# Including the Molding Effect in Enhanced Structure CAE Analysis on Automotive Parts

A growing number of automotive parts are made of engineering plastic because of its low cost and excellent material properties, for example, fiber-reinforced plastic valve. During the manufacture of automotive products, fiber-reinforced engineering plastic is applied to replace metal materials because of its high heat distortion temperature and superior mechanical properties.

The conventional structure analysis for automotive part involves performing CAE analysis based on the assumption of one or more isotropic materials. Conversely, the material property of the plastic part largely depends on the molding process. Fiber-induced anisotropic mechanical properties are process-induced properties that may not be conducive to the structural requirement of end products. Moreover, the analysis results may not be accurate.

The injection molding of fiber-reinforced thermoplastics is known to be a complex process. The reinforced composites lack isotropic material properties, and the composite’s mechanical and thermal properties largely rely on the fiber orientation pattern. The composite is weaker in the transverse direction and stronger in the fiber orientation direction. In this article, the structure analysis and injection molding are integrated through an interfacing program to conduct structure analysis with molding effects for fiber-reinforced plastic automotive parts.

## Theory

### Filling

The polymer melt is assumed to act as Generalized Newtonian Fluid (GNF) for the filling/packing process. Therefore, the following equations mathematically describe the non-isothermal 3D flow motion:

 (1)

 (2)

 (3)

 (4)

Where

u = the velocity vector
T = temperature
t = time
p = pressure
σ = total stress tensor
ρ = density
η = viscosity
k = thermal conductivity
CP = specific heat
= shear rate

### Fiber Orientation

A 2nd-order orientation vector A represents the fiber orientation state at each point in the part:

 (5)

Advani and Tucker proposed the equation of orientation change for the orientation tensor, which is now applied for the analysis:

 (6)

where CI stands for the interaction coefficient with the value ranging from 10−2 to 10−3. A closure approximation is required for the fourth-order tensor Aijkl.

### Integration Approach

This method is to connect the data between structure analysis and mold-filling analysis. Using the mechanical properties and fiber orientation of a composite material, the thermal expansion coefficients and anisotropy moduli of the fiber-reinforced polymer can be established. Such anisotropy mechanical properties will be put into structural elements for structure analysis later. The molding-induced material properties will be considered in structure analysis.

Moreover, the mesh requirement may not be the same for structure analysis and mold-filling analysis. While it is possible to focus the mesh of structure analysis on the area of stress concentration, the mesh of mold-filling analysis is stressed on the higher element resolution over the thickness direction. Through this method, the mapping function is further developed to map the element properties from mold-filling-specified mesh to structure-specified mesh. It accurately matches the elements and maps the material properties despite the fact that the mesh properties are entirely different, as illustrated in Figure 1.

Figure 1. Map element properties between different meshes

## Results and Discussions

In order to validate the prediction of fiber orientation, a 100 x 50 x 1 mm rectangular plate molded with glass-fiber reinforced PET is simulated. The filling pattern and the part geometry are shown in Figure 2. The gate is located in the middle of the plate. The fiber orientation on the different cut planes is shown in Figure 3.

Figure 2. Filling results of center-gate plate

Figure 3. Fiber orientations distribution of center-gate plate

The lines’ orientation denotes the most conducive orientation direction, and the color of each line indicates the degree of orientation. In the vicinity of mold wall, the shearing flow is seen to align the fibers along the flow. The flow is shear-free in the center cut plane, and therefore, the orientation of the fiber is perpendicular to the flow direction. The prediction shows the fiber alignment along the welding line (see Figure 4). These analysis results are in good agreement with the experimental observation.

Figure 4. Filling results of side-gate plate

Figure 5 (a) shows a throttle valve made of fiber-reinforced engineering plastic. The model is meshed by 4-node tetrahedral element. As illustrated in Figure 5(b), three gates are located on the same side. PET is the resin used, which contains 50% glass-fiber. The melt temperature and the mold temperature are 230 °C and 90 °C, respectively. The filling time is approximately 2.0 seconds. The predicted melt front distribution on the surface of the cavity is shown in Figure 6(a). To further show how this cavity is filled, the iso-surfaces of melt front are plotted in Figure 6(b).

