Nonlinear stress properties of poly(styrene-block-butadiene-block-styrene) melt under elongational and shear deformation

Effects of block copolymerized structure on nonlinear stress properties under elongational and shear deformation were investigated. Samples used in this study were poly(styrene-block-butadiene-block-styrene) (SBS, weight rate of S/B = 40/60) and polystyrene (PS) as a reference. Tensile stress–strain and shear stress relaxation properties were measured at the molten state. SBS showed high elasticity after reaching the yield point under elongational deformation at room temperature. PS melt showed substantial tensile stress increase after the yield point as strain rates increased. However, SBS melt did not exhibit noticeable tensile stress rise at higher elongation, and this property was almost independent of strain rates. Stress relaxation experiments revealed that the damping function of SBS melt was more strain-softening than that of PS melt. The results suggested that the block copolymerized structure decreases melt elasticity under elongational and shear deformation. A transmission electron micrograph indicated that the lack of melt elasticity in SBS melt is caused by orientation of the lamellar structure toward the stretched direction during deformation. © 1995 John Wiley & Sons, Inc.     

Experimental study of elongational flow and failure of polymer melts

A new and simple instrument for measurement of elongational flow response of polymer melts in constant uniaxial extension rate experiments is described. Quantitative stress development data are presented for a series of low-density polyethylene (LDPE), high-density polyethylene (HDPE), polystyrene (PS), polypropylene (PP), and poly(methyl methacrylate) (PMMA) melts. For small elongation rate E, linear viscoelastic behavior was observed; while for large E, LDPE and PS showed exponential stress growth, while HDPE and PP showed only linear stress growth. Stress relaxation experiments were carried out for several of the same melts in the instrument. Elongation to break and mechanisms of filament failure were studied. HDPE and PP have a tendency to neck and exhibit ductile failure, while at high E, LDPE and PS seem to show cohesive fracture. The elongational flow stress response data were compared to predictions of nonlinear viscoelastic fluid theory, specifically the Bogue-White formulation. The qualitative differences in responses of the melts studied were explained in terms of different dependences of the effective relaxation times on deformation rate and, more specifically, on values of the a parameter in the theory.     

New extensional rheometer for elongational viscosity and flow birefringence measurements: some results on polystyrene melts

A new extensional rheometer allowing the simultaneous measurement of elongational viscosity and flow birefringence is described. Polystyrene melts have been tested at different temperatures and strain rates. It appears that the time-temperature superposition principle holds for elongational tests in the temperature range investigated, with the same shift factors as for linear shear experiments. It has been verified that the stress optical behaviour of the melts is linear for small values of the stress whereas significant deviations appear at higher stresses.     

The influence of titanium dioxide on the rheological and extrusion properties of polymer melts

An experimental study of the influence of titanium dioxide (TiO₂) on the rheological and extrusion properties of five polymer melts (two low-density polyethylenes, two high-density polyethylenes, and a polystyrene) has been carried out. Increasing TiO₂ loading increases the shear viscosity η, with the extent of increase being greater at lower shear rates. At moderate and high TiO₂ loadings, the filled melts may possess yield values. Empirical equations relating viscosity to filler loading have been developed. The first normal stress difference was measured for the melts and found to increase with increasing TiO₂ loading. However, the extent of increase was less than found for the viscosity function and interpretation in terms of the theory of viscoelasticity suggests that the characteristic relaxation time of the melts decreases with increasing TiO₂ level. Empirical equations relating the first normal stress difference coefficient to volume fraction of the filler have been developed. Addition of TiO₂ is found to decrease extrudate swell and retard the occurrence of extrudate distortion.     

Molecular orientation of polydimethylsiloxane induced by elongational and shearing strains

A study examining the molecular orientation of poly(dimethylsiloxane) for different combinations of elongational and shear strains is presented. Three different cases were studied: (1) pure elongational strain; (2) increasing shear and decreasing elongational strains; (3) increasing shear and increasing elongational strains. The experiments were performed in a converging flow cell (at room temperature), where elongational and shearing strain rates achieved values of 370 s^?1 and 640 s^?1 respectively. Values of the Hermans orientation function were obtained from measurements of birefringence and polarization angles while strain rates were estimated from laser Doppler anemometry velocity measurements. Prospects for predicting molecular orientation from the stress-optical laws and rheological flow models are outlined and commented on.     

