A rheological study of the injection molding of styrene polymers

Giovanni Pezzin, Sicedison Laboratory, Institute of Physical Chemistry, Universita’di Padova, Italy

This article describes correlation of the results of rheological data obtained for polystyrene in a capillary rheometer with the length of spiral flow over a broad range of temperatures, but for otherwise constant conditions in a specific injection molding machine.

A Rheological Study of the injection Molding

of Styrene Polymers

aluable information is obtainable from rheological v data on the injection molding behavior of thermo- plastics. If rheometric data are compared with the re- sults of a technological measure of polymer moldability, correlations between the two series of data can be ob- tained, and laboratory tests can be used to give an exact indication of the moldability of thermoplastics.

The evaluation of “processability” (or “moldability” ) is a fundamental problem in plastics technology. The normal methods of measuring the fluidity of molten polymers (1, 2 ) do not give reliable indices of mold- ability (3 ) .

A study of the rheology of polymer melts may be a better approach to the problem. Thermoplastic materials are now characterized not only by mechanical and ther- mal, but also by rheological data (4).

At present, however, there is not a simple way of in- terpreting the technological implications of rheological properties. In order to understand the essential features of the flow of polymer melts in cooled channels, a techno- logical measure of “moldability” can be used, together with parallel rheological measurements. Minimum mold- ing pressure, or temperature (5) , and spiral flow mold- ing (6, 7, 8) are widely used methods of measuring the processability of injection molding materials.

Studies on spiral molding have already been pub- lished (5,9, 10).

In this work, spiral flow was used as a quantitative in- dex of moldability for 17 styrene polymers and copoly- mers whose rheological properties were carefully studied in a capillary extrusion rheometer (11) over broad ranges of temperatures and shears.

Experimental Procedures Polymers-Seventeen different polymers and copoly-

mers were examined. They are indicated with capital letters from A to S. Ten samples are produced by Sicedi- son S.p.A. (Milan, Italy) and the remaining seven are commercial products of five other companies. Samples A to F are general purpose or heat resistant styrene poly- mers obtained by bulk or suspension polymerization. Their molecular weights and molecular weight distribu- tions are markedly different. Samples G to 0 are high impact styrene polymers, containing rubber (6 to 14%) and samples P to S are styrene-acrylonitrile (SAN) co- polymers.

Rheological measurements-Molten polymers were ex- truded in a constant velocity rheometer (11) in which temperature is controlled to +0.5”C and extrusion pres- sure is measured within 2 2 % . A capillary having a conical 90 degrees entrance and a diameter D = 0.061 in (0.155 cm) with a “length-to-diameter” ratio L/D = 66 was used. Eight temperature levels were explored, rang- ing from 175°C to 280°C in steps of 15°C. Ten extrusion

SPE TRANSACTIONS, OCTOBER, 1963 260

rates fixed by the plunger driving system of the rheometer were explored. They vary in geometrical progression from 22.10" in3/min (0.036 cmJ/min), to 2.2 in3/min (36 cms/min). Shear rates from 1.7 to 1.700 sec? and shear stresses from 0.1 to 60 psi (0.007 to 4.2 Kg/cm") can be explored.

Spiral molding-A screw injection molding machine (GBF Plastiniector V55) was used. The pressure on each melt was fixed at 14,000 psi (1000 Kg/cm') and the overall molding cycle was 35 sec, with a ram forward time (RFT) of 11 sec. Two valves prevented back-flow at the nozzle entrance and at the screw head. The cylin- der temperatures were chosen as "molding temperature" and they were set at the same levels as those used in the rheological measurements. The minimum nozzle diam- eter was 0.118 in (0.30 cm). The spiral mold had an approximately semicircular section, whose perimeter p was 0.467 in (1.187 cm) and area A was 0.0137 in" (0.0882 cm') . The hydraulic mean radius of the mold section, which can be calculated (5) from r = 2 A/p, was 0.0583 in (0.148 cm) . It compares well with the radius R of the largest circle inscribed in the section R = 0.059 in (0 150 cm.) The length of the sprue was 2 in ( 5 cm) . The mold temperature was main- tained at 50°C t 1°C. After ten preliminary moldings the lengths of 10 successive moldings were averaged to obtain the value L of spiral length. The standard devi- ation from L was never greater than 3%. The effect of RFT was occasionally checked: doubling it did not change L more than 5%. The rotation speed of the screw was fixed at 72 rpm. When set at 144 rpm, a change of 5% in L was found. The amount of polymer fed to the cylinder head was such that the spiral lengths L were independent from it.

