Prediction of residual stress and viscoelastic deformation of film insert molded parts.

INTRODUCTION

Film insert injection molding or simply film insert molding (FIM) is a relatively new injection molding technique in which molten polymer is filled into the cavity after a film is attached to one side of the mold walls. More manufacturers are recently using the cost effective technique to improve surface quality of products including durability, aesthetic value, colorful surface design, etc. Residual stresses are generally developed in an injection molded part and caused by a number of reasons including flow-induced residual stresses generated as a result of shear and extensional flows during processing (1), (2), packing stresses resulting from the high pressure imposed during packing, and thermal stresses formed during solidification and cooling (3-7). The residual stress distribution in a molded part is one of the major causes for deformation and reduction of impact resistance after ejection (8). In particular, the FIM process may cause severe residual stresses because it is designed to interrupt heat transfer in the perpendicular direction to the cavity wall where the film is attached to and different polymers are used as the film and substrate in most cases. Therefore, it is important to investigate the precise residual stress distribution and to predict viscoelastic deformation that is one of the most important behaviors of polymeric parts for practical applications.

It is well known that developing a manufacturing process by using computer-aided engineering (CAE) is much more profitable than the conventional method of trial and error in the aspects of money and time. Application of CAE to manufacturing is rapidly increased by using commercial softwares because they can satisfy the manufacturer's need for agile response in development stage of products and have the stability of analysis owing to the accumulated know-how for long period of time. Flow analysis of the FIM can be performed by using three-dimensional analysis with the capability of part insert in Mold-flow, a commercially available code for injection molding. However, residual stresses in the FIM part are obtained only in the substrate domain after ejection from the mold cavity by assuming isotropic elastic deformation. It is not possible to calculate residual stresses in the film domain since the interfacial bonding between the two domains can not be taken into account in the molding simulation.

In this study, full three dimensional flow and structural analyses were carried out for FIM process in order to predict residual stresses in both film and substrate domains and to evaluate long-term viscoelastic deformation of the FIM part caused by the residual stresses. For prediction of residual stresses and viscoelastic deformation, a stress analysis code, ABAQUS, was used. Hypermesh, which is frequently used as the preprocessor, was employed for mesh generation and interface handling.

VISCOSITY AND VISCOELASTIC MODELS

Three-dimensional flow analysis is performed by assuming that rheological behavior of the polymeric melt by following the Cross model with the Williams-Landel-Ferry (WLF) equation (9), (10).

[eta] = [[[eta].sub.0]/[1 + [([[[eta].sub.0][gamma]]/[[tau]*]).sup.(1 - n)]]]log [[[[eta].sub.0][[theta]*][[rho]*]]/[[[eta]*][theta][rho]]] = [[-[C.sub.1]([theta]-[[theta]*])]/[[C.sub.2] + ([theta] - [[theta]*])]] (1)

where [eta] is viscosity, [[eta].sub.0] is zero shear rate viscosity, [gamma] is shear rate, [tau]* is shear stress at the transition between Newtonian and power law behavior, [eta]* is viscosity at reference temperature, [rho] is density, [rho] * is density at reference temperature, and [theta]* is reference temperature. The change in the ratio, [theta]* [rho]*/[[theta].sub.[rho]], is small and often ignored. Typically [theta]* is chosen as the glass transition and [C.sub.1] = 17.44 and [C.sub.2] = 51.6 K for many polymers. Residual stresses and deformation of the injection molded part is analyzed by applying elastic properties of the solid polymer right after ejection from the mold cavity. However, various material properties can be applied to the part for prediction of the stress relaxation with respect to time and temperature, e.g., elastoplastic, hyperelastic, plastic, and viscoelastic properties. Viscoelastic property is particularly important to predict time-dependent deformation of polymeric parts which are exposed to various environmental conditions.

The viscoelastic model used in the stress analysis is the generalized Kelvin model that is represented by hereditary integrals and the effect of temperature is considered (11), (12).

[tau](t) = [G.sub.0]([theta])([gamma] - [[integral].sub.0.sup.t][g.sub.R]([xi](s))[gamma](t - s)ds) (2)

where the instantaneous shear modulus [G.sub.0] is temperature dependent and [gamma] is the shear strain.

[[g.sub.R]([xi]) = d[g.sub.R]/d[xi] [g.sub.R](t) = [G.sub.R]/[G.sub.0] (3)

where [G.sub.R](t) is the time dependent shear relaxation modulus that characterizes the material's response and [g.sub.R](t) is dimensionless form of the relaxation modulus. [xi] (t) is reduced time defined by the following equations.

