characterization, were found to be under 1.25 mm and were
added to the sizing study.
An additional set of 27 specimens, each with two cracks,
was selected for an “adjacent panel” study, providing at least six
cracks for testing for each material/hole diameter combination.
Figure 7b presents a plot of the distribution of the opti-
cally measured length and depth values for the 133 unique
cracks used in the sizing verification study. A histogram of
the aspect ratio (defined as the surface length divided by bore
length) for these cracks is shown in Figure 7c. The median
aspect ratio for the study was 1.39 (length ÷ depth). The dis-
tribution of aspect ratios for the study varied significantly
across all cracks, providing a very good challenge for the
model-based inversion scheme. Generally, the amplitude of
the eddy current response has a stronger correlation with
the cross-sectional area of the discontinuity. Estimating the
aspect ratio is a much greater challenge, requiring accurate
estimation of both length and depth.
3.2. BHEC Data Acquisition Study Plan
To validate this capability, a comprehensive experimental study
was designed to evaluate the crack sizing performance using
the specimen set previously described. The study acquired
data at both low and high frequencies: 200 kHz, 500 kHz, and
1 MHz for aluminum, steel, and titanium, respectively (low fre-
quency), and 500 kHz, 1 MHz, and 2 MHz for the same mate-
rials (high frequency). Three repeated trials were performed
for each case. An additional study, Trial 4, was performed with
all combinations of adjacent materials for each base material,
testing nine total material combinations.
A total of 984 crack indications were evaluated for size in
this study. The breakdown of the number of crack indications
evaluated for each study factor is presented in Table 2.
From a maintenance-action perspective, sizing accuracy in
terms of dimensions is more practical over a small to moderate
range of crack depths—specifically where it is feasible to ream
out the holes up to a prescribed limit of resizing based on the
ME
|
CRACKSIZING
1 2 3 4 5 0
0
0.5
1
1.5
2
2.5
3
Crack length — optical measurement (mm)
1 2 3 4 5 6 0
0
50
100
150
200
250
300
Aspect ratio (length ÷ depth)
5
5
5
Figure 7. (a) An aluminum specimen in a servo-hydraulic load frame (left), a view of a hole with a grown fatigue crack (center), and a traveling
microscope view (right) (b) plot of the distribution of optically measured length and depth values for the 133 unique cracks used in the sizing
verification study (c) histogram of the crack aspect ratio (length ÷ depth) for the 984 EVi scans in the study.
50
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
Crack
depth
—
optical
measurement
(mm)
Samples

original hole diameter. Members of the maintenance commu-
nity provided input on the number of viable hole resize steps
for removing small cracks. Each ream oversize can increase the
hole diameter by 0.40 mm, corresponding to a radial change of
0.20 mm. Due to limitations in oversizing holes, the results dis-
cussed here focus on the inversion model’s sizing performance
for cracks below 1.2 mm in depth. The study breakdown for
this small-crack range is also presented in Table 2.
3.3. Inspection Calibration Process and Model
Calibration Notes
Three calibration standards were used in the study: Standard
7075 Aluminum (National Stock Number [NSN] 6635-01-092-
5129), 4130 Steel (NSN 6635-01-512-4952), and Titanium (NSN
6635-01-390-1768). An example scan of the calibration standard
is presented in Figure 5, showing indications for a first-layer
near-corner notch (adjacent to air), a first-layer far-corner
notch (adjacent to material), and a third-layer through notch.
After every three unknown crack hole scans, the calibration
standard was scanned (for the matching hole size). These
calibration scans were performed both before and after each
BHEC instrument calibration cycle. Instrument calibration was
conducted at the start of each day and whenever the protective
tape on the probe tip degraded and was replaced. The calibra-
tion standard scans were subsequently used by the crack sizing
algorithms to provide a baseline for the liftoff state. In this
way, the datasets collected, as well as the degree of change in
the eddy current responses, were baselined to the calibration
standards.
Initially, an assumption was made that the top corner EDM
notch dimensions were 0.77 × 0.77 × 0.089 mm, with an ellip-
tically shaped discontinuity profile. However, the calibration
block notches actually have a triangle profile. This incorrect
early assumption resulted in the setting of the size for the cal-
ibration notch to be effectively larger in depth than reality,
leading to oversizing, especially for cracks in aluminum where
the model agreement was quite good. To convert the triangu-
lar notch response to an equivalent elliptical notch response,
one must determine which dimension metrics should be held
equivalent. Typically, with eddy current NDE, one goal is to
ensure the area of the notches are equivalent. Additionally,
due to the high frequencies used, BHEC is more sensitive to
near-surface features.
Originally, the centroid of the equivalent elliptical notch
was set to be equivalent for the triangular notch. Thus, a
0.77 × 0.77 mm (length × depth) triangular notch became a
0.63 × 0.61 mm equivalent semi-ellipse. However, since BHEC
is highly sensitive to near-surface length, this approach—
assuming an equivalent area and equivalent centroid—was
found to increase inversion error during initial testing. The
underlying issue appeared to be that this method did not rep-
resent the equivalent sensitivity to the very near-surface for
eddy currents, especially given the high frequencies that were
used. (The ratio for the equivalent elliptical notch length to
triangular notch length was 0.63 mm ÷ 0.77 mm =0.82.)
An alternative approach was implemented, fixing
the elliptical-to-triangular length ratio at 0.91 (reducing
the length difference based on a fixed centroid by 50%)
and then calculating the depth to maintain equivalent
cross-sectional area. Therefore, the triangular calibration notch
became 0.71 × 0.52 mm (length × depth) for an equivalent
semi-elliptical notch. Future work is planned to resolve this
transformation issue by building separate surrogate models for
triangular corner notches in each material.
A second early assumption was that calibration notch
dimensions did not vary sufficiently to affect model-based
inversion sizing. However, further investigation revealed that
the notch length, depth, and width varied enough for the cali-
bration standards to influence quantitative evaluation. For the
18 notches in this specimen, the lengths and depths ranged
from 0.734 mm to 0.81 mm and the notch widths ranged from
0.081 mm to 0.132 mm. This makes some difference with model
calibration. To address this, a process has been implemented
with the inversion code to acquire this information from a cal-
ibration look-up table to find the matching notch size for each
calibration scan.
Preliminary testing did not show a significant difference in
sizing results when using nominal values versus the matched
calibration notch values for each material and hole diameter.
However, additional analysis of the effect of calibration
TA B L E 2
Experimental runs for each factor in the crack sizing
study
Parameter Level Total
count
Total count for small
crack depths (1.2 mm)
Trial
1 210 124
2 213 125
3 212 124
4 341 193
Frequency
1 492 285
2 492 281
Material
Aluminum (Al) 330 178
Stainless steel
(SS) 324 192
Titanium (Ti) 330 196
Diameter
3.96 mm 330 215
6.35 mm 324 176
12.7 mm 330 175
Adjacent
material
Air 642 373
Al 114 64
SS 114 62
Ti 114 67
Total 984 566
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 51