Fiber Orientation (3D) Solver Verification and Validation

Transcription

1 AUTODESK MOLDFLOW INSIGHT 2 VALIDATION REPORT Fiber Orientation (3D) Solver Verification and Validation Executive Summary The fiber orientation at the injection locations was modified to a prescribed orientation profile, which is more realistic than the random orientation assumed in previous releases. The fiber orientation calculation was extended into one-dimensional beam elements, and the calculation in beam elements has been verified by comparison with MATLAB results. The fiber orientation calculation in tetrahedral elements has been verified by comparison with MATLAB results for simple geometries. The fiber orientation calculation on models of real parts has been validated by comparison with experimental measurements. Introduction In releases prior to Autodesk Moldflow Insight 2, in the 3D fiber orientation solver, the fiber orientation is assumed to be perfectly random at part injection locations and in runner systems modeled by one-dimensional beam elements. However, in reality fiber orientation is induced by the melt flow through the runner system and the barrel. Even if fibers are randomly oriented in the melt when entering the injection molding machine, the fiber orientation is no longer random once the polymer has reached the gate. In order to provide more realistic orientation predictions, in Autodesk Moldflow Insight 2 the inlet orientation at the injection locations was modified, and the orientation calculation was extended into beam elements. This change affects 3D analyses of fiber-filled materials for Thermoplastics Injection Molding, Thermoplastics Overmolding, and Gas-assisted Injection Molding processes when the option to perform Fiber orientation analysis if fiber material is selected. Inlet Orientation at Injection Locations In Autodesk Moldflow Insight 2, the new inlet fiber orientation profile assumed in 3D analyses is defined as aligned at skin and transverse at core, similar to the default inlet orientation applied in Midplane and Dual Domain analyses. In cases with a runner system modeled by beam elements and an injection location at the top of the sprue, the inlet orientation profile is applied to the layers of the first beam node which is at the injection location, and the fiber orientation is calculated in beam elements of the runner system and tetrahedral elements of the part. In cases with an injection location directly on the part, the inlet orientation profile is applied for all nodes within the gate diameter. In both cases, the inlet orientation profile is prescribed as a function of distance from the center of the injection location. The effect of the inlet orientation change is limited to a small region near the injection location because the flow near the gate is quite fast and the velocity gradient is usually large, and therefore the fiber orientation is quickly changed by the flow. This modification produces some effect on results for small parts but is hardly noticeable for large parts.

2 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation Three cases are presented to demonstrate the effect of the fiber orientation solver changes from Autodesk Moldflow Insight 2, Release 2 to Autodesk Moldflow Insight 2: Pipette case, with injection directly into the part (Figures to 4) Hager Cable Holder case, with injection directly into the part (Figures 5 to 8) Rhodia Box case, with injection into a runner system modeled by beam elements (Figures 9 to 2) Figures 2, 6 and illustrate how the fiber orientation was completely random around the gate in Autodesk Moldflow Insight 2, Release 2, but in Autodesk Moldflow Insight 2 it is slightly aligned. In the rest of the part, the fiber orientation predicted by Autodesk Moldflow Insight 2, Release 2 and Autodesk Moldflow Insight 2 analyses is almost the same for each case. Note too in Figure that the fiber orientation in beam elements in Autodesk Moldflow Insight 2 is now calculated rather than random. The Warp analysis results from Autodesk Moldflow Insight 2, Release 2 and Autodesk Moldflow Insight 2 analyses are compared in Figures 3, 7 and. For the Pipette case, the largest deflection occurs close to the gate, and the difference in predicted warpage between the two releases is over 2%. For the Hager Cable Holder and Rhodia Box cases, the warpage results are only slightly different, due mainly to the change in flow results between the two releases, as indicated by the fill time results for each case (Figures 4, 8 and 2). For details of the improvement in the flow solution accuracy in Autodesk Moldflow Insight 2, please refer to the Autodesk Moldflow Insight 2: Flow Front Advancement in the 3D Flow Solver validation report. Figure. Pipette case Geometry and 3D mesh. 2

3 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation Figure 2. Pipette case Comparison of fiber orientation prediction from Autodesk Moldflow Insight 2, Release 2 (left) and Autodesk Moldflow Insight 2 (right) analyses. Figure 3. Pipette case Comparison of warpage prediction from Autodesk Moldflow Insight 2, Release 2 (left) and Autodesk Moldflow Insight 2 (right) analyses. 3

4 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation Figure 4. Pipette case Comparison of fill time results from Autodesk Moldflow Insight 2, Release 2 (left) and Autodesk Moldflow Insight 2 (right) analyses. 4

5 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation Figure 5. Hager Cable Holder case Geometry and 3D mesh. Figure 6. Hager Cable Holder case Comparison of fiber orientation prediction from Autodesk Moldflow Insight 2, Release 2 (left) and Autodesk Moldflow Insight 2 (right) analyses. 5