[xi](t) = [[integral].sub.0.sup.t][[ds]/[A([theta](s))]](4)

where A([theta](t)) is a shift function at time t. The reduced time concept for temperature dependence is usually referred to as thermo-rheologically simple (TRS) temperature dependence. The shift function is often approximated by the WLF form,

log (A) = [[-[C.sub.1]([theta] - [theta]*)]/[[C.sub.2] + ([theta] - [theta]*)]] (5)

where [theta]* is the reference temperature at which the relaxation data are provided and [C.sub.1] and [C.sub.2] are calibration constants obtained at the temperature.

3D SIMULATION OF FIM

The FIM part consists of film and substrate materials, and it is not possible to predict melt flow into the cavity and development of residual stresses of the part with two dimensional numerical analysis. Three dimensional simulation of the molding process is required especially for numerical analysis of the viscoelastic deformation of the FIM part. A mesh generating program, HyperMesh, was employed to generate two dimensional finite element meshes for film and substrate domains of a simple rectangular plate as shown in Fig. 1. The two dimensional finite elements were created separately for film and substrate domains and three dimensional finite elements were created after they were imported to Moldflow and combined together. Six layers were built for modeling of the substrate and four layers for modeling of the film, and 5430 and 2821 finite elements were constructed for modeling of the substrate and the film, respectively.

[FIGURE 1 OMITTED]

TABLE 1. Material properties of the PC and PP.

                                PC                  PP

Elastic modulus (MPa)         2280                1385

Poission's ratio              0.417               0.408

Thermal conductivity (W/m C)  0.166 (at           0.11 (at
                                300 [degrees]C)     220[degrees]C)

Thermal expansion             7.3E-5              8.42E-5
coefficient

Specific heat (J/kg C)        1900 (at            2723 (at
                                300 [degrees]C)     220[degrees]C)

Solid density (kg/[m.sup.3])  1191.6              906.9

Melt density (kg/[m.sup.3])   1046.4              741.3

Polymer melt flow into the cavity was calculated numerically by using the three dimensional mesh. Properties of polycarbonate (Makroblend 1018p, Bayer) and polypropylene (Hipol X91, Mitsui) were employed for the flow analysis. Material properties of the PC and PP are summarized in Table 1 and two cases were analyzed: PC/PP model where the PC melt was injected into the cavity with the inserted PP solid film and PP/PC model where the PP melt was injected into the cavity with the inserted PC film. Processing conditions for the PC/PP model are also summarized in Table 2. At the end of the flow analysis, the output data was exported to the stress analysis program and the interface between the film and the substrate was joined as shown in Fig. 1d in order to predict the residual stress distribution and viscoelastic deformation.

The in-mold condition of the part was exported to the stress simulation code and used as the initial condition for structural analysis of the FIM part. The structural analysis was performed to predict residual stress development at the instant of ejection and to evaluate long-term viscoelastic deformation. the ejection step was dealt with by solving an elastic problem when fixed boundary conditions are removed suddenly and the viscoelastic deformation was predicted by assuming that the part was kept at 25[degrees]C for one month. Normalized shear relaxation moduli of the PC and PP are shown in Fig. 2 and used for the viscoelastic stress analysis. The raw data of the PC was measured by Mercier (13) and the other data was measured in this study. A complex geometry FIM part having a zigzag shape was also modeled numerically by using the PP/PC model in order to predict residual stresses and viscoelastic behavior of the complex geometry part.

[FIGURE 2 OMITTED]

TABLE 2. Processing conditions of the PC/PP and PP/PC models.

                                    PC/PP model   PP/PC model

Filling time (s)                       1.020        1.560
Packing pressure (MPa)                80           80
Packing time (s)                      10           10
Melt temperature ([degrees]C)        302          220
Mold temperature ([degrees]C)        115           40

RESULTS AND DISCUSSION

Residual stresses of the part were predicted after the results of injection molding simulation were exported to the stress analysis program and the interface between the film and the substrate was joined. The maximum principal stresses developed before ejection from the cavity were obtained for the PC/PP and PP/PC models and have the values of about 1.4 X [10.sup.8] and 2.2 X [10.sup.8] Pa. respectively. Those of the PC/PP and the PP/PC models before ejection are shown in Fig. 3a and b. The initial residual stress of the solid film was zero before ejection from the mold because the inserted film was considered as a solid during injection molding and the residual stress of the film part had not been developed in the cavity. In injection molding, it is well known that the thermally induced residual stress is dominant over the flow-induced residual stress. Assuming that the residual stress was not generated when the film was manufactured, it is an acceptable assumption that residual stresses are not present in the film. On the other hand, the substrate parts of both PC/PP and PP/PC models must have residual stresses in the cavity because the polymer melt is injected into the cavity and solidification occurs from the surface to the center with nonuniform temperature distribution and nonslip boundary conditions.

