Mechanics Research Commtmicsliom, Vol. 24, No. 1, pp. 49-56, 1997 cop~ght o 1997 E~evier Sci¢~ Lid Printed in the USA. All r igha re,e~ved

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PII soo~ .~D(~)eoe ' r74

I N V E S T I G A T I O N O F T H E S K I N M E L T ASSISTED INJECTION MOLDING

S. C. Chen, N. T. Cheng and M. J. Chang

Mechanical Engineering Department

Chung Yuan University, Chung-Li 32023, Taiwan, R.O.C.

F O R M A T I O N DURING GAS-

(Received 12 January 1996; accepted for print 31 July 1996)

I n t r o d u c t i o n

In the gas-assisted injection molding (GAIM) process, the mold is first partially filled with

polymer melt followed by the injection of inert gas into the mold [ 1-2]. This innovative molding

technology can substantially reduce operating expenses through reduction in material cost,

clamp tonnage and cycle time. Part qualities can also be greatly improved by reducting residual

stress, warpage and sink marks. Despite of these advantages, this process introduces new

parameters and makes the application more difficult. Key factors that involved in this process

include gas channel design, locations of gas injection points, amount of melt injection, delay

time, gas pressure and gas injection time. Due to the complexity of the GAIM, a design/molding

guideline, particularly using CAE simulation software, is expected to become a required tool to

assist in part design, mold design and process evaluation in the coming age.

For nearly a decade, simulation model based on the Hele-Shaw type of flow provides acceptable

predictions in describing the polymer melt flow in thin cavities. Now, the existing models meet

a new challenge for the new process. Although studies on the numerical simulations are now in

progress [3-5], it is still lack of a general model or empirical formula describing the thickness of

skin melt existing between the gas/melt interface and the cavity wall (Fig. la). Theoretical and

experimental investigations on bubble/liquid displacement in a tube were previously reported,

[6-11 ]. These studies focused on Newtonian fluid flowing at low capillary numbers (between 1

and 102 ) under isothermal conditions. Conditions for gas penetration within the non-isothermal

are quite different. It involves much higher capillary numbers (about 104 to 105). Also, polymer

melt is a highly viscous non-Newtonian fluid with shear-thinning behavior. Recent experiments

studying the effect of melt temperature, mold temperature, gas delay time as well as gas

pressure on skin melt thickness variation were reported [11-13]. These studies reported a rather

consistent result on the qualitative variation of skin melt thickness with processing parameters.

4 9

50 S.C. CHt~, N.T. CHENG and M.J. CHANG

A more recent study [ I 1 ] show that thickness ratio of skin melt increases with increased gas

pressure at low gas pressure and reaches a constant value of about 0.37 (Fig. 2a) at high gas

injection pressure. All recent studies indicate that skin melt formation is quite a complex issue

and it may involve a transient characterictics in the process in contrast to the steady-state

assumption used in the theoretical analysis. In this research, a simple formulation was first

derived based on a non-isothermal power-law fluid model in order to evaluate the effect of all

possible contributing factors to the skin melt formation during GAIM. Variation of skin melt

thickness with melt temperature, mold temperature, delay time, gas pressure as well as the melt

shear-thinning behavior was numerically analyzed. Then a glass-inserted spiral mold installed

with pressure sensors were also built to observe melt flow and gas penetration in the actual

molding process. Both predicted results and experimental observations were compared and

analyzed to evaluate the contributing parameters to the formation of the skin melt.

Modelin2 and Formulation

It has been generally accepted that the Hele-Shaw flow model provides a reasonably accurate

description of polymer melt flow in three-dimensional thin cavities. Therefore, the basic

assumptions and the relevant governing equations for the inelastic, non-Newtonian melt flow

under non-isothermal conditions in a tube are similar to those in conventional injection molding:

au - - = 0 (l) az

aP 1 a au - [r(rl-~r 1] (2)

az r ar

aT aT r l a aT ] au 2 oc <g + o g , = Lr g( k n(Tr) (3)

where P and T represent pressure and temperature, u is the velocity in the axial direction, z, r is

the radial direction. In addition, I], p, Cp and k represent viscosity, density, specific heat and

thermal conductivity for the polymer melt, respectively. Viscosity of the polymer melt is

described by a power-law model with Arrhenius temperature dependence, that is,

(Tb / (4a,b) ~(T,'y) = rl0(T)~ nl and "q0(T) = B exp -~-

Similar to the fountain flow of an advancing melt front, pressure near the gas front is gapwisely

dependent and melt velocity in the gapwise direction is unnegligible. However, the effect of

gapwisely dependent pressure and gapwise flow are believed to be important on the

microstructure but have less influence on the macro-parameters. Between the gas front and the

melt front region (Fig. lb), melt flow velocity u(r) can be obtained by integrating Eq. (2), i.e.,

