Non-linear SAW reflection: experimental evidence and NDE applications

Non-linear SAW reflection: experimental evidence and NDE applications I.Yu. Solodov, A.F. Asainov and Ko Sel Len t Department of Physics, Moscow State University, Moscow 119899, Russia t Department of Physics, Kim II Sung University, Pyongyang, Korea

Received 23 April 1992; accepted 24 June 1992

Acoustic non-linearity of the interface between solids that are pressed in contact has been experimentally demonstrated to make the principal contribution to the backscattered acoustic field of an incident SAW at high harmonic frequencies. Contact acoustic non-linearity has also been shown to represent a close simulation of non-linear elastic properties of fractured

defects in solids, whose non-linear reflection efficiency was found to be the highest. Consequently, non-linear SAW backscattering results in the primary detection of various kinds of surface imperfections in solids and has good prospects for the NDE of a wide range of materials with microcontact inhomogeneities.

Keywords: contact acoustic non-linearities; non-linear SAW reflection; nonlinear NDE Non-linear sound reflection in solids is a comparatively new type of non-linear acoustic phenomena which has been demonstrated by theoretical and experimental research of bulk acoustic waves 1'2 to be important for N D E applications. The interest in surface acoustic wave (SAW) reflection has been mainly concentrated on the problems of linear reflection by a system of topographic inhomogeneities a as a basis for the realization of frequency-sensitive components of acousto-electronic devices. Recent experimental investigations 4 have revealed the possibility of high local SAW non-linearity observation (the so-called contact acoustic non-linearity - CAN) in the region of mechanical contact between two optically polished solid-state surfaces. Such a contact interface can serve as an efficient source of non-linear SAW reflection and simulate acoustic non-linearity of the fractured defects in solids, which is of interest for N D E problems. In the present paper the results of experimental research into non-linear SAW reflection at the contact interface between solids, as well as into non-linear SAW scattering in the presence of crystal surface defects, will be presented. It will be shown that both processes include efficient backward SAW harmonic generation from the contact (defect) region. Highly non-linear behaviour of the interface elastic vibrations can be attributed to CAN mechanisms.

S A W non-linear reflection at the c o n t a c t interface The experimental set-up for non-linear SAW reflection investigations is similar to that used for CAN research 4. Interdigital transducers (IDTs) were deposited on the surface of a YZ-LiNbO 3 substrate (50 x 25 x 25 mm 3) for the incident 15 MHz SAW pulse generation (RF pulse amplitude up to 20V; pulse duration 0.1-0.2#s) see 0041-624X/ 93/ 020091-06 © 1993 Butterworth-HeinemannLtd

Figure 1. Analogous IDTs with central frequencies 15 and 30 MHz were used to detect the reflected (as well as transmitted) SAW at the fundamental (o9) and secondharmonic (209) frequencies. The insertion losses for SAW generation (detection) were measured to be - 6 dB and - 8 dB for co and 2o9 IDTs. The reflected wave pulses after amplification at the corresponding frequency (bandwidth />5 MHz) were observed on the oscilloscope screen. By measuring input and output pulse voltage amplitudes and IDT insertion loss one can determine the relative amplitudes of acoustic displacements for the incident and reflected waves and proceed with the calculation of reflection coefficient values for o9 and 209 frequency SAW. The CAN area was formed by pressing a glass sample (5 x 10 x 15 mm 3) against the substrate surface. The surfaces of the sample and substrate were optically

Load

1

2

3,

~

,

LiNbO3

"

~

J

Figure 1 Schematicdiagram of the experiment

Ultrasonics 1993 Vol 31 No 2

91

Non-linear S A W reflection." I. Yu. Solodov et al. reflection coefficient for the fundamental SAW K(~o) =

2

R 1 which undergoes saturation close to the value u,,/u ....

? £ x

== (3E

0

2

4

6

Load (MPa) F i g u r e 2 Linear and non-linear SAW reflection coefficients at different loads: O, K(~); [~. K2,.

