Strain History of the Melt in Film Blowing ROBERT FARBER and JOHN DEALY

Department of Chemical Engineering McGiU University

Montreal, Quebec, Canada

Techniques have been developed for measuring the strain and thermal histories of fluid elements as they move from the die lips to the freeze line. Motion pictures were analyzed to determine the rates of extension in the machine and trans- verse directions. A radiation pyrometer was used to measure the temperature of the film. These techniques were used to study the film blowing of polyethylene; a 2.5-in. diameter die was used, and blow-up ratios in the range of 1.8 to 3.4 were employed. Film thickness ranged from 2 to 4 mils. The maxi- mum measured extensional strain rates in both the transverse and machine direction were in the range of 0.15 to 0.6 sec-l. Standard shrinkage and impact tests were performed on the finished films, and an attempt was made to correlate the re- sults with several simple empirical norms of the strain history. No correlation could be discerned. The results of this study are inconsistent with some popular ideas about the origin of orientation in blown films, but they are consistent with some recently published data on the influence of deformation on orientation in melt-drawn capillary extrudate.

INTRODUCTION T h e unique mechanical properties of blown films

are associated with anisotropic molecular orienta- tion which is commonly thought to result from the peculiar strain history which the melt experiences as it passes from the die lips of the extruder to the freeze line. However, the nature of this strain history has not been studied in any detail. The purpose of the work reported here was to measure the strain rates in both the transverse and machine directions over as much as possible of the molten zone of the bubble of a film-blowing apparatus. In addition, since cooling plays an important role in film blowing, the tempera- ture history was also measured. Finally, some me- chanical properties of the final films were measured and an attempt was made to relate these to the strain histories.

The resin employed was a highly branched poly- ethylene film resin; Union Carbide DFDQ4400. This resin contains none of the additives often used to en- hance film properties. It has a density of 0.915 g/cc and a melt index in the range of 1.6 to 2.6. Figure 1 shows the shear viscosity of the molten resin at three temperatures as measured in a biconical rheometer similar to that used by Best and Rosen (1) and also in an IMASS Mechanical Spectrometer. The melt is highly non-Newtonian, and no zero-shear viscosity values could be estimated. To learn something about the viscoelastic nature of the melt a mechanical spec- trometer was also used to study stress relaxation after the cessation of steady shear. The shear rate used was 0.1 sec-'. The time required for the shear stress

POLYMER ENGINEERING AND SClENCE, JUNE, 1974, Vol. 14, No. 6

to fall to 20 percent of its steady state value ranged from 6 sec at 180°C to 11 sec at 140°C.

The resin was also studied by means of a differ- ential scanning calorimeter. The melting point of previously annealed resin in a heating cycle was about 100°C, but in a cooling cycle the solidification temperature decreased with increasing cooling rate. For example, with cooling from 185°C at a constant rate of 1O"C/min., the solidification temperature was about 91°C.

The film-blowing apparatus consisted of a 1-in. Wilmot extruder with an L/D of 24 to 1 and a 2.5 in. Visking spider die with a gap of 0.050 in. A conven- tional deep-dish air ring could not be used because it would have blocked from view a large portion of the

435

Robert Farber and John Dedy

Fig. 2. Schematic diagram of experimental apparatus.

molten zone of the bubble near the die. Therefore a special low-profile air-ring was constructed. A flat aluminum plate formed the upper wall of the air ring, and this was used as a platform for the pyrom- eter mounting and the film marking unit. This ar- rangement provided adequate cooling while blocking from view only the first inch above the die lips. Figure 2 is a schematic diagram of the experimental apparatus, and Table 1 lists the operating conditions of the 9 cases studied.

MEASUREMENT OF STRAIN RATES AND TEMPERATURE

In order to obtain the basic kinematic data neces- sary to calculate strain rates it was necessary to mea- sure velocity as a function of vertical distance above the die lips. It was also necessary to know the exact shape of the bubble. The natural frame of reference for representation of experimental data is a cylindri- cal coordinate system, r, 0, z , with its x-axis coincident with the axis of symmetry of the bubble. Thus, if R is the radius of the bubble, the basic experimentally measurable kinematic quantities are V,( z ) and R( z ) .

