Fatigue crack detection_in_metallic_stru (2)

Fatigue crack detection in metallic structures with Lamb waves and 3D laser vibrometry
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2007 Meas. Sci. Technol. 18 727
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INSTITUTE OF PHYSICS PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY
Meas. Sci. Technol. 18 (2007) 727–739 doi:10.1088/0957-0233/18/3/024
Fatigue crack detection in metallic
structures with Lamb waves and 3D laser
vibrometry
W J Staszewski1, B C Lee1 and R Traynor2
1
Dynamics Research Group, Department of Mechanical Engineering,
University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
2
Lambda Photometrics Ltd, Lambda House, Batford Mill, Harpenden, Herts AL5 5BZ, UK
E-mail: w.j.staszewski@sheffield.ac.uk
Received 30 October 2006, in final form 13 December 2006
Published 24 January 2007
Online at stacks.iop.org/MST/18/727
Abstract
The paper presents the application of ultrasonic guided waves for fatigue
crack detection in metallic structures. The study involves a simple fatigue
test performed to introduce a crack into an aluminium plate. Lamb waves
generated by a low-profile, surface-bonded piezoceramic transducer are
sensed using a tri-axis, multi-position scanning laser vibrometer. The results
demonstrate the potential of laser vibrometry for simple, rapid and robust
detection of fatigue cracks in metallic structures. The method could be used
in quality inspection and in-service maintenance of metallic structures in
aerospace, civil and mechanical engineering industries.
Keywords: fatigue crack, crack detection, non-destructive testing, Lamb
waves, 3D laser vibrometer
(Some figures in this article are in colour only in the electronic version)
1. Introduction
Structural health monitoring has become one of the major
research activities in maintenance of aerospace, civil and
mechanical infrastructure. Over recent years, a number of
new technologies have evolved with the potential for automatic
damage detection. Lamb wave inspection is the most widely
used damage detection technique based on guided ultrasonic
waves, i.e. ultrasonic wave packets propagating in bounded
media. A number of different approaches have been developed
over the last 20 years, as reported in the extensive literature; a
summary of various aspects related to monitoring strategy,
transducers used for damage detection, modelling, signal
processing techniques and application examples is given in [1].
Although Lamb waves have demonstrated great potential for
structural damage detection, to date, the practical commercial
exploitation of ultrasonic guided waves has been very limited.
This is related to three major drawbacks associated with
current Lamb-wave-based damage detection techniques.
Firstly, Lamb-wave-based monitoring strategies, often
associated with complex data interpretation, are not
appropriate for point-by-point field measurements taken by
modestly qualified NDT technicians. Even a single Lamb
wave mode used for monitoring may generate a variety of
other modes due to interactions with structural boundaries
such as stiffeners, joints or rivets, leading to complex response
signals which are difficult to interpret. The subtleties of
guided waves and the exceedingly complicated physics may
be appreciated by experts in the field, but not necessarily by
technical maintenance staff.
Secondly, current signal processing and interpretation
techniques used for damage detection utilize signal parameters
requiring baseline measurements, i.e. data representing a
‘no damage’ condition. These parameters can change due
to temperature or bad coupling between the transducer and
the structure. Any developments that can avoid baseline
measurements are thus very attractive for real engineering
applications.
Thirdly, a significant number of actuator/sensor
transducers are required for monitoring of large structures.
This is often not possible or acceptable, no matter how cheap
the transducers are. From the logistic point of view, it is
0957-0233/07/030727+13$30.00 © 2007 IOP Publishing Ltd Printed in the UK 727

W J Staszewski et al
not practical for a structure to have thousands of bonded or
embedded transducers. A portable scanner (i.e. a pair of
transducers) that can crawl on the surface of the monitored
structure and conduct scanning is one possible solution.
However, the difficulty is the need for liquid couplant. Dry
coupling methods using non-contact electromagnetic acoustic
transducers [2] and air-coupled transducers [3] can be used
but these transducers have very low sensitivity due to large
acoustic impedance mismatch between air and solid materials
and the high attenuation of ultrasound in air at frequencies
above 500 kHz.
Non-contact approaches also include optical/laser
techniques [4–8]. Laser-based techniques usually involve
high-energy lasers which have safety and deployment
implications. Applications of laser generation and sensing
of Lamb waves for structural health monitoring are not new
and include research work on damage detection in metallic
[9, 10] and composite [11–13] structures. Laser-based Lamb
wave sensing has found relatively less attention in practical
applications than laser-induced Lamb wave generation due
to perceptions of low sensitivity, high noise and high
costs. Although area or multi-locational measurements
are possible with electronic speckle interferometry, adaptive
optical interferometry, shearography and laser vibrometers
(e.g., [14–17]), the majority of recent applications involve
single-point measurements.
