Measurements of cycle time in injection molding of filled thermoplastics

Measurements of Cycle Time in Injection Molding of Filled Thermoplastics

ANTAL BOLDIZAR and JOSEF KUBAT

Chalmers University of Technology Department of Polymeric Materials

S -412 96 Gothenburg, Sweden

This study presents the results of measurements of the sealing and cooling periods of the injection molding cycle of filled thermoplastics, both periods constituting a major part of the cycle. The compounds used were based on HDPE, PP, and PS. The fillers were calcium carbonate, carbon black, and magnesium oxide. The latter two materials were chosen for their high thermal conductivity. The sealing time was determined by a gravimetric method, while the measurement of the cooling time was based on the assessment of the recovery of the ejector marks for samples ejected after varying times of cooling. Increasing filler content produced significant and reproducible reduc- tions of the cycle time. Such effects were especially pronounced with the high thermal conductivity fillers. The cooling process was also treated theoretically, starting from the heat conduction equation and producing a fully satisfactory description of the experimental data. Further- more, the value of the thermal diffusivity, exemplified by the HDPE/MgO compounds, was in good agreement with the values obtained from current composite expressions.

INTRODUCTION

he cycle time is one of the major factors to T determine the efficiency of the injection molding process. In view of the economic potential inherent in faster molding cycles, substan- tial effort has been centered around optimizing the movement of the various parts of the machine. Electronic control of the movement has been one of the main targets of developmental activities in this area. In contrast to this, little interest has been devoted to material-dependent parameters influencing the length of the molding cycle.

Primarily, the length of the molding cycle is determined by the low thermal conductivity of plastic materials. An obvious way to reduce the cycle time is to increase the conductivity by using mineral fillers. Such materials normally conduct heat better than the plastic matrix, thus offering a relatively simple route to increased productivity. Although filling cannot be used as a general method, its potential is significant and far from fully utilized, mainly due to insufficient information about the effects of filling on the cooling process in the mold. It is the purpose of this paper to provide such data

for polypropylene, polystyrene, and high density polyethylene, filled with magnesium oxide, carbon black, and calcium carbonate. The sealing time, t,, and the cooling time, t,, the latter counted from the instant that the sealing is completed to the ejection of the part, have been the focus of attention in this study as the material-dependent periods of the total cycle time. The machine-dependent periods, including the closing and opening of the mold, and the injection, were kept constant in order to ensure com- parability.

Magnesium oxide and carbon black were chosen in view of their outstanding thermal conductivity. At 30 percent weight filling level, a reduction of the combined sealing and cooling period by about 50 percent was achieved with these fillers. With calcium carbonate, the reduction was somewhat less. Normally, the t, + t, period amounted to around 80 percent of the total cycle.

For the determination of t,, a conventional method based on the weight variation of the molding (DIN 53 455 tensile test bars) was used. When determining the cooling time, a method was developed based on the recovery of the indentations produced in the part by the ejector

POLYMER ENGINEERING AND SCIENCE, MIDJULV, 1986, Vol. 26, No. 12 877

A. Boldizar and J. Kubat

pins. Before presenting the results, we reproduce in Table I data relating to the pertinent thermal parameters of the materials used. The thermal diffusivity a is connected with the conductivity X through the relation

where p and c denote the density and thermal capacity (specific heat). Basically, the time variation of the temperature during a cooling process is determined by a. Compared to common plastic materials, fillers have a higher density, while their c-values are lower. On the whole, differences in p and c are of minor importance, a being determined primarily by A. The data of Table 1 are to be considered as approximate figures only, relating to room temperature (1).

EXPERIMENTAL Materials

ff = X/(PC)

The polymers used were as follows. Polypropylene, Hostalen PPN 1060 (Hoechst),

density 0.905 g/cm3, MFI 9 g/lO min (230/5]: Polystyrene, Hostyren N 500 1 (Hoechst), density 1.05 g/cm3, MFI 3.5 g / l O min (200/5); High density polyethylene, DMDS 221 5 (Unifos Kemi), density 0.953 g/cm3, MFI 0.1 (190/2); DMDS 7007 (Unifos Kemi), density 0.965 g/cm3, MFI 7 (1 90/2).