Treatment of Data Rheological data were obtained as described in a pre-

vious paper (12). The extrusion pressure P, corrected for plunger friction to the walls of the rheometer barrel, is related to the maximum shear stress T~ by the equation:

T~ = PD/4L (1) where D and L refer to capillary diameter and length. The apparent shear rate y. is given by

32 Q Ya = --

rr D"

where Q is the flow rate, measured by plunger displace- ment.

The apparent viscosity is given by 7. = r,/y. The Rabinowitsch (13) correction was not applied to

the shear rates. No entrance correction to shear stress was made. This correction is not usually greater than 10 units of L/R (14, 15) so that it should not introduce (L/R = 132) errors greater than 8 % .

Heat generation can be a major source of error in rheo- logical measurements at high shears. To correct it is a difficult problem (4) . I t was verified that the maximum temperature rise in the flowing melts is dependent only on the product r,*y, and on the capillary diameter D (16). When shear rates are over 10" sec-' and the tem- perature is lower than 200"C, the viscosity data are prob- ably erroneous, due to heat generation, by amounts of

SPE TRANSACTIONS, OCTOBER, 1963

the order of 10%. However, they were not corrected. Small errors, not taken in account, can also be introduced by pressure losses in the rheometer barrel and by polymer expansion along the capillary (12).

At constant shear rate or shear stress the tempera- ture dependence of viscosity is given by the Arrhenius equation

where T is the absolute temperature in degrees Kelvin, R the gas constant and E is the "energy of activation" for viscous flow, which of course depends on shear rate or shear stress.

Spiral lengths L were measured in centimeters. Plots of L vs the injection pressure P (with P varying between 11,000 psi (800 Kg/cma) and 14,000 psi (1,000 Kg/cme) showed that pressure losses along the screw were less than 10% of total pressure, as generally happens in screw presses (17). Plotting the logarithmic values of L vs the reciprocal absolute temperature of the cylinder 1/T gave good straight lines ( & l o % of deviation in slopes) for any material, in the temperature range which has been explored.

The temperature dependence of the non-isothermal flow in spiral mold can be formally expressed through an Arrhenius-type equation:

(3) = k . eE/RT

(4) L = K . e - E ~ / R '