6 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation Figure 7. Hager Cable Holder case Comparison of warpage prediction from Autodesk Moldflow Insight 2, Release 2 (left) and Autodesk Moldflow Insight 2 (right) analyses. Figure 8. Hager Cable Holder case Comparison of fill time results from Autodesk Moldflow Insight 2, Release 2 (left) and Autodesk Moldflow Insight 2 (right) analyses. 6

7 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation Figure 9. Rhodia Box case Geometry and 3D mesh. Figure. Rhodia Box case Comparison of fiber orientation prediction from Autodesk Moldflow Insight 2, Release 2 (left) and Autodesk Moldflow Insight 2 (right) analyses. 7

8 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation Figure. Rhodia Box case Comparison of warpage prediction from Autodesk Moldflow Insight 2, Release 2 (left) and Autodesk Moldflow Insight 2 (right) analyses. Figure 2. Rhodia Box case Comparison of fill time results from Autodesk Moldflow Insight 2, Release 2 (left) and Autodesk Moldflow Insight 2 (right) analyses. 8

9 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation Verification of Orientation Calculation in Beam Elements For the fiber orientation calculation in one-dimensional beam elements, we assume that the flow is always in the axial direction no matter what the shape and type of the beams are and how their dimensions vary. Hence, only simple shearing is present in the flow and fibers tend to be aligned into the axial direction. As a verification test, we created a small 3D model with a long, uniform, cylindrical runner, as shown in Figure 3. This model is solely for test purposes and may have no realistic usage. We also developed a MATLAB script to predict the fiber orientation in isothermal flows of a Newtonian fluid and a power-law fluid through a cylinder, for which the analytical solution of the velocity and the velocity gradient are easily obtained. Based upon the analytical solution, the MATLAB script traces particles released at one end of the cylinder and integrates the orientation equation using the MATLAB function ode45 which implements the 4th-order Runge-Kutta method. Then, the fiber orientation predictions across the radius of the cylinder at selected locations from the Autodesk Moldflow Insight 3D analyses and MATLAB calculations were compared. The fiber orientation equation implemented in both Autodesk Moldflow Insight solver and the MATLAB script is the standard Folgar-Tucker model. The comparison is shown in Figures 4 and 5 for the Newtonian and power-law cases, respectively. The excellent agreement verifies that the orientation equation is solved correctly in beam elements in the Autodesk Moldflow software. Figure 3. 3D model with beam elements for verification test Geometry and mesh. 9

10 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation L = 5.5 mm A (Moldflow) A (Matlab) L =.5 mm A (Moldflow) A (Matlab) L = 25.5 mm A (Moldflow) A (Matlab) Figure 4. Beam elements Comparison of fiber orientation prediction by Autodesk Moldflow Insight 2 analysis and MATLAB script for an isothermal flow of a Newtonian fluid. Here L is the distance to the runner nozzle, represents the axial direction and 2 the radius direction of the cylindrical beams. The fiber interaction coefficient C I =.2.

11 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation L = 5.5 mm A (Moldflow) A (Matlab) L =.5 mm A (Moldflow) A (Matlab) L = 25.5 mm A (Moldflow) A (Matlab) Figure 5. Beam elements Comparison of fiber orientation prediction by Autodesk Moldflow Insight 2 analysis and MATLAB script for an isothermal flow of a powerlaw fluid. Here L is the distance to the runner nozzle, represents the axial direction and 2 the radius direction of the cylindrical beams. The fiber interaction coefficient C I =.2.

12 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation Verification of Orientation Calculation in Tetrahedral Elements The 3D fiber solver was further verified in tetrahedral meshes using two simple geometries: plaque and annular disk. The models and 3D meshes are displayed in Figures 6 and 7, respectively. The plaque is 9 mm long 6 mm wide.5 mm thick. The inner radius of the annular disk is mm, the outer radius 9 mm, and the thickness is.5 mm. Again, Newtonian and power-law fluids and isothermal flows are used in these verification tests. The analytical solution for pressure flows between parallel plates and parallel disks are implemented in the MATLAB script to solve the fiber orientation equation. The fiber orientation results from Autodesk Moldflow Insight 2 and the MATLAB script are compared in Figures 8 2 at selected locations in the plaque and disk, and they show excellent agreement. The slight difference is due to the inlet effect of the flow, which is not considered in the MATLAB calculation. Figure 6. Plaque Geometry and 3D mesh. Figure 7. Annular disk Geometry and 3D mesh. 2

13 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation L = 5 mm A (Moldflow) A (Matlab) L = 35 mm A (Moldflow) A (Matlab) L = 55 mm A (Moldflow) A (Matlab) Figure 8. Plaque Comparison of fiber orientation prediction from Autodesk Moldflow Insight 2 analysis and MATLAB script for an isothermal flow of a Newtonian fluid. Here L is the distance to the gate, represents the flow direction and 2 the cross-flow direction. The fiber interaction coefficient C I =.6. 3

