Uniaxial Elongation Research Articles

FILAMENT-STRETCHINGRHEOMETRY OFCOMPLEXFLUIDS

▪ Abstract Filament-stretching rheometers are devices for measuring the extensional viscosity of moderately viscous non-Newtonian fluids such as polymer solutions. In these devices, a cylindrical liquid bridge is initially formed between two circular end-plates. The plates are then moved apart in a prescribed manner such that the fluid sample is subjected to a strong extensional deformation. Asymptotic analysis and numerical computation show that the resulting kinematics closely approximate those of an ideal homogeneous uniaxial elongation. The evolution in the tensile stress (measured mechanically) and the molecular conformation (measured optically) can be followed as functions of the rate of stretching and the total strain imposed. The resulting rheological measurements are a sensitive discriminant of molecularly based constitutive equations proposed for complex fluids. The dynamical response of the elongating filament is also coupled to the extensional rheology of the polymeric test fluid, and this can lead to complex viscoelastic-flow instabilities such as filament necking and rupture or elastic peeling from the rigid end-plates.

Long-Chain Branching in Metallocene-Catalyzed Polyethylenes Investigated by Low Oscillatory Shear and Uniaxial Extensional Rheometry

This paper explores shear and extensional rheological behavior of unimodal, metallocene-catalyzed polyethylenes with low contents of long-chain branching (LCB). The polymers were produced in semibatch slurry polymerizations with methylaluminoxane (MAO) activated metallocene catalysts bis(n-butylcyclopentadienyl)hafnium dichloride (1), rac-[ethylenebis(2-tert-butyldimethylsiloxy)indenyl)]zirconium dichloride (2), rac-[ethylenebis(1-tert-butyldimethylsiloxy)indenyl)]zirconium dichloride (3), and rac-[ethylenebis(1-triisopropylsiloxy)indenyl)]zirconium dichloride (4). Melt properties in low oscillatory shear, in contrast to molecular weight and molecular weight distribution data from gel permeation chromatography, suggested that the polymers prepared with the ethylene-bridged complexes 2, 3, and 4 contain small but different amounts of LCB. In the melt uniaxial elongation experiments, the long-chain branched polymers exhibited strain hardening at all extension rates (rate range was from 1.0 to 0.01 s-1) with continual increase in strain hardening toward low strain rates. Unexpectedly, the behavior in LVE regime low shear and uniaxial elongation in the nonlinear range arranged the polymers in dissimilar order of apparently increasing LCB. Even though both these rheological techniques are sensitive to the molecular structure, they evidently reveal different features of it. Variation in the distribution (topology) of the long-chain branching due to differences in catalyst systems offers a plausible explanation of the differences in uniaxial elongation.

Flow birefringence and strain-induced hardening of cycloolefin copolymers under elongational flow

Strain-induced hardening behavior and flow birefringence were studied on copolymers of ethylene–tetracyclododecene (E–TD) and ethylene–norbornene (E–NB) of various compositions subjected to uniaxial elongation with constant Hencky strain rate between 0.01 and 1.0 s −1 in the temperature range from +40 to +60°C above their respective glass transition T g. When compared at the corresponding temperature of, e.g. T g+50°C, the E–TD copolymer exhibited stronger tendency of strain-induced hardening than the E–NB copolymer of the corresponding comonomer content. The stress optical rule (SOR) was obeyed for the E–NB copolymer in the whole range of its composition, while for the E–TD copolymer, the SOR was valid only for that of low TD content (<30 mol%), but invalid for that of high TD (≥30 mol%) content. The results suggest that the increase in the population of bulkier TD comonomer may be a molecular origin of the strong strain-induced hardening as well as a reason for the invalidity of SOR for the E–TD copolymer of high TD content. For the two copolymers that satisfy SOR, the stress optical coefficient C decreases exponentially with the comonomer content, and the tendency is stronger for E–TD than for E–NB, reflecting the comonomer size. The stress optical coefficient C vs. composition plots of the E–NB (block type) and E–TD copolymers are extrapolated at zero E limit to 5.5×10 −10 and 7.5×10 −12 Pa −1, respectively, which are expected to be the C for the NB and TD homopolymers if such polymers do exist.

