THE 3D VISCOELASTIC SIMULATION OF MULTI-LAYER FLOW INSIDE FILM AND SHEET EXTRUSION DIES

Transcription

1 THE 3D VISCOELASTIC SIMULATION OF MULTI-LAYER FLOW INSIDE FILM AND SHEET EXTRUSION DIES Kazuya Yokomizo 1, Makoto Iwamura 2 and Hideki Tomiyama 1 1 The Japan Steel Works, LTD., Hiroshima Research Laboratory, Hiroshima, Japan 2 The Japan Steel Works, LTD., Plastics Processing Machinery Dept., Hiroshima, Japan Abstract In this study, the multi-layer polymer flow inside film and sheet extrusion dies was researched by the multi-layer experiment and the simulation. From the experimental results, the phenomenon that the distribution of each layer changes severely near the edge was founded. That phenomenon was attributed to the second normal stress difference of viscoelastic fluid such a polymer. Therefore the multi-layer flow simulation was conducted by using a viscoelastic model which can calculate the normal stress effect. It showed that the simulation results of the distribution of each layer were well agreement with the experimental results. Introduction The extrusion die is one of the most significant equipment to influence the quality of film and sheet products. Demands for dies have become complicated and diversified because the market of film and sheet products requires a lot of functions. For multi-layer film and sheet products, width direction uniformity in ratio of each layer is also required. However, the problem that distribution in ratio of each layer does not become uniform sometimes occurs [1, 2]. In particular, that problem is likely to occur in multi-layer film processing by using a feed-block. The researches of multi-layer flow in extrusion dies are needed in order to solve this problem. It is considered that this problem is caused by the normal stress effect of viscoelastic fluid inside an extrusion die [3, 4]. Therefore, the 3D viscoelastic simulation in which the normal stress effect is calculated is needed in order to predict accurately the distribution of each layer in extrusion dies. However, such 3D viscoelastic simulation in extrusion dies has not been conducted. In this study, multi-layer flow inside an extrusion die was researched in detail by the multi-layer experiment. Then the 3D viscoelastic simulation was attempted and compared the distribution of each layer gotten by the experiment. Experiment In order to research the distribution of each layer inside the extrusion die, the following experiment was carried out. Experimental condition Figure 1 shows the experimental equipment. The Φ25 mm twin screw extruder (made by The Japan Steel Works, LTD.), the Φ35 mm single screw extruder (made by Tahara machinery LTD.), and the 270mm width extrusion die were used. In this equipment, each polymer was merged in the feed-block and made three layers. Then they were flowed into the extrusion die. The red pigment was blended to the resin for core layer in order to evaluate each layer. Used resins were two types of polypropylene (PP) and they were manufactured by Prime Polymer Co., Ltd. Both resins had melt density of 0.75 g/cm 3. The melt index (MI) for the resins were 3.0 and 7.0 g/10 min (230 o C, 2.16kg). In this study, the 3 MI PP and the 7 MI PP are referred as Polymer A and Polymer B. Shear viscosities for the resins are shown by Figs.2 and 3. Table 1 shows the experimental conditions. In condition 1, the same kinds of polymer (Polymer A) were flowed into the core layer and the skin layer. In condition 2, Polymer A was flowed into the core layer and Polymer B was flowed into the skin layer. Extrusion output was set up to make each layer ratio into 1:2:1 and both polymer temperatures were adjusted to 210 o C. In order to observe multi-layer samples from inside the die, the following process was conducted. After the extruders was stopped during flow condition and the die was cooled much slowly and completely, the die was deconstructed for getting the samples. In addition, the multi-layer samples were cut and then cross-sectional surfaces of flow channel in them were observed. Experimental Result The whole pictures of the multi-layer samples and the cross-sectional view of the inflow gate, the manifold and the rectangular channel (slit part) are shown by Figs.4 and 5. The distribution of each layer in the cross-sectional view proves to be different between condition 1 and condition 2 near the surface. The measurement results of each layer ratio in the slit part are shown by Figs.6 and 7. The result of condition 2 shows that the thickness of skin layer near the edge is thicker than the result of condition 1. Therefore, distribution of each layer in condition 2 is not uniform across width of the die and this phenomenon is called the encapsulation phenomenon. This phenomenon is same one SPE ANTEC Anaheim 2017 / 999

