A THEORETICAL MODEL FOR THE ULTRASONIC
DETECTION OF SURFACE-BREAKING CRACKS
WITH THE SCANNING LASER SOURCE TECHNIQUE
Irene Arias and Jan D. Achenbach
Center for Quality Engineering and Failure Prevention.
Northwestern University, Evanston, IL 60208
ABSTRACT. In work reported at last year's QNDE meeting, a first step towards the development of a model for the Scanning Laser Source (SLS) technique was presented, which provides
an analytical formulation for the transient response of an isotropic, homogeneous, linearly elastic half-space submitted to a pulsed laser line source operating in the therrnoelastic regime.
The formulation takes into account optical penetration into the material and thermal diffusion
from, the source, and is therefore a suitable representation not only for the far field, but also for
the field near the laser source, where these effects become significant. In the present paper, we
report the progress made in the numerical analysis by the Boundary Element Method of the
interactions of the previously obtained laser generated field with surface-breaking cracks. Some
preliminary simulations of SLS experimental observations are presented.
INTRODUCTION
Surface-breaking cracks in a structure can be ultrasonically detected using Lamb
and Rayleigh waves. Conventional ultrasonic flaw detection methodologies require the
generation of an ultrasonic wrave packet that travels through a structure and interacts
with existing flaws within the structure. Either reflected echoes or transmitted signals
may be monitored in the pulse-echo or pitch-catch modes of operation.
In order to generate the wa,ve packets for conventional pulse-echo and pitch-catch
techniques, high-power pulsed lasers have emerged as versatile therrnoelastic sources
of ultrasound. Indeed, laser based ultrasonic (LBU) techniques provide a number of
advantages over conventional ultrasonic methods such a..s higher spatial resolution, noncontact generation and detection of ultrasonic waves, use of fiber optics and ability to
operate on curved or rough surfaces [6].
In both the pitch-catch and pulse-echo methods, the source is expected to generate a well established ultrasonic wave, which then interacts with existing flaws. The
limitations on the size of the flaws that can be detected using these methods are determined by the ultrasonic reflectivity or transmittance of the flaw for the particular
wavelength used, and by the sensitivity of the ultrasonic detector. As might be expected, small flaws give rise to weak reflections or small changes in the amplitude of
transmitted signals, often too weak to be detected with existing laser detectors.
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
281
II
I
RECEIVER
III
Surface-breaking
crack
FIGURE 1.
FIGURE
1. Configuration
Configuration for
for the
the SLS
SLS technique.
technique.
Interferometer signal [mV]
4.0
4.0
-3
II
I
I 3'°
3.0
III
2.0
2.0
1.0
0
f^W^^
-1.0
-1.0
-2.0
-2.0
0
0.5
0.5
1.0
1.0
1.5
1.5
2.0
2.0
2.5
2.5
3.0
3.0
0
0.5
0.5
1.0
1.0
1.5
1.5
2.0
2.0
2.5
2.5
3.0
3.0
0
0.5
0.5
1.0
1.0
1.5
1.5
2.0
2.0
2.5
2.5
3.0
3.0
Ps]
Time
Time [[//s]
FIGURE 2.
FIGURE
2. Characteristic
Characteristic time
time signal
signal recorded
recorded at
at receiver
receiver for
for three
three different
different positions
positions of
of the
the laser
laser
c The
source relative
relative to
to the
the crack.
crack. Copyright
2000 source
Copyright 2000
©
The American
American Society
Society for
for Nondestructive
Nondestructive Testing,
Testing, Inc.
Inc.
Reprinted from
from [5]
Reprinted
[5] with
with permission
permission from
from Materials
Materials Evaluation.
Evaluation.
In this
Ill
this paper
paper we
we provide
provide the
the theoretical
theoretical background
background for
for an
an alternate
alternate approach
approach for
for
ultrasonic
detection
of
small
surface-breaking
cracks
using
laser-generated
ultrasonic detection of small surface-breaking cracks using laser-generated ultrasound
ultrasound
-– the
the Scanning
Scanning Laser
Laser Source
Source (SLS)
(SLS) technique
technique [5].
