Simultaneous determination of shear and extensional viscosities and wall slip by on-line rheometry with parameter fitting: an application to EPDM rubber

Shear and extensional viscosities and wall slip are determined simultaneously under extrusion processing conditions using an on-line rheometer. Because it is not possible to independently control flow rate and temperature, classical methods for interpretation of capillary data cannot be used with on-line rheometry. This limitation is overcome using computational optimization to fit parameters in a flow model. This consists of three parts, representing shear viscosity, extensional viscosity, and wall slip. Three-parameter, power law forms, based on local instantaneous deformation rates and including temperature dependence, are used for each, and analytic solutions applied for entry flow and flow in the capillary. For entry flow, the Cogswell–Binding approach is used, and for developed flow in the capillary a solution incorporating wall slip is derived. The rheometer, with interchangeable capillaries, is mounted in place of the die on a rubber profile extrusion line. Pressure drops and temperatures for extrusion of an EPDM rubber through 2 mm diameter capillaries of length 0, 2, 3, 4, and 5 mm are logged and flow rates determined for a range of extruder speeds (5 to 20 rpm). Pressures ranged from 60 to 75 bar and temperatures from 86 to 116 °C. Mean flow velocity in the capillaries was between 5 × 10⁻³ and 5 × 10⁻¹ m s⁻¹. The nine material parameters are optimized for best fit of the analytic pressure drops to experimental data, using about 100 data points, with the Levenberg–Marquardt method. It is concluded that flow is dominated by extension and wall slip. Shear flow appears to play little part. The slip model indicates that slip velocity increases much more rapidly than the wall shear stress (in the range 0.5–1 MPa) and decreases with temperature for a given stress level. Results for the (uniaxial) extensional viscosity represent an engineering approximation to this complex phenomenon at the high strains (approximately 200) and high extension rates (up to 800 s⁻¹) applying in the extrusion. Results indicate a slight extension hardening and a decrease with temperature. Results are put into the context of the available studies in the literature, which, particularly with regard to wall-slip and extensional flow, consider conditions far removed from those applying in industrial extrusion. The present methods provide a powerful means for flow characterization under processing conditions, providing data suitable for use in computer simulations of extrusion and optimization of die design.     

Flow-induced crystallization of high-density polyethylene: the effects of shear and uniaxial extension

The effects of shear, uniaxial extension and temperature on the flow-induced crystallization of two different types of high-density polyethylene (a metallocene and a ZN-HDPE) are examined using rheometry. Shear and uniaxial extension experiments were performed at temperatures below and well above the peak melting point of the polyethylenes in order to characterize their flow-induced crystallization behavior at rates relevant to processing (elongational rates up to 30 s^− 1 and shear rates 1 to 1,000 s^− 1 depending on the application). Generally, strain and strain rate found to enhance crystallization in both shear and elongation. In particular, extensional flow was found to be a much stronger stimulus for polymer crystallization compared to shear. At temperatures well above the melting peak point (up to 25°C), polymer crystallized under elongational flow, while there was no sign of crystallization under simple shear. A modified Kolmogorov crystallization model (Kolmogorov, Bull Akad Sci USSR, Class Sci, Math Nat 1:355–359, 1937) proposed by Tanner and Qi (Chem Eng Sci 64:4576–4579, 2009) was used to describe the crystallization kinetics under both shear and elongational flow at different temperatures.     

Rheostructural studies of a discotic mesophase pitch at processing flow conditions

The flow-induced microstructure of a mesophase pitch was studied within custom-made dies for changing wall shear rates from 20 to 1,100 s^− 1, a flow scenario that is typically encountered during fiber spinning. The apparent viscosity values, measured at the nominal wall shear rates ranging from 500 to 2,500 s^− 1 using these dies, remain fairly constant. The microstructure was studied in two orthogonal sections: r–θ (cross section) and r–z (longitudinal mid plane). In these dies, the size of the microstructure gradually decreases toward the wall (to as low as a few micrometers), where shear rate is highest. Furthermore, as observed in the r–θ plane of the capillary, for a significant fraction of the cross section, discotic mesophase has a radial orientation. Thus, the directors of disc-like molecules were aligned in the vorticity (θ) direction. As confirmed from the microstructure in the r–z plane, most of the discotic molecules remain nominally in the flow plane. Orientation of the pitch molecules in the shear flow conditions is consistent with that observed in controlled low-shear rheometric experiments reported earlier. Microstructral investigation suggests that the radial orientation of carbon fibers obtained from a mesophase pitch originates during flow of pitch through the die.     

