9
Experimental Study and Finite Element Analysis of the Injection Blow Molding Process W. P. HAESSLY and M. E. RYAN* Department of Chemical Engineering State University of New York at Buffalo Buffalo,New York 14260 A finite element numerical analysis of preform inflation associated with the injection blow molding process has been developed using a neo-Hookean constitu- tive model. The analysis is capable of predicting final wall thickness distributions for axisymmetric mold geometries. Experimental studies were conducted on a Uniloy injection blow molding machine (Model 189-3 and Model 122). A twelve ounce (355 mL) cylindrical bottle mold was instrumented with contact sensors, thermocouples, and pressure transducers. Visualization studies of the inflation process were performed using specialized tooling and high-speed video cameras. The experimental studies provide justification for analyzing the deformation by means of a static elastic approach. The predicted wall thickness distribution is in reasonable agreement with the experimental data. Nonuniformities in the temper- ature distribution in the preform were found to have the most significant impact on the inflation behavior and the resulting wall thickness. INTRODUCTION development of new parts. Currently, no comparable low molding is commonly used in the production B of hollow plastic articles, primarily containers. Blow molded plastic containers have successfully replaced glass, metal, and paperboard in many appli- cations. Desirable properties such as impact resis- tance, squeezability, light weight, design flexibility, and corrosion resistance have contributed to the growth of blow molding markets. Current obstacles and concerns for food packaging applications include the recycling of used containers, the ability of plastic containers to withstand pasteurization, retort, and higher filling temperature requirements of some food- stuffs, and the ability to provide the requisite bar- rier properties needed to maintain the freshness of sensitive products. Solutions to these problems are continually being sought and all are within the realm of technical feasibility. In addition to container applications, there exists a rapidly growing market for non-container blow molded articles. Many of these potential applications mandate higher quality and more rigorous structural performance than for containers. In general, these non-container blow molded parts are competing in markets which utilize plastic parts produced by either extrusion or injection molding. Computer simulation, particularly with regard to injection molding, has become a standard engineering design tool for the computer simulation package is commercial& avail- able for the design of blow molded parts. This lack of sophistication has been a practical detriment to the penetration of these high performance markets. Several different blow molding technologies have been developed including extrusion blow molding and injection blow molding, among others. In the injec- tion blow molding process, a reciprocating-screw injection molding machine is typically used to inject the molten polymer around a blowing mandrel or core rod. The injection molding of this preform in a closed mold provides good precision control of the preform weight and thickness profile as well as a high-quality neck finish. The blowing mandrel is rotated to a blowing station having a split mold pos- sessing the desired shape or contour of the finished product. The core rod extends slightly in order to permit air to inflate the preform.The polymer deforms, contacts the mold surface, cools, solidifies, and is ejected from the mold. Most commercial injection blow molding operations are found in applications related to relatively small- sue products such as packaging containers for the food, pharmaceuticals, or cosmetics markets. The process is particularly advantageous for high-volume applications or for situations where precision toler- ance neck finish is critical for compatibility with closures or other reasons. Another advantage of injection blow molding as compared to extrusion blow 'To whom correspondence should be addressed. molding is related to the fact that injection POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1993, Vol. 33, No. 19 1279

Experimental study and finite element analysis of the injection blow molding process

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Experimental Study and Finite Element Analysis of the Injection Blow Molding Process

W. P. HAESSLY and M. E. RYAN*

Department of Chemical Engineering State University of New York at Buffalo

Buffalo, New York 14260

A finite element numerical analysis of preform inflation associated with the injection blow molding process has been developed using a neo-Hookean constitu- tive model. The analysis is capable of predicting final wall thickness distributions for axisymmetric mold geometries. Experimental studies were conducted on a Uniloy injection blow molding machine (Model 189-3 and Model 122). A twelve ounce (355 mL) cylindrical bottle mold was instrumented with contact sensors, thermocouples, and pressure transducers. Visualization studies of the inflation process were performed using specialized tooling and high-speed video cameras. The experimental studies provide justification for analyzing the deformation by means of a static elastic approach. The predicted wall thickness distribution is in reasonable agreement with the experimental data. Nonuniformities in the temper- ature distribution in the preform were found to have the most significant impact on the inflation behavior and the resulting wall thickness.