[5].
THE SCANNING
SCANNING LASER
LASER SOURCE
SOURCE TECHNIQUE
TECHNIQUE
The
The Scanning
Scanning Laser
Laser Source
Source (SLS)
(SLS) technique
technique has
has been
been proposed
proposed by
by Kromine
Kromine et
et
al.
[5]
as
a
method
to
detect
surface
breaking
discontinuities
by
monitoring
the
al [5] as a method to detect surface breaking discontinuities by monitoring the changes
changes
in the
the laser
laser generated
generated ultrasonic
ultrasonic signal
signal as
the laser
laser source
source passes
passes over
over the
the discontinuity.
discontinuity.
in
as the
This
method
differs
from
conventional
techniques
in
that
it
is
the
direct
This method differs from conventional techniques in that it is the direct generated
generated
ultrasonic signal
that is
ultrasonic
signal that
is detected,
detected, rather
rather than
than the
the reflections
reflections of
of the
the generated
generated waves
waves by
by
the
defect.
the defect.
The proposed
proposed technique
technique employs
The
employs aa line
line focused
focused high
high power
power laser
laser source
source which
which
is
swept
across
the
test
specimen
and
passes
over
surface-breaking
anomalies.
is swept across the test specimen and passes over surface-breaking anomalies. The
The
generated ultrasonic
waves are
generated
ultrasonic waves
are detected
detected with
with an
an ultrasonic
ultrasonic detector
detector located
located either
either at
at aa
fixed
distance
from
the
laser
source
or
at
a
fixed
position
on
the
test
specimen.
This
fixed distance from the laser source or at a fixed position on the test specimen. This
technique can
can be
technique
be used
used to
to detect
detect discontinuities
discontinuities with
with arbitrary
arbitrary orientations.
orientations.
Kromine et
experimentally verified
Kromine
et al.
al. have
have experimentally
verified the
the SLS
SLS approach
approach by
by testing
testing an
an
aluminum
with aa surface
aluminum specimen
specimen with
surface breaking
breaking fatigue
fatigue crack.
crack. A
A schematic
schematic of
of the
the inspection
inspection
technique is
technique
is shown
shown in
in Fig.
Fig. 1,
1, where
where three
three representative
representative positions
positions of
of the
the source
source relative
relative
to the
the crack
crack have
have been
been plotted.
plotted. The
The variation
variation of
to
of the
the amplitude
amplitude and
and frequency
frequency of
of the
the
measured ultrasonic
measured
ultrasonic signals
signals was
was studied
studied as
as the
the laser
laser source
source approaches,
approaches, passes
passes over
over and
and
moves behind
behind the
the discontinuity
discontinuity (positions
moves
(positions (I),
(I), (II),
(II), and
and (III)
(III) in
in Fig.
Fig. 11 respectively).
respectively).
A
characteristic
signature
of
the
crack
was
found
as
both
a
specific
A characteristic signature of the crack was found as both a specific variation
variation of
of the
the
ultrasonic
amplitude
and
a
frequency
shift
of
the
generated
signals
(see
Fig.
3).
ultrasonic amplitude and a frequency shift of the generated signals (see Fig. 3). The
The
following aspect
signature in
the ultrasonic
ultrasonic amplitude
amplitude should
should be
be noted.
noted.
following
aspect of
of the
the signature
in the
282
5
II
5.0
4.0
I
Crack
Spectrum maximum, MHz
Ultrasonic amplitude [mV]
6.0
6.0
I
3.0
III
2.0
1.0
II
III
4
3
2
Position
Position of
of the
the crack
crac
1
0
0
1.0
1.0
2.0
2.0
3.0
3.0
4.0
4.0
5.0
6.0
0
0
SLS
SLS position
position [mm]
[mm]
1
2
3
4
5
6
SLS
SLS position,
position, mm
mm
FIGURE
FIGURE 3.