Using a technique similar to that of Dowd ( 2 ) , the surface of the melt film was marked with a reference dot as it emerged from the extrusion die. A pneu- matic punch and placement unit was designed to punch out a small circular dot of PVC electrical tape and push it gently onto the film surface. A movie camera was used to record the progress of the dot, and a scale and electric clock were also positioned in

Table 1. Operating Conditions for Experimental Cases

Linear Freeze Film produc- Mass Blow- AP, line thick.

tion rate, ftux, up inches height, ness, Case mmlsec Ibm/hr ratio water mm mils

1 74 17.3 1.8 0.18 340 3.5 2 69 29.3 3.4 0.26 276 3.4 3 67 24.4 2.9 0.20 392 3.4 4 76 24.1 2.6 0.20 427 3.3 5 100 22.0 3.3 0.22 457 1.8 6 98 21.8 2.9 0.21 236 2.0 7 95 17.0 2.2 0.26 263 2.2 8 96 12.2 2.3 0.22 225 1.5 9 115 19.2 3.0 0.21 254 1.5

the field of view. A detailed description of the equip- ment and procedure has been given by Farber (3) .

By analyzing the developed cinefilm it was pos- sible to obtain directly the height of the dot as a function of time, Z ( t ) , and also the bubble shape, H ( x ) . Differentiation of Z ( t ) produced V , ( t ) or, alternatively, V,( x).

In order to use the experimental data to calculate the principal strain rates it is necessary to make certain assumptions. Following Pearson and Petrie ( 4 ) , it is assumed that:

0 The flow is steady and axisymmetric 0 There are no velocity gradients across the film 0 The principal radius of curvature of the film is

much larger than the film thickness so that the film may be treated as locally planar.

In a frame of reference moving with an element of the melt the extension in any direction, y, is given by:

(1)

where L, is the length of the fluid element measured in the y-direction. In the case of film blowing the principal directions of stretching are the so-called machine and transverse directions. These directions partially define a curvilinear coordinate system whose coordinates we will designate as xM, xT and xN. The N coordinate direction is normal to the film, the 1' direction is perpendicular to the plane defined by the z and N dlrections, and M is in the direction of motion of the moving element of film.

For the transverse strain rate we have

In the fixed coordinate system, R, z, 0, this is:

(3 ) d T ( Z ) =-- I d R ( x ) V J x ) R ( z ) dz

The machine direction strain rate is more compli- cated. In the fixed N , M , T coordinate systan it is

(4)

In the fixed R, z, 0 coordinate system this becomes:

where

Thus, using the experimentally measured V,( Z ) and R ( x ) together with Eqs 3 and 5, it was possible to determine & ( z ) and tT ( Z ) . Furthermore, since 2 ( t ) had been measured directly it was possible to con- vert these strain relationships to strain histories, & ( t ) and EM ( t ) , where t is the time since an element of melt emerged from the die lips.

POLYMER ENGlNEERlNG AND SCIENCE, JUNE, 1974, Vol. 14, No. 6 436

Strain History of the Melt in Film Blowing

The temperature history, T ( t ) , was obtained by analyzing the output of a radiation pyrometer. The pyrometer was attached to a motorized stage which could be made to move up or down at a fixed speed, and the output was recorded by means of a strip chart recorder. In order to obtain the film tempera- tures all the way down to the die lips, the pyrometer was mounted at an angle with the horizontal. This meant that the strip chart output could not be inter- preted directly as T ( z ) . Thus, the bubble shape had to be taken into account in converting these experi- mental data to a plot of T ( x ) . Finally, using the Z( t ) data obtained in the kinematic studies, it was possible to convert T ( z ) to a thermal history, T ( t ) so that it could be compared with the strain-rate histories in a frame of reference which is meaning- ful for viscoelastic materials.

Figures 3-5 show the bubble shape, strain histories and thermal history for case 3. Figures 6-8 show the strain histories for cases 1, 4, and 7 respectively.

FILM PROPERTIES A simple, qualitative measure of the amount of

orientation in a film can be obtained by noting the shrinkage in the machine and transverse directions when a sample of the film is reheated. A number of

%in. diameter circular samples were cut from the film at each of four locations around the circumference O F the tubular film. The results were averaged to ac- count for variations around the periphery of the tube.

A sample, marked to show the machine and trans- verse directions, was placed in a shallow aluminum

2oo'

'O0I \ 80

0 2 4 6 8 10 12

T I M E SINCE EMERGENCE ( s e c l

F i g . 5. Thermal history-case 3.

A X I A L DISTANCE ( c m )

Fig. 3. Bubble shape-cuse 3.

TIYL SINCE EYLRQEWCE (Sac)

Fig. 6 . Strain history-case 1 .

I 1

TIME SINCE EWERQENCE (set)

Fig. 4 . Strain history-case 3.

POLYMER ENGINEERING AND SCIENCE, JUNE, 1974, Vol. 14, No. 6

TlYL SINCE l Y L R Q L N C C (S*C)

Fig. 7. Strain history-case 4.

