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Importance of elongational properties of polymer melts for film blowing and thermoforming.


Film blowing and thermoforming are important industrial processing operations, which are strongly dominated by empirical knowledge. This is mainly due to the pronounced elongational flow occurring in both processes and the fact that much less is known about the rheological behavior of polymer melts in elongation than in shear. First attempts to model film blowing go back to the 70s [1-4]. In Refs. 1 and 2, the kinematics of the bubble formation are described without taking the special properties of the melt and its correlation to the processing performance into account Ref. 3 deals with a description of the bubble contour and in Ref. 4 a constitutive equation is presented that tries to introduce material properties into the blowing process.

With growing importance of linear low density polyethylene (LLDPE) during the 80s, the interest in studies related to the influence of rheological properties on the film blowing performance of various polyethylenes grew. In Refs. 5 and 6, for example, the bubble stability of the low density polyethylenes LDPE and LLDPE was compared, in Refs. 7 and 8 the influence of long-chain branching on the extensibility of polyethylenes is investigated, and Refs. 9 and 10 discuss the role of elongational properties for bubble stability. In a more recent paper [11], for example, the development of novel high quality LLDPE resins and optimized processing equipment for their film extrusion is described.

No results can be found in the literature, however, on the homogeneity of film thickness and its relationship with molecular and rheological data although this is very important for many aspects of application.

Still less than for film blowing is found in the literature for thermoforming with respect to the influence of elongational properties on the wall thickness of processed items. In Refs. 12 and 13, for example, the relation between processing parameters and wall thickness distribution is discussed and in Ref. 14 the thermoforming of a long-chain branched polypropylene is described.

Owing to the progress in reliably characterizing the elongational behavior of polymer melts during recent years the question may successfully be addressed, now, as to what degree certain aspects of processing operations with a pronounced extensional flow component can be predicted from appropriate laboratory experiments.

In this article two pairs of polyolefins were selected with respect to differences in their elongational flow. One pair consists of polyethylenes and the other of polypropylenes. The polyethylenes were processed using a film blowing laboratory equipment and the polypropylenes by a thermoforming apparatus.



Two commercial polyethylenes were used. One of them is a low density polyethylene (LDPE) and the other a linear low density polyethylene (LLDPE). The LLDPE contains octene as the comonomer and was polymerized by using a Ziegler-Natta catalyst. Their characteristic data are given in Table 1.

The two polypropylenes are commercial products, too. PP1 is a linear ethylene/propylene-copolymer with an ethylene content between 3 and 8 wt%. PP2 is a homopolymer, which contains long-chain branches. A more detailed characterization of its branching structure is given in Ref. 15.

Measuring Techniques

The elongational behavior was investigated by a rheometer described in Ref. 16. Its measuring principle follows from Fig. 1. The cylindrical sample of typically 25 mm in length and 5 mm in diameter is attached with the one end to a force transducer and with the other to a pulling device. The surrounding silicone oil of a density matched to that of the polymer melt supports the sample and prevents it from sagging by buoyancy. Furthermore, it acts as a good heat transferring liquid affecting a very little temperature gradient along the length of 500 mm of the totally elongated sample. A sophisticated control unit in combination with a fast drive unit allows a great variety of deformation modes. At any state of deformation the measurement can be stopped. By lowering the silicone oil filled vessel, the elongated sample can be frozen in and then removed from the rheometer for further investigations. In this way it is possible to evaluate the homogeneity of sample deformation by measuring the diameters along its length.



The film blowing was performed using a laboratory equipment manufactured by the Goettfert company. The die of the blowing head had a diameter of 36 mm, slit width was 0.8 mm, and die land 15 mm. The melt was provided by an extruder with a screw diameter of D = 30 mm and a length to diameter ratio of L/D = 20. The film blowing machine was equipped with an air cooling device. The maximum take-up velocity was 0.5 m/s.

The take-up ratio is defined as

TUR = v/[v.sub.0] (1)

where v is the take-up velocity and [v.sub.0] the velocity of the extruded parison exiting the die. It describes the elongation in the machine direction. Perpendicular to it the parison is stretched due to blow up. This deformation is characterized by the blow-up ratio

BUR = R/[r.sub.0] (2)

with R being the radius of the bubble and [r.sub.0] that of the parison just after extrusion.

