Flow-induced crystallization of high-density polyethylene: the effects of shear and uniaxial extension

The effects of shear, uniaxial extension and temperature on the flow-induced crystallization of two different types of high-density polyethylene (a metallocene and a ZN-HDPE) are examined using rheometry. Shear and uniaxial extension experiments were performed at temperatures below and well above the peak melting point of the polyethylenes in order to characterize their flow-induced crystallization behavior at rates relevant to processing (elongational rates up to 30 s^− 1 and shear rates 1 to 1,000 s^− 1 depending on the application). Generally, strain and strain rate found to enhance crystallization in both shear and elongation. In particular, extensional flow was found to be a much stronger stimulus for polymer crystallization compared to shear. At temperatures well above the melting peak point (up to 25°C), polymer crystallized under elongational flow, while there was no sign of crystallization under simple shear. A modified Kolmogorov crystallization model (Kolmogorov, Bull Akad Sci USSR, Class Sci, Math Nat 1:355–359, 1937) proposed by Tanner and Qi (Chem Eng Sci 64:4576–4579, 2009) was used to describe the crystallization kinetics under both shear and elongational flow at different temperatures.     

Stress relaxation after a step strain in uniaxial extension of polyisobutylene and polyethylene

The morphology of molten polymeric materials is known to be less sensitive to shear than to extensional deformations. However, it is not easy to characterise molten polymeric materials in simple extensional flows due to the large number of experimental difficulties involved. This has led to the effective absence of a structure-preserving, morphology probing technique similar to the ones commonly found in shear, i.e., the equivalent of stress relaxation and oscillatory experiments. It is the aim of the present work to demonstrate the usefulness of a recently developed experimental technique that enables stress relaxation experiments after a step strain in uniaxial extension to be performed. Results are presented for two model melts (polyisobutylene, PIB, of different molecular weights) and for a series of linear low-density polyethylenes, LLDPE, in which the molecular structure (molecular weight, MW, molecular weight distribution, MWD and degree of long chain branching, LCB) is changed systematically. It is shown that, for both types of materials, stress relaxation experiments in extension yield quantitatively correct results and that this technique is more sensitive to differences in molecular structure than oscillatory experiments in shear.     

Atomistic simulation study on the crack growth stability of graphene under uniaxial tension and indentation

Meccanica - Combining a series of atomistic simulations with fracture mechanics theory, we systematically investigate the crack growth stability of graphene under tension and indentation, with a...     

Localised flow-induced crystallisation of a polyethylene melt

The sensitivity of flow-induced crystallisation (FIC) to the nature of flow type is demonstrated using a high-density polyethylene (HDPE) for two different flow geometries. A contraction–expansion slit geometry was used to create a mixed, but primarily simple shear flow, while a cross-slot geometry provided a region within the flow of high extension. Flow-induced birefringence was captured at a melt processing temperature of 155 °C to identify the principal stress difference within the two flows and determine regions of higher stress within the HDPE. The experiments were then repeated at 125 °C, and FIC was identified using bright-field observation. Crystallisation was observed within the regions that previously exhibited high stress levels. It was found that lower deformation rates in pure shear were required when compared with simple shear to create the crystal filaments.     

Atomistic/continuum simulation of interfacial fracture part I: Atomistic simulation

The phenomenon of interfacial fracture, as manifested by atomistic cleavage, debonding and dislocation emission provides a challenge for combined atomistic-continuum analysis. As a precursor for fully coupled atomistic-continuum simulation^[1] of interfacial fracture, we focus here on the atomistic behavior within a nanoscopic core surrounding the crack tip. The inter-atomic potential under Embedded Atom Method is recapitulated to form an essential framework of atomistic simulation. The calculations are performed for a side-cracked disc configuration under a remoteK field loading. It is revealed that a critical loading rate defines the brittle-to-ductile transition of homogeneous materials. We further observe that the near tip mode mixity dictates the nanoscopic profile near an interfacial crack tip. A zigzag interface structure is simulated which plays a significant role in the dislocation emission from an interfacial crack tip, as will be explored in the second part of this investigation. The project supported by the National Natural Science Foundation of China     