40

g-A 3O >

3

=3 g o

20

g o

n

1.5 X 1 0 - 3 at high load magnitude. As was noted in Reference 5, insignificant fundamental SAW reflection is in accordance with the concept of Stoneley wave formation in the contact, whose velocity (v~, ~-3.48 x 103m s - a ) is only slightly different from the incident SAW velocity for YZ-LiNbO3 (VR --~ 3.43 X 103m S-1). The reflected second-harmonic SAW demonstrates entirely different behaviour: it reaches a maximum for partly clamped contact (at Pc ~_0.8MPa), when a CAN maximum for the transmitted (forward) SAW has also been observed 4. The dynamic properties of non-linear SAW reflection at the contact interface are shown in Figure 3. It is seen that the amplitude of the reflected second-harmonic voltage V2~, grows almost quadratically with the increase in the input voltage at the fundamental frequency IDT. At V,, > 5 V the non-linear reflection coefficient for the second harmonic SAW K 2 ~ ~ = Uz,o/u,o R 1 exceeds the value of the linear reflection coefficient K(og) for the fundamental SAW. This means that despite the small amplitude, the reflected wave becomes extremely non-linear: N = uR,,/ R ~-- K(e)) > 1, which is, probably, an exclusive feature U/u,~ in the contact area (Figure 4). Values of n obtained from the experimental data are

10

l 3.0

20

0

2

4

6

Input voltage V~ (V)

> E

Z

F i g u r e 3 Dependence of the reflected SAW second-harmonic output ( A ) and second-harmonic reflection coefficient (IS]) on the input voltage of fundamental frequency IDT; ( )K((o) 1.5

10

polished and thoroughly cleaned. In order to avoid the effects of losses associated with SAW propagation along the contact interface, the external load was distributed over the sample in such a way so as to localize the contact area near the front line of the glass sample, parallel to the incident SAW front (beam a p e r t u r e - 5 mm). The applied load magnitude (up to 5 x 10 6 Pa) was measured with a dial dynamometer; the location of the reflection area could be controlled by checking the delay of the reflected wave pulse. Figure 2 represents the dependence of normalized amplitudes of the reflected fundamental and secondharmonic SAW pulses on the contact pressure. From these data one can easily calculate the amplitude

92

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7

-o o

g

I

5 I---

I

I

2

4

6

Input voltage V~ (V) F i g u r e 4 Variation of the transmitted second-harmonic output ( 0 ) and incident SAW non-linearity factor (IS]) with the input voltage V.,; ( - - ) K2,,,.

Non-linear SAW reflection: I.Yu. Solodov et al. 20

400

500 A

×

~6

15 O

300 "~

¢J

E

~4

10

200 _~

J

200 O

c-i

~2

100

o 100 ~.

=E r-

c

}-E

I!

I

2

4

6

Conductivity (arbitrary units)

Figure 5 Dependence of the transmitted fundamental SAW ( [] ) and reflected second-harmonic ( A ) output voltage on the conductivity of the CdS sample; ( - - - ) corresponds to the square of the fundamental SAW

in excellent agreement with the theoretical estimations of this quantity according to the relation:

2

4

Conductivity (arbitrary units)

Figure 6 Dependence of the transmitted ( A ) and reflected ( [ ] ) second harmonic output on the conductivity of the CdS sample

generation due to the CAN. This leads to the considerable increase in the SAW higher harmonic reflection coefficient for the contact boundary in solids - the parameter worthwhile using in ultrasonic NDE applications.