Scanning multi-point laser vibrometers are designed and
widely used for vibration measurements, modal analysis
and vibration-based damage detection in many areas of
engineering applications, predominantly in the frequency
domain. Examples in this area include [18–20]. Applications
of Lamb wave sensing for structural health monitoring
have been very limited and include damage detection in
metallic [21–25] and composite [26] structures. These studies
were based only on laser out-of-plane measurements of
antisymmetric Lamb wave modes. Three-dimensional (3D)
scanning laser vibrometers provide combined out-of-plane and
in-plane measurements. A number of 3D configurations have
been reported, implemented commercially and used for elastic
wave propagation measurements (e.g., [27, 28]). However, 3D
laser vibrometers have not been applied so far for Lamb wave
sensing and Lamb-wave-based damage detection according to
the best of the authors’ knowledge.
The aim of the paper is to demonstrate the application of
a 3D scanning laser vibrometer measuring Lamb waves for
fatigue crack detection. The objective is to explore both the
out-of-plane and in-plane scanning capability of 3D lasers
for Lamb wave sensing and damage detection in metallic
structures. The paper consists of four major parts. Section 2
describes the Lamb wave field used in the experimental
work. For the sake of completeness, this includes a brief
theoretical introduction to Lamb waves. The experimental
work performed to introduce a fatigue crack into an aluminium
plate is described in section 3. Section 4 gives details related
to Lamb wave generation and sensing. Crack detection based
on Lamb wave data is described in section 5. Finally, the paper
is concluded in section 6.
Figure 1. Principles of various guided wave polarization and
propagating directions.
2. Lamb wave propagation for damage detection
Guided waves propagate as a result of interactions with
boundaries. Lamb waves occur for traction-free forces on
both surfaces of the plate. Lamb wave inspection has been
proven to have great potential for damage detection in metallic
structures. For the sake of completeness, this section briefly
describes the theoretical background of Lamb waves. The
focus is on theoretical definitions related to Lamb waves and
practical aspects associated with damage detection. For more
details, readers are referred to [29–32]. The short introduction
to Lamb waves is followed by a simple experimental test
leading to frequency selection of propagating waves used in
the current work.
2.1. Background
The unbounded medium supports longitudinal (P) and shear
(S) waves, as illustrated in figure 1 where x and y directions
indicate the in-plane vibration and z direction the out-of-plane
vibration of the medium. Shear waves propagating in the plate
can be polarized in a direction parallel to the plate surface
leading to a series of SH modes. Perpendicular polarization to
the plate surface results in a series of SV modes. These two
series of wave modes exist in connection with the P wave. The
combined P + SV waves are known as Lamb waves. Lamb
waves are highly dispersive, i.e. their velocities of propagation
depend on frequencies.
A brief theoretical introduction to Lamb waves is given
here following the developments from [31]. Lamb wave
equations can be derived from the elastodynamic wave
equation for the particle displacement given as
ρüi = (sijkluk,l),i (1)
where ρ is the density, u is the displacement, s is the
stiffness tensor and the standard tensor index convention is
used. The method of potential transforms displacements in
equation (1) into field variables φ and ψ using the Helmholtz
decomposition. This results in uncoupled equations
∂2
ψ
∂x2
1
+
∂2
ψ
∂x2
3
=
1
c2
L
∂2
ψ
∂t2
(2)
∂2
ϕ
∂x2
1
+
∂2
ϕ
∂x2
3
=
1
c2
T
∂2
ϕ
∂t2
(3)
describing propagation of longitudinal waves and shear waves,
respectively. The constant CL indicates the velocity of
longitudinal waves and CT is the velocity of shear waves in
728

equations (2) and (3). Physical displacements of the plate can
be expressed in terms of the field variables used as
u1 =
∂ψ
∂x1
+
∂ϕ
∂x3
, u2 = 0, u3 =
∂ψ
∂x3
−
∂ϕ
∂x1
. (4)
Since the field variables involve sine and cosine functions
which are odd and even functions, the above displacements
are often split into symmetric and antisymmetric modes. The
displacement for the symmetric modes can be given as
u1 = ikC2 cos(px3) + qD1 cos(qx3) (5)
u3 = −pC2 sin(px3) − ikD1 sin(qx3) (6)
whereas the solution for the antisymmetric modes is
u1 = ikC1 cos(px3) − qD2 sin(qx3) (7)
u3 = pC2 cos(px3) − ikD2 cos(qx3). (8)
The variables p and q in equations (5)–(8) are given as
p2
= (ω/CL)2
− k2
, q2
= (ω/CT )2
− k2
(9)
where k is the wave number and ω = 2πf is the circular
frequency. The constants C1, C2, D1 and D2 in equations (5)–
(8) can be obtained from the traction-free boundary conditions
for the plane strain. Finally, the entire analysis leads to
Rayleigh–Lamb wave frequency relations
tan(qh)
tan(ph)
=
4k2
pq
(q2 − k2)2
(10)
for symmetric modes and
tan(qh)
tan(ph)
=
(q2
− k2
)2
4k2pq
(11)
for antisymmetric modes, where h is the half of the plate
thickness. The Rayleigh–Lamb equations can be solved
numerically for a given material leading to the so-called
dispersion characteristics, i.e. the phase velocity cp = ω/k
or group velocity cg = dω/dk represented as functions of
the f –d (frequency–thickness) product. In other words, for a
given thickness of the plate these equations predict velocities
of propagating Lamb wave modes.
