NONLINEAR LASER ULTRASONIC MEASUREMENTS OF
LOCALIZED FATIGUE DAMAGE
J. L. Blackshire1, S. Sathish2, J. Na3, and J. Frouin2
*Air Force Research Lab, WPAFB, OH, 45433
University of Dayton, Center for Materials Diagnostics (CMD), Dayton, OH 45469-0127
Veridian Engineering, Dayton, OH 45440
2
ABSTRACT. A nonlinear laser ultrasonic system was developed and used to characterize the fatigue
state of a fractured Ti-6Al-4V sample with high spatial-resolution and sensitivity. The measurement
system is built around a scanning heterodyne interferometer, which allows detailed displacement field
images to be created and visualized for propagating surface and bulk acoustic fields on a material
surface. An assessment of the local fatigue damage of the material was made using nonlinear
ultrasonic interaction principles, where the local amplitudes of the fundamental and second harmonic
displacement fields are monitored simultaneously. This provides a means for evaluating the local
acoustical nonlinearity parameter, p, which can be related to the accumulation of fatigue damage in a
material. A large increase in p was observed between the unfatigued area (near the grip section) and
the heavily fatigued area (gauge section) for a fractured dogbone specimen. The measurements show
the potential for spatially-resolving the local fatigue state of a material using laser ultrasonics.
INTRODUCTION
For more than 50 years, the nondestructive evaluation (NDE) community has
focused on detecting and characterizing fatigue cracks as the primary means for assessing
remaining life in aerospace materials and systems. A recent trend in NDE research
involves the assessment of a material through its entire fatigue life. Rather than waiting for
a crack to initiate (which typically indicates that failure is eminent), the gradual
accumulation of damage in a material would be monitored. If this were possible, and a
continuous assessment of fatigue state could be accomplished, the implications would be
profound, and a revolutionary way of doing NDE would be available.
One of the most promising new NDE techniques for monitoring accumulated
fatigue damage in a material involves nonlinear ultrasonics. Several researchers have
recently reported dramatic changes in the nonlinearity parameter, (J, generated in fatigued
aluminum 2024-T4, stainless steel 410Cb, and titanium Ti-6Al-4V alloys [1-5]. These
measurements have shown changes in the nonlinear parameter due to fatigue by the time
the material undergoes 30 to 40 percent of its total fatigue life. A direct correlation
between dislocation density levels within the fatigued material and an increase in harmonic
ultrasonic signals has also been reported [6,7]. The results clearly show the potential for
making quantitative NDE measurements of fatigue state using nonlinear ultrasonics.
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
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Several different experimental approaches have been applied successfully in
nonlinear ultrasonic measurements. Traditionally, piezoelectric transducers and/or
capacitive probes have been used to monitor the generation of harmonic energy in a
material substrate. These approaches suffer from a number of problems, however, that
place restrictions or limits on measurement capabilities. There are often special
requirements for specimen preparation, for example, that may require optically flat and
parallel surfaces, or specimen conductivity. In addition, measurements are typically limited
to a single measurement location, due to the hard-bonding of transducers, or restrictions
imposed by the placement of the probes. The spatial resolution capabilities of a typical
measurement are also very coarse in nature (1 mm2 - 1 cm2), and involve an averaged or
integrated signal over the entire receiver area, which can impact the quality of the
measurements.
An alternative method for detecting and characterizing the harmonic ultrasonic
field in a material involves the use of laser interferometry techniques [8,9,10]. Laser
interferometry has long been used for dynamic motion measurements, and it offers several
advantages for making nonlinear ultrasonic measurements. Because coherent light is used
as the probe, measurements can be made in a non-contact, remote, and non-intrusive
manner. High spatial resolutions are also possible (1-10 microns) without reductions in
measurement sensitivity. Interferometric measurements are also directly related to the
optical wavelength used, which provides an absolute measure of the ultrasonic
displacement levels. They also have a truly broadband frequency response, which is
difficult to achieve with piezoelectric probes. And finally, by raster-scanning the laser
beam position with respect to the material surface, a high resolution 'image' of the
harmonic (and fundamental) ultrasonic displacement field(s) can be created.
In this effort, a nonlinear laser ultrasonic detection system was developed and used
to characterize the fatigue state of a fractured Ti-6Al-4V sample with high spatialresolution and sensitivity. An initial series of tests were conducted using non-fatigued
material standards in order to check system linearity, harmonic and fundamental frequency
fidelity, and measurement sensitivity limits. Direct comparisons with traditional
piezoelectric and capacitive probe measurements were made. Raster-scanned images of the
5MHz (fundamental) and 10MHz (harmonic) displacement fields generated by the
propagation of surface acoustic waves (SAW) and bulk acoustic waves (BAW) were then
studied. The advantages and disadvantages of both configurations were evaluated. The
nonlinear laser ultrasonic signature of a fractured titanium dogbone specimen subjected to
low cycle fatigue was then investigated. The measurement results showed a dramatic
increase in the nonlinear parameter, P, near the fractured edge, that compared well with
capacitive probe measurements and theoretical considerations.