u~o~ = r , No k~(u~)2x

4

where x = 0.75cm and the value of the LiNbO 3 non-linear SAW parameter, FLNO- 2.5 (Reference 6). By comparison with the numerical data of Figures 3 and 4 one obtains n - 2 K2,o and, hence, u2Ro~-~ 0.5 U2¢o, i while R ~- 1.5 x 10-3 uo~. i Much more efficient from Figure 2: u~o second-harmonic reflection leads to an amplitude increased over two orders of magnitude in the reflected SAW, N / n - 4 x 102, which physically can be provided by double frequency backward SAW generation in the contact due to the non-harmonicity of the interface elastic vibrations. This fact can be confirmed experimentally if one tries to change the acoustic non-linear properties in the region between the generating IDT 1 and the contact area which could be realized, for instance, by placing a piezosemiconductor crystal on the substrate surface. It is well known (see, for example, Reference 7) that linear and non-linear SAW properties in such layered structures are strongly influenced by acousto-electronic interaction. As a result of acousto-electronic attenuation the amplitude of the fundamental SAW decreases (Figure 5), while acoustic non-linearity and the transmitted secondharmonic grows with the increase in the semiconductor (CdS) conductivity ~r (Figure 6). According to the experimental data of Figure 5 the reflected SAW second-harmonic behaviour is not similar to that for the transmitted SAW, which one would expect for the 'passive' second-harmonic reflection, but instead is determined by the fundamental SAW amplitude in the contact area. The assumption of the quadratic relation vRo,(a) ,~ [ V~(a)] 2 (see also Figure 3) results in a fair agreement between calculated and experimental data

(Figure 5). Hence, non-linear SAW reflection at the contact interface is accompanied by efficient backward harmonic

Non-linear SAW scattering by surface defects in crystals The highly non-linear characteristics of the contact boundary could be attributed to the following nonlinearity mechanisms of the elastic vibrations: Hertzian non-linearity 8, 'flapping' non-linearity 9, stress concentration at the surface asperities, etc. The conditions for such types of CAN display can be met for a wide range of microinhomogeneous media and compositie materials containing grain boundaries, structural frames, cracks and analogous continuity defects with microcontact regions. Therefore, experimental research of the acoustic non-linear properties for different kinds of defects in solids may be of interest for non-linear NDE of the materials and constructions 1° important for aviation technology, nuclear power engineering, microelectronics, etc. In the present section the results of the experimental observation of the acoustic non-linearity for single surface defects will be given. In the experiment we used the SAW non-linear reflection technique described above. Figure 7 shows microphotographs of the three main defects produced on the surface of the YZ-LiNbO3 crystal at distances of -~ 15, 20, 25 mm, from the 15 MHz SAW generating IDT 1 (see Figure 1). In Figure 8a one can see the oscilloscope picture of the fundamental frequency SAW pulses (z = 0.1 #s) reflection, detected with IDT 3. The positions of the pulses reflected from the corresponding defects were determined on the output signal amplitude variation caused by small liquid drop deposition onto the crystal surface in the defect region, and are indicated by arrows in the figure. The additional reflected pulses in the figure are due to the incident SAW transformation into bulk waves, which accompanies the scattering by the defects and IDTs. The linearity of the scattering at the fundamental frequency is confirmed by the dynamic reflection

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Non-linear S A W reflection: I. Yu. Solodov et al.

ii!i~

Figure 8 Oscilloscope pictures of (a) the fundamental and (b) second-harmonic SAW reflected from the defects 1 - 3

A

> E 5 O

<

03

4

r-

2 "o

p

Figure 7 Microphotographs of the defects on the surface of LiNbO 3 crystal: (a) defect 1 ; (b) defect 2; (c) defect 3

characteristics shown in Figure 9. The slope of the straight lines in the figure allows one to determine linear reflection coefficient values; these figures are - 5 0 , - 6 0 and - 5 5 dB for defects 1-3, respectively. It should be noted, that they are determined not only by defect sizes

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1

|

I

2

4

6

8

Input voltage V~ (V) Figure 9 Variation of the reflected fundamental SAW signals for the defects 1 - 3 with the input fundamental frequency voltage: A - d e f e c t 2; A - d e f e c t 3; [ ] - d e f e c t 1

Non-linear S A W reflection: I. Yu. Solodov et al.

reflection coefficient are shown to be minimal (see Figure 9), whilst the cracking is the highest (Figure 7). A direct test of the non-linear SAW generation by the defects, as noted before, can be carried out by using the variation of the linear (dissipative) and non-linear acoustic properties of the non-defective part of the crystal. Unlike on the preceding section, for this purpose we used here a non-linear contact itself, formed by a glass sample and an LiNbO 3 substrate surface in the region between the radiating IDT and defect 1. In this case, the CAN leads to the increase in the calibrating second-harmonic SAW transmitted through the contact (at the optimal load ofpo --- 1.2 MPa) (Figure 12). The oscillations of the

