## 2 Materials and Methods  
This study examines high modulus polyethylene (HMPE) rope. The HMPE rope was constructed by a braiding method using eight strands. Each strand was made from parallel fibers. Both the ropes and the strands were purchased from Hayami (Hayami Industry Co., Ltd., Shiga prefecture, Japan). The minimum break load (MBL) of the strands and ropes were 430 N and 1900 N, respectively. The MBL for the strands was experimentally determined, and the MBL for the ropes was obtained from the manufacturer. Linear density, expressed in grams per kilometer (tex = 1 g/1 km) is commonly used in textile engineering due to the presence of voids in the rope. In this study, the linear density of the strands was determined by cutting a strand to a length of 108 mm and weighing it (Shimadzu AX200). The linear density of the rope was determined by the same procedure but at a rope length of 43 mm. Figure 1 shows the braided HMPE rope consisting of eight strands and Table 1 summarizes the material properties of both the strand and rope.  
In this study, we followed the standard of CI 1500 (Cordage Institute International Standard) in our experiment. Cyclic loading tests were conducted for strands and ropes to measure the longitudinal modulus. Experimental conditions are shown in Table 2. The maximum load of the cyclic test was set to 20% of the MBL as this represents typical loads in practical applications [6]. As shown in Figure 2, the rope had a gauge length of 105 mm and was sewn at both ends to clamp it to the tensile testing machine (AG-I Shimadzu co., maximum load of 100 kN). The strain of the rope was measured by the non-contact method using a high-speed camera (Basler acA4600-10 uc) with a resolution of 4608 \(\times\) 3288 pixels. The change in the length between the two marked points (Figure 2a), initially 43 mm apart, was measured by the camera during the test. The change in the braided angle and the diameter of the rope were also measured during the test. The camera was controlled to take pictures at the same time interval as the load measurements from the tensile testing machine. To improve the reliability of the results, the diameter and braided angle were measured 5 and 10 times, respectively, and each averaged. For the strand experiment, glass fiber reinforced plastic (GFRP) plates were attached at both ends of the strand with epoxy adhesive (3M Scotch-WeldTM DP460) to clamp with the grip of tensile testing machine (Figure 2b). The strain of the strand was calculated using crosshead displacement of the tensile tester. Three samples of rope and strand were tested in this study and they were conducted at a crosshead speed of 1 mm/min. In this study, we did not change the crosshead speed since the viscoelastic effect was not taken into account because the stiffness varied with small range in 1.9% for strand and 5.0% for rope when the crosshead speed changes from 1 to 200 mm/min.  
\begin{table}
\begin{tabular}{c c c} \hline  & **Strand** & **Rope** \\ \hline Material & High modulus polyethylene (HMPE) \\ Fiber & IZANAS \\ Fiber model & DB-60 \\ MBL (Static) (N) & 430 & 1900 \\ Construction & 176 * tex & 1721 * tex, 8 strand braided \\ Diameter (mm) & 0.57 & 2 \\ Supplier & Fiber: Toyobo, Rope: Hayami industry \\ \hline \end{tabular}  
*: Obtained by weighing the strand and rope at the length of 108 mm and 43 mm, respectively.  
\end{table}
Table 1: Properties of braided HMPE strand and rope.  
Figure 1: Braided HMPE rope composed of eight strands.