Stress Growth Data Research Articles

Fracture in elongational flow of two low-density polyethylene melts

Samples of two commercial low-density polyethylene melts were investigated with respect to their fracture behavior in controlled uniaxial extensional flow at constant strain rate in a filament stretching rheometer. In order to assess the possible influence of grain boundaries on fracture, the samples were prepared by three different types of pre-treatment: by compression molding of (1) virgin pellets used as received, (2) pellets homogenized in a twin-screw extruder, and (3) pellets that were milled into powder by cryogenic grinding under liquid nitrogen. The elongational stress growth data were analyzed by the Extended Hierarchical Multi-mode Molecular Stress Function (EHMMSF) model developed by Wagner et al. (Rheol. Acta 61, 281-298 (2022)) for long-chain branched (LCB) polymer melts. The EHMMSF model quantifies the elongational stress growth including the maximum in the elongational viscosity of LDPE melts based solely on the linear-viscoelastic relaxation spectrum and two nonlinear material parameters, the dilution modulus GD and a characteristic stretch parameter {overline{lambda}}_m. Within experimental accuracy, model predictions are in excellent agreement with the elongational stress growth data of the two LDPE melts, independent of the preparation method used. At sufficiently high strain rates, the fracture of the polymer filaments was observed and is in general accordance with the entropic fracture criterion implemented in the EHMMSF model. High-speed videography reveals that fracture is preceded by parabolic crack opening, which is characteristic for elastic fracture and which has been observed earlier in filament stretching of monodisperse polystyrene solutions. Here, for the first time, we demonstrate the appearance of a parabolic crack opening in the fracture process of polydisperse long-chain branched polyethylene melts.

Modelling of Elongational Flow of HDPE Melts by Hierarchical Multi-Mode Molecular Stress Function Model.

The transient elongational data set obtained by filament-stretching rheometry of four commercial high-density polyethylene (HDPE) melts with different molecular characteristics was reported by Morelly and Alvarez [Rheologica Acta 59, 797–807 (2020)]. We use the Hierarchical Multi-mode Molecular Stress Function (HMMSF) model of Narimissa and Wagner [Rheol. Acta 54, 779–791 (2015), and J. Rheology 60, 625–636 (2016)] for linear and long-chain branched (LCB) polymer melts to analyze the extensional rheological behavior of the four HDPEs with different polydispersity and long-chain branching content. Model predictions based solely on the linear-viscoelastic spectrum and a single nonlinear parameter, the dilution modulus for extensional flows reveals good agreement with elongational stress growth data. The relationship of dilution modulus to molecular characteristics (e.g., polydispersity index (PDI), long-chain branching index (LCBI), disengagement time ) of the high-density polyethylene melts are presented in this paper. A new measure of the maximum strain hardening factor (MSHF) is proposed, which allows separation of the effects of orientation and chain stretching.

Modeling of nonlinear extensional and shear rheology of low‐viscosity polymer melts

AbstractThe hierarchical multi‐mode molecular stress function (HMMSF) model developed by Narimissa and Wagner [Rheol. Acta 54, 779–791 (2015), and J. Rheol. 60, 625–636 (2016)] for linear and long‐chain branched (LCB) polymer melts were used to analyze the set of transient elongational and shear viscosity data of two LCB low‐density polyethylenes (1840H and 2426 k), and a linear poly‐(ethylene‐co‐α‐butene), PEB A‐780090 as reported by [Li et al. J. Rheol. 64, 177 (2020)], who had developed a new horizontal extensional rheometer to extend the lower limits of elongational viscosity measurements of polymer melts. Comparison between model predictions and elongational stress growth data reveals excellent agreement within the experimental window, and good consistency with shear stress growth data, based exclusively on the linear‐viscoelastic relaxation spectrum and only two nonlinear model parameters, the dilution modulus GD for extensional flows, and in addition a constraint release parameter for shear flow.

