0.0
Circumferential (x) position (mm)
0.0
0.015
0.01
0.005
–0.005
–0.01
0.0 0.005 –0.005 0.01 –0.01 0.015 –0.015
X (Ohms)
Depth position (mm)
0.0
0.005
–0.005
0.01
–0.01 –0.015
1.25
0.0
5
0
10
15 ×10–3
–0.5 –1.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
–1.25 2.50 –2.50
R, VIC
X, VIC
R, exp
X, exp
R, VIC
X, VIC
R, exp
X, exp
VIC
exp
#10110, |beta| =0.005478, angle =7.8, RMS error =0.042182
Figure 4. Comparisons of the titanium corner notch model calibration results (a) before and (b) after a model phase transformation fix, leading to
improved fit quality (top left, circumferential response top right, phase plane response bottom, depth profile response).
0.0
Circumferential (x) position (mm)
#10137, |beta| =0.004917, angle =76.2, RMS error =0.063383
0.0
0.01
–0.01
0.02
–0.02
0.03
0.0 0.01 –0.01 0.02 –0.02 0.03 –0.03
X (ohms)
Depth position (mm)
0.0
0.01
–0.01
0.02
–0.02 –0.03
1.25
0.0
0.0
0.005
–0.005
0.01
0.015
0.02
0.025
–0.5 –1.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
–1.25 2.50 –2.50
R, VIC
X, VIC
R, exp
X, exp
R, VIC
X, VIC
R, exp
X, exp
VIC
exp
A U G U S T 2 0 2 5 • M AT E R I A L S E V A L U AT I O N 47
R, X
(ohms)
R
(ohms)
R,X
(ohms)
R, X
(ohms)
R
(ohms)
R,X
(ohms)

were made that greatly improved the depth profile response
alignment, as shown in Figure 4b. For this example, the RMS
error between the experimental and transformed model results
was reduced from 0.063 to 0.042, a 33% reduction in error. This
improvement is expected to produce improved length esti-
mates and, in turn, improved depth estimates as well.
Lastly, an iterative spatial alignment of the crack indica-
tion with the model was implemented, with the goal of further
improving inversion accuracy.
This model-based inversion software capability has been
fully integrated and demonstrated with the BHEC instrument.
Sizing estimates for a detected indication can be performed in
60–120 s using the unit’s onboard processing capabilities.
2.4. Liftoff Compensation Approach
Repeated BHEC inspections cause wear of the protective
tape on the probe over time, leading to varying degrees of
probe liftoff and, consequently, varying amplitude responses.
Compensating for sensitivity to tape wear was found to be
critical for improving model-based inversion crack sizing (Shell
et al. 2015). Figure 5 presents an example BHEC response from
a calibration panel, showing the processed view of the absolute
coil vertical channel (VAx). It was observed that the absolute
coil vertical channel exhibited significant variation at the edges,
especially for severely out-of-round holes. To produce the most
reliable liftoff metric, the average response around the hole
was evaluated at the center of each plate, as shown in Figure 5
(lower right).
A study shown in Figure 6 compares the peak differential
coil response with respect to the liftoff metric for an aluminum
test block run at 500 kHz and for varying hole diameters.
In general, the change in magnitude of the differential coil
response was found to be quite linear with respect to the liftoff
metric, where smaller values correspond to higher liftoff and,
thus, a smaller discontinuity response. However, due to vari-
ation in the BHEC instrument calibration process, the mag-
nitude trend varied from hole to hole and day to day. It was
ME
|
CRACKSIZING
0
2
1.5
1
0.5
0
45 90 135
Angular position (degree)
27 al 500 post, Ch1Y
VX1
pk
=8.2941, VY1
pk
=10.0529
Differential coil (VD) signal Absolute coil (VA) signal
180 225 270 315 360
5
5
–5
5
0
–5
–10
0
2
1.5
1
0.5
0
45 90 135
Angular position (degree)
180 225 270 315 360
0 0 0.5 1
8
6
4
2
0
0
20
40
60
80
100
120
140
160
180
200
–2
–4
–6
–8 1.5 2
Use VA
x
absolute coil component
–Evaluate ‘average’ VA
x
around hole
–Extract value at center of layers
2.5
0
5
–5
–10
–15
10
45 90 135
Angular position (degree) Depth
180 225 270 315 360
0
2
1.5
1
0.5
0
45 90 135
Angular position (degree)
180 225 270 315 360
1
2
3
4
5
6
7
27 al 500 post.csv, depth
profile (mag/phase)
Edge effect may impact
metric for thinner layers
Figure 5. An example BHEC response from a calibration panel with processed views of the differential coil and absolute coil responses. The
average absolute coil vertical response around the hole at the center of each layer was used as a liftoff metric.
0
0
2
4
6
8
10
12
–1 –2 1
dB_diff =18.55
Aluminum, 500 kHz, 6.3 mm diameter (set 1))
Aluminum, 500 kHz, 6.35 mm diameter (set 2)
Aluminum, 500 kHz, 12.7 mm diameter
Aluminum, 500 kHz, 3.96 mm
dB_diff =10.0–11.6611.6 dB_diff =15.73
dB_diff =14.2
2 3 4 5
Absolute coil — liftoff metric (dF_LIFTZ0)
– –
dB dif
Al k d
Al k d
,
Al k ddiameter
dif 10.0 dB dB_di
i
f
Figure 6. Trends in relative changes in the liftoff metric (dF_LIFTZ0)
with respect to peak differential coil response (dF_VY1pp) for repeated
calibration runs in aluminum at 500 kHz.
48
M AT E R I A L S E V A L U AT I O N • A U G U S T 2 0 2 5
Depth
in
hole
(in.)
Vx
channel
Vy
channel
Depth
in
hole
(in.)
R
(V) Absolute
coil
magnitude
(units)
Depth
in
hole
(in.)
Differential
coil
—
(dF_VY1pp)
amamplitude
reresponse
pp)
Absolute
co
i l phase
(degree)