3. Experimental
Experimental signatures
signatures of
ofthe
the defect
defect in
in the
the ultrasonic
ultrasonic amplitude
amplitude (left)
(left) and
and the
the maximaximum
mum frequency
frequency (right)
(right) of
of the
the generated
generated signal
signal as
as the
the laser
laser source
source scans
scans over
over aa surface-breaking
surface-breaking crack.
crack.
c The
Copyright
Copyright 2000
2000 ©
The American
American Society
Society for
for Nondestructive
Nondestructive Testing,
Testing, Inc.
Inc. Reprinted
Reprinted from
from [5]
[5] with
with
permission
permission from
from Materials
Materials Evaluation.
Evaluation.
(I)
(I) When
When the
the source
source is
is far
far ahead
ahead of
of the
the defect, the amplitude of the generated direct
signal
signal isis constant
constant and
and unaffected
unaffected by
by the
the presence
presence of
of the
the defect
defect (see
(see zone (I)
(I) in Fig.
3).
3). The
The signal
signal isis of
ofsufficient
sufficient amplitude
amplitude above
above the
the noise
noise floor
floor to
to be unambiguously
unambiguously
picked
picked up
up by
by the
the laser
laser detector.
detector. A
A weak reflection
reflection from the crack is barely visible
amidst
amidst the
the noise
noise (see
(see Fig.
Fig. 2(I)).
2(1)).
(II)
(II) As
As the
the source
source approaches
approaches the
the defect,
defect, the
the amplitude of
of the detected signal significantly
icantly increases.
increases. This
This increase
increase (from
(from aa level
level that
that was
was already
already sufficiently
sufficiently above
above
the
the noise
noise floor)
floor) isis more
more readily
readily detectable
detectable with
with aa laser
laser interferometer
interferometer than any
any
weak
weak echoes
echoes from
from the
the crack (see
(see Fig. 2(II)).
2(11)). The increase in signal amplitude is
attributed
attributed to
to two
two mechanisms:
mechanisms: (a)
(a) interactions
interactions of
of the
the direct
direct ultrasonic
ultrasonic wave with
the
the reflections
reflections from
from the
the crack,
crack, and
and (b)
(b) changes in
in the conditions of laser generation
ation of
of ultrasound
ultrasound when
when the
the laser
laser source
source isis in
in the
the vicinity
vicinity of
of the
the crack.
crack. The
The
changes
changes in
in generation
generation constraints
constraints play
play also
also aa role
role in
in the
the subsequent
subsequent drop in the
signal
signal amplitude
amplitude as
as the
the SLS
SLS passes
passes over
over the
the defect.
(III)
(Ill) As
As the
the source
source moves
moves behind
behind the
the defect, the amplitude remains constant and lower
than
than in
in zone
zone (I)
(I) due
due to
to the
the scattering of
of the generated signal by the crack (see
Fig.
Fig. 2(III)
2(111) and
arid zone
zone (III)
(III) on
on Fig.
Fig. 3).
3).
The
The modeling
modeling of
of the
the SLS
SLS technique
technique requires
requires an
an appropriate
appropriate description
description of
of the
the
two
main
mechanisms
involved
in
both
the
amplitude
and
the
spectral
variations
two main mechanisms involved in both the amplitude and the spectral variations in
in
order
order to
to develop
develop aa simulation
simulation tool
tool that
that combined
combined with
with the experimental method can
form
form the
the basis
basis for
for an
an inspection
inspection procedure
procedure using
using the
the SLS
SLS technique.
technique.