Universality of steady shear flow of Rouse melts

The data set of steady and transient shear data reported by Santangelo and Roland Journal of Rheology 45: 583–594, (2001) in the nonlinear range of shear rates of an unentangled polystyrene melt PS13K with a molar mass of 13.7 kDa is analysed by using the single integral constitutive equation approach developed by Narimissa and Wagner Journal of Rheology 64:129–140, (2020) for elongational and shear flow of Rouse melts. We compare model predictions with the steady-state, stress growth, and stress relaxation data after start-up shear flows. In characterising the linear-viscoelastic relaxation behaviour, we consider that in the vicinity of the glass transition temperature, Rouse modes and glassy modes are inseparable, and we model the terminal regime of PS13K by effective Rouse modes. Excellent agreement is achieved between model predictions and shear viscosity data, and good agreement with first normal stress coefficient data. In particular, the shear viscosity data of PS13K as well as of two polystyrene melts with M = 10.5 kDa and M = 9.8 kDa investigated by Stratton Macromolecules 5 (3): 304–310, (1972) agree quantitatively with the universal mastercurve predicted by Narimissa and Wagner for unentangled melts, and approach a scaling of Wi−1/2at sufficiently high Weissenberg numbers Wi. Some deviations between model predictions and data are seen for stress growth and stress relaxation of shear stress and first normal stress difference, which may be attributed to limitations of the experimental data, and may also indicate limitations of the model due to the complex interactions of Rouse modes and glassy modes in the vicinity of the glass transition temperature.Graphical abstract

Analysis on Nonlinear Stress-Growth Data for Shear Flow of Starch Material with Shear Process

The material function of liquid materials for packaging plays an important role in analysis of its mechanical behavior. The mechanical behavior of material affects the packaging process in many aspects, such as selection of packaging materials and preparation of packaging method. Therefore, research on the material function of the liquid material is very helpful to guide the packaging process and look into how the packaging quality and efficiency are affected by the mechanical properties of material. This paper established the material function for the starch solution under shear process. With the relaxation test of the starch solution specimens, theG(t)function and dumping function were established and verified. Based on the memory function of starch solution, the material function of starch solution was constructed and approved to be efficiently predict the mechanical behavior during the shear process. Therefore, such material function can be used to guide the operation on the shear flow.

Quantifying Extrusion Modification of LDPE with a Microcompounder

Abstract Processibility of LDPE is known to be sensitive to processing history. Significant changes in processibility and product properties can occur through repeated extrusion without detectable changes in molecular weight and molecular weight distribution. Such changes of LDPE rheology are simulated with DSM micro-compounder and characterized with the small angle oscillatory tests and the SER uni-axial extensional flow with a K-BKZ analysis. Both the linear and the nonlinear rheology data suggest the major mechanism in the extrusion with the DSM micro-compounder is the reduction of the effects of long chain branching. The linear rheology analysis, along with GPC and NMR characterization confirms that the changes in the extrusion are not due to chemical crosslinking, though an increase in backbone molecular weight at extreme conditions is perceivable through the minor increase in molecular weight distribution, the increase in zero-shear viscosity and the decrease of melt index. The extensional rheology results, on the other hand, reveal the depression of the strain hardening with prolonged extrusion at 190 degree C or higher extrusion temperature. The stress growth data were evaluated with a K-BKZ constitutive with exponential damping function. The depression of strain hardening is well characterized with the strain hardening factor and the non-linear exponent beta as function of the extrusion conditions. The damping factor β is observed to be especially effective as the parameter to follow the depression of the strain hardening due to microcompounder extrusion. The microcompounder extrusion and the SER analysis with the K-BKZ analysis prove to be a new useful tool for simulating the shear modification of the LDPE.

Note: Method for overcoming ductile failure in Münstedt-type extensional rheometers

The purpose of this note is to introduce an experimental technique to overcome ductile failure in uniaxial extensional flow and show a simple illustration of its effectiveness. Ductile failure prevents the rheological measurement of transient stress growth at higher strains for certain strain-hardening materials. This reduces the accuracy of nonlinear parameters for constitutive equations fit from transient stress growth data, as well as their effectiveness in modeling extensionally driven processes such as film casting. We propose an experimental technique to overcome ductile failure called encapsulation in which the material that undergoes ductile failure is surrounded by a resin that readily deforms homogeneously at higher strains. The materials are arranged in concentric cylinders and are deformed in parallel. A simple parallel model is shown to calculate the viscosity of the core material and is tested for its robustness in a linear low-density polyethylene/low-density polyethylene system in which the viscosities of each resin are known at all strains, strain rates, and temperatures investigated. Agreement is found at each strain rate investigated across all strains studied. The method is then extended to measure the viscosity of a sparsely branched high-density polyethylene (HDPE) system that undergoes ductile failure at higher strain rates. The technique shows good agreement with experimental results up to the onset of ductile failure in the pure resin and predicts viscosity growth of the HDPE resin well beyond the critical strain for the onset of failure seen in experimental measurements of the pure HDPE. Repeatability of the technique is also illustrated.