SKIN MELT FORMATION IN IN/EC~ON MOLDING 51

f RF r F apl o l'/n u(r) = / T ~ L - ~ J z > o / dr for 0 < r _< R (5)

and the mean velocity of polymer melt around the melt front, <u>, is given by

j, RI[R,[ r ( aP~ ]l/ndrlr,dr,

0 [~r L~°k-azz Jz--}*~] J (6) < U > =

fRrdr

Along meniscus of the bubble, the melt velocity, u(r, z), at a location with a rl distance between

melt/gas interface and the central line can also be obtained from Eq. (2) by applying an

appropriate boundary condition at the melt/gas interface, i.e., u(r, z) is

f R [ r ( OP / (1 ' ' n u(r, z) = ~r/~-~n~k-~Jz_<0 t, - ~ J / dr for rl _<r _< R (7)

The gas front velocity, ugf, then can be solved from Eq. (7) by setting rl = 0. Based on the

mass conservation, the following relation is satisfied:

7tR2.<u> = ugf.x~.2 (8)

Numerical Evaluation and Discussions

(1) Evaluation of Skin Thickness Ratio Under Isothermal Condition

Under isothermal condition, from Eq. (6) and Eq. (7) thickness ratio of skin melt becomes

~ 1 )" n+l 1 and f = ( - a P / (9& 10) R R V3n+l f ~ aZ./z=0 z~**

where f represents the ratio of pressure gradient at the gas front to that at the melt front.

For a Newtonian fluid, n = 1. Assuming f = 1 then the calculated skin thickness ratio is about

0.3, approximately close to the experimental values 0.37 and 0.34, measured by Cox [7] and

Taylor [6], respectively. For a non-Newtonian fluid, n < 1 and the predicted skin thickness ratio

will be less than 0.3. For example, if n = 0.4 then the calculated ratio is equal to 0.202. In real

gas injection molded parts, skin thickness ratio is greater than 0.37. This discrepancy indicates

that the non-isothermal molding condition, which introduces solidified melt near cavity wall,

may play an important role in determining the skin melt thickness. Besides, by changing the

pressure gradient ratio, f, skin thickness ratio also increase significantly. That f is greater than I

means that melt flow may not be fully developed due to the acceleration effect or a higher

pressure loss near the gas front region.

52 S.C. CHEN, N.T. CHENG and MJ. CHANG

(2) Evaluation of Skin Thickness Ratio Under Non-isothermal Condition

Non-isothermal molding conditions including melt temperature, mold temperature and gas

delay time were verified in order to evaluate their effect on the skin melt thickness. Near the cold

cavity wall, formation of the frozen melt will contribute to the skin melt thickness. In addition,

viscosity of the melt will also increase near cavity wall result in change in the flow velocity

profile. Due to fountain flow effect, melt temperature at the melt front is assumed to be uniform.

Melt temperature profile near the gas front is calculated using simulation codes described

elsewhere [14]. Some of the numerical results are listed in Table I. Basically, longer gas delay

time and lower mold temperature will increase skin melt thickness in consistence with the

experimental observation. For a higher melt temperature, the present model predicts a slightly

thinner skin melt. Such phenomenon was also observed in recent studies [11-13].

(3) Evaluation of Pressure Effect on Skin Thickness Ratio

Variation of skin thickness with pressure is the most complex issue. The predicted

pressure dependence of skin melt thickness from the present model is not straightforward. The

higher the gas pressure, the higher the gas pressure gradient. However, it is the ratio of the

pressure gradient at the gas front to that at the melt front which determines the variation of the

skin melt thickness. If the pressure gradient ratio (f) at low gas pressure is higher than that at

high pressure then the present model was also able to predict the decrease of skin melt thickness

with increasing pressure. The other possible contribution may result from shear stress at the

melt/gas interface. In derivation of Eq. (7) it is assuming that shear stress vanishes at the

melt/gas interface. Such an assumption was used in previous studies [6-9]. It there exist shear

stresses around the nose of gas front, then Eq. (7) becomes

u(r, z )= [R[ r ( - ~ P / (l-r~/-~ rl'lTrz(~rl)]l/ndr (1t) Jr {_21]0~ " o~ZJz~OI r2J rio r j

In such situation, the interface stress has an influence on melt velocity near the gas front. At low

gas pressure the influence from this interface stress term is unnegligible. However, when gas

pressure is increased to a high value then the interface stress term becomes less significant. As a

result, skin thickness ratio becomes independent of gas pressure. By incorporation of this term

into analysis, calculated results (Fig. 2b) show similar pressure dependence of skin melt

thickness variation on pressure.

