MODULATION ENHANCED DETECTABILITY OF CRACKS
USING SURFACE ACOUSTIC WAVES
J.-Y. Kirn, V. A. Yakovlev and S. I. Rokhlin
The Ohio State University
Nondestructive Evaluation Program
Edison Joining Technology Center
1248 Arthur E. Adams Dr.
Columbus, Ohio 43221
ABSTRACT. The parametric effect in surface acoustic wave interaction with a partially closed
fatigue crack initiated in the cavity-induced plastic yielding zone is investigated experimentally
and theoretically. In-situ ultrasonic measurements were made for different crack lengths and
variable static closure load during a fatigue test. Small periodic loading, superimposed on the
static closure load, changes the crack interfacial condition and/or the open crack segment length
resulting in nonlinear modulation of the surface wave reflected signals. The modulation
spectrum is related to the crack initiation and evolution and to the crack opening-closure
behavior. It is shown that the modulation even at a low mean load could enhance considerably
crack detectability. The increase of the second harmonic in the modulation spectrum is
pronounced when the modulation is applied at two critical mean static loads: when the crack is
nearly closed and when it is nearly open. It is also observed that the maximum modulation
occurs just before the crack is fully open. A low frequency scattering model is applied to predict
the modulation spectrum. The modeling results compare favorably with experiment. Overall, the
crack opening condition affects significantly and complicatedly the modulation of surface wave
reflection.
INTRODUCTION
The success of conventional linear ultrasonic techniques for detecting small
fatigue cracks is often limited by ultrasonic grain structure scattering or scattering from
other volumetric inhomogeneities that may generate a larger ultrasonic scattering signal
than the crack. Nonlinear acoustic methods have been found to be potentially promising
for material diagnostics and damage detection in complex media since it has been
established that imperfect interfaces related to damage generate significantly larger
nonlinearity. Both second harmonic generation [1,2] and modulation techniques [3,4]
have been explored. In the modulation techniques different modulating excitations have
been employed, including mechanical [3] (continuous vibration or impact) and thermal
[4]The ultrasonic wave reflectivity from the fatigue crack depends significantly on
crack closure [5,6]. Therefore one can expect crack closure to have strong effect on
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
867
modulation. The modulation of ultrasonic reflection from a crack results from the
change of the contact condition at the crack interface by an external load. The
application of a small modulation load may cause the modulation effect by two
mechanisms: 1) nonlinear contact of the crack rough surfaces and 2) modulationinduced change of the open/closure part of the crack. Often both mechanisms may exist
simultaneously. The intensity of the nonlinear interfacial effect depends strongly on the
level of crack closure. For example, when a crack is fully open it behaves like a
volumetric flaw and thus the output signal is weakly modulated. When the crack is
tightly closed the modulation of the output signal is also small. Intermediate crack
opening leads to modulation.
As the result, the modulation response of a crack is influenced mainly by the
contact condition of the crack branches and therefore to apply the modulation technique
as a diagnostic tool one needs to understand this effect. This paper aims to investigate
the effect of the low frequency modulation on ultrasonic surface wave interactions with
a fatigue crack initiated in the plastic zone of a surface cavity. The ultrasonic
measurements are performed in-situ during a fatigue test at different stages of crack
initiation and evolution and at different levels of closure stress. The partial closure of a
closed crack can be formed artificially by applying a static load. As demonstrated in this
paper, the modulation response can be enhanced by application of the static load along
with the dynamic modulation load. The influences of crack closure on the harmonic
amplitudes of the modulation are shown and physically interpreted. The low frequency
scattering model is applied to predict the modulation and higher harmonic amplitudes.
EXPERIMENT
Sample and Fatigue Test
The fatigue sample was machined from 1.6 mm thick Al 2024-T3 alloy plate
with 340 MPa the yield stress, 483 MPa ultimate tensile stress, and 17.5 % elongation.
Controlled-size small pit with depth of 250 |im and diameter of 230 |im was produced
by an electrical discharge machine (EDM) in the center of the sample. The frequency of
the fatigue load was 10 Hz, the stress ratio R was 0.1 and the stress range Aa was 231
MPa. The maximum fatigue stress level was 78 % of the yield stress. The high stress
concentration (kt—3A5) at the pit corners leads to a formation of a plastic yielding zone,
which exerts a compressional clamping stress on the initiated fatigue crack surface. The
fatigue life of the sample was 152,531 cycles.
