# Research on Lifespan Prediction of Cross-Linked Polyethylene Material for XLPE Cables
## 1 Introduction
### Mechanical Properties  
#### 2.2.1 Tensile Testing  
Tensile testing is one of the widely accepted methods for evaluating the aging performance of XLPE cables. On the basis of test results, some scholars propose to use two parameters, tensile strength and elongation, to characterize the aging degree of XLPE cables [14]. In this paper, the changing law of tensile strength and breaking elongation of samples after each aging process was assessed by tensile testing. The test methods of tensile testing are as follows.  
The tensile strength and breaking elongation of samples were inspected using 5 KNCMT-4503 from MASTER (a company manufactures measuring apparatus in China). In accordance with IEEE Standard 60811-1-1: 2001 [15], six samples of the same aging time should be cut into a dumbbell, with a width of 4 cm. In addition, the tensile strength and breaking elongation of samples can be calculated according to Equations (3) and (4).  
\[\sigma=\frac{P}{A}=\frac{P}{bd} \tag{3}\]  
where \(\sigma\) is the tensile strength, N/mm\({}^{2}\); \(P\) is the tensile force at fracture, N; \(A\) is the initial cross-sectional area, mm\({}^{2}\); \(b\) is the width of samples, mm; \(d\) is the thickness of samples, mm.  
\[\delta=\frac{\Delta l}{l_{0}}=\frac{l-l_{0}}{l_{0}} \tag{4}\]  
where \(\delta\) is the breaking elongation of samples; \(\Delta l\) is the increment of samples elongating at break, mm; \(l\) is the length between two marking lines at break, mm; \(l_{0}\) is the length of initial two marking lines, \(l_{0}=20\) mm.  
The test results for tensile strength and breaking elongation of XLPE cables aged for different years are listed in Table 2, and the standard deviation of tensile strength is denoted as \(a_{\sigma}\) along with that of breaking elongation, \(a_{\delta}\).  
Table 2 presents the following:  
1. With the increase in aging time, the tensile strength of XLPE cable samples gradually decreases. For samples aged for 2, 3, 5, 6 and 8 years, the tensile strength of samples decreases by 2.68%, 9.53%, 12.25%, 14.54% and 20.02%, respectively, compared with samples aged for 1 year.
2. With the increase in aging time, the breaking elongation of XLPE cable samples has an accelerated decreasing trend. For samples aged for 2, 3, 5, 6 and 8 years, the breaking elongation of samples decreases by 1.70%, 7.75%, 14.14%, 18.1% and 27.49%, respectively, compared with samples aged for 1 year.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Samples** & **b/mm** & **_d/mm** & **_P/N_** & **\(\sigma\)/MPa** & \(a_{\sigma}\) & \(\delta\)/\%** & \(a_{\delta}\) \\ \hline A\({}_{1}\) & 4 & 0.91 & 83.98 & 23.18 & 0.296 & 497.57 & 0.074 \\ A\({}_{2}\) & 4 & 0.86 & 77.61 & 22.56 & 0.318 & 489.10 & 0.086 \\ A\({}_{3}\) & 4 & 0.87 & 77.18 & 22.25 & 0.456 & 474.37 & 0.056 \\ A\({}_{4}\) & 4 & 0.81 & 68.12 & 20.97 & 0.800 & 459.02 & 0.063 \\ A\({}_{5}\) & 4 & 0.87 & 72.30 & 20.83 & 0.309 & 446.49 & 0.109 \\ A\({}_{6}\) & 4 & 0.92 & 74.85 & 20.34 & 0.276 & 427.24 & 0.076 \\ A\({}_{7}\) & 4 & 0.96 & 76.00 & 19.81 & 0.182 & 407.51 & 0.082 \\ A\({}_{8}\) & 4 & 0.94 & 71.52 & 19.02 & 0.805 & 388.15 & 0.095 \\ A\({}_{9}\) & 4 & 0.84 & 62.29 & 18.54 & 0.613 & 360.79 & 0.113 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results of tensile test of samples from Factory A.  
Moreover, as results in the previous research have shown, there is a correlation between tensile strength and the physicochemical properties of XLPE cables [14]. The reasons for the changing law of tensile strength and breaking elongation are that the crystallinity of samples decreases with the increase in aging time, as mentioned in Section 2.1.2, which, in turn, results in a more chaotic arrangement of molecules and more frequent molecular movements.