Experimental Investigation of Strain Rate Dependence of Nanocrystalline Pt Films

A new microscale uniaxial tension experimental method was developed to investigate the strain rate dependent mechanical behavior of freestanding metallic thin films for MEMS. The method allows for highly repeatable mechanical testing of thin films for over eight orders of magnitude of strain rate. Its repeatability stems from the direct and full-field displacement measurements obtained from optical images with at least 25 nm displacement resolution. The method is demonstrated with micron-scale, 400-nm thick, freestanding nanocrystalline Pt specimens, with 25 nm grain size. The experiments were conducted in situ under an optical microscope, equipped with a digital high-speed camera, in the nominal strain rate range 10⁻⁶–10¹ s⁻¹. Full field displacements were computed by digital image correlation using a random speckle pattern generated onto the freestanding specimens. The elastic modulus of Pt, E = 182 ± 8 GPa, derived from uniaxial stress vs. strain curves, was independent of strain rate, while its Poisson’s ratio was v = 0.41 ± 0.01. Although the nanocrystalline Pt films had the elastic properties of bulk Pt, their inelastic property values were much higher than bulk and were rate-sensitive over the range of loading rates. For example, the elastic limit increased by more than 110% with increasing strain rate, and was 2–5 times higher than bulk Pt reaching 1.37 GPa at 10¹ s⁻¹.     

Wall slip and melt fracture of poly(lactides)

The wall slip and melt fracture behaviour of several commercial polylactides (PLAs) as well as their rheological properties under shear and extensional have been investigated. The PLAs have had weight-average molecular weights in the range of 10⁴–10⁵ g/mol and studied in the temperature range of 160–200°C. The solution properties and linear viscoelastic behaviour of melts indicate linear microstructure behaviour. PLAs with molecular weights greater than a certain value were found to slip, with the slip velocity to increase with decrease of molecular weight. The capillary data were found to agree well with linear viscoelastic envelope once correction for slip effects was applied. The onset of melt fracture for the high molecular weight PLAs was found to occur at about 0.2 to 0.3 MPa, depending on the geometrical characteristics of the dies and independent of temperature. Addition of 0.5 wt.% of a polycaprolactone (PCL) into the PLA that exhibits melt fracture was found to be effective in eliminating and delaying the onset of melt fracture to higher shear rates. This is due to significant interfacial slip that occurs in the presence of PCL.     

Determination of the shear strength and modulus of water at low flow velocities

Damped inertial water flow in a cylindrical vessel is investigated. A return effect or "recoil" as the shear strain rate falks to a value of the order of 10⁻³s⁻¹ is observed. Over the range of low strain rates the water behaves like a medium with very low shear strength and a shear modulus of the order of 10⁻⁶ Pa. Ekaterinburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–7, January–February, 1997.     

Small and large strain rheology of wheat gluten

 The rheological properties of wheat gluten were studied under both small and large deformation and compared with those of the parent flours. The limiting strain of linear viscoelastic behaviour of gluten doughs, 3 × 10⁻², was an order of magnitude larger than that of the flour doughs, 10⁻³. The role of starch in the lower limiting strain of flour doughs was indicated by the exponential decrease in the limiting strain of gluten-starch mixtures with greater quantities of starch. Large strain measurements showed gluten doughs possessed greater shear and elongational viscosities than flour doughs and these differences were greatest at lower shear and elongation rates (0.01 and 0.1 s⁻¹). The larger viscosities of flour and gluten doughs at the low strain rates help to stabilise and prevent the collapse of gas bubbles during bread fermentation and baking. Increasing starch levels in gluten-starch mixtures, at either constant or optimal water levels, lowered the elongational viscosity. Dynamic measurements were, however, more sensitive to the level of water added to the gluten-starch mixtures. The storage modulus decreased with increasing starch levels when constant water levels were used to prepare the mixtures, but when optimal water levels were used the storage modulus increased. Gluten and starch are major contributors to the large and small strain rheological properties of flour doughs; however, gluten-starch mixtures were unable to duplicate exactly the rheological properties of flour doughs, indicating that other flour components such as pentosans, lipids and water soluble proteins also influence dough rheology. Received: 20 March 2001 Accepted: 11 July 2001     