Extensional Rheometry of Entangled Solutions

The seminal ideas of de Gennes and Doi and Edwards have provided the theoretical framework for much of the recent effort to model the rheological behavior of entangled polymer melts and solutions. Recent theoretical work has incorporated a number of important additions to the basic Doi−Edwards theory, including an explicit description of chain stretch and additional relaxation mechanisms such as contour length fluctuations (CLF) and convective constraint release (CCR). However, very little quantitative data has been published on the rheological behavior of entangled systems in strong flows. Hence, a comprehensive examination of the theoretical developments has not been possible. The experiments described in this paper use the filament stretching rheometer to obtain transient extensional stress growth data and steady state uniaxial extensional viscosity data for a number of entangled, narrow molecular weight distribution polystyrene solutions in the strain-rate regime characterized by a significant degree of both chain alignment and stretch. These results are then compared with theoretical predictions for a number of the current generation of reptation-based models, including mechanisms for chain stretching, contour length fluctuations, and convective constraint release. These comparisons demonstrate that when the model parameters are properly obtained from linear viscoelastic measurements, the recent model due to Mead, Larson, and Doi (Macromolecules 1998, 31, 7895) provides quantitative predictions for this class of flows for solutions spanning the complete range from very lightly to highly entangled solutions.

Morphological evolution of immiscible polymer blends in simple shear and elongational flows

The evolution of the morphology of the dispersed phase of immiscible polymer blends is studied in both shear and extensional flows. In the simple shear flow, predictions of the Lee and Park [H.M. Lee, O.O. Park, Rheology and dynamics of immiscible polymer blends, J. Rheol. 38 (1994) 1405–1425] and of the modified Lee and Park as well as the modified Grmela and Ait-Kadi [M. Grmela, A. Ait-Kadi, Comments on the Doi–Ohta theory of blends, J. Non-Newtonian Fluid Mech. 55 (1994) 191–195] models ([C. Lacroix, M. Grmela, P.J. Carreau, Relationships between rheology and morphology for immiscible molten blends of polypropylene and ethylene copolymers under shear flow, J. Rheol. 42 (1998) 41–62] are compared to stress growth data. The size of the dispersed phase is strongly affected by moderately finite strain imposed during the stress growth experiments. The morphological changes after stress relaxation are well predicted by the models for a polypropylene (PP), ethylene vinylacetate (EVA) and ethylene methylacrylate (EMA) blend [C. Lacroix, M. Grmela, P.J. Carreau, Relationships between rheology and morphology for immiscible molten blends of polypropylene and ethylene copolymers under shear flow, J. Rheol. 42 (1998) 41–62]. The prediction is less satisfactory for a polystyrene (PS)/polyethylene (PE) blend. The morphological evolution for the elongation flows of the PP/EVA/EMA blends has also been investigated. The morphologies of samples extracted before and after extrusion through an hyperbolic shaped (nozzle) die show that the elongational flow induces fibrillar structures. The extensional viscosity data, needed to solve the interface governing equations of the Lee and Park model, have been obtained from entrance pressure drop measurements. These equations are shown to qualitatively describe the transition from a spherical to a fibrillar morphology.

Extensional flow characterisation and extrusion blow moulding of high density polyethylene modified by calcium carbonate

Free surface elongational flow properties, including transient state stress growth and melt rupture data, have been measured on a range of calcium carbonate filled high density polyethylene (HDPE) compounds, using a Rutherford elongational rheometer operating at constant strain rate in the range 0·1–6·0 s-1. Results show that polymer molecular weight has a strong influence on both tensile stress growth and melt rupture data; in creasing elongational strain rate decreases the stress growth coefficient, in all compounds. At any specific elongational strain rate, the stress growth coefficient increases with volume fraction of particulate additives and also when using additives of fine particle size, as a result of packing fraction effects. Acid coatings added at super-monolayer levels influence the viscosity of highly filled compounds, by internal lubrication.Dynamic extrusion data obtained by experimental blow moulding of calcium carbonate modified HDPE materials show that modifications to melt state shear modulus result in reduced die swell, to an extent determined by filler coating. In combination with die swell, higher extensional viscosity of filled HDPE contributes significantly to enhanced parison sag resistance. Solid state modulus enhancement was consistently observed in calcium carbonate filled HDPE containers and if excellent filler dispersion can be achieved, it is feasible to retain the ductile mode failure of unfilled HDPE when containers are subjected to high velocity impact loads.

