Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
ESSENTIAL FACTORS IN IMPROVING THE CHARACTERIZATION OF CRACKS
AND CORROSION USING TRANSIENT EDDY CURRENTS.
Robert A Smith
Future Systems Technology Division
QinetiQ Ltd
Farnborough, GU14 0LX, UK
Tel: +44 1252 395655. Fax: + 44 1252 395000.
E-mail: [email protected]
Geoffrey R Hugo
Defence Science and Technology Organisation,
Aeronautical and Maritime Research Laboratory
GPO Box 4331, Melbourne, Victoria 3001, AUSTRALIA
Tel: +61 3 9626 7519. Fax: +61 3 9626 7087.
E-mail: [email protected]
David J Harrison
Future Systems Technology Division
QinetiQ Ltd
Farnborough, GU14 0LX, UK
Tel: +44 1252 395097. Fax: + 44 1252 395000.
E-mail: [email protected]
Abstract
Previous work using transient (or pulsed) eddy currents has quantified the capabilities of the technique for
defect detection in aluminum alloy structures over a range of depths to 0.450". A comparison of different
probe designs has shown that probe size, whilst important, is not the only factor that determines
performance. Increasing interest in transient eddy currents for crack and corrosion detection has resulted
in the need for a better understanding of the essential factors involved in improving its performance.
The ability to scan large areas of complex and variable structures without changing acquisition parameters
or probes is a requirement for which transient eddy-current methods are well suited. There is a resulting
dependence on analysis techniques to compensate for structural effects and to highlight defects, as well as
to quantify defect size and depth. Advances in these analysis methods will result in improved
characterization of both cracks and corrosion.
This paper addresses the factors that influence defect detectability, resolution and the characterization of
defects using transient eddy currents. Of particular interest is the detection of cracks near fasteners and
edges, and their characterization in terms of depth and size. In addition, an understanding of factors
affecting the determination of metal loss has resulted in improved accuracy for corrosion characterization.
The relationship between eddy-current density, probe size and defect detectability has been investigated
in order to better understand the influence of structural and material inhomogeneities and electrical noise.
These studies are presented using several examples of simulated crack and corrosion specimens where
appropriate.
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Introduction
Transient eddy-current non-destructive testing is arousing increasing interest for the detection of cracks
and corrosion in aging metallic aircraft structures. A major attraction is that a single scan over a large area
of structure contains sufficient information for both detection and characterization of defects, regardless
of structural variations. Such a scan can be performed with minimal operator training due to the simple
data acquisition procedures. A further benefit is the ability to use advanced analysis methods, supported
by analytical models, to determine location, depth, size and severity of defects.
For detection of a specific defect, in a particular thickness of material, it may be possible to develop a
technique with better sensitivity than transient eddy currents. However, that technique would not be
optimized over a different thickness or conductivity, or in the presence of substructure or edges. The
transient eddy-current method requires no parameter changes at acquisition time to allow for changes in
thickness or conductivity and the analysis methods enable the removal of lift-off, edge effects, and other
structural changes.
Previous publications have addressed the principles of transient (or pulsed) eddy-currents [(1)-(5)], the
development of the analysis techniques [(6)-(8)], and careful determination of the capabilities and
limitations of the method [(9),(10)].
In the transient eddy-current method an eddy-current pulse is generated at the surface of a structure and
propagates down into the structure over the course of a few milliseconds. The magnetic field measured at
the surface will be modified by any changes in the propagation path of the pulse, such as caused by
defects, conductivity changes, edges or interfaces. The eddy-current pulse contains a broad frequency
spectrum, which is of great benefit during analysis of the signals because it includes the equivalent of
numerous single-frequency scans using a conventional eddy-current system.
The TRECSCAN® system, developed by the authors, has been described in full on other occasions [(8)(10)] and comprises a probe, instrument and computer, with the TRECSCAN software library linked to a
scanning application such as ANDSCAN® or MAUS™. Positional information is acquired using one of
many different types of scanner controlled by these scanning applications. The probe (see Figure 1)
contains a coil to generate the eddy-current pulse and a Hall sensor to measure the perpendicular
component of the magnetic field at the surface of the structure, in the center of the coil.
Hall Sensor
Coil
Ferrite Core
Current
Perpendicular Field
Figure 1: Diagram showing a cross-section of the probe and the resultant magnetic field lines. Examples
of the eddy-current and magnetic-field profiles are also shown.
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
A low-pass filtered square-wave current, generated by the TRECSCAN instrument, is used to excite the
coil, which is connected to a third-party data acquisition card in a computer. Each time the current
reverses an eddy-current pulse is induced in the structure on which the probe is placed. Figure 2 shows
the time dependence of the magnetic field and the eddy-current pulses that the magnetic field induces.
Perpendicular Field
Eddy-current Pulse
Figure 2: Sketch showing the time dependence of the magnetic field and the induced eddy-current pulses.
The essential elements of the field generation and reception components of the TRECSCAN® system are
shown diagrammatically in Figure 3. The component of the magnetic field perpendicular to the specimen
surface, Hz(t), is measured using a Hall sensor located immediately above the specimen surface on the
axis of the coil.
input current i(t)
i(t)
time t
Hz(t)
Magnetic Field Hz
Coil Current i
With no specimen in front of the probe, the measured field Hz(air) is simply proportional to the drive
current i(t). The field Hz(specimen), measured when the probe is on a metallic specimen, has a much
longer rise time due to the eddy currents induced within the specimen which oppose the change in
incident field. In order to view the effect of the specimen, the transient field reflected by the specimen HRz
(ie. the field due to the induced eddy-currents within the specimen) can be calculated as the difference
between the Hz(specimen) and Hz(air).
Hz(air)
Hz(specimen)
DHz(defect)
time t
HRz = Hz(specimen) - Hz(air)
Ferrite core
Drive coil
First layer
Gap
Second layer
Hall effect probe
Corrosion
Figure 3: Schematic showing the probe on a multi-layer specimen with hidden corrosion between layers,
including typical input current i(t) and probe responses Hz(t).
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
In order to accentuate the signals due to defects within the specimen, it is normal to ‘balance’ the signal
on a good part of the structure in order to view variations in the transient response relative to this good
structure. Balancing generates a relative signal DHz(t) that is nominally zero unless the structure or its
properties change. In the TRECSCAN® system, this balancing operation can be performed at any time
during acquisition or subsequent analysis of the data as it does not affect the raw transient data Hz(t) that
is stored for subsequent off-line analysis. Typical signals measured using the Hall effect device are
illustrated in Figure 4.
As the transient response is a well-behaved and slowly varying curve, it is can be well represented by its
amplitude at a relatively small number of time points (referred to as time slices, since they represent slices
through the data in the time domain). Consequently, the TRECSCAN® system stores the transient
response at a series of time slices (typically twelve), which are (approximately) exponentially distributed
in time to exploit the fact that the transient response varies much more slowly at longer times than at
earlier times (see Figure 4). C-scan images are then formed by mapping the field data Hz(ti) at a selected
time slice ti to a colour palette. Optional processing can be applied to remove for the effects of probe liftoff (lift-off compensation) and edges (edge subtraction), and to produce C-scan maps of either the total
thickness of the specimen (total thickness mode) or percentage changes in total thickness (thickness
change mode) [(6), (8)-(10)].
