Shear stress at polymer/metal interface during melting in extrusion

Prediction of the screw horsepower requirement involves, among many others, the calculation of the shear stress (τ_s) between the solid polymer and the barrel surface during melting. Prediction of the solid bed down-channel velocity also requires the calculation of τ_s. However, the pseudoplastic nature and strong temperature dependence of melt viscosity make the mathematics of calculating τ_s extremely difficult. As a first step of developing a reasonable mathematical model for calculating τ_s, experimental measurements of τ_s were made over a wide range of metal temperature and sliding speed for five commercial polymers using molded, block samples. Although dependences of τ_s on metal temperature and sliding speed were found to have similar functionality to those of the dependences of melt viscosity on melt temperature and shear rate, this study showed that τ_s could not be expressed as a sole function of the melt rheological properties. Our subsequent study, to be reported in a follow up paper, will show that τ_s must be expressed as a function of the thermodynamic properties and melt density of the polymer as well as the melt rheological properties and the melting conditions.     

Effects of extrusion conditions on rheological behavior of acrylonitrile–butadiene–styrene terpolymer melt

The influence of temperatures and flow rates on the rheological behavior during extrusion of acrylonitrile–butadiene–styrene (ABS) terpolymer melt was investigated by using a Rosand capillary rheometer. It was found that the wall shear stress (τ_w) increased nonlinearly with increasing apparent shear rates and the slope of the curves changed suddenly at a shear rate of about 10³ s^?1, whereas the melt‐shear viscosity decreased quickly at a τ_w of about 200 kPa. When the temperature was fixed, the entry‐pressure drop and extensional stress increased nonlinearly with increasing τ_w, whereas it decreased with a rise of temperature at a constant level of τ_w. The relationship between the melt‐shear viscosity and temperature was consistent with an Arrhenius expression. The results showed that the effects of extrusion operation conditions on the rheological behavior of the ABS resin melt were significant and were attributable to the change of morphology of the rubber phase over a wide range of shear rates. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 606–611, 2002     

Flow behavior of concentrated solutions of an SBS block copolymer

The non-Newtonian viscosity of concentrated solutions of a styrene-butadiene-styrene, SBS, block copolymer was measured with a novel capillary viscometer. Polymer concentrations ranged from 0.165 to 0.306 g/cc. Apparent shear rates ranged from 1 to 10⁵ sec^?1. Five different solvents were employed. All of the flow curves can be reduced to a single master curve with the same shape exhibited by monodisperse polystyrenes and the Graessley theory. The shift factor for the shear rate axis, τ₀, approximately parallels the Rouse relaxation time, τ_R, but shows a residual concentration and solvent dependence not predicted by the Rouse form. For different solvents at the same concentration, better solvents show a minimum relative zero shear viscosity, η₀/η_s, and a maximum ratio τ_R/τ₀. It is concluded that all solvent effects are not adequately incorporated into the zero shear viscosity for the purposes of constructing master plots; however, the shape of the master plot is not affected by the solvent or the polymer block structure.     

Critcal stress and recoverable shear for polymer melt fracture

The phenomenon of extrudate distortion, which is called melt fracture, was studied for polystyrene samples of narrow and broad molecular weight distribution, and commerical samples of polypropylene and linear and branched polyethylene. It was experimentally found that the shear stress at the onset of melt fracture (τ_cr) is of the order of 10⁶ dynes/cm² and independent of the distribution of molecular weights. As the weight average molecular weight increases the shear stress τ_cr decreases. For polystyrene extruded at τ_cr the recoverable shear strain, which is defined to be half the ration (first normal stress difference/shear stress), was found proportional to the factor M _zM _z+1/M _w² which represents the distrubution of molecular weights. The proportionality is expected to hold for other polymer systems. The polymer behavior at the onset of melt fracture was explained in terms of Graessley's entanglement theory and his correlation between true and Rouse shear compliance.     

