Effects of Processing Conditions on Birefringence Development in Injection Molded Parts. II. Experimental Measurement

Polymer International 40 (1996) 251-259

Effects of Processing Conditions on Birefringence Development in Injection

Molded Parts. II. Experimental Measurement

Yung Cheng Chen," Chao-Hsun Chenb & Shia Chung Chen"*

a Mechanical Engineering Department, Chung Yuan University, Chung Li 32023, Taiwan * Institute of Applied Mechanics, National Taiwan University, Taipei, 10764, Taiwan

(Received 18 January 1996; accepted 1 March 1996)

Abstract: The birefringence of injection molded parts was measured using a digital photoelasticity system, which combines a digital image analysis technique and the half-fringe photoelasticity (HFP) method The effects of processing conditions, including melt temperature, mold temperature, filling time and packing pressure, on the birefringence development in the molded parts were investigated. It was found that temperature and pressure are the two dominant factors that determine the birefringence development in the parts during the molding process. Frozen-in birefringence of the molded parts decreases with increasing melt temperature, mold temperature and injection speed. Birefringence of the parts also increases with increased packing pressure, especially around the gate area. Numerical simulations using the Leonov viscoelastic fluid model predict similar dependence of birefringence of parts on processing conditions. Simulated results are also consistent with measured values.

K e y words: birefringence, injection molding, photoelasticity, digital image.

INTRODUCTION forced into the cavity under high pressure in order to compensate for the shrinkage due to solidification.

Injection molding is one of the most widely employed During the filling stage, polymer melt becomes solidified methods of polymer processing. As a result of the exten- near the cavity wall. The flow stresses are frozen within sive applications of plastics in all areas of industry, the solidified melt. In the subsequent packing and there is not only an increasing need for injection molds, cooling stages, these frozen-in stresses within the solidi- but also a strong demand for high quality parts. Forma- fied melt do not relax completely and appear as frozen- tion of defects in parts, such as uneven shrinkage, in birefringence and residual stress of flow-induced warpage, sink marks, residual stress and birefringence, origin. In addition, uneven temperature distribution may result from the entire history of the injection along part surfaces and in the gapwise direction may molding stages. These processing-induced defects also introduce residual thermal stress. These residual remain difficult issues to be solved from one mold stresses are one of the major factors in determining the design to the next. mechanical .properties of injection molded parts. In

The injection molding process consists of three major order to minimize residual stress in the parts, the effects stages: filling, packing and cooling. In the filling stage, of processing conditions on the formation of residual hot molten polymer is injected into the mold cavity. stress have been investigated both experimentally and Once the cavity is filled, additional polymer melt is

Experimental measurements of residual stress by * To whom all correspondence should be addressed. various methods have been r e p ~ r t e d . ~ - ~ Coxon' and

Polymer International 0959-8103/96/$09.00 0 1996 SCI. Printed in Great Britain 25 1

252 Y . C . Chen, C-H. Chen, S . C . Chen

Kubat6 measured the residual stress in plastic parts by a stress relaxation method. Only the average value of the residual stress over the whole of the part could be obtained. Siegmann et aL7 and Broutman8 applied a layer-removal technique to the solidified part. They employed a high-speed milling machine to remove uniform layers from the part surface and plotted the resulting curvatures as a function of the depth of the removed layer. The unknown longitudinal residual stress was then derived by measuring the relative curvatures along longitudinal and transverse dimensions of the plate. This was also a destructive measurement. To prevent the part from being destroyed, a photoelasticity method can be utilized. From the fringe pattern pro- duced by light interference, one can obtain the birefringence value for the part from the optical-stress relationship and photoelastic theory. Although residual stress analysis using the photoelastic technique and fringe pattern information is tedious and time- consuming, the measured birefringence can be considered as the relative residual stress distribution in the molded parts. Of all the methods of experimental stress ana ly~ i s ,~ -~ the photoelastic stress analysis method has the advantage of determining the complete stress distribution at any location in the art.^-'^ On the other hand, classic photoelasticity measurement demands materials with high birefringence, leading to an exten- sive use of plastics as a model mate~ial . '~- '~ Since the behavior of these materials is often different from that of the prototype materials, their use distorts the simi- larity relationship. In many contemporary problems this distortion is unacceptable. A new method for whole-field stress analysis called 'half-fringe photoelasticity' (HFP), was developed to overcome these problems, integrating modern digital imaging technology and classic photoelasticity. Small differences in birefringence can be resolved; this permits materials and loads to be chosen so that no more than one-half a fringe order appears in the area of interest. In addition, with the help of a modern digital imaging technique, it is possible to read-out the fringe position and the fringe order auto- matically, without the need of a compensator to allow for the optical path difference at any location in the part. 8-zo

