Kinetics of extrusion of polypropylene in the solid state

Kinetics of extrusion of polypropylene

2231

REFERENCES 1. V. M. KOPYLOV, D. Ya. ZHINKIN, P. L. PRIKHOD'KO, A. M. GASANOV and V. M. KOVYAZIN, Vysokomol. soyed. A23: 651, 1981 (Translated in Polymer Sci. U.S.S.R. 23: 3, 733, 1981) 2. V. M. KOPYLOV, P. L. PRIKHOD'KO and V. M. KOVYAZIN, Vysokomol. soyed. A23: 1751, 1982 (Translated in Polymer Sci. U.S.S.R. 24: 8, 1998, 1982) 3. K. A. ANDRIANOV, V. M. KOPYLOV, V. A. TEMNIKOVSKII and L. M. KHANANASHVILI, Vysokomol. soyed. A18: 1714, 1976 (Translated in Polymer Sci. U.S.S.R. 18: 8, 1959, ]976) 4. K. A. ANDRIANOV, E. I. KHUBULAVA, V. M. KOPYLOV, V. A. TEMNIKOVSKII, A. I. NOGAIDELI, L. M. KHANANASHVILI, Dokl. AN SSSR 229: 614, 1976 5. L. M. TARTAKOVSKAYA, V. M. KOPYLOV and A. A. ZHDANOV, Vysokomol. soyed. B26: 239, 1984 (Not translated in Polymer Sci. U.S.S.R.) 6. I. GENNIK, K. M. HARMON and J. HARTWIG, or. Inorg. Chem. 6: 2241, 1977 7. I. N. ROZHKOV and I. L. KNUNYANTS, Dokl. AN SSSR 199: 614, 1971

PolymerScienceU.S S.R. Vol.26, No. 9, pp. 2231-2236,1984 Printed in Poland

0032-3950/84 $10.00+ .00 © 1985PergamonPress Ltd.

KINETICS OF EXTRUSION OF POLYPROPYLENE IN THE SOLID STATE* A. N. KRYUCHKOV, A. O. BARANOV, I. YA. DORFMAN, N. A. YERINA, E. V. PRUT and N. S. YENIKOLOPYAN Institute of Chemical Physics, U.S.S.R. Academy of Sciences

(Received 29 April 1983) A kinetic study was made of extrusion of isotactic PP in the solid state with different dimensions of conical die plates. It was shown that there are several regions connected with transition from the nonstationary to stationary flow on curves showing the variation of the length of the extrudate. A mechanical approach was proposed to describe extrusion on the basis of the plasticity theory bearing in mind the orientational reinforcement of polymers. POLYMER extrusion below the melting p o i n t is n o w one of the m e t h o d s vigorously developed for o b t a i n i n g highly orientated materials [1, 2]. C o m p a r e d with other m e t h o d s o f o b t a i n i n g highly orientated polymers (cold drawing [3], o r i e n t a t i o n crystallization f r o m melt [4] or solution [5]), its advantage is the possibility of o b t a i n i n g p r o d u c t s f r o m industrial polymers with the requisite cross-section a n d increased rigidity a n d strength. * Vysokomol. soyed. A26: No. 9, 1993-1997, 1984.

2232

A . N . KR'dUCHKOVet al.

T h e s t u d y o f s o l i d - p h a s e e x t r u s i o n o f p o l y m e r s was s t a r t e d by P o r t e r et al. [6]. F u r t h e r efforts w e r e m a i n l y c o n c e r n e d w i t h t h e i n v e s t i g a t i o n o f the s t r u c t u r e a n d p h y s i c o - m e c h a n i c a l p r o p e r t i e s o f e x t r u d a t e s [7, 8]. It was o n l y r e c e n t l y t h a t a t t e m p t s h a v e b e e n m a d e c o n c e r n i n g process m e c h a n i s m

b e a r i n g in m i n d special f e a t u r e s o f the

p o l y m e r m a t e r i a l [9]. A s t u d y was m a d e in this p a p e r o f e x t r u s i o n kinetics o f P P in t h e solid state u n d e r v a r i o u s c o n d i t i o n s . A m e c h a n i c a l d e s c r i p t i o n o f the e x t r u s i o n p r o c e s s was p r o p o s e d . lsotactic PP of Mo= 3.38 × 105 with a melt index of 1.84 g/10 rain was examined. Figure 1 shows the fundamental layout of the device used for solid-phase extrusion. Temperature is controlled during extrusion by two thermocouples which show the temperature in the matrix and at the outlet from the die plate. The pressure required for extrusion was produced with an "lnstron 1196" testing machine.