The dispersion characteristics result in a number of
symmetric Si and antisymmetric Ai (i = 0, 1, 2, . . .) Lamb
wave propagation modes. The fundamental S0 and A0 modes
are the most widely used Lamb wave modes for damage
detection.
Lamb wave mode selection is important for damage
detection. Both fundamental modes are very good in terms
of the spatial resolution, i.e. they offer good compromise
between the bandwidth of the excitation signal and its duration,
as explained in [33]. The S0 mode is dominated by the
longitudinal vibration component whereas the A0 mode is
dominated by the shear component. The S0 mode is faster and
has much lower attenuation than the A0 mode. It is also, less
dispersive at lower frequencies if compared with the A0 mode.
However, the A0 mode is considered to be more sensitive to
damage. Nevertheless, a number of studies, summarized in
[1], demonstrate that the S0 mode works better for damage
detection than the A0 mode. It is important to mention that
the wavelength, which is directly related to the excitation
frequency, affects the sensitivity of damage detection; the
shorter the wavelength, the larger the sensitivity to small
Figure 2. Lamb wave dispersion characteristic for an aluminium
plate. The curve is zoomed on the fundamental modes.
damage severities. Also, the energy distribution for various
Lamb wave modes is different through the thickness of the
plate. This is due to the fact that in-plane and out-of-plane
displacements vary across the thickness, as illustrated in [34].
Lower modes have more uniform energy distribution than
higher modes and the S0 mode has a more uniform distribution
than the A0 mode, which exhibits higher levels of energy at
surfaces.
2.2. Wave propagation frequency—experimental analysis
The complexity of Lamb wave propagation, briefly described
in section 2.1, significantly affects damage detection
procedures used in practice. The work presented in the paper
involved the fundamental Lamb wave modes. In what follows,
the mode selection procedure is briefly described.
Firstly, the Rayleigh–Lamb dispersion characteristics
were calculated numerically using equations (11) and (12) and
material properties for the NS4 aluminium (Young’s modulus
E = 71 GPa, density ρ = 2.711 g cm−3
, Poisson’s ratio υ =
0.338, Lamé constants µ = 26.5 GPa and λ = 56.2 GPa). The
dispersion characteristic for the 6 MHz mm range is given in
figure 2.
Then, a simple experiment involving a rectangular 400 ×
150 mm2
aluminium plate of 2 mm thickness was performed.
Two piezoceramic transducers were surface-bonded in the
middle of the longer edges of the plate. One transducer was
used as an actuator, whereas the second transducer acted as a
sensor. A five-cycle sine tone burst was used as an excitation
signal. This signal was modulated with a Hanning window.
The peak-to-peak amplitude excitation signal was equal to 5 V.
The excitation signal was generated using the TTi-TGA 1230
arbitrary waveform generator. The Lamb wave responses were
captured using the LeCroyTM
WaveRunnerR

LT224 digital
oscilloscope. In order to find the Lamb wave modes, the
frequency range was altered from 30 to 500 kHz. This
guaranteed that only fundamental Lamb wave modes would
propagate in the plate used (see figure 2). When Lamb wave
responses were gathered from the sensor, the group velocities
were calculated and compared with the values in figure 2
in order to identify both fundamental modes. Maximum
amplitudes were recorded for both modes over the frequency
range mentioned before, resulting in the characteristics given
in figure 3. This shows that the maximum amplitude was
achieved at 115 kHz and 325 kHz for the A0 and S0 modes,
respectively. The 325 kHz frequency was selected for the S0
729

Figure 3. Amplitude of the fundamental Lamb wave modes versus
excitation frequency—experimental analysis.
fundamental Lamb wave mode. The frequency for the A0
mode was selected as 75 kHz to keep approximately the same
amplitude level for both fundamental modes (see figure 3). The
75 and 325 kHz frequencies led to single A0 and S0 wave mode
propagation, respectively, i.e. only the A0 mode was present at
75 kHz whereas the amplitude of the S0 mode was negligible
and only the S0 mode was present at 325 kHz whereas the
amplitude of the A0 mode was negligible. Additionally, the
190 kHz frequency was selected since it led to two fundamental
modes propagating together with approximately the same
peak-to-peak amplitudes (see figure 3). In summary, the 75,
325 and 190 kHz frequencies were selected for Lamb wave
generation in further experimental work.
3. Fatigue crack in metallic
specimen—experimental work
A simple fatigue test was performed to introduce a crack in an
aluminium specimen identical to the plate used in the Lamb
wave propagation experimental study in section 2.2. Eight
holes of 15 mm diameter were drilled at the top and bottom of
the plate to facilitate clamping in the fatigue machine. A hole
of 0.5 mm diameter was drilled in the centre of the specimen
and used to initiate a spark-eroded notch of 2 mm length.
The plate was instrumented with five surface-bonded SMART
LayerR

piezoceramic transducers of 5 mm diameter and
0.2 mm thickness, as shown in figures 4(a) and (b). The
transducer A was used for Lamb wave generation in the current
paper.