Rheological properties of low-density polyethylenes produced by tubular and vessel processes

Various rheological properties have been studied for two kinds of low-density polyethylenes (LDPEs): one is produced by tubular process (tubular LDPE) and the other by vessel process (vessel LDPE). The latter shows smaller g′-parameter, the ratio of intrinsic viscosity to that of linear polyethylene. It was found that both LDPEs exhibit marked strain hardening behavior, i.e. upturn departure from the low strain rate asymptote, in both uniaxial and biaxial elongational viscosities, with stronger strain hardening in uniaxial elongation. Further, the vessel LDPE exhibits larger upturn behavior than the tubular LDPE. In the stress relaxation measurement, the vessel LDPE shows larger damping function, while the tubular LDPE shows values similar to those predicted by the Doi–Edwards theory. Furthermore, there is a significant difference in the effect of the shear history on the melt strength. The melt strength of the vessel LDPE decreases more rapidly with the shear history than that of the tubular LDPE. All these differences between the two types of LDPEs are due to the difference in the branch structure. The complex, multi-branched structure of the vessel LDPE gives much more prominent elastic features.

Generation and properties of ascorbic acid-deficient transgenic tobacco cells expressing antisense RNA for L-galactono-1,4-lactone dehydrogenase.

In higher plants, the terminal step of L-ascorbic acid (AsA) biosynthesis is catalyzed by the enzyme L-galactono-1,4-lactone dehydrogenase (EC 1.3.2.3, GalLDH). We generated AsA-deficient transgenic tobacco BY-2 cell lines by antisense expression of the GalLDH cDNA that was amplified from BY-2 cells using PCR. Two transgenic cell-lines, AS1-1 and AS2-2, having a marked expression of antisense RNA were analyzed. Antisense suppression of GalLDH mRNA led to a significant decline in the GalLDH activity. The AsA levels in the transgenic cell lines were found to be 30% lower than the wild-type BY-2 cells. In synchronous cultures, division of AS1-1 and AS2-2 cells was restrained with a concomitant decrease in mitotic index that was probably due to a decline in AsA levels. The rate of cell growth was also found to be less than that of the wild-type cells. Interestingly, there was a significant phenotypic difference between the transgenic and wild-type cells. The calli of AS1-1 and AS2-2 appeared to be sticky and soft. Back extrusion method also showed that AsA-deficient BY-2 callus was rheologically soft. Furthermore, microscopic analysis revealed that AS1-1 and AS2-2 cells were abnormally slender, suggesting a potential for a significant and a uni-axial elongation. Thus, we observed that decline in the AsA levels has an adverse effect on the division, growth and structure of a plant cell.

Stress–strain relations in finite viscoelastoplasticity of rigid-rod networks: applications to the Mullins effect

Constitutive equations are derived for the time-dependent behavior of a network of rigidrod chains at finite strains. The stress‐strain relations are applied to describe the Mullins effect: a noticeable difference between the response of elastomers under tension and subsequent retraction during the first cycle of periodic loading. Adjustable parameters in the model are determined by fitting observations for several grades of particle-reinforced rubber at uniaxial elongation (up to 300%) with subsequent retraction and at uniaxial extension with the maximal strain up to 600%. Fair agreement is demonstrated between experimental data and results of numerical simulation. It is revealed that material constants alter with the filler concentration in a physically plausible way and demonstrate dramatic changes at the percolation threshold corresponding to transition from isolated clusters of particles to a filler network.

Apparatus for Studying the Effect of Mechanical Deformation on the Permeation of Organics through Polymeric Films

A new experimental apparatus for studying the effect of mechanical deformation on the permeation of organic compounds through polymeric membranes is described. The apparatus consists of a custom-built biaxial membrane stretching device and an ASTM F739 permeation cell. Infrared spectroscopy was used as the analytical technique to measure, in real time, the downstream concentration of organic compounds that passed through the membrane. The equipment was used to monitor the permeation of single organic liquids and organic mixtures through uniaxially and biaxially elongated membranes composed of polyisoprene rubber and carbon black. The steady-state flux of acetone through a 40% uniaxially deformed membrane increased by 100%, as compared to that for a nonelongated film, whereas the acetone flux decreased by 25% when the membrane was deformed biaxially 40x40%. Variations in membrane thickness with stretching were small and could not account for the observed change in acetone flux with uniaxial elongation. For an equivolume feed mixture of acetone, benzene, and hexane, the steady-state permeation of all three compounds increased when the membrane was elongated 40x40%, as compared to the nonstretched case. Some deterioration of the membrane occurred during permeation of pure benzene with biaxial stretching (40x40%), as evidenced by a step-jump increase in the benzene flux. No deterioration was observed with nonelongated and uniaxially stretched films.

