## 3 Results and Discussion  
This section includes the experimental results of tangential and normal MMM signals around five V-shaped notches in an ASTM-A36 steel pipe. The relations between these MMM signals and the size of the notches are studied. The MMM signals are measured along the perimeter of the steel pipe. We measured the tangential and normal MMM signals around each defect, considering a separation distance (z) between \(-2\) mm and \(2\) mm. Figure 3 shows six measurements of tangential MMM signals around first V-shaped notch (S1). These MMM signals registered a minimum peak (\(-252.83\)\(\mu\)T \(\pm\) 1.39 \(\mu\)T) close to the defect center (z = 0 mm). This MMM signal describes a behavior similar to a U-shaped curve. The tangential MMM signal reached its maximum variation (14.32 \(\mu\)T \(\pm\) 1.62 \(\mu\)T) at the defect center. This maximum variation is related to the depth (500 \(\mu\)m) of the defect on the outer surface of the pipe. In addition, Figure 4 illustrates the normal MMM signals close to the first notch (S1). Due to the two edges around the notch center, the normal MMM signals present two peak values, a maximum peak (71.22 \(\mu\)T \(\pm\) 0.66 \(\mu\)T) before the notch center and a minimum peak (43.27 \(\mu\)T \(\pm\) 0.52 \(\mu\)T) after the notch center. This normal MMM response shows a change in its variation direction close to the notch center. This change in variation direction is related to the curvature shift of the normal MMM signal, similar to that represented by an inflection point. These two peaks have a separation distance, parallel to the z-axis, that is related to a notch width of 1000 \(\mu\)m. Thus, the depth and width of the V-shaped notch alter the behavior of the tangential and normal MMM signals, respectively. However, the measured curves are not symmetric around the z = 0 of each defect. This could be caused by the influence of the self-magnetic field along the perimeter of the pipe related with the stress state of the material. Figure 5 shows six measurements of tangential MMM signals around the second V-shaped notch (S2), which registered a minimum peak (-224.38 \(\mu\)T \(\pm\) 1.31 \(\mu\)T) close to the defect center (z = 0 mm). Before this defect, the value of the tangential MMM signal decreased achieving its minimum magnitude near the notch center. After the defect center, the tangential MMM response increased. The magnetic field shift was caused by the defect depth (1000 \(\mu\)m) along the outer surface of the pipe, registering a maximum variation (16.08 \(\mu\)T \(\pm\) 1.86 \(\mu\)T) at the notch center. Six measurements of normal MMM signals around the second notch (S2) are shown in Figure 6. Before the first edge of the second notch,  
Figure 3: Variation of tangential MMM signals around the first V-shaped notch (1000 \(\mu\)m width and 500 \(\mu\)m depth) of the ASTM-A36 steel pipe, which were measured using six experimental tests. the normal MMM signals had values close to 113.80 \(\pm\) 0.28 uT. After the first edge of this defect, these signals decreased to 87.40 uT \(\pm\) 0.40 uT at the second edge of the notch. The width (1500 um) of the second notch affected the magnetic signal shift along a distance close to 1.5 mm. Figure 4: Variation of normal MMM signals around the first V-shaped notch (1000 um width and 500 um depth) of the ASTM-A36 steel pipe, which were measured using six experimental tests. Figure 5: Variation of tangential MMM signals measured around the second V-shaped notch (1500 um width and 1000 um depth) of the ASTM-A36 steel pipe, which were measured using six experimental tests. For the third V-shaped notch (S3), six measurements of tangential MMM signals registered a minimum peak (\(-\)202.90 \(\upmu\)T \(\pm\) 0.90 \(\upmu\)T) near the notch center (z = 0 mm). This peak was due to the depth (1500 \(\upmu\)m) of the third notch, as shown in Figure 7. Along the surface perimeter of the pipe, the tangential MMM response decreased at the defect center.