Figure 4: Typical transient responses showing (left) different responses from the back surface of
aluminium plate of between 1 and 8 mm depth (compared with a reference half-space) and the sample
times of ‘time slices’ that increase exponentially (right).
As the pulse propagates through the structure its amplitude decays and the spatial distribution of the
current broadens (see Figure 5). This spatial distribution can be described in terms of a spatial frequency
spectrum, in the same way as a temporal waveform can be described by a temporal frequency spectrum
using spectral analysis methods such as Fourier series and transforms. Probe design determines the
distribution of spatial frequencies in the incident magnetic field generated at the surface of the probe
when held in free space. This spatial frequency spectrum determines the spatial characteristics of the
eddy-currents generated in the specimen by the incident field when the probe is on the specimen. As this
eddy-current distribution propagates into the specimen, higher spatial frequencies are preferentially
attenuated and therefore the spatial frequency content of the eddy-current field that penetrates to a certain
depth will become increasingly dominated by lower spatial frequencies as the depth increases (see Figure
5). The specimen acts as a low-pass spatial filter. In general a probe with a high mean spatial frequency
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
will give good spatial resolution of near-surface corroded areas, and will be less affected by structure such
as fasteners, but will not penetrate as deeply into the structure as a larger probe with a lower mean spatial
frequency.
Figure 5: Diagram illustrating (left) how the field effectively becomes broader with depth in a conducting
half-space due to attenuation of the more compact components, and (right) how the eddy-current pulse,
plotted against time, decays in amplitude as a function of depth.
The spatial frequency distribution in free space for the probes used in this work were calculated from
temporal-frequency measurements using a method developed by Harrison [(10)]. An alternative method
of characterizing the probe uses a Hall sensor scanned across the face of the probe measuring the
perpendicular component of the magnetic field.
This paper concentrates on the important factors for improving defect detectability and characterization.
The first sections look at the differences between sensitivity and resolution and how the field
characteristics affect them. Then, after a section on discriminating between defects and structural effects,
a procedure is developed for characterizing single defects in terms of depth, severity and lateral size.
Sensitivity, Resolution and Defect Detectability
Sensitivity, resolution and defect detectability, are capabilities that are frequently confused when
considering small defects. The first two: sensitivity and resolution are quantifiable properties of an
inspection technique with a particular instrument, probe and defect type. The difference between these
capabilities may be demonstrated by considering a small defect that is just detectable when in the middle
of a uniform sheet of metal, but becomes indistinguishable from a larger defect or an edge when it is
closer to them than the resolution limit, and consequently is not detected. Defect detectability is the
parameter measured and used to determine these two properties. A highly sensitive technique with good
defect detectability in uniform structure may have such poor resolution that the defect detectability in
realistic structure with edges and fasteners is considerably reduced.
For the purposes of this paper the following definitions will apply:
q
Defect detectability is a measure of the minimum detectable defect severity (metal loss or crack area)
as a function of depth for a certain defect type and orientation and in a particular structural location.
For this work a detectability threshold is used based on a signal-to-noise ratio of 3:1 where the
‘signal’ is the difference in a particular timeslice value over the defect compared with over ‘good’
structure and ‘noise’ is the standard deviation of the same timeslice data within a region over a ‘good’
area.
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
q
q
q
The sensitivity of a technique will be considered to be the defect detectability in uniform structure for
a given defect type and orientation. For transient eddy-current methods, sensitivity is thought to be
dependent on:
·
amplitude of the eddy-current density as a function of depth
·
orientation of the defects to the eddy currents,
·
lateral size of the field as a function of depth – dependent on the probe geometry and construction
·
temporal noise levels, and
·
random spatial variations (spatial noise)
The lateral resolution of a technique will be the ability to distinguish a defect when close to an edge
in the same layer, as this is the most relevant situation. For transient eddy-current methods, this is
thought to be dependent on:
·
lateral size of the field as a function of depth – dependent on the probe geometry and construction
·
random spatial variations (spatial noise)
The depth resolution is the ability to distinguish between two defects at different depths and one
larger defect at some intermediate depth. For transient eddy-currents this is a function of the software
tools available for decomposing the transient response of the structure into contributions from defects
at different depths. No such tools are known to the authors on current transient eddy-current
equipment although they are in the process of developing one themselves.
Hence both the sensitivity and lateral resolution are dependent on the lateral size of the field, whilst
sensitivity is also a function of the amplitude of the current density at the defect and orientation of the
defect. These two aspects are inter-related and will be discussed in this paper. Depth resolution of
transient eddy-currents will not be addressed here because it is currently non-existent - due to the lack of a
technique to distinguish the effects of two defects separated only by depth.
A range of different probes will be used to demonstrate some of the real variations in sensitivity and
lateral resolution. These probes are briefly described in Table 1 in terms of the coil size and the type and
size of core, the factors that influence the size and shape of the incident field.
Probe
Size
Core
SF
TSF
TRSF
SMF
MF
FMF
TMF
LF
SCC
LP
Small
Small
Small
Small/Medium
Medium
Medium
Medium
Large
Small
Large Pancake
Ferrite Pot
Ferrite Pot
Ferrite Pot
Ferrite Pot
Ferrite Pot
Ferrite Pot
Ferrite Pot
Ferrite Pot
Ferrite Post
Air
Inner Coil
Diameter (mm)
5.9
5.9
3.9
7.5
9.2
9.2
9.5
11.3
3
5
Outer Coil
Diameter (mm)
11.9
11.9
11.9
15
18.4
18.4
18.4
20.5
9.5
20.7
Table 1: Probe coil dimensions.
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Sensitivity
Defect sensitivity has been measured by the authors using a versatile set of specimens (see Figure 6)
where a layer containing a range of defect sizes and defect severities can be moved to a variety of depths
in the structure.
As suggested above, defect sensitivity will decrease with increasing depth (see Figure 7) and decreasing
lateral size of the defect (see Figure 8) because the propagating eddy-current field changes in size, shape
and eddy-current density with depth. This section explores the way in which those changes occur.
Figure 6: Modified X-ray of the type of specimen used for defect detectability measurements. It is a
versatile set of aluminum alloy layers that can be stacked in any order. One layer of this multi-layer
structure contains flat-bottom holes with five different amounts of metal loss and five different diameters.
That defective layer can therefore be inserted at any of various depths in the structure.