Shear Failure of Inconel 718 under Dynamic Loads

Kinetics of deformation and fracture of nickel–iron alloy Inconel 718 under dynamic shear loading was measured using a split torsional Hopkinson bar facility and high-speed photography. Tubular specimens with a reduced gage length and a starter notch were sheared at strain rates up to 6 × 10³ s⁻¹. High-speed photographs of fiducial lines scribed on the specimen surface showed the development of local strains and cracking. This paper describes the experimental and analytical procedures, illustrates average and local plastic strain evolution, and presents shear crack initiation times and propagation speeds.     

High Strain Rate Torsion Properties of Ultrafine-Grained Aluminum

Mechanical properties of most metallic materials can be improved by reducing their grain size. One of the methods used to reduce the grain size even to the nanometer level is the severe plastic deformation processing. Equal Channel Angular Pressing (ECAP) is one of the most promising severe plastic deformation processes for the nanocrystallization of ductile metals. Nanocrystalline and ultrafine grained metals usually have significantly higher strength properties but lower tensile ductility compared to the coarse grained metals. In this work, the torsion properties of ECAP processed ultrafine grained pure 1070 aluminum were studied in a wide range of strain rates using both servohydraulic materials testing machines and Hopkinson Split Bar techniques. The material exhibits extremely high ductility in torsion and the specimens did not fail even after 300% of strain. Pronounced yield point behavior was observed at strain rates 500 s⁻¹ and higher, whereas at lower strain rates the yielding was continuous. The material showed slight strain softening at the strain rate of 10⁻⁴ s⁻¹, almost ideally plastic behavior at strain rates between 10⁻³ s⁻¹ and 500 s⁻¹, and slight but increasing strain hardening at strain rates higher than that. The tests were monitored using digital cameras, and the strain distributions on the surface of the specimens were calculated using digital image correlation. The strain in the specimen localized very rapidly after yielding at all strain rates, and the localization lead to the development of a shear band. At high strain rates the shear band developed faster than at low strain rates.     

Measurements and model predictions of transient elongational rheology of polymeric nanocomposites

Transient elongational rheology of two commercial-grade polypropylene (PP) and the organoclay thermoplastic nanocomposites is investigated. A specifically designed fixture consisting of two drums (SER Universal Testing Platform) mounted on a TA Instruments ARES rotational rheometer was used to measure the transient uniaxial extensional viscosity of both polypropylene and nanoclay/PP melts. The Hencky strain rate was varied from 0.001 to 2 s^− 1, and the temperature was fixed at 180°C. The measurements show that the steady-state elongational viscosity was reached at the measured Hencky strains for the polymer and for the nanocomposites. The addition of nanoclay particles to the polymer melt was found to increase the elongation viscosity principally at low strain rates. For example, at a deformation rate of 0.3 s^− 1, the steady-state elongation viscosity for polypropylene was 1.4 × 10⁴ Pa s which was raised to 2.8 × 10⁴ and 4.5 × 10⁴ Pa s after addition of 0.5 and 1.5 vol.% nanoclay, respectively. A mesoscopic rheological model originally developed to predict the motion of ellipsoid particles in viscoelastic media was modified based on the recent developments by Eslami and Grmela (Rheol Acta 47:399–415, 2008) to take into account the polymer chain reptation. We show that the orientation states of the particles and the rheological behavior of the layered particles/thermoplastic hybrids can be quantitatively explained by the proposed model.     