NONLINEAR ULTRASONICS AND MATERIAL FATIGUE
When a single frequency ultrasonic wave is launched into a material it will distort
as it propagates, and will also generate harmonics of the fundamental wave frequency if
material nonlinearities are present [11,12], Two of the most important and prominent
material characteristics that lead to the generation of harmonic energy include 1) lattice
anharmonicity (e.g. single crystal materials), and 2) dislocation structures. In most metallic
alloys, dislocation contributions to p are considerably larger than contributions due to the
anharmonicity of the crystal lattice [7]. This is especially true in the advanced stages of the
fatigue process. With regard to the fatigue of metallic materials, cyclic stresses promote
the formation of dislocation dipoles in the material, and this in turn causes increased levels
of harmonic energy generation.
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In a harmonic-generation experiment, the nonlinear ultrasonic parameter (3 can be
determined through measurements of the amplitudes \ and A2 of the fundamental and
second-harmonic displacement levels using the expression [13]:
8A
(1)
where k = coo/v is the ultrasonic wavevector, v is the phase velocity, coo is the fundamental
angular frequency, and z is the propagation distance. Measurements of the amplitudes of
the fundamental and harmonic signals can, therefore, be used to study the stress-strain
character of a nonlinear solid through the nonlinear parameter P using Equation 1.
NONLINEAR LASER ULTRASONIC SYSTEM
A schematic diagram of the experimental system is depicted in Figure 1. A
standard heterodyne interferometry system is used to measure the out-of-plane
displacements at a single point on the material surface, which have been induced by a
single-frequency, toneburst ultrasonic transducer. The interferometry system focuses the
light from a low power HeNe laser onto the material surface, where the focused spot size
ultimately determines the spatial resolution of the measurement. Scattered light from the
material surface re-enters the interferometry system, and mixes with a reference beam to
produce a light interference signal. Dynamic motions of the material surface cause phase
variations between the two interfering beams, which results in changes in light intensity. A
fast photodetector transforms the variations in light intensity into electrical signals that can
be measured and recorded.
Nonlinear ultrasonics measurements are made by splitting the interferometric
displacement signal into two separate channels. The weak harmonic displacement field
information is embedded in the dominant fundamental signal, and an appropriate narrow
bandpass filter and low-noise amplification is applied to one of the two channels to acquire
the harmonic displacement signal. A high-speed, 2-channel A/D board transfers the
resulting fundamental and harmonic signals to a computer for further processing and
recording.
Material
FIGURE 1. Schematic diagram of nonlinear laser ultrasonic detection system.
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Two-dimensional displacement field images were created by raster-scanning the
position of the focused laser beam relative to the material surface. Three separate images
were created during each measurement including: 1) a fundamental displacement field
image, 2) an harmonic displacement field image, and 3) a nonlinear parameter, p, image.
The fundamental and harmonic image fields represent a peak displacement level measured
at each location on the material surface. The p image field was calculated using the
measured fundamental and harmonic displacement amplitudes, and the expression given in
Equation 1. In-line averaging and time-gated detection was also used to discriminate
unwanted signal components, and to enhance signal-to-noise ratio.
RESULTS AND DISCUSSION
System Characterization Studies
A basic series of experiments were first conducted using material standards in
order to characterize system linearity, harmonic and fundamental frequency fidelity, and
measurement sensitivity limits. The material standards were made in such a way that a
direct comparison with traditional piezoelectric and capacitive probe measurements could
be made. The two primary material standards included: 1) a gold coated single crystal
silicon sample (<111> crystal orientation), and 2) an A12024-T3 aluminum sample. The
samples were 50 mm in length, and had a circular cross-sectional area, with a diameter of
25 mm. The end faces were polished (and gold coated for the silicon sample), and were
made parallel to each other. A 5 MHz single crystal transducer (LiNbO3, 15 mm diameter,
longitudinal cut) was bonded to the front face, while measurements were made with each
of the three techniques on the opposite face (see Figure 2). A high-power, narrowbandpass filter (center frequency of 5 MHz) was inserted just prior to the drive transducer
to insure drive frequency fidelity. A similar, low-power filter (center frequency of 10
MHz) was used to filter the detected harmonic signal.
