An experimental study on the effects of injection ... - Springer Link

Korea-Australia Rheology Journal Vol. 23, No. 3, September 2011 pp. 155-162 DOI: 10.1007/s13367-011-0019-1

An experimental study on the effects of injection-molding types for the birefringence distribution in polycarbonate discs Inki Min and Kyunghwan Yoon* Department of Mechanical Engineering, Dankook University, 126, Jukjeon-dong, Suji-gu, Yongin-si, Gyeonggi-do, 448-701, Korea (Received April 15, 2011; final version received June 29, 2011; Accepted June 30, 2011)

Abstract Even though injection molding technology has been developed for many years, it is still needed to study the effect of processing conditions on the final properties of injection–molded parts for producing precision products in optical field. The optical anisotropy, i.e., birefringence, is a significant factor which affects the function of many optical components. In the present study, we have focused on the effects of packing and compression processes on the birefringence structure remaining in the disc by examining the gap-wise distribution of birefringence and extinction angle. As a result, two extra birefringence and extinction peaks near the center in thickness direction showed the effect of packing pressure, which came from the extra flow during packing stage. Furthermore, more uniform birefringence distribution was found in injection/compression case than in conventional injection-molded case. Depending on the process condition, even the reversal flow was found from the distribution of extinction angle in injection/compression case. Finally, graphical representation technique of optical refractive indicatrix was suggested to show the difference of final birefringence structure for different process types. Keywords : injection molding, injection/compression molding, birefringence, optical indicatrix

1. Introduction Injection molding process has been widely used to manufacture not only macro scale products but also precision parts with micro features. Furthermore, injection molding is broadening its scope from home appliances to optical products, for example, micro camera lenses, DVDs, Blueray media, pick-up lenses, f-θ lenses and LGPs. There are merits in plastic products such as light-weight and inexpensiveness. In addition transparent plastic materials have been applied to 3D displays and home appliances to improve many functions and aesthetic view. Hence, plastic products are on the way of substituting for many metallic and glass products. In a manner managing optical stability is critical because defects can be seen easily with human eyes in the appearances inspection. A representative optical characteristic optical anisotropy is birefringence, which can cause noise and wrong signal in digital information transfer. Therefore, the effects of injection-molded processing types on the birefringence structure should be studied to minimize the birefringence level in the final product. The residual birefringence can be classified into two parts, one is flow-induced birefringence occurring while *Corresponding author: [email protected] © 2011 The Korean Society of Rheology and Springer

Korea-Australia Rheology Journal

the polymer is injected into the cavity(filling and packing phase) and the other is thermally-induced birefringence occurring in the cooling stage(Shyu, 1993; Lee et al., 2002, a, b). The residual flow-induced birefringence usually develops due to the incomplete relaxation of polymer chains deformed in the filling and packing stage. Meanwhile, residual thermally-induced birefringence originates from the non-uniform cooling before and after ejection from the mold. In many previous literatures they adopted Leonov model as viscoelastic constitutive equation in analyzing the birefringence numerically(Isayev and Hieber, 1980; Lee et al., 2002, a; Lee and Isayev, 2007, Weng et al., 2009). Isayev and Hieber(1980) showed numerical results of the flow-induced residual stresses and birefringence distribution in gapwise direction for a parallel plate during the filling and cooling stages using the Leonov model. Their process can be classified as injection-only, namely, there was no packing pressure applied after filling. The relaxation process of residual flow-induced stresses and birefringence was explained well without consideration of thermally-induced part. Lee et al.(2002) proceeded the numerical simulation further for the injection or injection/compression molding process including compression process to predict the residual stresses and birefringence in a center-gated polystyrene disc by employing the Leonov model. The predicted birefringence showed the effect of