Although HFP can provide an efficient way of examining birefringence and residual stress distribution within the molded parts, the method can only be applied to transparent materials. Therefore, it will be of great help if a simulation tool can be used to predict the birefringence in parts and the residual stress development during all stages of the injection molding process. Using these computer simulations for birefringence and residual stress, the physical origin of the residual stress formation can be understood better on a scientific basis. Numerical simulation of the frozen-in birefringence and the associated residual stresses in the molded parts using a viscoelastic fluid model, however, is a difficult

task. Recent reviews have been The major difficulty arises because of the viscoelastic nature of a polymer fluid subjected to large elastic deformation during the molding process. Among different viscoelastic models employed for the simulation of injection molding, the Leonov model seems to be more flexible and has promising capability for describing the viscoelastic nature of the polymer melt.zz-z8 In the first part of this paperz1 analysis of the injection molding process, based on the Leonov viscoelastic fluid model, has been developed to study the effects of processing conditions, including melt temperature, mold temperature, filling speed and packing pressure, on the residual stress and birefringence development in injection molded parts during the entire molding process. The simulated results may be verified experimentally. If the simulated results show good consistency with measured values, then the simulation can be applied to analyze the residual stress formation in molded parts which are not transparent.

In the present work, the birefringence of injection molded plates was measured using a half-fringe photoelasticity system and the digital image analysis technique. The effects of various processing conditions, such as melt temperature, mold temperature, filling speed and packing pressure on the birefringence development in the parts were investigated. All experimental results were compared with simulated predictions calculated by the Leonov viscoelastic fluid model, details of which are reported elsewhere.z1

BI R EFRl N G EN CE M EASU R E M ENT SYSTEM

Birefringence and stress-optical relationship

When the refractive index for a material in one direction of polarization is different from that in another direction, the material is said to be birefringent, or double refractive. If stress is applied to an isotropic material, the stress produces an index ellipsoid with a refractive index change as follows:

n, = nj = aa, + b(aj + ak) for i,j, k = 1, 2, 3 (1)

where a', r rz and a3 are the principal stresses, that is the stresses in the direction of the principal axes, and n, is the refractive index experienced by a light wave pol- arized in the direction of principal axis i. By taking the difference between the two axes i andj, one obtains

n, - nj = (a - b)@, - oj) = C(ai - r r j ) (2)

where C is the stress-optic coefficient. This is also known as the 'stress-optical law'. It can be seen that the change in the index of refraction is proportional to the difference in the principal stress. The stress-optic coefficient is usually measured in Brewsters (Br):

1 Br = 10-lz(N/mZ)-l = lo1' Pa (3)

POLYMER INTERNATIONAL VOL. 40. NO. 4, 1996

Birefrigence development in injection molded parts. 11 253

Photoelastic theory the relationship

(1 1) Z = BIY

where B is a proportionality constant and y is the slope of the CCD camera sensitivity curve. To calibrate the system for photoelasticity, a reference intensity I , is introduced; eqn (6) is rewritten to incorporate this reference intensity for a particular model polariscope com- bination. As a result, eqn (1 1) becomes

Z = BIIo sin’(N~)]~ (12) To obtain the relationship between fringe order N and gray level Z, the procedure reported previously was fol- lowed.” From eqn (11) the maximum response of the system is

zm, = BIkm (13)

Therefore

For a two-dimensional problem, the stress-optic law of linear elastic stress birefringence is

where A is the relative retardation for the light at normal incidence to the plane of the sample, al and a2 are in-plane principal stresses, d is the thickness in the propagation direction of the light, c is the relative stress-optic coefficient in Brewsters, and C is the stress- optic coefficient. Equation (4) can be rewritten as

( 5 )

where N (= A/2n) is the relative retardation in terms of complete cycles of retardation, f, (=IZ/c) in units of number/fringe-my when m is the material’s fringe value or the photoelastic fringe constant.

