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Materials testing by ultrasonic spectroscopy
Materials testing by ultrasonic spectroscopy A. F. BROWN
Ultrasonic spectroscopy is a development of the pulse-echo technique which uses broadband (0.5-10 MHz) ultrasound and analyses the spectra of the echo pulses. It has already proved its value in cases where the geometry is essentially two-dimensional. Examples include the determination of grain size in metals and quality control in carbon-fibre composites and glued joints, while a new development has opened up the possibility of measuring the depth and width of surface cracks down to sub-millimetre size. When the problem is essentially three-dimensional, as in characterization of discrete defects in metals, full interpretation of the echo signal cannot as yet be achieved except in a few special cases. This paper is the first of two reviews on ultrasonic spectroscopy. the generation and reception of wideband ultrasound.
Introduction The name ‘ultrasonic spectroscopy’ seems to have been first used by 0. R. Gericke who devised and patented 1 a device whereby ultrasonic echo pulses from internal discontinuities in a test specimen could be displayed on an oscilloscope alon with their frequency spectra. Basically the idea is simpl$ : in . conventional ultrasonic inspection techniques the ultrasonic frequencies are limited to a narrow band, so the information has to be deduced solely from amplitude variations. Broadband techniques, by analogy with visual inspection with white light, give additional information corresponding to the colour of the inspected item. The experimental difficulties of producing and receiving pulses of ultrasound of the desired bandwidth are formidable since transducers of a new type have to be made and excited. Provided the signals they receive can be converted to broadband ac, commercial spectrum analysers are ,available, but at such a price as to make them unattractive for routine testing. While the development of practicable equipment (wideband transducers and their excitation sources, wideband amplifiers, spectrum analysers and spectrum-free gates) has been an essential part of the development of ultrasonic spectroscopy, this review will do little more than refer to them and will concentrate on their applications to materials testing. Furthermore, the discussion will be confined to the pulse-echo method of ultrasonic testing: for other methods, in particular sweptfrequency techniques and through-transmission techniques, the reader is referred to a recent article by Gericke.3 Professor A. F. Brown is in the Department of Physics, The City University, London, UK. He is currently a visiting professor in the Department of Physics, Western Australian Institute of Technology, South Bentley, Australia. Paper received 12 February ,1973.
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The second will cover
There are three main fields in which ultrasound is used in materials testing. These are the detection and characterization of discrete defects, the study of extended interfaces and the investigation of the properties of bulk materials. Although all are interrelated, it is profitable to discuss them, and the application of ultrasonic frequency analysis to them, separately. Properties of the bulk material Grain
size determination
The use of ultrasonic spectroscopy in grain size determination has been illustrated by Gericke 2 who interrogated metal plates with broadband ultrasound. In these experiments the loop response of the transducer, as measured with an aluminium test plate, showed a frequency characteristic with two well defined humps centred on frequencies of about 3.5 and 6 MHz respectively. The corresponding loop frequency responses of steels of varying grain sizes showed that, as the mean grain size increased from 0.05 to 0.10 mm, the ratio of the heights of the two frequency humps changed, the higher frequency being preferentially attenuated by coarser grained material. Comparison of relative attenuation of more closely-spaced frequencies ~ for example by attempting to account for changes in the shape of each hump in Gericke’s published spectra ~ does not yield such a simple law. Presumably this is because such detailed structure is affected by the distribution of grain size around the mean and explains why a wide spectrum of frequencies is needed to give an unequivocal measurement of the mean. Lloyd 4 has attempted to construct a mathematical model to describe the frequency dependence of grain boundary scattering. The model, which is similar mathematically to
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that used to describe the response of discrete targets in a later section, adds up the time domain responses of many small grains randomly distributed throughout the matrix. While the model is probably more applicable to the case of a dispersed precipitate than to that of grains which fill up the whole volume of the matrix, two predictions of the theory have been confirmed by experiment. The first of these is that the back-scattered spectral response from coarse-grained material should have a lower-frequency cutoff than that from fine-grained material: this is demonstrated by experiments on gunmetal shown in Fig.1. Here the frequency characteristics of the transducer were uniform in the range shown and the curves were obtained under identical conditions of amplification. The second prediction of the theory is that the amplitude of the response at a given frequency should be proportional to the product of the number of scattering centres and their reflectivity. The first inference of this second prediction is that the back-scattered response will be low for very coarse material, increasing as the grain size decreases. The correctness of this is also shown by Fig.1 but a second inference is that the increase in response will come to a maximum and fall again as the material becomes very fine grained. This predicted maximum has not yet been observed but it is doubtful if the model can be taken, without further consideration, to apply to very large grains from which, as mentioned below, a collimated beam can be specularly reflected. A dark-field