Figure 5. Throttle valve model with 3 gate

Figure 6. Predicted melt front distribution

The predicted fiber orientation on the surface of the cavity and inside the cavity is shown in Figure 7. The orientations strongly depend on the filling patterns. The predicted anisotropy mechanical properties are shown in Figure 8. These properties will be put into subsequent structure analysis. The temperature of the entire molded part is increased to 100 °C as the external condition to further replicate the thermal deformation of the fiber-reinforced plastic valve. Figure 9 shows the constraint condition. This analysis was performed using “NENastran”— the commercial stress. The deformation from structure analysis is shown in Figure 10, and the stress distribution is shown in Figure 11. These results demonstrate how the stress distributions and part deflections strongly depend on the injection molding process.

Figure 7. Predicted fiber orientation distribution

Figure 8. Predicted anisotropy mechanical modulus

Figure 9. Constraint set for thermal stress analysis

Figure 10. Deformation (a) simulation with fiber orientation effects (b) simulation with random orientation effects.

Figure 11. Von-mises stress (a) simulation with fiber orientation effects (b) simulation with random orientation effects.

Figure 12(a) and Figure 12(b) also show a bumper with two runner designs. This model is a characteristic thin-walled part with an average wall thickness of 2.9 mm. Good analysis results can be easily obtained through the traditional 2.5D method. 7.331 3-node triangular plate element is applied in injection molding analysis. PET is the resin used, which contains 45% glass-fiber. Figure 13(a) and Figure 13(b) show the fiber orientation distributions of two mold designs. Different fiber orientation distributions are obtained from different mold designs. ABAQUS — the commercial CAE — is used for performing the impact analysis of a bumper. The accuracy of analysis is increased and the computational loading is reduced by creating a mesh composed of 3-node triangular plate elements and 4-node quadrilateral plate elements, as illustrated in Figure 14.

Figure 12. Bumper models with two mold designs

Figure 13. Average fiber orientation distributions

Figure 14. Specified mesh for impact analysis

The fiber-induced anisotropic properties are mapped correctly to this specified mesh using the proposed mapping method. It is assumed that the weight of imaginary vehicle behind the bumper is 800.0 kgw and the impact is a rigid column with the rate of 4.0 km/hour. In Figure 15, the fixed constraints on bolts are given as red points; the time period is 0.5 seconds. Figure 16 shows the results of arbitrary orientation effects, and Figures 17 and 18 illustrate the results of molding-induced orientation effects for various mold designs. Further comparison of the displacement history of sensor nodes between different mold designs is depicted in Figure 19. These results demonstrate that the structure analysis of the injection-molded plastic part is strongly dependent on mold design and molding conditions.

Figure 15. Models and constraints for impact analysis

Figure 16. Deflection of random orientation effects

Figure 17. Deflection of mold design 1

Figure 18. Deflection of mold design 2

Figure 19. Displacement histories of sensor nodes (node 1: red line, node 2: light blue line.

## Conclusions

In this article, a built-in CAE solution for injection-molded automotive part has been proposed. The results from various demonstrations reveal that the structure analyses of fiber-reinforced plastic parts largely rely on the molding process. This approach can be used by part designers for assessing the mold design and part design. This will be a cost-effective tool for the analysis of plastic part from the design phase to the manufacturing phase.

## Reference

[1]. S.G. Advani and C.L. Tucker, J. Rheol., 31, 751 (1987).

[2]. “Flow-induced alignment in composite materials”, ed. by T.D. Papathansiou and D.C. Guell, Cambridge (1997).

[3]. W.H. Yang, David C. Hsu, Venny Yang and R.Y. Chang, “Computer simulation of 3D short fiber orientation in injection molding,” 470, ANTEC 2003, Nashville (2003).

[4]. Allen Peng, Yorker Chang, Anthony Yang, Venny Yang and F.C. Chuang, “3D fiber orientation and warpage analysis of injection-molded throttle valve,” 3rd Automotive Composite Conference, Detroit (2003).

[5]. CoreTech System internal reports.

This information has been sourced, reviewed and adapted from materials provided by Moldex3D.

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