A

> E

4

O

.u_

3

E to

2

ID

== n-

25

1

20 0

2

4

6

8

10

Input voltage Vto (V)

Figure 10 Variation of the reflected second-harmonic signals for defects 1 - 3 with the input fundamental frequency voltage: I - d e f e c t 2; D - d e f e c t 1 ; A - c a l i b r a t i n g second-harmonic SAW ¢-

(correspondingly, ~350, ~70 and ~350#m), but also by the divergence of the quasi-cylindrical backscattered SAW and its detection losses with plane IDT electrodes (aperture "~8 mm). Essentially different non-linear behaviour demonstrates dynamic reflection characteristics in the detection of the SAW second harmonic (Figure 10). Here, one can also see the curve, corresponding to the second-harmonic SAW generated due to material non-linearity of LiNbO 3, reflected from IDT 5 (Figure 1) at the opposite side of the crystal, and which will be used as a calibrating second-harmonic wave. The oscilloscope picture for the reflected second-harmonic SAW (Figure 8b) also displays a significant difference from the linear case. First of all, it demonstrates a lack of parasitic reflected signals. According to the picture, the efficient non-linear reflection takes place for nothing but defects 1 and 2: the amplitude of the SAW non-linearity reflected from defect 3 is negligible. Referring to the microphotographs one can easily see that the special feature of the latter photograph is the quite-rounded shape, unlike the sharp-edged defects 1, 2. In addition, one can also notice subsurface cracks in the pictures of defects 1 and 2. These factors, evidently, testify to the possibility of the microcontact area formation for defects 1, 2 (contrary to defect 3) which could display CAN properties and lead to the SAW non-linear reflection effects described above. To confirm that SAW non-linear scattering has nothing to do with the reflection of the SAW second-harmonic generated in the non-defective part of the crystal, we proceed with the numerical calculations of the reflected SAW non-linearity. Similar to the above, from Figures 9 and 10 one obtains the values of the non-linearity factors N~ = ~U2o~/R/~uo~Rfor a SAW reflected from the ith defect. The data presented in Figure 11 show that N~.2 >> n (see also Figure 3), this is evidence of non-linear generation of the backward second-harmonic SAW by the defects. It is worthwhile noting that the maximum non-linearity factor N corresponds to defect 2, whose size and linear

-T 10 co

z

0

I

I

I

I

2

4

6

8

10

Input voltage V~ (V)

Figure 11 Calculated values of the non-linearity factors for SAW reflected from the defects: A - d e f e c t 1 ; l~-defect 2 60

:=L

% 50 P x

~ 4o O

.2 ¢O

"O tO

~ 20

"O

10 t

0

1

2

3

4

5

Load (MPs)

Figure 12 Dependence of the reflected and transmitted SAW second-harmonic output on the contact load: A - d e f e c t 1; ~ - d e f e c t 2; E3-calibrating second harmonic SAW-°VR, o (p)

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Non-linear SAW reflection. I. Yu. Solodov et al. 20

20 A

>

"T

=L

C)

%

v

x

15

== E

10

15~ -I O

!

.__

2: E 0

g

E t-0

2

4

6

Load (MPa) Figure 13 Variation of the transmitted fundamental SAW output voltage (1~) and second harmonics reflected from defects 1 ( A ) and 2 (/k ) with the contact load; ( - - - ) corresponds to the square of the transmitted fundamental SAW