In-situ Ultrasonic Measurements
The experimental setup includes a 5 MHz ultrasonic surface wave transducer, a
pulser/receiver, a mechanical testing system (MTS) and an ultrasonic data acquisition as
shown in Fig. 1. For an in-situ measurement, the transducer assembly is clamped on the
sample under the fatigue and modulation loads so that the ultrasonic signals are
collected at different load levels of fatigue and modulation loads during cycling. An
ultrasonic couplant was applied between the ultrasonic wedge and the sample. In-house
software for fatigue and modulation control and for synchronized real-time ultrasonic
data acquisition was developed. The software control 12 bit, 125 MHz digitizing
computer board was used for data acquisition. The data acquisition and the ultrasonic
868
pulser/receiver are triggered by a software control counter at predetermined times and
fatigue and modulation loads. The low amplitude ultrasonic measurements were
performed in the pulse mode with a repetition frequency 300 Hz.
Load profiles versus time (number of cycles) with indicated times of ultrasonic
measurements are shown in Fig.2. At the predetermined numbers of cycles, ultrasonic
surface wave reflection signals are obtained at different loads in a single loadingunloading fatigue cycle. Since ultrasonic event occurs during very short time the fatigue
load during the event can be considered as static. After predetermined numbers of
cycles, the modulation vibrations were superimposed on different levels of static load as
shown in Fig. 2. The amplitude of the modulation was as low as 0.17 kN at 10 Hz. The
static load varies from 0.31 kN to 2.36 kN. Thirty ultrasonic reflection signals were
acquired during each cycle over 100 cycles of the modulation load. After performing the
ultrasonic measurements at different levels of static load with modulation, the fatigue
cycling resumed. The collected series of ultrasonic signatures represent pulse modulated
sequences at different static loads (crack closures) and different numbers of cycles
(crack lengths).
EXPERIMENTAL RESULTS
As an example, Figure 3 shows the frequency spectra of the modulated
reflection signals at 10 and 2,500 cycles. Small background modulation is observed
after 10 cycles (Fig. 3(a)). It is due to slight deformation of the surface cavity and
related change of the reflected signal. Higher level of modulation is observed at 2,500
cycles (Fig. 3(c)). This change is due to an initiated crack which is less than 40 |0,m [5].
Since the crack initiated in the cavity-induced plastic yielding zone, the compressional
stress due to the unrestored plastic deformation [6] tends to close the crack. Therefore,
at a lower static load (0.3 kN) the crack is closed. At a higher load (1.42 kN) the crack is
fully open and the modulation amplitude decreases. For comparison, the normalized
reflection amplitude versus number of cycles for different static loads is shown in Fig.
3(d). It shows no sensitivity to crack initiation.
Figure 4 summarizes the modulation amplitudes versus the mean static load for
different numbers of fatigue cycles. The number of fatigue cycles is related to the crack
length [5]. The maximum modulation occurs at mid static load except for 2500 cycles.
SAW
FIGURE 1. Setup for in-situ ultrasonic
experiment during fatigue tests
FIGURE 2. Segment of modulation measurements
during a fatigue test: Solid circles indicate ultrasonic
measurement events which occur at different levels
of fatigue (static) and modulation loads.
869
(a) 10 cycles, 03 kN
0
10
20
30
40
(d) Quasi-static
SO
Nyffife&f Of €y«!ig$
(c) 2,500 cycles, L42 kN
(b) 2,500 cycles, 0-3 kN
20
30
40
10
•«»qa<mey {Hz}
20
30
40
Fr$qu$ney (Hx)
FIGURE 3. Frequency spectra of modulation amplitudes (a), (b) and (c) at different numbers of cycles
and normalized reflection amplitude from quasi-static measurements during fatigue test (d).
As mentioned before, the crack at 2,500 cycles is so small that it is opened
entirely by a small load tending to behave as a volumetric flaw, (it is important since
higher modulation is obtained with small static load on a tightly closed very small
crack). As the closure (opening) stress changes with the crack growth [6], the maximum
modulation occurs at different static load levels: e.g. 1.7 kN at 50,000 cycles and 1.96
kN at 130,000 cycles. Physically the modulation amplitude is proportional to the
derivative of the pulse reflection amplitude dependence on the load (proportional to the
crack opening rate). Therefore the modulation is maximized at such static loads when
the crack opening rate is highest with load.
The normalized reflection amplitude versus the static load is shown in Fig. 5 (a).
