# Research on Lifespan Prediction of Cross-Linked Polyethylene Material for XLPE Cables
## 1 Introduction
### Physicochemical Properties
#### 2.1.2 Differential Scanning Calorimetry (DSC) Test  
Cross-linked polyethylene material is composed of a semi-crystalline polymer, whose property is closely related to the crystal aggregation structure. To investigate the changing state of the crystallinity of samples throughout the aging process, some researchers have proposed the use of the crystallinity parameter [13]. The test methods for the DSC test are as follows. TAQ 50 from the USA was used to perform this test. The DSC tests reported in this paper were conducted in a nitrogen atmosphere. In each test, about 10 mg of XLPE cable samples was heated from ambient conditions to 140 \({}^{\circ}\)C at 10 \({}^{\circ}\)C/min. The DSC test results are shown in Figure 2.  
Figure 2 presents the following:  
1. There are two melting peaks in the samples with different aging times, which are distributed in two ranges: temperature 70-80 \({}^{\circ}\)C (denoted as peak 1) and 100-110 \({}^{\circ}\)C (denoted as peak 2). 2. With the increase in aging time, the melting temperature of samples moves towards a low temperature in melting peak 1, along with an increase in the area of melting peak 1. However, the change regularities of melting peak 2 are different to melting peak l, and can be divided into two ranges. When the operating time is within 2.5 years, the melting temperature moves towards a higher temperature and the area of melting peak 2 gradually increases. When the operating time exceeds 2.5 years, the melting temperature moves towards a low temperature and the area of melting peak 2 gradually decreases. Figure 1: Test results of gel content test. Since the crystallinity is directly related to the enthalpy fusion, which is proportional to the area under the main endothermic peak of crystalline fusion, the degree of crystallinity was deduced using relationship [13]:  
\[X_{c}=\frac{\Delta H_{m}}{\Delta H_{0}}\times 100\% \tag{2}\]  
where \(X_{c}\) is the crystallinity of samples; \(\Delta H_{m}\) is the enthalpy of fusion, J/g; \(\Delta H_{0}\) is the specific melting enthalpy for 100% of samples, \(\Delta H_{0}\) = 287.3 J/g. Combining the enthalpy fusion of samples obtained in test results with Equation (2), the crystallinity of samples of XLPE cables with different aging years from Factory A is listed in Table 1, and the standard deviation of the crystallinity of samples with the same operating time is denoted as \(\sigma_{X}\). Table 1 shows the relationship between crystallinity and operating time. In can be seen that the crystallinity of XLPE insulation presents an increase when the operating time is less than 2.5 years. However, a rapid decrease in crystallinity can be found when the operating time exceeds the critical time. The reason for this phenomenon is the thermal oxidation and pyrolysis reaction on XLPE cables, which, in turn, enhances molecular polarity and shortens macromolecular chains. Due to some antioxidants remaining in XLPE insulation, the thermo-oxygen aging reaction is offset, which, in turn, leads to an increase in the enthalpy of fusion. Meanwhile, when antioxidants are expended out, the crystallinity decreases with the increase in operating time. In addition, as the content of small \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Samples**} & **Operating** & **Enthalpy of** & \multirow{2}{*}{**Crystallinity \(X_{d}\)/\%**} & **Standard** \\  & **Time/Year** & **Fusion \(\Delta H_{m}\)/(J/g)** & & **Deviation \(\sigma_{X}\)** \\ \hline A\({}_{1}\) & 1 & 97.86 & 34.1 & 0.002 \\ A\({}_{2}\) & 2 & 98.68 & 34.3 & 0.003 \\ A\({}_{3}\) & 2.5 & 99.52 & 34.6 & 0.002 \\ A\({}_{4}\) & 3 & 96.36 & 33.5 & 0.003 \\ A\({}_{5}\) & 3.5 & 95 & 33.1 & 0.003 \\ A\({}_{6}\) & 5 & 92.56 & 32.2 & 0.005 \\ A\({}_{7}\) & 6 & 90.09 & 31.4 & 0.003 \\ A\({}_{8}\) & 7 & 88.21 & 30.7 & 0.002 \\ A\({}_{9}\) & 8 & 86.33 & 30.1 & 0.004 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The crystallinity of cross-linked polyethylene (XLPE) for each cable sample. Figure 2: Test results of differential scanning calorimetry (DSC) test.