZ) type constitutive equation to predict steady shear stress. The suggested constitutive model satisfies simple shear at lower fractions of clay while the damping function behaves similar to pure polymer thought to result from the absence of filler–filler interactions and chain length degradation. The unusual rheological behavior for maximum clay concentration studied is explained on experimental as well as theoretical basis. Thus, the results of this investigation would improve the theoretical understanding of possible molecular orientations at different clay concentrations during elongational and shearing flows.     

Tensile creep of a long‐fiber glass mat thermoplastic composite. I. Short‐term tests

This work is part of a larger experimental program aimed at developing a semi‐empirical constitutive model for predicting creep in random glass mat thermoplastic (GMT) composites. The tensile creep response of a long‐fiber GMT material has been characterized for 3‐ and 6‐mm thick material. Tensile tests showed that the variability within and between plaques are comparable with an overall variability of about 6% and 8% for the 3‐ and 6‐mm thick materials, respectively. The thicker material exhibited slightly higher variability and directional dependence due to greater flow during molding of the plaques. Short‐term creep tests consisting of 30 min creep and recovery, respectively, were performed over the stress range between 5 and 60 MPa. Three tests for determining the linear viscoelastic region were considered which showed that the 3‐ and 6‐mm thick GMT are linear viscoelastic up to 20 and 25 MPa respectively. The 6‐mm thick GMT consisting of a higher fiber weight fraction was linear over wider stress range. Furthermore, it was found that plastic strains were accumulated during creep, which suggests that a nonlinear viscoelastic–viscoplastic model would be more appropriate for long‐term creep at relatively high stresses, which will be presented in our companion paper. The magnitude of the plastic strains developed in the creep tests presented here was lower because a single specimen was loaded at multiple stress level over short durations. Hence, a nonlinear viscoelastic constitutive model has been developed for the two thickness materials. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers     

Rate‐dependent constitutive equations for carbon fiber‐reinforced epoxy

A rate‐dependent constitutive model for carbon fiber‐reinforced polymers was developed by assuming that the rate‐dependent characteristics of the composite could be described by stress relaxation of the polymer matrix. Relaxation functions in longitudinal, transverse, and in‐plane shear modes were derived in terms of separate matrix and fiber properties and the rules of mixture. The epoxy was represented as two Maxwell elements in parallel with a linear elastic spring, while the carbon was modeled as a linear elastic spring. The rate‐dependent, laminate stiffness matrix for a unidirectional IM6G/3501–6 carbon/epoxy laminate was found by fitting the rate‐dependent constitutive equations to material test data at constant strain rates ranging from 0.01 to 2,500 s⁻¹. The transient deformation response of a [(0₈/90₈)₂/0 ₈]_s IM6G/3501–6 carbon/epoxy composite laminate under dynamic in‐plane loading could be predicted within 5% of experimental data using this laminate stiffness matrix. The rate‐dependent constitutive equations were also incorporated into LS‐DYNA3D via a user‐defined material subroutine and used to predict the transient response of a 32 ply AS4/3501–6 carbon/epoxy laminate under projectile loading. The maximum contact force between the projectile and laminate was found to be 7% higher than the experimental data. POLYM. COMPOS. 27:513–528, 2006. © 2006 Society of Plastics Engineers.     

E‐Glass/DGEBA/m‐PDA single fiber composites: The effect of strain rate on interfacial shear strength measurements