I

0 0 0

0 © © --2x~

~

0_ 6/

\3

FIG. 1. Device for solid-phase extrusion: / - m a t r i x , 2 - p i s t o n , 3 - d i e plate, 4 - h e a t i n g system, 5, 6 - thermocouples. PP in the solid state was extruded by the following method: PP granules were melted at 220°; then after thermostatic control for 30 rain PP was slowly cooled to 100 ° at a rate of 2 deg/min at a constant pressure of 10 MPa, in order to prevent the appearance of macro-cavities and defects. A macroscopically perfect solid blank was obtained. The blank was then heated to the requisite temperature of extrusion, which was thermostatically controlled for 30 min. Extrusion was carried out at constant rate of movement of the piston of l ram/rain. Extrusion pressure and the length of the extrudate at the outlet from th.e draw plate were measured during the experiment. Conical brass die plates with an angle of inlet of 2~'=45 °, inside diameter D = 10 mm and various outside diameters d = 3 , 4, 5 and 7 mm were used as moulding tools. Cylindrical portions of the die plates of length l were characterized by a ratio of lid of 3"30; 3.25; 3-40 and 3.14, respectively. One of the main parameters characterizing the material extruded through a conical die plate is the maximum degree of elongation 2,,ax determined by the formula 2m,,,,=(D/d) 2. Therefore, die plates with outside diameters 3, 4, 5 and 7 mm had a value of 2ma. = 11' 1; 6"25; 4"0 and 2'04. PP was extruded in the solid state without using lubricant. The temperature of the matrix (150 °) and temperature at the outlet from the plate (145 °) were the same in all experiments. During extrusion of PP below the melting point through a conical die plate transparent extrudates were obtained with a smooth surface, without visible external defects, except for the extrudate

Kinetics of extrusion of polypropylene

2233

with 2maz= 11' 1 of high rigidity. The surface of the extrudate with 2,~a,= 11.1 had defects in the form of cracks twisted in a spiral. The diameter of extrudates obtained slightly exceeded the outside diameter of dies.

During extrusion of PP at constant rate of piston movement (%) the rate of length variation of the extrudate L is proportional to the rate of piston movement, as shown by the ratio Ve=2m.x%. Consequently, the dependence of L on time is linear: L=v d =2m.xVpt. However, Fig. 2 showing experimental dependences of the length variation of the extrudate on extrusion time, proves that an induction period is observed at the initial stage of extrusion, during which independent of 2. . . . the material cannot generally be extruded; a section follows then showing a deviation of the dependence of L(t) from the linear and the size of this nonlinear section increases with an increase of the maximum degree of elongation 2m.,. L cm 0

p,t'lpa

30-

f

3 ZO 2

tO0

10

7O

I

I

I

20

30

WO

Time, min FIG. 2,

3

/~

2 I

10

I

ZO 3O qO Time, rain FIO. 3

FJG. 2. Dependence of the length of the extrudate on extrusion time. Here and in Figs. 3 and 4 2=,, =2-04 (•); 4"0 (2); 6.25 (3) and 11-1 (4). FIG. 3. Dependence of extrusion pressure on extrusion time.