Page 7 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
10
Minimum Detectable Metal Loss (mm)
1
0.1
0.01
0.001
0
2
4
Low Current SF
High Current SF
SMF
FMF
LF
High Current SF
FMF
SMF
1% of Defect Depth
LF
6
8
10
12
Defect Depth (mm)
Figure 7: Graph showing how the defect detectability varies with depth for four probes and large (30 mm
diameter) volumetric (metal-loss) defects. The specimens used are shown in Figure 6 and a signal-tonoise threshold of 3:1 was used to determine the detectability threshold. An exponential curve of best fit is
drawn for each different probe size.
The most important concept in understanding how sensitivity depends on depth is that the decay of the
eddy-current field is not just dependent on the temporal frequency (as often assumed in conventional
eddy-current testing) but also on the spatial frequency distribution in the incident field. It is true to say
that at high temporal frequencies and for large probes the temporal frequency effect dominates. In this
regime the conventional concept of the Standard Depth of Penetration is valid. However, for low temporal
frequencies or small probes the spatial frequency distribution becomes more important and the 1/e depth
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
of penetration deviates from the definition of Standard Depth of Penetration. In fact, for small probes
below a certain temporal frequency, the spatial frequency is the only factor in determining the depth of
penetration.
10
Minimum Detectable Metal Loss (mm)
1
0.1
0.01
4 mm Dia.
5 mm Dia.
10 mm Dia.
20 mm Dia.
30 mm Dia.
5 mm Dia.
30 mm Dia.
10 mm Dia.
1% of defect depth
20 mm Dia.
4 mm Dia.
0.001
0
2
4
6
8
10
12
Defect Depth (mm)
Figure 8: Graph showing how the defect detectability varies with depth and defect diameter for the FMF
probe. An exponential curve of best fit is drawn for each different defect diameter.
A modelling exercise was undertaken, the aim of which was to take the spatial frequency spectra of a
range of probes and propagate it down into a structure, mapping how the magnitude, size and shape
change with depth. Through this exercise a greater understanding was achieved of the reasons for one
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
probe having a particular sensitivity or lateral resolution. Details of the modelling can be found in
Appendix A. In this section certain key outcomes are highlighted.
Conventional skin depth (Standard Depth of Penetration) d is only defined for k=0 and hence is only valid
for large probes. A more realistic, k-dependent depth of penetration dk can be defined as the depth at
which the amplitude has decayed to 1/e of its original value, and is defined in equation (1).
dk = 1
[
Re k 2 + jwms
]
(1)
where k is the spatial angular frequency, w is the temporal angular frequency, m is the permeability, and
s is the conductivity. Hence it can be seen that for high temporal frequencies, k is less significant, but for
low temporal frequencies, k dominates the depth dependence. Figure 9 illustrates how this skin depth
varies as a function of temporal and spatial frequency in 40 %IACS aluminum. The horizontal asymptote
of each curve represents the Standard Depth of Penetration whereas the diagonal asymptote (top-left to
bottom-right) is the region of total dependence on spatial frequency.
1/e Depth of Penetration in 40 %IACS (mm)
100
Temporal
Frequency
(kHz)
10
0.03
0.1
0.3
1
3
10
1
30
100
0.1
0.01
0.1
1
10
-1
Spatial Frequency, k (mm )
Figure 9: Graph showing how the penetration depth is dependent on both temporal and spatial frequency
for the ranges being used by TRECSCAN –the shaded area. For each curve, the horizontal asymptote for
low spatial frequencies is the Standard Depth of Penetration, whereas the diagonal asymptote is the
regime where the penetration is dependent purely on spatial frequency, k.
Figure 10 shows typical temporal-frequency spectra for incident transient fields using TRECSCAN whilst
Figure 11 shows the equivalent spatial-frequency distributions for a variety of probes. From these three
graphs it can be seen that, over much of the range in use for TRECSCAN, the penetration is highly
dependent on spatial frequency, k and the distribution of spatial frequencies in the field is related to probe
size and geometry.
The spatial frequency distributions shown in Figure 11 were measured for the various probes using a
method developed by Harrison [(11)] and represents the size and shape of the field at the surface with the
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
probe in air. These distributions are modified as the field propagates into the structure and it is possible to
calculate them at each depth using equation (3) of Appendix A.
If the fields at the surface, represented in Figure 11, are propagated down into the structure using this
method, the field strength decreases rapidly and the the shape of the spatial frequency spectrum changes.
The modelling shown in Appendix A gives a more complete description of how the field strength, size
and shape varies as a function of depth in a conducting half-space.
A useful parameter to define at this stage is an equivalent diameter at a given depth. This is the diameter
of a single-turn coil that would have the same peak in its spatial-frequency spectrum, the field of which
could therefore be regarded as representative of (‘equivalent’ to) the field distribution found at that depth.
Appendix A explains that the peak of the spatial-frequency spectrum of a single-turn coil occurs at
4 / diameter. Hence:
Equivalent Diameter = 4 / Peak Spatial Frequency
(2)
A plot of such a parameter as a function of depth (see Figure 13) gives an indication of how the field
distribution spreads out with depth for a single probe at various temporal frequencies, whilst Figure 14
shows the same dependence but for various probes at one temporal frequency.
Relative Amplitude
10
Time constant
1
30 us
70 us
100 us
0.1
0.01
0.1
1
10
100
Frequency (kHz)
Figure 10: Graph showing the temporal frequency spectrum in the transient excitation with different
time-constants for the field-reversal. Recent hardware improvements allow time-constants down to 30 ms.
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Normalised Estimated Amplitude
1.2
LP
LF
MF
TMF
FMF
SMF
SF
TSF
TRSF
SCC
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
0.01
0.1
1
10
-1
Spatial Frequency k (mm )
Figure 11: Graph showing the distribution of spatial frequencies in the field for each of the probes used
in the current work. Each curve is normalized to the peak spatial frequency for that probe.
Estimated Amplitude at Peak
Spatial Frequency (Tesla)
1.0E-03
1.0E-04
1.0E-05
1.0E-06
LP
TMF
SF
SCC
1.0E-07
1.0E-08
0.0
5.0
LF
FMF
TSF
FMF
10.0
MF
SMF
TRSF
15.0
20.0
25.0
30.0
Depth (mm)
Figure 12: Estimated amplitude at the peak of the spatial-frequency spectra at various depths in
40 %IACS aluminum alloy half-space, for various probes using a temporal frequency of 300 Hz. The line
is an exponential fit to the FMF probe data in Figure 32 in Appendix A.
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Equivalent Diameter (mm)
45
40
35
30
25
20
15
Frequency (kHz)
10
5
0
0
0.10
0.40
0.15
0.60
0.20
1.00
4.00
8.00
0.30
10
20
0.30
2.00
30
Depth (mm)
Figure 13: Calculated depth dependence of field size for various temporal- frequencies for the FMF
probe. A linear-regression line is plotted for the 300 Hz data as this is a mid-range frequency and is used
for Figure 14.
