Characterization in Hostile Environments
Anthony Puckett, Ph.D.
Candidate; Michael “Mick” Peterson, Ph.D.
Advanced Inspection and
Monitoring Lab, University of Maine
A number of applications exist in materials
research where the ability to obtain real-time properties in a hostile
environment would greatly facilitate the development of new materials,
material treatments and manufacturing techniques.These hostile environments include extreme
temperatures, both high (2100 ºC) and low, extreme pressures, and corrosive
environments.Among the applications
are densification and sintering of ceramics, chemical vapor deposition and
infusion processes, float zone refining, and degradation processes such as
In-situ ultrasonic nondestructive monitoring has
been previously used in applications for material characterization [Peterson,
1994].Limitations on the operating
temperatures of traditional piezo-ceramics make it is necessary to isolate the
transducers from the environment.Solid
cylindrical waveguides have been used by a number of investigators to isolate
the ultrasonic transducers from the hostile environment in these applications
[Jen et al., 2001].Large diameter
waveguides are required for adequate energy transfer through the couplants and
sample.An ultrasonic pulse is used to
acquire length scale information about the material.The broadband nature of the pulse coupled
with the thick waveguide produces multiple dispersive propagating modes. The
multiple dispersive modes cause a broadband ultrasonic signal to expand in
time, Figure 1.This work explores
generation of a signal with compact support in the time domain with
experimental and analytical time reversal techniques.
Solid cylindrical waveguides made from optical
grade fused quartz can be used for temperatures up to 1200 °C.At higher temperatures (up to 2100 °C) a
single crystal sapphire waveguide is required.At high frequencies geometrical dispersion
is present in the waveguides for both cases, although material dispersion is
negligible.Geometrical dispersion in
cylindrical waveguides is a result of multiple paths and mode conversion at
the boundary.Spherical waves from a
point source can be represented by plane waves.The plane waves propagate along different
length paths from one end of the cylinder to the other resulting in different
arrival times.At each reflection a
longitudinal wave can excite a shear and longitudinal wave in order to satisfy
the boundary conditions.These two
phenomena cause the dispersion.Mathematically, the multiple dispersive modes are predicted by the
Pochhammer-Chree frequency equation.
Time Reversal Mirror
A time reversal mirror is used to
produce a signal with compact support in the time domain despite the
dispersive effects of the cylindrical waveguide.Time reversal and the time reversal mirror
are based on the property of time reversal invariance.For acoustics the concept is simply
described (Ing and Fink, 1998):
reversal invariance of the acoustic wave equation means that, for every burst
of sound diverging from a source - and possibly reflected, refracted or
scattered by any propagation media - there exists in theory a set of waves
that precisely retraces all of these complex paths and converges in synchrony,
at the original source, as if time were going backward.”
For the cylindrical waveguide this means that there
is a signal that will reconstruct in the waveguide to generate a pulse at the
opposite end.The time reversal mirror
(TRM) will determine this signal.A TRM
is the series of steps to recreate a signal at a source regardless of the wave
interactions between the receivers(s) and the source.The source and receiver are the transducers
at either end of a cylindrical waveguide, Figure 2.
Analytic Time Reversal
The time reversal mirror can also be implemented
with analytical inputs instead of experimental inputs.Model based sensors can create a more robust
system as well as providing the potential to interrogate modes separately.An accurate model that describes the
dispersion in a waveguide can be used to determine the time reversed signal
for any signal.The analytic model
currently being developed predicts the dispersed signal using the propagating
modes and the Pochhammer-Chree equations.The relative amplitudes of each mode are determined from the pressure
distribution on the end of the waveguide.A phase shift is calculated from the phase velocity of each mode at
each frequency.Finally, the modes are
summed over the end of the waveguide and averaged.Currently the models predicts qualitatively
the shape of the dispersed signal.Future work will be required to increase accuracy. Figure 5 shows the
analytic model and compares the analytical signal with the actual experimental
Figure 1. Effect of
dispersion in a solid cylindrical waveguide.The top graph is the excitation signal and the bottom graph is the
received signal at the opposite end of the waveguide.
