## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Polypropylene (PP)** & **UHMWPE** \\ \hline Modulus of elasticity (MPa) & 1325 & 25,000 \\ Shear modulus (MPa) & 432.29 & 10,417 \\ Poisson’s ratio & 0.43 & 0.20 \\ Bulk modulus of elasticity (MPa) & 3154.8 & 13,889.0 \\ Density (kg/m) & 904 & 950 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of PP and UHMWPE. and according to the modeling results, the lower the aspect ratio, the more the UHMWPE fibers were chopped and dispersed over a large area. According to these results, the circular disk-shaped fibers were oriented. This appears as shown in y-axis section of Figure 6. Since the aspect ratio of the fiber was low, the length in the longitudinal direction (the height of the fiber) was greater than the length of the fiber. Hence, the longitudinal direction of the fiber changed in that same direction. Therefore, when the aspect ratio was less than one, the elastic modulus in the E\({}_{22}\) direction was high. The tendency of E\({}_{22}\) to be high decreased until the aspect ratio of the UHMWPE fiber became 1, and then converged from an aspect ratio of 15 to 1550 MPa. According to the numerical analysis using the Halpin-Tsai model, convergence was observed at 1502 Mpa. Since the elastic modulus in the E\({}_{22}\) direction is generally related to the cross-sectional shape of the fiber, it converged to a constant value in the circularly simulated UHMWPE fiber. Figure 4: Y-Z section of the finite element analysis model. (**a**) Aspect ratio 0.4, (**b**) Aspect ratio 15. Figure 3: Elastic modulus (E\({}_{11}\)) according to the UHMWPE aspect ratio. The shear modulus calculated in this study is shown in Figure 7. In the case of the shear modulus, the cross-section of the UHMWPE fiber is located on the cross-section of the PP matrix, and it is determined according to its influence. Therefore, if a fixed volume fraction of 5% is maintained in the finite element analysis, the shear modulus is temporarily calculated because the cross-sectional density of UHMWPE fibers is high in areas with low aspect ratios. However, the number of fibers decreases as the aspect ratio increases so convergence to 510 MPa can be confirmed. The Halpin-Tsai model converges at 470 MPa. In this study, the results of the predicted composite material elastic properties using the Halpin-Tsai model and finite element analysis showed that the properties were generally higher through the finite element analysis. However, most of the results were within a range of 10%, which is quite similar. This difference can be attributed to a deep relationship with the finite element analysis model. Since the theoretical Halpin-Tsai model has only a reinforcing factor (\(\xi\)) that can experimentally substitute for the effect of the aspect ratio, the results of the model are consistent with the finite element analysis model. Figure 5: Elastic modulus (E\({}_{22}\)) according to the UHMWPE aspect ratio. Figure 6: The x-y section of the finite element analysis model. (**a**) Aspect ratio 0.4, (**b**) Aspect ratio 15.  
no factor exists that can represent other effects such as the cross-sectional shape of the UHMWPE fiber. However, in the case of the finite element analysis, the direction and other factors according to the shape of the UHMWPE were reflected, and the results were derived, showing a different trend from that of the theoretical model. As a result of predicting the elastic properties of the composite material considering the aspect ratio, the elastic modulus in the longitudinal direction increased as the aspect ratio increased; however, no significant effect was observed for aspect ratios of 40 or higher. As the aspect ratio of UHMWPE fibers exceeded 40, results similar to those of the continuous-fiber mechanism were obtained. In the future, finite element analysis must be performed considering the volume fraction and aspect ratio of UHMWPE fibers in composite materials.