In a dark field circular polariscope set-up, the intensity of the transmitted light emerging from the analyzer is

(6) A 2

I = I , sin’ - = I , sin’(Nn)

where I , is a constant. Hence, extinction occurs when I = 0, i.e. when

(7) A - = Nn for N = 0, 1, 2, 3, . . . 2

The resulting dark lines are called isochromatic fringes and the corresponding numbers are called full fringe orders. For these values, N is always an integer.

In the light field set-up for a circular polariscope, the intensity is given by

A 2

I = I , COS’ -

Hence, extinction occurs when I = 0, i.e. when

n for N = 0, 1, 2, 3, ... (9) A 2 N + 1 2 2 -

or

These are often called ‘half-order’ fringes. In the present fringe measurement, the dark field circular polariscope set-up was utilized.

Calibration of the image analysis system

In the image analysis system, the digital output value, or the gray level, Z, is related to the light intensity, I , by

For a selected half-fringe interval, N,, = 1/2 and sin(N,, n) = 1 ; eqn (14) becomes

L -- ‘7 - [sin(Nn)lZy

or

A set of values of N and Z can be obtained by employ- ing the Tardy compensation method’* on an unloaded specimen. The least squares method is then used to establish the parametric relationship between N and Z. An ifitercept term, A, will normally be introduced to account for the least squares fitting process. The relationship between fringe order N and gray level Z can be written as

If the digital photoelasticity method is applied to find the fringe order N at a specific part location, the corresponding birefringence is then given by

NIZ An =-

d

PROCESS FORMULATION AND NUMERICAL S I M U LATlO N

The mathematical modeling and the assumptions used for the simulation of the injection molding process are basically similar to those of previous The relevant components of the governing equations for continuity, momentum and energy describing the injection molding of a simple plate in terms of the Hele-


254

TABLE 1. Material properties of polystyrene

Y. C. Chen, C-H. Chen, S. C. Chen

Shaw flow model are

1. Thermal properties

2. Rheological properties (Leonov viscoelastic model) at 463 K p = 940 kg/m3; C, = 21 00 J/(kg K) ; K, = 0.1 5 W/(m K)

N = 2; s = 0.09; 8, = 0.8s; 8, = 0.027 s; qo = 7000 Pas; /I, = 5440 Pas; q2 = 1500 Pas; T, = 373 K; Tref = 407 K; C, = 20.378: C2 = 101.6 K

P = 186 MPa; 3. Constants in Spencer-Gilmore type PVT equation of state

= 1 220kg/m3; f i = 80 J/(kg K)

where t is the time, p the density, C, the specific heat, K the thermal conductivity, P the pressure, T the temperature, z is the gapwise direction, z,, the shear stress in the x direction and U the gapwise injection speed in the x direction. The term $h is the dissipation function defined e l~ewhere .~~

The constitutive equations used for the analysis com- prise the Leonov viscoelastic model described by

1

N q k

' l o = c - k = l (l - s,

where qo is the zero-shear-rate viscosity, q k is the shear viscosity of the kth mode, e k is the relaxation time of the kth mode, s is a rheological constant (0 < s -= l), z is the stress tensor and Ck is the elastic strain tensor of the kth mode. For self-consistency there is a constraint on c k

such that

det[Ck] = 1 (25)

The temperature dependence of qo , q k and e k is based on the Williams-Landel-Ferry shift factor aT , namely ek(T) = ek(TO)aT/aTo and qk(T) = ?k(TO)a?'/aTo 3 where

Tef is the reference temperature, sition temperature, and C, and C2 are constants.