September 2011 Vol. 23, No. 3

155

Inki Min and Kyunghwan Yoon

packing and compression reasonably. However, thermallyinduced stresses and birefringence was calculated separately. Lee and Isayev(2007) also showed the effect of compression for the final flow-induced birefringence in injection/ compression molded discs. Weng. et al.(2009) predicted the in-plane direction birefringence and residual stress in a PMMA micro-lens using a commercial code, Moldflow, in various injection molding conditions. Recently, Kim(2009) showed the effects of compression and co-injection on the birefringence structure by experiments and numerical simulation. However, compression process was used for filling which is somewhat different from the process used in the industry. Although there have been extensive researches on birefringence distributions, good experimental data showing comparisons between different injection molding processes are still needed. In the present study, gapwise birefringence distributions will be shown for polycarbonate discs made by four different injection molding types, namely, injection-only, conventional injection molding, injection/ compression with or with packing, respectively. Finally, a new graphical technique was introduced to show the gapwise distribution of residual birefringence using optical indicatrix.

2. Theory 2.1. Injection/Compression molding Conventional injection molding is one of the most popular processes in plastic industry, and it consists of three stages, i.e., filling, packing and cooling stages. The polymer melt of high temperature is injected into the cavity of cold mold through the gate at high speed in filing stage. For compensating the shrinkage during solidification packing pressure should be applied after the end of fill. Extra material is forced into the cavity during the packing stage. Then the gate freezes and injection-molded part should be cooled down sufficiently during the cooling stage. High molecular orientation and optical anisotropy generated during the filling and packing processes is major disadvantages to be overcome. The technique substituting the packing stage to compression of the mold was proposed and showed many advantages. The reduction of clamp force and uneven shrinkage are the major ones. In injection/compression molding (ICM) process, initially the mold cavity is set to be larger than the nominal thickness of the part, δ, before the polymer melt is injected into the cavity, and the mold is completely closed by pressing the movable part after the cavity is partially or fully filled with molten polymer. Injection/Compression molding can be classified into two types of compression method depending on the mold structure as shown in Fig. 1. 156

Fig. 1. Two different types of Injection/ Compression Molding ; total compression(a), partial(core) compression(b).

The total compression or injection-press molding process has the mold structure as shown Fig. 1(a). The total movable mold-half should be controlled by the clamping mechanism of injection molding machine. On the other hand, the core compression molding process has the mold structure to press the polymer using a movable core while the mold is in closed position. Usually this moving core has separate source of movement and control unit. In conventional injection molding, the molded parts are exposed to high pressure near the gate and the pressure effects decrease far from the gate. Hence anisotropic distribution of the deformation and shrinkage of the final parts are not avoidable in conventional injection molding process. The distribution of birefringence in injection-molded polystyrene and polycarbonate discs and the pressure history showed the uneven effects in our previous paper(Yoon, 1995). The peak values of flow-induced birefringence formed during filling and packing stage decreased away from the gate in radial direction. However, in case of the injection/compression molding, the polymer is injected into thicker cavity because of initial open distance(δ). Then, the polymer could experience lower shear stress and strain rate than those in conventional injection molding. It is the main source of reduction for flow-induced orientation of polymeric material and maximum clamping force required. The uniform distribution of pressure applied in compression stage another merit in injection/compression molding. It has been shown to improve the dimension stability, transcription characteristics (Chen et al., 1998; Lee et al., 2002; Min et al., 2006; Weng et al., 2009).

2.2. Photo-elasticity, birefringence and optical indicatrix In 1816 David Brewster found that even the isotropic material could change its structure of refractive index to be anisotropic under the application of stress(JaneschizKorea-Australia Rheology Journal

An experimental study on the effects of injection-molding types for the birefringence distribution in polycarbonate discs

Kriegl, 1983). It is called linear photo-elasticity, and the difference of refractive index is proportional to the difference of principal stresses. The linear photo-elastic theory can be written as follows: ni – nj = C ( σi – σj )