INTRODUCTION development of new parts. Currently, no comparable low molding is commonly used in the production B of hollow plastic articles, primarily containers.

Blow molded plastic containers have successfully replaced glass, metal, and paperboard in many appli- cations. Desirable properties such as impact resis- tance, squeezability, light weight, design flexibility, and corrosion resistance have contributed to the growth of blow molding markets. Current obstacles and concerns for food packaging applications include the recycling of used containers, the ability of plastic containers to withstand pasteurization, retort, and higher filling temperature requirements of some food- stuffs, and the ability to provide the requisite bar- rier properties needed to maintain the freshness of sensitive products. Solutions to these problems are continually being sought and all are within the realm of technical feasibility.

In addition to container applications, there exists a rapidly growing market for non-container blow molded articles. Many of these potential applications mandate higher quality and more rigorous structural performance than for containers. In general, these non-container blow molded parts are competing in markets which utilize plastic parts produced by either extrusion or injection molding. Computer simulation, particularly with regard to injection molding, has become a standard engineering design tool for the

computer simulation package is commercial& avail- able for the design of blow molded parts. This lack of sophistication has been a practical detriment to the penetration of these high performance markets.

Several different blow molding technologies have been developed including extrusion blow molding and injection blow molding, among others. In the injec- tion blow molding process, a reciprocating-screw injection molding machine is typically used to inject the molten polymer around a blowing mandrel or core rod. The injection molding of this preform in a closed mold provides good precision control of the preform weight and thickness profile as well as a high-quality neck finish. The blowing mandrel is rotated to a blowing station having a split mold pos- sessing the desired shape or contour of the finished product. The core rod extends slightly in order to permit air to inflate the preform. The polymer deforms, contacts the mold surface, cools, solidifies, and is ejected from the mold.

Most commercial injection blow molding operations are found in applications related to relatively small- sue products such as packaging containers for the food, pharmaceuticals, or cosmetics markets. The process is particularly advantageous for high-volume applications or for situations where precision toler- ance neck finish is critical for compatibility with closures or other reasons. Another advantage of injection blow molding as compared to extrusion blow

'To whom correspondence should be addressed. molding is related to the fact that injection

POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1993, Vol. 33, No. 19 1279

W. P. Haessly and M. E. Ryan

blow molded parts do not need to be trimmed of flash and consequently there is no inherent scrap generation due to deflashing.

Several different types of injection blow molding have been developed with the essential differences being related to the design of the plasticating unit or the manner by which the core rod and preform are transported or indexed from one station to another. A more detailed discussion of the process technology is given elsewhere (1 -3).

Since the ultimate wall thickness distribution of the final product is directly influenced by the initial dimensions of the preform and the manner by which the preform deforms, it is important to develop a sound scientific understanding of the deformation and dynamics of the process. A reliable computer- based simulation of the inflation process would be invaluable in the design of new tooling by reducing the lead time and eliminating the need for prototype tooling. These considerations are particularly rele- vant for non-container applications where limited experience is available and product designs may be complex.

The purpose of this paper is to provide experimen- tal results as well as a mathematical analysis of the process of preform inflation.

EXPERIMENTAL EQUIPMENT AND INSTRUMENTATION

Two types of experimental studies were conducted under typical production conditions. In the first set of experimental studies an instrumented twelve ounce (355 mL) cylindrical bottle mold was run on a Uniloy Injection Blow Molding Machine (Model 189-3). Three types of sensors were mounted in the tooling. Three Sensotec LVDT sensors (Model MSMS- 100H) were situated at various axial positions in order to detect contact of the inflating polymer with the mold surface. The armature of each LVDT sensor was spring loaded such that the end of the armature extended approximately 0.5 cm into the mold when unloaded. A small threaded brass cap was screwed onto the end of the armature. Contact of the inflating polymer with the protruding armature forced the cap back into a recess in the mold wall and triggered a signal indicating that surface contact had been made. On the opposite side of the mold, three Omega ther- mocouples (Type SEFE) were positioned at the same axial locations as the LVDT sensors. These thermo- couples indicated both the surface temperature and the relative time of contact of the polymer with the wall. An Omega pressure transducer (Model PX612) was mounted near the upper comer of the mold to monitor any increase in cavity pressure due to air entrapment between the inflating polymer and the mold contour. A similar pressure transducer mounted in the air line provided a continuous record of the inflation pressure.