In
work
reported
at
last
year’s
QNDE
meeting
In work reported at last year's QNDE meeting [1],
[1], aa first
first step
step in
in the
the modeling
of
the
SLS
technique
was
presented,
which
involves
the
formulation
of
a
model
of the SLS technique was presented, which involves the formulation of a model for
for the
transient
response
of
an
isotropic,
homogeneous,
linearly
elastic
half-space
submitted
transient response of an isotropic, homogeneous, linearly elastic half-space submitted
to
to aa pulsed
pulsed laser
laser line
line source
source operating
operating in
in the
the thermoelastic regime. The formulation
takes
takes into
into account
account optical
optical penetration
penetration into
into the
the material
material and
arid thermal diffusion
diffusion from the
laser
laser source,
source, and
and isis therefore
therefore aa suitable
suitable representation
representation not
not only
only for
for the
the far field,
field, but
but
also
also for
for the
the field
field near
near the
the source,
source, where these effects
effects become significant.
significant. In the present
paper,
paper, we
we report
report the
the progress
progress made
made in
in the
the analysis
analysis of
of the
the interactions
interactions of
of the
the previously
obtained
obtained laser
laser generated
generated field
field with
with surface-breaking
surf ace-breaking cracks.
cracks.
283
THEORETICAL APPROACH
The development of a model for the SLS technique starts with the solution of
the problem of laser generation of ultrasound in the presence of a discontinuity. As a
first approach, we have considered the two dimensional problem of an infinitely long
line thermoelastic laser source impinging on an isotropic, homogeneous, linearly elastic
half-space with an infinitely long, mathematically sharp crack both perpendicular to the
surface of the half-space and parallel to the line source. By virtue of linear superposition,
the complete problem of obtaining the total field generated by a laser source impinging
on a half-space in the presence of a surface breaking crack can be decomposed into
two subproblems. The first one entails obtaining the so-called incident field which
is generated by the laser source impinging on an uncra.cked half-space. The second
involves the determination of the so-called scattered field, which is generated in the
cracked half-plane by the application of tractions on the crack faces which are equal in
magnitude and opposite in sign to the corresponding tractions due to the incident field
in the uncracked half-plane.
The Incident Field
In previous work [1], we studied the generation of ultrasound by lasers and
developed a theoretical model for the incident field generated by laser illumination in
the thermoelastic regime which takes into account the effects of thermal diffusion and
optical penetration. The necessity of including these mechanisms in the formulation in
order to obtain an accurate description of the generated field near the laser source wa..s
shown in the context of the modeling of the SLS technique.
The problem of the incident field was treated as a one-way coupled thermoelastic
problem in plane strain by using the thermal stress approximation which neglects the
coupling of the elastic displacement field to the governing differential equation for the
temperature [4].
The statement of the one-way coupled thermoelastic problem for the incident
field based on the hyperbolic heat equation may be written as follows:
2
\7
v T
J — —T
J- — —T
92 J.
K
—
—
—n
q
C
//V 2 u-f (A-f/^)V(V - u ) = pu + ,3VT
(1)
where T is the temperature, K is the thermal diffusivity, c is the heat propagation speed
which ha..s been chosen equal to the longitudinal wave speed, q is the laser induced heat
source, u is the displacement, j3 is the thermoelastic coupling constant: (3 = (3A+2//)aT,
aT is the coefficient of linear thermal expansion and A, JJL stand for the Lame elastic
constants. For a discussion on the appropriateness of the use of the hyperbolic heat
equation in the modeling of laser generated ultrasound see reference [1].
A possible expression for the heat source induced by laser line illumination q was
derived from the expression proposed by Spicer [7] for point illumination as:
*>0
(2)
where E is the energy of the laser pulse per unit length,./?^ is the surface reflectivity
and k is the thermal conductivity, % is the extinction coefficient which controls the
284
0.2
0.3
0.4
0.5
time (|o.s)
FIGURE 4. Comparison between the solution provided by the complete model (solid line) and the
distribution of shear dipoles model (dotted line) for normal stress axx on a vertical plane at depth
z — 1.0 mm for the near field (x — 0.1 mm) and the far field (x — 5.1 mm), respectively [1].
exponential decay with depth z of sub-surface sources arising from optical penetration,
RG id the radius of the Gaussian distribution assumed for the cross section of the laser
beam and v is the pulse rise time in the assumed temporal distribution of the laser
pulse.
