## 3 Experimental Results and Discussion
### Peel Strength of the Welding Joints  
Peel strength is generally used to measure the bond strength of a material, typically the adhesive and the thermal bonding. Because the area ratio (s) of the welding area (S\({}_{0}\)) to the cycling area (S\({}_{1}\)) is an important factor when considering the relationship between roller patterns and peel strength, it is presented first. The definition of the welding area (S\({}_{0}\)) to the cycling area (S\({}_{1}\)) is as follows: The welding area (S\({}_{0}\)) is generally defined as the solid area in the pattern, while the cycling area (S\({}_{1}\)) is the rectangular area covering the welding area in one cycle. For easy calculation, the cycle was set as 20 mm in length. The area ratio of the welding area to the cycling area in the patterns was mostly different in the welding area and the geometry. As a result, a matrix of all of the roller profile cases is listed in Table 4.  
In order to investigate the influence of the different roller profiles on the load and the peel strength of the welding joints, a strength test of all of the designed patterns (No. 1-No. 8) was conducted. Four samples of each pattern were welded and tested to obtain the average value of the load and the peel strength. The average load and the average peel strength of the four groups were drawn, and are presented in in Figures 11 and 12, respectively. According to the groups, the load and the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**No.** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline S\({}_{0}\) (mm\({}^{2}\)) & 34 & 50 & 37.3 & 68 & 88 & 102 & 40.7 & 97.1 \\ S\({}_{1}\) (mm\({}^{2}\)) & 40 & 200 & 130 & 110 & 140 & 160 & 200 & 200 \\ s = S\({}_{0}\)/S\({}_{1}\) (\%) & 85.0 & 25.0 & 28.7 & 61.8 & 62.9 & 63.8 & 20.4 & 48.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Welding area (S\({}_{0}\)), cycling area (S\({}_{1}\)), and area ratio (s) of the designed patterns. peel strength can be compared, which shows that generally, the load distribution is opposed to the strength distribution. In the case of the solid line of the welding joints in group one, the load of No. 2 is larger than the load of No. 1. This is because the welding joint of No. 2 is larger than that of No. 1. The load of No. 4 is significantly larger than that of No. 3. This can be explained by the fact that the solid line in pattern 3 created a continuous welding area, and it can be seen in the SEM image (Figure 8a) that inside the welding area, the fibers are mostly melted and solidified. Therefore, the linkage area between the fibers and the solidified area around the edges of the No. 3 is smaller than that of No. 4. This explanation can also be used to describe the reason why the load of pattern 6 is larger than that of No. 5. The load of No. 7 and 8 is almost same due to only a slight change in the thickness of the pattern lines. According to area ratio as described above, No. 2 offers the highest load with the smallest area ratio (s). Meanwhile, No. 7 provides the lowest load with a large area ratio (s). From the results above, it can be considered that the load is proportional to the area ratio and it depends on the roller profile. In summary, the maximum load of the ultrasonic welding joints can be obtained with No. Figure 11: Relationship between the load and the area ratio with different patterns. Figure 12: Relationship between the peel strength and the area ratio with different patterns. 2, and a brick structure (No. 4 and No. 6) offers a greater load than the other structures. Meanwhile, patterns with a solid line (No. 3, No. 5, and No. 7) show less load than the others. Generally, the peel strength is decreased from No. 1 until No. 5. In No. 5 and No. 6, it is mostly unchanged. The peel strength is lower in No. 8 in comparison to No. 7. Even though the load is maximal (230.39 N) in No. 2, the peel strength is maximal in No. 1 (6.22 MPa). This can be explained by the fact that the welding area in No. 2 is much larger than in No. 1. The peel strength in the case of No.