## 2 Materials and Methods  
The ferritic 9 Cr low-carbon steel was used in this study. The creep-fatigue was conducted by a servo-hydraulic fatigue test machine. It was achieved under load control with a hold time of 60 s and 600 s at the maximum tensile. The test sample was prepared with a cylindrical shape in a dimension of 16 mm length and 10 mm diameter. For the NDE test of damaged structural materials, the test coupons were prepared with different levels of creep-fatigue damages by the interruption test. The interruption time was varied on the basis of the number of fatigue cycles. Table 1 shows the creep-fatigue test parameters such as fatigue life fraction (fraction to the fracture cycle, \(N_{\text{f}}\)), cycle, test duration, and total hold time.  
To examine the morphology and crystal structure of the precipitates, a thin film specimen of carbon extraction replica was prepared and examined by transmission electron microscopy (TEM) [17]. The chemical composition of precipitates was analyzed by the energy dispersive spectroscopy (EDS). Further, the crystal structure of precipitates was evaluated by the selective area diffraction (SAD) pattern. To observe the dislocation substructures, thin foils of 3 mm diameter disc specimens were finally prepared by electrolytic polishing in a solution of 125 mL H\({}_{2}\)SO\({}_{4}\) and 875 mL methanol.  
The X-ray diffraction patterns were obtained to measure the dislocation density with monochromatic Cu \(K_{\text{c}1}\) radiation using a high-resolution X-ray diffractometer (HRXRD). The plastic strain was measured by the X-ray diffraction (XRD) line profile, then converted to the breadth of  
\begin{table}
\begin{tabular}{c l l l l l l l} \hline \hline \multicolumn{2}{c}{**Fatigue Life Fraction**} & \multicolumn{1}{c}{\(\mathbf{0.1N_{f}}\)} & \multicolumn{1}{c}{\(\mathbf{0.2N_{f}}\)} & \multicolumn{1}{c}{\(\mathbf{0.4N_{f}}\)} & \multicolumn{1}{c}{\(\mathbf{0.6N_{f}}\)} & \multicolumn{1}{c}{\(\mathbf{0.8N_{f}}\)} & \multicolumn{1}{c}{\(\mathbf{1N_{f}}\)} \\ \hline \multirow{4}{*}{60 s} & Cycle & 330 & 660 & 1320 & 1980 & 2640 & 3300 \\ \cline{2-8}  & Test duration (s) & 384 & 768 & 1536 & 2310 & 3078 & 3840 \\ \cline{2-8}  & Total hold time & 330 & 660 & 1320 & 1980 & 2640 & 3300 \\ \hline \multirow{4}{*}{600 s} & Cycle & 95 & 190 & 380 & 570 & 760 & 950 \\ \cline{2-8}  & Test duration (s) & 960 & 1920 & 3840 & 5790 & 7722 & 9600 \\ \cline{1-1} \cline{2-8}  & Total hold time & 948 & 1896 & 3738 & 5700 & 7596 & 9498 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Creep-fatigue parameters of tempered ferritic 9 Cr steel.  
the strain distribution using the Hall-Williamson method [18]. A surface layer of about 50 \(\upmu\)m was removed by an electrolytic polishing method in 10% Nital acid at a voltage of 24 V, before the X-ray diffraction experiments. The micro Vicker's hardness test was carried with the same samples of optical micrograph observation after vibration polishing with 0.01 \(\upmu\)m Al\({}_{2}\)O\({}_{3}\) suspension.  
A ferrite yoke type probe was applied to eliminate the demagnetization effect and wound by pickup coils, AC perturbing coils, and DC magnetizing coils. The test specimen was prepared in a dimension of 15 mm \(\times\) 7 mm \(\times\) 1 mm by the wire cutting process. The specimens were magnetized using a sinusoidal wave current of 0.05 Hz with a maximum applied magnetic field of 12.0 kA/m.  
The voltage was induced in the pickup coil and obtained by a lock-in amplifier (EG&G PAR 5210). A more detailed experimental system was previously reported [19]. The reversible permeability (RP) profile can be successfully obtained during a slow varying cycle with current using an I/O board.  
The maximum permeability may correspond to the dynamic coercivity when the magnitude of the modulation field is negligible compared with coercivity. Therefore, dynamic coercivity could be obtained from the reversible permeability profile.