is the glass tran-

Since the polymer melt is considered to be compress- ible, the change of melt density should follow a PVT (pressure-volume-temperature) relationship. In this study, the Spencer-Gilmore type PVT equation is used and is given by

where p, 9 and ff are constants. Once the pressure, the velocity, the shear rate, the elastic strain tensor and the stress tensor have been calculated, the first normal stress difference NiF, the shear stress z,, , and the corresponding birefringence ANF of flow-induced origin in the x-z plane are computed according to the following equations :

ANF = CAT = C[NfF + 4~:,]"~ (30) where C is the stress-optical coefficient taken16 as a value of 4.8 x m3/N. The thermal-induced stresses are formulated under a plane strain condition, i.e. assuming that E, = 0, E,, = 0 and E,, = 0. As a result, the stress-strain relation can be described by

c fi

z x x = [(l - V)E, + VE, - E j - ] 1 - v - 2v2

E 1 - v - 2v2 [YE, + (1 - V)E, - ET] T,, =

E zxz = ___

2(1 + v ) (33)

where v is Poisson's ratio, E is Young's modulus, CI is the thermal expansion coefficient and AT the temperature difference. Stress zyy also exists. However, it does not contribute to the birefringence formation of thermal origin in the x-z plane. The stresses in eqns (31)-(34) are solved using the principle of virtual work." The first normal stress difference NIT and the corresponding birefringence ANT, resulting from thermal


Birefrigence development in injection molded parts. II 255

*

unit : mm

Fig. 1. Geometry of the injection molded plate.

stresses, are therefore expressed by

NIT = (Txx - Tzz)T

ANT = CAT = C[NfT + 4~:,]"~ (35) (36)

In the present case, ANT is about one to two orders of magnitude lower than ANF under even cooling condi-

Light So

- 1 Analyzer 2 Quarter-Wave Plate 3 Polarizer

0 TVMonitor LJ I

0

Fig. 2. Schematic diagram of the half-fringe photoelastic system used for birefringence measurements.

tions for both sides of the mold cavity walls. Therefore, the measured birefringence is assumed to be of flow- induced origin. In order to compare the simulated results with measured birefringence, gapwise averaged values of ANF along the flow direction were computed. Detailed mathematical procedures for this have been r e p ~ r t e d . ~ ' . ~ ~ All the material constants required for the simulations are listed in Table 1.

EXPERIMENTAL

A one line gated plate mold giving a specimen of 2mm uniform thickness, as shown in Fig. 1, was built to

Fig. 3. (a) Fringe pattern of part molded without applying packing pressure. (b) Fringe pattern of part molded with 18MPa packing pressure. (c) Fringe pattern of part molded with 40MPa packing pressure. (d) Fringe pattern of part molded with

61.5 MPa packing pressure.


256 Y . C. Chen, C-H. Chen, S. C . Chen

Fig. 4. (a) Fringe pattern of part molded under 210°C melt temperature. (b) Fringe pattern of part molded under 230°C melt temperature. (c) Fringe pattern of part molded under 250°C melt temperature.

conduct the process studies. A 75 ton Battenfeld 750/750 co-injection molding machine was used for the present experiments.Transparent polystyrene (CHI MEI/PG- 33) was utilized as the material. The injection melt temperatures were 210, 230 and 250°C. Mold temperatures were 25,45 and 65°C. Filling times used were 0-48, 1-41 and 2.5 s. The packing and holding pressures were also varied from 0 MPa to 61.5 MPa.

A schematic diagram of the half-fringe photoelasticity system is shown in Fig. 2. The system consisted of a regular polariscope with a radiation source of Na light having a wavelength of 589.31~11. Two polarizers ( D = 400mm) formed a basic plane polariscope, A CCD (type SP475B) camera was placed behind the polariscope to scan the image field and a digital computer was linked to the camera so that the gray level Z could be obtained for analysis. The system was set up and calibrated according to the procedures reported by Vol- oshin 8z Burger.'*

RESULTS

Figures 3a-3d show the fringe patterns photographed by the polariscope for parts molded under packing pres-

sures of 0 MPa, 18 MPa, 40 MPa and 61.5 MPa, respec- tively. The fringe patterns for parts molded under 210, 230 and 250°C are shown in Figs 4a-4c. From these fringe patterns, the gapwise-averaged birefringence distribution along the melt flow direction can be obtained by digitial image analysis. Figure 5 shows the gapwise- averaged birefringence distribution along the flow direction for parts molded under different injection speeds