Melt extrudate swell behavior of multi‐walled carbon nanotubes filled‐polypropylene composites

The extrudate swell behavior of polypropylene (PP) composite melts filled with multi‐walled carbon nanotubes (MWCNTs) was studied using a capillary rheometer in a temperature range from 190 to 230°C and at various apparent shear rates varying from 50 to 800 s⁻¹. It was found that the values of the extrudate swell ratio of the composites increased nonlinearly with increasing apparent shear rates, while the values of the extrudate swell ratio decreased almost linearly with increasing temperature. The values of the melt extrudate swell ratio increased approximately linearly with increasing shear stress, while decreased approximately nonlinearly with an increase of the MWCNT weight fraction. In addition, the extrudate swell mechanisms were discussed with observation of the fracture surface of the extrudate using a scanning electronic microscopy. This study provides a basis for further development of MWCNTs reinforced polymer composites with desirable mechanical and thermal properties. POLYM. COMPOS., 38:2433–2439, 2017. © 2015 Society of Plastics Engineers     

Die–swell behavior of glass bead‐filled low‐density polyethylene composite melts at high extrusion rates

The extrudate swell behavior of glass bead‐filled low‐density polyethylene (LDPE) composite melts was investigated using a constant rate type of capillary rheometer at high extrusion rates and test temperatures varied from 140 to 170°C. The results show that the die swell ratio (B) of the melts increases nonlinearly with increasing apparent shear rates for the system filled with the surface of glass beads pretreated with a silane coupling agent, while the B for the system filled with uncoated particles remains almost constant when the true wall shear rate is greater than 2000 s⁻¹ at a constant temperature. The values of B for both the pure LDPE and the filled systems decreases linearly with an increase of the temperature and an increase of the die diameter at fixed shear rates, and the sensitivity of B on the die diameter and temperature for the former is higher than that of the latter. Furthermore, the effect of the filler content on B is insignificant, while the values of B decreases, obviously, with an increasing glass bead diameter (d) when d is smaller than 50 μm; then B varies slightly with d. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 419–424, 2000     

Elongational behavior of short glass fiber reinforced polypropylene melts

The Rheometrics Elongational Rheometer was employed to study the uniaxial extensional flow of glass fiber filled polypropylene melts, in which the fiber concentration, c, varied between zero and 40 weight percent. The constant strain rate mode was used for strain rates, \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document}, between 0.003 and 0.6 s⁻¹. Steady state elongational viscosities were observed in most cases for fiber filled polypropylene melts, even at rates at which the stress continued to increase for unfilled polypropylene. The rate of relative stress growth increased with \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document} and was affected by the addition of fibers. The steady elongational viscosity of the fiber reinforced melts was found to decrease with increasing \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document} and to increase with increasing c. Yield stresses were observed in elongational flow at high concentrations, although there was no clear evidence of yield in steady shear.     

Viscosity and die swell of acrylonitrile-butadiene-styrene filled with glass beads and glass fibers

Shear viscosity and die swell ratio of acrylonitrile-butadiene-styrene filled with glass beads and glass fibers were measured. The relative viscosity of the composites increased with filler content, but decreased with shear rate. At low shear rates, fiber filled systems had higher relative viscosities than bead filled systems. At high shear rates, the opposite was observed. The die swell ratio of the unfilled material increased linearly with the logarithm of the shear rate. Systems highly filled with glass beads or fibers showed a maximum in the die swell ratio at medium shear rates. The magnitude of the maximum in the die swell ratio increased with the filler content and the die length, up to a certain length, in a series of dies that had the same radius. The presence of a maximum in the die swell ratio of the filled melts is explained by an order-disorder phenomenon observed earlier by Wu.     

Tensile stress measurements on linear and branches low-density polyethylene melts. Interpretation of results with a generalized Maxwell model

Dynamic shear experiments in the linear range of deformation and extensional tests at constant strain rate have been carried out on a linear low-density polyethylene (LLDPE) melt and on two branched low-density polyethylene (LDPE) melts with different amounts of long-chain branching. Both the dynamic shear moduli and the tensile stress obey the time–temperature superposition principle. A simple model based on a nonaffine generalized Maxwell model with two relaxation times is proposed to describe the rheological behavior in elongation of these melts. Close agreement between the model and the experimental data can be obtained by adjusting the two relaxation times and the “slip parameter” of entanglements. The variations of these parameters with strain rate and their relationship with molecular structure are discussed.     