Each of the LVDTs was connected to an Omega signal conditioner (Model OM3-LV) which provided an excitation voltage and amplified the output signal.

The thermocouples were also connected to signal conditioners (Omega, Model OM3-ITC) as were the pressure transducers (Omega, Model OM3-MV). The excitation voltage for the pressure transdu- cers was provided by a Hewlett-Packard DC power supply (Model 62005A). The signal conditioners were mounted in an Omega OM3 backplane which was connected to an Omega WB-800 multifunction analog/digital input-output board mounted in an IBM personal computer. LABTECH NOTEBOOK soft- ware was used to control the WB-800 board and record the data on disk. The maximum data acquisi- tion rate for the simultaneous data collection from 8 channels was 20 Hz for the particular IBM PC based on an Intel 8088 CPU chip operating at 4.77 MHz. Higher data acquisition rates are possible using a math co-processor or a faster PC.

The second set of experimental studies involved visualization experiments using high-speed video cameras. The experiments involved either uncon- strained inflation in the absence of a mold or inflation within a transparent acrylic mold having the same size and geometrical configuration as the instru- mented mold. The video recordings were made on a NAC 200 at 100 frames/s or on a Kodak Ektapro 1000 which operated at 500 frames/s. Thermal imag- ing was done using an AGA Thermovision 782 but the quantitative results were unsatisfactory and are not reported here. The visualization studies were con- ducted on a Uniloy Injection Blow Molding Machine (Model 122).

The same preform mold and set of core rods were used in all experiments. Three thermal conditioning units were used to provide heated oil to control the temperature of the preform mold. A grid was etched into the surface of the preform mold to impart a grid pattern on the molded preform which could then be used to measure the local extent of deformation of the molded bottle.

MATERIALS

Five commercial injection blow molding resins were examined and are listed in Table 1. The variation of viscosity with shear rate and temperature for each of these resins was determined with the aid of a Rhec- metrics Mechanical Spectrometer (Model RMS-705). Two sets of fixtures were employed, namely parallel plates and cone and plate. The diameter of the plates was 2.5 cm with a gap between of 2.0 mm. The cone and plate fixtures also had a diameter of 2.5 cm and the cone angle was 0.04 radians (2.26"). The details of determining the viscosity as a function of shear rate in these two shearing flows have been extensively analyzed and are readily found in any standard text- book on rheology (4). These rotational measurements are restricted to relatively low shear rates. For high shear rate viscosity measurements an MCR capillary rheometer attachment was used in conjunction with an Instron Universal Testing Machine (Model 1125). The operation of the capillary rheometer involves the measurement of the force required to extrude

1280 POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1993, VOl. 33, NO. 19

Experimental Study and Finite Element Analysis

the material at a fixed volumetric flow rate. This force is measured by means of a load cell and is directly proportional to the shear stress at the wall of the capillary. The details of the analysis can be found elsewhere. The Rabinowitsch correction (4, 5) was applied to the results.

The viscosity data were fitted to a Bird-Carreau expression (4) of the form

where 7 is the viscosity, qo is the zero shear rate viscosity, y is the shear rate, A is a time constant, and n is a power-law exponent. The data were fitted to Eq 1 by means of a graphical technique as sug- gested by Abdel-Khalik, et a1 (6). The values of the three parameters in the Bird-Carreau equation, for the five resins studied, are reported in Table 1 . Vis-

material. The temperature dependence of the zero shear rate viscosity can be approximately described by means of a simple Arrhenius expression as follows

g,=Aexp -- (2) ( 2) where A is a constant, A E is the flow activation energy, R is the gas law constant, and T is the absolute temperature. The values of the flow activa- tion energies for each resin are also given in Table I.

Dynamic rheological properties were measured using the Rheometrics Mechanical Spectrometer. The dynamic storage modulus, G ' ( w ) , and the dynamic loss modulus, G ( w ) , were measured over the fre- quency range from 0.1 - 100 rad/s.

