## 1 Introduction  
The ferritic 9 Cr steel has been recognized as a key material for turbines, rotors, pipes, etc. in nuclear and fossil power plants. In this ferritic low-carbon steel, the Cr element increases generally high-temperature creep strength, oxidation resistance, and corrosion resistance, which has superior physical and chemical properties than low Cr content steels [1; 2; 3]. However, mechanical softening causing strength drop and embrittlement is inevitable for high-temperature structural materials because of long-term exposure to high temperature and high pressure, such as creep and fatigue. The mechanical softening is physically evolved to the microstructural variation in a generation and coarsening of the secondary phases, the recovery of dislocations, the growth of martensite lath width, and depletion of the solute atoms [4; 5]. Structural facilities subjected to high temperature and high pressure for long-term exposure can be deteriorated and fractured during their operation due to mechanical softening. Since the damage and fracture are localized and accelerated without notice, the monitoring and characterization of structural components are very important and necessary. Therefore, in-service inspections and nondestructive evaluation (NDE) methods are indispensable to evaluate safety periodically. To monitor the mechanical softening during long-term exposure, the microstructural variation should be quantified and evaluated [6; 7; 8].  
Reversible magnetic permeability is the limited value of the incremental permeability when the incremental permeability is at \(\Delta H\)\(\rightarrow\)0 [9]. Magnetic properties are usually measured at the fixed magnetic field applied to the test samples in most magnetic techniques. However, for the dynamic method, the modulation field is also applied in addition to the magnetization field. Then, the induction of the samples are obtained. The maximum permeability value generally corresponds to the coercivity field (\(H_{\text{c}}\)) of the sample. Under dynamic conditions, it is easy to measure the dynamic coercivity from a plot of \(\mu_{\text{r}}\) (reversible permeability) versus \(H_{\text{a}}\) (applied magnetic field), taking into account the magnitude of small modulation \(H_{0}\), such as \(H_{0}<<H_{\text{c}}\)[10].  
For many years, the magnetic properties of ferromagnetic materials have been known to depend on their microstructural characteristics, such as composition, dislocation, precipitates, and grain size. [PERSON] [11] reported that the saturation magnetization is not strongly influenced by purity, while coercivity and permeability strongly depend on the purity and crystallographic features in iron. In addition, [PERSON] et al. [12] studied the precipitates in extra-low-carbon steel by characteristic magnetic parameters measured from major and minor magnetization loops. Most of all, the dependence of coercivity on grain size is well-known to be an inverse square root relationship. The coercivity linearly increases with the reciprocal of the square root of grain size as well as theoretical calculation [13,14]. [PERSON] et al. assumed that coercivity is due to the pinning of Bloch walls by second-phase particles considering that the wall are rigid walls [15]. [PERSON] et al. investigated that the dislocation should be the Bloch wall pinning site in a similar manner to the mechanical problem of dislocation bowing of the pinning center [16]. Such relationships strongly suggest that magnetic measurements could be a potential technique as a nondestructive evaluation method for the determination of the physical properties of materials. This experimental study deals with the NDE of creep-fatigue in ferritic steel using a magnetic property to examine the effects of nonmagnetic inclusions and dislocations on the dynamic coercivity.