Download Optical Measurements of Interface Acoustic Waves Guided by the

OPTICAL MEASUREMENTS OF INTERFACE ACOUSTIC WAYES GUIDED BY
THE BOUNDARY BETWEEN TWO ELASTIC SUBSTRATES
Ch. Mattei:, X. Jia and G. Quentin
Groupe de Physique des Solides, Universites Paris 7 et Paris 6
Unite associee au CNRS n017, Tour 23,2 place Jussieu
75251 Paris Cedex 05, France
INTRODUCTION
Surface acoustic waves propagating at the interface between two solids are very
important for Non Destructive Evaluation of layered media [1]. Dispersion features and
transmission losses of such waves strongly depend upon the elastic constants of the
solids as well as the mechanical boundary conditions at the interface between the solids.
One particular kind of interface waves is the Stoneley wave, which can exist at the
interface between certain specifically combined elastic half-spaces in rigid contact [2].
The acoustic field of this wave, travelling with no loss along the interface, decays away
from the interface in each medium (Fig. la). Murty studied interface waves in another
extreme case, i.e. slip contact [3]. For such type of contact, only the normal stress and
displacement components are continuous but shear stresses are cancelled at the interface.
In the slip contact case, Murty's study revealed also that the conditions of existence of the
Stoneley-like wave are much less rigorous. When material combinations and/or boundary
conditions are not satisfied to support the Stoneley-like wave, interface waves may
become lossy [3] and radiate acoustic energy through mode conversion into bulk waves
(Fig. Ib), like the case of the leaky Rayleigh wave propagating at a solid-liquid interface.
Besides, if the presence of a coupling layer between the two half-spaces is taken into
account as in most practical conditions, the features of interface waves depends also on
the viscoelastic parameters and thickness of the coupling layer[4,5]. Up till now, most of
Review of Progress in Quantitative Nondestructive Evaluation, Vol. 14
Edited by D.O. Thompson and D.E. Chimenti, Plenum Press, New York, 1995
409
medium 1
medium 1
x
medium 2
z
z
a)
b)
Figure 1 Representation of Stoneley-like wave (a) and leaky interface wave (b)
propagating along the interface between two solids.
the investigations involving interface waves are indirect ones using ultrasonic reflection
and transmission measurements [6], and some others are related to dispersion
measurements using interdigital or wedge transducers [4,5]. Few experiments were
reported illustrating the field distribution of interface waves. Claus and Palmer observed
the Stoneley wave [7] using an optical interferometer. The wave displacements were only
detected by the probe beam focused at the Nickel-Pyrex interface.
We describe in the present paper another optical detection method that not only permits
velocity and attenuation measurements but also gives access to the field distribution of
interface acoustic waves strains provided the solids are optically transparent. This optical
method, combining interferometry with photoelastic interaction, was previously used to
measure bulk, Rayleigh and Lamb waves [8-10]. In this work, the interface waves are
investigated at the following interfaces: Silica/Silica, Silica!Tungsten, and Silica/
Plexiglas. Two limiting boundary conditions corresponding to a slip contact and a rigid
bond are basically investigated. The effects of the coupling layer upon interface waves is
being also studied.
PruNCWLEOF OVITCALDETECTlON
Fig. 2 shows schematically the arrangement used to study interface waves. A
water wedge transducer is used to generate a Rayleigh wave upon one substrate. When
the Rayleigh wave reaches the interface between the two substrates, one part of the
incident wave power is converted into interface waves. As shown in Fig. 2, the laser
beam crosses normally the acoustic beam inside the transparent solid. Because of the
photoelastic effect, the laser beam undergoes an additional phase shift caused by
ultrasonic waves. According to a detailed analysis, this optical phase shift induced by
guided waves can be related to the acoustic strains by [10]:
410
ro
-
ro
n3
A<l> = (c) An L = (c) L2" (Pll +pIi) (Sxx +S;u)
Here ro, c are respectively the angular frequency and the speed of the light, L is the
acoustic beam width, An is the mean index of refraction variation, n is the initial index
and Pij are the photoelastic coefficients. As shown, the induced optical phase shift A<l> is
proportional to the sum of acoustic strains A = Sxx + Szz, that is, the dilatation, or relative
change in material volume of the solid. With the help of an heterodyne interferometer,
this phase shift is demodulated and calibrated at the output [8, 11], giving the value of the
dilatation associated with guided interface waves propagation. By moving the probe beam
along the X and Z axes, respectively, the velocity, attenuation and dilatation field of the
interface waves can be measured.
In this work, three different material combinations fonning the interface waveguide are
investigated: Silica/Silica, SilicalTungsten, Silica/Plexiglass. The slip contact at the
interface is realized with a very thin layer of water between the two optically polished
substrates. To approach rigid contact condition, the two substrates are bonded by a glue
film with a thickness far smaller than the ultrasonic wavelength. Broadband pulses as
well as tone bursts are used to generate the Rayleigh wave. The signal received from the
probe is sampled and averaged by a digital oscilloscope and then recorded and plotted.
RESULTS AND DISCUSSION
For each combination of materials, the present optical method allows us to
measure the wave velocity and the attenuation along the propagation direction, and also to
explore the dilatation field distribution in the solids if they are transparent. The first
experiment was performed with the Silica/Silica combination which supports theoretically
Light probe beam
Figure 2
Arrangement for investigating interface waves by optical detection.
