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  • 1
    Electronic Resource
    Electronic Resource
    Elongational behaviour of a low density polyethylene melt (1978)
    Springer
    Rheologica acta 17 (1978), S. 415-425 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung An Schmelzen des verzweigten Polyäthylens IUPAC A wurden die Dehnviskositätenµ s im stationären Bereich über sechs Dekaden der Dehngeschwindigkeit gemessen. Bei niedrigen Dehngeschwindigkeiten verhält sich die Schmelze linear-viskoelastisch. Es gilt dieTrouton-Beziehungµ 0 = 3η0. Die Dehnnachgiebigkeit beträgt ein Drittel der Schernachgiebigkeit. Mit wachsender Dehngeschwindigkeit durchläuft die Dehnviskosität ein ausgeprägtes Maximum der Höheµ s ≈ 7 µ0. Im stationären Bereich wurden reversible Dehnungen bis zuε r,s = 2,16 gemessen. Die Meßergebnisse von Dehnkriechversuchen und Messungen mit konstanten Dehngeschwindigkeiten stimmen quantitativ überein. Es wird gezeigt, wie der Einfluß der Grenzflächenspannung zwischen der Polyäthylenprobe und dem umgebenden Silikonöl, der insbesondere bei niedrigen Dehngeschwindigkeiten nicht zu vernachlässigen ist, experimentell berücksichtigt werden kann.
    Notes: Summary The steady-state elongational viscosityµ s of melts of the low density polyethylene IUPAC A was investigated over six decades of strain rate. At low elongation rates the melt behaves as a linear viscoelastic liquid. TheTrouton relationµ 0=3η0 is valid. The tensile compliance is one third of the shear compliance. With increasing strain rate the elongational viscosity goes through a pronounced maximum of the heightµ s≈7µ0. Steadystate recoverable strains up toε r,s=2.16 have been measured. The results from tensile creep tests and constant stretching rate tests are in quantitative agreement. It is shown how the influence of the interfacial tension between the polyethylene sample and the surrounding silicon oil which is not negligible at small strain rates can be taken into account experimentally.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01525957
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  • 2
    Electronic Resource
    Electronic Resource
    Elongational behaviour of a low density polyethylene melt (1979)
    Springer
    Rheologica acta 18 (1979), S. 492-504 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung In Ergänzung früherer Ergebnisse vonMeißner an einem Polyäthylen niedriger Dichte, die im linearen Bereich der Verformung für die zeitabhängige Dehnviskosität das Dreifache der Scherviskosität ergaben, konnte die Gültigkeit der Beziehung $$\mathop D\limits^ \circ (t) = 1/3\mathop J\limits^ \circ (t)$$ gezeigt werden. $$\mathop D\limits^ \circ (t)$$ und $$\mathop J\limits^ \circ (t)$$ sind die Nachgiebigkeiten in Dehnung und Scherung. Im nichtlinearen Bereich steigtJ(t) mit zunehmender Spannung an, währendD(t) abfällt. Die Zeitabhängigkeit der Viskosität, definiert als der Quotient aus Spannung und Geschwindigkeit des viskosen Deformationsanteils, ist in Scherung und Dehnung ebenfalls unterschiedlich. Die Scherviskosität fällt von dem Wert der Nullviskositätη 0 mit wachsender Scherung auf einen stationären Wert ab, die Dehnviskosität dagegen steigt von 3η 0 auf einen höheren stationären Wert an. Die Temperaturabhängigkeit wurde aus Messungen des stationären Wertes der Dehnviskosität bei konstantgehaltener Zugspannung und aus einer Verschiebung der bei unterschiedlichen Temperaturen, aber konstanten Spannungen gemessenen Nachgiebigkeiten in bezug auf die Zeit bestimmt. Sie ist dieselbe wie in Scherung. Dieses Ergebnis konnte indirekt durch Messungen mit konstanter Dehngeschwindigkeit bestätigt werden. Die reversible Dehnung im stationären Zustand wurde bei konstanter Zugspannung als von der Temperatur unabhängig gefunden.