Rheological Behaviour of Short Silk Fiber Filled Rubber Compounds

Abstract

Rheological behaviour of rubbers (natural (NR), nitrile (NBR) and polychloroprene (CR)) and short silk fiber filled rubber compounds have been studied. The shear viscosity-shear rate relationship of both non-fiber filled and short fiber filled rubber compounds obey power law model for fluids and is similar to that of short fiber filled polymer melts. The effect of fiber concentration on the shear viscosity is more pronounced at lower shear rates. Both extrudate deformation and die swell become less on the addition of fibers to the mixes and the improvement is more significant at higher fiber concentrations. Extent of fiber breakage by the shear force during mixing is severe and is similar for all the rubbers.     

Shear and extensional flow of a thermotropic liquid crystalline polymer

The flow of a thermotropic liquid crystalline polymer (unfilled and glass fiber filled) was studied using a capillary rheometer and an instrumented injection molding machine. Despite different thermal histories, the techniques gave similar results. From 330 to 350°C, viscosity was independent of temperature. At 340°C, where most measurements were carried out, pronounced shear-thinning occurred and the shear flow curves were nonlinear, the power law exponent decreasing from 0.51 at a shear rate of 10 s⁻¹ to 0.35 at 10⁴ s⁻¹. A previously reported model was used to derive elongational flow curves from die entry pressure data. Because of the nonlinearity of the flow curves, quadratic log-stress vs. log-strain rate plots were needed to model behavior over the strain rate region studied. The elongational flow curves were similar in shape to the shear flow curves, with an effective Trouton ratio of 30. Despite orientation and structure present in the melt, the extensional viscosities and Trouton ratios were within the range found with normal thermoplastic melts. The results suggest that extensional flow may be inhomogeneous, the flowing units possibly being partially ordered domains.     

Rheology of 1‐butyl‐3‐methylimidazolium chloride cellulose solutions. III. Elongational rheology

The elongational rheology of solutions of cellulose in the ionic liquid solvent 1‐butyl‐3‐methylimidazolium chloride ([Bmim]Cl) was measured at 80, 90, and 100°C; 8, 10, and 12 wt% cellulose; Hencky strains 5, 6, 7; and strain rates from 1 to 100 s^?1. Master curves were generated by shifting the elongational viscosity curves with respect to temperature and Hencky strain. Also, general master curves were generated by simultaneously shifting with respect to both temperatures and Hencky strain. From the Arrhenius plots of the temperature shift factors, the activation energy for elongational flow was determined. The elongational rheology of these solutions was elongational strain rate thinning similar to that of their shear behavior and polymer melts and they were also strain hardening. Both effects and the viscosity increased with cellulose concentration. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Extensional flow of mica-filled polyethylene

Extensional flow of mica-filled high density polyethylene was studied at 150°C in a Rheometrics elongational rheometer. The constant strain-rate mode at a rate of 10⁻³ to 1.0 s⁻¹, and the constant stress mode were used. The mica content was 0, 25, 40, and 60 weight percent. In both testing modes, the steady state elongational viscosities were obtained; those for the filled samples were about ten to twenty times larger than the shear viscosity at corresponding (low) rates of deformation.     

Flow properties of natural rubber composites filled with defatted soy flour

The linear and nonlinear viscoelastic properties of natural rubber composites reinforced with defatted soy flour (DSF) were studied. DSF is an abundant, renewable commodity, and its rigid nature makes it suitable as a reinforcement phase in rubber composites. At small strain, the elastic modulus of a 30% filled composite was about 20 times higher than the unfilled rubber. Greater reinforcement was observed for carbon black filled composites than for DSF filled composites at filler concentrations of 10 and 20%. At high strain, values of the relaxation modulus dropped more rapidly for highly filled DSF composites. At high shear rates in a capillary viscometer, a small reinforcement effect remained for all composites, and lower die swell was observed for DSF composites. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Effect of the Secondary Transition on the Behaviour of Epoxy Adhesive Joints at High Rates of Loading

The shear yield behaviour of a modified epoxy joint has been investigated over a wide range of strain rates (γ˙ = 10^–2 s^–1 – 10⁴s^–1) and at different temperatures (–30°C, 24°C, 60°C, 80°C).