- 0 0 2 3.0 X

0)

- 2 ; 2.0 .- h c h s

2 P w 1.0 M

> I e ,i O'O

U

Tmelt=ZlO *C 3 \ h a l l = 25 *C Packing Pressure = 39.7 MPe

4 20 40 60 80

Distance from gate(mm) 0

Fig. 5. Distribution of the gapwise-averaged birefringence An along the flow direction for different injection speeds.

POLYMER INTERNATIONAL VOL. 40, NO. 4, 1996

Birefrigence development in injection molded parts. II 257

0 0 9 3.0 A I -

Fill lime =l .41 sec Paekin; Pressure = 39.7 MPa Wall Temperature = 25 ' C - h e l t = 2 l 0 *C - j ~ e l t = 2 3 0 - Tmelt=ZBO 'C

0.0 j I 80 I00 'g 0 20 40 60

0 5 Distance from gate(mm)

Fig. 6. Distribution of the gapwise-averaged birefringence An along the flow direction for different melt temperatures.

corresponding to filling times of 0-48, 0.71 and 1-41 s. As the filling time increases, the birefringence also increases. The smaller the filling time, the higher the averaged melt temperature at the end of the filling process. As a result, the birefringence value is also lower. In the filling process, hot melt enters the mold cavity. Once the melt contacts the cold cavity wall, the

.y LL 0.0 40 80 80 100 t o 20

4 Distance from gate(mm) 0

Fig. 7. Distribution of the gapwise-averaged birefringence An along the flow direction for different mold temperatures.

/\\;:I. - Paeking kz:E:?8.0 Pressure=3S.7 - Packing Preasure=61.5

Filling Time = 1.41 sec

01 .y 0.0 .........,-. < . . , . . X I , . . . , . . , . .

20 40 80 80 t 00

Distance from gate(mm) L o 0

Fig. 8. Distribution of the gapwise-averaged birefringence An along the flow direction for various packing pressures.

0.0 0.0 0.2 0.4 0.6 0.8 1 .O

,

(b)

Filling Time = 1.41 sec Trnell = 230 *C

U

P l.oc 0.0

0.0 0.2 0.4 0.6 0.8 0

z/b

Fig. 9. (a) Simulated distribution of birefringence An along the gapwise direction at the end of the filling, packing and cooling stages at location 3 for the case of 210°C melt temperature. (b) Simulated distribution of birefringence An along the gapwise direction at the end of the filling, packing and cooling stages at location 3 for the case of 230°C melt tem-

perature.

melt starts to cool down. The solidified thickness increases as the contact time with the mold wall increases. Due to the fountain flow effect at the melt front and the small flow length of the present experimental part, the averaged melt temperature in the

0

D Distance from gate(mm)

Fig. 10. Comparison of the simulated and measured distribu- tions of the gapwise-averaged birefringence An along the flow

direction for different injection speeds.


258 Y . C . Chen, C-H. Chen, S . C . Chen

1 W ip\ .!? 0.0 L O 20 40 KO 80 100 a m Distance from gate(mm) 0


direction for different melt temperatures.

gapwise direction varies only slightly along the flow direction. Near the gate area (position 2), the thickness of the solidified layer is larger than that away from gate area (position 6) [see Fig. 11. Therefore, the velocity

- 0 0 0 1.2

X

Y

- - : 2 0.8 .- L 01

z

2 P w 0.4 M

2

I W

2 0.0

& V

Distance from gate(mm)


direction for different mold temperatures.

a

X

2 2.5 - e 2.0

E P

L. 1.5 L W

.I

z 1.0

P W M

k 0.5 m

m W .z 0.0 F

CI k2

Si la td PaddngPrerrure 0 MPa S i ' P w P r e r r u r e l 4 MP. Mcasurcd:P.ckioePrc~urr 0 MPa Marud.packjngPnuureI4 YPS