(1)

where i, j, k=I, II, III and i ≠ j ≠ k And σI, σII, σIII represent the principal stresses in the direction of three principal axes, ni is the refractive index experienced by a light wave polarized in the direction of principal axis i, C is the (relative) stress-optical coefficient(SOC). This linear stress-optical relation has been tested and verified in wide range of conditions for various polymeric materials(Janeschiz-Kriegl, 1983). The stressoptical coefficient of polycarbonate(PC) used in this experiment is known as about 3,500~3,700 Br(1Br = 10−12 Pa−1) at melt state, that is, at the temperature of much higher than glass transition temperature and about 60~70 Br in glassy state. On the other hand, the stress-optical coefficient of polystyrene(PS) is known as about -4,800 Br at melt state, and about 8~10 Br in glassy state (Janeschiz-Kriegl, 1983; Baumer, 2010). Because of the difference for the ratio of SOC’s between melt and glassy states polystyrene has been widely used to study the flow-induced birefringence in injection-molded parts(Isayev and Hieber, 1980; Lee et al., 2002; Lee and Isayev, 2007). Fig. 2 shows the state of stresses imposed on a fluid element under the simple shear case and the representation of familiar Mohr’s. The refractive index tensor can be represented with Mohr's circle by applying the linear stressoptical relation as shown in Fig. 2(b). The angle between principal axes I, II and coordinate axes 1, 2 is called as the extinction angle χ. The relation between the maximum refractive index difference n and the extinction angle χ can be written as follows; ∆n sin 2χ = 2n12 = 2Cσ12

(2)

∆n cos 2χ = n11 – n22 = 2C ( σ11 – σ22 )

(3)

2

∆n = C ( σ11 – σ22 ) + ( 2σ12 )

2

(4)

Fig. 2. Stress distribution on the fluid element of stresses for the simple shear case (a). And Mohr’s circle representation for the stress field and the index of refraction tensor for positive C(b).

If the sign convention of stress optical coefficient is kept, more precise expression is as follows; 2 2 σ 11 – σ 22 ∆n = C ( σ11 – σ22 ) + ( 2σ12 ) -------------------σ11 – σ22

(5)

If the dependency of stress optical coefficient on temperature and time were considered, so called, photo-viscoelastic theory should be considered (Shyu, 1993). On the other hand, an optical anisotropic structure of substance can be described with indicatrix as in the crystal model. The general biaxial crystal shows the optical anisotropy due to the different light velocity depends on the vibration direction(Hecht, 1987), and the structure can be represented with an ellipsoid as shown in Fig. 4. The nI, nII and nIII represent the refraction indices of light vibrating in the X, Y and Z direction, respectively. The equation of biaxial indicatrix can be written as follows;

Table 1. Process conditions of four different cases Fill time (sec)

Packing Pressure (MPa)

Compression (MPa)

Mold temp.

Melt temp.

( C)

( C)

None

None

75

2.0

None

75

case 1 case 2

o

0.5

o

Remarks Injection Only Injection + Packing

320

case 3

None

2.0

75

Injection + Comp.

case 4

2.0

2.0

120

Inj. + Pack + Comp.



157


Fig. 3. Graphical representations of biaxial indicatrix(a) and 2dimensional indicatrix ellipse(b). 2

2

2

Y- -----Z X ----2- + ---+ 3- = 1 2 nI nII nIII

(6)

This ellipsoid forms three symmetric elliptic surfaces in the XY, XZ and YZ plane as shown in Fig. 3(a). Using this projected ellipsoid in the XY plane, an elliptic shape of refractive indices can represent the distribution of index depending on vibrating direction as shown in Fig. 3(b). Extinction angle χ can be defined as the angle between the principal axes X-Y and coordinate axes x-y as shown in Fig. 2(b). In the present paper the gapwise distribution of birefringence and extinction angle is presented graphically using those ellipses. At each point in thickness direction the length of long axis was defined as ‘a’ and that of short axis as ‘b’. Because the difference of refractive index or birefringence was so small that scale factor α was introduced. The value of α used in this paper was 50,000. a – b = α( nI – nII )

(7)

It is also noted that various values of scale factor was tested and the length of short axis was fixed for better understanding of the gapwise distribution of birefringence and extinction angle.