437

Robert Farber and John Dealy

Table 2. Film Properties

TIYE SINCE EYERGENCE Isec)

Fig. 8. Strain history-case 7 .

cup filled with silicone oil at 115°C. A thin, polished aluminum wafer was placed over it to minimize dis- tortion during shrinkage. A curve of shrinkage vs time was obtained for each case by removing con- secutive samples at various times and quenching them in water at room temperature. The final shape of the sample was always roughly an ellipse with major axis in the transverse direction and minor axis in the m,achine direction. The difference between the length of each axis and the original sample diameter was divided by the original diameter and expressed as a percentage. The shrinkage results for case 8 are shown in Fig. 9.

The shrinkage in one direction is not independent of the shrinkage in the other, and this can be seen in Fig. 9 at times less than 2 minutes where the oscilla- tions in the shrinkages in the two directions are closely related. This means that raw shrinkage data do not represent a quantitative measure of the rela- tive orientation in the two directions. Menges and Wubken ( 5 ) have suggested a procedure for calcu- lating “corrected shrinkages which are more precise measures of orientation. However, their method of analysis is based on assumptions which do not as yet have a strong theoretical or experimental basis and was not used in the present study. Ultimate observed shrinkage values are shown in Table 2.

TIME ls.4

Fig. 9. Shrinkage behavior of flm-case 8.

438

Film thick- Machine Transverse ness, direction direction NMFE,

h, mm shrinkage, shrinkage, (kg-m)/ mm percent Case x 102 percent

1 8.89 2 8.64 3 8.64 4 8.38 5 4.57 6 5.08 7 5.59 8 3.81 9 3.81

77 15 1.26 72 30 1.37 65 45 1.40 66 38 1.44 70 53 2.22 77 45 2.00 77 26 1.90 82 29 - 79 47 -

Impact failure tests were conducted according to ASTM test D3029. Tests for each case were con- ducted on a minimum of 21 specimens taken from positions on the film representing an even distribu- tion around the film tube. The results from all the specimens were used to calculate the mean failure weight (MFW) and the normalized mean failure en- ergy defined as:

( MFW) (drop height) NMFE (g-cm/mm) = ( film thickness ) ( 7 )

The results are shown in Table 2.

CORRELATION BETWEEN SHRINKAGE AND STRAIN HISTORY

This study was undertaken in the expectation that the orientation in the film would be shown to be closely related to the transverse and machine direc- tion strain histories. Thus, while recognizing that the as-measured shrinkage values were imperfect mea- sures of orientation, and without inspecting the ex- perimental results in any detail, we tested several simply defined norms of the strain history as cor- relating parameters for the shrinkage results. These norms were simply the total strain, eu(tl), over some arbitrarily selected period of time, tl, just prior to reaching the frost line where t = tr.

Several values of tl were tried including:

a ) one second, b ) two seconds, c ) the time at which T = 116OC, d ) the time at which T = 132”C, e) the time at which T = 149°C.

The results for choice (b ) are shown in Table 3. In order to give some idea of the general levels of

strain rates observed in each case, the maximum observed strain rate in each direction is also given in Tabb 3. For the transverse direction, the maximum observed strain rate always (except for case 9) cor- responded to a clear peak as shown in Figs. 3, 6-8.

POLYMER ENGINEERING AND SCIENCE, JUNE, 1974, VoI. 14, No. 6

Strain History of the Melt in Film Blowing

Table 3. Measures of the Strain History

max. ob- max. ob- rn w sewed d ~ , sewed i~ ,

Case (2 sec) (2 sec) sec-1 sec - 1

0.232 0.200 0.239 0.257 0.172 0.276 0.151 0.232 0.220 0.475 0.471 0.603 0.349 0.408

0.370 0.805 - -

0.26 0.21 0.21 0.18 0.34 0.44 0.39 0.93 0.28

0.13 0.15 0.21 0.18 0.33 0.42 0.32 0.42 0.64

But for the machine direction, the maximum ob- served strain-rate was always the first value calcu- lated (corresponding to a point 1-inch above the die lips) as over the observable range of times, this strain rate always decreased monotonically.

DISCUSSION AND CONCLUSIONS By comparison of Tables 2 and 3 it can be seen

that the correlation between simple measures of the melt strain history and the film shrinkage is very poor. Although only one of the strain history norms is shown in Table 3 the others were no more success- ful as correlating parameters than one shown. A more revealing comparison, however, is that between the behavior in the transverse and machine directions. In Table 2 we see that the machine direction shrink- age is always greater than the transverse shrinkage, the ratio between the former and latter ranging from 2 to 5. However, as can be seen from Figs. 4,6-8 and from Table 3 the transverse strain rate was not con- sistently lower than the machine direction strain rate except near the die where the bubble diameter was growing only very slowly. Indeed, in some cases the transverse strain rate was higher than the machine direction strain rate over the entire last half of the strain history.