Elastomers in large-amplitude oscillatory uniaxial extension

In this work, we subject elastomers to a fixed pre-stretch in uniaxial extension, ε _p , upon which a large-amplitude, ε ₀, oscillatory uniaxial extensional (LAOE) deformation is superposed. We find that if both ε _p and ε ₀ are large enough, the stress responds with a rich set of higher harmonics, both even and odd. We further find the Lissajous-Bowditch plots of our measured stress responses versus uniaxial strain to be without twofold symmetry and, specifically, to be shaped like convex bananas. Our new continuum model for this behavior combines a new nonlinear spring, in parallel with a Newtonian dashpot, and we call this the Voigt model with strain-hardening. We consider this three-parameter (Young’s modulus, viscosity, and strain-hardening coefficient) model to be the simplest relevant one for the observed convex bananas. We fit the parameters to both our LAOE measurements and then to our uniaxial elongation measurements at constant extension rate. We develop analytical expressions for the Fourier components of the stress response, parts both in-phase and out-of-phase with the extensional strain, for the zeroth, first, second, and third harmonics. We find that the part of the second harmonic that is out-of-phase with the strain must be negative for proper banana convexity.     

Numerical simulation of large amplitude oscillatory shear of a high-density polyethylene melt using the MSF model

We study the flow response in large amplitude oscillatory shear of the molecular stress function (MSF) model that has recently been proposed by Wagner et al. [M.H. Wagner, P. Rubio, H. Bastian, The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release, J. Rheol. 45 (2001) 1387–1412]. The MSF model is derived from molecular theory and has only two parameters to describe the non-linear material response. The model predictions are analysed in both the frequency and time domain. It shows good agreement with experimental data for a linear high-density polyethylene melt. At low and medium strains, MSF model predictions are in excellent agreement with experimental data and predictions of a six-mode Giesekus model which has six parameters to describe the non-linear material response. At medium strains, the basic Doi–Edwards model, which has no non-linear parameters, already underpredicts the data. At high strains, the MSF model predictions agree slightly better with the experimental data than the Giesekus model. Surprisingly, however, it is the Doi–Edwards model that shows excellent agreement with experimental data at high strains. For the linear melt we consider, it outperforms the models that have non-linear parameters, both in the time and frequency domain.     

Elongational behaviour of a low density polyethylene melt

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 could be demonstrated where and 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 3 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.

---

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 gezeigt werden. und 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 Nullviskosität ₀ mit wachsender Scherung auf einen stationären Wert ab, die Dehnviskosität dagegen steigt von 3 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.

---

---

With 17 figures     

Plane constrained uniaxial extension of a single crystal strip

Within continuum dislocation theory the plane constrained uniaxial extension of a single crystal strip deforming in single or double slip is analyzed. For the single and symmetric double slip, the closed-form analytical solutions are found which exhibits the energetic and dissipative thresholds for dislocation nucleation, the Bauschinger translational work hardening, and the size effect. Numerical solutions for the non-symmetric double slip are obtained by finite element procedures.     

Strain-coupling effects in steady planar extension

This study is concerned with an evaluation of the capability of the strain-coupling model to predict steady shear and steady planar extensional flows. A comparison is made between the predictions of the K-BKZ and strain-coupling theories.     

Lubricated cross-slot flow of a low density polyethylene melt

Flow-induced birefringence and particle tracking velocimetry are used to investigate the lubricated flow of a low density polyethylene melt in a cross-slot geometry. The numerical predictions of the extended Pom-Pom (XPP) model in its original and modified (mXPP) version as well as those of the Giesekus model are analyzed along selected streamlines in two-dimensional (2D) complex flows involving a mixture of shear and planar extensional deformations at two Weissenberg numbers of Wi=21 and 29. Oil film light reflections perturbing the particle tracking velocimetry data analysis together with multiple orders of retardation occurring within the laser beam close to the stagnation point prevent a conclusive discrimination between the mentioned models. Although the agreement with the experimental data is mostly qualitative, the Pom-Pom model does not overestimate the data along the cross-slot symmetry lines contrary to what was observed in other cross-slot experiments without lubrication. This is a clear indicator that end effects play a central role in unlubricated cross-slot geometries having a large aspect ratio.     