Precise measurements of fiber break regions have been made during the single fiber fragmentation test (SFFT) procedure on E‐glass/diglycidyl ether of bisphenol‐A (DGEBA)/meta‐phenylenediamine (m‐PDA) test specimens. From these measurements, the location and size of each fiber fragment was determined, and the resulting information was used to construct fragmentation maps of the tested fiber. By comparing these maps, the fragmentation process supports random fragmentation along the length of the fiber. Since the interfacial shear strength (IFSS) or the interfacial shear stress transfer coefficient (I‐STC) is obtained from the fragment length data at the end of the test (saturation), frequency histograms of the fragment length data were constructed to determine the repeatability of the fragmentation process. Since the SFFT is performed by sequential step‐strains of the test specimen, test protocols were developed by controlling the step size of each strain increment and the time between each step‐strain (dwell time). For the testing protocols used in this research, the E‐glass/DGEBA/m‐PDA frequency histograms of the fragment lengths were found to be generally repeatable. However, when the effective strain rate of the test was altered by changing the dwell time between strain increments, the fragment distribution at saturation of the E‐glass/DGEBA/m‐PDA SFFT specimens changed. The direction of the change was found to be inconsistent with the effect one might expect when only the nonlinear viscoelastic behavior of the matrix is considered. However, the magnitude of the change observed in the E‐glass/DGEBA/m‐PDA SFFT specimens is not universal. Fragmentation data obtained on E‐glass/polyisocyanurate SFFT specimens revealed a much smaller change in fragment length distributions with the same change in testing protocols. Consistent with the results obtained on the E‐glass/DGEBA/m‐PDA, fiber fragmentation occurs when the polyisocyanurate matrix exhibits nonlinear viscoelastic behavior. The implication of these results for interfacial shear strength measurements is discussed.     

On Mooney and Mooney stress relaxation. II. A nonlinear viscoelastic description: Experimental and numerical results

It has been investigated whether the stress build‐up and the stress relaxation involved in a Mooney test, with subsequent Mooney stress relaxation, can be described by nonlinear viscoelastic theory, more particularly the Wagner constitutive model. For this purpose, the viscoelastic behavior of three nonvulcanized EPDM materials, with similar Mooney viscosity but varying elasticity, has been studied. Relaxation time spectra were obtained from dynamic mechanical experiments, from which the step‐strain stress‐relaxation modulus was calculated. Stress build‐up experiments were performed with a cone and plate system in order to obtain the so‐called damping function (a measure for the deformation sensitivity) of the materials. Using these material functions, the Mooney test was successfully described with the Wagner constitutive model. Experimental and theoretical Mooney stress‐relaxation rates are in close agreement. The predicted Mooney viscosity is up to 25% lower than the measured value. This may be due to nonideal conditions during the Mooney test, such as inhomogeneous heating and secondary flows, and to inaccuracy of the damping function. The model calculations confirm the strong experimental dependence of Mooney measurements on small variations in instrumental conditions such as geometry, rotation speed, and so forth. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 1220–1233, 1999     

Modeling and simulation of conditionally volume averaged viscoelastic two‐phase flows

Conditional volume averaging is used to develop a model capable of simulating two‐phase flows of viscoelastic fluids with surface tension effects. The study is started with the single‐phase mass and momentum balances, which are subsequently conditionally volume averaged. In doing so, we arrive at a set of equations having unclosed interfacial terms, for which closure relations for viscoelastic fluids are presented. The resulting equations possess a structure similar to the single‐phase equations; however, separate conservation equations are solved for each phase. As a result, each phase has its own pressure and velocity over the entire domain. Next, our numerical implementation is briefly outlined. We find that a Poiseuille single‐phase flow is predicted correctly. The closure terms are examined by considering a two‐phase shearing flow and a quiescient cylinder with surface tension. A convergence analysis is performed for a steady stratified two‐phase flow with both phases being viscoelastic. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3914–3927, 2013     

Rheological behavior of noncompatibilized and compatibilized PP/PET blends with SEBS‐g‐MA

The rheological behaviors of noncompatibilized and compatibilized polypropylene/polyethylene terephthalate blends (80/20) in relation with their morphology were studied at two constant levels using maleic anhydride‐modified styrene‐ethylene‐butylene‐styrene polymer. By scanning electron microscopy of cryofractured surfaces, the morphology of the blends was examined after etching. The frequency sweep and step strain experiments were carried out for the blends. The frequency sweep results indicated that increasing the compatibilizer causes behavioral changes of the rheological properties, which could be related to the aggregation of the dispersed particles with rubbery shell. Also, the frequency sweep and step strain experiments in linear region, after cessation of simple steady shear flow with various preshear rates (higher shear stress values than G′_p), were done on compatibilized blend. The results showed that the morphology characteristics, defined by the aggregation of the dispersed particles based on rheological experimental data, were destroyed and replaced by an alignment in the flow direction for present imposed shear rates. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Investigation and prediction on the nonlinear viscoelastic behaviors of nylon1212 toughened with elastomer