38 mm dia.
Fused Quartz rod, 10 mm dia.
485 mm length
A cylindrical waveguide can be used in both a pulse
echo configuration and a through transmission configuration.The time reversal mirror is effective in
both configurations. The pulse echo configuration uses the same transducer to
send and receive the ultrasonic signal.Figure 4 illustrates the experimental set up of the pulse echo
configuration.However, for some
applications two waveguides are required since multiple reflections through
the sample cannot be received at a single transducer due to the high level of
attenuation within the sample.For
these cases a waveguide is placed on either side of the sample in a through
transmission configuration. One transducer sends a signal and a second
transducer receives the signal with the ultrasonic signal passing through each
waveguide once.The experimental setup
would be similar to the one in Figure 2 with a sample between two waveguides
replacing the single waveguide.
Figure 3. Signals in a
time reversal mirror.The signals from
top to bottom are: the original excitation signal, the dispersed signal, the
time reversed dispersed signal (new excitation signal), the new measured
signal, and the new signal reversed in time for comparison to the original
Figure 2. Through
transmission TRM experimental setup.
Future work is focused on refining and developing
the model.The analytical model shows
promise, but needs to be revised to be more useful.Experimentally, future work will included
applying the presented techniques to actual material characterization
Figure 6. Current
model (top) and comparison of experimental and analytic dispersed signals
R.K., and Fink, M. (1998). “Time-reversed lamb waves,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 45,1032-1043
•Jen, C.-K., Franca, D.R.,
Sun, Z., and Ihara, I. (2001). “Clad polymer buffer rods for polymer process monitoring,” Ultrasonics. 39,
G., Roux, P., Derode, A., Negreira, C., and Fink,M. (2001). “Generation of very high pressure pulses with 1-bit time
reversal in a solid waveguide,”
J. Acoust. Soc. Am. 110, 2849-2857.
•Peterson, M.L. (1994). “A High
temperature Ultrasonic Process Monitoring System Utilizing Signal Processing to Separate Multiple
Wave Guide Modes.” Ph.D. diss.,
•Peterson, M.L. (1999). “Prediction of longitudinal disturbances in a multi-mode cylindrical waveguide,” Experimental Mechanics. 39, 36-42.
For the TRM considered in
this research the desired signal is a pulse.The pulse contains sufficiently high frequencies such that the pulse is
distorted as it travels down the waveguide due to the different group velocities
of the mode in waveguide.The first
step of the TRM is to acquire this distorted or “dispersed” signal.This signal is reversed in time.When the reversed signal is now applied as
the excitation signal, the received signal has the shape of the original
pulse. This signal reversed in time will match the original excitation pulse.Figure 3 illustrates the signals involved in
the time reversal mirror.An advantage
of the waveguide is the symmetry normal to the cylinder axis at the center of
the waveguide allowing the receiver and source to be interchangeable.
38 mm dia.
Quartz rod, 25 mm dia.
mm in length
Research has been conducted using TRM with solid
cylindrical waveguides by Montaldo et al (2001). The work by Montaldo et al is
focused on developing large pressure pulses at point in a fluid for
lithotripsy.Signal accuracy is not
required, so multiple transducers are used on the end of a waveguide with a
1-bit method TRM for maximum energy generation.
The current research is focused on material
characterization, and the accuracy of the signals is critical.Current techniques use a single transducer
on the end of the waveguides.The pulse
echo configuration has demonstrated the ability to distinguish a change in
acoustic impedance at the end of the waveguide.Figure 5 compares received signals from the
previous experimental setup without and with an aluminum block on the end of
Figure 4. Pulse echo
Figure 5. Received
signals, without (top) and with aluminum block.
This research is sponsored by the Ballistic Missile
Defense Organization through the Office of Naval Research (ONR), Science
Officer Dr. Y. D. S. Rajapakse.