Synthesis and electrorheological properties of polar molecule-dominated TiO 2 particles with high yield stress

Two types of amorphous TiO₂ particles with different particle sizes were synthesized by a simple sol–gel method and were characterized by X-ray diffraction analysis, field emission scanning electron microscopy, and Fourier transform infrared spectrometry. The electrorheological (ER) results show that the TiO₂/silicone oil suspensions exhibited a remarkable ER effect. The static shear stress can be up to 130 kPa (shear rate 0.2 s^− 1) under the DC electric field of 4 kV/mm at room temperature. The polar molecules present on the particles’ surface play a decisive role for the observed giant ER effect, which arises from the alignment of polar molecules in the gap between neighboring particles.     

Viscoelastic properties of ultra-high viscosity alginates

Ultra-high viscosity alginates were extracted from the brown seaweeds Lessonia nigrescens (UHV_N, containing 61% mannuronate (M) and 2% guluronate (G)) and Lessonia trabeculata (UHV_T, containing 22% M and 78% G). The viscoelastic behavior of the aqueous solutions of these alginates was determined in shear flow in terms of the shear stress σ ₂₁, the first normal stress difference N ₁, and the shear viscosity η in isotonic NaCl solutions (0.154 mol/L) at T = 298 K in dependence of the shear rate [(g)\dot]\dot{\gamma} for solutions of varying concentrations and molar masses (3–10 × 10⁵ g/mol, homologous series was prepared by ultrasonic degradation). Data obtained in small-amplitude oscillatory shear (SAOS) experiments obey the Cox–Merz rule. For comparison, a commercial alginate with intermediate chemical composition was additionally characterized. Particulate substances which are omnipresent in most alginates influenced the determination of the material functions at low shear rates. We have calculated structure–property relationships for the prediction of the viscosity yield, e.g., η–M _w–c–[(g)\dot]\dot{\gamma} for the Newtonian and non-Newtonian region. For the highest molar masses and concentrations, the elasticity yield in terms of N ₁ could be determined. In addition, the extensional flow behavior of the alginates was measured using capillary breakup extensional rheometry. The results demonstrate that even samples with the same average molar mass but different molar mass distributions can be differentiated in contrast to shear flow or SAOS experiments.     

The effect of mixing particles of different size on the electrorheological response under steady shear flow

 The effect of mixing particles of different sizes on the electrorheological response of suspensions under steady shear flow was investigated. Two sizes, 15 μm and 50 μm, of monodisperse spherical sulfonated poly(styrene-co-divinylbenzene) particles were used. Several electrorheological fluids were made containing different proportions of small and large particles dispersed in silicone oil, but with constant overall particulate concentration. It was found that the mixed size system produced the highest electrorheological response under the shear rates used (10 s⁻¹ to 500 s⁻¹), which is the opposite trend to previous studies of bimodal systems with larger size ratios. Received: 21 December 2000 Accepted: 29 March 2001     

Rheology and birefringence of Fomblin YR at very high shear rates

The rheological and structural properties of perfluoropolyether (PFPE) lubricant films including viscosity, shear stress, and birefringence were measured at relatively low to extremely high shear rates using a rotational optical rheometer. The viscosity of various films with different thicknesses exhibit Newtonian behavior up to a shear rate 1 × 10⁴ s⁻¹, with a transition to shear-thinning behavior obvious at higher shear rates. Birefringence of these films was also measured for the first time, and these results indicate chain alignment with shear in the shear-thinning regime. The shear rate at which alignment occurs is similar to that of the onset of shear thinning. This correlation between chain alignment and shear thinning provides direct evidence that the ability of PFPEs to lubricate hard drives at high shear rates is a direct consequence of the ability of the applied shear field to align the molecules on a molecular level.     