2 which become a problem in actual multi-layer film forming processing. This is attributed to quadratic flow which is caused by the second normal stress difference of viscoelastic fluid such a polymer [3, 4]. Multilayer Flow Simulation In order to predict the distribution of each layer which was measured in the experiment, the following multi-layer flow simulation was carried out. Simulation Method The flow simulation software (PlanetsX Extrusion Edition: made by Cybernet Systems Co., Ltd.) based on FEM (Finite Element Method) was used for multi-layer flow simulation. In this software, the CEF (Criminale Ericksen Filbey) model [5, 6] which is a viscoelastic model and can calculate the normal stress effect was used because it is assumed that the encapsulation phenomenon is caused by the second normal stress difference. This CEF model is shown by the following expression. τ = 2ηD Ψ 1 D + 4Ψ 2 D D D = D + ν D L D D LT t D = 1 (L + 2 LT ), L = ( ν) T (1) where τ is the extra stress tensor, η is the shear viscosity, D is the rate of strain tensor, L is the velocity gradient tensor, t is the time, ν is the flow velocity vector, Ψ 1 and Ψ 2 are the first and second normal stress difference coefficient. Shear viscosities for the resins were modeled using a four constants Cross-Arrhenius equation as follows: η 0 η =, η 1+C 1 (η 0 γ ) C 2 0 = C 3 exp ( C 4 T ) (2) where γ is the shear rate (1/s), T is the temperature ( o C), C s are curve fit coefficients. The constants are provided in Table 2. The fitting curves for shear viscosity are also shown in Figs.2 and 3. Ψ 1 and Ψ 2 are related to the first and second normal stress difference (N 1, N 2) and are shown by the following approximate equation. N 1 (γ ) = 2G (ω) ω=γ Ψ 1 (γ ) = N 1 ω 2, Ψ 2 (γ ) = 0.1Ψ 1 (γ ) (3) ω=γ where G is the storage elastic modulus (Pa), ω is the angular frequency (1/s). Ψ 1 for the resins are shown by Figs.8 and 9 and were modeled using a linear approximate equation as follows: Ψ 1 = A 1 γ A 2 exp (A 3 T) (4) where A s are curve fit coefficients. The constants are provided in Table 3. Ψ 2 for the resins were also modeled by the linear approximate equation. In this simulation, a Decoupling method which calculate the thermal flow field and the viscoelastic stress field separately was used. The simulation scheme used for this simulation is shown by Fig.10. Simulation Of The Simple Model In order to check the multi-layer flow simulation with the CEF model, the simulation for the simple rectangle flow channel was conducted. Figure 11 shows the simulation model and Table 4 shows the simulation conditions. Polymer A was flowed into core layer and Polymer B was flowed into skin layer. In addition, the simulation of purely viscous fluid was also conducted in order to compare the simulation with the CEF model. The simulation result of the distribution of each layer at the outlet is shown by Fig.12. It shows that the distribution of each layer tends to be uniform across the width direction in the simulation of purely viscous fluid. On the other hand, thickness of the skin layer is thick near the edge in the simulation with the CEF model. Therefore it is considered that the encapsulation phenomenon was replicated by the simulation. From this simulation result, it is suggested the possibility of prediction of the distribution of each layer in extrusion dies. Simulation Of The Extrusion Die The simulation model of the extrusion die which was used in the experiment is shown by Fig.13. The 1/2 symmetry model was used to reduce a computation load. The simulation conditions are shown by Table 5. The simulation was conducted by the same condition as the experimental condition. Figures 14 and 15 show comparison of the experimental result and the simulation result in the cross-sectional view. It shows that the distribution of each layer in the simulation results accords well with the experimental results. The inflow gate already shows distorted core layer. This seems to be coming from how the layers are arranged and not from viscoelastic effects. Although, it is considered that how to merge the polymer in this simulation is right way because the simulation results in the inflow gate are well agreement with the experimental results. Figures 16 and 17 show the purely viscous simulation results and the simulation results with the CEF model of the distribution of each layer in the slit part. In addition, the experimental results are superimposed on the simulation results in Figs.16 and 17. The purely viscous simulation results are not agreement with the experimental results especially near the edge. On the other hand, the simulation results with the CEF model SPE ANTEC Anaheim 2017 / 1000