Assuming that high polymers exhibit pure viscous yield, the sharp increase of the yield stress in the strain rate sensitivity at high strain rates is explained in terms of a difference in relaxation times at low strain rates and high strain rates (α and β). The Bauwens's approach, which is a modification of the Ree-Eyring theory, gives an acceptable fit to the data. The yield behaviour of the modified epoxy joint, above a critical strain rate γ˙_β(T), may be described by the sum of the partial stresses τ_α and τ_β required to free the different kinds of molecular motions implied in the deformation process.

A good correlation between high impact resistance and the presence of the β mechanical loss peak in the range of the explored strain rates is established.

At very low temperature (-30°C), the data do not accurately fit the Ree-Eyring equation, meaning a heterogeneous deformation process characterized by the formation of local adiabatic shear bands and a permanent evolution of the molecular structure.     

Investigation of Unsteady Elongational Flow of Polymer Melts

Abstract

A method for estimation of the viscoelastic characteristics of polymer melts in the prestationary elongational flow is given. The experimental data show that at specific strain rates the polymer starts to respond to dynamic deformation as a highly elastic material. The viscoelastic characteristics of the polymer in the prestationary extensional flow can be described by a modified Maxwell equation.     

The influence of particle size and surface coating of calcium carbonate on the rheological properties of its suspensions in molten polystyrene

The rheological properties of polystyrene melts filled with 30 vol % of CaCO₃ particles of varying particle size are described. The influence of surface coating the particles with stearic acid is considered. Generally, the compounds with the uncoated particles exhibit viscosities which increase at ever greater rates as the shear rates decrease. It appears that these compounds exhibit yield values. Elongational flow data also suggest the existence of yield values. Difficulties exist in measurement of normal stresses in compounds with sizeable yield values. The principal normal stress difference at fixed shear stress of the PS/CaCO₃ compounds is lower than that of the PS melt. The magnitude of viscosity increases and yield values increase with decreasing particle size. Coating of particles with stearic acid results in major viscosity reductions and decreases in apparent yield values. The surface coating is most effective with the smallest particles. It presumably reduces interaction between particles and the extent of aggregation.     

Swell and distortions of high-density polyethylene extruded through capillary dies

The effect of varying the die entrance angle and the die length on extrudate swell and on the onset of extrudate distortion in capillary extrusion has been studied. Using theory from the literature, we have analyzed the contribution to the total pressure drop from the elongational and shear deformation in the entrance region, and from the capillary pressure drop in the land region of the die. From the contribution of the elongational deformation, we obtained an estimate for the elongational viscosity of the polymer. The same analysis was used to study the influence of the die geometry on the stick-slip instability. It is found that the elongational component at the inlet region mainly influences the extrudate distortions. The onset of the stick-slip instability occurs within 10% at a wall stress τ_w of 0.3MPa, where τ_w is calculated from expressions assuming fully developed flow. The variation around this average value is systematic with changes in die geometry, and the observed variations are probably due to the non-homogeneous pressure field in the die. We also propose a model for predicting extrudate swell. Input to the model are material parameters obtainable from oscillatoric measurements of the loss and storage modulus and residence times calculated from the geometry of the die. The swell model includes a fitting parameter that sets the overall scale of the swell.     

Rheological and solid wall boundary condition characterization of unvulcanized elastomers and their compounds

An extensive fundamental investigation of the rheological properties and solid wall boundary condition shear stress of elastomers and elastomer–carbon black compounds has been carried out. The elastomers were an emulsion butadiene–styrene copolymer (SBR 1500) and a polybutadiene. Shear flow rheological properties were measured using a newly designed sandwich rheometer, in both constant shear rate and creep modes as well as in a capillary rheometer. A constant elongation rate rheometer for elastomers was developed. Stress relaxation measurements were also carried out in the sandwich rheometer. The shear viscosity of the gum elastomers exhibits a constant very high shear zero viscosity (8 × 10⁸ Pa.s for SBR 1500 at 100°C) and decreases with increasing shear rate. The compounds exhibit yield values of similar magnitude to carbon black compounds of molten plastics. Only the SBR 1500 and its compounds were studied in the elongational flow mode. It was not possible to achieve a steady state in these experiments. An apparatus for measurement of shear stress as a function of velocity (shear rate) at a specified pressure was developed. The instrument, which we call a friction tester, was used not only to determine wall shear stress but to investigate the regime of flow and potentially determine conditions for the onset of slip. Evidence of changing flow regimes were found, and the implications discussed.