Miniaturized Compression Test at Very High Strain Rates by Direct Impact

A modified miniaturized version of the Direct Impact Compression Test (DICT) technique is described in this paper. The method permits determination of the rate-sensitive plastic properties of materials up to strain rate ∼10⁵ s⁻¹. Miniaturization of the experimental setup with specimen dimensions: diameter d _S = 2.0 mm and thickness l _S = 1.0 mm, Hopkinson bar diameter 5.2 mm, with application of a novel optical arrangement in measurement of specimen strain, makes possible compression tests at strain rates from ∼10³ s⁻¹ to ∼10⁵ s⁻¹. In order to estimate the rate sensitivity of a low-alloy construction steel, quasi-static, Split Hopkinson Pressure Bar (SHPB) and DICT tests have been performed at room temperature within the rate spectrum ranging from 5*10⁻⁴ s⁻¹ to 5*10⁴ s⁻¹. Adiabatic heating and friction effects are analyzed and the final true stress versus true strain curves at different strain rates are corrected to a constant temperature and zero friction. The results have been analyzed in the form of true stress versus the logarithm of strain rate and they show two regions of a constant rate sensitivity : relatively low up to the strain rate threshold ∼50 s⁻¹, and relatively high above the threshold, up to strain rate ∼4.5*10⁴ s⁻¹.     

Wall slip of mayonnaises in viscometers

The shear flow of mayonnaise is generally characterized by an apparent yield stress, shear thinning in steady flow, stress overshoots upon inception of flow and other time-dependent effects. These observations are usually understood to be the result of structural rearrangement within the material. Additionally and separately, the possibility that emulsions may exhibit apparent wall slip on a microscopic scale at a solid-liquid boundary has been reported by some researchers. Thus, observed rheological behavior is likely to be the result of the interplay between these two phenomena. In the present work, it is demonstrated that when measurements are sought to be made on mayonnaise using rotational viscometers visible wall slip occurs, rendering such instruments ineffective for the purpose of making viscosity measurements even at shear rates as low as 10^–3s^–1. The factors that influence the onset and extent of slip are investigated with the help of parallel plate viscometers, and it is concluded that the observed “yielding” of mayonnaise is actually an artifact of the onset of macroscopic slip. Slip effects are also found in capillary flow but are ameliorated with increasing shear rate. To circumvent these problems, it is proposed that extensional viscometry be employed for determining the flow behavior of mayonnaises. Received: 18 August 1997 Accepted: 1 April 1998     

Behaviour of a simple crystallisation model in tube and channel flow

A formulation describing the rheology of crystallising polymers is discussed. For some semi-crystalline polymers where spherulites form as part of the crystallisation process, the use of a suspension-type model is appropriate. Whilst it is possible to so describe simple shearing and elongational rheology during on-going crystallisation with such models, the flow through a capillary tube is much more complex and numerical solution is usually necessary. To give some insight into this complex flow, a ‘step function’ or ‘amorphous-frozen’ model of the viscosity changes due to crystallisation has been devised so that a semi-analytical approach is feasible. We use this simple model and compare the results with recently published experiments in tubes and channels at high (O(10³ s^− 1)) shear rates using poly(butene-1). A direct correlation between simple shear and tube flow crystallisation onset times is found.     

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.     

Effect of melt viscosity of polypropylene on fibrillation of thermotropic liquid crystalline polymer in in situ composite film

 Various grades of polypropylene were melt blended with a thermotropic liquid crystalline polymer, a block copolymer of p-hydroxy benzoic acid and ethylene terephthalate (60/40 mole ratio). The blends were extruded as cast films at different values of draw ratio (slit width/film thickness). Fibrillation of TLCP dispersed phase with high fiber aspect ratio (length/width) was obtained with the matrix of low melt flow rate, i.e., high viscosity and with increasing film drawing. Melt viscosities of pure components and blends measured using capillary rheometer were found to decrease with increasing shear rate and temperature. Viscosity ratios (dispersed phase to matrix phase) of the systems being investigated at 255 °C at the shear rate ranged from 10² to 10⁴ s⁻¹, were found to lie between 0.04 and 0.15. The addition of a few percent of elastomeric compatibilizers; a tri-block copolymer SEBS, EPDM rubber and maleated-EPDM, was found to affect the melt viscosity of the blend and hence the morphology. Among these three compatibilizers, SEBS was found to provide the best fibrillation. Received: 10 January 2000/Accepted: 24 January 2000