Rheological properties of short fiber filled polypropylene in transient shear flow

doi:10.1016/j.jnnfm.2004.06.005

Journal of Non-Newtonian Fluid Mechanics

Volume 123, Issue 1, 15 October 2004, Pages 19-32

https://doi.org/10.1016/j.jnnfm.2004.06.005 Get rights and content

Abstract

The behavior of a commercial short glass fiber filled polypropylene has been studied. It is well known that a thermoplastic polymer filled with short fibers with an initial isotropic orientation state exhibits a viscosity overshoot when sheared in the parallel plate geometry of a rheometer in the molten state. In this work, following a first deformation, the sample has been sheared in the reverse direction and a small viscosity overshoot has been measured. Similarly under stress growth experiments a large normal stress overshoot was observed. When the flow was reversed the normal stresses were initially negative and then exhibited a small positive overshoot. A model has been used to simulate these viscosity and normal stress overshoots. It is based on the Folgar–Tucker equation for fiber motion and the Lipscomb constitutive equation. This equation has been empirically modified to correctly predict the overshoots.

Introduction

Plastics are increasingly replacing conventional materials, mainly due to their low production costs and their lower density. Fibers and other fillers are added to plastics to improve their mechanical properties and hence their competitiveness with metallic materials. Short fiber filled thermoplastics represent a major class of growing importance since conventional equipment (extruder and injection machines) can be used to produce final parts. The mechanical properties of the produced parts depend strongly on the process itself, on the rheological properties of the filled polymer and on the orientation of fibers during processing.

The rheology of fiber-filled polymers is quite complex due to fiber–fiber and wall–fiber interactions, fiber breakage and migration. These add considerable complexities to the already complex rheology of the polymer matrix. Hence, the study of the rheological properties of concentrated suspensions in polymer melts remains most challenging.

The flow of fiber filled thermoplastics in the molten state is modified by the presence of fibers and reciprocally the fiber motion and rotation is affected by the flow. Relations between flow and fiber orientation can be studied using a rheometer equipped with a parallel-plate geometry. A thermoplastic sample containing initially isotropic fibers sheared between two plates exhibits a viscosity or stress overshoot [1], [2].

The pioneering work on the flow of fiber suspensions by Jeffery [3] was followed by those of Batchelor [4], Cox and Brenner [5], Hinch and Leal [6] and many others. These studies were restricted to dilute suspensions. Fiber–fiber interactions have been introduced in models developed for elongational flows of aligned fibers in Newtonian [7] and non-Newtonian fluids [8]. Later, Dinh and Armstong [9] developed a model with interactions for random fibers in a Newtonian fluid and which was extended by Gibson and Toll [10] to a non-Newtonian matrix. Following Jeffery [3], Hand [11] and Giesekus [12], Lipscomb [13] has proposed a constitutive equation for dilute suspensions of ellipsoidal particles with large aspect ratio.

For non-dilute fibers suspensions, interactions between fibers modify their motions. For dilute and semi-dilute suspensions, Sundararajakumar and Koch [14] proposed a simple model predicting that collision between two fibers shortens the fiber rotation cycle. This model prediction was found to be in agreement with experiments [15], although Ranganathan and Advani [16] believed that interactions between fibers should slowdown their rotational motion. This is taken into account by a diffusion term incorporated by Folgar and Tucker [17].

In this paper, we will review the main problems associated with the measurements of rheological properties of fiber-filled polymers. Typical results obtained for creep and stress growth experiments with a commercial glass fiber-filled polypropylene will be presented. Simulation results based on a modified Folgar–Tucker [17] model will be presented and compared with experimental data.

Section snippets

Orientation tensors

A fiber orientation can be described with an orientation vector p, a unit vector parallel to the main axis of the fiber. For a population of fibers, a statistical orientation distribution function ψ(p) can be used to describe the average state of orientation in a fluid element. A second- and a fourth-order orientation tensors have been defined by Advani and Tucker [18]: $a_{2} \Leftrightarrow a_{i j} = \int_{p} p_{i} p_{j} ψ (p) d p,$ $a_{4} \Leftrightarrow a_{i j k l} = \int_{p} p_{i} p_{j} p_{k} p_{l} ψ (p) d p,$ where a₂ is a symmetric tensor with trace equal to one. A closure approximation

