## 2 Samples and Experimental Details
### Barkhausen Noise Measurement  
MBN measurements provide the most discriminating quantities to characterize material conditions. The MBN is an RMS (Root Mean Square) magneto-elastic parameter which is expressed as a function of magnetizing voltage, current and frequency applied to the material under test. A specified time window of several bursts (see in Figure 4.) would indicate the general response from the feedback coil  
Figure 3: Time variation of magnetizing current (**a**) and the detected permeability loops (**b**). (these responses would essentially be repeats and provide trend data with high confidence). The RMS of the MBN response signal is given by (3):  
\[\text{RMS}=\sqrt{\frac{\sum\limits_{i=1}^{n}y_{i}^{2}}{n}} \tag{3}\]  
where \(n\) is the total number of MBN signal bursts captured within a specified frequency range and \(y_{i}\) is the amplitude of the individual burst. Within the Rollscan 350 Analyser system used in this work. There are a number of parameters that need to be set for the stimulated electromagnetic waveform. Such parameters are the voltage, frequency as well as a high-frequency pickup response filter. Taking advantage of the skin effect equation, the lower the frequency the greater the depth of penetration into the material. Both magnetizing voltage and frequency sweeps were undertaken to identify optimum parameters based on the displayed material response. A penetration depth between 0.01 and 1 mm is achieved by using the frequency pickup filter of 70 kHz down to 200 kHz. Using the Microscan software, repeated measurements were then recorded for 5 s durations. The Barkhausen parameters are described in greater detail in [18]. For consistency and repeatability, 2 V and 120 Hz was used as the parameters for this surface quality study. This selection was based on previous tests investigating the detection of embrittlement as well as being in good agreement with the frequency and voltage sweeps of the tested materials. Figure 4 displays the response of MBN pickup for longitudinal (a) and transversal (b) measurements for sample material 23. Longitudinal measurement means that the direction of magnetization is parallel to the length of the sample. Longitudinal measurement for sample material 26 can be seen in Figure 4c. Here differences can be seen in regard to the signal when applied to different surface conditions. Specifically, Figure 4a has a greater in amplitude when compared with Figure 4c, where both signal responses are for same sensor direction albeit different material conditions. This is expected as Figure 4a  
Figure 4: Top (**a**) Plot of Longitudinal MBN measurement for sample 23. Middle (**b**) Plot of Transversal MBN measurement for sample 23. Bottom (**c**) Plot of Longitudinal MBN measurement for sample 26. Sinusoidal signals for both relate the input magnetizing current resulting from a given set of input parameters (2 V and 120 Hz). response is correlated to a much lower surface roughness than that of Figure 4c where the surface roughness is nearly five times coarser and therefore, less field energy penetrating the material surface. Energizing the local material area electro-magnetically is carried out from magnetizing/sensing via a soft ferrous yoke. Ferrous yoke is in contact with the workpiece material under test. The surface quality of in-service safety-critical structures can vary from well-maintained to very coarse, high surface roughness. These differences impact on the coupling between the magnetic yoke and surface and in severe cases can influence the results to give totally misleading responses where the value obtained is based on both surface quality and different material conditions. This is a well-known problem with magnetic sensing technologies. To mitigate these effects the application of a spacer between the yoke and sample is proposed.