    Notes: Summary In addition to earlier findings ofMeißner on a low density polyethylene that in the linear range of deformation the time-dependent elongational viscosity is three times the shear viscosity the validity of the relationship $$\mathop D\limits^ \circ (t) = 1/3\mathop J\limits^ \circ (t)$$ could be demonstrated where $$\mathop D\limits^ \circ (t)$$ and $$\mathop J\limits^ \circ (t)$$ describe the compliances in elongation and shear, respectively. In the nonlinear rangeJ(t) was found to increase with stress whereasD(t) decreases. The nonlinear viscosity-time behaviour is different in shear and elongation, too. The shear viscosity obtained by relating the stress to the rate of viscous strain decreases with shear from the zero shear viscosity to its steady-state value. The elongational viscosity goes up with time from 3η 0 to a higher steady-state value. The temperature dependence which was determined by measuring the steady-state elongational viscosities at different constant stresses as a function of temperature and by shifting the tensile creep compliancesD(t) measured at constant stress with respect to time, was found to be exactly the same as in shear. This result could indirectly be verified by some constant stretching rate tests. It was shown experimentally that the recoverable strain in the steady-state is independent of temperature if measured at constant stress.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01736955
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  • 3
    Electronic Resource
    Electronic Resource
    Polymer melt rheology with a slit die (1983)
    Springer
    Rheologica acta 22 (1983), S. 171-185 
    Details
    ISSN: 1435-1528
    Keywords: Slit die rheometry ; LDPE melt ; pressure dependent viscosity ; entrance pressure loss ; exit pressure loss
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract A piston driven high pressure slit die rheometer with three pressure holes along the die and one in the barrel was used to investigate viscosity, entrance and exit pressure losses, and pressure coefficient of viscosity of a LDPE melt. Hydrostatic calibration of melt pressure transducers can be performed in the rheometer. The slit die results are compared with measurements on circular dies assuming linear and parabolic pressure profiles in both cases. A simplified conversion from apparent to true viscosity, applicable for single point measurements, has been used. In spite of the different symmetries the Bagley correction from the linear pressure profile of circular dies was found to be equal to the sum of exit and entrance pressure losses in the slit. The magnitude and sign of the exit pressure loss depend on the type of pressure profile used. The influence of a pressure dependent viscosity and a temperature gradient along the die on the curvature of the pressure profile is discussed. To directly investigate the effect of pressure the pressure level at constant flow rate was increased stepwise by means of a valve attached to the exit of the slit die.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01332370
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  • 4
    Electronic Resource
    Electronic Resource
    Orientation effects and rheology of short glass fiber-reinforced thermoplastics (1984)
    Springer
    Colloid & polymer science 262 (1984), S. 257-269 
    Details
    ISSN: 1435-1536
    Keywords: Fiber filled melts ; fiber orientation ; transient stresses ; recoverable strains ; shear and elongational flows
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The rheology of polyolefines, polyamide 6, and polystyrene-acrylonitrile filled with glass fibers of different concentrations and aspect ratios have been investigated in simple shear flow, capillary rheometry, and uniaxial elongation. A comparison is made with unfilled and glass bead-filled melts. Fiber orientation was investigated by X-ray microradiography. Steady-state viscosities are obtained on fibers aligned parallel to the direction of flow. Entrance pressure losses, the shape of the viscosity function, and the appearance of a yield stress are depending on the fiber aspect ratio. The temperature dependence of the viscosity function is not significantly different from that of the unfilled melt. Transient shear stresses were measured on samples of different initial orientations of the fibers. The change of fiber orientation during shear flow gives rise to a pronounced overshoot of shear stress and normal stress difference. Elastic strains in shear are increased by the fibers but elastic elongational strains are reduced. Mechanisms are proposed to explain the experimental observations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01410464