EXPERIMENTAL. RESULTS

cosity measurements were cbnducted for at least three different temperatures for each resin. The tem- perature range selected was typical of the tempera- ture range associated with the processing of the

The preform mold temperature settings and the inflation pressure for some of the experimental runs are given in Table 2. The experimental data recorded by the LVDT contact sensors, the pressure trans-

Table 1. Values of Rheological Parameters for Resins Studied.

T rl0 A n A€ Resin Manufacturer Grade ("C) Pa - s S - J/gmole

High density Allied Chemical PAXON 150 55,000 20 0.40 1.6 x 104

Polypropylene El Paso Products REXENE 200 10,700 3.0 0.42 1.1 x 105

Polystyrene Huntsman 91 00 175 60,000 12 0.38 8.9 x 104

Polyethylene AD60-007 170 45,000 25 0.40 (PE) 200 34,000 31 0.44

(PP) 231 n2CS198 225 1900 0.29 0.40 250 800 0.09 0.40

(PS) 200 8200 1.3 0.40 225 1250 0.1 0.34 250 930 0.25 0.40

(PA) PA3426 230 2800 15 0.70 240 2200 28 0.72

terephthalate 260 70 0.19 0.80 (PET) 270 45 0.30 0.80

Nylon Du Pont SELAR 220 5200 13 0.74 1.1 x 105

Polyethylene Eastman Kodak PM9921 250 110 0.48 0.86 1.1 x 105

Table 2. Experimental Run Conditions.

Preform Mold Temperature Settings Inflation Pressure Settings

Run "C "C "C kPa kPa Zone 1 Zone 2 Zone 3 Steel Mold Free/Confined

PE1

PE2

PE3

PP1

PP2

PS1

PS2

NYLON

PET

88 (1 90°F)

88 (1 90°F)

99 (21 0°F)

99 (21 0°F)

99 (21 0°F)

49 (1 20°F)

49 (1 20°F)

85 (1 85°F)

63 (1 45°F)

110 (230°F) 110

(230°F) 82

(1 80°F) 102

(21 5°F) 102

(21 5°F) 118

(245°F) 118

(245°F) 85

(1 85°F) 63

(145°F)

60 (1 40°F)

60 (1 40°F)

54 (1 30°F)

71 (1 60°F)

71 (1 60°F)

71 (1 60°F)

71 (1 60°F)

82 (1 80°F)

66 (1 50°F)

759 (1 10 psi)

379 (55 psi)

759 (1 10 psi)

759 (1 10 psi)

379 (55 psi)

759 (1 10 psi)

379 (55 psi)

759 (1 10 psi)

759 (1 10 psi)

827 (1 20 psi)

276 (40 psi)

276 (40 psi)

827 (120 psi)

276 (40 psi)

827 (1 20 psi)

276 (40 psi)

827 (1 20 psi)

827 (120 psi)

POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1993, Vol. 33, No. 19 1281

W. P. Haessly and M. E. Ryan

ducer in the upper comer of the mold cavity, and the pressure transducer in the air line are shown in Fig. I for a typical run, in this case polypropylene (PPl). Since data are collected every 50 ms it can be concluded that mold contact occurred in less than 100ms after the initiation of inflation. The middle sensor (LVDT2) is contacted first as might be expected from the shape of the inflating preform The sensor near the top of the mold (LVDT3) is contacted prior to the sensor near the bottom of the mold (LVDT1) since the preform temperature was higher in the neck region (zone 1) as compared to the base (zone 3).

It is interesting to note that mold contact occurs in advance of the inflation pressure attaining its maxi- mum value. As can be seen in Fig. 1, mold contact occurs at a pressure level of approximately 172 to 207 kPa (25 to 30 psi). The pressure increase in the mold cavity is less than 6.9 kPa (1 psi) indicating adequate venting permitting easy displacement of air from the cavity. Similar data are shown in Eg. 2 where the inflation pressure has been halved. The results are comparable but the inflation rate was somewhat slower with mold contact occurring within a period of less than 150 ms after the start of inflation.

Similar results were obtained for the other materi- als used in this study particularly at the elevated inflation pressure of 758 kPa (1 10 psi). In particular, mold contact occurred well before the pressure level attained its set-point level and in a period of less than 100 ms.

