## Materials and Methods
### Micromagnetic Methods
This triangular variation of the magnetizing field, with time \(t\) and a voltage signal \(U\), is induced in the pick-up coil for each \(k\)th sample:  
\[U(\mathrm{d}F/\mathrm{d}t,\,F,A_{j},\,\varepsilon_{k})=K\times\partial B( \mathrm{d}F/\mathrm{d}t,\,F,A_{j},\,\varepsilon_{k})/\partial t=K\times\mu( \mathrm{d}F/\mathrm{d}t,\,F,A_{j},\,\varepsilon_{k})\times\mathrm{d}F/ \mathrm{d}t, \tag{1}\]  
where \(K\) is a constant determined by the geometry of the sample and by the experimental arrangement; \(\varepsilon\) is the independent degradation variable, in our case, Vickers hardness, yield strength, or transition temperature. As long as \(F=F(t)\) sweeps linearly with time, i.e., \(\mathrm{d}F/\mathrm{d}t\,\,\mathrm{\rvert}\) is (the same) constant for measurement at each of the samples, Equation (1) states that the measured signal is simply proportional to the differential permeability \(\mu\) of the measured magnetic circuit as it varies with the applied field \(F\) within each minor loop amplitude \(A_{j}\) for each \(k\)th measured sample. If we wish to obtain correct results that are not  
Figure 6: Photo of the specimen holder. A Charpy specimen is placed on the top (V-notch is opposite the magnetizing yoke) [29]. Figure 7: The time variation of the magnetizing current (**a**) and the measured permeability loops (**b**) [30]. influenced by any previous remanence, each sample has to be thoroughly demagnetized before it is measured. The permeameter works under the control of a notebook, which sends the steering information to the function generator and collects the measured data. An input/output data acquisition card accomplishes the measurement. The computer registers two data files for each measured family of minor loops. The first one contains detailed information about all the preselected parameters of the demagnetization and the measurement. The other file holds the course of the voltage signal \(U\) induced in the pick-up coil as a function of time \(t\) and of the magnetizing current \(I_{F}\) and/or field \(F\). As an illustration, Figure 7b presents the families of permeability loops. Large amounts of data were generated, and our task was to compare them and find the most suitable data for characterizing the changes between samples. Instead of keeping the signal and the magnetizing field in shapes of continuous time-dependent functions, it is practical to interpolate the family of data for each \(\epsilon_{k}\) sample into a discrete square (\(i\), \(j\)) matrix, \(U(F_{i}A_{j},\epsilon_{k})\), with a suitably chosen step, \(\Delta A=\Delta F\). Because \(\mathrm{d}F/\mathrm{d}t\) is a constant, identical for all measurements within one experiment, it is not necessary to write it explicitly as a variable of \(U\). MAT is a relative method (practically all the nondestructive methods are relative), and the most suitable information regarding the degradation of the investigated material can be contained in the variation of any element of such matrices as a function of \(\epsilon\), relative to the corresponding element of the reference matrix \(U(F_{i}A_{j},\epsilon_{0})\). So, we divided all \(U(F_{i},A_{j},\epsilon_{k})\) elements by the corresponding elements \(U(F_{i}A_{j},\epsilon_{0})\) of the reference sample matrix and obtained the normalized elements of the matrices of relative differential permeability \(\mu(F_{i}A_{j},\epsilon_{k})=U(F_{i},A_{j},\epsilon_{k})/U(F_{i},A_{j}, \epsilon_{0})\), and their proper sequences  
\[\mu(F_{i}A_{j},\epsilon)=U(F_{i},A_{j},\epsilon)/U(F_{i},A_{j},\epsilon_{0}) \tag{2}\]  
as normalized \(\mu\)-degradation functions of the inspected material. These \(\mu\) elements are referred to as MAT descriptors, and they characterize the degradation of the material. Numerous MAT descriptors are calculated during evaluation; their number depends on the density and how \(\mu(F_{i}A_{j},\epsilon_{k})\) points are calculated. Normally, about 1000 MAT descriptors are calculated.