**3. Results**

This experiment was performed according to the following methodology. Eight samples (S01–S08) made of S355 were magnetized to record a quasi-sinusoidal pattern. Next, the 2D distribution of the magnetic field caused by the residual magnetization of the sample was measured using a magnetometer. Subsequently, each sample was loaded to a different degree in elastic and plastic regions' volume using an Instron Universal Testing machine (Figure 4 and Table 1). In order to investigate possible changes in the magnetization pattern, the magnetic field was measured once again. The signals measured for each sample before and after stress-loading were stored and used to prepare plots presented in this section.



**Figure 4.** The stress–strain curve obtained for the sample made of S355. S01–S08—eight samples loaded to a different degree in elastic and plastic regions' volume depicted on the curve.

The measurements of the magnetic field changes were carried out following the methodology described in Section 2. As a result, two sets of two-dimensional signals for each sample (S01–S08) were obtained: the first plot for the specimen before tensile loading and the second for the specimen after tensile loading. Figure 5 shows examples of two-dimensional signals measured in both cases for the sample S05. Similar graphs obtained for other samples were omitted because they would increase the article's length without introducing important information. The plots show only two components *Bx* and *Bz* because the third component, *By*, was a small amplitude signal unused for evaluation.

**Figure 5.** Results of 2D measurements of the magnetic field in the case of sample S05. (**a**) Component *Bx* before tensile loading; (**b**) component *Bz* before tensile loading; (**c**) component *Bx* after tensile loading; (**d**) component *Bz* after tensile loading.

In order to straightforwardly demonstrate the usability of the proposed method, the analysis was limited only to one-dimensional signals taken from the central part of the samples. The average signals of the *x* and *z* magnetic field components were calculated for each sample. Plots of the averaged signals for all samples before and after tensile loading are shown in Figure 6. The plots depict variations in the amplitude of the components depending on the sensor position along the *x*-axis. In the central part of the sample, an evident change in the signals can be observed.

**Figure 6.** *Cont*.

**Figure 6.** Components of the magnetic field measured for the magnetized samples before (red line) and after tensile loading (blue line): (**a**) *Bx* for sample S01, (**b**) *Bz* for sample S01, (**c**) *Bx* for sample S02, (**d**) *Bz* for sample S02, (**e**) *Bx* for sample S03, (**f**) *Bz* for sample S03, (**g**) *Bx* for sample S04, (**h**) *Bz* for sample S04, (**i**) *Bx* for sample S05, (**j**) *Bz* for sample S05, (**k**) *Bx* for sample S06, (**l**) *Bz* for sample S06, (**m**) *Bx* for sample S07, (**n**) *Bz* for sample S07, (**o**) *Bx* for sample S08, (**p**) *Bz* for sample S08.

Detailed analysis of the signals measured for samples S01–S05 (Figure 6) allows us to conclude that as the stress level increased, the magnetic field amplitude decreased in the central part of the measuring area, and frequencies *fBx*, *fBz* remained practically unchanged. In the case of the samples loaded over the yield point (S06–S08), the amplitudes and frequencies *fBx*, *fBz* of the signals measured after tensile loading significantly decreased compared to the parameters measured before tensile loading (Figure 6).

Evaluating the condition of samples based solely on direct observation of the signal before and after tensile loading can be problematic due to the minor differences. For this reason, characteristic parameters were determined, and additional charts were prepared to visualize the changes taking place. First, the relative change in the magnetic field amplitude as a function of strain is presented (Figure 7). As can be seen from Figure 7a,b, the curve of the above relation consists of two parts separated by the point defining the elastic limit of the samples. For samples S01 to S04, the values increased approximately linearly. Then, starting with sample S04, the curve slopes sharply down to the value corresponding to the yield point sample S05. After the yield point was exceeded, the curve increases again to a point corresponding to the sample S08, but slower than its initial part. Thus, it can be concluded that an increase in the deformation level of the samples increased the value of the relative change in the residual magnetization.

**Figure 7.** Relative mean changes in the magnetic field in the case of the samples S01–S08 plotted versus the strain: (**a**) component Δ*Bx*; (**b**) component Δ*Bz*.

Another two sets of plots contain the relative mean change in magnetic field Δ*B* as the function of applied stress *σ* for the samples S01–S04 (Figure 8) and strain *ε* for the samples S05–S08 (Figure 9), respectively. The reason for separating the parameter analysis of samples S01–S04 from samples S05–S08 is the change in mechanical properties at the point corresponding to sample S05. In the case of the first four specimens, the stresses induced an elastic deformation of the structure, and in the case of the remaining four specimens, plastic deformation was induced.