The fillers had the following characteristics. Magnesium oxide, Ultra Light, density 3.2 g/ cm3, 200 mesh (Malmsten & Bergwall, Gothen- burg]: Magnesium oxide, “Heavy” powder, <10 pm (laboratory reagent, Kebo, Gothenburg); Carbon black, Flammenruss 101 (Degussa), density 2.2 g/cm3, c. 0.1 pm; Calcium carbonate, Snowcal 8/SW (Malmokrita AB, Malmo), density 2.7 g/cm3, <20 pm; Calcium carbonate, GG-Kalcit 100 (Nordiska Mineralprodukter AB, Orebro), density 2.6 g/cm3, <125 pm.

The “Heavy” grade of MgO was used in the PP/MgO compounds, while all the others were based on MgO “Light”. No difference between the two grades was noted with regard to the molding and thermal characteristics of the compounds.

The DMDS 7007 grade of HDPE was used only in the experiments discussed under the heading “Surface temperature measurements”.

Machinery -Compounding The various polymer/filler combinations were

compounded in a Buss Kneader, PR-46, at a temperature of 200°C (screw diameter 46 mm, L/D 11, exit die 6 mm). The residence time in the compounding extruder was about 3 min. The compounded material was passed through a granulator, Rapid GK 20, whereafter it was subject to a further homogenizing step in a drum mixer.

For injection molding, a conventional machine, Arburg Allrounder, 221E/170R, with a locking force of 250 kN was used, producing tensile test bars according to DIN 53 455.

Table 1. Physical Characteristics of the Materials Used, RT (1). p-density, A-thermal conductivity, a-thermal diffusivity.

P A a [g/cm31 rw/mocl rcm2/s1

Magnesium oxide 3.2 3 0.9 Graphite, carbon 2.2 160 1 .o Calcium carbonate 2.7 0.7-0.9 0.003-0.004 PP 0.9 0.23 0.0013 PS 1 .o 0.16 0.0012 PE 0.96 0.42 0.002

Before compounding, the fillers were dried at 105°C for 30 h. During this procedure, MgO lost about 1.2 percent in weight. The compounded material was also subjected to renewed drying at 105°C for 24 h prior to injection molding.

Processing conditions

tion molding step were as follows: The processing conditions during the injec-

PE PP PS melt temperature, “C 200 230 270 mold temperature, “C 40 40 70 injection pressure, MPa 150 100 60 holding pressure, MPa 130 100 45 These data apply to the Arburg machine. In

the experiments presented under the heading “Surface temperature measurements”, the moldings were produced on a Klockner Ferro- matic machine, type F 150, with a locking force of 800 kN. The injection and holding pressure was 54 MPa, the melt temperature 18O”C, and the mold temperature 40°C.

Cycle Time Measdement By definition, cycle time is the time elapsing

between two identical points in two subsequent cycles of the injection molding process. The cycle consists of a number of sequential opera- tions, their length being determined both by the parameters of the machine and the physical characteristics of the material. In the present investigation, two of the main components of the cycle time; namely, the sealing time, t,, and the cooling time, t,, were determined, Fig. 1 .

Sealing Time The sealing time, t,, is the period of time

which elapses between the moment that the filling of the mold is completed, and the moment that the sealing of the gate by the solidifying melt occurs. The sealing point was found by, changing the length of the pressure holding period between 2 and 20 s and determining thc weight of the sample. These measurements were based on the back-flow of the unsolidified material out of the mold until the gate became closed. Decreasing the holding pressure period enhanced the back-flow tendency of the melt, thus reducing the weight of the sample (2). The graphical representation of the sample weight us. holding pressure period consisted approxi-

___._

878 POLYMER ENGINEERING AND SCIENCE, MIDJULY, 1986, Vol. 26, No. 12


PP

b.

mately of two straight lines as exemplified in Fig. 2. The t,-value was identified as the time needed to attain constancy of the sample weight.