All of the molded bottles were cut along the parting line and wall thicknesses along the parting line were measured with a micrometer. A plot of the wall thick- ness us. perimeter distance for polyethylene (PE1) is shown in Flg. 3. The bottom comer of the bottle is arbitrarily chosen as the origin for measuring the perimeter distance. Thickness measurements were made at each grid point position. As is readily appar-

PP 1 7 ] p L ~ O ~ l o ~ Mold filled.

0 LVDT 1

A LVDT 3 0 LVDT 2

I :: .:

0.0 0.2 0.4 0.6 0.3 1 .o T ime, s e c

F'ig. 1 . Transducer signals for mold contact, mold pressure, and injlation pressure for polypropylene ( run PPl).

0 LVDT 1

A LVDT 3 0 LVDT 2

1 .

o+. - J I

lnflotion pressure a

4 I

0 4 0.4 0.6 0.3 1 .o 0.0 0.2

Time, sec Fg. 2. Transducer signals for mold contact, mold pressure, and injlation pressure for polypropylene (run PP2).

Bottle

I

0.0 I 7 I I n T-rTTT-1 I I I-I-IT~ 1 I 1 I- I - rn+- r r i~

Perimeter length (cm)

C r ; -2.5 -0.0 2.5 5.0 7.5 10.0 12.5 15.0

Fg. 3. Wall thickness distribution forpolyethylene( run PEI).

ent from Fig. 3, the wall thicknesses at the bottom and at the shoulder are much greater than the wall thickness along the side.

The grid mark locations were also measured and are shown in the upper part of lQg. 3. Dashed lines have been used to connect the original grid mark positions in the preform with the corresponding grid mark locations in the molded bottle. The dashed lines are merely drawn as a visual aid but may be consid- ered to approximately indicate the trajectories of the grid points during inflation. In this run the lower part of the preform was hotter than the upper part. As can be seen in Fig. 3 the grid point spacing was greater and the wall thickness was thinner in the bottom part of the molded bottle. Figure 4 shows correspond- ing data for another run at similar conditions except that the inflation pressure was reduced by a factor of two (PE2). The reduction in inflation pressure has virtually no effect on the grid point positions or final wall thickness distribution.

1282 POLYMER ENGlNEERlNG AND SCIENCE, MID-OCTOBER 1993, Vol. 33, No. 19

Experimental Study and Finite Element Analysis

0.4 - n

S f " 0 . 3 - m - I n - a , -

v - 1 - I - . .

2 0.2 - .- -

0.1 -

Figure 5 gives the results of a polyethylene run where the upper portion of the preform was at a more elevated temperature than the lower part of the pre- form. In this case the axial stretching is greater and the wall thickness is thinner in the upper part of the molded bottle.

Similar results for the variation of wall thickness with perimeter distance were obtained for the other materials studied. Figures 6 and 7 give the wall thick- ness distribution data for two polypropylene runs (PPl.PP2). The wall thickness along the side of the molded polypropylene bottles is quite uniform indi- cating that the initial temperature distribution along the length of the preform was fairly uniform. As men- tioned previously, the level of the inflation pressure had negligible effect on the axial stretch ratios or wall thickness distributions.

Inflation of the polyethylene was not axisymmetric. The wall thickness variation around the circumfer- ence of the molded bottle at the mid-plane is shown in Fig. 8. This unevenness indicates that the circum- ferential temperature distribution in the preform was

C Y lJ f 0.05 - t- .-

0.00

0 HDPE 1

A HDPE 3 0 PS 1

0 PS 2

I , , , , , , , I I I I I , I , I , I I I I I I I I 1 I I I $ 3 , I I I I 0 4 1 4 0 12 16

I I I I I

I I I I I //

I I I

0.0 j l i 7 - r r n l T r l 1 1-1-1 I I I 1 1 - 1 I 1 -IT I 1-11! I I I r -2.5 -0.0 2.5 5.0 7.5 10.0 12.5 15.0

Perimeter length (cm)

Fig. 4. Wall thickness distribution for polyethylene ( run PE2).

I "0.3 I

I I I I I I

I I

I I

0.0 -L I I Ld.6 I I i:5' I 1 i:o' I I ?:5' I I i d . d " i n l j o Perimeter length (cm)

Fig. 5. Wall thickness distribution for polyethylene( run PE3).