Equivalent Diameter (mm)
40
35
30
25
20
15
LP
MF
FMF
SF
TRSF
Linear (FMF)
10
5
0
0
10
20
LF
TMF
SMF
TSF
SCC
30
Depth (mm)
Figure 14: Depth dependence of field size for different probes at 300 Hz. A linear regression line has
been drawn through the FMF probe data as this probe was used for Figure 13.
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
The important rules-of-thumb to note from this study are:
q
that the amplitude at the peak of the spatial frequency spectrum of the field of a probe decreases by
approximately a decade for every 0.5” (12.7 mm) in 40 %IACS aluminum alloy at 300 Hz (see Figure
12).
q
that the field at a depth of 0.625” (16 mm) in 40 %IACS aluminum alloy is approximately 50%
broader than at the surface (see Figure 13) for the range of temporal frequencies in the transient.
q
that the field from a small probe remains smaller than that from a large probe despite the fact that the
fields from all probes expand with depth because the more compact components of the field decay
more rapidly (see Figure 14)
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Lateral Resolution
Lateral resolution can be considered to be the ability of the technique to distinguish the difference
between two small closely-spaced defects and one large defect. The last point made above is important to
consider for lateral resolution as the size of the eddy-current field at the depth of the defect will affect the
resolution.
An example of this is given for the specimen in Figure 15 where scans have been performed using both
medium (MF) and small (TRSF) ferrite-cored probes - see Figure 16 and Figure 17. Note that the probe
was mounted in a stiff brush and was tilted and raised during scanning to mount the exterior strap. The
effect of this lift-off was removed from the scans illustrated using a lift-off compensation algorithm [12].
Probe
1.80 mm (0.071”)
1.14 mm (0.045”) or
0.83 mm (0.032”)
Brush
1.60 mm (0.063”)
1.91 mm (0.075”) or
3.18 mm (0.125”)
Tapered and stepped
1.5 mm (0.060”) to
4.7 mm (0.185”)
1)
2)
3)
4)
5)
Figure 15. Enhanced X-ray image and diagram of a DC10 Crown specimen showing cracks in the five
layers. Total thickness is over 10 mm in places. Annotated X-ray image courtesy of NDT Solutions Inc.
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Figure 16: Images of a DC10 crown-splice specimen containing cracks. Timeslice 2 with lift-off
compensation. The left-hand image was produced using the medium-sized MF probe and the right-hand
image with the small-sized TRSF probe.
Figure 17: Images of a DC10 crown-splice specimen containing cracks. Timeslice 10 with lift-off
compensation. The left-hand image was produced using the medium-sized MF probe and the right-hand
image with the small-sized TRSF probe. These scans show just the deepest layers.
Note that the smaller (TRSF) probe retains better resolution despite the deeper penetration required for
the Timeslice 10 images (Figure 17). This is partly due to the much greater amplitude of current density
achievable with the TRSF probe compared with the more primitive design of the MF probe. The
conclusion from these scans is in support of the modelling results in Figure 14. Although considerable
degredation of image quality is experienced deeper in the structure, a smaller probe with better resolution
near the surface will retain that resolution advantage even at greater depths.
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Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
All the cracks shown in Figure 15 could be detected in various timeslice images from the scan using the
TRSF probe, except the deep crack in the tapered doubler at the far side of the structure and some of the
cracks in the 2nd-layer finger doublers. The deep crack was very close to two edges and was in line with
those edges. It was thought that at the depth of the deep crack, at least 6.5 mm (0.250”), the field size
would be so large that the crack would not be resolved due to its proximity to the edges.
To test this theory, a further experiment was conducted to determine how close to an edge a crack can be
resolved as a separate defect, as a function of depth and for different probes. The test specimen is shown
in Figure 18 and a typical TRECSCAN image of it is shown in Figure 19.
Figure 18: Enhanced X-ray image of the crack resolution test specimen containing four layers of
thickness 4 mm (0.160”) aluminum alloy of 40 %IACS conductivity. Each layer contained a crack
diagonally approaching an edge. There was no edge in that proximity in any of the other three layers.
The method for determining crack resolution was to take a cross-section graph from the timeslice image,
similar to the one at the top of Figure 19, and find the crack distance from the edge at which there was no
Page 17 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
reduction in signal between the edge and the crack. This was more difficult for the top-layer crack
because the edge gave a smaller signal than the crack due to the lift-off compensation that had been
applied.
Figure 19: Typical TRECSCAN image of the crack resolution test specimen showing timeslice 10 with
lift-off compensation on, using the SMF probe.
This experiment was designed to investigate how the proximity of an edge affects the resolution of a
crack. It is not, however, representative of short cracks, or cracks perpendicular to the edge, which may be
more common in real structures. Also, the crack breaks out of the edges of its layer and so there is no
eddy-current path around the crack. The graphs in Figure 21 and Figure 22 are reproduced in units of
inches in Appendix B.
The graph in Figure 20 shows that, as expected, the crack resolution becomes worse with depth in the
structure. At the depth of the deep crack in the DC10 structure (see Figure 15), 6.5 to 10 mm deep, the
TRSF probe should be able to resolve a crack provided it is 10 mm from an edge. In the DC10 specimen
the doubler in which the crack exists is approximately 25 mm wide, making the crack almost swamped by
the edge effects.
The expected link between crack resolution and equivalent field diameter is shown in Figure 21 where
they are directly compared across all the probes and depths.
Page 18 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Crack Resolution (mm)
25
20
SF
TSF
TRSF
SMF
MF
LP
TMF
SCC
FMF
LF
15
10
5
0
0
2
4
6
8
10
12
14
Depth (mm)
Figure 20: The dependence of crack resolution on depth in a 40%IACS structure. The depth shown is a
quarter of the way from the top of the crack.
30.000
Crack Resolution (mm)
25.000
20.000
15.000
10.000
5.000
0.000
0.000
5.000
10.000
15.000
20.000
25.000
30.000
Equivalent Diameter (mm)
Figure 21: The dependence of crack resolution on equivalent field diameter across all probes and depths
that were measured. The line is a linear regression fit through the data.
Page 19 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Defect Discrimination
Defect discrimination falls into two categories:
q
discrimination between a defect and normal structure, and
q
discrimination between different types of defect – the obvious example being corrosion (metal loss)
and plate separation (gap).
Various tools are available within the TRECSCAN software for aiding the discrimination between defects
and structural changes. These require comparison of the measured transient at each location with a
‘balance transient’ taken from ‘good’ structure. The edge subtraction method modifies that balance
transient based on proximity to an edge, thus removing the effects of the edge from the displayed image.
There is also a thickness compensation method where the balance transient is modified according to the
measured total thickness of the structure at each location. Obviously this needs to be used with caution
when inspecting for corrosion! Ultimately the ideal situation would be to have a different balance
transient for each location on the structure, representing the transient that would be measured on ‘good’
structure at that location.
An example of edge subtraction is shown in Figure 22 where the edge close to the crack in the top layer
of the specimen in Figure 19 has been removed, discriminating the crack from the edge.
Figure 22: Crack resolution specimen, timeslice 2 scan with edge subtraction, showing just the crack in
the top layer.