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  • 5
    Electronic Resource
    Electronic Resource
    Orientation of macromolecules and elastic deformations in polymer melts. Influence of molecular structure on the reptation of molecules (1987)
    Springer
    Colloid & polymer science 75 (1987), S. 111-136 
    Details
    ISSN: 1435-1536
    Keywords: Polymermelt ; elastic properties ; molecularorientation ; molarmass distribution ; branching
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Melt elasticity has a strong impact on both the processing behaviour of polymers and end use properties of fabricated parts. This paper compiles in the first part relations describing time-dependent and steady-state orientations (flow birefringence) as well as elastic strains for different deformation histories. Analytical expressions based on the relaxation time spectrum and rubber-like liquid theory are obtained for small shear or elongational strains. An at least approximate description is possible for high deformation rates and strains. Some fundamental theoretical predictions are compared with experimental results obtained on polystyrene and polyolefine melts of different molecular structure. In addition, the second part presents fundamental experimental results on the influence of average molar mass and molar mass distribution on dynamic moduli, viscosity functions, normal stress coefficients, recoverable shear strains, extrudate swell, entrance pressure losses, and flow instabilities. The kind of side groups of the C-C-backbone as well as the type and number of chain branches in polyolefines affects the viscosity level and the temperature dependence (flow activation energy) of the rheological quantities. Long chain branching causes deviations from a thermorheologically simple behaviour. The experimental results are discussed in simple model images, taking into account the reptation motion of the molecules.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01188364
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  • 6
    Electronic Resource
    Electronic Resource
    Nonlinear rheological properties of polymer melts and their prediction based on the relaxation time spectrum (1987)
    Springer
    Colloid & polymer science 75 (1987), S. 136-138 
    Details
    ISSN: 1435-1536
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01188365
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  • 7
    Electronic Resource
    Electronic Resource
    Nonlinear shear creep and constrained elastic recovery of a LDPE melt (1978)
    Springer
    Rheologica acta 17 (1978), S. 138-148 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Es wird über Kriech- und Retardationsversuche an einer bekannten Polyäthylen-Schmelze niedriger Dichte berichtet, die mit Hilfe eines Weissenberg-Rheogoniometers durchgeführt wurden. Die Temperaturabhängigkeit der Scherdeformation und der 1. Normalspannungsdifferenz wird diskutiert. Die Ergebnisse der Messungen werden mit den Voraussagen einer rheologischen Zustandsgleichung in Integralform verglichen, die, wie bereits früher für die gleiche Schmelze gezeigt wurde, das Anlaufverhalten beim Anlegen einer konstanten Schergeschwindigkeit und das Relaxationsverhalten nach Beendigung einer stationären Scherströmung richtig beschreibt. Dabei muß betont werden, daß diese Zustandsgleichung keine anpassungsfähigen Parameter enthält. Der linear-viskoelastische Teil der Gedächtnisfunktion hängt mit dem linear-viskoelastischen Relaxationsspektrum zusammen, während der nicht-lineare, deformationsabhängige Teil mit Hilfe von „rapid-strain“-Experimenten bestimmt wurde. Schreibt man, wie bei Kriech- und Retardationsexperimenten, die Spannungsgeschichte vor, so kann die Zustandsgleichung nicht geschlossen gelöst werden, sondern muß mit numerischen Methoden invertiert werden. Die Übereinstimmung zwischen den berechneten und den gemessenen Werten der Scherdeformation und der 1. Normalspannungsdifferenz bei Kriech- und Erholungsversuchen ist recht zufriedenstellend. Innerhalb der experimentellen Fehlergrenzen läßt sich auch die Abhängigkeit der reversiblen Scherung von der Scherdeformation und der Schergeschwindigkeit berechnen.