A representative set of interferometric displacement field signals (time versus
displacement) is provided in Figure 3 for the silicon sample, along with the spectral
components present in each signal trace (arbitrary units in all cases). A 25-cycle, toneburst
signal (sinusoidal) was used to drive the LiNbO3 transducer. The 5 MHz fundamental
displacement levels (peak displacements) were on the order of ten nanometers, while an
amplification factor of 35 dB applied to the 10 MHz harmonic signal corresponded to
picometer displacement levels. Several burst signals are depicted in each plot, representing
multiple reflections within the specimen. As shown in the figure, there was good frequency
fidelity present in the measured fundamental and harmonic signals. Similar results were
obtained for the A12024-T3 specimen, and for the piezoelectric and capacitive probe
measurements.
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FIGURE 2. Schematic diagram of experimental setup used in system characterization studies.
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Fundamental 5MHz Silicon sample [111]
Second harmonic 10 MHz Silicon sample [111]
(using interferometric system)
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0.005 0.000
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Frequency (Hz)
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FIGURE 3. Interferometric displacement signals for single crystal silicon reference sample.
A 2 vsAj 2 Al-2024 using Interferometric system
A2 vs At2 Silicon sample [111] using Interferometric system
1100 -
1200 -
1000 900 -
S
1000 -
700 -
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400 -
300 200 -
200 100 0
10000 20000 30000 40000 50000 60000 70000 80000 90000100000110000
0
20000 40000 60000 80000 100000 120000 140000 160000 180000
^ (mV2)
FIGURE 4. Displacement amplitude ratios for variation of input drive level.
System linearity and measurement sensitivity limits were checked by varying the
input drive voltage to the bonded 5 MHz transducer, and measuring the corresponding
A2/Aj2 amplitude ratio on the opposite face. Equation 1 predicts a constant amplitude ratio,
A2/Aj2, if the sample length and the ultrasonic frequency remain constant throughout the
test. The results of the test are presented in Figure 4, with the single crystal silicon sample
depicted on the left, and the A12024-T3 aluminum sample on the right. The measured
A2/At2 amplitude ratio is seen to increase with a constant slope for both materials as
expected, verifying a linear instrument and material response. A lower displacement
sensitivity level of less than one nanometer was also measured for the fundamental
ultrasonic field, which corresponds to a harmonic displacement sensitivity level of
approximately one picometer (after low-noise amplification and bandpass filtering).
Two-dimensional Imaging Studies
Two different types of spatially-resolved measurements were made in order to
evaluate the nonlinear ultrasonic 'imaging' capabilities of the system. These included bulk
acoustic wave (BAW), and surface acoustic wave (SAW) excitation/propagation. The
results of the BAW study are presented in Figure 5, where the A12024-T3 aluminum
material standard was used. Displacement field images for the fundamental (5 MHz) and
harmonic (10 MHz) signals are shown on the right. A plot depicting cross-sectional cuts
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D is placement (a. u.)
— 2nd Harmonic — Fundamental Squaredl
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Axial Position (a.u)
FIGURE 5. Fundamental and harmonic displacement field images for bulk acoustic wave propagation.
taken through each of the images is shown on the left. The images depict 8-bit, gray-level
representations of the out-of-plane displacement level at each position on the material
surface, where white represents large motions (nanometer for the 5 MHz image, and
picometer for the 10 MHz), and black represents zero motion. Both images show
circularly-symmetric displacement fields, which correspond to the expected far-field beam
profiles for a circularly symmetric excitation transducer. Although there are some
noticeable differences between the 5 MHz and 10 MHz images and cross-sectional cuts,
there is still an excellent spatial correlation between the fundamental and harmonic fields.
Differences in the beam diffraction characteristics of the 5 MHz and 10 MHz
frequencies are expected to cause spatial variations in the axial and transverse directions as
the ultrasonic waves propagate through the material [8]. In the far-field, the beam profiles
may, however, be sufficiently similar to allow for an point-by-point evaluation of the
nonlinear ultrasonic parameter, p. The choice of transducer, specimen thickness/travel
distance, and fundamental frequency would allow for some control over diffraction effects,
but it is anticipated that for this type of thru-transmission measurement, diffraction effects
would always need to be taken into account. It is also interesting to note that traditional
piezoelectric and capacitive measurements do not usually take into account spatially
varying effects, which can dramatically change the measurement results if alignment is not
precise, and at the very least will add noise or statistical variations to the measurements.
The results of the SAW study are presented in Figures 6 and 7, where again an
A12024-T3 aluminum material standard was used. Figure 6 depicts the fundamental and
harmonic displacement field images, as well as the A2/Aj2 amplitude ratio image.
Prominent beam-spreading is again evident in the images due to diffraction effects. The
spatial characteristics of the fundamental and harmonic displacement field images are
MHz
10 MHz
A2/A,2
SAW
FIGURE 6. Fundamental and harmonic displacement field images for surface acoustic wave propagation.