The examples given in Fig. 2 may be considered as typical of the results obtained in the present study. The holding pressure period was changed in steps of 1 s, while the injection time was kept constant at 0.7 s in all experiments. Before determining the weight of the samples, the gating was removed in a standardized manner. The maximum error in the &-value was 21 s.

Cooling Time

A method for determining the cooling time, t,, had to be developed since available literature does not seem to report on such measurements. rhe method was based on the tendency of in- sufficiently cooled samples to recover their di- mensions after an indentation had been made by the ejector pins. In a sense, the pins were used as a kind of hardness tester, where the recovery of the indentation was followed as a function of the cooling time. The shorter the cooling time, the softer was the molding, and bhe larger its recovery after being taken out from the mold.

It was found that only the ejector mark at the far end of the sample produced useful results. Using the mark opposite the gate gave results with an appreciably higher scatter. A further reduction of the scatter was obtained by replac- ing the thickness by the thickness/weight ratio.

tm t , t s t c t m

Fig. I . Schematic representation of the injection molding cycle. t , = machine movement time, t , = injection time, t , = sealing time, t, = cooling time.

....... 0, .

. I . 0 5 10 15 20

Pressure holding t i m e , s

Fig. 2. Examples of the variation of the sample wetght with the length of the holding pressure period. Sealing times, t,. marked by arrows. Every point is the average of 5 measurements. PP/MgO compounds. a = 0 percent, b = 31 percent, c = 6.6 percent, d = 10.9 percent MgO (by volume).

Typical examples of the variation of this ratio with the cooling time are given in Fig. 3. As can be seen, the weight-reduced thickness de- creases with increase in the length of the cooling period until it levels out at a constant value. The attainment of constancy is identified as the &value. Again in this case, the cooling period was varied in steps of 1 s. One second after the sealing point was used as the starting point of the cooling period. This point was determined in each case prior to the commencement of the t, measurements. The maximum error was k1 s.

Measuring the distance between the ejector marks, i.e. the length of the samples, did not produce any useful data: this length increased in a continuous fashion, without a breaking point which could be used as a measure of t,.

In evaluating the t,-results, regression lines were used. Every point in the diagrams shown in Figs . 2 and 3 was based on five single mea- suremen ts.

RESULTS The results presented in this section relate

primarily to the values of the sealing time, t,, and the cooling time, t,, as determined according to the procedures described above. The values obtained are given as percentages of the corresponding figures measured with the unfilled material.

Figure 4 shows the variation of t, with the filler content by volume, for PP and PS containing magnesium oxide (MgO), carbon black (CB), and calcium carbonate (CaC03). With PP, addi- tional experiments with another grade of MgO and CaC03 were carried out. As can be seen, the relative reduction in the t,-value due to filling is significantly larger for PP than it is for PS.

Considering the results obtained with PP, one finds that the points for CB and the two grades of MgO nearly coincide. The two CaC03 grades, also close to each other, appear to be less effi-

-G S

Ic

* . - . T ' i *....*..

t

3.470

? E E

E -. c

3.465

1 0 10 20 30

Cooling t i m e , s

Fig. 3. Example of the method used for the determination of the cooling time. t,, from the variation of the thickness/ weight ratio with the length of the cooling period. The thickness is measured a t the ejection mark at the f a r end from the gate. The t , values are marked by arrows. Every point is the average of 5 measurements. Curve a = PP, curve b = PP16.6 percent MgO [by vol.).

POLYMER ENGINEERING AND SCIENCE, MID-JULY, 1986, YO/. 26, NO. 12 879

A. Boldizar and J. Kubcit

too I 1

“1 40

A 6 0 1 I

I I I 0 5 10 15

Fi l ler content, % (by vol.)