14 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation L = 5 mm A (Moldflow) A (Matlab) L = 35 mm A (Moldflow) A (Matlab) L = 55 mm A (Moldflow) A (Matlab) Figure 9. Plaque Comparison of fiber orientation prediction from Autodesk Moldflow Insight 2 analysis and MATLAB script for an isothermal flow of a power-law fluid. Here L is the distance to the gate, represents the flow direction and 2 the cross-flow direction. The fiber interaction coefficient C I =.6. 4

15 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation R = 5 mm A (Moldflow) A (Matlab) R = 35 mm A (Moldflow) A (Matlab) R = 55 mm A (Moldflow) A (Matlab) Figure 2. Annular disk Comparison of fiber orientation prediction from Autodesk Moldflow Insight 2 analysis and MATLAB script for an isothermal flow of a Newtonian fluid. Here R is the radius, represents the radial direction and 2 the tangential direction. The fiber interaction coefficient C I =.6. 5

16 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation R = 5 mm A (Moldflow) A (Matlab) R = 35 mm A (Moldflow) A (Matlab) R = 55 mm A (Moldflow) A (Matlab) Figure 2. Annular disk Comparison of fiber orientation prediction from Autodesk Moldflow Insight 2 analysis and MATLAB script for an isothermal flow of a powerlaw fluid. Here R is the radius, represents the radial direction and 2 the tangential direction. The fiber interaction coefficient C I =.6. 6

17 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation Validation of Fiber Orientation Solver in Real Parts A number of end-gated plaques and center-gated disks were molded by Delphi Corporation. The ISO-standard plaques were 8 mm wide and 9 mm long, and the radius of the disks was 9 mm. The cavity thicknesses for each shape were varied from.5 mm to 6 mm, and three different injection rates (slow, medium, and fast) were applied for each thickness. Fiber orientation measurements were performed on three sections, each mm wide, starting at mm, 3 mm, and 6 mm away from the gate on the cut along the centerline of each plaque and along the radius of each disk. The sections are denoted as regions A, B, and C, respectively. The geometry and the mesh distribution of the plaque and disk models are illustrated in Figures 22 and 23, respectively. Six layers through the thickness are used for all models in the following simulations and comparisons. In Figure 24, the predictions from Autodesk Moldflow Insight 2, Release 2 and Autodesk Moldflow Insight 2 are compared with experimental data measured at region B along the centerline for the.5 mm thick plaque filled with a slow rate. The results from both releases are almost identical, and the difference introduced by the fiber orientation calculation in the beam elements in Autodesk Moldflow Insight 2 is negligible. The comparisons of the orientation predicted by Autodesk Moldflow Insight 2 with the experimental data for selected cases are plotted in Figures 25 and 26. Overall, the fiber orientation predictions match the measured data in both plaques and disks. The solver predicts the shell-coreshell fiber orientation structure, and the results agree with the experimental data in both the shell layers and the core. Figure 22. ISO-standard plaque Geometry and 3D mesh. 7

18 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation Figure 23. Center-gated disk Geometry and 3D mesh A (data) A22 (data) A (Moldflow 2-R2) A22 (Moldflow 2-R2) A (Moldflow 2) A22 (Moldflow 2) Figure 24. ISO-standard plaque,.5 mm thick, slow fill rate Comparison of fiber orientation results at region B from Autodesk Moldflow Insight 2, Release 2 and Autodesk Moldflow Insight 2 analyses with measured data. Here, represents the flow direction and 2 is the cross-flow direction. 8

19 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation A (data) A22 (data) A (simulation) A22 (simulation) Figure 25. ISO-standard plaque, 3 mm thick, medium fill rate Comparison of fiber orientation results at region B from Autodesk Moldflow Insight 2 analysis with measured data. Here, represents the flow direction and 2 is the cross-flow direction A (data) A22 (data) A (simulation) A22 (simulation) Figure 26. Center-gated disk,.5 mm thick, slow fill rate Comparison of fiber orientation results at region B from Autodesk Moldflow Insight 2 analysis with measured data. Here, represents the radial direction and 2 is the tangential direction. 9

20 Autodesk Moldflow Insight 2: Fiber Orientation (3D) Solver Verification and Validation Acknowledgements Autodesk, Inc., wishes to thank: Professor Charles L. Tucker III for providing the MATLAB script solving the fiber orientation equation Hager GmbH of Germany and Rhodia Engineering Plastics of France for providing models of their injection molded parts Delphi Corporation for providing models and fiber orientation data, which were used in this report. Revised 9 March 2. 2 Autodesk, Inc. All rights reserved. Except as otherwise permitted by Autodesk, Inc., this publication, or parts thereof, may not be reproduced in any form, by any method, for any purpose. Trademarks Autodesk and Moldflow are trademarks or registered trademarks of Autodesk, Inc., in the USA and/or other countries. All other brand names, product names, or trademarks belong to their respective holders. Disclaimer THIS PUBLICATION AND THE INFORMATION CONTAINED HEREIN IS MADE AVAILABLE BY AUTODESK, INC. "AS IS." AUTODESK, INC. DISCLAIMS ALL WARRANTIES, EITHER EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE REGARDING THESE MATERIALS. 2