Experiments

A commercial unfilled polypropylene (PP, Targor PPN 0160D1) and a filled polypropylene containing 30 wt.% short glass fibers (PP30, Targor Hostacom G3 N01L) have been used. Other fiber suspensions with different fiber contents were also prepared. They consisted of same treated glass fibers with a density of 2.5 g/mL and of same polypropylene with a melt density of 0.76 g/mL at 200 °C. The glass fibers had an average diameter of 14 μm. Their nominal length was 500 μm, but the average length measured

Experimental results

First, it was crucial to verify that the rheological results were independent of the gap used to carried out the experiments. The absence of slip at the wall has been verified by Mobuchon [33] using the same material. Moreover, several creep tests have been carried out for three different gaps, 1.1, 1.4 and 1.9 mm. Fig. 2 shows the creep viscosity as a function of strain for PP30 for experiments carried out at 1000 Pa. In Fig. 2a, we report the transient data for three different samples for

Model predictions

The model predictions have been calculated for a single point in simple shear for forward and reverse stress growth experiments. The corresponding predictions for creep experiments are much more difficult to calculate and are not reported in this section. The fiber initial orientation was assumed to be isotropic. The strain was taken as $γ = \dot{γ} t$ , where $\dot{γ}$ is the shear rate. The viscosity of matrix was taken to be 1 Pa s and the other parameters were r = 20, ϕ = 0.1, μ₂ = 300. Using the hybrid

Discussion

The simulation results presented in Section 5 have shown that the Folgar–Tucker and Lipscomb model can qualitatively describe the transient viscosity and normal stress differences of glass fiber filled polymers. However, the model underpredicts the width of the viscosity and normal stress overshoots. Industrial composites contain a large quantity of fibers, well above the semi-dilute suspension limit and the experimentally observed reverse viscosity overshoot width of about 50 strain units is,

Conclusion

The rheological properties of suspensions of short glass fibers in polypropylene have been studied in the molten state for transient shear flows in parallel plate rheometry. An acceptable thermal stability was obtained by adding 1 mass% of Irganox B225 to the polymer and the absence of slip at the walls has been verified.

Experiments were carried out in the forward and reverse directions for creep and stress growth experiments. Viscosity and normal stress overshoots have been observed and

Acknowledgements

This work was supported by the France–Quebec collaboration program and funded by NSERC (Natural Science and Engineering Research council of Canada). We wish to thank Professor. Charles L. Tucker III for helpful discussions and providing the program for the calculations of the orthotropic and natural closure approximations used in the model. Finally the materials used in the study were given by Targor, for which the authors wish to thank Dr. G. Krotkine.

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Rheological properties of short fiber filled polypropylene in transient shear flow

Abstract

Introduction

Section snippets

Orientation tensors

Experiments

Experimental results

Model predictions

Discussion

Conclusion

Acknowledgements

J. Non-Newtonian Fluid Mech.

J. Non-Newtonian Fluid Mech.

J. Non-Newtonian Fluid Mech.

J. Non-Newtonian Fluid Mech.

Int. J. Multiphase Flow

J. Non-Newtonian Fluid Mech.

Comp. Struct.

Orientation effects and rheology of short glass fiber-reinforced thermoplastics

Coll. Polym. Sci.

Rheology of short fiber reinforced polypropylene

J. Rheol.

The motion of ellipsoidal particles immersed in a viscous fluid

Proc. R. Soc. Lond.

The stress system in a suspension of force-free particles

J. Fluid Mech.

The rheology of a suspension of particles in a Newtonian fluid

Chem. Eng. Sci.

Constitutive equations in suspension mechanicsPart 1. General formulation

J. Fluid Mech.

The stress generated in a non-dilute suspension of elongated particles by pure straining motion

J. Fluid Mech.

Tensile behavior of power-law fluids containing oriented slender fibers

J. Rheol.

A rheological equation of state for semi-concentrated fiber suspensions

J. Rheol.

A theory of dilute suspensions

Arch. Rat. Mech. Anal.

Elasto-viskose flüssigkeiten, für die in stationären schichtströmungen sämtliche normalspannungskomponenten verschieden gross sind

Rheol. Acta

Fiber–fiber interactions in homogeneous flows of nondilute suspensions

J. Rheol.

Orientation behavior of fibers in concentrated suspensions

J. Reinf. Plast. Compos.