## 3 Results and Discussion  
The dynamic coercivity was successfully obtained from the reversible permeability profile assuming the position of maximum reversible permeability. The variation in dynamic coercivity exponentially decreased as a function of fatigue cycles at each hold time, as shown in Figure 1a. The decreasing rate of 600 s holding time shows higher than that of 60 s holding time. The dynamic coercivity of the fracture at the holding time of the 60 s shows the same level right before fracture. However, at a holding time of 600 s the dynamic coercivity of the fracture increases and shows higher than right before fracture. The dynamic coercivity decreased with fatigue cycles showing a magnetically softening phenomenon. The magnetization is physically related to the domain wall motion, and the coercivity depends on the degree of pinning of the domain wall. Therefore, inclusions, dislocation, and grain boundary may hinder the domain wall movement, which are potentials of pinning sites of the domain wall. We investigate microstructural evolution during creep-fatigue damage of 9 Cr steel with the support of microstructural observation techniques. The Vickers's hardness continuously dropped, indicating mechanical softening. Figure 1b depicts the relationship between Vicker's hardness and dynamic coercivity showing good linear relation and high R-square of 0.9. [PERSON] et al. also reported that the good correlations of magnetic coercivity with Vicker's hardness. They studied magnetic coercivity of 2.25 Cr steel subjected to long-term thermal aging and showed the precipitate dependence on the magnetic coercivity [20]. Most metallic components undergo mechanical softening during their high-temperature and high-pressure exposure due to the coarsening of the secondary phases and the recovery of dislocations resulting in a decrease in mechanical strength [21]. Therefore, this dynamic coercivity should be a potential method to evaluate the degradation of structural materials. Figure 2 shows the TEM micrographs at each fatigue cycle and the SAD pattern of precipitates. The martensitic lath structures consist of dislocation substructures and fine precipitates. The as-tempered specimen shows a typical martensite structure as shown in Figure 2. The previous austenite grain (PAG) size was 20 \(\upmu\)m and the lath width was 0.21 \(\upmu\)m. The PAG size does not change during the test. The tempered ferritic 9 Cr steel showed elongated lath substructures, as shown in Figure 2a. The dislocations were tangled with a high density. The dislocation density decreased with the creep-fatigue test of 0.2\(N_{f}\) (see Figure 2b). The martensite lath continuously increased with creep-fatigue (see Figure 2c) and the dislocation density was lower than in Figure 2a. The growth of the lath width is attributed to the recovery of dislocations within and recombination of the lath boundaries due to the migration of the lath boundary [22]. The dislocation density of each deformed sample was calculated by the XRD strain measurement. Figure 1: Variation in dynamic coercivity and Vicker’s hardness; (**a**) dynamic coercivity with fatigue cycles and (**b**) correlation between hardness and dynamic coercivity. Figure 2: _Cont._  
The precipitates slightly increased after fatigue failure of 600 s hold time as shown in Figure 3. The total increase in the size of the precipitates was less than 10%. The agglomeration and coarsening at the grain boundaries and lath interfaces were dominant during the creep-fatigue damage. The M\({}_{23}\)C\({}_{6}\) carbides were present as (Cr, Fe, Mo)\({}_{23}\)C\({}_{6}\) and (Nb\({}_{X}\) V\({}_{1\cdot X}\)CN; MX) types, where \(x\) varies from one to zero. Laves Fe\({}_{2}\)(Mo,W) phases were reported to nucleate on martensite lath boundaries during long term aging, fatigue, and creep deformation, with a high growth rate, which has a significant effect on the decrease of creep strength [23, 24].