Y Preform I

I 0.5 7 I

0.4 4 : I

0.0 - I I I I I I I I I I I I I I I Ijl I I I I -2.5 -0.0 2.5 5.0 7.5 10.0 12.5 15.0

Perimeter length (crn)

Fig. 6. Wall thickness distribution for polypropylene (run PPl).

Bottle I

: " 0 . 3 1 2 0.2

t- o. 1

I I

0.0 r1"7"'71 I I 1 1 I I I I 1 1 ' ' 1 I I l l I I I I -2.5 -0.0 2.5 5.0 7.5 10.0 12.5 15.0

Perimeter length (crn)

.i 1 Flg. 7. Wall thickness distribution for polypropylene (run PP2).

POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1993, Yo/. 33, No. 19 1283

W. P. Haessly and M. E. Ryan

not uniform. This suggests that the two-dimensional modeling approach to be described subsequently may not be adequate even though the preform and molded part possess an axisymmetric geometry. For poly- styrene and polypropylene the circumferential wall thickness was very uniform. The circumferential wall thickness variation for polystyrene is shown in Fig. 8.

The evolving shape of the inflating preform was recorded by means of a high-speed video system described earlier. Free inflation studies were con- ducted without the bottle mold assembly. A special tool was designed to fit into the blow mold clamp in order to securely hold the neck of the preform in place. A pin was mounted in the clamp assembly which prevented the end or tip of the preform from moving during the inflation process. Once the pre- form had completely lifted off of the core rod, the initial stage of the inflation process was fairly uni- form in all cases. Ultimately a bulge would form which would continue to rapidly propagate until rupture occurred. The location of the bulge was always the same for a particular core rod. This was most proba- bly due to a hot spot associated with a specific core rod as a result of a particular pattern of air cooling within the core rod.

Typical inflation profiles are shown in Fig. 9 for the case of polyethylene (PE1). The profiles were gener- ated by measuring several free surface coordinates from the video screen, correcting for the distortion of the video projection, and then fitting a spline curve through the points. At a time equal to 2 ms the preform begins to lift up from the tip of the core rod where the material is hottest. This initial bulge propa- gated very rapidly along the entire length of the pre- form. The inflation then proceeds uniformly until a subsequent bulge or aneurism forms which ulti- mately ruptures. Typical blow-up ratios at break for polyethylene were approximately 6 for inflation pres- sures of either 276 kPa (40 psi) or 827 kPa (120 psi). A typical time to rupture was 230 ms at 276 kPa (40 psi) and 46 ms at 827 kPa (120 psi).

Figure 10 shows the free inflation behavior for polystyrene (PS2) which is notably different from that of high-density polyethylene. At the low inflation pressure of 276 kPa (40 psi) polystyrene deformed

rapidly and ruptured after only 50 ms. Typical blow- up ratios or radial stretch ratios at break were 2.5 to 3, approximately one half of the value of high-density polyethylene.

After rupture the material returned almost com- pletely to the original preform shape except in a small region immediately surrounding the rupture or tear where the material had thinned to a great extent and cooled significantly. The significance of this observ- ation is that the rapid inflation process is highly elastic in nature.

Confined inflation studies were conducted using a transparent acrylic mold. The curvature of the inner cylindrical surface caused a significant distortion of the recorded visual image of the inflating polymer. The distortion was corrected by assuming that the recorded image was linearly related to the actual position within the mold. Since this is not strictly valid the confined inflation results should be viewed in a qualitative manner. Figure 1 1 shows typical con- fined inflation results for high-density polyethylene (PE1). The free surfaces are actually smooth. The apparent waviness in Fig. 1 1 is due to measurement inaccuracies caused by the nonlinear distortion through the acrylic mold. The hotter material near the bottom contacted the lower comer after 80 ms whereas the cooler material in the upper part of the preform required 3 10 ms to contact the rest of the mold. As can be seen from Fig. 1 1 only 40 ms elapsed before initial contact was made with the mold surface.

It is common in industrial practice to use a sequence of two different inflation pressures. An initial low pressure is employed to lift the preform off of the core rod followed by a higher pressure to inflate the preform in the blow mold. The visualiza- tion studies conducted here indicate that for polyeth- ylene most of the deformation and mold contact occurs during the initial lower pressure stage. The higher pressure accelerates the final deformation into

c n i IPC

0 4 8 12 ?6 = (cm)

Fig. 10. Free inflation profiles for polystyrene.

