**3. Results**

#### *3.1. Results of MAT, 3MA and MBN Measurements Made on All Samples*

3.1.1. Evaluation of Data without Normalization

In Figure 3 it is shown how the optimally chosen MAT descriptor depends on the transition temperature for the two investigated materials, 15kH2NMFA and A508 Cl.2. We use the terminology "Optimally chosen MAT descriptor" for those parameters, picked up from the generated big data pool, which characterize the best the correlation with the given independent parameter. In the present case this is the material embrittlement generated by neutron irradiation [8,9]. This parameter ensures the largest sensitivity together with good reproducibility. In the case plotted in Figure 3, this descriptor is characterized by ha = −30 mA and hb = 1080 mA magnetic field values for 15kH2NMFA material and by ha = −780 mA and hb = 1200 mA values for A508 Cl.2. material. (ha: magnetizing field, hb: minor loop amplitude).

**Figure 3.** Optimally chosen MAT descriptor vs. transition temperature for all measured 15kH2NMFA and A508 Cl.2 samples.

Similarly, the results of 3MA are shown in Figure 4. By applying 3MA, clear trend between several magnetic parameters and DBBT was found. In Figure 4 the P3 parameter is given. This is the amplitude of the third harmonics obtained from upper harmonics analysis in the time domain signal of the magnetizing current. Results of MBN measurements, the RMS parameter as a function of transition temperature for all measured 15kH2NMFA and A508 Cl.2 samples can be seen in Figure 5.

**Figure 4.** Dependence of the amplitude of third harmonics P3 parameter of 3MA as a function of transition temperature for all measured 15kH2NMFA and A508 Cl.2 samples.

**Figure 5.** MBN RMS parameter as a function of transition temperature for all measured 15kH2NMFA and A508 Cl.2 samples.

It is seen that irradiation caused salient measurable modification of magnetic parameters. Magnetic parameters are significantly affected by the material degradation that changes the DBTT and there is a more or less linear correlation between magnetic parameters and DBTT (except the MBN measurements performed on A508 Cl.2 samples). However, the most visible conclusion, drawn from all measurements is the big scatter of points, regardless of the actual measurement method.

It can also seen very well in Figures 3–5 that even the magnetic parameters of not irradiated (reference) samples scatter a lot. This fact gives a possible reason of scatter of measurements points: the samples behave rather differently, despite the fact that the Charpy specimens were cut from the same block. Magnetic measurements do not make anything else but reflect this material inhomogeneity. It is not a surprise that the points will scatter also after irradiation. To have an impression about the behavior of individual samples, the next section investigates how the magnetic properties of individual samples are modified due to neutron irradiation.

### 3.1.2. Evaluation of Normalized Data

In Figures 3–5, all measurement results are given and samples are not marked. Another—and perhaps more useful—way is to consider the change of magnetic parameters for each individual sample. For this purpose, other graphs are shown below (Figures 6–8). In these graphs, the modifications of magnetic characteristics are given, this is with respect to the same magnetic parameter that is obtained on the same sample before irradiation

giving a baseline condition. This means that the first point (Ratio = 1) is the same for all samples, while each of the other points are connected with specific numbered samples. These points represent how the magnetic behavior of a given sample was modified due to neutron irradiation. (The labeling of points is avoided in order to preserve the clarity of the graphs.)

**Figure 6.** Normalized MAT descriptor vs. transition temperature for all 15kH2NMFA and A508Cl.2 samples.

**Figure 7.** Normalized 3MA P3 parameter as function of transition temperature for all 15kH2NMFA and A508Cl.2 samples.

**Figure 8.** Normalized MBN RMS parameter as function of transition temperature for all 15kH2NMFA and A508Cl.2 samples.

As can be seen very well in the above graphs, the scatter of points is rather large in the normalized cases, too. This is proof that the scatter of points in Figures 3–5 is not the result of the originally different behavior, but also of the fact that neutron irradiation generates different material embrittlement, depending on the individual samples' behavior.

### *3.2. Selection of Samples*

In the above sections, the influence of neutron irradiation has been investigated as if all measured samples are taken into account. As already mentioned above, it has been found that even reference samples are different from the point of view of magnetic properties, so it is not surprising that they behave differently also after irradiation. In this section, the method of the selection of samples is presented, based on permeability measurements of the samples. In the following section, it will be shown how the correlation of magnetic parameters with DBTT looks if only the selected samples are taken into consideration.

The selection of samples is based on measured permeability loops. Evidently this selection was made before any further evaluation of irradiated samples. These permeability loops were measured on reference samples (before irradiation). The criteria in this case was the similarity of the magnetic behavior. These samples were selected which were similar to each other from a magnetic point of view. A good characteristic is the maximal permeability, which can be determined easily from directly measured permeability loops. This means that this selection does not take into account the neutron irradiation generated material embrittlement, it reflects solely on the behavior of samples with initial conditions.