For the thermoforming experiments a vacuumforming machine manufactured by the GEISS company was employed. The forming temperature was 180[degrees]C. Plates of 250 mm squared with a thickness of 1.5 mm were used.

More details about the experimental conditions can be found in Ref. 17.



The elongational behavior of the polyethylenes was characterized using the apparatus presented in Fig. 1. As Fig. 2 shows, the LDPE exhibits strain hardening, which is well known for long-chain branched polyethylenes [18, 19]. The strain-hardening factor is defined as the elongational viscosity at a time t related to its linear value at the same time. As can be seen it is pronounced at higher strain rates [dot.[epsilon].sub.0] and gets weaker with decreasing strain rate. The LLDPE shows a strain hardening, which is contrary to that of the LDPE. No strain hardening can be observed at high strain rates whereas strain hardening increases from strain rates of [dot.[epsilon].sub.0] = 0.1 [s.sup.-1] to [dot.[epsilon].sub.0] = 0.005 [s.sup.-1]. The strain hardening observed for the LLDPE can have various reasons. It can be due to some few long-chain branches or high molar mass components, which are not detectable by classical analytical methods. Some authors relate strain hardening of LLDPE to a phase separation in the molten state [20].



Figure 3 shows the elongational viscosities of the two polypropylenes for a wide range of strain rates. For PP1 all curves of the transient elongational viscosity superimpose on the linear viscoelastic curve, which corresponds very well with the threefold value of the linear start-up viscosity 3 [[eta].sub.0.sup.+](t) in shear. This can be expected for linear polymers as shown by Munstedt and Laun [21] for an HDPE, for example. PP2, however, exhibits an elongational behavior, which is qualitatively similar to that of long-chain branched polyethylenes (cf. Fig. 2). Remarkable, however, is the fact that its strain hardening is more pronounced than that for the LDPE. A more detailed discussion of this finding is given in Ref. 15.


General Considerations

Strain hardening should have a positive effect on the homogeneity of sample deformation as it becomes obvious from Fig. 4, which shows typical functions of the elongational viscosities of a strain hardening (a) and a non-strain hardening material (b). In the case of a strain hardening material, an inhomogeneity occurring somewhere in the sample will disappear as the larger elongation of the thinner cross section area leads to a higher elongational viscosity and following from that a more pronounced resistance to deformation. This behavior can be regarded as a kind of self-healing mechanism. For a non-strain hardening material, the inhomogeneity becomes more pronounced by stretching it further, and the sample will finally break.


Homogeneity of sample deformation after uniaxial elongation

To assess the homogeneity of sample deformation, a so-called inhomogeneity factor r is defined as

r = a/[d.sub.e] with a = [1/n][n.summation over (i=1)] [square root of (([d.sub.i] - [d.sub.e])[.sup.2])] (3)

where [d.sub.e] is the expected diameter of the sample under the assumption of a homogeneous elongation, n is the number of diameters [d.sub.i] measured along the sample. In Fig. 5 the results are represented for the two polyethylenes as a function of the elongational rate. The total Hencky strain was [epsilon] = 2.9. The sample homogeneity reflects the influence of the strain hardening behavior as described before. The LDPE exhibits a more pronounced strain hardening at higher elongational rates than at lower ones and according to that the homogeneity becomes better with increasing [dot.[epsilon].sub.0]; for the LLDPE it is just the other way round (cf. Fig. 2). Over the whole range of elongational rates the inhomogeneity factor of the LDPE is lower than that of the LLDPE, however. At [dot.[epsilon].sub.0] = [10.sup.-2] [s.sup.-1], the inhomogeneity factor of the two samples approach each other reflecting their strain hardening behavior.

For the two polypropylenes one gets a similar relationship. PP1, which does not show any strain hardening, deforms very inhomogeneously, PP2 with pronounced strain hardening gives very homogeneous samples over a wide range of elongational rates (cf. Fig. 6).