from which the energy of activation for spiral flow E,, can be derived. Values of EL, together with values of E for viscosities calculated at shear rates y. = 3 and 1500 sec-l and at the shear stress rw = 10 psi (0.7 Kg/cm"), are shown in Table 1.

~~~~~~~ ~~~

Table 1. Energies of Activation for Spiral Flow (EL) and for Viscous Flow (Ell) at Shear Rate 3 see-' and 1500 sec", and for Viscous Flow at Shear Stress 10 psi (0.7Kg/cm2). Values Given in Cal/mole (kcal/mole)

Sample

A B C D E F G H I L M N 0 P Q R S

EL _.__

4.6 4.8 4.7 4.8 4.6 4.7 5.2 4.8 4.6 4.5 4.3 2.9 2.3 6.0 4.7 4.3 4.6

E 7 h a = 3 sec-9

19.0 18.5 16.0 17.5 16.0 16.5 18.0 18.0 16.0 16.0 12.5 10.5 7.0

18.0 20.0 16.5 17.5

__-

EJy. = E,(t, = 10 psi) 1500 sec-'1 (0.7 Kglcm2)

6.9 26.0 6.8 25.0 7.3 25.5 7.2 25.0 7.1 25.2 6.7 24.5 7.6 24.0 7.0 23.5 7.0 23.0 6.6 22.5 5.9 22.5 4.4 20.0 3.4 15.5 9.0 30.5 6.3 25.0 6.2 24.5 6.8 23.0

- ~.

261

1oc

1 to‘ 1 0‘ 1 0”

bQ = & (set-')

1000

100

rl

10 0 7 -

I

0.1

Figure 1. Flow curves for two impact polystyrenes (Samples G. and 0) plotted 0 s maximum shear stress tw vs average shear rate yA. Temperatures are given in “C.

Polymer Flow Curves The isothermal flow curves obtained from the capillary

extrusion measurements are plotted as shear stress 7, vs shear rate ya on a log-log scale.

Figure 1 shows the complete set of flow curves for samplcs G and 0, two impact polystyrenes both contain- ing 7% of rubber. A single straight line cannot describe an isothermal flow curve over the shear range explored. The power Iaw (4)

does not hold over a shear rate range larger than one decade. The “flow index” n is dependent on shear rate. Furthermore the flow curves are clearly not parallel, which means that the flow index n is also dependent on temperature.

The isothermal curves “viscosity versus shear rate” for samples G and 0 are plotted in Figure 2, while the curves log 7 vs 1/T, at several shear rates, are plotted in Figure 3.

It can be seen that similar polymers can often be ex- tremely different in rheological properties. When the shear rate increases from 3 to 1,000 sec-’, at 220°C, the vis- cosity of sample G decreases by a factor of 6.5, while the viscosity of sample 0 decreases by a factor of 55. When the temperature changes from 175°C to 280”C, the vis- cosities, at ya = 10 sec-l, for samples G and 0, decrease by a factor of 30 and 4, respectively. The shear sensi- tivity of viscosity is much greater for sample G than for sample 0, while the reverse is true for the temperature sensitivity of viscosity.

Melt index data were also obtained for several samples, at 220”C, 44 psi (3.1 Kg/cm2) of pressure and with a standard orifice ( 2 ) .

rw = K-y,” ( 5 )

Figure 2. Differences in shear sensitivity. Plots of viscosity va = ~ ~ / y ~ vs shear rate ya for the samples of Figure 1 .

Spiral lengths measured at the cylinder temperature 220°C are plotted vs Melt Index (M.I.) in Figure 4. The correlation cannot be said to be good: going from samples N and 0 to samples B, C and L, and from sample F to sample G, the spiral lengths decrease while the M.I. in- creases.

Figure 5 is a plot of the spiral lengths L of all poly- mers, at all the 8 cylinder temperature explored, vs the coresponding viscosities va calculated at the constant shear rate y. = 3 sec-’ and at the same temperatures. Points are scattered over a large area and it can be seen that any material is characterized by a different L/v curve. SAN polymers lay, for example, on the lowest re- gion of the above mentioned area, and samples E, 0 and N on the highest side.

A semilogarithmic plot of spiral lengths vs viscosities at constant shear stress r x = 10 psi (0.7 Kg/cm’) is shown in Figure 6. The data are scattered and each ma- terial, as in Figure 5, gives a different L/T curve. Simi- lar results were obtained at all shear stresses which were examined.

Neither viscositics at constant shear stress nor vis- cosities at constant “Low” shear rate can be taken as re- liable indices of polymer moldability in injection molding.

When viscosities are measured at high shear rates a better correlation is obtained. Figure 7 shows a plot of spiral lengths against viscosities calculated at shear rate 7. = 1500 sec-*.

The correlation shows no appreciable scattering. The mathematical relation between L and rllja, can be

derived from a log-log plot (Figure 8). The straight line of Figure 8 corresponds to the equation

L = 2.5. ( ~ l m ) 4 ~ ’ a ( 6 )

262 SPE TRANSACTIONS, OCTOBER, 1963

10

1

h N .- . g 0)

F:

y? n - d

0,o 1

0,OO'

80

I

I" I .

I

I - -. ----

lo3/ T

Figure 3. Differences in temperature sensitivity. Arrhenius plots of vis- cosity a t several constant shear rates for the samples of Figure 7.

where L is in centimeters and ?Ism in lb sec/in". In terms of fluidity

4 = 1/7 L = 2.5- (+m)o.70 ( 7 )

can be written as plotted in Figure 9. These equations , express a relation between mold-

