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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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
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distributed at the discontinuity boundary, which increases the
magnetic field strength in this region and ultimately enhances
the amplitude of the collected magnetic leakage signal.
To illustrate the transition of the axial signal from a single
to a double crest, we take a right-angled trapezoidal discon-
tinuity with an edge angle of 63° as an example, keeping the
other parameters unchanged. By varying the width of the dis-
continuity and the magnitude of the magnetizing current, we
obtain the graphs shown in Figures 5e and 5f. A comparative
study of Figures 5e and 5d reveals that the effects of varying
the discontinuity width and the discontinuity edge angle on
the axial signals are similar, both leading to a change in the
number of wave crests.
The specific reason is that an increase in the discontinuity
width leads to a significant increase in the dispersion of the
magnetic field lines at the discontinuity edge (Li et al. 2017).
When the magnetic field lines pass through discontinuities
with larger widths, there is a significant scattering effect at the
discontinuity edges, leading to increased bending and reflec-
tion of the magnetic field lines, which generates multiple wave
peaks in the magnetic leakage signal. On the other hand, as
the edge angle of the discontinuity increases, the distribution
of the magnetic field lines on both sides of the discontinu-
ity changes (Feng et al. 2022), and a stronger magnetic field
gradient is generated in the discontinuity region. When the
magnetic field gradient is concentrated in a certain region,
the detection signal will show a single peak characteristic. In
the center region of the discontinuity, the signal strength is
weakened due to the highly dispersed magnetic field lines,
resulting in a divergent distribution. This change in distribu-
tion pattern eventually leads to a shift in the axial signal from a
single to a double peak.
By analyzing the changes in radial and axial signals, the
morphological dimensions of the discontinuity and the size of
its edge angle can be evaluated.
Simulation and Analysis of Magnetic Leakage Signal for
Inner and Outer Discontinuities
All of the above studies have explored the relationship between
the edge angle of unilateral discontinuities and the variation
of the magnetic leakage signal. However, the effect of edge
angle changes on the magnetic leakage signal on both sides of
the inside and outside of the sample still needs to be further
investigated.
ME
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MAGNETICLEAKAGE
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45° 63° 34°
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45°
34°
63°
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63° 45° 34°
Figure 6. Inner and outer discontinuities and their magnetic leakage signal distributions: (a) model of the inner and outer discontinuities
(b) trend plot (c) radial signal component (d) axial signal component.
36
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