As in processing operations like film blowing and thermoforming, biaxial deformation dominates, and it is of particular importance for an assessment of laboratory experiments with respect to practice whether strain hardening occurring in uniaxial elongation is found in biaxial deformation, too.

Therefore, biaxial experiments on a linear and a long-chain branched polypropylene were performed using the method of squeezing flow described in Ref. 22. The results are represented in Fig. 7. The branched polypropylene in Fig. 7 is the same as the PP2 investigated in this article, and the linear polypropylene, however, is distinguished from PP1 by a slightly higher mass--average molar mass of 456 kg/mol. Besides that it is a homopolymer. According to elongational flow experiments on various polypropylenes it can be assumed that strain hardening is not related to their chemical composition but to their molecular structure only [23]. The long-chain branched polypropylene exhibits a distinct strain hardening in comparison to the linear polypropylene. From these results it can be concluded that samples with strain hardening in uniaxial deformation do exhibit this feature in biaxial deformation, too. Similar findings were obtained on polyethylenes with a different experimental method [24]. Thus, the correlation found between strain hardening and sample homogeneity in uniaxial stretching experiments can be assumed to be qualitatively valid also for deformations with biaxial components at least at a laboratory scale.




With respect to processing it is interesting to find out whether the results obtained in laboratory experiments can be used to explain features of real manufacturing processes where elongational flow is involved. Of particular interest in this aspect is the uniformity of processed items as the thinnest part is decisive for their mechanical properties. The more uniform a film is, the more accurately its applications for a certain purpose can be assessed, for example. Film blowing and thermoforming were chosen as processing operations.

Film Blowing of Polyethylenes

The films blown with the equipment described in a previous section were investigated with respect to the homogeneity of their thickness. In Fig. 8 the inhomogeneity index is plotted as a function of the take-up ratio. The inhomogeneity index of the blown film is determined using Eq. 3 in which the diameters of the elongated cylindrical samples are replaced by the thicknesses at different positions on the film. The blow-up ratio was chosen as 2. Take-up ratios between 5 and 33 as given in Fig. 8 correspond to Hencky strains between 1.6 and 3.5, which are in the range of the total deformation attained in the laboratory tests. At low take-up ratios both polyethylene films exhibit a similar uniformity. The LDPE films show only a slight increase of inhomogeneity whereas the values of LLDPE increase with the take-up ratio.


A direct correlation with the homogeneity of the sample stretched in the tensile rheometer (cf. Fig. 5) is not straightforward insofar as the laboratory tests were performed at constant elongational rates, whereas the elongational rates along the films run through a maximum. They are zero just at the die and at the frost line again. Their maximum values were assessed to be 0.8 [s.sup.-1] at the lowest take-up ratio and 2.2 [s.sup.-1] at the highest [17], which are in the range of elongational rates applied in the laboratory experiments.

Taking into account, however, that the elongational experiments on the LDPE do not show a dependence of the homogeneity of sample deformation on the elongational rate [dot.[epsilon].sub.0] for 0.01 [s.sup.-1] < [dot.[epsilon].sub.0] < 1 [s.sup.-1] (cf. Fig. 5) the experimental findings on the homogeneity of the film blown from the LDPE are in convincingly good agreement with those of the laboratory tests (cf. Fig. 8).

A qualitative relation between the findings in the laboratory test and the film blowing experiment holds for the LLDPE, too, whose homogeneity of the elongated sample deteriorates with growing elongational rate (cf. Fig. 5) owing to the negligible strain hardening at [dot.[epsilon].sub.0] > 0.05 [s.sup.-1]. Therefore, a beneficial effect of strain hardening with respect to the uniformity of film thickness cannot be expected in the case of the LLDPE.

The results demonstrate that qualitative conclusions regarding the uniformity of blown films can be drawn from laboratory experiments in uniaxial deformation.

Thermoforming of Polypropylenes

As polypropylene is widely used in thermoforming, which comprises a pronounced biaxial elongational component of deformation, too, beakers were processed from the two polypropylenes characterized in elongation. Their geometry is sketched in Fig. 9.