Fig, 4 . Dependence of the sealing time. t., onfilling level [volume basis) relative to the t,-value of the unfilled material. 0 = MgO Light, 0 = MgO Heavy. = carbon black, V = calcium carbonate, V = calcite.

cient in reducing the t,-level. Such a difference, although less pronounced, is also noted for PS containing fillers with higher (CB, MgO) and lower (CaC03) thermal conductivity.

The difference between the fillers, and also between PP and PS appears to be largely elimi- nated when considering the effect of filling on the value of t,, the cooling time, given as per- centage of the corresponding t,-figure for the unfilled material in Fig. 5. There is, neverthe- less, a tendency for the more efficient fillers (CB, MgO) to produce a larger reduction in the relative value of t, for PP. On the whole, the reduction in t, is somewhat less than that ob- served with t,.

Figure 6 summarizes the results of the t, and &-data given in Figs . 4 to 5, showing the dependence of the sum t, + t,. again relative to the unfilled material, on the degree of filling. In this case, the points for the various fillers form two distinct lines, the reduction in the t, + tc-value reflecting the thermal conductivity. This is true of both the polymers used.

For example, at the highest filling levels, 30 percent by weight (about 1 1 percent by volume, MgO Ultra Light), the reduction in the combined sealing and cooling time amounts to approximately 50 percent.

The scatter of the data given in Figs . 4 to 6 is about +5 percent (abs.) of the corresponding percentages.

As a supplement to the above results, a series of experiments with HDPE as the matrix material was carried out. The results are not reproduced here since they were very similar to those reported above for PP. The fillers were MgO and CB.

Figure 7 shows the variation of the ratio t,/ ( t , + t,). While the points measured with PP containing the various fillers arrange them- selves rather well along a common line, thus showing a certain dependence on the level of filling, the PS results show no such dependence.

1

0 5 10 15 1 I I

Fi l ler content ,% (by vol.)

Fig. 5. Dependence of the cooling time, t,. on filling level by volume relative to the tc-value of the unfilled material. Symbols as in Fig. 4.

0 5 10 15 Fi l ler content , %(by vol.)

Fig. 6. Reduction in t , + t,, relatiue to the value of the unfilled material, as a function of the filling degree. Sym- bols as in Fig. 4 .

0 5 10 15 Filler content . % (by vol.)

Fig. 7. Variation of the ratio t,/(t. + t,) with the degree of filling. Symbols as in Fig . 4.

It may be noted that in this case, in contrast to the results shown in Figs. 4 to 6, the ratio t,/ ( t , + t,) it is not related to the corresponding value for the unfilled material; it only gives the sealing time as a fraction of the combined sealing and cooling periods. The results obtained with PS show that ts and t, have approximately the same value. Although both these values decrease with filling, they remain nearly equal. For PP, the t,-period constitutes a somewhat smaller fraction of t, + t,.

880 POLYMER ENGINEERING AND SCIENCE, MIDJULY, 1986, Vol. 26, No. 12


Surface Temperature Measurements The method for the determination of the cool-

ing time, t,, described above is but one of the procedures which could have been chosen for that purpose. A major advantage of the present method is its close relation to normal injection molding practice where the cooling time is often assessed in terms of the size of ejection pin marks that can be tolerated. A physically more appealing method would be the measurement of, for instance, the surface temperature as function of the cooling time. To supplement the above data, we carried out a series of such experiments with HDPE filled with MgO. In these experiments, we used the DMDS 7007 HDPE grade. The moldings were produced on a Klockner Ferromatic machine (test bars according to IS0 3167).

The surface temperature was measured at the gate end of the test bars 30 s after ejection using a contact thermometer. The heat lost during the transfer to the contact device was compensated by adding 9°C to the temperature readings. This value was found by calibration. The design of the measurements was somewhat different from those discussed above, in that the sealing time was not determined separately for each HDPE/MgO combination. Instead, the pressure holding time was set at 10 s, while the subsequent cooling period was varied between 10 and 50 s in steps of 5 s.

