# Research on Residual Life Estimation Method for KMN Steel Based on Nonlinear Ultrasonic Testing
## 3 Results
### Micro-Cracks Statistics  
As the number of fatigue cycles increases, the microstructure of the specimen shows microscopic defects, such as holes and pits and further micro-cracks, form. The micro-cracks continue to grow and eventually lead to the failure of the material. Therefore, the increase in fatigue cycles leads to the initiation and propagation of fatigue cracks. Combined with the microstructure analysis of the dangerous section of the KMN bending fatigue specimen, the number and length of fatigue cracks in the 10-standard field (500 \(\times\) 500 \(\upmu\)m) of view of each specimen are counted, as shown in Table 4, where the equivalent crack length refers to the sum of all crack lengths in the field of view. Since the received signal of the nonlinear ultrasonic Lamb wave is the sum of the second harmonic generated by all defects in the sampling area, it is more reasonable to use the equivalent crack length in the research process than the single crack length. It can be seen from Figure 6 that the number of cracks, the maximum crack length and the equivalent crack length all increase with the increase in the number of fatigue cycles, reflecting the process of continuous crack propagation inside the specimen.  
Figure 4: The relationship curve between normalized nonlinear coefficient and fatigue cycles under bending fatigue (A–D corresponds to four test points of different fatigue cycles).  
Figure 5: SEM microscopic morphology of KMN bending fatigue specimens. (**a**) The cross-sectional morphology of the specimen at point A in Figure 4; (**b**) The cross-sectional morphology of the specimen at point B in Figure 4; (**c**) The cross-sectional morphology of the specimen at point C in Figure 4; (**d**) The cross-sectional morphology of the specimen at point D in Figure 4; (**e**) The cross-sectional morphology of the specimen in 3k magnification; (**f**) The cross-sectional morphology of the specimen in 3k magnification.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Fatigue Cycle** & \(\mathbf{5\times 10^{4}}\) & \(\mathbf{10^{5}}\) & \(\mathbf{5\times 10^{5}}\) & \(\mathbf{7\times 10^{5}}\) & \(\mathbf{10^{6}}\) & \(\mathbf{5\times 10^{6}}\) & \(\mathbf{10^{7}}\) \\ \hline Number of cracks & 0 & 0 & 1 & 3 & 4 & 6 & 12 \\ Crack length & 0 & 0 & 8 & 6, 7, 12 & 4, 8, 18, 26 & 10, 12, 14, 16, 25, 30 & 5, 7, 8, 9, 10, \\ \(\mathrm{\mu m}\) & 0 & 0 & 8 & 6, 7, 12 & 4, 8, 18, 26 & 10, 12, 14, 16, 25, 30 & 11, 11, 12, 13, 25, 31, 58 \\ Equivalent crack length/\(\mathrm{\mu m}\) & 0 & 0 & 8 & 25 & 56 & 107 & 181 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Statistics of internal micro-cracks and equivalent crack length of KMN bending fatigue specimens.  
The mapping relationship between the micro cracks inside the KMN bending fatigue specimen and the measured nonlinear coefficients is further analyzed, and the corresponding curve (i.e., the \(\beta\)-\(a\) curve) between the equivalent crack length of the material and the nonlinear coefficient is established, as shown in Figure 7. Due to the decrease of the nonlinear coefficient caused by the internal signal attenuation of the material in the late fatigue stage (after \(10^{6}\) cycles), we focus on the analysis of the corresponding relationship in the early stage of fatigue. It can be seen from Figure 7 that, as the effective length of the crack increases, the nonlinear coefficient of the material is also increasing. Especially in the initial stage of fatigue crack initiation, the nonlinear coefficient is very sensitive to the effective size change of the fatigue crack. Therefore, we can use the change of the nonlinear coefficient to reflect the initiation process of fatigue micro-cracks in the material at the early stages of fatigue.  
Figure 6: The relationship curve between equivalent crack length and fatigue cycles under bending fatigue.  
Figure 7: The relationship curve between equivalent crack length and normalized nonlinear coefficient under bending fatigue.