Page 20 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Blind corrosion trial
In order to illustrate the defect discrimination tools available in ANDSCAN for corrosion detection, a
specimen used in a round-robin will serve as an example. It contained three layers of thickness: 0.063”
(1.5 mm). The specimen contained 16 fasteners and was bonded and painted. There were six unknown
defects as well as a region where the cladding layer had been removed from the top surface of the top
skin. Some plate separation from left to right had also been introduced.
Time-slice scans from this specimen (such as Figure 23) show a gradual trend from left to right and also a
step change just below the third row of fasteners down. At this stage these effects could have been caused
by lift-off, changes in sealant/adhesive thickness, plate separation or metal thickness changes.
Figure 23: Time-slice 6 scan of the specimen (left) with no lift-off or edge compensation applied, showing
a gradual trend from left to right and also a step change just below the third row of fasteners down. The
step change just below the third row of fasteners was largely compensated for by turning on lift-off
compensation (right), suggesting either lift-off or metal loss at the top surface.
By applying lift-off compensation to the scan on the left of Figure 23, the improved image shown on the
right was obtained. This clearly shows that the lower third of the scan has now been brought into line with
the upper two-thirds. If this effect was produced by removing lift-off then it was highly likely at this stage
that the metal may have been machined back prior to painting and the paint thickness enhanced to give a
flat paint finish.
Figure 24: Time-slice 6 scan of the specimen with lift-off compensation and edge subtraction (left) and a
Percentage Thickness Change scan (right) after correcting for the left-to-right taper in the specimen.
Page 21 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
The right-hand image in Figure 24 is in thickness change mode and shows percentage metal loss relative
to the chosen balance position. The metal loss in the lower third (1.5% to 1.7% thinning) indicates that the
lift-off seen in Figure 23 was caused by machining off the top of the top layer.
Defect Characterization
Once a defect has been detected it is essential to be able to evaluate it in terms of the following three
defect characteristics:
q
Depth (which layer the defect is in and whether at the top, bottom or middle of that layer)
q
In-plane size (area of corrosion or crack length)
q
Severity (out-of-plane extent in terms of metal loss for corrosion, or crack depth for cracks)
However, with eddy-current inspection the parameters that can be measured are not simply related to
these three defect characteristics. They each depend on all three defect characteristics. Transient eddycurrent data is superior to that from conventional eddy-current methods because it simplifies the process
of extracting the defect characteristics from the measured parameters.
Parameters measured using transient eddy-currents are:
q
In-plane two-dimensional profile of the field-defect interaction by scanning, yields:
·
q
-6 dB width of the defect
Temporal profile of eddy-currents reflected by the defect (reflected transient) HRz. For the purposes of
this analysis the temporal profile provides two types of information:
·
Time-to-peak of the ‘balanced transient’ DHz(t) related to defect depth.
·
Long-time extrapolation parameters related to total metal loss and percentage metal loss
(severity).
Accurate determination of the defect characteristics from the measured parameters requires a full
inversion method, which is complex, computationally laborious and time-consuming. However,
reasonable approximations can be obtained using simple relationships and then correction curves
developed for that probe can be used to refine the defect characterization.
Each defect characteristic is closely related to one measured parameter and less affected by the other
measured parameters. Hence, the procedure adopted involves extracting a characteristic from a closelyrelated measured parameter and applying corrections based on its known dependence on the other
measured parameters. The first characteristic extracted is the one most closely related to a measured
parameter where the corrections and errors will be smallest.
Defect Depth
The first defect characteristic to be extracted is the defect depth, which needs to be determined from a
calibration curve of ‘time-to-peak’ measurements versus actual depth of the correct type of defect. A
Time-To-Peak scan plots literally the time to the peak of the balanced transient signal. For a given defect
type this time value should increase with increasing depth of the defect. It is necessary to use the correct
conductivity for the specimen and the calibration curve, or to correct for any difference in conductivity.
Different types of defect will have different calibration curves. The main source of error in this
measurement is caused by the ‘effective depth’ of a metal-loss defect being dependent on the depths of
both the top and bottom of the defect, and the temporal and spatial frequency of the eddy-current field.
Page 22 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
For a thin defect, the effective depth corresponds to the mid-point of the metal loss but for a thick defect it
is nearer the top surface. In practice reasonable agreement has been achieved for representative defects
with an effective depth below the top of the defect by 1/e (37%) of the metal loss. An example of a
calibration curve taken from some reference specimens is shown in Figure 25. A scan of time-to-peak for
the specimen described above is shown in Figure 26.
0.5
Time To Peak (ms)
0.45
0.4
0.35
0.3
0.25
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
30 %IACS 1/e Depth (inch)
Figure 25: Calibration curve based on measurements of Time-To-Peak for reference specimens. The
parabolic nature of the curve has been determined in previous work.
Figure 26: Time-to-Peak scan of the specimen described above, showing the depths of the six defects
which all seem to be at the first interface.
Page 23 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Defect Sizing
The lateral extent of metal-loss or crack defects is ‘blurred’ by the use of eddy-currents to map them. The
image obtained is a convolution of the defect with the eddy-current field. Hence the smaller the field the
more accurately the defect will be mapped. Conversely, the smaller the defect, the more closely the image
represents the actual eddy-current field distribution – hence the doughnut-shape of small defects!
As the field tends to broaden out with increasing depth, deeper defects are not mapped as accurately. A
full spatial deconvolution algorithm is being developed for use in TRECSCAN that will allow the
‘subtraction’ of the field distribution from the scan image and give more accurate images of defects.
In the meantime, a ‘–6 dB drop’ defect sizing method similar to that used for ultrasonics [(11),(13)] has
been tested on a range of defect sizes with different metal losses. This method is explained in more detail
in Appendix C.
Severity - Metal Loss Measurement
Metal Loss measurement is accomplished in TRECSCAN using an analytical method that calculates
change in total metal thickness relative to the balance point. It gives a value that does not need to be
calibrated apart from knowing the thickness of some of the ‘good’ material, provided certain criteria are
met from the assumptions of the underlying theory. One criterion is that defects should be larger than the
interrogating field. If this is violated then a correction must be applied.
TRECSCAN can measure metal loss to first-order accuracy but the interaction of the metal loss, defect
lateral size, field size and shape is complex and causes systematic uncertainties in the measurements.
These are second-order effects that need to be corrected for in order to increase the measurement
accuracy.
A strategy has been developed that uses the values that are measured with the smallest uncertainty to
correct the parameters with the highest uncertainties. This strategy is shown as a flow diagram in Figure
27. The time-to-peak measurement with a simple correction and the defect lateral size based on –6 dB
width are the two most accurate values. These are then used to correct the metal loss measurements.
Page 24 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Measure Time-toPeak.
Measure –6 dB width
and interrogation width
Use calibration curve for this
probe and defect type to
determine depth
Based on known field width at each
depth, assign –6 dB or interrogation
width to be the defect width
Calculate metal loss correction due
to finite size of defect using depth
and defect size information.