°V~(p) curve are due to the inhomogeneity of the contact over the SAW beam aperture. On the contrary, the amplitude of the fundamental SAW incident on the defects decreases as the contact pressure increases (Figure 13), this was explained 5 by partial redistribution of the elastic energy into the glass sample. As illustrated in the same figure, the amplitude of the second-harmonic reflected from defect 2 is not related to the growth in the incident second harmonic (calibrating SAW) at p = P0, but reduces roughly proportionally to the square of the fundamental SAW amplitude variation in the defect area. It allows one to conclude that SAW non-linear scattering by the defect is also not due to 'passive' reflection of the incident SAW harmonics, but results from the non-linear generation of the second harmonic by the defect itself. A similar remark is applicable mainly to defect 1 ; however, the slight increase in 1 V2,,,(P) R at p = Po (see Figure 12) is, obviously, attributed to the presence of the linear scattering component for the incident second-harmonic SAW. In this assumption from the data of Figure 12, one obtains the background level of the linear scattered second harmonic for defect l" LV2,,) R ~ 1V2~,)(po)/3, R and attains 5% of the total amplitude of the reflected second harmonic SAW ( V2o)). R " L U2w/U2w R R Since = K(2w)n/K(w)N, this estimation, along with the experimentally determined values n and N (see Figures 4 and 11), leads to the physically acceptable relation between the coefficients of linear reflection for the fundamental and doublefrequency SAW at defect 1: K ( 2 w ) / K ( w ) ~- 2.5. Finally, it should be noted that non-linear SAW

96

Ultrasonics 1993 Vol 31 No 2

scattering effects are subject to long-time (hours, days) ageing as can be seen in the reflected harmonics' amplitude decrease in time without any visible change of the defect structure. As a rule, the efficiency of defect non-linear scattering could be recovered after thorough cleaning of the crystal surface with a solvent. In our opinion, this can be attributed to the removal of microparticles which prevent CAN manifesting itself as elastic vibrations of the fractured surface defects.

Conclusions According to the experimental data presented, acoustic non-linearity of a contact interface can be considered as a close simulation of non-linear elastic properties of defects in solids, and makes a principal contribution to the backscattered higher harmonic acoustic field of the incident SAW. This is particularly valid for surfacefractured defects whose non-linear reflection efficiency was found to be the highest. Consequently, C A N may be regarded as one of the fundamental mechanisms of acoustic non-linearity for such kinds of imperfections in solids and in a wide range of materials with microcontact inhomogeneities. The data obtained also illustrate the intrinsic difference between the results of linear and non-linear acoustical imaging of the defects in the reflection mode: in the latter case one can attain primary detection of the fractured defects being the sources of CAN and the forerunners of the main cracking and subsequent fracture an extremely important performance for ultrasonic N D E systems.

References 1 2 3 4 5 6 7 8 9 10

Shui, Y. and Solodov, l.Yu. Nonlinear reflection of bulk acoustic waves in solids Proe II WESTPA Hong Kong (1985) B1-6 188-192 Nigul, U.K. Nonlinear Acoustodiagnostics Sudostroyenie, Leningrad 1981 ) (in Russian) Guliaev, Yu.V. and Plessky, V.P. Surface acoustic waves propagation in periodic structures Uspekhi Phisich Nauk (1989) 157( 1 ) 85 127 (in Russian) Ko, Sel Len. Severin, F.M. and Solodov, l.Yu. Experimental observation of contact acoustic nonlinearity for bulk and surface acoustic waves Soy Phys Acoust (1991) 37 1165 1169 Asainov, A.F., Ko Sel Len and Solodov, l.Yu. Experimental observation of Stoneley wave on the contact interface between solids Soy Phys Acoust (1992) 38(3) 536-540 Solodov, I.Yu. Nonlinear acoustic and acoustoelectronic interactions on the interface between solids DSc Dissertation (1989) Moscow State University, Moscow, Russia Mozhaev, V.G. and Solodov, I.Yu. Second harmonic generation of acoustic surface waves in a layered piezoelectric insulator semiconductor structure Sot, Phys Acoust (1980) 26(3) 236-240 Landau, L.D. L!fshitz Theory qfElasticity Moscow, Nauka (1987) (in Russian) Richardson, J.M. Harmonic generation at an unbonded interface I. Planar interface between semi-infinite elastic media. Int J Eng Sci(1979) 17(1)73 85 Buck, O. and Thompson, R.B. Acoustic harmonic generation for measurement of plastic deformation and fatigue Int Syrup Nonlinear Acoustics (1976) Blacksburg, USA, Abstracts 95-98