The aluminium plate was clamped in a 240 kN Schenck
fatigue-testing machine controlled via a Roell Amsler K7500
servo controller. The plate was fatigued up to 305 000 cycles
using the tensile static loading of 20 kN and the dynamic
cyclic loading of ±9 kN. This led to the 41.05 mm fatigue
crack, illustrated in figure 4(c). The large severity of damage
was selected intentionally for the explorative work with a 3D
laser vibrometer.
4. Lamb waves sensing with 3D laser vibrometry
This section describes Lamb wave generation and sensing
procedures used for crack detection. The former was
achieved using piezoceramic excitation whereas the latter was
performed using a 3D scanning laser vibrometer.
4.1. Lamb wave generation
The piezoceramic transducer A (see figures 4(a) and (b)) was
used for Lamb wave generation. The actuator was excited by a
series of burst signals comprising five cycles of sine wave with
the Hanning window envelope. The peak-to-peak amplitude
of excitation was equal to 20 V. The study involved three
different frequencies of excitation, i.e. 75, 325 and 190 kHz,
as selected experimentally and explained in section 2.2. The
excitation signals were generated using the TTi-TGA-1230,
arbitrary waveform generator. The excitation burst signals
were triggered every 50 ms to minimize the overlapping of the
oncoming and reflected waves.
4.2. Lamb wave sensing using 3D laser scanning mode
Lamb wave responses were sensed using a 3D laser vibrometer.
These vibrometers measure surface motion utilizing the
Doppler shift phenomenon to obtain the velocity of the surface
vibration. For a single measuring point, 3D components of
out-of-plane and in-plane vibration can be obtained using three
spatially independent laser heads focusing at this point.
Sensor heads generate three laser beams which acquire
the v1, v2 and v3 velocity components along their lines of
incidence (see figure 5). The measuring point is located in
the intersection point of the laser beams which is the origin
of the orthogonal coordinate system (X, Y, Z). All velocity
amplitudes are measured with respect to this system.
Alignment of the 3D scanning laser vibrometer comprised
positioning the three sensor heads in a triangular configuration
in front of the plate. Using a target volume encompassing the
plate, with dimensions in both the X and Y axes, plus depth
(Z axis), four to seven arbitrary positions within this volume
were defined and measured for distance using the sensor head
fitted with a rangefinding geometry scan unit. The other two
heads were aligned to these points and angle and range data for
the points and the positional relationship for all three sensor
heads was calculated within the scanning vibrometer software.
When completed, any locations visible to all three lasers within
the volume could be accessed and measured for X, Y and Z
motion. More details related to the alignment procedure can
be found in [35].
A higher frequency variant of the standard 3D Polytec
PSV-400-3D laser vibrometer was used in the current damage
detection work for Lamb wave sensing. The experimental
set-up used in this work is shown schematically in figure 5.
The data were acquired using the near dc to 2 MHz
frequency capability of the laser vibrometer. This vibrometer
used consists of three independent PSV-I-400 LR (OFV-505)
optical scanning heads (one fitted with a location/rangefinding
Geometry Module), OFV-5000 controller, PSV-E-400-3D
junction box and a data management computer system. The
scanning heads were used simultaneously. The OFV-5000
provides power for the scanning heads, controls the rotation of
the mirrors in the OFV-505 heads, scans the laser beams, and
also processes the heterodyne interferometry signal from the
OFV-505 sensors, outputting the signals as simple analogue
time history voltage values. The PSV software in the
data management computer system controls the measuring
converters, laser focus/position, vibrometer electronics and
the live video system. A velocity range of 10 mm (s V)−1
730

(a)
(c)
(b)
Figure 4. Aluminium specimen used in the experimental work: (a) schematic diagram, (b) photograph and (c) detailed view of the crack.
was chosen to give adequate velocity (at an output voltage of
approximately 5 V, equivalent to about 5 m s−1
) with good
resolution.
The National Instruments PCI-6110E A/D card was used
for data acquisition in the time domain. Signal lengths were
equal to 2048 data samples. The maximum 2.56 MHz data
acquisition frequency bandwidth of the laser system was used.
The data were low-pass filtered to a frequency of 1.5 MHz.
The data acquisition utilized 150 averages in order to improve
the signal-to-noise ratio.
The scanning laser vibrometer was aligned following the
procedure described in section 4.2 and used to measure 3D
vibration associated with Lamb waves propagating in the
aluminium specimen. The calculations required to separate
in-plane and out-of-plane vector components were performed
automatically by the PSV system. Figure 6 gives examples of
laser-sensed Lamb waves in X (horizontal in-plane), Y (vertical
in-plane) and Z (out-of-plane) directions for the 75, 325 and
190 kHz. The 75 kHz excitation led to the A0 Lamb wave
mode propagating in the plate. This mode is dominated by
the out-of-plane component in figure 6(a) (right column). The
first wave package in the response signal is the incident wave
whereas the remaining wave packages are reflections from
the plate boundaries and the crack. The amplitude of the
in-plane components of the 75 kHz Lamb wave signal in
figure 6(a) (left and middle columns) is relatively small when
compared with the out-of-plane component, as expected. The
325 kHz excitation led to the S0 Lamb wave mode propagating
in the plate. Again, as expected, this mode is dominated by the
in-plane X-direction component in figure 6(b) (left column).