3. Experiments 3.1. Instruments and injection molding types for the experiment Injection and compression molding experiments were conducted with VDCII-IC(Jin-Hwa Glotech) and NH50 (Nissei) injection molding machines. Both of those include core compression function, 50 ton of clamping force, the maximum injection pressure of 2,912 kgf/cm2, and the maximum injection flow rate of 256 cm3/s. PC(polycarbonate, Teijin Chemical, AD-9502) was used in the experiment. For the pre-process resin was dried for 4 hours. The cylinder temperature was set at 320oC, and both of moving and stationary mold parts were set at the same temperature. The initial injection molding condition was set up through the short shot test, such as injection speed, packing pres158

Fig. 4. The geometry and coordinate system of a disk sample.

sure and shot volume. In the present study process conditions for four different process types are summarized in Table 1. For the first three cases, the injection time was 0.5 second, melt temperature was fixed at 320oC and the mold temperature were set at 75oC. The mold temperature was set at 120oC for the case #4, exceptionally. The process type chosen for case #1 was injection-only process, namely, there was no packing pressure or compression after the filling process. Case 2 was the conventional injection molding process with constant packing of 2.0 MPa applied for 3.0 seconds after the end of fill. From this case the effect of packing pressure on the residual birefringence can be found easily. Case 3 is the experiment related to the compression effect, only the compression pressure of 2.0 MPa was applied for 3.0 seconds after the end of fill with the mold open 0.1 mm. Compression pressure was set at the same value of packing pressure of case #2. This type of process was chosen to find the effect of compression on the structure change of residual birefringence distribution in thickness direction. Finally, in case #4 both the packing pressure of 2.0 MPa for 0.5 second and the compression pressure of 2.0 MPa for 3.0 seconds after the end of fill were applied after injection with a higher mold temperature. This final type of process was chosen to emulate the condition of mass production of discs in commercial product line. For the case 4 NH50(Nissei) was used for faster control of switch over between packing and compression, which could not be achieved with VDCII-IC(Jin-Hwa Glotech). In addition, mold temperature was set at 120oC to match the commercial process.

3.2. A sample geometry As shown in Fig. 4 the geometry of disc sample is 43 mm in radius and 1.2 mm thick. The samples were cut in radial direction with a diamond saw(Buhler) and were polished with two different types of polishing clothes. The Korea-Australia Rheology Journal


Fig. 5. Gapwise distribution of birefringence ∆n (a) and extinction angle (b) of case 1 at various radial locations (Extinction angles are shifted by 50 degrees).

Fig. 6. Gapwise distribution of birefringence ∆n (a) and extinction angle (b) of case 2 at various radial locations(extinction angles are shifted by 50 degrees).

distribution of birefringence in gapwise direction was measured with a polarizing microscope(Nikon) at five different radial locations, namely, 2.0, 2.5, 3.0, 3.5, 4.0 cm from center. The distribution of birefringence and extinction in gapwise direction was shown as an abscissa with z/h, where h was taken as half-gap thickness of the disc in z axis in Fig. 4. The extinction angle was represented by shifting 50 degrees to show in a graph.

From differential cooling process skin layer cools first and center layer cools later. It forms residual compression near skin and extensional stress near center. The birefringence peaks near the wall(z/h = ±1) came from another source, namely, flow-induced stresses(Isayev and Hieber, 1980; Lee et al., 2002; Lin, 2009). Fig. 5(b) describes the extinction angle in gapwise direction at each measured position. Near the center position(z/h = 0), the extinction angle is almost zero because the shear stress was relaxed to almost zero at all radial positions. As predicted by Isayev and Hieber(1980) the value of birefringence decreases as radial location increases.

4. Experimental Results 4.1. Case 1 (Injection-only process) Fig. 5 shows the birefringence and extinction angle distributions for the process type of injection-only case. In Fig. 5(a), the birefringence distribution forms a parabolic curve near the center in thickness direction and has the peak value of 6.3 × 10−4 at z/h = 0. This kind of parabolic distribution is well known and can be explained with thermally-induced residual stress distribution for freely quenched experiment and numerical simulation(Wust and Bouge,1983; Shyu, 1993). Korea-Australia Rheology Journal

4.2. Case 2 (Injection and packing; conventional injection molding) Fig. 6 shows the distribution of birefringence and extinction angles of case 2. Conventional injection molding process was applied with constant packing pressure after filling. Compared with case 1 in Fig. 5, case 2 shows extra birefringence peaks near z/h= ±0.5, which represent apparent effect of extra flow and stresses during packing pro-


159


Fig. 7. Gapwise distribution of birefringence n (a) and extinction angle (b) of case 3 at various radial locations (Extinction angles are shifted by 50 degrees).