The results are presented in Fig. 8 showing the surface temperature 30 s after ejection as function of t ' = tph + t:, where tph denotes the constant pressure holding time and tl. the cooling time measured from the end of the pressure holding period. On the whole, these results support the findings presented above; that is to say, increasing the MgO content markedly reduces the time needed to attain a given surface temperature of the molded part. A further illustration of this is given in Fig. 9, showing the

I I 1 HOPE

b a

A 0 20 40 60 80

Fig. 8. Surface temperature of injection molded test bars 30 s after ejection asfunction of the total cooling time t' = tph + t:. Pressure holding period tph kept constant a t 10 s. the subsequent cooling period t f varied. HDPE with 0 to 40 percent MgO Light, b y weight. Machine 11. HDPEI MgO Light compound. a = 0 percent, b = 3.2 percent, c = 7.0 percent, d = 11.4 percent, e = 16.7 percent (by uot.).

I I I

tph + t'c I s

reduction in t' to reach a surface temperature of 50°C for HDPE compounds with varying content of MgO. I t must be pointed out, however, that the results reproduced in Figs. 8 to 9 are not directly comparable with those shown above. Not only was the t, interval not measured in this case, but also the injection machine used and the HDPE-grade were different. On the other hand, the general trend towards markedly reduced cycle times when using fillers with a relatively high thermal conductivity is a valid and significant result also in this case.

Thermal Properties

Due to the particular thermal characteristics of the component of the systems discussed here, the energy needed to melt or heat a certain quantity of a filled material can be expected to be lower than for the matrix. Figure 10 il- lustrates this effect for the HDPE/MgO compound. I t shows the melting enthalpy, A H , and the enthalpy difference A H ' between 50 and 160°C both measured with a DSC-device (Mettler TA 3000). On the other hand, the quantities A H and AH' taken per unit volume remain approximately independent of the filler content.

I I I I 1

I 3 0 t = = .. *\

-: c 201

OO I 5 10 15 20

F i l l e r content , % (by vol.)

Fig. 9. Reduction in total cooling time t' [for definition, see Fig. 8) to reach a surface temperature of 50°C for HDPE filled with MgO Light, Machine 11. TB = 180°C.

I I I I I 1

H D P E 4

1 I I I 0 5 10 15 20

Fi l ler content , % (by v o l )

Fig. 10. Melting enthalpy, A H . and the enthalpy drffer- ence AH' between 160 and 50°C for HDPEIMgO Light, DTA-measurements. scan speed I O"C/min.

88 1 POLYMER ENGINEERING AND SCIENCE, MID-JULY, 1986, Vol. 26, NO. 12

A. Boldizar and J . Kuba t

Mechanical Properties The mechanical properties of the test bars are

not included in this paper since the fillers were not surface treated. On the whole, the results obtained followed a pattern to be expected for systems containing untreated fillers.

Sealing Time-Comparison with Calculated Values

As a supplement to the experimental data presented above, the value of t, for the HDPE/ MgO compounds was calculated using two different methods, the first starting from a simplified solution of the heat conduction equation, the second from current concepts about the properties of composite materials. In both cases, the main step in the calculations was the determination of the value of thermal diffusivity a for the various compounds.

I t may be noted that the values of a and h are averages assumed to be independent of temperature within the interval discussed here.

For the calculations involving the cooling rate, the following formula for the sealing time t, was used (2, 3).

where t, denotes the time needed to attain a peak temperature Tps at the sealing point in the sample molded from a melt with a temperature TB (barrel) in a mold kept at TM. H is the thickness of the sample and a the average thermal diffusivity within the temperature interval under consideration. When the peak value Tps is replaced by the average temperature across the sample, the factor 4/r , in the parentheses of E q 1, is replaced by 8/r2.