Figure 6(c) shows the 190 kHz Lamb wave responses. Two
dominant wave packages can be observed in the in-plane
X-direction (left column) and the out-of-plane (right column)
components. These two components are contributing to the S0
and A0 Lamb wave modes propagating in the plate.
5. Crack detection results
The cracked aluminium plate was scanned using the 3D laser
vibrometer. The scanned area was a 60 × 110 mm2
rectangle
around the impact position, as indicated in figure 7. The grid
of 420 points where measurements were taken is shown in
figure 7; this is equivalent to 420 contact transducer
measurements in classical Lamb wave inspection. This section
describes the results obtained from the amplitude analysis.
731

Piezoceramic
actuator
Monitored specimen
Laser sensor heads
Fatigue crack
Data management system
v1
v2
v3
x
vY
vZ
Orthogonal
coordinate system
Arbitrary waveform generator
v
Figure 5. Experimental set-up for damage detection and measurement geometry of the 3D laser system.
(a) X direction
0 0.1 0.2 0.3 0.4
Time [ms]
−1
−0.6
−0.2
0.2
0.6
1
Amplitude
[mm/s]
Y direction
0 0.1 0.2 0.3 0.4
Time [ms]
−1
−0.6
−0.2
0.2
0.6
1
Amplitude
[mm/s]
−1
−0.6
−0.2
0.2
0.6
1
Amplitude
[mm/s]
Z direction
0 0.1 0.2 0.3 0.4
Time [ms]
(b) X direction
0 0.05 0.1 0.15 0.2
Time [ms]
−3
−2
−1
0
1
2
3
Amplitude
[mm/s]
Y direction
0 0.05 0.1 0.15 0.2
Time [ms]
−3
−2
−1
0
1
2
3
Amplitude
[mm/s]
−3
−2
−1
0
1
2
3
Amplitude
[mm/s]
Z direction
0 0.05 0.1 0.15 0.2
Time [ms]
(c) X direction
0 0.1 0.2 0.3 0.4
Time [ms]
−2
−1
0
1
2
Amplitude
[mm/s]
Y direction
0 0.1 0.2 0.3 0.4
Time [ms]
−2
−1
0
1
2
Amplitude
[mm/s]
−2
−1
0
1
2
Amplitude
[mm/s]
Z direction
0 0.1 0.2 0.3 0.4
Time [ms]
Figure 6. Examples of Lamb wave responses acquired with the 3D laser vibrometer. Excitation frequency equal to: (a) 75 kHz, (b) 325 kHz
and (c) 190 kHz.
5.1. Peak-to-peak amplitude analysis
The first step involved the peak-to-peak amplitude analysis
for all scanned grid points and different wave propagation
moments in time. This study allows for simultaneous wave
propagation analysis in the spatial (for all scanned grid points)
and time (for selected moments in time) domains. The results
are presented in figures 8–12.
732

Scanned area Piezoceramic actuator
60 mm
110
mm
110
mm
Figure 7. Laser scanned area with indicated data grid points used
for Lamb wave sensing.
Figure 8. Example of 3D Lamb wave propagation.
Figure 8 shows an example of the combined 75 kHz
X–Y–Z 3D Lamb wave propagation plots for 35.5 and 50 µs.
These (and figures 9–12) were taken from the animated
sequential images obtained from the scanning vibrometer
software, with all points phase-referenced to the triggered
piezoceramic actuator burst excitation. Large peak-to-peak
amplitude can be observed in the vicinity of the piezoceramic
actuator in the 35.5 and 50 µs responses in figure 8. The wave
energy is spread semicircularly in the plate. This pattern is
disturbed (increased and decreased amplitude) in the 50 µs
response in figure 8(b) when the wave hits the crack in the
plate.
The 3D wave propagation responses for the 75, 325
and 190 kHz were separated into in-plane and out-of-plane
vibration components, as shown in figures 9–12.
Figure 9 gives software animation snapshots showing
the peak-to-peak time domain amplitude contour plots for
the 75 kHz Lamb wave propagating in the plate at different
times after plate excitation. These snapshots were selected
to demonstrate features resulting from the wave interaction
with the crack. The amplitude pattern, i.e. a semicircular
geometric beam spreading profile of the actuator, can be
seen in all vibration components. However, the strongest
pattern can be observed in figure 9(c) where the out-of-plane
(a) 41.8 µs 48.8 µs 74.2 µs
(b) 40.6 µs 46.5 µs 72.3 µs
(c) 36.3 µs 55.1 µs 64.8 µs
Figure 9. Lamb wave propagation contour plots in the time domain
for 75 kHz excitation: (a) in-plane X direction, (b) in-plane Y
direction and (c) out-of-plane Z direction.
55.5 µs 56.2 µs 58.2 µs 58.6 µs
60.5 µs 61.3 µs 62.5 µs 63.7 µs
Figure 10. Lamb wave interaction with the fatigue crack. The
in-plane X direction contour maps in the time domain for 75 kHz
excitation.
component is presented. The in-plane X-direction component
exhibits large amplitude in the vicinity of the actuator at
733

(a) 12.5 µs 17.2 µs 19.1 µs
(b) 12.5 µs 18.0 µs 19.5 µs
(c) 12.5 µs 17.2 µs 25.4 µs
Figure 11. Lamb wave propagation contour plots in the time
domain for 325 kHz excitation: (a) in-plane X direction, (b) in-plane
Y direction and (c) out-of-plane Z direction.
