## 3 Results and Discussion  
### Lifetime Prediction Methods  
This experiment utilizes a strain-hardening algorithm to forecast the life of polyethylene aging pipes. The advantages of using this algorithm to predict pipe life are the small measurement variation (no specimen notch and surfactant required) and the short time-consuming test time. The principle of the strain-hardening test is that at room temperature, the polyethylene material is prone to intermolecular slippage and untangling during the stretching process, forming the so-called tethering phenomenon. Slow crack growth (SCG) is one of the most important failure mechanisms of polyethylene gas and water pipes. Slow crack expansion is the main determinant of the service life of polyethylene pipes, and to resist the tendency of crack expansion, strain-hardening effects are produced by the microfibers in the silver grain. There is a clear relationship between the resistance of PE materials to slow crack extension and the inherent characteristics of the material, and [PERSON] et al. proposed that the SCG resistance of PE materials is mainly controlled by the inherent strain-hardening response of microfibers, verifying a positive correlation between the inherent characteristics of the material and its SCG resistance at the microscopic level [22]. The strain-hardening (SH) test developed by [PERSON] et al. has been used for the performance evaluation of various PE and resin materials, and the test results have shown that the SH test is very promising for assessing the resistance to slow crack expansion of various PE pipes in short-term tests and reproducible experiments [23]. The inherent characteristics of PE materials can therefore be characterized by measuring the strain-hardening modulus of the PE material, which can be used to predict the time to failure of the pipes. The strain-hardening algorithm requires that the specimen be stretched above its natural tensile ratio, at which point strain-hardening will occur. The strain-hardening modulus \(Gp\) is based on the relationship between the number of measurement points N in the strain-hardening interval (usually stretching ratios 8 to 12) [24], the stretching ratio \(\lambda\) of the specimen (i.e., the ratio of the stretching length between specimen moments to the initial specimen distance recorded at a certain point in the test), and the true stress \(\sigma\) to which the specimen is subjected during the stretching process. [PERSON] et al. applied, the Pennsylvania Notch  
Figure 5: Experimental flow chart. Test (PENT) [25], Cyclic load notched round bar (CRB) test, and SHT to one single-peaked polyethylene (PE80), four bimodal polyethylenes (three PE100 and one PE100-RC), and one PE-BF (for blow molding) to obtain a comparison of the strain-hardening modulus with the failure time results of the PENT test and the full notch creep (FNCT) [26] test, plotted failure time versus strain-hardening modulus with the data obtained, and then fitted the data to obtain the relationship between failure time and strain-hardening modulus [27]. Due to the relationship between failure time and strain-hardening modulus discovered by [PERSON], [PERSON], and colleagues [23; 24; 25; 26; 27], the failure time of PE pipes can be determined. After fitting the data, a graph of failure time versus acidity of the corrosive solution was obtained. This enabled us to further propose a mathematical model for life prediction of buried natural gas PE pipes under acid and alkaline corrosion conditions, with the following prediction algorithm:  
Strain-hardening modulus is the strain-hardening interval where the stress-strain curve will begin to show a sharp increase in stress when the specimen is stretched to its natural tensile ratio in a tensile test. The slope of this part of the curve is defined as the strain-hardening modulus. The strain-hardening modulus is a measure of a material's ability to resist strain-hardening.