This figure shows the wall thickness d at different distances from the rim. The wall thickness is more evenly distributed for PP2 than for PP1, which exhibits a pronounced minimum of the wall thickness. The better homogeneity of the beaker from PP2 is mirrored by the more homogeneous sample deformation of PP2 compared to PP1 (cf. Fig. 6), which could be related to the occurrence of strain hardening (cf. Fig. 3).

To demonstrate that the found correlation between the homogeneity of the wall thicknesses of the thermoformed beakers and strain hardening in uniaxial elongation is not an accidental one, some experimental results have to be discussed. The first one is that strain hardening found in uniaxial elongation can qualitatively be transferred to biaxial deformation, too, as documented by Fig. 7. As pronounced strain hardening occurs at higher strain rates and above a total strain of [[epsilon].sub.H] [approximately equal to] 1.5, only, (cf. Fig. 3) conclusions with respect to the relevance of strain hardening for the homogeneity of the wall thickness of the thermoformed beakers can be drawn if the respective elongations and strain rates are high enough. In Ref. 17 it is shown that Hencky strains up to 1.8 and elongational rates up to 2 [s.sup.-1] were obtained in the thermoforming process. These values are within the range in which strain hardening was observed in the laboratory experiments.


From the measurements presented in this article two conclusions can be drawn. First, the homogeneity of an elongated sample is related to strain hardening in such a way that it becomes the better the more pronounced the strain hardening is. It cannot be said from the results reported in this article, however, whether a certain amount of strain hardening is sufficient for achieving an optimum in the uniformity of deformation. A hint to an answer of this question may be taken from foaming experiments on blends of a linear and a long-chain branched polypropylene. It was found that above a certain limit of strain hardening a further improvement of foam properties related to the elongational behavior of the melt could not be observed [25]. Second, the sample homogeneity measured in uniaxial laboratory experiments provides a correlation with the uniformity of processed items like the thickness of blown polyethylene films and the wall dimensions of thermoformed beakers made of polypropylenes, although these processes comprise biaxial components. One explanation for this finding can be that the deformation perpendicular to the machine direction was small for both applications described in this article. But larger blow-up ratios showed the same tendency between the uniformity of deformation and strain hardening in uniaxial experiments [17, 26]. This result is not surprising taking the qualitative similarity of strain hardening behavior in uniaxial and biaxial deformation into consideration. Moreover, the relevance of strain hardening in uniaxial elongation for an assessment of the uniformity of deformation in predominantly biaxial processing operations was convincingly demonstrated in foaming experiments [25].

Therefore, uniaxial elongational experiments, which are rather easy to perform at a laboratory scale, are a versatile method to develop and optimize polymer grades for processing operations that are governed by elongational flow, even if they show pronounced biaxial components.

These conclusions drawn from the film blowing and thermoforming of one pair of polyethylenes and polypropylenes are supported by investigations on a large number of polyethylenes and their blends comparing their elongational properties and film blowing behavior [26].


The authors are grateful to Prof. Koyama and his coworkers at the Department of Polymer Science and Engineering of the Yamagata University in Japan for the opportunity to carry out the equibiaxial elongational experiments. Jens Stange thank the German Academic Exchange Service (DAAD) for funding his research at the Yamagata University.


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Helmut Munstedt, Stefan Kurzbeck, Jens Stange

Department of Materials Science, Institute of Polymer Materials, University Erlangen-Nurnberg, Martensstr. 7, D-91058 Erlangen

Correspondence to: Helmut Munstedt; e-mail:

Current address for Stefan Kurzbeck: INA-Schaeffler KG, Industriestrasse 1-3, D-91074 Herzogenaurach, Germany

Contract grant sponsor: German Academic Exchange Service.
TABLE 1. Characteristic data of the polyolefins.


Density at 25[degrees]C 0.918 0.919 0.905 0.909
MFI (190[degrees]C, 2.16 kg) 1.5 1.0 0.3 3.9
 (g/10 min)
[M.sub.w] (kg/mol) 240 105 409 587
[M.sub.w]/[M.sub.n] 14 3 4.1 9.5
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Author:Munstedt, Helmut; Kurzbeck, Stefan; Stange, Jens
Publication:Polymer Engineering and Science
Date:Sep 1, 2006
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