41.8 µs in figure 9(a) (left column). When the wave hits the
crack (indicated schematically by two black lines in figure 9
and all subsequent figures in the paper) at 48.8 µs (middle
column), two small areas of locally increased amplitude can
be observed in front of the upper and lower parts of the
crack. This is when the incoming incident wave constructively
interferes with the outgoing wave reflected from the crack.
This effect has previously been observed in experimental work
with piezoceramic transducers and in numerical simulations
[30]. The same feature is exhibited very strongly at 74.2 µs
(right column). Here, the bottom part of the crack produces
a larger amplitude increase than the upper part of the crack
due to different orientation of the two sections of the crack;
the upper part of the crack is not parallel to the plate edges.
The in-plane Y-direction component, presented in figure 9(b)
(middle and right columns), shows a similar crack feature.
However, this feature is not exhibited by the upper part of the
crack and the locally increased amplitude resulting from the
wave interaction with the lower part of the crack is smaller
than for the X-direction component. It is because at this point
in the time snapshots, the wave does not have time to come
back to interact with the crack. Also, the orientation of the
widely dispersed, propogated and attenuated wave does not
have the energy to show any meaningful interactions with
the crack. The out-of-plane component in figure 9(c) shows
that the semicircular wave propagation profile at 36.3 µs (left
(a) 22.3 µs 25.8 µs 33.6 µs
(b) 20.3 µs 29.7 µs 39.1 µs
(c) 23.8 µs 28.1 µs 39.5 µs
Figure 12. Lamb wave propagation contour plots in the time
domain for 190 kHz excitation: (a) in-plane X direction, (b) in-plane
Y direction and (c) out-of-plane Z direction.
column) is broken by the crack at 55.1 (middle column) and
64.8 µs (right column); wave reflections from the crack and
attenuation of the wave transmitted through the crack can be
observed.
Lamb wave interaction with the crack for the in-plane X-
direction component of the 75 kHz excitation can be observed
in more details in figure 10, where eight different time-domain
snapshots, gathered between 55.5 and 63.7 µs after plate
excitation, are given. The study shows that the incident wave
hits the bottom of the crack first. The interaction with the crack
results in an area of locally increased amplitude, as explained
above. The crack acts as a guide sweeping the area of large
amplitude from the top to the bottom of the lower part of
the crack between 55.5 and 62.5 µs. The intensity of this
interaction is greatest at 60.5 µs. This is when the upper part
of the crack is hit by the wave and the energy is guided to the
lower part of the crack. The interaction with the upper part
of the crack is intensified at 73.7 µs when the interaction with
the bottom part of the crack is completed and the same effect
is observed, but in the reverse direction.
The peak-to-peak amplitude of Lamb wave responses
has also been analysed for the 325 and 190 kHz responses.
Figure 11 shows the results for the 325 kHz response
dominated by the S0 Lamb wave mode. The results for the
190 kHz excitation are given in figure 12. The fundamental
Lamb wave modes propagate with similar amplitudes for this
734

C-D amplitude profile
0 25 50 75 100 125
Distance [mm]
0.05
0.1
0.15
0.2
0.25
Amplitude
[mm/s]
A
B
C
D
(a)
(b)
(c)
A-B amplitude profile
0 20 40 60
Distance [mm]
0.05
0.1
0.15
0.2
0.25
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.05
0.1
0.15
0.2
0.25
Amplitude
[mm/s]
A
B
C
D
A
B
C
D
0 20 40 60
Distance [mm]
0.05
0.1
0.15
0.2
0.25
Amplitude
[mm/s]
A
B
C
D
0 20 40 60
Distance [mm]
0.05
0.1
0.15
0.2
0.25
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.05
0.1
0.15
0.2
0.25
Amplitude
[mm/s]
A
B
C
D
0 20 40 60
Distance [mm]
0.05
0.1
0.15
0.2
0.25
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.05
0.1
0.15
0.2
0.25
Amplitude
[mm/s]
A
B
C
D
0 20 40 60
Distance [mm]
0.05
0.1
0.15
0.2
0.25
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.05
0.1
0.15
0.2
0.25
Amplitude
[mm/s]
A
B
C
D
0 20 40 60
Distance [mm]
0.05
0.1
0.15
0.2
0.25
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.05
0.1
0.15
0.2
0.25
Amplitude
[mm/s]
Figure 13. RMS amplitude contour plots and amplitude profiles across the crack for 75 kHz Lamb wave propagation: (a) in-plane X
direction, (b) in-plane Y direction and (c) out-of-plane Z direction.
excitation. Similar features related to the fatigue crack, as
described above for the 75 kHz component, can be observed
in both analysed cases. The semicircular amplitude pattern
of wave propagation, best seen in the in-plane components
in figures 11(a) and (b) and figures 12(a) and (b), is broken
when the wave hits the crack (middle and right columns).