Equations (1) and (2) with, the appropriate boundary and initial conditions are
solved for the case of line illumination of an isotropic, homogeneous, linearly elastic
half-space by a semi-analytical procedure [1].
The solution provided by the above formulation which accounts for the effects
of both thermal diffusion and optical penetration was compared with simplified models
available in the literature, in particular the shear traction dipole model [6]. This model
is based on the intuitive notion that the actions of a local generation of a temperature
field and the application of an elastic dipole should be expected to produce equivalent
fields. The laser source is thereby reduced to a localized action in space and time.
Although simple, this model is very useful since it can be understood as a fundamental
solution in the sense that it can account for any distribution of the source in space
and time by appropriate convolution. However, by definition this model neglects the
thermoelastic nature of the source and therefore does not account for thermal diffusion
and optical penetration. Consequently, ina.ccurate predictions of the field near the
source should be expected.
The comparison between the complete model and the distribution of dipoles
allows to clearly identify the effects of thermal diffusion and optical penetration in the
near field. Indeed, only the complete model is able to predict a special feature of the
near field waveform: the so-called precursor. The precursor is a sharp, initial spike
at the longitudinal arrival observed experimentally in measurements of the near field.
It has been shown that the precursor is caused by the subsurface sources arising from
thermal diffusion or optical penetration [3]. On the other hand, both models lead to
undistingulshable solutions for the far field as expected (see Fig. 4).
It should be pointed out that the laser generated waveforms exhibit a considerable
sharpness which increases as the width of the laser line source or the duration of the
pulse decreases [1]. The resulting relative high frequency content of the signal has some
numerical implications in the computation of the scattered field as will be shown in the
next section.
285
The Scattered Field
In recent work, the interactions of the previously obtained laser generated field
with surf ace-breaking cracks have been studied. According to the proposed theoretical
approach, the scattered field is defined as the field generated in the cracked half-space
by tractions acting on the faces of the crack such that, when added to the tractions
generated by the incident field on the plane of the crack, the condition of traction free
crack faces is satisfied by the total field.
By taking into account symmetry of geometry and symmetry of normal tractions
and anti-symmetry of shear tractions respectively, the problem in the half-space can be
restricted to a quarter-space and the symmetric and anti-symmetric contributions can
be obtained independently. Ea.ch of these two problems in the quarter space is treated
as an isothermal elastic problem in plane strain, thereby assuming that the presence of
the crack does not affect the propagation of heat. This assumption is considered to be
realistic for small fatigue cracks and has proven to be sufficiently accurate.
The scattered field has been obtained numerically by a direct frequency domain
Boundary Element Method (BEM). The BEM is ideally suited for the treatment of
unbounded domains since the radiation condition at infinity is naturally included in
the formulation.
As the BEM is based on an boundary integral equation formulation in which
displacements and stresses everywhere in the domain are expressed in terms of their
boundary values, only the boundary of the quarter-space needs to be discretized. As
this boundary is infinite, it needs to be truncated somewhere for numerical computation
purposesln order to select the location of the truncation point, the simplest approach
is based on the following considerations [2].
a. It is well known that body waves exhibit geometrical attenuation. Therefore, in
order to reduce the error of the truncation associated with this type of waves, the
truncation point should be loca.ted far enough from the domain of interest for the
contribution of the omitted part of the boundary to be negligible.
b. On the other hand, Rayleigh surface waves in two dimensions do not decay with
distance to the source. Consequently, the truncation of the boundary leads to considerable reflections. The criterion in this case is that these artificially generated
reflections reach, the domain of interest outside the time window of interest.
This approach, although effective, leads to quite large computational meshes. In
addition, the sharpness of the incident signal previously pointed out imposes stringent
conditions on the number of frequencies to be computed and the boundary element
sizes required for stability of the numerical scheme. The combination of these two
circumstances leads to a considerable computational cost, even if artificial damping is
added to the material.