ability, as measured by spiral lengths, and high shear viscosity, measured at the temperature of the cylinder. They are, of course, independent of temperature and material, in the range of temperature and polymers examined in this work.

Equation 6 can be written

ln(L/K) = -0.70 In (Vm/k) (8)

EL = 0.70 E7Im (9)

and applying the Arrhenius equation (3) and (4)

The energy of activation for spiral molding EL must be 0.70 times the energy of activation for viscous flow at shear rate ya = 1500 sec-'

A plot of EL vs E?, is shown in Figure 10. The slope is 0.70.

Melt Index (22OOC)

Figure 4. Correlation between spiral length L and Melt Index for 12 samples. Me l t Index expressed as grams of polymer extruded in 10 min through a standard orifice (D = 0.0825 in, L / D = 3.82) under 44 psi (3.1 Kg/cm3 pressure.

SPE TRANSACTIONS, OCTOBER, 7963 263

100

80

60

CI

E, 40 ._

2

20

O O

R GlL

P 5

SQ

1 I

1 I

0,4 08 1,2 1,6 20 2,4

w E0

0

L- li

' A

C F

D M B A

C

R P 0 I

L 0

0

I

n 0 n

T-

v-

i P RL

I

Figure 5. Correlation between spiral length L and melt vis- cosities at constant shear rate ya =3 sec-'. Each sample is identified by i t s letter. Melt viscosity a t a given temperature

is plotted against the corresponding spiral length obtained at the same cylinder temperature.

Figure 6. Spiral flow lengths L plotted vs logarithmic melt viscosities at constant shear stress tw = 10 psi (0.7 Kg/cme). The viscosity range extends over 3 decades.

Similar plots can be obtained for other values of shear rate or shear stress. For example, when T~ = 10 psi (0.7 Kg/cm") a plot of EL versus ETJ gives a slope of 0.18, which means that an equation

L = k' (TJ.=lo) -"' (10) where n' = 0.18, can roughly describe the curve of Fig- ure 6.

The ratio between ETJ and EL is of course of the order of 5 in such conditions.

Activation energies of viscous flow vary with shear rate, as can be seen in Figure 3 and in Table 1 .

The energies of activation for viscosities at several shear rates (yl = 3, 10, 30, 100, 300, 1000, 1500 sec-') are plotted against logarithmic shear rates in Figure 11. It can be seen that they decrease, tending to approach the values of the activation energies of spiral molding EL, which are in the range of 3-6 Cal/mole.

The energies of activation for viscous flow, calculated at constant shear stress T ~ , are in the range 20-30 Cal/ mole when T~ = 10 psi (0.7 Kg/cm*) (Table 1). They do not vary with shear stress.

SPE TRANSACTIONS, OCTOBER, 1963 264

Figure 7. Spiral flow lengths L plotted vs vis- c o s i t i e s a t c o n s t a n t "high" shear rate = 1500 set-'. The viscosity ronge is reduced to 1 decade and a good corre- lotion i s obtained, inde- pendently of material and temperature.

Figure 8. Log-log plot of the data of Figure 7. A simple equation describes the relation between spiral length and constant shear rate viscosity.

SPE TRANSACTIONS, OCTOBER, 1963 265

Review of Literature Several papers deal with the well-known fact that data

on the fluidities of molten polymers, as measured with Melt Index apparatus (2) , do not correlate well with the true moldability of thermoplastic materials (3, 18, 19, 20,21,22).

Moldability was defined as a “measure of speed and ease with which a polymer can be fabricated to a certain given specification” ( 2 3 ) ,

Minimum molding cycle and minimum molding pres- sure or temperature (5) can be quantitative indices of moldability. They do not correlate well with M.I. data (24,25).

Spiral molding (6, 7, 8) is probably the best quan- titative index of moldability although it does not give a measure of molding speed.

Spiral molding can be, however, a reliable techno- logical method for testing laboratory measurements of moldability. It does not correlate well with M.I. data (9, 26).

Fluidity, as measured with M.I., cannot be taken as an index of spiral moldability for different polyolefines ( 2 7 ) , for samples of polyethylene having different den- sities (25), or manufactured by different companies (28) .

General purpose and rubber polystyrenes give different correlations between spiral lengths and M.I. (29) .

The extrusion pressure in M.I. is 44 psi (3.1 Kg/cm“) which is much lower than pressures used in injection molding. Several authors suggest that a higher pressure be applied in M.I. measurements, for example 440 psi (31 Kg/cm”) or 1400 psi (98 Kg/cm”) (25, 26, 30) .

A “constant shear stress” fluidity was suggested by other authors as a measure of moldability. The high

Figure 9. Data of f igure 7 plotted as spiral length L vs reciprocal melt vis- cosity.

shear stress, characteristic of injection molding, was chosen as rw = 10 psi (0.7 Kg/cm‘) (17, 19, 31, 32).

However, high pressure M.I. data do not seem sub- stantially better than the low pressure ones in predicting moldability (33) and there are not, at present, published experimental reports in which the “high shear stress” fluidities are demonstrated to be good indices of poly- mer moldability.

