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)

observed that the results appeared to correlate with the relative
gain between the absolute coil and the differential coil (dB_
diff see Figure 6), versus being sensitive to the varying hole
diameter. Therefore, to compensate for liftoff, relative changes
with respect to a baseline calibration scan were evaluated.
A comprehensive series of experimental studies was con-
ducted, including many repeated scans of corner EDM notches
oriented in various material stack-ups, at near- and far-side
positions, along with repeated scans of a calibration panel
(every fourth scan) for three materials and at two frequencies.
To supplement the dataset for building liftoff compensation
relationships, all combinations of relative changes between
the calibration notch liftoff metric (defined as the change in
the metric dF_LIFTZ0) with respect to the change in the peak
differential coil response (defined as the change in the metric
dF_VY1pp) were evaluated.
By fitting a correction model using these relative changes,
the liftoff correction model was no longer so sensitive to the
varying calibration gain levels. Statistical model fits were per-
formed for two different model types. First, a simple linear
fit was performed between the calibration notch change in
the liftoff metric (dF_LIFTZ0) with respect to the change in
the peak differential coil response (dF_VY1pp). Second, a
model was fit to test the significance of interactions between
the change in liftoff metric, along with other factors, such as
hole diameter, absolute coil gain, and differential coil gain. It
was determined that the simple linear model describing the
primary relationship between the liftoff metric and the peak
differential coil response was sufficient—additional factors and
higher-order model terms did not show a statistically signifi-
cant relationship with the response.
In practice, BHEC data is evaluated for both the unknown
indication and a previous calibration panel scan. The differ-
ence in the liftoff metrics—evaluated for the type of indica-
tion (e.g., corner crack adjacent to air, corner crack adjacent
to material, or through-thickness crack)—was paired with
the most relevant calibration notch. The relative change in
the liftoff metrics was evaluated and used to apply an ampli-
tude normalization factor to the new BHEC scan data with
unknown indications. This preprocessing step was found to
help compensate for signal magnitude changes due to varying
liftoff levels.
For plates less than 3.1 mm in thickness, acquiring a
reliable liftoff metric is not feasible with this approach, because
edge effects hinder a quality liftoff evaluation. Such thin panels
were not included in the sensitivity study.
3. Sizing Evaluation Study Design and Considerations
This section presents details on the sizing evaluation study,
including sample preparation and the distribution of cracks
considering the study. Details are presented on the execu-
tion of the experimental study design and notes highlight key
factors with the inspection calibration process.
3.1. Sample Preparation and Crack Distribution
To evaluate the BHEC inversion capability, specimens con-
taining natural fatigue cracks were manufactured following
the NIAR (National Institute for Aviation Research) fatigue
specimen design, shown in Figure 7a. Three different materials
were used in the study: 2024-T351 Aluminum, 17-7PH Stainless
Steel (heat treated to condition TH1050), and 6Al-4V Titanium
(solution treated and aged). All plate material was 6.35 mm
thick, and three different hole diameters were manufactured
for the study: 3.96 mm, 6.35 mm, and 12.7 mm. At least 12
fatigue crack specimens were created for each material/hole
diameter combination, producing over 108 specimens in total.
To produce natural fatigue cracks in the six-hole panel config-
uration, starter notches were added to two randomly selected
holes in each panel, generating two cracks per specimen. For
two of the six holes, a 0.5 mm thick lip was left in place, and a
saw-cut notch was added to the initiator to act as a stress con-
centration site. After initial fatigue cycling, the crack was grown
from the initiator into the material. The initiator was subse-
quently reamed, and the 0.5 mm initiator lip was removed.
Fatigue cycling was performed until the cracks were grown
to the desired length. (For more information on the artificial
seeding of fatigue cracks, see Yanishevsky et al. 2010.)
A wide variety of corner cracks was grown, with depths
(bore lengths) up to 2.5 mm and surface lengths up to 5.0 mm.
One objective of the crack sizing study was to produce a
balanced range of crack sizes to challenge the model-based
inversion capability over a range of sizes of interest. Depending
on crack size, different maintenance actions could be per-
formed, such as repeated hole reaming for smaller cracks, or
panel repair/replacement for larger cracks. Ten crack size bins
from 0 to 2.5 mm in depth were defined, with step sizes of
0.25 mm, targeting an even distribution across the bins. The
0.25 mm step size is close to the ream process radial change. It
was difficult to manufacture cracks smaller than 0.25 mm and
especially below 0.13 mm, but some successes were achieved
and used in the evaluation.
The crack specimen set build plan was performed and
resulted in 55 panels, each with two cracks. This plan achieved
the desired 12 cracks for testing for each of the nine material/
hole diameter combinations. Optical microscopy was used
to verify both crack length and bore length (crack depth) to
within ±0.025 mm. A traveling optical microscope plus mirror
configuration was developed to measure crack depth along the
bore surface. All fatigue cracks grown for the study were corner
cracks, enabling optical measurement of the crack length and
depth and reducing the need for destructive characterization.
Some pilot specimens were broken open via overload
fracture to verify the profile, the crack growth rate (da/dN),
and any internal extensions of the lengths. Maximum depths
and lengths in these fractured specimens were found to
not exceed 5% of the optically measured surface values.
Additionally, some unexpected cracks were discovered
during the BHEC study and inversion process. Many of these,
after BHEC detection and subsequent optical microscopy
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 49