Melt rheology of nanometre‐calcium‐carbonate‐filled acrylonitrile–butadiene–styrene (ABS) copolymer composites during capillary extrusion

The melt flow properties during capillary extrusion of nanometre‐calcium‐carbonate‐filled acrylonitrile–butadiene–styrene (ABS) copolymer composites were measured by using a Rosand rheometer to identify the effects of the filler content and operation conditions on the rheological behaviour of the sample melts. The experiments were conducted under the following test conditions: temperature varied from 220 to 240 °C and shear rate ranged from 10 to 10⁴ s^?1. The filler volume fractions were 0, 10, 20, 30, 40 and 50%. The results showed that the shear flow did not strictly obey the power law under the test conditions, and that the entry pressure drop (ΔP_en) and the extension stress (σ_e) in entry flow increased nonlinearly, while the melt shear viscosity (η_s) and extension viscosity (η_e) decreased with increasing the wall shear stress (τ_w) at constant test temperature. The dependence of the melt shear viscosity on the test temperature was approximately consistent with the Arrhenius expression at fixed τ_w. When τ_w was constant, η_s and η_e increased while ΔP_en and σ_e decreased with the addition of the filler volume fraction. © 2002 Society of Chemical Industry     

Flow property analysis of irregular powders

Accurate yield locus analysis using computer techniques can now be carried out on simple and complex irregular powders, as well as on regular powders, by performing a least squares regression on the equation n log(τ_i/τ_L) = log [(T_s + σ_i/σ_L)/(T_s + 1)]This equation reduces any number of yield loci having a common shear index value, n, to a single straight line of slope n provided that all individual shear stress,τ_i, and normal stress, σ_i points are divided by their respective steadystate stress values τ_L and σ_L, and that the correct value for specific tension, T_s = T/σ_L is entered for each locus. Improved values for both n and T_s are found by successive reiteration of the above regression and by subsequent regeneration of individual yield locus values for cohesion, C, and tension, T, from a solution of the equation.

Simple irregular powders which show a constant n, but a variable angle of static internal friction, ψ_s, are easily handled by this technique. Complex irregular powders, in which both n and ψ_s vary, present greater difficulty, but can be analysed by taking a large number of points and operating on individual loci in pairs or one at a time. Examples are given of industrial powders showing both simple and complex irregularity, and particular reference is made to the effect of variable friction characteristics on overall flowability, ζ_i.     

First normal stress difference in capillary extrusion flow of nanometer calcium carbonate‐filled PLLA biocomposites

The nanometer calcium carbonate (nano‐CaCO₃)‐filled poly‐L ‐lactide (PLLA) biocomposites were prepared using a twin‐screw extruder. The first normal stress difference of the composites were measured by means of a capillary rheometer under experimental conditions with temperatures ranging from 170 to 200°C and shear rates varying from 50 to 10³ s^?1. The first normal stress difference (N₁) increased roughly linearly with increasing shear stress (τ_w). The sensitivity of the N₁ to τ_w increased with an increase of the die length–‐diameter ratio, and the N₁ value varied slightly with the filler weight fraction (?_f) as test temperature was constant. When the shear stress was fixed, the N₁ reached a minimum value for ?_f = 1%. The values of the N₁ of the composite melts decreased roughly linearly with a rise of temperature when the shear rate was constant. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers     

Effect of inter-plies on the short beam shear delamination of steel/composite hybrid laminates

Interlaminar shear test methods (ILS) were implemented to characterize the delamination behavior of asymmetric steel/carbon fiber reinforced plastic (CFRP) hybrids. To improve the delamination behavior thermoplastic inter-plies were inserted between CFRP and steel. Supported by optical strain measurement the maximum shear stress (τ_MAX), the shear stress at interfacial delamination (τ_IF) and the shear stress at large-scale CFRP ply delamination τ_D were evaluated. The significant effect of inter-plies on the adhesion was best reflected by the shear stress value at interfacial delamination. Finite element analysis of the actual shear stress distribution in an asymmetric hybrid sample without inter-ply revealed that the calculated shear strength is just slightly overestimated compared to the standardized evaluation procedure.     

