*5.2. Analysis of Results*

Averaged *NoETOT* distributions were obtained using the data-analysis procedure described in Section 3 for three measuring configurations and two magnetization directions perpendicular to each other. The absolute value was also determined according to Relation (2). For Configuration C1, distributions of *R*<sup>2</sup> as a function of *Ug*, after strong oscillations in the *Ug* range from 0 to about 0.4 V, stabilize, taking values close to 1 for the parallel direction (Figure 14a) and for the absolute value (Figure 14c), and values oscillating between 0.9 and 1 for the normal direction (Figure 14b). The selection of discrimination voltage *Ug*, for which the correlations presented in Figure 15a–c were developed, is decided by the global maximum of the *RECOF* distribution. In the case under analysis, the maximum of voltage *Ug* is about 0.8 V. The obtained values of determination coefficient *R*<sup>2</sup> take values higher than 0.97, which proves a very good correlation.

**Figure 14.** Averaged *NoETOT* distributions and distributions of coefficients *RECOF.* and *R*<sup>2</sup> as a function of threshold voltage *Ug*—Configuration C1 (**a**) parallel direction; (**b**) normal direction; (**c**) absolute value.

**Figure 15.** Linear correlations between *NoETOT* and *HV5* hardness—Configuration C1 (**a**) parallel direction, *Ug* = 0.8 V; (**b**) normal direction, *Ug* = 0.74 V; (**c**) absolute value, *Ug* = 0.79 V.

For Configuration C2, the distributions of *R*<sup>2</sup> depending on *Ug* (Figure 16a–c) are characterized by considerable variability with two local maxima reaching the value of 1. The *RECOF* distributions also demonstrate high variability and have a global maximum that decides the value of discrimination voltage *Ug* for which the correlations shown in Figure 17a–c were developed. For Configuration C2, the voltage values are higher compared to Configuration C1 (from 1.12 to 1.22 V). The obtained values of determination coefficient *R*<sup>2</sup> take lower values compared to Configuration C1. They are included in the range from about 0.89 to about 0.96, which proves a good correlation.

**Figure 16.** Averaged *NoETOT* distributions and distributions of coefficients *RECOF* and *R*<sup>2</sup> as a function of threshold voltage *Ug*—Configuration C2 (**a**) parallel direction; (**b**) normal direction; (**c**) absolute value.

**Figure 17.** Linear correlations between *NoETOT* and *HV5* hardness—Configuration C2 (**a**) parallel direction, *Ug* = 1.12 V; (**b**) normal direction, *Ug* = 1.22 V; (**c**) absolute value, *Ug* = 1.19 V.

For Configuration C3, the determination coefficient in the *Ug*-dependent distributions of *R*<sup>2</sup> (Figure 18a–c) takes values higher than 0.95 for the *Ug* range from 0.1 to 0.4 V. This is also the range for which the *NoETOT* values are higher than 0.

**Figure 18.** *NoETOT* distributions and distributions of coefficients *RECOF* and *R*<sup>2</sup> as a function of threshold voltage *Ug*—Configuration C3 (**a**) parallel direction; (**b**) normal direction; (**c**) absolute value.

The *RECOF* distributions for this voltage range have a local maximum that decides the selection of discrimination voltage *Ug* (from 0.1 to 0.16 V) for which the correlations presented in Figure 19a–c were developed. The values of determination coefficient *R*<sup>2</sup> are included in the range from about 0.97 to about 0.987, which proves a very good correlation.

**Figure 19.** Linear correlations between *NoETOT* and *HV5* hardness—Configuration C3 (**a**) parallel direction, *Ug* = 0.1 V; (**b**) normal direction, *Ug* = 0.16 V; (**c**) absolute value, *Ug* = 0.14 V.

In each of the configurations under analysis, a rise in hardness involves a drop in the number of events (*NoETOT*). For the tested specimens, martensite refinement increases with a rise in hardness, which means that a smaller number of events (*NoETOT*) corresponds to a structure with a smaller grain size. Similar results are obtained in [34,35], whereas completely opposite relations are found in [8]. This proves that the Barkhausen noise affects not only the grain size but also the nature of grain boundaries and their mutual orientation [35]. Moreover, for a specific configuration of factors affecting the Barkhausen noise, a repeatability of results is achieved. The electromagnetic phenomena occurring in the microscale due to the effect of the size of the measuring converters make use of diagnostic relations developed based on macroscale parameters (averaged information on the material state from the macro area). Compared to the conclusions presented in [36], the diagnostic information obtained in this manner is both repeatable and reliable.