    Notes: Summary Shear creep and constrained elastic recovery experiments on a well characterized low-density polyethylene melt are reported. The temperature dependence of the shear strain and the primary normal stress difference is discussed in detail. Comparison is made with predictions of a strain-dependent single integral constitutive equation, which has already been successfully used for the same polymer melt to describe the stress growth after sudden imposition of a constant shear rate flow and stress relaxation after cessation of steady shear flow. It should be emphasized that this constitutive equation contains no adjustable parameters. The linear-viscoelastic part of the memory function is related to the linear-viscoelastic relaxation spectrum, while the nonlinear, strain-dependent part was determined from rapid-strain experiments. In the case of a prescribed shear stress history the resulting integral equation cannot be solved by closed integration but has to be inverted by numerical methods. Agreement between theoretical predictions and experimental data is rather encouraging for shear strain and primary normal stress difference during creep and retardation tests. Within experimental error, the strain and shear rate dependence of the recoverable portion of the total strain can be correctly predicted.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01517704
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  • 8
    Electronic Resource
    Electronic Resource
    Elastic properties of polyethylene melts at high shear rates with respect to extrusion (1982)
    Springer
    Rheologica acta 21 (1982), S. 464-469 
    Details
    ISSN: 1435-1528
    Keywords: Polyethylene melt ; recoverable shear strain ; normal stress coefficient ; extrudate swell ; stick-slip transition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract At high shear rates a steady state of shear flow with constant shear rate, constant shear stress, and constant recoverable shear strain is observed in the short-time sandwich rheometer after some few shear units already. The melt exhibits rather high elastic shear deformations and the recovery occurs at much higher speed than it is observed in the newtonian range. The ratio of first normal stress difference and twice the shear stress, being equal to the recoverable strain in the second-order fluid limit, significantly underestimates the true elastic shear strains at high shear rates. The observed shear rate dependence of shear stress and first normal stress difference as well as of the (constrained) elastic shear strain is correctly described on the basis of a discrete relaxation time spectrum. In simple shear a stick-slip transition at the metal walls is found. Necessary for the onset of slip is a critical value of shear stress and a certain amount of elastic shear deformation or orientation of the melt.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01534320
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  • 9
    Electronic Resource
    Electronic Resource
    Das viskoelastische Verhalten von Polyamid-6-Schmelzen (1979)
    Springer
    Rheologica acta 18 (1979), S. 478-491 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Summary The rheological behaviour of nylon 6 melts of different molecular weights was investigated by means of capillary viscometers, a modified Weissenberg rheogoniometer, a sandwich creep apparatus, and an oscillatory viscometer. The influence of moisture content and residence time on the stability behaviour of the melts is demonstrated by measurements. Due to the comparable Schulz-Flory molecular weight distributions of the melts a mastercurve for the viscosity functions can be constructed by normalizing the viscosity and the shear rate by means of the zeroshear viscosity. The mastercurve is not only temperature invariant but also independent of the molecular weight. Temperature and molecular weight invariant plots are also obtained for the extrudate swell and entrance pressure losses as functions of the wall shear stress. Coincident values for the steady-state compliance are determined from oscillatory measurements, the recoverable shear strains, and the primary normal stress differences in the linear range of shear flow. As a consequence of the constant ratio $$\bar M_w /\bar M_n = 2$$ the steady-state compliance is independent of the molecular weight. The temperature dependence of the zeroshear viscosity follows an Arrhenius relation with a constant activation energy ofE 0 = 60 kJ/Mol.