Influence of a particulate nucleating agent on the quiescent and flow-induced crystallization of isotactic polypropylene

Flow induced crystallization of commercial isotactic polypropylene (iPP) and its blends with sodium 2,2′-methylene bis-(4,6-di-tert-butylphenyl) phosphate (also known as NA11) is studied by means of in-situ time resolved small-angle X-ray scattering (SAXS). The isothermal crystallization at 145 °C (i.e. well below melting temperature of polymer) is performed after the application of steady shear to probe the anisotropic structure formation. In order to separate the influence of shear rate and shear time on polymer crystallization, four different shear conditions (60 s⁻¹ for 1 s, 30 s⁻¹ for 2 s, 15 s⁻¹ for 4 s and 6 s⁻¹ for 10 s) are applied while maintaining the same imposed strain in the polymer melt. Further the effect of different concentration of nucleating agent on the crystallization kinetics of iPP is examined both under quiescent and shear flow conditions. For instance, under quiescent condition, the crystallization half-time (τ_1/2) decreases with the increasing concentration of nucleating agent in the polymer. Under shear flow conditions, our observations are as follows: In the case of neat iPP, τ_1/2 decreases significantly at higher shear rates (≥30 s⁻¹). Compared to the neat iPP, for the same concentration of NA11 in the NA11/iPP blends differences in τ_1/2 with the increase in applied shear rates are significantly smaller. In other words, the crystallization kinetics is dominated by the amount of nucleating agent in the NA11/iPP blends as opposed to shear rates in the neat iPP. The present study shows that the critical value of shear rate required for chain orientation in the molten polymer is lower in the presence of the nucleating agent compared to neat iPP. The self-nucleation process investigated with the aid of differential scanning calorimetry (DSC), indicates that the nucleating efficiency of NA11 on iPP is around 60%.     

FRICTION AND ADHESION MEASUREMENTS BETWEEN A FLUOROCARBON SURFACE AND A HYDROCARBON SURFACE IN AIR

The friction and adhesion between a fluorocarbon monolayer-coated surface against a hydrocarbon monolayer-coated surface has been directly measured. The friction was found to be lower than the friction between a hydrocarbon monolayer against a hydrocarbon monolayer and a fluorocarbon monolayer against a fluorocarbon monolayer. No stick-slip sliding was observed for speeds from 0.8?µm/s to 2.6?µm/s. The fluorocarbon–hydrocarbon interface was adhesive, with the energy of interaction measured to be 14.9?mJ/m²?±?1.0?mJ/m². As predicted from theory, the magnitude of the adhesion of a fluorocarbon monolayer against a hydrocarbon monolayer is between that measured for a fluorocarbon monolayer against a fluorocarbon monolayer and a hydrocarbon monolayer against a hydrocarbon monolayer. One may note that the interfacial energy, γ, follows the general trend γ_FC/FC?<?γ_HC/FC?<?γ_HC/HC, whereas the shear stress, τ, varies according to τ_FC/HC?<?τ_HC/HC?<?τ_FC/FC.     

The rheology of homogeneously gas-fluidized solids,studied in a vertical standpipe

The rheology of homogeneously gas-fluidized cracking of catalyst held at various porosities has been studied in a vertical standpipe. It was found that the rheology can be described by means of a Bingham-plastic model with the inclusion of slip at the wall.Yield stress and viscosity could both be correlated with linear functions of the porosity.The wall slip velocity v_w could be described by a relation ?μ_wv_w = τ_w ? τ_w0 in which μ_w is some kind of wall slip viscosity, τ_w the wall shear stress and τ_w0 a wall yield stress. Both μ_w and τ_w0 depend again on porosity. τ_w0 also depends on the wall roughness.     

Rheological behavior of polymer blends

Steady and oscillatory shearing flow properties of compatible and incompatible polymer blend systems were measured, using a cone-and-plate rheometer. The compatible blend systems investigated are blends of two low-density polyethylenes (LDPE) having different values of molecular weight and blends of poly(methyl methacrylate) (PMMA) with poly(vinylidene fluoride) (PVDF). The incompatible blend system investigated is a blend of poly(methyl methacrylate) (PMMA) with polystyrene (PS). It was found that (1) plots of first normal stress difference (τ₁₁ – τ₂₂) vs. shear stress (τ₁₂) and plots of storage modulus (G′) vs. loss modulus (G″) for the LDPE blends become independent of temperature and blend composition; (2) plots of τ₁₁ – τ₂₂ vs. τ₁₂, and G′ vs. G″ for the PMMA/PVDF blends become independent of temperature but dependent upon blend composition. It was found further that, for the incompatible PMMA/PS blends, the dependence of τ₁₁ – τ₂₂ on blend composition, when plotted against τ₁₂, is different from the dependence of G′ on blend composition, when plotted against G″. However, in both compatible and incompatible blend systems, plots of τ₁₁ – τ₂₂ vs. τ₁₂ and plots of G′ versus G″ are independent of temperature. The seemingly complicated composition-dependent rheological behavior of the incompatible blend system is explained with the aid of photomicrographs describing the state of dispersion.     