In parallel with determining L(t) a study was made of the pressure variation (P) according to the time of extrusion. Curves showing the dependence of P(t) are given in Fig. 3. It should be noted that dependences of P(t) for dies with different 2ma, values have three typical sections: rapid increase of extrusion pressure up to a certain maximum value of P~ax; a sudden reduction in extrusion pressure to the value of Pc; slight linear reduction of pressure. When describing extrusion of PP through a conical die it is necessary to bear in mind that the polymer which at the start of extrusion is in the conic part of the die, undergoes varying degrees of elongation during extrusion. Considering the continuity of the material during extrusion and using geometrical characteristics of the die, the following dependence of the variation of elongation in the length of the extrudate may

2234

A.N. KRYUCHKOVet al.

be derived 2 = ( 1 +--5--6tan~L)'~3/2

(1)

while 2 increases from 2= 1 to 2=2ma x and then remains constant. Figure 4 shows the dependence of the degree of elongation on the length of the extrudate for die with different values of 2max. Comparison of dependences given in Figs. 2 and 3 with results of calculating elongation according to the length of the extrudate (Fig. 4) enables extrusion of PP to be expressed in the following form: at the initial stage of extrusion material is condensed and micro-defects formed during preparing the blank are closed up; extrusion pressure shows a linear increase to a certain value determined probably by forces of friction of PP against the wall of the matrix and die. This is followed by extrusion of the material and rapid increase of pressure up to Pmax(Fig. 3); material with variable degree of elongation is then extruded from the cone of the die. On reaching Pmax the material attains maximum ~longation )~max"The variability of extrusion observed from the deviation of L(t) from linearity (Fig. 2), may be due to a gradual formation of the zone of plastic flow which extends from the outlet of the die and then fills the entire conic part. A further reduction of pressure after reaching Pmaxis due to transition of the material to stationary conditions of extrusion and is explained by different static and dynamic friction values of PP in the die. In this section transition is observed from nonlinear to linear dependence of the length of the extrudate L(t) on time (Fig. 2). The next stage of extrustion is characterized by a stationary process of plastic flow of the material in the cone of the die and a steady range of plastic flow. The length of the extrudate shows a linear dependence on extrusion time. A subsequent slight reduction of P~ is due to lower friction loss as a consequence of a reduction of the contact surface of the polymer with walls of the cylindrical matrix. As noted previously, this paper is aimed at describing the extrustion mechanism of polymers in the solid state, particularly of PP. The direct application of the theory of processes of volumetric compression of metals [10, 11] for describing extrusion of PP in the solid state does not give positive results. When studying volumetric compression of metals experimentally and theoretically it was shown that compression pressure depends logarithmically on the degree of elongation [12]. However, as shown by Fig. 5, the dependence of extrusion pressure in a stationary section of Po (and also maximum extrusion pressure Pmax) on )~m~ for PP is close to the linear, which cannot be explained from the point of view of theoretical ideas of plasticity normally used for metals. To explain the linear dependence derived it is natural to adopt the model of plastic flow which allows for the presence of clearly expressed orientation reinforcement of polymers, i.e. assume that the yield point o" of the material undergoing deformation, is the function of the degree of elongation 2, which characterizes this deformation. We assume that the exponential law of reinforcement holds a = cr0 2m, (2)

Kinetics of extrusion of polypropylene

2235

where 0-0 is the yield point of the unoriented material, 2 - d e g r e e of elongation and m is a parameter deteImined in a separate experiment. The formula for extrusion pressure, i.e. for the pressure, which is established during transfer at constant rate, may be derived from the plasticity theory by the following method. We adopt approximate radial plastic flow [12], which provides satisfactory results with small angles of ~,. Let axis z of the coordinate system be directed along the axis of the cone, 0- be the yield point of PP; at = -q0-, 0"2=0"3 = --p0" the main stress values; Q = Q ( z ) - t h e force acting in the direction of axis z on the cross-section which is at distance z from the top of the cone; r=r(z) is the radius of the section examined. Since Q=lrr2q0-, the force acting on the layer [z, z+dz] of the polymer is dQ=zrr20-dq

+ 7rr2qd0"+ 2~zrq0-dr. This force is counterbalanced by the total of frictional forces and forces of normal pressure on the cone wall, which is equal to dF=21rp0-(l+k cot ~v).rdr, where k is the coefficient of friction on the m e t a l - p o l y m e r boundary. Equating these forces, bearing in mind the law of solidification (2) adopted and the condition of plastic flow p - q = 1, we obtain -