Out of the variables in E q 1 , a is normally not known for composites of the present type. The peak temperature Tp in the sample at time t after the completion of the injection cannot be determined without recourse to advanced measuring techniques. The same applies to the average temperature. The procedure used in the present case to obtain Tps was to eliminate a from E q 1 by inserting different values of TB and the corresponding experimentally determined values of the sealing time t,. This leads to the following expression.

T - T, = - ( T ~ - ~ ~ ) t l - t P . ( ~ ~ - T~)G (2)

where, for simple indexing, TI and Tz denote the barrel (melt) temperatures TB1 and TBZ, and t l and t2 the corresponding (experimental) sealing times tSl and tSz. Using these values, E q 2 gives the peak temperature Tps at t,, under the simplifying assumption that Tps may be considered constant within the range of the two TB temperatures on which E q 2 is based.

Figure 1 1 shows the variation of t, with TB

t l t2 4 r PS

for three T,-values, 200, 220, and 240°C as determined experimentally according to the gravimetric method for the system HDPE/MgO. Considering the variation of t, relative to the value for the unfilled polymer, it is found that the reduction of t, due to filling is largely independent of TB within the range 200 to 240°C. These results relate to T , = 40°C. Three pairs of TB-values, namely 200 to 220, 200 to 240, and 220 to 240°C together with the corresponding values of t, were then inserted in E q 2 in order to calculate Tps. The result, Fig. 12, shows that the peak temperature at the sealing point varies relatively little with either the melt temperature or the degree of filling. This is to be expected as the sealing point implies the attainment of a certain degree of solidification of the molten material. There is a slight tendency for Tps to increase with the MgO-content. The differences due to TB are not commented upon, due to the approximate nature of the procedure used.

Having determined the approximation value of Tps we now proceed to calculate the value of a of the HDPE/MgO-compounds. In order to sim- plify the calculations, we used Tps = 162°C which is an approximation obtained by aver- aging the data of Fig. 12. Inserting this value together with TM = 40°C in Eq 1 produces the

1 I I I 0 5 10 15

F i l le r content , %(by vol.) Fig. 1 1 . Variation of the sealing time with MgO-content a t dqferent melt temperaturefor HDPEIMgO Light. 0 - T B = 240"C, 0 - T B = 220°C. V - TB = 200°C.

140 1 4 ~

0 5 10 15 F i l l e r c o n t e n t , % (by vol.)

Fig. 12. Maximum temperature in the sample at sealing point, Tps. at dijJerent melt temperatures, TB. HDPEIMgO Light compounds. Symbols as in Fig. 1 1 .

882 POLYMER ENGINEERING AND SCIENCE, MID-JULY, 1986, Yo/. 26, NO. 12


result shown in Fig. 13, illustrating the effect of the MgO-content on the a-value of the filled material. I t may be noted that this value relates to the sealing temperature. As evident from Fig. 13, the melt temperature TB does not influence the results: this is due to the fact that an average of Tps has been used, cf. Fig. 12. Were the T,,-values as shown in Fig. 12 used instead, a would vary with TB. producing a variation of about k 10 percent around the line reproduced in Fig. 13.

The above method of obtaining a starts from a solution of the heat conduction equation for the case of the cooling of a relatively thin plate as expressed by E q 1, the calculation being based on time and temperature data relating to the cooling process. An independent method of calculating CY for filled systems is provided by common composite theories, combining in an appropriate way the a-values of the components. The starting point of the present approach is the following equation proposed by Lewis and Nielsen (4).

a = ai(1 + AB42)/(1 - B$dJ2), (3) where a and a1 denote the thermal diffusivity of the composite and the matrix material, re- spectively, 42 the volume fraction of the filler, and A a form factor given by A = (kE/&) - 1, with kE denoting the Einstein coefficient. The filler particles are assumed spherical.