Atomistic/continuum simulation of interfacial fracture Part II: Atomistic/dislocation/continuum simulation

Coupled atomistic/dislocation/continuum simulation of interfacial fracture is performed in this paper. The model consists of a nanoscopic core made by atomistic assembly and a surrounding elastic continuum with discrete dislocations. Atomistic dislocations nucleate from the crack tip and move to the continuum layer where they glide according to the dislocation dynamics curve. An atoms/continuum averlapping belt is devised to facilitate the transition between the two scales. The continuum constraint on the atomic assembly is imposed through the mechanics atmosphere along the overlapping belt. Transmissions of mechanics parameters such as displacements, stresses, masses and momenta across the belt are realized. The present model allows us to explore interfacial fracture processes under different mode mixity. The effect of atomistic zigzag interface on the fracture process is revealed: it hinders dislocation emission from the crack tip, especially under high mode mixity. The project supported by the National Natural Science Foundation of China     

On uniaxial extension of an elasto-viscous cylinder

Summary This paper deals with slow processes of extension of an elasto-visoous cylinder under conditions where the theory of linear viscoelasticity is applicable. Kinematic dependences are given and four nonstationary problems are solved concerning the extension of a cylinder when one of the following parameters is constant: strain rate, extension rate, stress, and tensile force.Experiments were performed on a low-molecular polyisobutylene at 25° and constant extension rates. The changes in total deformation and stresses, and after unloading, in highly elastic and irreversible deformation, were determined. The effect of the forces of surface tension on the elastic recovery of the samples was taken into account. The formulas of the linear theory of viscoelasticity are shown to apply within the range of extension rates studied. The viscosity and rubbery elasticity modulus were determined and found to agree well with the results obtained during steady shear flows.     

Rupture in rapid uniaxial extension of linear entangled melts

We have carried out uniaxial extension experiments on a monodisperse entangled melt to illustrate the origin of failure in the glass-like zone defined by Malkin and Petrie (J Rheol 41:1–25, 1997). The entangled melt was found to undergo a yield-to-rupture transition beyond a critical rate. We show that the onset of the “glass-like” zone defined by Malkin and Petrie is actually in the middle of the rubbery plateau where the mechanical response of entangled melts is not dictated by glassy chain dynamics. The rupture occurs plausibly through chain scission in the limit of finite chain extensibility.     

The growth of the void in a hyperelastic rectangular plate under a uniaxial extension

In the present paper, the finite deformation and stress analysis for a hyperelastic rectangular plate with a center void under a uniaxial extension is studied. In order to consider the effect of the existence of the void on the deformation and stress of the plate, the problem is reduced to the deformation and stress analysis for a hyperelastic annular plate and its approximate solution is obtained from the minimum potential energy principle. The growth of the cavitation is also numerically computed and analysed.Project supported by the National Natural Science Foundation of China     

Investigation of the uniaxial extension of polystyrene monofilaments

Summary The investigations carried out have shown that when the PS filament is stretched continuously, the same changes in the viscoelastic and mechanical properties of the polymer occur as under conditions of constant rate of deformation and constant true stress. Any of the three extension schemes indicated may be used for obtaining master temperature-time curves for the extension of PS and a correlation between its strenghtening and deformation conditions.

---

Zusammenfassung Die ausgeführten Untersuchungen zeigen, daß bei kontinuierlicher Verstreckung von Polystyrol-Monofilen die gleichen Änderungen in den viskoelastischen und mechanischen Eigenschaften auftreten wie unter den Bedingungen konstanter Dehngeschwindigkeit bzw. konstanter wahrer Spannung. Aus jedem der drei genannten Verfahren kann man daher für die Polystyrol-Verstreckung Master-Kurven des Temperatur-Zeit-Verhaltens und eine Korrelation zwischen den Verfestigungs- und Deformationsbedingungen ableiten.

---

---

With 6 figures