It is emphasized that we did not use backward reasoning to decide which data points fit the best to our hypothesis. Clarifying this statement, the selection process is shown: (1) A large scatter of all magnetic parameters measured on irradiated and reference samples was observed. (2) Independently of the result of magnetic measurements, the magnetic behaviors of the reference samples were compared to each other. Several samples were found with very similar permeability curves. (3) The MAT, 3MA and MBN evaluations were made again, but only the selected, magnetically similar samples were taken into account. No information about the behavior of the irradiated samples was available, since selection was performed prior to irradiation.

Selection reduces only the number of samples, which are taken into account. A serious argumen<sup>t</sup> for this selection is, that in the case of the 3MA and MBN method, this selection resulted in a very similar result as in the case of MAT method.

The series of permeability loops measured on 15kH2NMFA samples are shown in the left side of Figure 9. Magnified parts of the loops can be seen in the right side of the figure, but here only the envelope of the large amplitude minor loops are presented, to make visible the difference between loops, and to provide easy selection from a visual perspective. Four samples have been found that are similar from magnetic point of view. These samples are numbers 172, 173, 178, and 183.

Series of permeability loops measured on A508 Cl.2 samples are shown in Figure 10. Again, four samples have been found, which are similar from magnetic point of view. These samples are numbers 579, 583, 586, and 588.

**Figure 9.** Measured permeability loops of 15kH2NMFA samples before irradiation. The right panel shows the magnified part of the left graph [11].

**Figure 10.** Measured permeability loops of A508 Cl.2 samples before irradiation. The right panel shows the magnified part of the left graph.

#### *3.3. Results of 3MA, MAT and MBN Measurements Considering Selected Samples Only*

In this section it is shown how the scatter of points is modified if the evaluation of magnetic parameters has been repeated taking into account only the magnetically preselected samples. Results are shown in Figures 11–13, respectively.

**Figure 11.** Optimally chosen MAT descriptor vs. transition temperature for selected 15kH2NMFA and A508 Cl.2 samples.

**Figure 12.** 3MA P3 parameter vs. transition temperature for selected 15kH2NMFA and A508 Cl.2 samples.

**Figure 13.** MBN RMS parameter as a function of transition temperature for selected 15kH2NMFA and A508 Cl.2 samples.

### **4. Discussion**

By this analysis it has been proven that the experienced big scatter is connected with the different behavior of the samples, and the reason is not really the measurement errors of the applied magnetic methods.

It should be emphasized that MAT descriptors were determined for all the samples independently, before any selection and later any time (see Figure 11) the same parameters (ha = −30 mA, hb = 1080 mA for 15kH2NMFA and ha = 780 mA, hb = 1200 mA for A508 Cl.2) were used. Selection reduces only the number of samples, which are taken into account. A serious argumen<sup>t</sup> for this selection is, that in the case of 3MA and MBN method, this selection resulted in a very similar result as that in the case of the MAT method.

If we compare Figure 11 with Figure 3, Figure 12 with Figure 4 and Figure 13 with Figure 5, it can be seen that the scatter of points dramatically decreased if evaluation was performed only on the selected samples with similar magnetic behavior. An obvious linear correlation with low scatter of points has been found between magnetic parameters and DBTT for both investigated materials and for the three considered magnetic methods.One exception is the MBN RMS parameter for the A508 Cl.2 material. In this latter case, the scatter has been also decreased, similarly to all other cases, but we cannot speak about neither linear nor even monotonous correlation. This observation needs some more discussion. However, the correlation between MAT and 3MA measurements are more than satisfactory. Neither the correlation between magnetic parameters and DBTT, nor the behavior of scatter does not depend on the actual method of measurement. This fact is

very promising for the future practical application of magnetic methods. The results of the different methods verify one another.

We have found relevant differences in magnetic behavior, which resulted in big scatter in MAT, 3MA and also in MBN vs. DBTT plots. These differences are rather surprising and unexpected, because the samples were cut from the same block. As three different NDT methods indicated the differences, these can not be assigned to the uncertainity of any one of them, although the structure and chemical composition of the different samples should be the same. Describing this effect we cannot use any other word than "inhomogeneity of the material", without knowing anything about the character of inhomogeneity. This result is considered one of the most important messages of our work.

In this paper we have presented figures about the scattering of the destructive mechanical tests and of the non-destructive magnetic measurements. Both types of experiments indicate that the source of the observed scattering is related to the differences between the tested specimens either from a mechanical or magnetic point of view. We cannot provide evidence that the scattering of the mechanical properties and of the magnetic features have identical causes. However, the quality of the linear relationship between the determined DBTT and the MAT, 3MA, and MBN values can be considered as a telling argumen<sup>t</sup> in this direction.

We know that further analysis to verify the effect of the local inhomogeneity of the material is extremely important and perhaps this result would be crucial for the whole nuclear industry. We believe that if we call the attention of the scientific community to this fact, it is important by itself. Evidently, the work should be continued, and we want to do this.