3 show that the change of the distribution of each layer near the edge in the simulation result of condition 2 is larger than that in the simulation result of condition 1. This tendency is the same as the experimental results. Compared with the experimental results and the simulation results with the CEF model, the error between simulation values and experimental values are within 5~8%. Therefore, the simulation results of both conditions are highly compatible with the experimental results. It was confirmed that the normal stress effect is related to the non-uniform distribution of each layer in dies because the simulation results with the CEF model were well agreement with the experimental results. In multilayer flow, the power works to the direction of layer boundary near the center by quadratic flow which is caused by N 2. The power depends on the size of Ψ 2. In the range of shear rate in the die at the experimental condition, Ψ 2 of Polymer A is larger than one of Polymer B. Consequently, it is estimated that Polymer A in the core layer pushed Polymer B in the skin layer near the center and Polymer B in the skin layer flowed into near the edge. As a result, it is assumed that this non-uniform distribution of each layer was caused. Because the Weissenberg number (We) is a dimensionless number which quantifies viscoelastic effects, it is possible to consider about encapsulation phenomenon also from the viewpoint of We. We is defined as We = 2λγ and λ is the relaxation time [7]. Because it was considered that the distribution of each layer changes most in the manifold, We in the manifold was calculated. We of Polymer A is and We of Polymer B is Viscoelastic effects of Polymer A is larger than that of polymer B. Therefore above mentioned consideration is supported also from the viewpoint of We. Conclusion The multi-layer flow experiment was conducted in order to research the distribution of each layer inside film and sheet extrusion dies. From the experimental results, the encapsulation phenomenon which is attributed to the difference of Ψ 2 was founded in condition 2. Therefore the multi-layer flow simulation was conducted with the CEF model which can calculate the normal stress effect. As the simulation results, the simulation results of the distribution of each layer were well agreement with the experimental results in both conditions. By using this 3D viscoelastic simulation, it is possible to design optimum flow channels of feed-blocks and extrusion dies for getting film and sheet products with uniform distribution of each layer. References 1. A. Karagiannis, H. Mavridis, A. N. Hrymak, J. Vlachopoulos, Polym Eng Sci, 28, 982 (1988). 2. M. E. Nordberg III, H. M. Winter, Polym Eng Sci, 30, 408 (1990). 3. D. Borzacchiello, E. Leriche, B. Blottiere, J. Guillet, J. Non-Newtonian Fluid Mech., 200, 52 (2013). 4. P. Yue, J. Dooley, J.J. Feng, J. Rheol, 52, 315 (2008). 5. E. Mitsoulis, J. Vlachopoulos, F. A. Mirza, Polym Eng Sci, 24, 707 (1984). 6. R.B.Bird, R.C. Armstrong and O. Hassager, Dynamics of Polymetric Liquids, Vol. 1, J. Wiley (1977). 7. R. J. Poole, Rheology Bulletin, 53(2), (2012). Fig.1. Experimental equipment Fig.2. Shear viscosity for Polymer A (the 3 MI PP) Fig.3. Shear viscosity for Polymer B (the 7 MI PP) SPE ANTEC Anaheim 2017 / 1001

4 Table 1. Experimental conditions Fig.4. Sample picture and Cross-sectional view in condition 1 Fig.5. Sample picture and Cross-sectional view in condition 2 Fig.6. Relationship between Each layer ratio and Position across width of a die in condition 1 Fig.7. Relationship between Each layer ratio and Position across width of a die in condition 2 SPE ANTEC Anaheim 2017 / 1002

5 Fig.8. Relationship between Ψ 1 and Shear rate for Polymer A Fig.9. Relationship between Ψ 1 and Shear rate for Polymer B Table 2. Shear viscosity model parameters Table 3. Ψ 1 model parameters Fig.10. Simulation scheme used for simulation with the CEF model Fig.11. Simple rectangle flow channel used for the flow simulation Table 4. Simulation condition for the simple model Fig.12. Relationship between Each layer ratio and Distance from the center SPE ANTEC Anaheim 2017 / 1003

6 Table 5. Simulation conditions for the extrusion die model Fig.13. Extrusion die model (1/2 symmetry model) used for the flow simulation Fig.14. Comparison of the experimental result and the simulation result in the cross-sectional view in condition 1 Fig.15. Comparison of the experimental result and the simulation result in the cross-sectional view in condition 2 Fig.16. Relationship between Each layer ratio and Distance from the center of a die in condition 1 Fig.17. Relationship between Each layer ratio and Distance from the center of a die in condition 2 SPE ANTEC Anaheim 2017 / 1004