Note that while the reflection from the crack increases with load the total reflection
(from crack and pit) decreases with crack opening due to destructive interference of the
pit and crack reflections [1]. As an example Figure 5(b) shows the dependence of first
and higher modulation harmonics on the static crack opening load at 97,000 cycles. The
crack opening loads determined from the plate bottom reflection signals [6] are shown
in Fig. 5(c). The first harmonic (modulation amplitude) shows a rapid increase at around
0.75 kN and has a maximum at 1.3 kN and a local minimum at 2.9 kN. The initial
modulation increase at 0.75 kN demonstrates the sensitivity of the modulation method
to the static load, compared with no measurable change of reflected amplitude (Fig.
5(a)) at the same loads. If we add to the static load the maximum modulation load, the
crack starts to open. The increase of sensitivity at loads higher than 0.75 kN is due to
crack length change, which produces a stronger modulation effect than interfacial
condition change at 0.75 kN. The local minimum of the first modulation harmonic at
about 1.75 kN corresponds to minimum of the reflection amplitude versus load (Fig.
The second harmonic peaks appear in the modulation spectrum at loads around
1.1 kN and 2.2 kN. These loads are slightly above the crack-mouth-opening (0.8 kN)
and slightly below the crack-fully-opening (2.3 kN) loads as marked in Fig. 5(b) and
Fig. 5(c). When the modulation load is applied while the static load is slightly above the
crack-mouth-opening load, the crack during the modulation period undergoes transition
between the following states: tight closure <-> loose closure <-> mouth opening <-> partial
opening.
870
1 10:
# of cycles
(Crack length)
140,000
-130,000
- 70,000
~
0,1
0.0
0.5
1.0
1.5
2.0
FIGURE 4. Modulation
amplitudes of the reflection
signals versus the mean static load
for different numbers of cycles
(crack length).
2,5
Mean static load (kN)
(a)
1-.2-1
(b)
97,800 cyei
97,500
10
Fully
),0
0,S
1.0 1.5 2.0
Load <kN)
jjOfaek«fuliy-op®nirjg load
Load (kN)
FIGURE 5. (a) Normalized reflection
amp-litude versus load at 97,500 cycles
(amplitude decrease due to interference
of crack/pit reflected signals) (b).
Amplitude of modulation harmonics
versus the mean static load at 97,500
cycles, (c) Crack closure (opening) loads
versus number of cycles.
This nonlinear crack opening/closure behavior leads to distortions of the modulated
signal and is responsible for the considerable increase of the second harmonic
amplitude. Similarly modulation at a static load above the crack-fully-opening load
leads to nonlinear crack opening behavior. When the modulation load is above the
crack-fully- opening load the modulation of the reflected signal is saturated leading to
higher harmonics. These experimental observations are supported by the model
simulations described in the next section.
Levels of the static load at which the modulation amplitude reaches maximum
are shown versus number of cycles in Figure 6. They are given together with crackmouth and crack-fully opening loads. The crack-fully-opening load has its maximum
value and the mouth-opening load starts to decrease at 110,000 cycles as the crack
grows out of the cavity-induced plastic yielding zone [6]. The decrease in crack opening
load is attributed to crack growth out of the plastic yielding zone and reduction of the
residual compressive stresses in the sample. At 110,000 cycles, one observes a sudden
increase of the static load at which the maximum modulation amplitude occurs. The
load changes from about 1.4 kN to slightly lower than the crack-fully-opening loads.
With crack growth this static load decreases similar to the above-mentioned decrease of
the crack-opening loads.
871
When the fully-open crack is deeper than the plastic yielding zone, the
distribution of the compressive stress on the crack surface changes as the crack is open
by the applied load. Until the open crack segment length reaches the plastic yielding
boundary, the whole part of the crack is constrained by the uniform compressive stress,
thus it becomes fully open gradually. As the open crack segment increases out of the
plastic yielding zone, the crack is suddenly open because the remaining part of the crack
is not under compressive load. For this reason, the maximum crack opening rate always
occurs at loads just below the crack-fully-opening loads. Detailed interpretation of this
phenomenon will be presented elsewhere.
MODEL FOR MODULATION OF SURFACE WAVE REFLECTION FROM
CRACK
We simulate the modulation of the surface wave reflection due to the openingclosure of small fatigue cracks using the low frequency scattering model developed in
[5]. It should be noted that a fresh fatigue crack has perfectly conforming surfaces and
thus under compressional stress the crack is closed and nearly transparent to acoustic
waves. Therefore, the effective crack length as seen by ultrasonic waves is the open part
of the crack as shown in Fig. 7. The modulation load changes the length of the open
crack segment and consequently the reflection amplitude, which is determined from the
model.