The quantities B and $ are defined as follows

(4)

(5)

with a2 denoting the thermal diffusivity of the filler, and +,,, the maximum packing fraction of the dispersed particles.

Equat ion 3 is commonly used for calculating the modulus of composite systems. I t may, how-

HDPE

I I I 1

0 5 10 15 Fi l ler content , % (by vol.)

Fig. 13. Thermal dgfusiuity, a, of MgO Light, filled HDPE calculated from experimental T, t-data according to E q 1 for TB 200" (V), 220" (01, and 240°C (a). Assuming constant Tps at the sealing point (=162"C). Solid line = theoretical values calculated according to Lewis-Nielsen, Eq 3 from the a-values of the constituents.

ever, also be applied to the thermal or electrical parameters of such systems (5). The constant A is related to the shape and orientation of the dispersed particles, while B takes account of the relative thermal diffusivity of the two components. I) is given by the maximum packing degree of the particles, defined as their true volume divided by the volume they would oc- cupy if packed as densely as possible.

The following set of data was inserted in E q s 3 to 5:

a1 = 0.077 mm2/s a2 = 9.0 mm2/s A = 3.16

dJ,,, = 0.601

and the a-value of the filled material calculated for different MgO-contents. The result is shown in Fig. 13 as a solid line together with the values calculated from T, t-data. As can be seen, there is a good agreement between the two methods.

The a-value of unfilled HDPE as shown in Fig. 13 is in excellent agreement with the a- value determined in a similar way from injection molding data by Wubken (6). In his work also, a was an average taken between two lim- iting temperatures of the molding cycle.

The calculations presented above may be re- fined further, for instance by taking account of the slight variation of Tps with the MgO-content as evident from Fig. 12, the average Tps- value of 162°C being replaced by Tps = (162 + 0.3 42)0C. In this way, further improvements in the quantitative description of the experimental data were achieved. For all practical purposes, however, we consider the results presented in Figs. 11 to 13 to be a sufficient illustration of the usefulness of the theoretical approaches outlined in a simplified fashion above.

DISCUSSION The results presented above appear to sup-

port common expectations concerning the reduction of sealing and cooling times with filled materials. Despite the rather simple experimental techniques used in determining these two time parameters, the data obtained seem to show a rather high degree of reliability. Not only do they discriminate between different fillers in the order of their thermal diffusivity values, but they are also amenable to a theoretical interpre- tation with a relatively high degree of accuracy.

The enhancement of thermal conductivity of plastics by incorporation of fillers has been the subject of several studies. For instance Sund- strom and Lee (7) studied the influence of particulate fillers, including glass, CaO, A1203, and MgO, on the A-value of LDPE and PS at volume fractions up to 0.3. At 10 percent (vol) MgO, X increased by about 80 percent, a value in good agreement with the result presented above in Fig. 13, obtained from measurements of t, and calculated using the Lewis-Nielsen formula, E q

POLYMER ENGINEERING AND SCIENCE, MIDJULY, 1986, Vol. 26, No. 12 883

A. Boldizar and J . Kubat

3. The compounds based on the other oxides had similar A-values, while glass was significantly less efficient. The results were interpreted in terms of the theories of Bruggeman and Cheng-Vachon, both producing a reasonable agreement. Nielsen (8) later demonstrated that the data of Ref. 7 produced a significantly better f i t when accommodated to the theory of Kerner (9) as modified and simplified by Lewis and Nielsen (5, 8, 10). This equation is considered as the most suitable for the treatment of elastic and thermal properties of polymer composites containing particulate fillers (1 1).

Among other reports on the thermal properties of composites, we mention the work of Niel- sen (5) analyzing the applicability of various theoretical approaches to polymers containing aluminium and glass spheres, aluminium fibers, and carbon fibers. McGee and McCullough (1 2) find that the Lewis-Nielsen approach pro- vides a good f i t also at high volume fractions of the filler (>0.5), while other formulae normally reproduce the data up to about 0.3. The increase in X is especially high with metallic fillers. Kusy and Corneliussen (13) report on an approximately 20 times higher A-value for PVC containing 15 vol. percent copper (-5 pm). Significantly lower values are found by Bhattacharya and Chaklader (14) for an epoxy resin filled with particulate copper (1 0 to 100 pm).