The flow of polymer melts in cooled channels is a typical “unsteady state” flow, which differs considerably from the isothermal “steady state” flow (34). Differences are due of course to heat transfer from the melt to the walls of the mold.

Both rheological and thermal properties of materials will influence their injection molding behavior.

If the effect of pressure on viscosity is neglected, the rheological properties can be defined by the relation:

(11) which is obtained with steady state rheological meas- urements. It is often expressed graphically due to the relatively large number of independent constants which are required for an accurate mathematical representa- tion of equation 11.

The most important thermal properties are glass tran- sition temperature T, and thermal diffusivity

7 = f (T , r ) = F(T,T)

a = k/pC (12)

where k is thermal conductivity, p specific gravity and C specific heat.

They influence the cooling rate of polymer melts in the mold, while rheological properties influence the fill- ing rate (35).

Figure 10. The energy of activation for spiral f low EL plotted vs the energy of activation for viscosity at y. = 1500 sec-’. The slope is 0.70 as required by equation 9.

266 SPE TRANSACTIONS, OCTOBER, 1963

In a given class of polymers (e.g. polystyrenes) the thermal properties are relatively constant, while the rheological properties may be widely different, due to their sensitivity to molecular weight, molecular weight distribution and branching.

During the molding cycle temperature and shear con- ditions of the melt change as a function of position and time, in the mold. For this reason it has been suggested by several authors that an average value of viscosity, calcula,ted over a range of shear rates and temperature, be taken as a measure of moldability. A difficult task is the integration of equation 11 which does not lend itself readily to a simple mathematical form.

A graphical integration was suggested by Schreiber (36). He used a parameter A defined by the relation

On plots such as those of Figure 1 the value of A is given by the area between shear stresses r1 and r2, and between shear rate y1 and the isothermal flow curve chosen for integration. Schreiber found that A was a sufficiently good index of power consumption in extru- sion when appropriate values of rl, r2 and yl were chosen.

The use of a complex parameter asTV, defined by

(where T,, is the viscosity measured at the standard con- ditions y. and T,) was introduced by Weir (10) in the study of injection molding. The physical meaning of aSTV is that of an average fluidity calculated in given ranges of shear rates and temperatures. However, un- less those ranges are very limited, the flow curves can- not usually be approximated, as required by the Weir method, by parallel straight lines, and inaccurate ap- proximations are introduced in calculating asTV.

The most careful study of unsteady flow in cooled channels was made by Toor et al. ( 3 7 ) . In their pro- cedure both rheological and thermal properties must be known in order to calculate flow distance as a function of the molding variables. Mathematical difficulties make this method quite impractical.

The choice of a simple “constant shear rate” fluidity as a measure of moldability was made by Skinner and Taylor ( 5 ) . They suggested a method for calculating the shear rate of the melt in the mold and found that spiral lengths could be well correlated, for a number of polystyrenes, with a “medium shear rate” viscosity (7. = 140 sec-l) due to the relatively large diameter of their spiral mold.

Similar results were obtained by Gouza and Freygang (9) on a few different polymers and in a limited range of spiral lengths and temperatures, using high shear rate viscosities (y. = 2000 sec-l) .

To sum up: several authors suggest the use of the data obtainable from capilIary rheometry for studying the injection molding of polymers. Some are of the opin- ion that a satisfactory index of moldability is a constant

SPE TRANSACTIONS, OCTOBER, 1963

shear stress fluidity; others prefer an average fluidity value, calculated over given ranges of temperature and shear; finally, still others use a constant shear rate fluidity.

One of the most surprising features of injection mold- ing is the low temperature coefficient of this process, as compared with the energy of activation for vis- cous flow in M.I. or similar apparatus ( 7 ) . In addition the temperature coefficients of the injection process of many different polymers are similar (25) . From the results of other workers the following values of EL have been calculated: for polyethylene and polypropylene 4-5 Cal/mole ( 7 , 8, 27, 28); for polymethylmethacrylate 8-9 Cal/mole (8, 9) ; for polyvinylchloride 5-7 Cal/mole (7) . For the spiral flow of styrene polymers, EL = 3-6 Cal/mole was found.