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FIGURE 7. Schematic diagram of nonlinear laser ultrasonic detection system.
however, not substantially different. This is further evidenced in the A/A^ amplitude ratio
image, which shows a nearly uniform ratio across the full lateral and axial extents of the
propagating SAW. For an isotropic, non-fatigued material, the A2/A:2 amplitude ratio
should be uniform across the entire material surface. The variations in the A/A^ amplitude
ratio that are observed are primarily due to a lack of signal where the SAW has not
propagated. Diffraction variations are again evident, but only constitute a minor variation
in the observed ratio, as shown in Figure 7. Axial variations were measured at only 0.24%,
while transverse variations were only 0.5%. A slight downward trend in the axial A2/Aj2
ratio was observed as the SAW propagated, while a slight Gaussian/Bessel curvature was
observed in the transverse profiles. Both of these effects can be attributed again to
diffraction effects and variations in how the 5 MHz and 10 MHz beams propagate.
Local Damage Measurements
The primary goal of this effort was to develop and use a nonlinear laser ultrasonic
system to assess the local fatigue/damage state of a material. In order to accomplish this
goal, a Ti-6Al-4V titanium sample was fractured under low cycle fatigue conditions (amax
= 850 MPa, f = 1.0 Hz and R = 0.1), and was characterized using a traditional capacitive
probe nonlinear ultrasonic technique and the nonlinear laser ultrasonic technique. Figure 8
b
1
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FIGURE 8. A 1.5 mm thick slice cut from the center of fractured Ti-6Al-4V cylindrical fatigue sample.
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SAW
FIGURE 9. Fundamental and harmonic displacement field images for a fractured Ti-6Al-4V fatigue sample.
shows a schematic diagram of the sample preparation after the fatigue/fracture test had
been completed. A 1.5 mm thick slice was cut from the central section of the broken
cylindrical dogbone specimen as shown in the figure. Both sides of the sample were
polished, and were made flat and parallel, to accommodate the capacitive detector
measurements.
The nonlinear laser ultrasonic displacement field image results (using SAW
propagation) are shown in Figure 9. Surface acoustic waves (10-cycle, tone-burst) were
generated in the grip region of the specimen and were propagated toward the fracture
surface in the gauge region. A bright/dark hatched region in the central portions of the
images can be noticed that is due to edge reflections from the sides of the sample as the
gauge region reduces in its transverse dimension. The two image fields show similar
spatial structure, however, the hatched region in the 5 MHz image is more pronounced.
Thru-Transmit Capacitive
10
15
* Nonlinear Laser Ultrasound SAW Data
20
25
30
35
Distance from Fracture (mm)
FIGURE 10. Variation of nonlinear parameter, beta, for the fractured Ti-6Al-4V fatigue sample.
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Figure 10 depicts the final capacitive and laser ultrasonic results showing variations
of the calculated nonlinear parameter, p, for the fractured Ti-6Al-4V fatigue sample. The
capacitive probe measurements were taken at eight separate locations along the axial
direction between the grip section and fractured edge. The laser ultrasonic measurements
were extracted from the local measured amplitudes of the fundamental and harmonic
image fields, and resulted in 120 measurement points along the axial direction.
The nonlinear ultrasonic parameter in the grip section (virgin, non-fatigued
material) was approximately 5, and grew to a value of approximately 20 near the fracture
surface for both the capacitive and laser ultrasonic measurements. This corresponds to a
large increase of more than 320%. As the distance from the grip section increased, the
nonlinear acoustic parameter increased almost exponentially (an exponential curve fit is
superimposed on the plot in Figure 10). The laser ultrasonic measurements did, however,
show a distinct modulation structure that is likely due to side-reflection effects (see Figure
10), and not due to actual variations in the spatially-resolve beta response. The basic trends
evident in both the capacitive and laser ultrasonic measurements are encouraging,
however.
CONCLUSIONS
A nonlinear laser ultrasonic system was developed and used to characterize the
fatigue state of a fractured Ti-6Al-4V sample. The system provides a means for visualizing
fundamental and harmonic displacement fields propagating as surface and bulk acoustic
waves. A series of tests were conducted using material standards to check system linearity,
harmonic and fundamental frequency fidelity, and measurement sensitivity limits. The
nonlinear laser ultrasonic signature of a fractured titanium dogbone specimen subjected to
low cycle fatigue was then investigated. The measurement results showed a dramatic
increase in the nonlinear parameter, p, near the fractured edge, that compared well with
capacitive probe measurements and theoretical considerations. Variations in the
propagating characteristics of the fundamental and harmonic fields were observed that
have been attributed primarily to diffraction and side-wall reflections effects. These
variations made it difficult to do a point-by-point, spatially-resolved evaluation of p.
ACKNOWLEDGEMENTS
The authors would like to thank and acknowledge the University of Dayton's
Center for Material Diagnostics (CMD) for their generous assistance and use of facilities
and equipment during this research effort. The authors would also like to thank Mr. Tim
Campbell and Mr. Ed. Klosterman for their assistance in the experimental measurements.
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