411
a Stoneley wave for the slip contact conditions. The fact that the two solids are
transparent allows us to explore the dilatation field on each side of the interface. Figure 3
shows the typical time signals measured on both sides. The measured value of the wave
velocity is 3400 mIs, equal, within experimental errors, to that of the Rayleigh wave in
Silica predicted by the theory for two identical half-spaces [3]. The two dilatation signals
with 1t-phase shift have the same amplitude because we have identical materials on both
sides. This 1t-phase shift is due to the flexural characteristic of the boundary motion.
Figure 4 shows the dilatation field distribution of the Stoneley-like wave measured at
different depths from the interface in each solid. This experimental result is in good
agreement with the calculated decays of dilatation fields for the Stoneley wave
(continuous lines). In the case of the rigid contact, the two identical solids become
mechanically a single one and no interface wave can exist. This has been confirmed by
measurements using rigidly bonded Silica/Silica interface, in which only a shear bulk
wave was detected.
The same investigations were done for the Tungsten/Silica combination. An interface
wave, propagating along the interface without measurable loss, is detected for the two
boundary conditions. The velocity of the interface wave is 2730 m/s for slip conditions
and 2860 m/s for the bonded conditions. These measured velocities are in good
agreement with the velocities calculated by Murty [3]. This combination represents the
case where a Stoneley wave exists for both slip and bonded conditions.
Silica/Plexiglass corresponds to a material combination that is theoretically unable to
support a lossless Stoneley-like wave whatever the boundary conditions are at the
interface [3]. Fig. 5 shows dilatation fields of the corresponding interface wave obtained
in each medium. Inside Silica, an exponential decay is measured but in Plexiglas little
decay is seen. This field distribution looks like that of the Rayleigh wave propagating at
the fluid-solid interface: a leaky Rayleigh wave in Silica with a bulk wave radiated in
Plexiglas.
When the coupling material becomes viscous and acoustically thick, the properties of
interface waves become much more complicated [4-6]. In this experiment, we present
only attenuation measurements. A coupling film used for shear transducers is inserted at
the Silica/Tungsten interface. Two thicknesses of the coupling film approximately equal
to 60 11m and 200 11m are used. The interface wave propagates along the interface with an
attenuation due to the presence of the viscous film. The attenuation of these waves is
obtained using a spectral analysis method [12]. Figure 6 presents the measured
attenuation versus frequency for different coupling thickness. It is seen that the
attenuation is higher when the layer of viscous coupling is thicker. The comparison of
these preliminary results with theoretical models is in progress.
412
o.
o.
z = - O.Olmm
o.
e o.
'2
Cfl
Cfl
'2
E.N o.
N
N
N
+
><
+
><
><
><
Cfl -0.
Cfl_O.
-0.
-0.
-0.
4
Figure 3
= +0.01 mm
o.
6
8
10
12
14
-0.
IlS
4
10
6
12
14
Dilatation waveforms of the interface wave propagating at the slip interface
between two Silica half-spaces measured on both sides of the interface
1.2
N
N
S
C/l
+
e
X
J; 0.8
If \
OJ
~ 0.6
Ci
E
'"
-g0.4
.!:l
(ii
§ 0.2
z
o
Silica
L.~
~
L
!.
.............
-r
~
"-
I~
z/l.
-0.5
-0.3
-0.1
0
0.1
0.3
0.5
Distance from the interface (normalized by wavelength)
Figure 4
Measured dilatation amplitude of an interface wave propagating along the slip
interface between two Silica half-spaces. Continuous lines represent the theoretical
decays.
413
N
N
•• i..
en
~
~ 0.8
~
1l 0.6
~
]
.i ..•.....
, ...... j... .
Silica
h~lf-space
i
i···; • ••
i Plexiglas~ half-spa e
i.
~
.. f....................... .....
......... -:- ...................•...
.i
0.4~----~i--~.~~--+-~------~------~
1
o 0.2
Z
i ••
.......................... ~ .............................+ ......................... j....
o~-'-~'---l--c~-'-~-'-L-'----i--c--c~-+~--'--'-~ z fA
-0.5
-0.3
-0.1
0.1
0.3
0.5
Distance from the interface (nonnalized by the wavelength)
Figure 5 Dilatation field distribution of the leaky interface wave propagating at the slip
boundary between Plexiglass and Silica.
5
--e=60/lffi
8'u
-~
S
~
4
c-----j
- - - e=200/lffi
3
0
.~
::s
~
2
~
<:
o
0.5
Figure 6
...
~
'" '"
,,"
",'"
.....
--"'-
1.5
2
-- '"
-
2.5
Frequency (Mhz)
Measured attenuation of the interface wave propagating at the interface
between Silica and Tugsten. The coupling is achieved by a film of viscous coupling of
thickness 60 Ilm and 200 Jlill
414
CONCLUSION
An interferometric detection method for acoustic dilatation measurement inside
transparent solids has been applied to study the propagation of interface acoustic waves.
In addition to velocity and attenuation measurements, the present interferometric method
allows us to identify the confined or leaky natures of acoustic waves guided by the
interface with slip or rigid contact. The attenuation of interface wave caused by the
presence of a coupling viscous fllm between the solids has been also investigated.
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2. R. Stoneley ,Proc. Roy. Soc. London, A-106, 416 (1924).
3. G.S. Murty, Physics of the Earth and Planetary Interiors. 11,65 (1975)
4. P.W Staecker and W.C Wang, J. Acoust. Soc. Am. 53 (1),65 (1973).
5. S. Rokhlin, M. Refets and M. Rosen, J. Appl. Phys. 51, 3579 (1980)
6. S. Rokhlin and Y.J Wang, J. Acoust. Soc. Am. 89 (2),285 (1991).
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11. D.Royer and E Dieulesaint, Proceedings of 1986 Ultrasonics Symposium,
(IEEE, New York, 1986), p 527.
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