The only way that the concept of strain rate in- duced orientation can be preserved is to postulate that the early strain-history, where the machine-di- rection strain rate is always higher, governs the final orientation in the film regardless of the later history. But in the light of what is known about polymer viscoelasticity such a postulate must be rejected. Molten polymers have a fading memory; it is the most recent history which should have the greatest influ- ence on their state at any time. Furthermore, higher temperatures are associated with shorter relaxation times which means that the memory fades faster at higher temperatures. Thus, the cooling of the film as it moves up amplifies the fading memory effect.

It must be concluded that melt rheology does not play an important role in the generation of the orientation which is observed in blown films. It is necessary to take into account the change in mor- phology of the polymer as it cools near the freeze line. Although the experimental study of this phe-

POLYMER €NGINEERING AND SCIENCE, JUNE, 1974, Vol. 14, No. 6

nomenon in film blowing would be very difficult, there have been a number of such studies of the melt spinning process. Melt spinning is closely re- lated to film blowing as both processes involve ex- trusion, melt-drawing, cooling, and solidification. The central difference between the two processes is that in melt spinning the deformation field is principally uniaxial extension whereas in film blowing it is bi- axial extension.

Kitao et al. (6) have shown that in the spinning process melt drawing 'does not introduce substantial strengthening of the fiber but does condition the polymer in such a way as to make it more susceptible to cold drawing. Southern and Porter ( 7 ) have shown that extensional flow of the melt during cooling has it dramatic effect on the size and type of crystals which are formed. Fung et al. ( 8 ) recently reported on the particular morphology which results from melt-spinning. Walczak (9) suggests that melt draw- ing does not induce a significant orientation in spun fibers but does enhance subsequent cold drawing. He postulates that the orientation which is observed in as-spun fibers is a result of plastic deformation just above the freeze line rather than extensional melt deformation but that the melt flow does enhance the effects of this small amount of plastic deforma- tion.

Carrying over the results of the melt-spinning studies to the case of film blowing it can be postulated that the orientation in the film results from plastic deformation in the immediate neighborhood of the freeze line, and that the extensional melt deforma- tion below the freeze line aids this process without itself introducing significant orientation in the film.

ACKNOWLEDGMENTS The resin used in this study was contributed by

Union Carbide Canada Ltd., and the authors grate- fully acknowledge the use of the film blowing equip- ment and laboratory facilities located at the Com- pany's Montreal East technical center. Financial sup- port for this investigation was received from the National Research Council of Canada.

NOMENCLATURE V,( t ) = vertical upward velocity of melt element

in moving coordinate system V,( z ) = vertical upward velocity of melt in fixed

coordinate system z, r7 8 = cylindrical coordinates Z( t ) = elevation of melt element at time t R( z ) z radius of bubble in fixed coordinate system R( t ) = radius of bubble following a melt element t = time since melt element emerged from die L, = length of film element measured in y direc-

xM, x,, xT = curvilinear orthogonal coordinate system T ( z ) = temperature of bubble surface-fixed coor-

T ( t ) = temperature of bubble surface following

MFW = Mean Failure Weight, g

tion

dinates

melt element

439

Robert Farber and John Dedy

NMFE = Normalized Mean Failure Energy (see

tf = time at which melt element reaches frost

z,( t l ) = norm of strain history (see Eq. 8) CY = extensional strain rate (see Eq. 1 ) @( z ) = slope of bubble surface (see Eq. 6 ) AP = gauge pressure inside bubble

Eq. 7)

line

REFERENCES 1. D. M. Best and S. L. Rosen, Polym. Eng. Sci., 8, 116

2. L. E. Dowd, SPE J., 28,22 (March 1972). (1968).

440

3. R. Farber, M. Eng. thesis (Chem. Eng.), McGill Univ. (1973).

4. J. R. A. Pearson and C. J. S. Petrie, P h t . Polym., 85 (April 1970).

5. G. Menges and G. Wubken, Plastuemrbeiter, 23, 318 (1972).

6. T. Kitao, S. Ohya, J. Furukawa, and S. Yamashita, PTOC. 5th Int. Cong. Rheol., 4, p. 409, Univ. Park Press, Balti- more (1970).

7. J. H. Southern and R. S. Porter, J. AppE. Polym. Sci., 14, 2305 (1970).

8. P. Y.-F. Fung, E. Orlando, and S. H. Carr, Polym. Eng. Sci., 13,295 ( 1973).

9. Z. Walczak, J. Appl. Polym. Sci., 17, 177 (1973).

POLYMER ENGINEERING AND SCIENCE, IUNE, 1974, Vol. 14, No. 6