In the model, the time domain reflection signature from the cavity with the
emanating crack is represented by the sum of the signals reflected from the crack and
the cavity r(t,a=Q\
(1)
r(t,a) = r(t,a = 0)
(2)
3EP
where F(co) is the frequency response of the measuring system, i is the imaginary unit,
co is the angular frequency, D is the cavity diameter, FR is the surface wave velocity, a is
the crack depth, vis Poisson's ratio, E is Young's modulus, P is the input power into the
transducer, dl is the line element on the crack front /"and p(r) is defined in [1].
FIGURE 6. Comparison of crack opening
loads and loads which produce maximum
modulation response. At 110,000 cycles, the
crack depth is equal to the size of the plastic
yielding zone. Open circle: crack-fullyopening loads; open square: crack-mouthopening loads; solid square: static loads at
maximum modulation.
120
140
160
Number of kilocycles
872
FIGURE 7. Crack closure phenomenon: length change of the open part of the crack under load
The cavity reflection coefficient in the presence of the crack is approximated by the
cavity reflection coefficient without the crack r(t, a = 0) that can be measured prior to
the fatigue. The crack reflection coefficient R^ is approximated by Eq.(2) where K\(d)
is the mode I stress intensity factor for symmetric corner cracks at a through-thickness
hole in a plate subject to bending [7]. The open crack length is accounted for in the
integration contour. Using Eqs. (l)-(2), the reflection coefficients versus the open crack
segment length (OCSL) and the modulation load are obtained.
Based on the measured ultrasonic signal the length of the open crack segment
was calculated as function of load (Fig. 8(a)). How changes of the modulation load
transformed to the oscillating open crack length change is also shown in the figure for
three different static loads. Figure 8(c) presents the computational procedure of the
modulation spectrum. At the static loads 0.5 kN and 2.3 kN, the multiple modulation
harmonics appear (Fig. 8(b), (d) and (f)) since modulation occurs on the strongly
nonlinear part of the OCSL-load dependence. Second harmonic generation at these
loads is supported by the experimental results presented in Section III. At 1.4 kN static
load, the changes are almost linear and therefore the harmonic generation is not strong
and the first harmonic has the largest amplitude (the slope on the OCSL-load curve
shown in Fig. 8(a) is highest).
(a)
(b)
(c)
<cycles
distortion
iWWWVM
L4kN
4CT
0.5 KN0.0
0,2 0,4
0.8 0.8
Ttea {Sec}
10
Normalized
vs. crack
load.
Length of open
vs. crack
load
Slope
Modulation amplitude
and
FIGURE 8. Change of open crack segment length (OCSL) for modulation at different static load levels.
Results obtained from ultrasonic reflection data at 87,000 fatigue cycles, (a) OCSL vs. static load; (b)
Change of OCSL with time by the modulation load at different static load levels; (c) Procedure of
calculating modulation spectrum using the model; (d), (e) and (f) Normalized modulation spectrum at 0.5
kN, 1.4 kN and 2,3 kN static loads.
873
1.0
\ Experiment
I Model
87,000 cycles
0.6l
2 Experiment
• Model
87,000 cycles
0.4-
-a o>
il
"O Q.
.9
o
c ~
0.5-
0.0
0.5
8%
1.0
1.5
2.0
2.5
Mean static load level (kN)
0.0
'0.5
1.0
1.5
2.0
2.5
Mean static load level (kN)
FIGURE 9. Comparison of calculated and measured modulation harmonic amplitudes for different mean
static loads at 87,000 cycles, (a) Modulation (first harmonic) amplitude, (b) Second harmonic amplitude.
Figure 9 shows comparison of the predicted first and second modulation
harmonics with experiment. The relative magnitudes of the modulation spectra are in
quite close agreement.
CONCLUSION
It is shown that the modulation amplitude depends strongly on the crack length
and the crack closure condition. For a closed fatigue crack under compressional stress,
the modulation loading at a low mean static load can enhance considerably the
modulation amplitude. The modulation is minimal when a crack is completely closed or
completely open. There also exists an optimum static load, on which the modulated
signal is overlaid, such that maximum modulation occurs. The change in optimum static
load occurs abruptly when the fatigue crack grows larger than the plastic yielding zone.
Strong second harmonic generation is observed when the modulation is applied at loads
near the crack-fully-opening or the crack-mouth-opening loads. The response of the
cracks under modulation and the generation of higher harmonics are predicted by the
scattering model. The theoretical and experimental results are in good agreement.
ACKNOWLEDGEMENT
This work was partially sponsored by the Federal Aviation Administration (FAA)
under contract #97-C-001.
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