Fig. 8. Gapwise distribution of birefringence n (a) and extinction angle (b) of case 4 at various radial locations(Extinction angles are shifted by 50 degrees).

cess. The extinction angle shows more distinct difference, namely, the remaining peak values can be found about 25 degree at |z/h| = 0.4~0.6, which cannot be found in case 1. Even though the relaxation of stresses the additional flow and stresses occurred at low temperature during packing phase affects the structural change of residual birefringence(Lee et al., 2002; Lin, 2009). The effect of packing decreases as the distance from the gate increases, which can be seen easily from the data at r=4.0 cm.(Yoon, 1995) It is also noted that the peak values near the wall induced from filling phase are similar to injection-only case. Furthermore, the birefringence values at the center(z/h=0) in thickness direction are almost the same as the ones of case 1.

angle the values were stayed less than 5 degrees at most radial locations similar to the results of case 1. Of course this kind of birefringence structure cannot be said to be universal. However, it can be concluded that the effect of compression process would reduce the double peak and high orientation in molded product. It is also noted that the shape of birefringence distribution except near the wall is not parabolic.

4.3. Case 3 (compression only after filling) Fig. 7 shows the distribution of birefringence and extinction angles of case 3, where only the compression pressure of 2.0 MPa without packing was applied after the end of fill. In comparison with previous experimental results of case 2 quite constant distribution of birefringence can be found except near the wall. In the distribution of extinction 160

4.4. Case 4 (both packing and compression applied after filling) Fig. 8 shows the distribution of birefringence and extinction angles of case 4. Both packing and compression pressures were applied sequentially with a higher mold temperature 120oC. By increasing the mold temperature to 120oC both the flow-induced birefringence near the wall and the birefringence at the center were reduced remarkably as shown in Fig. 8(a). After applying the compression process, the birefringence pattern has changed more uniform at radial locations of 2.5 cm, 3.0 cm and 3.5 cm. It is interesting that the double peaks were found clearly at the Korea-Australia Rheology Journal


Fig. 9. The optical indicatrix representation of birefringence and extinction angle distribution of cases 1~4 corresponding to Figs. 5~8.

nearest(r=2.0 cm) and farthest(r=4.0 cm) radial locations from the gate. In the distribution of extinction angles in Fig. 8(b) the change of sign at farthest(r=4.0 cm) location was found compared with the result at r=2.0 cm, it is clear that reverse flow occurred near the end of the cavity during the final compression process(Isayev, 1987; Lee et al., 2002).

magnitude of birefringence, and the angle of long axis for each ellipse represents extinction angle. The effect of packing and compression could be found easily with this graphical technique, especially the sign change of extinction angle could be identified clearly through the ellipse angle change in case 4.

5. Conclusions 4.5. Grapghical representation of bi-refringence with optical ellipses Finally, the distributions of birefringence and extinction angle in gapwise direction for four different process types were shown in Fig. 9, which include optical ellipse explained in Fig. 3. In Fig. 9 the amount of aspect ratio or the length of the long axis of each ellipse represents the Korea-Australia Rheology Journal

In the present study, the goal was to find the effect of different injection molding process types on the birefringence distribution in optical disc experimentally. From the measurement of gapwise distribution of birefringence and extinction angle, the followings were concluded; 1) In injection-only case the birefringence pattern showed


161


a parabolic shape except near the wall. Parabolic pattern is from thermally-induced stress and the peak values near the wall is induced from flow-induced stresses during filling phase. 2) In the case where packing pressure was applied after the end of fill clear extra double peaks of birefringence were found in the middle zone, which are formed by additional flow after the end of fill. 3) The birefringence pattern showed nearly uniform value in gapwise direction when only the compression instead of packing pressure was applied. The possibility of reducing double peaks can be found from the application of compression. 4) For the case of both packing and compression force applied sequentially double peaks were clearly shown at the nearest(r=2.0 cm) and farthest(r=4.0 cm) radial locations from the gate. Interestingly, the change of sign for the extinction angle was found at r=4.0 cm. This is the evidence of the reverse flow occurred near the end of the cavity during compression process. 5) The graphical representation technique using an optical refractive ellipse was found to be very useful to express and understand the birefringence distribution.