Also, the locally increased Lamb wave amplitude due to the
positive interaction of the incoming incident wave and the
outgoing wave reflected from the crack can be observed in
the in-plane and out-of-plane components of the 325 and
190 kHz Lamb wave responses in figures 11 and 12 (right
columns), respectively.
5.2. Root-mean-square amplitude analysis
The root-mean-square (RMS) amplitude of Lamb wave in-
plane and out-of-plane components for all scanned grid points
was analysed in the next step. In contrast to the peak-to-
peak amplitude analysis presented in section 5.1, the RMS
amplitude was calculated for the entire length of the signal.
The results, given in figures 13–15, reflect the energy spatial
distribution of the propagating wave.
Figure 13 gives the RMS amplitude contour plot and
amplitude profiles for the in-plane and out-of-plane 75 kHz
Lamb wave components. The contour plots for the in-plane
735

A
B
C
D
0 20 40 60
Distance [mm]
0.05
0.1
0.15
0.2
0.25
0.3
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.05
0.1
0.15
0.2
0.25
0.3
Amplitude
[mm/s]
A
B
C
D
0 20 40 60
Distance [mm]
0.05
0.1
0.15
0.2
0.25
0.3
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.05
0.1
0.15
0.2
0.25
0.3
Amplitude
[mm/s]
A
B
C
D
0 20 40 60
Distance [mm]
0.05
0.1
0.15
0.2
0.25
0.3
Amplitude
[mm]
0 25 50 75 100 125
Distance [mm]
0.05
0.1
0.15
0.2
0.25
0.3
Amplitude
[mm/s]
A
B
C
D
0 20 40 60
Distance [mm]
0.05
0.1
0.15
0.2
0.25
0.3
Amplitude
[mm]
0 25 50 75 100 125
Distance [mm]
0.05
0.1
0.15
0.2
0.25
0.3
Amplitude
[mm/s]
A
B
C
D
(c)
(b)
(a)
0 20 40 60
Distance [mm]
0.05
0.1
0.15
0.2
0.25
0.3
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.05
0.1
0.15
0.2
0.25
0.3
Amplitude
[mm/s]
A
B
C
D
0 20 40 60
Distance [mm]
0.05
0.1
0.15
0.2
0.25
0.3
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.05
0.1
0.15
0.2
0.25
0.3
Amplitude
[mm/s]
components in figures 13(a) and (b) exhibit locally increased
amplitude in front of the centre of the crack. This effect can
clearly be observed in the amplitude profiles in figures 13(a)
and (b). Here, the RMS amplitude is increased sharply
between 30 and 45 mm in the A–B profile along the wave
propagation direction and in the C–D profile between 50
and 80 mm across the width of the plate. This increase is
more pronounced for the X-direction than for the Y-direction
component.
When the out-of-plane Z-direction component is analysed
in figure 13(c) the results are different. Firstly, the largest RMS
amplitude, observed in the vicinity of the actuator, attenuates
exponentially, as illustrated in the amplitude contour plot in
figure 13(c) and the amplitude A–B profile in figure 13(c).
This effect is due to the actuator beam spreading profile when
the wave propagates in the plate. Secondly, the amplitude is
increased locally due to the crack in the plate. This can be
observed in the amplitude contour plot in figure 13(c) near
the centre of the crack. The damage can also be seen in
amplitude profiles shown in figure 13(b), across the A–B and
C–D paths indicated in figure 13(c). The RMS amplitude is
increased locally between 30 mm and 45 mm in the A–B profile
along the wave propagation direction and in the C–D profile
between 25 and 75 mm across the width of the plate. The later
736

A
B
C
D
0 20 40 60
Distance [mm]
0.2
0.4
0.6
0.8
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.2
0.4
0.6
0.8
Amplitude
[mm/s]
A
B
C
D
0 20 40 60
Distance [mm]
0.2
0.4
0.6
0.8
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.2
0.4
0.6
0.8
Amplitude
[mm/s]
A
B
C
D
0 20 40 60
Distance [mm]
0.2
0.4
0.6
0.8
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.2
0.4
0.6
0.8
Amplitude
[mm/s]
A
B
C
D
0 20 40 60
Distance [mm]
0.2
0.4
0.6
0.8
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.2
0.4
0.6
0.8
Amplitude
[mm/s]
A
B
C
D
0 20 40 60
Distance [mm]
0.2
0.4
0.6
0.8
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.2
0.4
0.6
0.8
Amplitude
[mm/s]
A
B
C
D
0 20 40 60
Distance [mm]
0.2
0.4
0.6
0.8
Amplitude
[mm/s]
0 25 50 75 100 125
Distance [mm]
0.2
0.4
0.6
0.8
Amplitude
[mm/s]
(a)
(b)
(c)
profile is ‘broken’ around 35–40 mm due to the asymmetrical
orientation of the crack. Thirdly, the amplitude sensed in the
area behind the crack is attenuated. This time the attenuation
is due to the crack. Both attenuation effects described in this
section have previously been reported in experimental studies
[23, 24, 36] and numerical simulations [36].