An interface model for the prediction of Young's modulus of layered silicate-elastomer nanocomposites

Recent experiments on layered silicate-elastomer nancomposites by Burnside and Giannelis have shown that there is a discrepancy between theoretical modulus predictions and experimental modulus measurements. A theory is proposed to explain this discrepancy. We hypothesize that the discrepancy is due to imperfect bonding between the matrix/inclusion interface which effectively reduces the aspect ratio and the volume fraction of the inclusion. We use a simple interface model to quantify the imperfect interfacial bonding. From this model, we introduce the concept of the effective aspect ratio and effective volume fraction of the inclusions. These effective quantities depends on a single material parameter, namely, the constant interfacial shear stress, τ. The interfacial shear stress for the elastomer-silicate nanocomposites is found by fitting the theory to the experimentally measured modulus of Burnside and Giannelis. The interfacial shear stress is in the range of thousands of Pascals. For the elastomer-silicate nanocomposite systems considered here, the interfacial shear stress can be decomposed into two parts; intrinsic shear stress τ_i and frictional shear stress τ_f. The intrinsic interfacial shear stress τ_i depends only on the volume fraction of inclusions and decreases with increasing volume fraction of inclusions. On the other hand, the frictional shear stress τ_f is found to increase linearly with the applied strain. Since the mean stress is also proportional to the applied strain, this gives rise to an effective coefficient of friction, which is found to be 0.0932 for the nanocomposite system considered here.     

Stress transfer in polyacrylonitrile/carbon nanotube composite fibers

Gel spun polyacrylonitrile/carbon nanotube (PAN/CNT) composite fibers have been produced, and the stress-induced G′ Raman band shifts in the CNTs have been monitored to observe stress transfer during fiber strain. Improvements in CNT quality, CNT dispersion, and post-processing fiber drawing are shown to increase the stress transfer from the matrix to the CNT. Radial breathing mode (RBM) intensity of specific CNT chiralities confirms CNT debundling during fiber processing. During PAN/CNT fiber straining, there reaches a plateau in the CNT G′ downshift, signifying that the stress on the CNT is maintained despite continued straining of the PAN/CNT fiber. Correlating CNT strain with CNT modulus and volume fraction allows for the interfacial shear strength (τ_i) of the PAN-CNT interface to be determined. The as-spun and fully drawn PAN/CNT-A (99/1) nano composite fibers exhibit τ_i of 13.1 and 30.9 MPa, respectively, while an improved CNT dispersion (PAN/CNT-A (99.9/0.1)) results in τ_i equal to 44.3 MPa.     

Shear-induced gelation of associative polyelectrolytes

Copolymer of N,N-dimethylacrylamide (DMA) and acrylic acid (AA) was functionalized with pendant alkyl groups. Their dynamic mechanical properties in aqueous solution were investigated using continuous shear and oscillatory shear. Shear flow showed an abrupt divergence of the viscosity at a critical shear stress (σ_c). Oscillatory shear showed, with increasing applied stress, slight shear thinning followed by strong shear thickening above σ_c. The effect of the polymer concentration and the oscillation frequency (ω) was investigated. The behaviour at all concentrations and frequencies was fully determined by the product of the oscillation frequency and the terminal relaxation time (τ) of the systems at rest. Master curves of the data determined at different concentrations and frequencies were obtained if the reduced shear modulus was plotted versus the reduced applied stress at constant ω.τ. The effect of shear increased with decreasing value of ω.τ. At low frequencies the storage shear modulus crossed the loss modulus with increasing shear. A model is proposed for this phenomenon of shear-induced gelation.     

Effect of polymer matrix on the rheology of hydroxyapatite‐filled polyethylene composites

The effect of matrix polymer and filler content on the rheological behavior of hydroxyapatite‐filled injection molding grade high‐density polyethylene (HDPE) has been studied. Studies of the flow curves revealed that the matrix and the composite exhibit three distinct regions in the flow curve, namely, a pseudoplastic region at low to moderate shear rates, a plateau and a second pseudoplastic region at high shear rates. The shear stress corresponding to the plateau (τ_c) is dependent on both the filler concentration and the melt temperature. Addition of HA in the HDPE matrix increases the value of τ_c and decreases compressibility of the melt. An increase in temperature also raises the value of τ_c. From the nature of flow curves it is concluded that the matrix polymer largely decides the rheology of the composite.     