1 I 1 1

0 4 8 12 16 z (cm)

Fig. 1 I. Confined inflationprofiles forpolyethylene( run PEI).

1284 POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1993, VOl. 33, NO. 19

Experimental Study and Finite Element Analysis

POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1993, VOI. 33, NO. 19 1285

the mold comers, forces the polymer into more inti- mate contact with the mold contour, and results in a better definition of the molded part.

Visualization experiments were also conducted where an inflation pressure of 276 kPa (40 psi) was applied for 800 ms and subsequently relieved. In this experiment the mold surface was completely con- tacted by the polymer, but after the pressure was relieved, the material retracted almost completely to the original preform shape. A very slight amount of permanent deformation was evident around the mid- plane of the preform which had been in contact with the acrylic mold for the longest time. This observation of almost complete elastic recovery further supports the inference that the material response is highly elastic during the rapid inflation phase of the blow molding process. The Deborah number associated with inflation is high suggesting that time-dependent viscoelastic effects may be neglected. However, under conditions where the inflation may be slow, the Deborah number may be sufficiently low that viscous effects become significant.

THEORETICAL ANALYSIS

Although thermoplastic polymers are generally regarded as viscoelastic, the theoretical approach adopted here considers the inflating polymer to behave as an incompressible, nonlinear, elastic mate- rial. For injection blow molding this assumption is strongly supported by experimental evidence cited in the previous section. Other experimental studies (7-9) have also indicated that at relatively high strain rates the response of the polymeric material is dominated by its elastic nature. Thus, the rubberlike behavior of the material can be adequately modeled by means of constitutive equations that have typically been used to describe large deformation elasticity. A well-known relationship is the neo-Hookean model which is given b Y

E

6 W= - (A? + A; + A: - 3) (3)

where W is the strain energy density function, E is Young’s modulus, and the hi‘s are the primary stretch ratios.

In the present analysis, the preform and bottle geometry are axisymmetric. The profile of the preform is divided into linear elements and a force balance is made between the pressure and elastic forces at each node. The initial thickness and modulus associated with each element are specified. The inflation is pre- sumed to occur so rapidly that any temperature change prior to mold contact is considered to be negligible. Applying the principle of virtual work, the virtual work of internal stresses is equal to the virtual work of external forces. The elastic forces can be calculated from the following relationship

dW lJ du,

F..= V - (4)

where cj are nodal forces, V, is the element volume, and uij are nodal displacements. The thin shell approximation is used and forces in the thickness direction are neglected. The set of resulting equations are nonlinear and are solved by means of a Newton- Raphson method (10). The details of the formulation are based on the inflation analysis of elastic mem- branes in relation to thermoforming developed by Chamer, et aL (1 1, 12). Additional details relating to the theoretical development and numerical analysis are given elsewhere (13, 14).

In general the shape of the deformed preform is not a unique function of pressure and consequently it is computationally more convenient to specify small incremental changes in the radial stretch ratio. The solution from the previous step is used as the initial guess for the Newton-Raphson method.

The mold geometry is defined by a series of points connected by lines. After each successive deformed shape is determined, each nodal position is compared to the location of the mold surface. If any node is at or slightly beyond the mold surface, that node is then fured at the mold surface and no longer allowed to move. The incremental changes in the successive calculated shapes are kept sufficiently small that no node moves significantly beyond the mold surface from one step to the next. If mold contact occurs for a node not directly adjacent to a node already in con- tact with the mold, the problem is then subdivided into two separate problems with the recent contacted node held fixed for the two new series of deformation calculations. Successive solutions are obtained until all nodes have come into contact with the mold surface.

COMPARISON OF THEORETICAL PREDICTIONS WITH

EXPERIMENTAL RESULTS

The dimensions of the preform and bottle mold geometry were used as inputs to the computer model. The temperature distribution was used to determine the storage and loss modulus distributions from which a shear relaxation modulus and Young’s mod- ulus could be calculated. This procedure is based on a method proposed by Ninomiya and Ferry (15, 16) and is described elsewhere ( 14). Table 3 gives Young’s modulus as a function of temperature for four of the resins used in this study. For PET the dynamic stor- age modulus of the melt was negligible and therefore no data based on the procedure described above are presented. Due to the static nature of the elastic analysis, a characteristic time must be chosen in order to evaluate the shear relaxation modulus from which the Young’s modulus is determined. As indi- cated in Table 3 a characteristic time of 0.1 s was selected as being typical for the inflation stage associated with blow molding.