Transient shear and extensional properties of biodegradable polycaprolactone

AbstractTransient shear and extensional properties of two grades of partially crystalline biodegradable aliphatic polyesters, poly ε caprolactone (PCL), were investigated at three different temperatures. Uniaxial extensional viscosity at a constant strain rate was obtained using the Meissner apparatus. The magnitudes of the stress‐over‐shoot during stress growth experiments were smaller than those typically observed for other polymers. Higher melt temperature and higher strain led to faster relaxation, while the lower molecular weight PCL 767 relaxed faster than the higher molecular weight PCL 787. The relaxation moduli are independent of strain for strain values below 0.1. Transient extensional measurements were conducted at strain rates of 0.01 to 1.0 s−1. At small stresses the extensional viscosity has the threefold value of shear viscosity as predicted by Trouton. There appeared to be no steady state regime for either grade of PCL studied and as a result ηe(ε) could not be determined. The departure from the linear limit is fastest for the highest extensional rate. Extension thickening behavior is observed at Hencky strains ranging from 1.0 to 2.0. PCL 767 displayed greater extension thickening than PCL 787 at the same temperatures. The Wagner integral constitutive equation was found to give an acceptable fit to the stress growth data in shear and extension, with the fit being better for PCL 767 than for PCL 787.

Uniaxial Extension of a Lyotropic Liquid Crystalline Polymer Solution

Uniaxial extensional stress growth of a lyotropic liquid crystalline polymer solution consisting of 40 wt% (hydroxypropyl)cellulose in glacial acetic acid was measured using a filament stretching technique. The Doi molecular theory and a modified Leslie-Ericksen continuum theory were used to predict the experimental results. While the Doi theory agreed with both steady shear and steady extensional data, it failed to predict the transient stress growth data. On the other hand, the modified Leslie-Ericksen theory gave a better qualitative prediction of the transient curve, although it predicted that both steady shear viscosity and steady extensional viscosity were constants. The steady state data agrees with the results obtained by Metzner et al., who used a fiber-spinning technique

On the use of stress growth data to determine strain-dependent material functions for factorable K-BKZ equations

The procedure of using experimental stress growth data to determine strain-dependent, or damping, functions for factorable K-BKZ constitutive equations is examined. Damping functions obtained using stress growth data from simple shear and planar extensional flows in conjunction with integrated forms of factored K-BKZ models are compared with the damping function obtained from shear step-strain experiments. Results for the low-density polyethylene (LDPE) known as IUPAC X are presented that demonstrate the difficulties encountered with this method, which can be quite serious for planar extensional flow. These results appear to be consistent with previous studies on several polymer melts where uniaxial extension stress growth data were used to determine damping functions. This body of evidence raises important questions about the use of this procedure and the strain-dependent and, apparently, test-dependent functions that are obtained. An explanation for these results is proposed which suggests that these observations may be due to an intrinsic shortcoming of K-BKZ theories.

Measurement of extensional viscosity of polymer solutions

A filament stretching technique for measuring the extensional viscosity of polymer solutions at constant stretch rate is presented. The liquid sample is held between two coaxial discs and stretched by moving the bottom disc downwards with a speed that increases exponentially with time. This is illustrated using a constant viscosity, elastic fluid consisting of 0.185% polyisobutylene in a solvent of kerosene and polybutene. For the case of this particular fluid, two distinct stretch rate regions are found to arise. The stretch rate in the first region is much higher than in the second, which is, in most cases, close to the overall stretch rate imposed on the sample. Nonetheless, all the results of any given run can be represented using an average extensional rate. The extensional stress growth data, plotted as the Trouton ratio against time, show an initial linear viscoelastic region where T R rises to a value of 3, independent of extensional rate. Beyond this region, T R depends on the stretch rate and rises dramatically to values in excess of 10 3; the higher the extensional rate, the faster is the increase in T R. These data do not seem to reach a steady state and appear to be similar to polymer melt data obtained by others in the past. The reproducibility of the results is very good and all this suggests that it is now possible to obtain unambiguous constant-stretch-rate stress-growth data for polymer solutions stretched from a state of rest.

Material properties of viscoelastic liquids in uniaxial extension

Based on a simple analysis using the Larson model, a superposition procedure is proposed for constant stretch rate data from fiber spinning experiments. This procedure appears to be able to account for the shear prehistory undergone by the fluid in the spinneret and yields true extensional stress growth data. The effectiveness of this method is demonstrated with the help of previously published isothermal fiber spinning data on one polymer melt and new data on one polymer solution. For constant stretch rate spinning at constant force, it is further shown that all the data can be represented by a single equation with known coefficients. Comparison with literature data on the transient extensional viscosity suggests that this same equation may also hold for the high stretch‐rate filament stretching of molten polymers at constant stretch rate. This result should lead to a considerable reduction in the amount of experimental work needed to characterize polymeric fluids.