Numerical simulation of entry flow of the IUPAC-LDPE melt

Numerical simulations have been undertaken for the creeping entry flow of a well-characterized polymer melt (IUPAC-LDPE) in a 4:1 axisymmetric and a 14:1 planar contraction. The fluid has been modeled using an integral constitutive equation of the K-BKZ type with a spectrum of relaxation times (Papanastasiou–Scriven–Macosko or PSM model). Numerical values for the constants appearing in the equation have been obtained from fitting shear viscosity and normal stress data as measured in shear and elongational data from uniaxial elongation experiments. The numerical solutions show that in the axisymmetric contraction the vortex in the reservoir first increases with increasing flow rate (or apparent shear rate), goes through a maximum and then decreases following the behavior of the uniaxial elongational viscosity. For the planar contraction, the vortex diminishes monotonically with increasing flow rate following the planar extensional viscosity. This kinematic behavior is not in agreement with recent experiments. The PSM strain-memory function of the model is then modified to account for strain-hardening in planar extension. Then the vortex pattern shows an increase in both axisymmetric and planar flows. The results for planar flow are compared with recent experiments showing the correct trend.

Elongational flow birefringence of ethylene–tetracyclododecene copolymer

Simultaneous measurements of transient tensile stress σ( ϵ ̇ 0;t) and birefringence Δn( ϵ ̇ 0;t) were conducted under uniaxial elongation with constant Hencky strain rate ϵ ̇ 0 on new olefin-copolymer of ethylene (E) and tetracyclododecene (TD) of three different TD content from 20 to 41 mol%. For the low TD content copolymer, the extentional viscosity η E ( ϵ ̇ 0;t)(≡σ( ϵ ̇ 0;t)/ ϵ ̇ 0) showed only moderate increase with elongation time t or Hencky strain ϵ(= ϵ ̇ 0t) and the stress optical coefficient C( ϵ ̇ 0;t)(≡ Δn( ϵ ̇ 0;t)/σ( ϵ ̇ 0;t)) was nearly constant for the whole range of σ examined. On the other hand, for other samples of high TD content (≥30%), we observed strong uprising of η E often referred to as strain-induced hardening, and rapid decrease in C with increasing σ. As the copolymer chains were stretched out from the entangled state, the larger amount of the bulky TD groups in the latter may suppress the flow-induced conformational change to take place and suppress the disentangling of the chains, leading to the increase in σ and decreasing of C.

Elongational flow-induced morphology change of block copolymers. 2. A polystyrene-block-poly(ethylene butylene)-block-polystyrene triblock copolymer with cylindrical microdomains

Elongational flow behavior of a polystyrene-block-poly(ethylene butylene)-block-polystyrene (SEBS) triblock copolymer melt with cylindrical morphology is investigated by elongational flow opto-rheometry (EFOR), transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS). The SEBS film is first roll-processed to align the PS cylinders in a preferred direction. The uniaxial elongation is applied either parallel (denote Case I) or perpendicular (Case II) to the cylinder axis. Transient tensile stress σ(ϵ̇0;t) and birefringence Δn(ϵ̇0;t) are measured with a constant Hencky strain rate ϵ̇0 ranging from 0.01 to 1.0s−1 at various temperatures between PS glass transition, Tg(PS), and the order–disorder transition, TODT, of the SEBS. The data suggest that either the PS or PEB domains is preferentially elongated in the early stage of elongation, depending on the initial alignment of the cylinder phase. On further elongation, the elongational viscosity of the Case I melt exhibits strain-induced softening behavior in the final stage of elongation, whereas that of the Case II melts clearly displays strain-induced hardening behavior. The TEM and SAXS data of the samples elongated with a ϵ̇0=1.0s−1 show that the cylinders are mostly inclined approximately by 40–50° to the direction of elongation, whereas they are mostly aligned, parallel to the elongation direction on slower elongation. The morphology of highly elongated SEBS melts is governed by the applied strain rate and temperature, regardless of the initial orientation of the cylinders.

New Process Produces Superplastic Aerospace/Automotive Aluminum Alloy

A new thermomechanical process has been developed which renders an Al-Mg-Si-Cu alloy superplastic, making this material a candidate for superplastic forming (SPF). Industrial capabilities were taken into account during process development. The alloy investigated falls within the composition ranges of both aluminum alloys 6013 and 6111. The refined microstructure has an average grain diameter of approximately 10 μm and an average grain aspect ratio near 1.6 and exhibits superplasticity above 500 °C. The uniaxial elongation reached 375 %.

