# Research on Residual Life Estimation Method for KMN Steel Based on Nonlinear Ultrasonic Testing
## 5 Conclusions  
Nonlinear ultrasonic testing was used to calculate the relationship curve between the nonlinear coefficient and number of fatigue cycles of KMN steel. The experimental results show that:  
1. The non-linear coefficient of the material first increases and then decreases with an increase in the number of fatigue cycles. Through a microanalysis of the section of the dangerous position of the specimen, it was found that, as the fatigue cycle increases, the microstructure of the specimen gradually deteriorates and micro-cracks occur.
2. The relationship between the growth of micro-cracks inside the material and the nonlinear coefficient was studied, and it was shown that nonlinear ultrasonic testing can be used to characterize the initiation of early micro-cracks due to material fatigue and that the material's nonlinear coefficient \(\beta\) can be used to reflect the internal fatigue damage degree and fatigue life of the material.
3. Numerical statistics of the fatigue cracks inside the specimen were carried out, and the extreme value of the fatigue cracks was calculated using the Gumbel distribution. An empirical formula for the relationship between the nonlinear coefficient of KMN steel and the equivalent crack length at the early fatigue stage (before 10\({}^{6}\) cycles) was established, and then a method for estimating the residual fatigue life of KMN steel based on nonlinear ultrasonic testing was proposed and verified.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Specimen No.** & \(\beta\) & \(a\)\(\mu\)**m** & **Model Prediction Results \(N_{\text{i}}+N_{\text{p}}\)** & **Test Results \(N_{\text{f}}\)** & **Relative Error** & **Residual Life \(N_{\text{r}}\)** \\  & & \(/\mu\)**m** & **/Cycle** & **/Cycle** & **/Cycle** \\ \hline
1\# & 10.19 & 32.37 & 1.72 \(\times\) 10\({}^{6}\) & 7 \(\times\) 10\({}^{5}\) & 146\% & 1.08 \(\times\) 10\({}^{6}\) \\
2\# & 8.5 & 22.90 & 1.1 \(\times\) 10\({}^{6}\) & 7 \(\times\) 10\({}^{5}\) & 57\% & 2.7 \(\times\) 10\({}^{6}\) \\
3\# & 11.86 & 39.62 & 1.98 \(\times\) 10\({}^{6}\) & 1 \(\times\) 10\({}^{6}\) & 98\% & 1.82 \(\times\) 10\({}^{6}\) \\
4\# & 11.58 & 39.68 & 1.99 \(\times\) 10\({}^{6}\) & 1 \(\times\) 10\({}^{6}\) & 99\% & 1.81 \(\times\) 10\({}^{6}\) \\
5\# & 12.2 & 42.95 & 2.08 \(\times\) 10\({}^{6}\) & 1 \(\times\) 10\({}^{6}\) & 108\% & 1.72 \(\times\) 10\({}^{6}\) \\
6\# & 18.32 & 72.81 & 2.54 \(\times\) 10\({}^{6}\) & 3 \(\times\) 10\({}^{6}\) & 15\% & 1.26 \(\times\) 10\({}^{6}\) \\
7\# & 14.52 & 55.16 & 2.32 \(\times\) 10\({}^{6}\) & 3 \(\times\) 10\({}^{6}\) & 23\% & 1.48 \(\times\) 10\({}^{6}\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of test results and model prediction results of KMN steel residual life.  
involved in project administration. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (Grant No. 519058484) and Zhejiang Province Public Welfare Technology Application Research Project (Grant No. LGG20E050018).  
Not applicable.  
Thanks for the test equipment provided by Shandong University.  
The authors declare no conflict of interest.