Simulation and Analysis of V-shaped Discontinuity
Magnetic Leakage Signal
Under normal conditions, when the sample to be tested is
magnetized, the magnetic lines of force are evenly distrib-
uted inside the sample. When a discontinuity is present, the
magnetic lines of force leak and generate a leakage magnetic
field at the discontinuity’s edge. As shown in Figure 4a, using a
V-shaped discontinuity as an example, the width of the discon-
tinuity is determined to be 4 mm, the thickness of the sample
is 5 mm, and the edge angles are 20°, 45°, and 65°, in that
order. The variation in the magnetic leakage signal is shown in
Figures 4c and 4d.
Figure 4c shows that the peak-to-peak values of the
radial component of the discontinuities gradually increase
as the edge angle increases. Meanwhile, the peak point of
the magnetic leakage signal becomes progressively wider in
the horizontal direction relative to the center position of the
discontinuity as the edge angle changes from 20° to 65°. The
peak value of the waveform of the axial signal in Figure 4d also
increases with the increase of the edge angle. Assuming the
discontinuity width remains constant, the change in the hori-
zontal direction of the axial signal is consistent with the change
in the radial signal.
From Figure 4b, it can be seen that the signal peak grad-
ually increases as the edge angle increases. Additionally,
relative to the center position of the discontinuity at 10 mm,
the larger the edge angle, the farther the peak point moves
from the center. This indicates that as α increases, the value of
sin(​​ ​ 1​​ − α​ decreases. As a result, the refraction angle ​​ ​ 2​​​ of the
magnetic field lines decreases, causing the refracted magnetic
field lines at the media interface to approach the normal of
the interface. This leads to a denser concentration of refracted
magnetic field lines. Consequently, the magnetic field lines
after refraction become more concentrated, resulting in a
larger magnetic induction intensity (B) for both the axial and
radial signals. The peak-to-peak spacing also increases.
This study also observed changes in the depth of the dis-
continuities, highlighting the need for further research on the
correlation between the variable edge angle and the magnetic
leakage signal.
ME
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MAGNETICLEAKAGE
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Scanning path (mm) Scanning path (mm)
15 20 0 5 10
Edge angle (degrees)
45°
45°
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20°
65°
65°
15 20
65°
45°
20°
65°
45°
20°
Figure 4. V-shaped discontinuity and magnetic leakage signal variation distribution for different edge angles: (a) V-shaped discontinuity model
(b) trend plot (c) radial signal component (d) axial signal component.
34
M AT E R I A L S E V A L U AT I O N • M AY 2 0 2 5
B
(mT)
B
(mT)
B
(mT)
L
point

Simulation and Analysis of Trapezoidal Discontinuity
Magnetic Leakage Signal
It was shown that there is indeed a link between the disconti-
nuity edge angle and the magnetic leakage signal, which is par-
ticularly evident in the radial component. To further determine
the effect of edge angle on the magnetic leakage signal, the
study continued with other discontinuity models. These were
changed to rectangular and right-angle trapezoidal disconti-
nuities, with a width of 4 mm, a depth of 2 mm, and a sample
thickness of 5 mm. As shown in Figure 5a, a constant angle of
90° was maintained on one side of the discontinuity, while the
edge angles on the other side were 39°, 45°, 53°, 63°, 76°, and
90°, respectively.
As shown in Figures 5b and 5c, the radial magnetic leakage
signal changes as the edge angle changes. The specific trend
is that as the edge angle increases, the peak intensity of the
radial signal increases, and the distance from the peak point
to the center of the discontinuity becomes wider. The increase
in peak value accelerates as the edge angle increases. A regres-
sion analysis was performed on the edge angle and peak point,
and the results are shown in Table 2.
As can be seen from the table, the multiple R-value is
about 0.976, which exceeds 0.75, indicating a strong correla-
tion between the size of the edge angle and the location of the
signal peak (Domenech-Asensi et al. 2005). The regression
equation can be expressed as follows: ​ ​
(10)​ y =8.3889 − 0.0063x​
where
the independent variable ​ ​ is the edge angle magnitude, and ​
y​ is the location of the peak point of the radial magnetic
leakage signal.
Figure 5d illustrates that variations in the edge angles
influence the amplitude of the axial signal. Specifically, the
larger the edge angle, the larger the amplitude. As the edge
angle increases, the axial signal gradually transitions from a
single wave peak to a double wave peak. The reasons for this
are explained as follows.
The refraction angle ​​ ​ 2​​​ of the magnetic field lines at the dis-
continuity boundary decreases due to the increased influence
of the edge angle α on the magnetic field lines. This causes the
propagation of the magnetic field lines to become more centrally
TA B L E 2
Relationship between edge angle and peak position
Regression statistics
Multiple R 0.976070929
R-square 0.952714458
Adjusted R-square 0.940893073
Standard error 0.030167813
Observed value 6
39° 45° 53°
63° 76° 90°
60 8.20
8.15
8.10
8.05
8.00
7.95
7.90
7.85
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0 39° 45° 53° 63° 76° 90° 5 10
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39°
3 A
4 A
5 A
6 A
7 A
1 mm
2 mm
3 mm
4 mm
5 mm
Figure 5. Trapezoidal discontinuity and magnetic leakage signal distributions under different conditions: (a) trapezoidal discontinuity model
(b) trend plot (c) radial signal components at different edge angles (d) axial signal components at different edge angles (e) axial signal
components at the same edge angle for different discontinuity widths (f) axial signal components at the same edge angle for different
magnetizing currents.
M AY 2 0 2 5 • M AT E R I A L S E V A L U AT I O N 35
B
(mT)
B
(mT)
B
(mT)
B
(mT)
B
(mT)
L
point