Studies on the nonlinear viscoelastic behaviors of nylon1212 toughened with styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer (SEEPS) were carried out. The linear relaxation curves at relatively low shear strains show good overlap, the relaxation time and modulus corresponding to the characteristic relaxation modes were also acquired through simulating the linear relaxation modulus curves using Maxwell model. The nonlinear relaxation curves of nylon1212 blends at different shear strains have been obtained and their damping functions were evaluated. Meanwhile, it is found that most blends in the experimental windows follow the strain‐time separation principle and Laun double exponential model can predict damping curves well. The successive start‐up of shear behavior was investigated. The results showed that Wagner model, derived from the K‐BKZ (Kearsley‐Bernstein, Kearsley, Zapas) constitutive equation, could simulate the experiment data of nylon 1212 blend with 10 wt % SEEPS well, but there exists some deviation for experiment data of nylon1212 blends with high SEEPS concentrations. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Thermoforming of a PMMA transparency near glass transition temperature

To simulate the thermoforming of a transparency, constitutive equations are proposed for the nonlinear viscoelastic behavior of poly(methyl methacrylate) near glass transition temperature, which include large deformations. In a first step, they are fitted on a set of uniaxial tension‐relaxation tests at various strain levels and strain rates. In a second step, their implementation in a finite element code is performed. Finally, the thermoforming of a transparency at a constant and uniform temperature is simulated and compared with experimental results. POLYM. ENG. SCI., 50:2004–2012, 2010. © 2010 Society of Plastics Engineers     

The Effects of Molecular Weight on the Single Lap Shear Creep and Constant Strain Rate Behavior of Thermoplastic Polyimidesulfone Adhesive

The bonded shear creep and constant strain rate behavior of zero, one, and three percent end capped Thermoplastic Polyimidesulfone adhesive were examined at room and elevated temperatures. End capping was accomplished by the addition of phthalic anhydrides.

The viscoelastic Chase-Goldsmith and elastic nonlinear relations gave a good fit to the experimental stress strain behavior. Ultimate stress levels and the safe levels for creep stresses were found to decrease as molecular weight was reduced.

The primary objective was to determine the effects of molecular weight on the mechanical properties of the adhesive in the bonded form. Viscoelastic and nonlinear elastic constitutive equations were utilized to model the adhesive. Crochet's relation was used to describe the experimental creep failure data. The effects of molecular weight changes on the above mentioned mechanical behavior were assessed.     

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.     

Robust Direct Numerical Simulation of Viscoelastic Flows

Many technical processes involve viscoelastic flows, which makes the subject interesting for CFD. Despite the complex fluid rheology and related numerical problems in solving the constitutive equations, recent stabilization approaches allow for a robust simulation of viscoelastic flows in the technical relevant range at high degrees of fluid elasticity. A recent general‐purpose numerical stabilization framework, based on the finite‐volume method of OpenFOAM is presented and its capability for the robust simulation of viscoelastic single‐, as well as two‐phase flows is shown.     

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     

Melt‐spun hollow fibers: Modeling and experiments

Polypropylene hollow fibers were prepared via melt spinning at speeds of 1000–2500 m/min. The outside diameters of the fibers were measured on‐line with high‐speed photography. The fiber formation process was modeled with momentum, energy, and two continuity equations (one for the polymer, and one for the lumen fluid). The equations were solved numerically, and the results were compared to the on‐line diameter data. Both Newtonian and viscoelastic constitutive equations were considered.     

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...     

Filtered two‐fluid models of fluidized gas‐particle flows: New constitutive relations

New constitutive relations for filtered two‐fluid models (TFM) of gas‐particle flows are obtained by systematically filtering results generated through highly resolved simulations of a kinetic theory‐based TFM. It was found in our earlier studies that the residual correlations appearing in the filtered TFM equations depended principally on the filter size and filtered particle volume fraction. Closer inspection of a large amount of computational data gathered in this study reveals an additional, systematic dependence of the correction to the drag coefficient on the filtered slip velocity, which serves as a marker for the extent of subfilter‐scale inhomogeneity. Furthermore, the residual correlations for the momentum fluxes in the gas and particle phases arising from the subfilter‐scale fluctuations are found to be modeled nicely using constitutive relations of the form used in large‐eddy simulations of single‐phase turbulent flows. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3265–3275, 2013