An adaptation of the separable KBKZ equation for comparable response in planar and axisymmetric flow

A specialisation of the ‘separable’ form of the KBKZ equation [M.H. Wagner, J. Non-Newtonian Fluid Mech. 4 (1978) 39–55] is presented that allows strain-hardening response to both planar and uniaxial elongation, while simultaneously giving shear-thinning behaviour. The specialisation expresses the strain-damping function in terms of a single invariant measure of strain. It is demonstrated that comparable planar and uniaxial elongational viscosities are predicted for IUPAC LDPE, with an over-prediction of the first normal stress difference in shear flow. It is shown that it is possible to fit transient data, for an LDPE melt that exhibits strain-hardening, for both planar and uniaxial elongational data simultaneously. It is shown that the new damping model gives vortex growth for simulations of both planar and axisymmetric contraction flows of LDPE, in contrast to a popular existing model that has been demonstrated to fail to predict vortex growth in planar contraction flow [P. Olley, R. Spares, P.D. Coates, J. Non-Newtonian Fluid Mech. 86 (1999) 337–357]. The finite-element based method used to find the flow solution is described including a novel method for implementing streamline tracking. Details are given of the iterative method used to compute flow fields, according to the stress field, and for the associated method to implement under-relaxation. Two new vortex measures are defined in order to quantify simulated vortices that can have an ‘hourglass’ shape (a shape that has been reported experimentally for LDPE contraction flows). To allow a broad assessment, comparisons are given as geometry type, contraction ratio, damping model, and the number of available strain-damping parameters are varied. Results for planar and axisymmetric contractions are compared, and contraction ratios of 8:1 and 4:1 are studied for planar flow. Results obtained using the new damping model are compared with well-established results obtained using an existing damping model for 4:1 axisymmetric contraction flow. The quantitative effects on flow simulations from using ‘single- β’ and ’multiple- β’ damping functions are assessed.

Mesoscopic bead-and-spring model of hard spherical particles in a rubber matrix. I. Hydrodynamic reinforcement

Exploiting an electrostatic analogy, we show that the elastic forces between a set of rigid particles embedded in a phantom polymer network can be represented by a simple bead-and-spring model. The beads represent the particles and the springs the rubber matrix. The model is validated by Monte Carlo simulation of rubbers filled with hard spherical particles, at volume fractions between 0.1 and 0.3. We derive both the moduli and the full stress–strain curves, under uniaxial elongation. The model reproduces and extends previous theoretical results on the so-called hydrodynamic reinforcement effect.

Quality assessment of a mechanically deformed silicon polyester coated galvanised steel system

In this paper the influence of a mechanical deformation on the corrosion behaviour of a silicon polyester coated galvanised steel is investigated. The electrochemical behaviour of samples subjected to several degrees of uniaxial elongation (1–10% of total strain) is compared with the one of the samples bent over different mandrel diameters. First, the coating aspect of the different types of samples was investigated, by optical microscopy and with scanning electron microscopy (SEM). Strain effects causes damage up to the formation of cracks in the coating. Further, a relationship between the strain introduced by uniaxial deformation and the strain caused by bending of the sample could be formulated. Finally, the influence on the corrosion resistance after uniaxial deformation is compared with that caused by bending deformation. To conclude, it was possible to confirm the theoretically formulated relationship between uniaxial and bending deformation by means of microscopy and by electrochemical techniques.

Elongational flow-induced morphology change of block copolymers Part 1. A polystyrene-block-poly(ethylene butylene)-block-polystyrene-block-poly(ethylene butylene) tetrablock copolymer with polystyrene spherical microdomains

Simultaneous measurements of transient tensile stress and birefringence are conducted as a function of Hencky strain rate ϵ̇0 and elongation time t on a polystyrene-block-poly(ethylene butylene)-block-polystyrene-block-poly(ethylene butylene) tetrablock copolymer with a weight fraction of polystyrene (PS) of 0.205, which displays spherical morphology. The measurements are carried out at high temperatures between the glass transition temperature of PS and the order–disorder transition temperature (TODT∼190°C) of the block copolymer under uniaxial elongation with ϵ̇0 between 0.01 and 1.0s−1. The data exhibit strain-induced softening under high ϵ̇0 (∼1.0s−1) at low temperatures, but strain-induced hardening under low ϵ̇0 (∼0.01s−1) at high temperatures. The stress-optical coefficient C(ϵ̇0;t) is almost constant under high ϵ̇0 at low temperatures, close to the value of low-density polyethylene melt (∼2.2×10−9Pa−1), whereas it increases by approximately 10–50 times under low ϵ̇0 at high temperature. The plots of the C(ϵ̇0;t) vs. t/aT (aT being the WLF shift factor) are roughly fitted into a single curve, indicating that the C(ϵ̇0;t) depends on t/aT, rather than Hencky strain ϵ. Such behavior, especially under low ϵ̇0, reflects the contribution of form birefringence Δnf of the deformed PS domains. Small angle X-ray scattering and transmission electron microscopy observation reveal that under high ϵ̇0, the spherical PS-domains are not appreciably changed, whereas under low ϵ̇0, they are deformed into cylinders and oriented along the direction of elongation, thereby resulting in the large contribution of Δnf.