(4) Experimental Observation of Melt Flow and Gas Penetration

To verify that if a pressure gradient difference does exist between the gas front and melt front

regions, a glass-inserted sprial mold installed with four pressure transducers was built. Through

the glass window, one can observe melt flow and gas penetration during the molding process.

SKIN MELT FORMATION IN INJF_J2TION MOLDING 53

A high speed video equipped with timer was used so that the melt front velocity and gas front

velocity can be measured. A typical pressure variation is shown in Fig. 3a. From these pressure

curves, at the switch from melt injection to gas injection, pressure within the melt is released.

Within the hollowed region cored out by gas, gas pressure is not the same. This pressure loss

may result from the stresses at the gas/melt interface. In the earlier stage of gas injection, melt

pressure rises at different speeds indicating that pressure gradient difference does exit within the

melt, melt acceleration (Fig. 3b) in the filling stage was well observed via melt velocity tracing.

(5) Discussion

Although the present model can not predict the quantitative skin thickness ratio due to the

insufficient data of stress at the gas/met interface and the different pressure gradients existing at

the gas and melt fronts, respectively, however, it does provides an advanced idea and include a

more complete consideration of contributing parameters to the skin melt formation during gas

penetration period in the gas-assisted filling stage of GAIM. In additional to the melt

temperature, mold temperature, viscosity and shear-thinning behavior of polymer melt which

were recognized as the influence parameters [11-13] on the skin melt formation, the present

investigation also found that stress at the gas/met interface and the different pressure gradients

existing at the gas and melt fronts are two very important contributing factors regarding the

formation of skin melt thickness. This indicates that stress-free boundary condition at gas/liquid

interface and steady-state assumption used in the previous models [6-11] are not suitable to

describe skin melt formation for GAIM process. The preliminary experiment in the present

study using glass-insert spiral mold does show the transient nature of the GAIM process and

verifies the present model qualitatively. A more detailed experiment via transparent tube

combined with laser tracing technique and a fully analysis of flow field around gas front are

being designed in order to conduct a further investigation leading to a complete quantitative

prediction of skin melt ratio.

Conclusions

A simple formulation based on a non-isothermal power-law fluid model is derived and

numerically solved in order to evaluate the effect of various processing parameters as well as

melt rheological behavior on the skin melt formation during gas-assisted injection molding in a

quasi-quantitative manner. This model predict a thickness ratio of about 0.3 for a Newtonian

fluid under isothermal condition. The shear-thinning behavior of melt decreases the skin

thickness ratio. The non-isothermal analysis shows that the solidified melt increases the skin

thickness ratio and the predicted dependence of skin thickness ratio on melt temperature, mold

temperature and gas delay time are consistent with experimental observations. Calculated results

54 S.C. CHEN, N.T. CHENG and MJ. CHANG

from this model also suggests that the ratio of pressure gradient at the gas front to that at the

melt front has a significant effect on the skin thickness ratio, that is, the transient nature of melt

flow caused by gas penetration may exist in actual molding process. Flow observation

experiments verify that pressure gradient difference does exist around the gas front and melt

front regions. Melt acceleration was also clearly found. The interface stresses at the melt/gas

interface, as evidenced from the gas pressure loss within hollowed gas core, may play an

important role in determining skin melt thickness especially at low injected gas pressures.

Acknowledgmcn|- This work was supported by National Science Council under NSC grant

84-2622-E033-002R.

Referencgs

1. K. C. Rush, "Gas-assisted Injection Molding - A New Technology is Commercialized",

Plastics Engineers, July, 35 (1989).

2. S. Shah, "Gas Injection Molding: Current Practices", SPE Tech. Paper, 37, 1494 (1991).

3. S. C. Chen and K. F. Hsu, "Simulation of the Melt Front Advancement in Injection Molded

Plate with A Rib of Semicircular Cross Section", Numerical Heat Transfer., part A, 28, 121

(1995).

4. L. S. Turng, "Computer-Aided-Engineering for the Gas-Assisted Injection Molding

Process", SPE Tech. Papers, 38,452 (1992).

5. S. C. Chen, N. T. Cheng and K. S. Hsu, "Simulation of Gas Penetration in Thin Plate

Designed with A Gas Channel of Semicircular Cross Section During Gas-Assisted Injection

Mold Filling Process", Int .J. Mech. Sci. , 38, 335 (1995).