[FIGURE 3 OMITTED]

TABLE 3. Dimension of the PC/PP and PP/PC models after ejection.

         Dimension of the PC/PP model predicted by Moldflow

Number          Length (mm)    Width (mm)     Height (mm)

1                  49.41         9.89           2.97
2                  49.71         9.9            2.97
3                  49.74         9.96           2.97
4                  49.4          9.89           2.97

         Dimension of the PC/PP model Predicted by
                         ABAQUS

Number          Length (mm)    Width (mm)     Height (mm)

1                  49.42         9.89           2.97
2                  49.62         9.94           2.97
3                  49.62         9.93           2.97
4                  49.42         9.87           2.97

Number                        Variation (%)

1                  -0.02         0              0
2                   0.18        -0.4            0
3                   0.24         0.3            0
4                  -0.04         0.2            0
Mean variation      0.12         0.225          0

         Dimension of the PC/PP model predicted by Moldflow

Number        Length (mm)    Width (mm)     Height (mm)

1                48.08         9.65           3.00
2                49.60         9.77           2.81
3                49.59         9.94           2.99
4                48.08         9.65           3.00

         Dimension of the PC/PP model Predicted by
                         ABAQUS

Number          Length (mm)    Width (mm)     Height (mm)

1                47.19         9.62           2.90
2                48.96         9.96           2.90
3                48.96         9.96           2.89
4                47.19         9.93           2.90

Number                       Variation (%)

1                 1.85         0.31           3.33
2                 1.29        -1.94          -3.20
3                 1.27        -0.20           3.34
4                 1.85         0.21           3.33
Mean variation    1.565        0.665          3.30

Variation (%) = (dimension predicted by Moldflow -
dimension predicted by ABAQUS)/dimension predicted
by Moldflow X 100
Mean variation = |variation1| + |variation2| +
|variation3| + |variation4|/4

The residual stresses developed right after ejection are shown in Fig. 4. The predicted residual stresses in the PC/PP and PP/PC models were in the range of between -5.2 X [10.sup.6] and 9.9 X [10.sup.7] Pa and between -6.4 X [10.sup.7] and 6.1 X [10.sup.8] Pa, respectively. The results indicate that considerable amounts of residual stresses were caused by elastic deformation at the moment of removing fixed boundary conditions that restrained the part from deformation. As shown in the Figure, residual stresses were newly developed in the film after ejection, that is, the residual stress developed in the mold was redistributed in the ejected part as the fixed boundary conditions were removed. The free boundary conditions imposed at the moment of ejection also influenced residual stress development at the interface between the film and substrate. The tensile stress was relaxed further in the substrate near the mold wall and shrinkage of the solid film side was lower than that of the other side because the constraints and nonslip conditions were eliminated at the wall. Therefore, the FIM parts were bent such that the film side was protruded as shown in the Figure. It was found that warpage of the PP/PC model was larger than that of the PC/PP model due to the fact that the PP substrate of the PP/PC model, a semicrystalline polymer, will shrink more than the PC substrate of the PC/PP model, an amorphous polymer. It is commonly accepted that semicrystalline plastics shrink more than amorphous ones because of the closer packing of the crystalline structure (14). Dimensions of the PC/PP and PP/PC models are shown in Table 3 and the width, length, and height numbers are defined as illustrated in Fig. 5. The plate model has the dimension of 10 mm width, 50 mm length, and 3 mm height (2.5 mm for substrate and 0.5 mm for film) before deformation. Deflection of the FIM part was obtained by the numerical simulations when it was ejected from the mold and the residual stress distribution in both the film and substrate domains were predicted by applying the interfacial joining method.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Viscoelastic deformation of the plate was calculated assuming that it is stored at room temperature for one month after ejection and the residual stresses are shown in Fig. 6a and b. The residual stresses remaining in the PC/PP and PP/PC models were in the range of between -3.2 X [10.sup.6] and 4.3 X [10.sup.7] Pa and between -6.3 X [10.sup.7] and 3.6 X [10.sup.8] Pa, respectively. Compared with the residual stress data after ejection, stress relaxation was progressed and the dimension must have been changed by the viscoelastic deformation. The dimensions of the PC/PP and PP/PC models predicted by the viscoelastic stress analysis are also listed in Table 4 by using the same width, length, and height numbers. As mentioned above, the dimensional change was confirmed. Residual stresses in the entire FIM part after ejection and long-term thermo-viscoelastic deformation were predicted by using both the molding simulation software and the stress analysis program with full three dimensional finite elements.