-

1" dq - - +(1 - m) q - ( 1 + k cot W)(1 + q ) = 0 2 dr

Integration of this equation allowing for boundary conditions at the outlet from the cone of the draw plate q = 0 when r=d/2 results in the formula l + k c o t l / / [(d[)2(m+kc°t$)

q m+kcotv Hence

]

--1

1 + k cot V Be=no

-

-

r(•max)

(m+kc°t*)-

m+kcot~,

1]

(3)

The coefficient of friction k was evaluated from the reduction of extrusion pressure under stationary conditions (Fig. 3), which is linked with a reduction of the contact P,MPa

2

SOD-

10-

6

2

~

I

3

y 1

"

I00

11

1 I

I

2O FIG. 4

I

qO L mm

[

2

6

10

}t

FIG. 5

FIo. 4. Variation of the degree of extension in th.e length of the extrudate. FJo. 5. Comparison of experimental dependences of extrusion pressure P~ (1) and maximum extrusion pressure Pma, (2) on ttle maximum degree of elongation 2ma,with theoretical dependence (3).

2236

A.N. KRYUCHKOVet al.

surface Of the material and the draw plate. F r o m this evaluation we find that k is of the order of 0.05 so that the term k cot g may be ignored in every case. As far as index m is concerned, it may be established by independent experiments by determining the yield point o f PP subjected to varying degrees o f elongation. We used an initial extrudate segment for this purpose in which, according to formula (l), parts may be f o u n d subjected to any degree o f elongation between 1 and 2max (Fig. 4). These investigations showed that the value of m = 1.4 satisfactorily describes orientation reinforcement o f PP. Figure 5 shows the dependence (broken line) of P(2 .... ) according to formula (3) when m = 1-4, k cot ~u-((l, where Cro= 8 M P a is the value of yield point at extrusion temperature. Curves 1 and 2 in this Figure describe experimental values of extrusion pressure observed in continuous plastic flow and in the initial phase, respectively. It m a y be assumed that there is satisfactory agreement between curve 1 and formula (3) which describes the dependence of Pe (2re,x) under conditions of stationary extrusion. Within the scope o f this approach it becomes clear how spiral defects are f o r m e d during extrusion through a die with a high value o f 2 .... . This is due to the fact that with high degrees o f elongation yield point becomes close to the tensile strength and any local heterogeneity o f flow breaks down the material. The mechanical description proposed for extrusion in the solid state is evidently suitable for a wide range of a m o r phous-crystalline polymers. Translated by E. SEMI/RE

REFERENCES

1. 2. 3. 4. 5. 6.

A. G. GIBSON and I. M. WARD, Polymer Engng Sci. 20: 1229, 1980 D. M. BIGG, Polymer Engng. Sci. 16: 725, 1976 G. CAPACCIO, Macromolec. Chem. 4: 197, 1981 d. C. TORFS and A. J. PENNINGS, J. Appl. Polymer Sci. 26: 303, 1981 P. SMITH and P. J. LEMSTRA, J. Mater. Sci. 15: 505, 1980 d. SOUTHERN and R. S. PORTER, Polymer Preprints 10: 1028, 1969 7. A. E. Z A C H A R I A D E S , M. T. MEAD and R. S. PORTER, Chem. Revs 80: 351, 1980 8. K. N A K A Y A M A and H. K A N E T S U N A , J. Mater. Sci. 10: 1105, 1975 9. L M. WARD, Angew. Macromolec. Chem. 109/110: 25, 1982 10. G. Ya. GUN, Teoreticheskiye osnovy obrabotki metallov davleniyem, Nauka, Moscow, 1980 11. E. YANG, Ch. THOMSON and Sh. KOBOYASHI, Mekhanika plasticheskikh deformatsii pri obrabotke metallov, Moscow, Maskinostroyeniye, 1969 12. O. HOFFMAN and G. Z A K S , Vvedeniye v teoriyu plastichnosti, Mashgiz, Moscow, 1957