Whatever is the method chosen for using rheometric data in predicting the injection molding behavior of thermoplastic materials, it must not only give fluidity values which correlate well with the actual moldability of the investigated samples, but it must also give a satis- factory explanation of the low temperature coefficient of the injection process.

Interpretation of Results The flow curves obtained from capillary rheometric

measurements show that both the shear and temperature sensitivities of the viscosities are markedly different for different materials ( see Figures 2 and 3 ) .

The spiral molding results, when compared with M.I. data, show that even when Melt Indices are ob- tained at the molding temperature they cannot be a reliable measure of moldability (see Figure 4 ) . In addition the results show that also the constant shear stress viscosities ( T ~ = 10 psi) do not correlate well with spiral molding (Figure 6) . It has been noted that no “constant shear stress” viscosity is a good mold- ability index.

When viscosities are calculated at constant and low shear rate, the correlation with s iral lengths is also

cosities are chosen, an almost perfect correlation is ob- tained (Figure 7) which is valid for all materials and temperatures.

No attempt was made to calculate from capillary data average viscosity values. If they were obtained with Weir’s method (10) rough approximations ought to be necessarily introduced, due to the fact that the flow curves deviate markedly from the parallel straight lines model required by Weir.

In any event the results show that the calculations of average fluidity (10, 37) and the above mentioned rigorous mathematical treatment (38) may be unneces- sary for many practical purposes.

It seems, in fact, that within a given material class, the only important parameter in the injection process is the viscosity calculated at the shear rate and tempera- ture to which the melt is subjected at the entrance of the mold. The choice of shear rate at which the viscosity is calculated is of course a question of great importance. From the work of Ballman et al. (34 ) , in which the ve- locities of fluids in the mold were measured, it was calculated that the shear rates at the entrance of the molds were between 400 and 2,000 sec-’. These rela-

unsatisfactory (Figure 5 ) but w K en high shear vis-

267

tively high values seem to be characteristic of the in- jection process in several molds. A good index of mold- ability is obtained when viscosities are measured at ,the appropriate high shear rate.

The results seem to confirm that the method used by Skinner and Taylor in calculating it is substantially cor- rect (5). In fact in the mold used here, the injection time being approximately 1-2 sec, the value of y., cal- culated from the hydraulic mean diameter, was of the order of 1000-2000 sec-l, which compares well with the shear rate chosen in Figure 7. It is interesting to notice that a value of zero for spiral lengths is obtained when the fluidity approaches zero ( Figure 9) . This does not happen in Weir’s work (10).

The reliability of the correlation of Figure 7 is sup- ported by the results on energies of activation plotted in Figures 10 and 11 and in Table 1.

Spiral flow of styrene polymers has energy for activa- tion EL = 4.5 -t- 1.5 Cal/mole (Figure 10) while for M.I. data it is of the order of 20 f 5 Cal/mole. En- ergies of activation of the same order of magnitude are found also for high pressure M.I. (22, 26, 30) or “con- stant shear stress” viscosities (17, 19, 31, 32) as can be seen in Table 1 . Viscosities at constant shear rate also give similar results if the shear rate is not properly chosen. Only when viscosities are calculated at a suf- ficiently high shear rate does the energy of activation decrease, tending to approach the value of EL (Figure 1 1 ) .

These results can be easily understood. For pseudo- plastic fluids the energy of activation for viscosities at

Figure 11. Plot of the energies of activation for viscosity a t constant shear rate Ey vs logarithmic shear rate. A decrease in Ey i s evident a t increasing shear rates, slowly approaching the values of spiral flow activation energy EL.

constant shear stress E, is always greater than for vis- cosities at constant shear rate E, (38). While E, is usually constant (39), with increasing shear stress, E, decreases when y increases. If the power law (equation 5) can be applied, the relation between E, and E, is given by (38) :

E,/E, = n (15)

where n is the flow index. At high shear rate n is gen- erally close to 0.30 f 0.10 for many polymers so that at such shears E, is 3-5 times E,. A survey of the litera- ture can show that with increasing shear rate the values of E, decrease for all materials, approaching the corre- sponding values of EL, while E, is several times greater than EL.

When the shear rate is of the order of 1000 sec-l the values of E, are: 3-6 Cal/mole for polyethylene (39, 40); 8-9 Cal/mole for polypropylene (15); 10-12 Cal/ mole for polymethylmethacrylate (4) ; 6-8 Cal/mole polyvinylchloride (4) and 4-9 Cal/moIe for styrene poly- mers (Figure 11 ) .

