variability in crack sizing could be necessary if further
improvements in sizing accuracy are required.
4. Results and Discussion
Table 3 presents crack sizing error results for all cracks in the
study, grouped by base material. All sizing error results pre-
sented in this section are expressed in terms of size dimen-
sions (mm), rather than percentages, to more directly inform
maintenance-action decisions. Sizing results are presented for
crack depth, crack length, and a combined metric: the square
root of the estimated area. Model-based inversion for crack
length yielded the least error across all three materials over
the full range of crack sizes studied. Crack bore length, given
the near-surface proximity to the probe, should be inherently
easier to estimate. The square root of the area was shown to
have the lowest error overall for aluminum, relative to the
TA B L E 3
Trends in corner crack sizing performance for all crack sizes in various materials
Parameter Level Depth average absolute error
(mm)
Length average absolute error
(mm)
Sqrt(area) average absolute error
(mm)
Material Aluminum 0.35 0.18 0.17
Material Stainless steel 0.47 0.27 0.32
Material Titanium 0.41 0.22 0.23
TA B L E 4
Trends in corner crack sizing performance for actionable crack sizes
Parameter Level Depth average absolute error
(mm)
Length average absolute error
(mm)
Sqrt(area) average absolute error
(mm)
Trial
1 0.21 0.15 0.13
2 0.21 0.15 0.12
3 0.28 0.12 0.13
4 0.23 0.17 0.15
Frequency
1 0.22 0.14 0.13
2 0.22 0.15 0.14
Material
Aluminum (Al) 0.21 0.12 0.12
Stainless steel (SS) 0.23 0.19 0.17
Titanium (Ti) 0.23 0.13 0.12
Material
(Frequency)
Al (200 kHz) 0.19 0.13 0.11
Al (500 kHz) 0.23 0.11 0.12
SS (500 kHz) 0.23 0.17 0.16
SS (1 MHz) 0.24 0.21 0.17
Ti (1 MHz) 0.25 0.13 0.12
Ti (2 MHz) 0.20 0.13 0.12
Diameter
3.96 mm 0.23 0.15 0.13
6.35 mm 0.20 0.15 0.13
12.7 mm 0.24 0.14 0.14
Adjacent material
Air 0.21 0.15 0.13
Al 0.21 0.15 0.14
SS 0.28 0.12 0.15
Ti 0.23 0.17 0.15
Average 0.22 0.15 0.14
ME
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CRACKSIZING
52
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 and length estimates. This strong correlation between
eddy current response and cross-sectional area has been seen
in past studies (Shell et al. 2015). To successfully distinguish
length and depth reliably, a combination of amplitudes and
unique shape features with respect to the depth profile curve
in the eddy current response are needed. To achieve such
features, the crack length generally needs to approach the
diameter of the probe. A good example is shown in Figure 1,
with both amplitude and shape features present for the
1.98 × 2.34 mm (depth × length) corner crack.
Higher error was observed for cracks in stainless steel.
A contributing factor discovered during the study was a
high level of material noise in the stainless-steel calibration
specimen. The poor signal-to-noise ratio for the top notch
indication in the calibration panel was determined to be unac-
ceptable, so a change was made to use only the second notch
(adjacent to steel) for calibration. This solution was sufficient
to generate inversion results but contributed to poorer overall
performance in stainless steel.
Table 4 presents corner crack sizing performance for small
cracks (1.2 mm), considering variation in base material, fre-
quency, hole diameter, material adjacent to the crack, and
repeated trials. On average, sizing error results were much
lower than the results that include the largest crack sizes. The
lower frequency results in Table 4 show slightly better sizing
performance than higher frequency results. This was antici-
pated considering the standard depth of penetration for the
frequencies tested. For example, aluminum at 500 kHz has the
lowest standard depth of penetration in BHEC inspection—
only 0.11 mm. Thus, operating at 500 kHz for aluminum, there
is very little sensitivity to even moderately sized cracks at this
frequency. We should note that these inspection frequencies
were chosen to detect small discontinuities, not to provide
sensitivity to resolve moderate-to-large discontinuities with
increasing depth. Therefore, it is more challenging to deter-
mine the depth of moderate-to-large cracks at higher frequen-
cies. However, it can be hypothesized that the depth accuracy
for deeper cracks could be improved with additional data col-
lected at lower frequencies.
To provide some perspective on the level of variability in
this study, results for peak amplitude signal versus known
crack length are presented in Figure 8a. In general, there exists
a roughly 10× range of variability in the magnitude of the peak
response for cracks of similar length, and across nearly all
lengths. This high level of amplitude variability was due to the
wide variation in crack aspect ratio incorporated into the study,
as well as having repeated scans that generate natural variation
due to the tape wear over time, the calibration process, and
possibly human factors associated with different inspectors.
Corresponding plots of the model-based inversion results for
estimated crack square root of the area, crack length, and crack
depth are presented in Figures 8b, 9a, and 9b, respectively.
Length and depth estimates were found to provide a much
better metric of crack size than amplitude signal alone. While
the crack depth inversion algorithm incorporating liftoff com-
pensation may not be perfect, it clearly provides more quan-
titative information to inspectors about the dimensions of the
crack indications.
Additional trends were observed in the crack sizing study.
Average errors for crack length and square root of the area
were quite low, especially for aluminum and titanium. While
there was not a great difference between the repeated trials,
Trial 3 did have the worst crack depth estimates, while Trial 4,
where all tests included adjacent material (rather than air)
near the crack, had higher length estimates. Adjacent stainless
steel produced the highest depth error. Trends with varying
hole diameter were not linear, but the 6.35 mm diameter case
yielded the best inversion results. The best material/frequency
combination for crack depth accuracy was aluminum at the
lower frequency of 200 kHz.
While the average absolute error is useful as a metric for
studying trends in sensitivity studies, it is also important to
generate uncertainty bounds on the accuracy of the depth esti-
mates. Consideration is given here on the evaluation of the 95%
safety limit against undersizing (LUS) bound. Before imme-
diately evaluating any quantitative metrics, it is important to
first consider the assumptions behind the metrics and verify
the expected trends (Annis et al. 2015). Normal probability
0
0
2
4
6
8
10
12
Aluminum
Steell
Titanium
0.2 0.4 0.6 0.8 1.0
Known crack length (mm)
1.2 1.4 1.6 1.8 2.0 0
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.2 0.4 0.6 0.8 1.0
Known crack sqrt (area) (mm)
1.2 1.4
Aluminummuminu
Steelle
Titaniumm
Alu
0 2 0 0 0 8 0 2 8 2 0
Al
S
T
Figure 8. Plots of (a) peak amplitude versus known crack length and (b) estimated versus known crack sqrt(area), grouped by material.
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 53
(V)
Estimated
crack
sqrt
(area)
(mm)
AmAmplitude