Measure Total
Thickness
Measure % Metal
Loss
Apply corrections for finite defect
size and excessive total specimen
thickness to Metal Loss
Use calculated depth and corrected
metal loss to determine which
layer(s) the defect is in
Defect Depth
Layer(s) Containing defect
Metal Loss
Defect Size
Figure 27: Flow diagram showing the method for extraction of the defect characteristics (blue boxes)
from the measured parameters (red boxes).
One particular criterion for the theoretical basis of the thickness measurements is that defects should be
larger than the interrogating field. Corrections for smaller defect sizes must be applied based on prior
measurements with the probe for known defect sizes at a range of depths. An example of a correction
curve is shown in Figure 28 with two curves for defects at 1.1 mm and 2.4 mm in material of
conductivity: 40 %IACS.
Page 25 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
1.5mm, 40 %IACS Defect Plate
0.9
Measured % Loss / Actual % Loss
0.8
0.7
1.5 mm Depth
3 mm Depth
0.6
4 mm Depth
0.5
5.5 mm Depth
0.4
7 mm Depth
0.3
8 mm Depth
0.2
9.5 mm Depth
0.1
1.1
7 mm Depth
11 mm Depth
2.4
0
-0.1
-0.2
0
10
20
30
Defect Size (mm)
Figure 28: Correction graph for metal-loss measurements as a function of defect size, calibrated for
defects in 40 %IACS aluminum alloy.
Finally the metal loss measurements are plotted as a function of actual loss for some known reference
specimens before and after correction, in Figure 29.
It is important to note that reasonably accurate measurements can be made based on prior calibrations
using generic reference panels that do not need to accurately represent the structure being inspected. In
the limit that the defects are large compared with probe diameter good measurements can be obtained
without any prior calibration provided the total thickness of the structure is not too large.
Page 26 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
10
10
9
9
8
8
Corrected Measured % Metal Loss
Measured % Metal Loss
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
7
6
5
4
3
2
7
6
5
4
3
2
1
1
0
0
0
1
2
3
4
5
6
Actual % M etal Loss
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
Actual % Metal Loss
Figure 29: These graph show the TRECSCAN measured percentage metal loss compared with the stated
amount of loss before (left), and after (right) correcting for small defect size.
Conclusions
An initial but comprehensive study has been presented of the essential factors in defect detection,
discrimination and characterisation with transient eddy-currents.
Defect detection capability is highly dependent on the field magnitude, size and shape at the depth of the
defect and the important rules-of-thumb from this study are:
q
that the amplitude at the peak of the spatial frequency spectrum of the field of a probe decreases by
approximately a decade (a factor of 10) for every 0.5” (12.7 mm) in 40 %IACS aluminum alloy at
300 Hz.
q
that the field at a depth of 0.625” (16 mm) in 40 %IACS aluminum alloy is approximately 50%
broader than at the surface for the range of temporal frequencies in the transient.
q
that the field from a small probe remains smaller than that from a large probe despite the fact that the
fields from all probes expand with depth because the more compact components of the field decay
more rapidly.
Lateral resolution has been investigated in terms of discriminating between a defect and a nearby edge.
This ability has been shown to be depth-dependent because it relies on the spatial characteristics of the
field.
For defect discrimination, various tools are available for removing the effects of lift-off, plate separation,
edges and thickness changes if necessary.
Finally, a procedure for characterising volumetric defects (corrosion) in terms of depth, metal loss, and
lateral size, has been developed and shown as a worked example. This includes corrections for the
interdependence of the various measurements that are possible.
Page 27 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Acknowledgements
The authors acknowledge the help of Lyn Jones of QinetiQ Ltd and Mr Jesse Skramstad of NDT
Solutions Inc, for scanning some of the specimens illustrated in this paper. Part of this work was
supported by the US Air Force Research Laboratory through its “Pulsed eddy-current technologies for
corrosion evaluation” contract with NDT Solutions Inc.
REFERENCES
(1)
D. J. Harrison, 1989, “Progress in the detection of cracks under installed fasteners using eddy
currents.” AGARD Conference Proceedings No 462, Impact of Emerging NDE/NDI Methods on
Aircraft Design Manufacture and Maintenance, Brussels.
(2)
D. J. Harrison, 1994, “Eddy-current inspection using Hall sensors and transient excitation,”
Defence Research Agency Technical Report DRA/SMC/TR941008, DRA Farnborough, UK.
(3)
D. J. Harrison, 1995, Nondestructive Testing of Materials, Studies in Applied Electromagnetics
and Mechanics, Vol 8, eds. R. Collins, W. D. Dover, J.R. Bowler and K. Miya, (IOS Press,
Amsterdam, 1995), pp 115–124.
(4)
W.W. Ward III and J.C. Moulder, 1998, “Low frequency, pulsed eddy currents for deep
penetration,”Review of Progress in QNDE, Vol 17A, pp 291–298.
(5)
J. A. Bieber, C.C. Tai and J. C. Moulder, 1998, “Quantitative assessment of corrosion in aircraft
structures using scanning pulsed eddy current,” Review of Progress in QNDE, Vol 17A, op. cit.,
pp 315–322.
(6)
S.K. Burke, G.R. Hugo, and D.J. Harrison, 1998, “Transient eddy-current NDE for hidden
corrosion in multilayer structures,” Review of Progress in QNDE, Vol 17A, eds. D. O. Thompson
and D. E. Chimenti, (Plenum, New York), pp. 307–314.
(7)
S. Giguère, B.A. Lepine and J.M.S. Dubois, 2000, “Pulsed eddy-current (PEC) characterization of
material loss in multi-layer structures.” Canadian Aeronautics and Space Journal, Vol. 46, No. 4,
pp. 204-208.
(8)
G. R. Hugo and D. J. Harrison, 1999 Review of Progress in QNDE, Vol 18B, eds. D. O.
Thompson and D. E. Chimenti, (Kluwer Academic/Plenum Publishers), pp 1401-1408.
(9)
R A Smith and G R Hugo, 2001 “Transient eddy-current NDE for aging aircraft - Capabilities and
limitations”, Insight - The Journal of The British Institute of NDT, Vol 43, No 1, pp 14-20.
(10)
R A Smith and G R Hugo, 2001 “Deep Corrosion and Crack Detection in Aging Aircraft using
Transient Eddy-current NDE”, Proc 5th Joint NASA/FAA/DoD Conf on Aging Aircraft, Orlando.
(11)
D J Harrison, 2001 “The characterisation of cylindrical eddy-current probes in terms of their
spatial frequency spectra”. IEE Proceedings; Science, Measurement and Technology (SMT),
Special Issue on Non-Destructive Testing and Evaluation, Vol 148, No 4.
(12)
R A Smith, 1994, “Ultrasonic Defect Sizing in Carbon-fibre Composites - an Initial Study”.