Acknowledgement Financial supports via ‘Precision Rapid-Injection/Compression Molding for Large Area Plate-type Optical Components with Multi-Functions’(Project No. 10033710) and ‘platform Technology for Production Process of Electronic Mobile Components(Project No. 10033493) by the Ministry of Knowledge Economy are greatly appreciated. It is also noted that late professor Tai Hun Kwon’s comment for this study was always helpful and appreciated.

Nomenclatures ∆n : birefringence C : stress optical coefficient (Pa−1) ni : refractive index at i-direction σi : principal stress (Pa) α : scale factor χ : extinction angle (degree) h : half gap thickness of disk (mm) Tg : glass transition temperature (oC) Br : Brewster(1 Br = 10−12 Pa−1)

162

References Baumer, S., 2010, Handbook of plastic optics, Eindhoven, Netherlands, WILEY-VCH. Chen, S. C., Y. C. Chen, and N. T. Cheng, 1998, Simulation of injection-compression mold-filling process, Int. Comm. Heat Mass Transfer 25, 907-917. Hecht, E., 1987, Optics, Berlin, Massachusetts, Addison-Wesley. Isayev, A. I., 1987, Injection and compression molding fundamentals, New York and Basel. Marcel Dekker INC. Isayev, A. I. and C. A. Hieber, 1980, Toward a viscoelastic modelling of the injection molding of polymers, Rheol. Acta 19, 168-182. Janeschiz-Kriegl, H., 1983, Polymer melt rheology and flow birefringence, Berlin, Springer Verlag. Kim, N. H., 2009, Injection-compression and co-injection molding of amorphous polymers; viscoelastic simulation and experiment, Dissertation, U. of Akron. Lee, H. S. and A. I. Isayev, 2007, Numerical simulation of flowinduced birefringence: comparison of injection and injection/ compres-sion molding, Inter. J. of Precision. Eng. And Manuf. 8, 66-72. Lee, Y. B., T. H. Kwon, and K. H. Yoon, 2002a, Numerical prediction of residual stresses and birefringence in injection/compression molded center-gated disk. part I: basic modeling and results for injection molding, Polym. Eng. Sci 42, 2246-2272. Lee, Y. B., T. H. Kwon, and K. H. Yoon, 2002b, Numerical prediction of residual stresses and birefringence in injection/compression molded center-gated disk. part II: effects of processing conditions, Polym. Eng. Sci 42, 2273-2292. Lin, T. H., 2009, Birefringence, anisotropic shrinkage and luminance in injection molded light-guide plate; modeling and experiment, Dissertation, U. of Akron. Min, I. K., J. S. Kim, Y. B. Ko, H. P. Park, K. H. Yoon, and C. J. Hwang, 2006, An experimental study on the improvement of pattern replication and birefringence in LGP by adding compression effects, Trans. of Maters. Process 15, 27-33. Shyu, G. D., 1993, Birefringence and residual stresses in molded articles of amorphous polymers, Dissertation, U. of Akron. Weng, C., W. B. Lee, S. To, and Bing-yan Jiang, 2009, Numerical simulation of residual stress and birefringence in the precision injection molding of plastic microlens arrays, Int. Comm. Heat Mass Transfer 36, 213-219 Wust, C. J. and D. C. Bogue, 1983, Stress optical behavior in polystyrene; residual stresses and birefringence in large, quenched samples, J. of Appl. Polym Sci. 28, 1931-1947. Yoon, K., 1995, An experimental study on precision injection molding of center-gated disk. part I: basic modeling and results for injection molding, The Korean J. of Rheol. 7, 19-27.