6. G. I. Taylor, "Deposition of A Viscous Fluid on the Wall of A Tube", J. Fluid Mech., 10,

161 (1960).

7. B. G. Cox, "On Driving A Viscous Fluid Out of A Tube", J. Fluid Mech., 14, 81 (1962).

8. D. A. Reinelt and P G. Saffman, "The Penetration of A Finger into A Viscous Fluid in A

Channel and Tube", SlAM J. Sci. Stat. Comput., 6, 542 (1985).

9. L. W. Schwartz, H. M. Princen and A. D. Kiss, "On the Motion of Bubbles in Capillary

Tubes", J. Fluid Mech., 172, 259 (1986).

10. A. J. Poslinski and V. K. Stokes, "Gas-Assisted Displacement of a Viscous Liquid in a

Tube" SPE Tech. Paper 39,68 (1993)

11. S. C. Chen, K. S. Hsu and J. S. Huang, "An experimental Study on Gas Penetration

Characteristics in A Spiral Tube During Gas-Assisted Injection Molding", Industrial & Eng.

Chem. Res., 34, 416 (1995).

12 B. S. Burton and L. S. Turng, "General Design Guideline for Gas-Assisted Injection

Molding Using a CAE Tool", SPE Tech. Paper, 38, 421 (1994).

SKIN MELT I~RMATIObl IN INJEL-'TIObl MOLDING 55

13. H. Findeisen, "Possibility of the Prediction of Gas Penetration and the Resulting Polymer

Thickness", 1st Int. Conf. on Gas Injection Tech., November, Columbus, OH (1994).

14. S. C. Chen, N. T. Cheng and K. S. Hsu, "Simulation and Verification of the Secondary

Gas Penetration in A Gas-Assisted-Injection Molded Spiral Tube", Int. Commu. Heat &

Mass Transfer, 22, 319 (1995).

1"1 o I " ~ . C ~ G I Flew I r e ~ m / ] q l w d ] ~ m ~ 1 ~ : ~' k 4 J Flew ~ ) 4 J

(.)

M i 8

, - o ~ )

Fig. 1 (a) Schematic of gas penetration along a gapwise direction during GAIM process. (b) Schematic of melt velocity profiles around gas front and melt front.

Table I Thickness Ratio of Skin Melt Under Non-Isothermal Condition

Shear Tmelt:230*C l'hinnin8 Twall:60*C

Index tdelay 0.0 sec

f = 1.0 n = 0.4 0.3349 n = 0 . 6 n= 1.0

Tmelt:210°C Twall:60*C tdelay 0.0 sec

f = 1.0 0.3359

Tmelt:230°C Twall:40*C tdelay 0.0 sec

f = 1.0 0.3605

Tmelt:230*C Twall:60°C tdelay 0.5 sec

f= 1.0 0.3732

Tmelt:230*C Twall:60*C tdelay 0.0 sec

f = 1.1 0.4036

0.3549 0.3553 0.3708 0.3788 0.4041 0.3784 0.3808 0.3870 0.3946 0.4073

5 6 S . C . C H E N , N . T . C H E N G a n d M J . C H A N G

0

:./

0 . 3 5 •

0 . 5 0

0 . 4 3 '

0 . 4 0 '

0 . 3 5 '

spiral tube o f 6 m m d iamete r

T w ~ 6 0 " C T m 230 ° C de lay t i m e - 0 .0 sec

t a a u de lay t i m e = 0.5 ~ c

0.415 ¸

J * "

O.JS

: : : : ; f ~ l . O

dc lav 6m¢ - ! . 0 s0¢ 0,,90 0.3040 . . . . 60' . . . . 80' . . . . I00' . . . . 1:20' . . . . 1401 . . . . 160 " " " . . . . . I040' . . . . . . . . . 300' . . . . . . . . . 3M' . . . . . . . . . 404' . . . . . . . . . $410'"

Gas pressure (bar) c,~ ~ ¢ a w ) (a) Co)

Fig.2 (a)Variation of skin thickness ratio with injected gas pressure.(Courtesy of gef.[ 11]) (b)Predicted variation of skin thickness ratio with injected gas pressure.

i . i I : ~ e u r ~ a ~ R ~ on mni~aqu~ X' ~. h,da~tnd mkr~st,~ A

2 4 6 8 I0 12

|-- O " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0 IQO am 3110 481

stir i;tow L a ~ (ram)

(a) (b) Fig.3 (a)Gas (A) and melt (B,C) pressure variations in molding process at difference location. (b)Measured melt flow velocity during the filling stage.