Insight - Journal of the British Institute of NDT, Vol 36 (8) 595-605.
(13)
R A Smith, L D Jones, S J Willsher, and A B Marriott, 1998, “Diffraction and shadowing errors
in -6 dB defect sizing of delaminations in composites”, Insight - Journal of the British Institute of
NDT, Vol 40, No 1, pp 44-49.
© Copyright Qinetiq Ltd, 2002. Published with the permission of Qinetiq Ltd and the Australian Defence
Science And Technology Organisation.
ANDSCAN and TRECSCAN are Registered Trademarks of QinetiQ Ltd.
Page 28 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Appendix A. Modelling the field strength, lateral size and shape in a conducting half-space.
The aim of this modelling exercise was to take the spatial frequency spectra of a range of probes and
propagate them down into a structure, mapping how the magnitude, size and shape change with depth.
Through this exercise a greater understanding is achieved of the reasons for one probe having a particular
sensitivity or lateral resolution.
For a given spatial frequency k and temporal frequency w the equation governing the penetration of the
field is of the form:
A(w , k , r , z ) = A0 (w , r , k )[1 + G(w , k )]e -g × z
(3)
where A is the circumferential vector potential at depth z below the centre of the probe, A0 is the value of
A in air at the bottom surface of the probe, G is the reflection coefficient due to the structure and is given
for a conducting half-space as:
G=
k -g
k +g
(4)
and g is the propagation parameter, which is dependent on the temporal angular frequency w , the spatial
angular frequency k , the conductivity s , and the permeability m ,as follows.
g 2 = k 2 + jwms
(5)
Note that in air s = 0 and hence g = k , G = 0 and:
A(w , k , r , z ) = A0 (w , r , k )e - k × z
(6)
The depth-dependence of the vector potential is contained solely in the exponential term.
The spatial-frequency spectra calculated for depths of 0.25” (6.35 mm) and 0.5” (12.7 mm) in 40 %IACS
aluminum alloy are shown in Figure 30 and Figure 31 respectively. Study of these graphs shows that the
peak spatial frequency for all the probes gradually shifts down in spatial frequency. The rapid decrease in
field strength is illustrated in Figure 32, where the spatial-frequency spectra are shown at various depths
for a single probe, and in Figure 33 and Figure 34 where that trend is plotted for various probes and
various frequencies respectively. The normalized spectra in Figure 35 clearly show the gradual decrease
in peak spatial frequency with depth.
It is useful to define an equivalent diameter at a given depth. This is the diameter of a single-turn coil that
would have the same peak in its spatial-frequency spectrum, the field of which could therefore be
regarded as representative of (‘equivalent’ to) the field distribution found at that depth.
For a single-turn coil:
r0
d
a(k ) =
m 0 r0
J 1 (kr0 )e - kd
2
(7)
Page 29 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
where a(k) is the amplitude of the field for a given spatial angular frequency k , r0 is the radius of the coil,
and d is the distance below the coil. The first peak of J1 is when kr0 » 2. Hence:
Equivalent Diameter = 4 / Peak Spatial Frequency
(8)
A plot of such a parameter as a function of depth (see Figure 36) gives an indication of how the field
distribution spreads out with depth for a single probe at various temporal frequencies, whilst Figure 37
shows the same dependence but for various probes at one temporal frequency.
Normalised Estimated Amplitude
0.00040
0.00035
0.00030
0.00025
LP
MF
FMF
SF
TRSF
LF
TMF
SMF
TSF
0.00020
0.00015
0.00010
0.00005
0.00000
-0.00005
0.01
0.1
1
-1
Spatial Frequency, k (mm )
Figure 30: The spatial-frequency spectra of the fields represented in Figure 11, after propagation down
into the structure to a depth of 0.25” (6.35 mm) in 40 %IACS aluminum alloy using a temporal frequency
of 300 Hz. Each curve is normalized to the peak spatial frequency at zero depth for that probe.
Page 30 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Normalised Estimated Amplitude
0.00010
0.00008
0.00006
LP
MF
FMF
SF
TRSF
LF
TMF
SMF
TSF
0.00004
0.00002
0.00000
-0.00002
0.01
0.1
1
-1
Spatial Frequency, k (mm )
Figure 31: The spatial-frequency spectra of the fields represented in Figure 11, after propagation down
into the structure to a depth of 0.5” (12.7 mm) in 40 %IACS aluminum alloy using a temporal frequency
of 300 Hz. Each curve is normalized to the peak spatial frequency at zero depth for that probe.
Page 31 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Estimated Amplitude at Max I (Tesla)
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Depth (mm)
0.00025
0.1
6.35
12.7
19.05
25.4
0.00020
0.00015
3.175
9.525
15.875
22.225
28.575
0.00010
0.00005
0.00000
-0.00005
-0.00010
0.01
0.1
1
-1
Estimated Amplitude at Max I (Tesla)
Spatial Frequency, k (mm )
Depth (inch)
0.00025
0.004
0.250
0.500
0.750
1.000
0.00020
0.00015
0.125
0.375
0.625
0.875
1.125
0.00010
0.00005
0.00000
-0.00005
-0.00010
0.1
1
10
100
-1
Spatial Frequency, k (inch )
Figure 32: Spatial-frequency spectra at various depths in 40 %IACS aluminum alloy half-space, for a
single probe (FMF) using a temporal frequency of 300 Hz.
Page 32 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Estimated Amplitude at Peak
Spatial Frequency (Tesla)
1.0E-03
1.0E-04
1.0E-05
1.0E-06
LP
TMF
SF
SCC
1.0E-07
1.0E-08
0.0
5.0
LF
FMF
TSF
FMF
10.0
MF
SMF
TRSF
15.0
20.0
25.0
30.0
1.0
1.2
Estimated Amplitude at Peak Spatial
Frequency (Tesla)
Depth (mm)
1.0E-03
1.0E-04
1.0E-05
1.0E-06
1.0E-07
1.0E-08
0.0
LP
LF
MF
TMF
FMF
SMF
SF
SCC
TSF
FMF
TRSF
0.2
0.4
0.6
0.8
Depth (inch)
Figure 33: Estimated amplitude at the peak of the spatial-frequency spectra at various depths in
40 %IACS aluminum alloy half-space, for various probes using a temporal frequency of 300 Hz. The line
is an exponential fit to the FMF probe data shown in Figure 32.
Page 33 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Estimated Amplitude at Peak
Spatial Frequency (Tesla)
0.001
0.0001
1E-05
1E-06
1E-07
1E-08
1E-09
Frequency (kHz)
1E-10
0.10
1.00
2.50
5.00
1E-11
1E-12
1E-13
0
5
0.30
1.40
3.20
0.30
10
0.60
1.90
4.00
15
20
25
30
Depth (mm)
Estimated Amplitude at Peak
Spatial Frequency (Tesla)
0.001
0.0001
1E-05
1E-06
1E-07
1E-08
1E-09
1E-10
Frequency (kHz)
1E-11
0.10
1.00
0.30
1.40
0.60
1.90
1E-12
2.50
5.00
3.20
0.30
4.00
1E-13
0.000 0.200 0.400 0.600 0.800 1.000 1.200
Depth (inch)
Figure 34: Estimated amplitude at the peak of the spatial-frequency spectra at various depths in
40 %IACS aluminum alloy half-space, for various temporal frequencies using the FMF probe. The line is
an exponential fit to a frequency of 300 Hz as shown in Figure 33.