The corresponding values of E, are: 15-20 Cal/mole for polyethylene (40) ; 15-20 Cal/mole for polypropylene ( 10) ; 20-25 Cal/mole for polymethylmethacrylate (4) and for polyvinylchloride; 20-25 Cal/mole for styrene polymers (41). Remembering the above mentioned values of EL, it can be said that when viscosities meas- ured at constant pressure or shear stress are chosen as indices of moldability it will be always found that their temperature coefficients are 3-5 times greater than for the injection process.

Such a difference suggests that shear stress is not the essential parameter in injection molding.

The low temperature coefficient of the injection proc- ess (7) can be explained if it is supposed that the shear rate of molten polymers in the mold is the most im- portant parameter of the process.

Moldability-in Terms of Rheological Concepts These results, together with those of Figure 7, seem

to suggest that the unsteady flow in cooled channels depends primarily on the steady-state, constant-shear- rate viscosity that the polymer melts have in the first part of the mold, where the melt temperature is still very close to the cylinder temperature.

For a given polymer class the results can be sum- marized by the equation

L = k‘ ( qy) -”’ (16) where k‘ and n’ depend on the mold shape and thick- ness, the press type, the injection cycle and pressure, and the shear rate chosen for correlation, but do not depend on the polymer properties and the cylinder tem- perature. The exponent n‘ must be close to 1 for a good correlation.

It was shown by Ballman et aI. that the flow in in- jection molding can be described in terms of the steady- state rheological properties of the melts (42). They also demonstrate that very simple equations describe the mold filling rate:

V = V, . edtIB

L = V,B (17)

(18)

268 SPE TRANSACTIONS, OCTOBER, 1963

where V and V, are the mean flow speeds at time t and t = 0, L the final length of flow or “fill-out”, and B is an experimental constant. V, and B vary with the press and mold parameters and with the rheological and thermal properties of the polymers (42).

These equations were obtained under molding condi- tions such that the pressure had reached its maximum value before the melt entered the mold and was con- stant during the flow process (die-controlled flow).

If the injection pressure changes as polymers flow in the mold, the process is “machine-controlled”. It is imagined that the polymer flows at a relatively constant mean speed during the first stage of filling (23), that is, at a constant shear rate at the mold entrance. If the characteristics of this first stage are the controlling factors for the overall flow in the mold, the main feature of our results (i.e., a constant shear rate viscosity as flow- controlling parameter) could well be explained.

For a “die-controlled process the flow-controlling parameter should be a constant shear stress viscosity, and the energy of activation for flow should be of the order of 20 Cal/mole for styrene polymers.

The energy of activation for some “die-controlled’’ data of Ballmari et al. has been calculated (42) . From their papers, runs No. 4 to 7 yield EL = 6 Cal/mole for a sample of polystyrene. From the same data, the energy of activation for viscosity at constant shear rate (-yA = 1500 sec-’) is 6 Cal/mole, while for viscosity at constant shear stress ( T ~ = 10 psi) the energy of activation is 16 Cal/mole.

It seems that the “die-controlled flow is not substan- tially different from other types of injection processes. The relationships (17) and (18) obtained by Ballman et al. (42) may have general validity and can possibly be applied to this data.

From equation 18, it can be seen that the fill-out L depends only on the initial melt velocity V, and on the constant B. This latter is claimed to depend “at least on the rheological and thermal properties of the polymer” on the die and inlet polynier temperatures and on the press and mold parameters (34) . However these results suggest that B depends only on the operating variables and is independent of the rheological properties of the polymer and the inlet temperature. In this case the fill- out (or spiral length) L is a function only of the initial velocity of the polymer V,, which in turn depends only on the constant shear rate viscosity of the polymer at the entrance of the mold.

Some data o€ Ballman et al. (42) show that when the press and mold variables are fixed and only the cylinder temperature changes, a roughly constant value of B is obtained. Note, for example, Ballman’s runs No. 4, 5, 6, 7 (B = 0.3) and runs No. 14, 15, 26, 27, 29, 42, 43, 44 ( B = 0.52 2 0.09). If I) is independent of the inlet temperature and of the rheological properties of the polymer, the results reported in this article, as expressed by equation 6 and Figure 7, would be simply derived from Ballman’s equations 17 and 18. In fact the mean inlet velocity V, depends only on the inlet melt viscosity. Equation 6 can be directly derived from Ballman’s equa- tion 18 if the exponent in equation 6 is l, and it is be- lieved that a proper choice of the shear rate used for the correlation can probably bring it very close to 1. A