Mechanisms of Deformation in Fully Conjugated Conducting Gels. Stretching and Swelling

Uniaxial elongation and swelling of well-defined fully conjugated poly(3-octylthiophene) gels of various functionalities and cross-link concentrations are studied above the melting temperature. The gels exhibit rubber elasticity (elastic modulus E in the range 0.2 < E < 0.7 MPa) and swell in chloroform. A linear relationship is established between E and the inverse of the mean number of skeletal bonds between consecutive cross-links (1/N av ). Variations of the transverse relaxation rate of protons attached to the polymer network with 1/N av are also linear whether NMR observations are performed on dry unconstrained networks or on fully swollen gels. The results show that the active network chain segments which give rise both to elastic and swelling properties are the linear strands comprised between adjacent cross-links. Moreover, we show that when doped by iodine in chloroform these gels are conducting while they remain swollen.

Chain mobility in the amorphous region of nylon 6 observed under active uniaxial deformation

A specially designed solid-state deuterium nuclear magnetic resonance probe was used to examine the effect of uniaxial elongation on the chain mobility in the amorphous region of semicrystalline nylon 6. In measurements conducted near the glass transition temperature, there was measurable deformation-induced enhancement of the mobility of the amorphous chains up to the yield point. This enhanced mobility decayed once deformation was stopped. Enhanced mobility was not observed in deformation at room temperature. The mechanics of deformation can be explained by the Robertson model for glassy polymers near the glass transition temperature, which states that applied stress induces liquid-like behavior in the polymer chains.

In vitro stability of polyether and polycarbonate urethanes.

The in vitro structural stability of poly-ether-urethanes (PEUs) and poly-carbonate-urethanes (PCUs) was examined under strong acidic (HNO3) or alkaline (NaClO) oxidative conditions and in presence of a constant strain state. Polyurethane (PU) samples were represented by sheets solvent-cast from commercial pellets or by tubular specimens cut from commercial catheters. The specimens were strained at 100% uniaxial elongation over appropriate extension devices and completely immersed into the oxidative solutions at 50 degrees C for 7-14 days. The changes induced by the oxidative treatments were then evaluated by molecular weight analysis, tensile mechanical tests, and scanning electron microscopy. In the experiments with solvent-cast samples, the PEU Pellethane was degraded more in the alkaline oxidative conditions and mainly in the absence of an applied uniaxial stress. All the tested PCUs were, on the contrary, more affected by the acidic oxidative agent. All the PCUs proved to have overall better stability than the PEU. The susceptibility to oxidation was also dependent on the shape and bulk/surface organisation acquired by the same polymer during its processing. When the oxidative test was applied to catheters made of a PEU and a PCU, the results confirmed the better stability of poly-carbonate-urethanes.

A Practical Criterion for Rheological Modeling of the Peeling of Pressure Sensitive Adhesives

The transient extensional viscosity of non-crosslinked pressure sensitive adhesives (PSA's) and physically-crosslinked PSA's is measured and compared with theoretical predictions based on the linear viscoelastic (LVE) properties of the PSA's and the use of linear and quasi-linear constitutive equations. Based on a previously-derived expression for the relative contributions of individual relaxation modes of a polymeric material to its transient extensional viscosity, a criterion for whether large extensional deformations can be modeled on the basis of the LVE spectrum is proposed and evaluated for each PSA. The relevance to adhesion is demonstrated in peel tests, where the deformation of adhesive is quantified in images of the peel front under the assumption of uniaxial elongation and used to obtain theoretical peel forces in excellent agreement with measurements. This demonstrates the applicability of the criterion to the peeling process.

Phase behaviour of SMA/PMMA blends: the influence of processing at low and high deformation rates

The influence of processing parameters (deformations) on SMA/PMMA blend phase behaviour is studied. It is found that injection moulding does change polymer blend phase behaviour. Phase separation kinetics are important to understand the injection moulding experiments and the kinetics are probably influenced by the deformations caused by the injection moulding proces. Capillary flow causes a complex change of polymer blend phase behaviour showing both deformation induced mixing and redemixing. Short capillaries, causing almost only uniaxial elongation in combination with pressure, cause no change to polymer blend phase behaviour. This is probably due to the short time the deformation is imposed to the material: it is expected that elongation is a main parameter causing changes in polymer blend phase behaviour. Parallel plate rheometer experiments show that applying only shear causes a complex change of phase behaviour showing both shear induced mixing and redemixing.