The RMS amplitude results for the 325 and 190 kHz
Lamb wave responses in figures 14 and 15, respectively,
are very similar to the 75 kHz results shown in figure 13.
The crack presents similar in-plane and out-of-plane features.
However, the background amplitude level in the in-plane
vibration characteristics for the 190 kHz Lamb wave in
figures 15(a) and (b) is much higher if compared with the
relevant characteristics for the 75 and 325 kHz in figures 13(a),
15(a) and (b), respectively.
5.3. Discussion and summary
A few interesting observations can be made regarding wave
propagation and damage detection.
Although the experimental work based on piezoceramic
sensing was successful in selecting frequencies for which the
amplitude of one of the fundamental modes was suppressed,
the 3D laser vibrometer was sensitive enough to observe
the existence of both modes in the Lamb wave responses
investigated.
737

The out-of-plane component attenuated significantly
whereas the in-plane components did not show significant
signs of attenuation in the Lamb wave responses investigated.
This was revealed by the peak-to-peak amplitude contour plots
and amplitude profiles along the direction of wave propagation.
Since the A0 mode is dominated by the out-of-plane vibration
and the S0 mode is dominated by the in-plane vibration, this
confirms previous findings that symmetrical modes are less
attenuated than antisymmetrical modes. The Lamb wave
attenuation effect related to the actuator beam spreading profile
was more significant that the attenuation due to the crack, as
previously observed in [23, 24, 35].
The largest local increase of amplitude has been observed
in the vicinity of the crack where the incoming incident wave
interacts with the outgoing wave reflected from the crack. This
not only confirms previously obtained numerical simulation
[36] and experimental results [23, 24, 36] but also clearly
demonstrates the first major advantage of the non-contact,
laser-based scanning technique above any contact, sensor-
based method. The best chance to detect damage is to position
sensors in its proximity. However, this is not possible in
practice when bonded, piezoceramic sensors are used since
damage location is not known in advance. The quick and easy
identification of the location of damage features is the second
advantage of the laser-based technique.
The locally increased amplitude of Lamb wave responses
in the proximity of the crack, revealed when the specimen
is scanned with a laser vibrometer, shows that baseline
measurements can be avoided. This is the third major
advantage of the method presented. In fact, the current study
did not involve any laser scanning of the undamaged plate.
The method not only allows for damage localization but
also for the estimation of its severity. The C–D amplitude
profiles are indicative of the length of the crack. Although,
the increased amplitude across the width of the plate for the
in-plane components (along 30 mm) underestimates and for
the out-of-plane component (along 50 mm) overestimates the
41.05 mm crack, the averaged 40 mm value is very close to
the actual crack length.
The 3D laser-based method allows for easy separation
of in-plane and out-of-plane Lamb wave components. The
S0 Lamb wave mode is dominated by the in-plane vibration
whereas the A0 mode is dominated by the out-of-plane
component. The study shows that both in-plane and out-
of-plane Lamb wave vibrations can be used for impact
damage detection in metallic plates. However, damage
features observed and related to the in-plane and out-of-plane
components were not the same. Also, very little difference
was observed between the sensitivity of the in-plane and out-
of-plane vibration components.
It is important to note the two crucial elements of the
performed analysis: (a) Lamb wave dispersion characteristics
are not needed for the crack detection work presented; (b)
the study has not involved any complex signal processing and
interpretation usually associated with Lamb waves. This is the
fourth major advantage of the method presented. The RMS
amplitude was easier to use than the peak-to-peak amplitude
since it did not require any snapshot selection in the time
domain to reveal the crack.
Environmental aspects, such as temperature variation,
are always a major issue in Lamb-wave-based damage
detection techniques which utilize piezoceramic transducers
and baseline (i.e., undamaged condition) measurements. Since
the method does not involve any piezoceramic sensors for
sensing and baseline measurements for damage detection,
temperature variations during the test are not an issue. This is
the fifth advantage of the proposed technique.
6. Conclusions
The application of Lamb waves and a 3D laser vibrometer
for fatigue crack detection in metallic structures has been
demonstrated. A full Lamb wave field has been obtained
with a laser vibrometer working in a scanning mode. The 3D
laser vibrometer has allowed for separation of in-plane and
out-of-plane Lamb wave components.
Simple laser scans of Lamb wave amplitude have been
used to locate the crack and estimate its severity. The method
allows for non-contact measurements at multiple locations that
cannot be achieved with a small number of currently used
contact transducers. No sensors needed to be fixed either
permanently or temporarily to the structure, with associated
risk of damage to that structure. Damage detection has not
involved any studies of complex Lamb wave propagation in
the monitored structures, neither any baseline measurements
for undamaged structures, nor any signal post-processing
performed to extract damage-related features. The analysis
and interpretation of the results is very straightforward. The
method is simple, fast and reliable and cannot be influenced
by environmental effects.
Although damage detection based on Lamb waves and
utilizing a 3D scanning laser vibrometer has a great potential
for impact damage detection in large metallic plate-like
structures, further work is required regarding sensitivity to
damage. Future work should also concentrate on other
types of damage, higher frequencies of excitation and more
comparative studies of in-plane and out-of plane components.
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