linear relation is then found between L and melt fluidity at the mold entrance.

A number of conclusions can be drawn from these results (which probably can be applied only to molds havinp a constant transverse section) :

0

Viscosity, as measured in laboratory-scale tests, can be an index of polymer moldability only if it is obtained at an appropriate temperature and shear rate and not at constant shear stress. The choice of the correct shear rate depends on the press and mold and on the operating variables. The most important parameters in injection molding are probably the rheological properties of the polymer and the ram speed of the press, which both influence the initial velocity of the molten polymer in the mold.

Literature References 1. ASTM D569-48 Standard Method of Test, ASTM Standard on

2. ASTM ’D1238-57T Tentative Method of Test, ASTM Standard

3. Stanb, R. B., Technical Papers, Vol. VIP 1961 ANTEC. 4. Bernardt, E. C., “Processing of Thermoplaitic MLterials”, Reinhold

5. Skinner, S.”J., Taylor, W., Trans. Plastics Inst. (London) , 28, No.

6 . Camubell. G.. Griffiths. L.. “Plastics Prot?ress”. Iliffe & Sons Ltd.,

Plastics p. 452 (1957).

on Plastics, p. 398 ( 1958).

Publ. Corp New York, 1959.

78 (1960). , , I _

London 1955. 7. Griffiths: L Modern Plastics 34 111 (Aug. 1957). 8. Ronzoni 1:: Materie Plastiche, b, 193 (March 1959). 9. G?u~?,-i. I., Freygang, G. G. , Technical Papers, VoZ. VIP, 1961,

10. 11. 12. 13. 14.

15. 16. 17.

ANILC;. Weir, F. E., Technical Papers Vol. V l W 1962 ANTEC. Merz, E. H., Colwell, R. E., ASTM Bull& N o . b32 (1958) . Pezzin, G., Materie Plastiche, p. 1042 (Aug. 1962). Rabinowitsch, B., 2. physik. Chem., A 145 1 (1929) . Wagner, H. L., Wissbum, K. F., Technicai Papers, Vol. VIIIo, 1962, ANTEC. Ryder, L. B., Technical Papers, Vol. VIP, 1961, ANTEC. Ballman R. L Pezzin G. unpublished results. M:E~-L. W.:’Mighton, f. W., Technical Papers, Vol. VIIIO, 1962, AN’I‘KC.

18. Wolheim J. B Technical Papers Vol. Vo 1959, ANTEC. 19. Folt, V.’L., Eytinger, R. J., Tecinical Paiers, Vol. VIZO, 1961,

20. Basset, H. D., Burns, N. M., Christensen, R. E., Technical Papers,

21. Folt, V . ’L., TLchnicaZ Papers, Vo2. VIIIO, 1962, ANTEC. 22. Wechsler, R. L., Baylis, T. H., Technical Papers, Vol. Vu, 1959,

ANTEC.

Vol. VIP 1961 ANTEC.

ANTUP _^_._I_.

23. Bever. C. E.. Spencer. R. S.. “Rheolow”, Edited by F. R. Eirich, _. Academic Press,-New York, 1960.

24. Staub, R. B., Technical Papers, Vol. VP , 1960, ANTEC. 25. Staub, R. B., Technical Papers, Vol. VIIIO, 1962, ANTEC. 26.. Slartinovich, R. J., Boeke, P. J., McCord, R. A., Technical Papers,

Vol. V P , 1960, ANTEC. 27 Heumann W E Technical Papers, Vol. VZO, 1960 ANTEC. 28: Metzger, ’A. P., ‘?Technical Papers, Vol. VP, 1960: ANTEC. 29. Orthmann, A. I., Kunststofle 52, 587 (1962) . 30. Clegg, P. L., Trans. Plastics Inst. (London) , p. 151 (April 1958). 31. Karam, H. J., Cleereman, K. J., Williams, J. L., Modern Plastics

32. McCormick H. W., Brower, F. M., Kin, L., 1. Polymer Sci. 39, 32, 129 (March 1955).

87 (l959).’ - . ~ 33. Van der We@ A. K., Wilson, W. R. K., “SympoPium on Tech-

niques of PoZyAer Sciences”, (London), September 27-28 ( 1962). 34. Ballman, R. L., Shusman, T., Toor, H. L., I d . Eng. Chem. 51,

847 I19.59). 35. Beye;,-C.-E., Spencer, R. S., “Rheology”, Edited by F. R. Eirich,

Academic Press, New York, Vol. 1110, p. 549 (1960) . 36. Schreiber, H. P., Technical Papers, Vol. VIP, 1961 ANTEC. 37. Toor, H. L., Ballman, R. L., Cooper, L., “Internatidnal Congress

1960 on the Technology of Plastics Processing”, Amstcrdani, October igfin.

35. Beye;,-C.-E., Spencer, R. S., “Rheology”, Edited by F. R. Eirich,

36. Schreiber. H. P.. Technical Papers, Vol. VIP, 1961. ANTEC. Academic Press, New York, Vol. 1110, p. 549 (1960) .

37. Toor, H.’L., Ballman, R. L., Cooper, L., “International Congress 1960 on the Technology of Plastics Processing”, Amstcrdani, October igfin.

38. McKelvey, J. M., “Polymer Processing”, J. Wiley & Sons, Inc., London, 1962.

39. Schott, H., Kaghan, W. S., 1. Applied Polymer Sci. 5, 175 (1961) . 40. Philippoff, W., Gaskins, F. H., I . Polymer Sci. 21, 205 (1956) . 41. Rudd, J. F., 1. Polymer Sci. 44 , 459 (1960) . 42. Ballman R. L., Shusman, T., Toor, H. L., Modern Plastics 37,

No. 1, Ib5 (1959); No. 2, 115 (1959). THE END

Acknowledgment The author wishes to express his appreciation to Dr. G. Biglione

for obtaining the spiral flow data, and to the Sicedison S.p.A., Milan, Italy, for permission to publish this work.

Adapted from a paper presented at the XIV Congress0 Intemazionale delle Materie Plastiche Torino (Italy), September 1962.

SPE TRANSACTIONS, OCTOBER, 1963 269