Therefore, efforts have been made towards the development of an alternative
approach that allows to reduce the size of the computational domain. In order to
reduce the requirements related to the body waves, the infinite boundary element has
been used. This element, proposed by Watson in the context of the BEM, reproduces
the geometrical decay of the body waves [8], thereby reducing the truncation error and
allowing to locate the truncation point closer to the domain of interest.
On the other ha..nd, we are currently developing a rigorous correction for the
truncation error associated with the Rayleigh surface wave. We expect that this im-
286
V erticdisplacement at receive
>
-H
<D
0.4
0.4
00.4
.4
0.4
I
III
II
II
0.3
00.3
.3
0.2
0.2
00.2
.2
0.1
0.1
0.1
0.1
0
00
u -0.1
cti -o.
-0.1
--0.1
0.]
-0.2
-0.2
--0.2
0.2
-0.3
-0.3
--0.3
0.2
§
M
V
cti
I
0.3
°' 3
°' 2
0o
(L>
-
Lj
3
>
-0.4
-0.
0
0.5
1
1.5
2
-0.4
0
--0.4
0.4
0.5
1
1.5
2
0
0.5
1
1.5
2
time \JJLS]
[µs]
time
FIGURE
signal at
at receiver
receiver simulated
simulated for
for three
three different
different positions
positionsof
ofthe
thelaser
laser
FIGURE 5.
5. Characteristic time signal
source relative to the
the crack.
crack.
the model
provement of the
model will
will both
both allow
allow to
to significantly
significantly reduce
reducethe
thesize
sizeofofthe
themesh
meshand
and
provide additional stability to
to the
the numerical
numerical scheme.
scheme. Both
Both contributions
contributions will
willresult
resultinin
the desired reduction of the
the computational
computational cost.
cost.
PRELIMINARY NUMERICAL
NUMERICAL RESULTS
RESULTS FOR
FOR THE
THE TOTAL
TOTAL FIELD
FIELD
The total field
field is obtained
obtained by
by superposition
superposition of
of the
the incident
incident arid
and the
the scattered
scattered
fields.
In
this
paper
we
present
some
preliminary
results
for
the
simulation
fields.
present some preliminary results for the simulation ofof the
the
total field
field at the
the location
location of the
the receiver.
receiver. Three
Three representative
representative positions
positions of
of the
the laser
laser
source relative to
to the
the crack
crack have
have been
been considered:
considered: far
far ahead
ahead (I)
(I) , , very
very close
closetoto (II)
(II)
and far behind (III)
(III) the
crack
(see
Fig.
1).
Fig.
5
shows
the
simulated
the crack (see Fig. 1). Fig. 5 shows the simulated time
time signal
signal
at the receiver corresponding to
to the
the three
three positions
positions of
of the
the laser.
laser. The
The peak-to-peak
peak-to-peak
amplitude and the
maximum
frequency
of
the
Rayleigh
wave
have
been
the maximum frequency of the Rayleigh wave have beenplotted
plottedversus
versus
the SLS position (see Fig. 6). The
The simulations
simulations show
show good
good qualitative
qualitative agreement
agreement with
with
experimental observations. The
The proposed
proposed model
model is
is able
able to
to simulate
simulate the
the characteristic
characteristic
variations observed experimentally
experimentally as the
the SLS
SLS passes
passes over
over the
the defect.
defect.
It should
should be
be noted
It
noted that
that the
the difference
difference between
between the
the amplitude
amplitude level
levelfar
farahead
aheadand
and
far behind
behind the
far
the crack
crack is
is related
related to
to the
the depth
depth of
of the
the crack
crackrelative
relativeto
tothe
thecenter
centerwavelength
wavelength
of the
the generated
of
generated Rayleigh
Rayleigh surface
surface wave.
wave. In
In the
the case
case shown
shown inin Fig.
Fig.6,6,the
thedepth
depthofofthe
the
crack is
is much
much smaller
smaller than
crack
than the
the center
center wavelength,
wavelength, so
so that
that aa substantial
substantial portion
portion of
of the
the
incident energy
energy transmits
incident
transmits past
past the
the crack.
crack.
