**6. Summary and Conclusions**

The Barkhausen noise and *HV* hardness were tested in specimens subjected to plastic strain and thermochemical treatment. The measurement data were processed numerically, which resulted in distributions of the total number of events (*NoETOT*) as a function of discrimination voltage *Ug*. Next, the linear correlation determination coefficient (*R*2) and the resolution coefficient (*RECOF.*) introduced by the authors were analyzed in parallel to find the optimal correlation. The obtained results prove the great potential of using the Barkhausen noise total number of events (*NoETOT* BN) for the development of correlations enabling hardness determination. Distributions of the total number of events (*NoETOT*) in selected intervals of threshold voltage *Ug* make it possible to develop correlations characterized by a high determination coefficient *R*<sup>2</sup> in the case of changes in hardness due to both strain hardening and thermochemical treatment.

A new methodology was developed for the determination of diagnostic correlations to solve inverse problems of non-destructive testing consisting of hardness evaluation based on the Barkhausen noise total number of events (*NoETOT* BN). However, it has to be emphasized that if these correlations are to be applied, factors that affect the diagnostic signal, such as the surface shape and roughness or the element edge impact, must be taken into account. The factors are described in detail in [7,17]. The sampling frequency can also play a significant role, because some pulses could overlap in the time scale.

Compared to classic static and dynamic methods of hardness evaluation using an indenter, the developed method of measuring hardness based on the total number of events (*NoETOT*) of the Barkhausen noise causes no plastic strain on the tested surface and makes it possible to perform hardness measurements in the same place repeatedly.

Additionally, it is possible to utilize other properties of the Barkhausen noise to develop multi-property correlations [15], where each property will have a specific weight established based on an analysis of the determination coefficient (*R*2) and the resolution coefficient introduced by the authors (*RECOF.*).

The authors, as well as other scientists [37], are aware of the deficit in basic research on the relations between changes in a broadly understood state of the material and changes in electromagnetic properties, both at the micro and macroscopic scale. Another important research issue that emerged while analyzing the testing results is the impact of the plastic strain process (whether it proceeds continuously or in stages) on changes in parameters of the Barkhausen noise quantitative description. The results of such research would enable more confident actions in inverse problems of non-destructive testing using electromagnetic phenomena.

**Author Contributions:** conceptualization, M.R. and K.F.; methodology, K.F.; software, K.F.; validation, M.R. and K.F.; investigation, M.R. and K.F.; resources, K.F.; data curation, K.F.; writing—original draft preparation, M.R., K.F. and K.S.; writing—review and editing, M.R., K.F. and K.S.; visualization, K.F.; supervision, M.R. and K.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