A comparison of the theoretical prediction of the wall thickness distribution with experimentally mea-

W. P. Haessly a n d M. E. Ryan

Table 3. Young’s Modulus as a Function of I Bottle I I I

Temperature for Elastic Analysis.

T E(t = 0.104

High density polyethylene (PE) 150 2.58 x 105 I

2.17 x 105

Polypropylene (PP) 200 1.73 x 105 225 8.26 x lo4 250 5.88 x lo4

Polystyrene (PSI 175 4.27 x 105

225 5.09 x 104

Nylon (PA) 220 4.18 x lo4 230 1.77 x 104 240 8.96 x 103 0.0

-Preform-- - I_ Resin (“C) (Pa) 0.5

1 170 I 200 1.79 x 105 0.4 I

200 1.87 X lo5 1.36 X lo4 250

0.1

-2.5 -0.0 2.5 5.0 7.5 10.0 12.5 15.0 Perimeter length (cm)

I Bcttle I I I

1

J I 0.4

C J

I I

5 : -0.3 1

0.1 i

i

I I I -

1 4 ! T

I ; + I Model prediction

I Exper’mentol points I L L - - - I I

0.0 ] , , , , / , , , , ] , I , 1 1 1 1 1 , , 1 1 1 1 1 1 1 1 1 ] ~ 1 1 # I )

-2.5 -0.0 2.5 5.0 7.5 10.0 12.5 15.0 Perimeter length (crn)

Fig. 12. Comparison of theoretical prediction of wall thick- ness distribution with experimental results for polyethylene (run PEI).

sured data is shown in Figs. 12 and 13 for two different runs (PE 1 and PE3). The experimental points are an average of the values measured circumferen- tially around the perimeter of the bottle. The error bars indicate the circumferential variability.

Qualitatively the theoretical predictions are in reasonable agreement with the experimental results but quantitatively the differences are somewhat disappointing. For the PE1 run, the correct trend of the predicted wall thickness profile is evident (Fig. 12). For the PE3 run, the predicted wall thick- ness profile is more uniform than the measured p r e file. In general, there is better agreement in the regions where the preform was cooler. The theoretical predic- tions are poorest in the hotter regions due most probably to the excessive deformation and relaxation processes associated with these regions.

The disparity between the model predictions and the data may be attributed to several factors. One obvious shortcoming is the lack of accurate informa- tion with regard to the temperature distribution par- ticularly in the neck region which deformed very little.

Fig, 13. Comparison of theoretical prediction of wall thick- ness distribution with experimental results for polyethylene ( run PE3).

Another limitation is due to the assumed neo- Hookean behavior of the material. There is also the general question of the applicability of rheological data obtained in shear being applied to an exten- sional deformation. Specification of the boundary conditions and the assumption of no slippage at the mold wall could also be a source of error. In the experimental studies the mold became heated after extended operation and the assumption that the material freezes instantly upon contact is questionable.

The theoretical model assumes no density change during inflation or solidification. The polyethylene bottles are subject to shrinkage on solidification which has not been accounted for by the model. However, the magnitude of the shrinkage is on the order of 5% to 7% and is not sufficient to account completely for the observed disparity.

CONCLUSIONS

The blow molding experiments provide strong s u p porting evidence for the basic assumption that the inflation stage of the injection blow molding process may be modeled by means of a static elastic analysis. The experiments indicate that the shape of the deforming preform and the wall thickness distri- bution do not depend on the magnitude of the infla- tion pressure for typical pressure levels used in commercial operations.

An elementary computer simulation of the inflation stage of the injection blow molding process has been developed. The model possesses flexibility and can be used iteratively in order to relate the preform wall thickness distribution to the wall thickness distribu- tion in the blown part. The model is in good quali- tative agreement with experimental results but requires more detailed input information in order to be useful as an accurate quantitative tool.

1286 .POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1993, VOl. 33, NO. 19

Experimental Study and Finite Element Analysis

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