    Notes: Zusammenfassung Das rheologische Verhalten von Polyamid-6-Schmelzen mit verschiedenen Molekulargewichten wurde mit Hilfe von Kapillarviskosimetern, einem modifizierten Weissenberg-Rheogoniometer, einem Parallelplatten-Kriechrheometer und einem Schwingungsviskosimeter untersucht. An Meßbeispielen wird der Einfluß der Feuchte und der Meßzeit auf das Stabilitätsverhalten der Schmelze diskutiert. Auf Grund ihrer gleichartigen Schulz-Flory-Molekulargewichtsverteilungen läßt sich für die Viskositätsfunktionen bei einer Normierung der Viskositäts- und Schergeschwindigkeits-Skala mit der Nullviskosität eine Masterkurve konstruieren, die nicht nur temperaturinvariant, sondern auch vom Molekulargewicht unabhängig ist. Die Strangaufweitungen und Einlaufdruckverluste bei Düsenströmung können als Funktionen der Schubspannung an der Düsenwand ebenfalls temperatur- und molekulargewichtsinvariant dargestellt werden. Die aus dynamischen Messungen, aus Messungen der reversiblen Scherung und der 1. Normalspannungs-differenz im linearen Fließbereich ermittelten Gleichgewichts-Nachgiebigkeiten stimmen überein. Als Folge des konstanten Verhältnisses von $$\bar M_w /\bar M_n = 2$$ ist die Gleichgewichts-Nachgiebigkeit unabhängig vom Molekulargewicht. Die Temperaturabhängigkeit der Nullviskosität folgt einer Arrhenius-Beziehung mit einer vom Molekulargewicht unabhängigen Aktivierungsenergie vonE 0 = 60 kJ/Mol.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01736954
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  • 10
    Electronic Resource
    Electronic Resource
    Comparison of the elongational behaviour of a polyethylene melt at constant stress and constant strain rate (1976)
    Springer
    Rheologica acta 15 (1976), S. 517-524 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Zwei verschiedene Apparaturen zur Untersuchung des Dehnverhaltens von Polymerschmelzen unter konstanter Zugspannung und konstanter Dehngeschwindigkeit werden beschrieben. An einem Polyäthylen niedriger Dichte wurden Messungen bis zu Verstreckgraden von 400 durchgeführt. Die ausreichend homogene Probenverformung erlaubt in beiden Versuchsführungen das Erreichen eines stationären Dehnfließens mit zeitlich konstanter Zugspannung und Dehngeschwindigkeit. Durch Entlasten des Schmelzestranges ist der reversible Dehnungsanteil für jeden Verformungszustand direkt zu messen. Die reversible Dehnung steigt mit wachsender Dehnverformung an, bis sich im stationären Bereich ein konstanter Wert einstellt. Die aus der Geschwindigkeit des viskosen Dehnfließens berechnete Dehnviskosität stimmt nur für den Grenzfall kleiner Deformationen mit der Trouton-Viskosität überein. Mit wachsender Dehndeformation steigt die Dehnviskosität bis zu einem Gleichgewichtswert an, der bei den gemessenen Dehngeschwindigkeiten von 0,03 s−1 und 0,1 s−1 um etwa einen Faktor 6 über dem Wert der Trouton-Viskosität liegt. Die unter gleichen Versuchsbedingungen mit beiden Apparaturen bestimmten Dehnviskositäten und reversiblen Dehnungen im stationären Bereich stimmen überein.
    Notes: Summary Two different apparatuses for measuring the elongational behaviour of polymer melts at constant tensile stress and constant elongational strain rate are described. Measurements on a low density polyethylene were carried out up to stretching ratios of 400. The homogeneity of sample deformation in both test methods was sufficient to reach a steady-state of elongational flow where the tensile stress and the strain rate as functions of time are constant. By unloading the molten rod the recoverable strain can be determined at any state of deformation. The recoverable strain increases with growing deformation and reaches a constant value in the steady-state. The elongational viscosity calculated from the rate of viscous flow agrees with the Trouton viscosity in the case of very small deformations only. With growing deformation the elongational viscosity increases up to a constant value in the steady-state which is greater than the Trouton viscosity by about a factor of six at measured strain rates of 0.03 s−1 and 0.1 s−1, respectively. The elongational viscosity and the recoverable strain in the steady-state measured with the two different test methods under the same experimental conditions are in good agreement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01515874
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