## 3 Results and Discussion  
In this study, changes in the elastic properties attributed to the aspect ratio of PP/UHMWPE fibers were analyzed using finite element analysis and the Halpin-Tsai model. Numerical analysis using finite element and Halpin-Tsai analyses were performed at a 5% volume fraction of UHMWPE fibers. The higher the volume fraction of the fiber, the better the elastic properties. Due to the complexity and convergence of the finite element analysis, it was performed by setting a different aspect ratio at 5% of the UHMWPE volume fraction. Finite element analysis was performed for aspect ratios of 0.2 to 30; numerical analysis using the Halpin-Tsai model was performed for aspect ratios of 0.2 to 100 to examine the theoretical results. Therefore, from the influence of UHMWPE short fibers on the PP-based matrix, the elastic property behavior when continuous fibers were used was predicted and comparatively analyzed. As the structure of the fiber is oriented in its longitudinal direction, it presents as an anisotropic material. According to the comparative analysis in the E\({}_{11}\) direction shown in Figure 3, when the aspect ratio of the UHMWPE fiber was 0.2, the modulus of elasticity was calculated to be 1518 MPa, and when the aspect ratio was 30, it was found to be 2365 MPa. Theoretical numerical analysis indicated that the modulus of elasticity was 2415 MPa when the aspect ratio was 100. The finite element analysis and Halpin-Tsai model converged with similar results up to an aspect ratio 9 for the UHMWPE fiber. However, for aspect ratios of 9 or higher, the longitudinal elastic modulus value according to the finite element analysis result was larger than that of the numerical analysis result using the Halpin-Tsai model; this trend was the same until the aspect ratio was 30. The larger value of the longitudinal elastic modulus according to the finite element analysis can be explained by the shape modeled by the analysis. In the analysis model, as the volume fraction of 5% was set as a fixed variable, the UHMWPE fibers were modeled as if they were evenly distributed in the cross-section at a low aspect ratio. This is shown in Figure 4a; the influence of anisotropy is small. However, if the aspect ratio is increased at a fixed volume fraction of 5%, the cross-sectional arrangement density of the UHMWPE fiber decreases, as shown in Figure 4b. Therefore, the anisotropy increases, and the elastic modulus in the longitudinal direction can be large. By contrast, in the numerical analysis using the Halpin-Tsai model, this effect does not appear because it is a theoretical result value without a modeling shape. Hence, it may differ from the finite element analysis result. As such, the influence of the cross-section is increased from an aspect ratio of 9 or higher. In addition, according to the numerical analysis results using the Halpin-Tsai model, the increase rate of the elastic properties decreased from an aspect ratio of 40 or higher and converged to 2400 MPa. According to the results of this study, it is effective to assume continuous fibers at aspect ratios of 40 and higher. E\({}_{22}\) is at a right angle to the orientation direction of the fiber; it can be calculated using the Halpin-Tsai equation. Figure 5 shows the elastic modulus in the E\({}_{22}\) direction calculated via finite element analysis. Since the result calculated using the Halpin-Tsai model is the value calculated through \(\xi_{22}\) of the UHMWPE fiber, theoretically, it is not affected by the aspect ratio of the fiber. As \(\xi_{22}\) is affected by the height and width of the fiber, the shape of the UHMWPE used in this study is circular. Therefore, the height and width of the fiber are the same, indicating that it has a constant value irrespective of the aspect ratio. However, the finite element analysis results differed from those of the Halpin-Tsai numerical analysis model according to the modeled UHMWPE fiber orientation within the PP matrix. As mentioned previously, the UHMWPE volume fraction was maintained at 5%,