## Materials and Methods
### Micromagnetic Methods
Therefore, \(Z\) describes a loop in the impedance plane throughout one hysteresis cycle [19]. Figure 2 illustrates the parameters derived from this loop. 2. Incremental permeability (IP) analysis is a method of separating magnetic permeability information from electrical conductivity information in EC analysis [16; 17]. Plotting the change in EC coil impedance (DZ) against drive voltage U leads to an incremental permeability plot (Figure 3, left) [19]. Several parameters are derived from the incremental permeability curve (Figure 3). Figure 3: Schematic illustration of the incremental permeability curve and the parameters derived. Figure 2: Schematic illustration of the impedance loop and derived parameters. 3. The measured magnetizing current exhibits a low-frequency distortion due to hysteresis in the magnetic circuit. The fundamental and harmonic components can be determined numerically using a fast Fourier transform; thus, the distortions of the magnetizing current are quantified. The harmonic components determined through this procedure allow for the determination of material properties (Figure 4) [19]. Figure 5 shows the 3 MA-X8 device, including a probe and a PC. The 3 MA-X8 measurements were performed at a magnetization frequency of 50 Hz, a magnetization current voltage of 2 V, and a superimposed EC frequency of 2000 Hz. The 3 MA-X8 device is controlled by modular measuring system (MMS) software. The output of the data acquisition and evaluation module was a set of 21 magnetic parameters derived from the 3 MA-X8 measurements, as listed on the right-hand side of Figures 2-4. A specimen holder and a probe holder improved reproducibility by minimizing positioning variations. The Centre for Energy Research developed and applied the MAT method. The MAT method uses the systematic measurement of large families of minor hysteresis loops from minimum amplitudes up to, possibly, the maximum (major) on degraded ferromagnetic samples/objects. From the large volume of recorded data, the data that reflect material degradation in the most sensitive, or otherwise most convenient, manner are applied for evaluation of the degradation. These data, best-adapted for the investigated case, were used as the MAT parameter(s), and their dependence on an independent variable accompanying the inspected degradation is referred to as the MAT degradation function(s). Figure 4: Schematic illustration of the harmonic analysis in the time domain signal of the magnetization current. Figure 5: The micromagnetic multiparameter microstructure and stress analysis (3 MA)-X8 system, including 3 MA-X8 device, probe, and PC (**left**); (**right**) specimen holder and probe holder. The magnetic induction method appears to be the easiest method of systematic measurement for MAT. A specially designed permeameter [28], with a magnetizing yoke, was applied for the measurement of families of minor loops of a magnetic circuit's differential permeability. Measurement of the hysteresis loops was performed by a magnetizing yoke, which is placed on the flat surface of the Charpy specimens. A C-shaped laminated Fe-Si transformer core was used. The yoke had a cross-section of 10 \(\times\) 5 mm and a total external length of 18 mm. This size was chosen to fit the size of the investigated specimens. The specimen holder, designed for hot-cell measurements, is shown in Figure 6[29]. The driving coil wound on the yoke produces triangular variations in the applied magnetic field, with stepwise increasing amplitudes and a fixed slope magnitude in all the triangles (Figure 7a). The signal coil picks up the induced voltage, proportional to the differential permeability of the sample.