CONCLUSIONS
CONCLUSIONS
In this
this paper,
In
paper, aa model
model for
for the
the novel
novel Scanning
Scanning Laser
Laser Source
Source (SLS)
(SLS)technique
techniquefor
for
laser-based
ultrasonic
detection
of
small
surf
ace-breaking
cracks
has
been
laser-based ultrasonic detection of small surface-breaking cracks has been presented.
presented.
The cracked
cracked test
The
test specimen
specimen is
is modeled
modeled as
as an
an isotropic,
isotropic, homogeneous,
homogeneous, linearly
linearly elastic
elastic
half-space
with
a
two-dimensional,
mathematically
sharp
surface-breaking
half-space with a two-dimensional, mathematically sharp surface-breakingcrack,
crack,which
which
is perpendicular
perpendicular both
both to
is
to the
the direction
direction of
of scanning
scanning and
and the
the free
free surface
surface of
of the
thehalf-space.
half-space.
The ultrasonic
ultrasonic response
The
response of
of the
the cracked
cracked half-space
half-space to
to aa pulsed
pulsed laser
laser line
line source
sourceoperatoperating
in
the
thermoelastic
regime
is
decomposed,
by
virtue
of
linear
superposition,
ing in the thermoelastic regime is decomposed, by virtue of linear superposition, into
into
the incident
incident and
the
and the
the scattered
scattered fields,
fields, which
which can
can be
be obtained
obtained separately.
separately. The
Theincident
incident
field is
is generated
generated by
by the
field
the line
line laser
laser heat
heat source
source in
in the
the uncracked
uncracked half-space.
half-space. The
Theformuformu-
287
10
j 0.7
0.7
crack
crack
maximum frequency [MHz]
peak−to−peak amplitude [nm/mJ]
0.8
0.8
£. 0.6
0.6
I
0.5
0.4
0.4
0.3
0.3
2
0.2
i °-
crack
8
6
4
2
f 0.1
0.1
0
0
11
22
33
44
0
0
5
SLS position
position [mm]
[mm]
SLS
1
22
3
3
SLS position
position [mm]
[mm]
SLS
4
4
5
FIGURE 6.
6. Simulated
Simulated signatures
signatures of
ofthe
the defect
defect in
in the
the ultrasonic
ultrasonic amplitude
amplitude (left)
(left) and
and the
the maximum
FIGURE
frequency (right)
(right) of
of the
the generated
generated signal
signal as
as the
the laser
laser source
source scans
scans over
over aa surface-breaking crack.
frequency
lation takes
takes into
into account
account the
the effects
effects of
of thermal
thermal diffusion
diffusion from
from the source and optical
lation
penetration into
into the
the material.
material. The
The corresponding thermoelastic problem is solved semipenetration
analytically. The
The resulting
resulting model
model provides
provides an
an accurate
accurate simulation
simulation of
ofthe
the near
near field,
field, while
while
analytically.
the
far
field
simulations
show
excellent
agreement
with,
simplified
models.
The
scatthe far field simulations show
agreement with simplified
tered
field
in
the
cracked
half-space
is
obtained
by
a
direct
frequency
domain
boundary
tered field in the cracked half-space is obtained by a direct frequency domain boundary
element method.
method. Preliminary
Preliminary simulations
simulations of
of the
the total
total field
field at
at the
the receiver location show
element
good
qualitative
agreement
with
SLS
experimental
observations.
The next
next step
step is
is to
to
good qualitative agreement with SLS experimental observations. The
extract
quantitative
information
from
the
theoretical
model.
extract quantitative information from the theoretical model.
ACKNOWLEDGEMENTS
ACKNOWLEDGEMENTS
This work
work was
was carried
carried out
out in
in the
the course of
of research funded by the Federal
This
Aviation
Administration
under
Contract
#DFTA
03-98-D-0008
through the Air TransAviation Administration under Contract #DFTA 03-98-D-0008 through
portation
Center
of
Excellence
in
Airworthiness
Assurance.
portation Center of Excellence in Airworthiness Assurance.
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