Melt temperature = 210 'C W m I I temperature = 25 'C Filling Time = 1.41 sec

m

0 20 40 60 80

Distance from gate(mm)


direction for various packing pressures.

profile at position 2 becomes more sharply delineated with an increase in the maximum value at the gap center. Thus, the associated shear stress and shear rate as well as the birefringence values also increase. As a result, birefringence of the part decreases with increasing distance from the gate. Figure 6 shows the gapwise- averaged birefringence distribution for parts molded under different melt temperatures. The higher the melt temperature, the lower the birefringence value. The same situation occurs for variation of mold temperature, as seen in Fig. 7. Figure 8 shows the effect of the applied packing pressure on the birefringence distribution. As the packing pressure increases, birefringence of the part also increases. However, the effect is more significant around the gate area, as seen by the increase of the fringe pattern strips in Figs 3a-3d. This is because there exists a pressure drop in the flow direction within the mold cavity. As a result, a location near the gate area is subjected to a larger molding pressure than that away from the gate. In addition, the part located near the gate area becomes solidified later than that away from the gate. Therefore, flow-induced residual stress is more concentrated around the gate area. Generally speaking, temperature and pressure are the two dominant factors that determine the birefringence development in the part during the molding process.

Figures 9a and 9b show two typical examples of the simulated birefringence distribution in the gapwise direction at part location 3. The gapwise birefringence development at the end of the filling, packing and cooling stages of the injection molding process are illustrated. A detailed picture resulting from the simulations of the gapwise birefringence development at different part locations and at different molding stages was described in the first part of this paper." Figure 10 shows a comparison between the simulated and the measured dis- tributions of the gapwise-averaged birefringence for parts molded at different injection speeds. Simulation shows a similar effect of the injection speed on the birefringence distribution. Simulation also shows a similar dependence of birefringence on the variation of melt temperature, mold temperature and packing pressure, as illustrated in Figs 11-13. All the simulated results show fairly good agreement with the measured birefringence values from the engineering application viewpoint. The only slightly large difference occurs for the case of molding under a very large packing pressure.

CONCLUSIONS

Birefringence in injection molded parts was measured using a polariscope and a digital image analysis system. The effects of various processing conditions including melt temperature, mold temperature, filling time and packing pressure on the birefringence development in


Bireffigence development in injection molded parts. I1 259

the molded parts were investigated. The experimental results were compared with numerical predictions obtained from simulations. The following results were found. 1989 Chapter 2.

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1 Isayev, A. I. 8~ Upadhyay, R. K., in Injection and Compression Molding Fundamentals, ed. A. I. Isayev. Marcel Deker, New York,

The half-fringe photoelasticity method and the digital image analysis technique provide an efficient way for the birefringence measurement of parts. The present method permits materials and loads to be chosen so that no more than one-half a fringe order appears in the area of interest. It also requires no compensator to allow for the optical path difference at any location in the part. It was found that temperature and pressure are the two dominant factors that determine the birefringence development in the part. Frozen-in birefringence of the molded part decreases with increasing melt temperature, mold temperature and injection speed. Birefringence in parts also increases with increasing packing pressure, especially around the gate area. Gapwise-averaged birefringence decreases with increasing distance from the gate. Around, the gate area the hot melt is in contact with the cold cavity wall longer than away from the gate in the filling stage. Thus, the solidified melt is thicker near the gate, resulting in a larger flow stress and a corresponding beirefringence value. In the post-filling process, there exists a pressure drop in the flow direction within the mold cavity. As a result, a location near the gate area is subjected to a larger molding pressure than one away from the gate. In addition, a part located near the gate area becomes solidified later than one away from the gate. Therefore, flow- induced residual stress is more concentrated around the gate area. Simulation of the injection molding process based on the Leonov viscoelastic fluid model was performed to predict the birefringence development of the molded parts throughout the entire stages of the molding process. Numerical simulations showed a similar dependence of birefringence of parts on processing conditions. Simulation results were also consistent with measured values.

ACKNOWLEDGEMENT

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Documents

Effects of Processing Conditions on Birefringence Development in Injection Molded Parts. II. Experimental Measurement