[FIGURE 6 OMITTED]

A zigzag geometry shown in Fig. 7 was chosen and analyzed by using the PP/PC model in order to recognize possibility of application to more complex geometry part. About 28,465 elements (six layers) and 14,187 elements (four layers) were constructed for the substrate and film parts, respectively. As shown in Fig. 7, the residual stresses of PP/PC model were predicted after ejection and the viscoelastic stress analysis was performed to identify the long-term behavior of the FIM part. Deflection and maximum principal stress distribution of the part after ejection and long-term viscoelastic deformation are shown in the Figure. It is shown that considerable amount of stress relaxation has occurred even at room temperature.

[FIGURE 7 OMITTED]

CONCLUSIONS

Three dimensional simulation of film insert molded parts was performed by employing commercial programs in order to predict the residual stress distribution and time-dependent viscoelastic deformation. Elastic deformation of the FIM part was predicted and residual stresses present in the film and substrate were calculated assuming isotropic elastic material right after ejection. The residual stress distribution in the FIM part was acquired by removing the constraints at the boundary of the mold cavity. The time-dependent viscoelastic behavior of the FIM part was estimated by three dimensional stress analysis. Longtime viscoelastic deformation of the FIM part was predicted by performing viscoelastic stress analysis in order to understand long-term behavior of the FIM part when exposed to room temperature. Residual stresses in the part after viscoelastic relaxation were different from those in the part ejected from the mold. Flow simulation and thermo-viscoelastic analysis of the FIM part will contribute to the design of the polymeric part and mold.

TABLE 4. Dimension of the PC/PP and PP/PC models predicted
by the viscoelastic stress analysis.

             Dimension of the                  Dimension of the
               PC/PP model                        PC/PP model

Number    Length   Width  Height  Number    Length     Width  Height
           (mm)    (mm)    (mm)              (mm)      (mm)    (mm)

1         49.51    9.90    2.98     1       46.97       9.63   2.89
2         49.61    9.94    2.98     2       48.96      10.00   2.90
3         49.61    9.94    2.98     3       48.96      10.00   2.89
4         49.51    9.90    2.98     4       46.98       9.64   2.90

REFERENCES

(1.) A.I. Isayev and D.L. Crouthamel, Polym. Plast. Tech. Eng., 22, 177 (1984).

(2.) B. Haworth, C.S. Hindle, G.J. Sandilands, and J.R. White, Plast. Rubber. Proc. Appl., 2, 59 (1982).

(3.) A. Sen and M. Bhattacharya, Polymer, 41, 9177 (2000).

(4.) T.A. Osswald and G. Menges, Materials Science of Polymers for Engineers, Hanser, Munich (1996).

(5.) L.D. Coxon and J.R. White, Polym. Eng. Sci., 20, 230 (1980).

(6.) J.H. Jung, S.W. Lee, and J.R. Youn, Macromol. Symp., 148, 263 (1999).

(7.) S.C. Lee and J.R. Youn, J. Reinf. Plast. Comp., 18, 186 (1999).

(8.) X. Zhang, X. Cheng, K.A. Stelson, M.Bhattacharya, A. Sen, and V.R. Voller, J.Therm. Stresses, 25, 523 (2002).

(9.) P. Kennedy, Flow Analysis Reference Manual, Moldflow Pty (1993).

(10.) C.W. Macosko, Rheology, Principles: Measurements, and Applications, Wiley-VCH, New York (1994).

(11.) Analysis User's Manual Vol. 3, Materials, ABAQUS, Pawtucket (2003).

(12.) W. Flugge, Viscoelasticity, Springer-Verlag, Berlin (1975).

(13.) J.P. Mercier, J.J. Aklonis, M. Litt, and A.V. Tobolsky, J. Appl. Polym. Sci., 9.447 (1965).

(14.) R.A. Malloy, Plastic Part Design for Injection Molding an Introduction, Hanser Publishers, Munich (1994).

Seong Yun Kim, Hwa Jin Oh, Sung Ho Kim, Chae Hwan Kim, Seung Hwan Lee, Jae Ryoun Youn

Department of Materials Science and Engineering, Research Institute of Advanced Materials (RIAM), Seoul National University, Shinlim-Dong, Gwanak-Gu, Seoul, Korea

Correspondence to: J.R. Youn; e-mail: [e-mail]

Contract grant sponsor: Korea Science and Engineering Foundation.