Ideas about reptation, tube renewal and tube relaxation applied to the description of the non-linear viscoelastic behaviour in shear of some polydisperse polyethylene melts

In melts of polydisperse linear polymers like high-density polyethylene (HDPE) the dynamics of a given macromolecule are affected by the renewal of the confining tube owing to movements of surrounding molecules, the more so according as the matrix contains more shorter molecules. At large strains, the relaxation of the tube due to the retraction of matrix molecules also contributes to stress relaxation. For long-chain branched molecules in a polydisperse melt like that of low-density polyethylene (LDPE), the dynamics are dominated by tube renewal and tube relaxation effects. It is argued that for melts of HDPE as well as LDPE the combination of these ideas leads to a rheological constitutive equation consisting of the sum of two integrals. Both integrands are factored into the product of a strain-independent time function and a time-independent nonlinear strain tensor. Using the relaxation spectrum from oscillation experiments and the nonlinear strain measure from first normal stress growth data, this equation satisfactorily describes the decay of the stresses after step strain or after cessation of steady shear flow for melts of two commercial HDPEs and of two LDPEs. For the HDPE samples one integral suffices, but for the LDPE melts the additional time and strain dependences of the integral relating to tube relaxation are indispensable for a good fit of the experimental curves.

Test of Strain-Time Correspondence Principle with Gel-Containing Elastomers

Abstract With four NBR samples and one EPR, oscillatory measurements and stress-growth measurements were performed, the former being at very small deformation and the latter leading to large deformation. The Rheometrics mechanical spectrometer was used with a cone-plate fixture. The temperature was 100°C. The stress-growth data of NBR's, converted to complex viscosity-frequency data through the application of stress-time correspondence principle, were in good agreement with those observed in the oscillatory measurement. Thus, the stress-growth data including the large deformation were “linearized” to form a master curve. With the EPR sample, such a linearization was not necessary. The stress-growth data were adequately treated with the linear viscoelastic theory up to shear stresses approaching the steady state. The difference in behavior between the NBR's and EPR is caused by differences in type and extent of long branching and gel present in the samples.

A ?constrained-chain? network model for viscoelastic fluids

A specific case of the general “constrained-chain” strain-dependent integral viscoelastic model is evaluated with steady simple shear data, stress growth and relaxation data, and steady elongational viscosity data. The model is qualitatively correct and quantitatively reasonable in its predictions and, on balance, compares favourably with strain-dependent, strain-rate-dependent, and stress-dependent models from the current literature. Specific model comparisons are made to demonstrate the effect of the “constrained-chain” or finite extensibility feature of the model.

A biaxial extensiometer for molten plastics

AbstractWhile biaxial stretching plays a central role in several polymer processes, there has been no technique suitable for laboratory study of controlled biaxial stretching of molten thermoplastics at typical melt processing temperatures. The sheet inflation technique, which has been used previously to study rubbers and very high viscosity melts, has been adapted for use with molten thermoplastics by the use of oil as an inflation medium. Problems encountered in the use of the first prototype were eliminated in a second model, which is thought to produce reliable results. Stress growth data are presented for a low density polyethylene and for a polystyrene. A basic limitation of the technique is that the maximum achievable strain is in the range of 1.3 to 1.7, and this is often insufficient to bring out the nonlinear viscoelastic behavior of the melt.

The use of large transient deformations to evaluate rheological models for molten polymers

The prediction of models proposed by Acierno et al. (ALMRT) and by Phan-Thien and Tanner (PTT) are compared with data for a low density polyethylene film resin and a high density blow molding resin. The deformations involved are interrupted shear, reduction in shear rate, large amplitude oscillatory shear and uniaxial extension. Both models predict characteristic times for ”reentanglement“ that are significantly larger than stress relaxation times, but that are still much smaller than observed values. The origin of this effect is shown to be quite different in the two models. The ALMRT model fails to predict the observed nonlinearity in the response to large amplitude oscillatory shear. The PTT model predicts nonlinearity and gives the correct value of the maximum stress, but the predicted shape of the stress curve is incorrect. Extensional stress growth data were not in agreement with the predictions of the ALMRT model except in the linear region. It was not possible to fit the PTT model to these data.