Page 34 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Depth (mm)
Normalised Estimated Amplitude
1.2
0.1
6.35
12.7
19.05
25.4
1
0.8
3.175
9.525
15.875
22.225
28.575
0.6
0.4
0.2
0
-0.2
-0.4
0.01
0.1
1
-1
Spatial Frequency, k (mm )
Depth (inch)
Normalised Estimated Amplitude
1.2
0.004
0.250
0.500
0.750
1.000
1
0.8
0.125
0.375
0.625
0.875
1.125
0.6
0.4
0.2
0
-0.2
-0.4
0.1
1
10
100
-1
Spatial Frequency, k (inch )
Figure 35: Spatial-frequency spectra at various depths in 40 %IACS aluminum alloy half-space, for a
single probe (FMF), normalized to the peak spatial frequency at each depth, at 300 Hz.
Page 35 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Equivalent Diameter (mm)
45
40
35
30
25
20
15
Frequency (kHz)
10
0.10
0.40
4.00
5
0
0
0.15
0.60
8.00
10
0.20
1.00
0.30
20
0.30
2.00
30
Depth (mm)
Equivalent Diameter (inch)
1.8
1.6
1.4
1.2
1
0.8
0.6
Frequency (kHz)
0.4
0.10
0.15
0.20
0.30
0.2
0.40
0.60
1.00
2.00
4.00
8.00
0.30
0
0.000
0.200
0.400
0.600
0.800
1.000
1.200
Depth (inch)
Figure 36: Calculated depth dependence of field size for various temporal frequencies for the FMF
probe. A linear-regression line is plotted for the 300 Hz data as this is a mid-range frequency and is used
for Figure 14.
Page 36 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Equivalent Diameter (mm)
40
35
30
25
20
15
LP
MF
FMF
SF
TRSF
Linear (FMF)
10
5
0
0
10
LF
TMF
SMF
TSF
SCC
20
30
Depth (mm)
Equivalent Diameter (inch)
1.6
1.4
1.2
1
0.8
0.6
LP
MF
FMF
SF
TRSF
Linear (FMF)
0.4
0.2
0
0.000
0.200 0.400
0.600
LF
TMF
SMF
TSF
SCC
0.800 1.000
1.200
Depth (inch)
Figure 37: Depth dependence of field size for different probes at 300 Hz. A linear regression line has
been drawn through the FMF probe data as this probe was used for Figure 13.
Page 37 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Appendix B. Lateral Crack resolution graphs in inches.
Crack Resolution (inch)
This appendix shows versions of Figure 21 and Figure 22 with units of inches instead of mm.
0.900
SF
TSF
TRSF
SMF
0.800
MF
LP
TMF
SCC
FMF
LF
0.700
0.600
0.500
0.400
0.300
0.200
0.100
0.000
0.000
0.100
0.200
0.300
0.400
0.500
0.600
Depth (inch)
Figure 38: The dependence of crack resolution on depth in a 40%IACS structure. The depth shown is a
quarter of the way from the top of the crack.
1.200
Crack Resolution (inch)
1.000
0.800
0.600
0.400
0.200
0.000
0.000
0.200
0.400
0.600
0.800
1.000
1.200
Equivalent Diameter (inch)
Figure 39: The dependence of crack resolution on equivalent field diameter.
Page 38 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Appendix C. –6 dB Defect Sizing.
A ‘–6 dB drop’ defect sizing method similar to that used for ultrasonics [(11),(13)](see Figure 40 and
Figure 41) has been tested on a range of defect sizes with different metal losses.
Two values are obtained: the –6 dB width, and the ‘interrogation width’ which is related to the size of the
interrogating field for large defects or to the size of the defect for small defects (which effectively
interrogate the field). Thus, when the defect is larger than the effective field, the defect width is given by
the –6 dB width. When the defect is smaller than the effective field, the defect width is given by the
interrogation width.
Figure 40: Illustration of how a simple disc theory used in ultrasonics predicts an overestimation of -6 dB width and area for defect-gated ultrasonic scans and an under-estimation
for back-wall echo-gated or through-transmission scans. For transient eddy-currents the
scans are all effectively defect-gated.
Page 39 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Interrogation Width
Interrogation Width
Interrogation Width
Defect signal
-6 dB height
‘Good’ material
-6 dB Width
-6 dB Width
-6 dB Width
Defect
Field
Figure 41: Diagram showing the relationship between defect size, field size, measured –6 dB width and
the ‘interrogation width’.
Measurements on defects at 1.5 mm and 4.5 mm depth in the specimens in Figure 6 are shown in the two
graphs in Figure 42 and Figure 43. The –6 dB width tends to the field size (blue horizontal line) for small
defect sizes because the defect is effectively interrogating the field. Then the ‘interrogation width’ gives a
better value for the defect width. For larger defects the ‘interrogation width’ is nearer to the field size
(blue horizontal line). Note that for deeper defects the field is larger and the uncertainties in these
measurements are far greater.
Page 40 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.
Proc. 6th Joint FAA/NASA/DoD Conference on Aging Aircraft, San Francisco, Sept. 2002.
Measured -6 dB Width & Interrogation Width
(mm)
40
0.04 mm Loss
0.07 mm Loss
0.14 mm Loss
0.24 mm Loss
0.46 mm Loss
Interrogation Width
30
20
10
0
0
10
20
30
40
Actual Defect Diameter (mm)
Figure 42: -6 dB drop method defect sizing measurements for circular flat-bottom holes 1.5 mm deep in
40 %IACS aluminium. This data was collected using the sameFMF probe as used to scan the specimens
in Figure 23 to Figure 26. The horizontal line represents the effective field width which is approximately
12 mm at 1.5 mm depth in 40 %IACS aluminum.
Measured -6 dB Width & Interrogation Width
(mm)
40
0.04 mm Loss
0.07 mm Loss
0.14 mm Loss
0.24 mm Loss
0.46 mm Loss
Interrogation Width
30
20
10
0
0
10
20
30
40
Actual Diameter (mm)
Figure 43: -6 dB drop method defect sizing measurements for circular flat-bottom holes 4.5 mm deep in
40 %IACS aluminum. This data was collected using the same probe as used to scan the specimens for this
paper. The horizontal line represents the effective field width, which is approximately 19 mm at 1.5 mm
depth in 40 %IACS aluminum
Page 41 of 41
Smith, Essential Factors In Improving The Characterization Of Cracks & Corrosion Using Transient Eddy Currents.