Figure 8a shows the relative mean change in the magnetic field Δ*Bx*, Δ*Bz* (Equation (3)) in the case of the samples S01–S04. Component Δ*Bx* increased exponentially with the rise in the stress level. On the contrary, the curve for the component Δ*Bz* (Figure 8b) rises slower and resembles the cubic polynomial. Due to the monotonicity of the curves, these graphs allow evaluating the sample conditions straightforwardly. Plots presented in Figure 9 show the relative mean change Δ*Bx*, Δ*Bz* in the magnetic field as the function of strain *ε* for the samples S05–S08.

**Figure 8.** Relative mean changes in the magnetic field in the case of the samples S01–S04 plotted versus the stress: (**a**) component Δ*Bx*; (**b**) component Δ*Bz*.

Figure 9a,b indicates that the values of Δ*Bx* and Δ*Bz* increase exponentially with growing strain values. After passing the yield point corresponding to sample S05, the curve bends. This change is the transition from the elastic region through the yield point to the plastic region in the following samples. Plots showing the relative change in frequency Δ*fBx,* Δ*fBz* (Equation (4)) as a function of strain *ε* can also be used to evaluate the conditions of the samples S05–S08 (Figure 10). In the case of both components (*Bx* and *Bz*), the curves increase to the point of the maximum strain (sample S08). There is an inflection of the curve at the point corresponding to sample S07.

**Figure 9.** Relative mean changes in the magnetic field in the case of the samples S05–S08 plotted versus the strain. (**a**) component Δ*Bx*; (**b**) component Δ*Bz*.

**Figure 10.** Relative changes in the signal frequency in the case of the samples S05–S08 plotted versus the strain. (**a**) <sup>Δ</sup>*fBx*; (**b**) <sup>Δ</sup>*fBz*.

### **4. Discussion**

The tests of the proposed method of nondestructive testing, which was presented in the previous section, covered several dozen samples made of the same material (S355) and should be treated as a first attempt to verify the suitability of the method.

The strictly defined signals (e.g., a sinusoid of a specific frequency) enable the use of dedicated filtering algorithms that effectively eliminate external disturbances. For example, a simple pass-band digital filter could eliminate a DC (Direct Current)) component from the signals presented in Figure 6. The parameters of the measured signals (e.g., the amplitude and frequency of the sine wave) can be determined by proven and reliable algorithms. These parameters allow for unambiguous identification of the material condition both in the elastic (Figure 8) and plastic regions (Figure 9). It should also be noted that external sources of DC magnetic fields have a limited impact on the results obtained in the proposed method. For example, such DC fields would not affect the frequency of the measured sinusoidal signal in any way. Such frequency change (Figure 10) is a very reliable parameter, but, unfortunately, it can only be observed in the case of samples loaded over the yield point.

The achieved results of the tests can generally be assumed as promising, and the method can help identify the condition of elements made of ferromagnetic materials subjected to loads. However, as the method is new, it is necessary to conduct further detailed tests to clarify existing doubts and improve the test procedure. The following aspects of the inspection procedure should be investigated and analyzed: the magnetization process, the residual magnetization measurement process, and the algorithms for analyzing the received signals.

One of the problems that has to be addressed is the decreasing magnetization of the tested elements over time. For this purpose, samples have been retained, and measurements will be repeated during the following year. Unfortunately, it was impossible to conduct comparative tests using other NDT methods before this time elapsed.

When comparing the results obtained by the proposed method with the results from other testing methods applied to very similar samples but made of SS400 steel, some significant differences can be observed. For example, in the case of the hysteresis loop observation method [36], unambiguous identification of the sample state is possible, but this method is less sensitive in the elastic range (measurements carried out after removing the load). Moreover, in this method, the spatial resolution is lower due to the larger dimensions of the transducer, and its implementation requires the use of a more complex measurement system.

Similarly, lower sensitivity in the elastic range can be observed in the case of the results obtained from the eddy current method [37] and the residual magnetization observation method with the GMR (Giant MagnetoResistance) transducer [38]. Additionally, measured parameters of the signals did not allow for unequivocal identification of the sample state as the same value was obtained for the samples before and after the yield point. A considerable advantage of the eddy current testing is the independence of the results on the magnetic history of the tested object.

The advantage of all the compared methods over the proposed Magnetic Recording Method is that there is no need to magnetize the sample with a specific pattern beforehand. Therefore, the proposed method can be applied only in some specific cases, for example, when it is necessary to constantly monitor crucial elements of the structure.

Due to the limited number of tests of a new method, it is not easy to make a reliable comparison with other methods. A comparison should also be made using the same or very similar samples. Unfortunately, during the experiment, it was not possible. Therefore, the comparison of the proposed method with the other nondestructive electromagnetic methods presented in Table 2 should be considered only as a preliminary attempt and will be updated after the next set of experiments.

**Table 2.** Comparison of the Magnetic Recording Method with other magnetic methods.