Effects of shear thinning on forward roll coating

This paper described the forward mode roll coating process of generalised non-Newtonian fluids characterised by the Ellis model. The fluid in the coating bead and the free surface formation are described by the lubrication approximation and the stability is also considered using a perturbation analysis of the downstream meniscus. Results highlight the complex behaviour of this coating process and volume flow rate and film thickness results are obtained for a range of operating conditions. The stability of the downstream meniscus is observed to improve with increasing level of shear thinning when τ_1/2 (the shear stress at which the viscosity is half that of the zero shear stress viscosity) is small, however as τ_1/2 increases the meniscus stability decreases with increasing levels of shear thinning.     

Fast transient fluorescence (FTRF) technique to study swelling of densely and loosely formed gels

A Strobe Master System (SMS) is introduced for studying the swelling of cylindrical densely (DG) and loosely (LG) formed gels. Gels were prepared by free radical copolymerization of methyl (methacrylate) (MMA) and ethylene glycol dimethacrylate (EGDM). Pyrene (P) was introduced as a fluorescence probe during polymerization, and the lifetimes of P were measured using (SMS) during in situ swelling processes. Chloroform was used as a swelling agent. A model is derived for low quenching efficiencies to measure mean lifetimes 〈τ〉 of P, and it was observed that 〈τ〉 values decreased as the swelling proceeded. The Li‐Tanaka equation was employed to determined the time constants, τ_c, and cooperative diffusion coefficients, D_c, which were found to be around 400 min and 10⁻⁵ cm²s⁻¹, respectively. No differences were detected in τ_c and D_c values of DG and LG gels. Quenching rate constants, κ, and the mutual diffusion coefficient, D_m, were measured and found to be around 10⁵ M⁻¹s⁻¹ and 10⁻¹⁰ cm²s⁻¹ for DG and LG gel samples. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 1494–1502, 2000     

Shear modulus in closely packed gel suspensions

Rheological properties and swelling were examined in a series of concentrations of particles of crosslinked polyacrylate gels in water or salt solutions. The modulus during steady shear G_s = 2τ²/P₁₁-P₂₂ was determined from shear stress τ and primary normal force difference P₁₁-P₂₂ in a cone-and-plate rheometer. G_s was nearly constant with shear rate for the gel particles in the closely packed condition. The dynamic storage modulus G′ determined by ecentric rotating disc rheometry increased with increasing frequency for all concentrations. The apparent equilibrium shear modulus G_e determined by stress relaxation agreed closely at all concentrations and ionic strengths with the corresponding values of G_s, and hence G_s is considered a good estimate of equilibrium shear modulus for this gel material.     

Detection of fast and slow crystallization processes in instantaneously-strained samples of cis-1,4-polyisoprene

Cross-linked samples of natural rubber (NR) and synthetic cis-1,4-polyisoprene (IR) were instantaneously expanded to a predetermined strain ratio, α_s, using a newly-designed high-speed tensile tester. Crystallization behavior after the cessation of deformation was investigated. The high-cycle wide-angle X-ray diffraction (WAXD) measurements could successfully reveal the drastic progress of crystallization within the first a few hundred milliseconds. Quantitative analysis of diffraction intensity clarified coexistence of fast and slow crystallization processes; time constants τ_f and τ_s, and amplitude I_f and I_s, respectively, were estimated for these processes. The values of τ_f were in the range of 50–200 ms, while τ_s ranged between 2.5 and 4.5 s. Almost linear dependence of I_f and I_s on α_s was clarified. The crystallite size in the directions both parallel and perpendicular to the stretching direction decreased with the increase in time-averaged nominal stress. The crystal lattice deformed almost linearly with the average nominal stress. For the fast process, correlation between crystallization and stress relaxation was not recognized, while linear relationship between them was found for the slow process. In every case, strain-induced crystallization was found to be the major origin of stress relaxation. Based on the results, effects of strain on crystallization of polymer melt were discussed.