The increase in X by thermally active fillers such as metals depends significantly on the particle shape. The higher the aspect ratio, the higher is also the increase in A. Experimental data and theoretical results regarding such systems may be found in Refs. 1 5 to 18.

Ott ( 1 9) reports on measurements of X on both thermosets and thermoplastics containing fi- brous reinforcements (glass, asbestos) and particulate fillers (quartz, fused silica, zirconia). Again, the results are interpreted with various theoretical models. The main interest is devoted to the temperature dependence of X (from -180 to + 140°C). The increase in X of PE due to filling with carbon black is discussed in Ref. 20.

Some more recent models are discussed in Ref. 21 for thermally active fillers, and in Ref. 12 for fiber reinforcement. In the latter case the role of anisotropy is considered.

An interesting comment is made by Bielek, e t al. (22) who found a significant increase in-X of CaC03-filled PE at about 30 vol percent, inter- preting this effect in terms of a percolation threshold. The authors assume that at this con- centration the filler particles form a connecting network facilitating the transport of thermal phonons. According to this concept, significant improvements of the thermal properties of filled composites are to be expected at filling levels exceeding around 30 vol percent, a value con- firmed in numerous instances of percolating systems. It may be noted that indications of such behavior can also be found in Ref. 23.

Agari and Uno demonstrated recently the ex-

istence of such an effect in CB and graphite filled PE and PVC. They found an exponential increase in thermal conductivity above about 20 percent filler content (by volume) (24). In the present case, the filling levels were not sufficiently high in order to observe effects of this

When applying theoretical models to experimental data in a rigorous manner, account should be taken of the variability of some of the parameters with the temperature. For instance, the value of X of HDPE may fall by 50 percent between RT and the normal melt temperature. For amorphous polymers, like PS, X remains practically constant (25).

In the present case, the fillers were incorpo- rated into the matrix without the use of coupling agents. Reference 26 reports an increase in X for PP/30 percent CaC03 containing 10 percent of an ethylene oxide oligomer (1 0 percent of the filler). Among other factors influencing X, we only mention the degree of orientation (27) and annealing (1 9).

The solution of the Fourier equation (heat conduction) according to Refs. 2 and 3 is not commented on further. It may suffice to note that there exist numerous studies dealing with this problem, e.g. (28, 29). Despite the simplifying assumptions underlying such calculations, the results obtained show a surprising degree of agreement with experimental data. A comparison of the a-values calculated inde- pendently from the composite model of Lewis and Nielsen appears to show that, in fact, the values of the sealing time may be converted with reasonable accuracy into the corresponding a-values. In this respect, an injection molding machine may be considered as a relatively accurate device for the determination of thermal conductivity of filled and reinforced plastics.

Although faster cycling of filled polymers has been repeatedly mentioned (30-32), there have been no quantitative verification of the actual potential of this method to improve the efficiency of the molding process. Needless to say, the benefits of shorter cycle times should be included in the calculations of the cost reduction due to the incorporation of fillers. Apart from this, thermally active fillers may also bring other benefits, perhaps not easily quan- tified in terms of cost, but in many cases equally important. The reduction of thermal stresses in MgO-filled plastics (33) may illustrate this point.

type.

ACKNOWLEDGMENT

The authors wish to express their thanks to the Swedish Board for Technical Development for financial support. Thanks are also due to Mrs. K. Thorneby for skillful assistance in the preparation of the manuscript.

884 POLYMER ENGlNEERlNG AND SCIENCE, MID-JULY, 1986, Vol. 26, NO. 12


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Documents

Measurements of cycle time in injection molding of filled thermoplastics