## 3 Results of Experiments and Their Discussion
### MBN Measurements
Moreover, the height of the negative envelopes is lower, which is quite surprising since the shift of the MBN envelope to the stronger magnetic fields is usually linked with its lower height, and vice versa [4,29]. Figure 11: MBN signal, \(\varepsilon=15\%\), magnetising voltage 5V, magnetising angle \(0^{\circ}\) (RD). Figure 12: Asymmetry in MBN (rms values) between the positive and negative bursts. (**a**) Angular evolution of MBN with indicated error bars, (**b**) difference in MBN between the positive and negative bursts. Figure 10: MBN signal, \(\varepsilon=2.5\%\), magnetising voltage 5V, magnetising angle \(0^{\circ}\) (RD). Figures 13d and 14 depict that the asymmetry in the MBN envelope's positions and the corresponding \(PP\) drops down along with \(\varepsilon\) (as well as with the magnetising angle). Moreover, Figure 14 illustrates a quite interesting phenomenon when \(PP\) for the positive magnetisation grows abruptly as soon as the elastic straining is replaced by the plastic one, and remains untouched with further plastic straining \(\varepsilon\). On the other hand, \(PP\) for the negative magnetisation is shifted to the lower magnetic fields at lower \(\varepsilon\), and grows progressively with \(\varepsilon\). Figure 13b,c and Figure 15 demonstrate that the degree of MBN asymmetry, expressed as the difference in \(PP\) between the positive and negative magnetisation \(\Delta PP\), is also a function of magnetising voltage and the corresponding \(\mathrm{d}H/\mathrm{d}\tau\). Magnetising voltage as well as frequency were optimised in the preliminary phase of experiments by the use of voltage and frequency sweeps [32,33]. On the one hand, these magnetising conditions provide maximum sensitivity of MBN technique with respect of the investigated body. However, the remarkable asymmetry in MBN can be obtained just at these optimised conditions (see Figure 15) at a magnetising voltage near 4V, followed by a decrease along with increasing magnetising voltage. It is also worth to mention that the aforementioned asymmetry does not vanish entirely, but noticeably remains even at the strongest magnetic fields produced by the sensor. The origin of the MBN asymmetry is driven by the non-homogenous character of plastic straining with respect of the neighbouring grains. Dislocation shearing at lower \(\varepsilon\) is initiated in those grains having suitable orientation against the direction of the load, according to the Schmid law (the shear stress attains a maximum when the angle between  
Figure 13: MBN envelopes in RD. (**a**) \(\varepsilon\) = 2.5%, 5V, (**b**) \(\varepsilon\) = 15%, 5V, (**c**) \(\varepsilon\) = 15%, 10V, (**d**) \(\varepsilon\) = 40%, 5V. the direction of loading and crystallographic orientation is about 45\({}^{\circ}\)[34]). Figure 4 illustrates that the crystallographic orientation inside the grains varies. However, the dislocation straining is non-homogenous, as Figure 6b,c indicate. Therefore, the heavily strained grains of high dislocation density and the corresponding magnetic hardness are neighbours with the unaffected ones of low dislocation density and lower magnetic hardness. MBN asymmetry is therefore a product of magnetic coupling between the grains of variable magnetic hardness. Asymmetry in MBN under the weaker magnetising fields is due to magneto-coupling between the heavily strained and softer unaffected grains. Applying the theory of [PERSON] et al. [22] about magnetic coupling, it can be reported that the heavily strained grains produce the magnetostatic field in the unaffected ones, for instance, negative (no matter whether the applied field is positive or negative). This hinders the positive saturation and favours the negative one. A graphical illustration further explaining the aforementioned effect can be found in [18,22]. The sample history with respect to its magnetic anisotropy in the RD plays a significant role since the aforementioned effect occurs in the RD only, and vanishes towards the TD.