ultrasonic
Y Transducer
a
Specular reflectionfrom
-face
technique
Free surface
A useful technique in ultrasonic examination of bulk material has been developed by following up a theoretical observation of Bhatia 5 who calculated the polar diagrams for scattering by systems of discrete centres. Applied to the problem of detection of sub-surface scattering centres such as the metal grains described above, theory suggested that maximum back-scattered energy would be in the direction straight back to the transducer while the surface would behave more like a mirror. Thus with the transducer axis normal to the free surface (Fig.2a), echoes from subsurface features are superposed on echoes from the surface. However, if the transducer axis is inclined at an angle 6 to the surface, response from sub-surface features is still preferentially directed back to the transducer but the sur-
\\\\\\\\’
11’
\\\\“\‘\““”
Dark-field ultrasonics. Polar diagrams for reflection from Fig.2 sub-surface feature: a - normal incidence; b - angle-probe technique
face echoes are specularly directed away from the transducer. The dark-field technique shown in Fig.2b with 0 - 25 degrees provides an alternative to electronic gating for removing the effect of a noisy surface, and is more delicate than gating in allowing study of immediate sub-surface features. The technique has been used for the grain size experiments described previously and for the experiments on carbon fibre reinforced plastics described below. Carbon
2 MHz Fig.1 Variation of frequency response with grain size for two specimens of gunmetal. Top trace: fine grain (-1 mm). Middle trace: coarse grain (-5 mm). Bottom trace: frequency calibration, the peaks are at 2 MHz and 6 MHz
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fibre reinforced
plastics (CFRP)
CFRP is a difficult material to test because the large specular return from the surface in water swamps the response from sub-surface features. This difficulty has been overcome by use of the dark-field or angle-probe technique described above. In Fig.3 back-scattered energy in the frequency ranges l-3 MHz and 4-6 MHz has been integrated and displayed
203
on an x-y plotter against distance along the central axis of a test piece of CFRP. All traces were made with identical geometrical set-up and amplification. The two lowest traces show responses in these two frequency ranges from a virgin specimen of high-quality material. The topmost curve shows the total energy back-scattered in the l-3 MHz range from a similar specimen after torsional fatigue to an estimated 50% of fatigue life. The next highest curve similarly shows the total energy in the 4-6 MHz range from the same specimen. There was no visible indication of fatigue damage. In terms of Lloyd’s model for scattering from grains or precipitates in a matrix, these four curves may be interpreted as follows: in virgin specimens there are few scattering centres; back scattering is of small amplitude and all frequencies are treated alike. Fatigue damage leads to nucleation and growth of distributed scattering centres and to reduction in high-frequency response relative to low frequency. A complication arises with high damage for then the scattering centres become large enough to reflect the better collimated high frequencies directly back to the transducer.
and the maintenance of their shape after passage through the specimen. Secondly, the frequency analysis part of ultrasonic spectroscopy is an aid to measurement of transit times between features when these times are comparable to, or even less than, the normal pulse length. Pulse shaping by wideband
techniques
Conventional pulse-echo equipment tends to be monochromatic, the pulse of nominal length At being generated by a few cycles of ac at a high frequency which might typically be about 5/At. Using wide bandwidth techniques, however, a square pulse of length At can be generated by use of a band of frequencies the highest of which need not exceed 1/At. When the pulse is required to go deep into the medium, the higher frequencies in the band are preferentially absorbed, which is equivalent to lengthening the pulse. Resolution can, however, be restored by differential amplification of the higher frequencies. This is the sweptgain technique.6 Bonded structures
application of ultrasonic spectroscopy to quality testing of interfacial bonds is conveniently introduced by consideration of some structures devised by Weight 7 who made up a test piece consisting of two sheets of aluminium glued together (Fig.4). A number of simulated debonds were introduced by milling slots of various widths I and about 2.50 pm deep into one surface as shown. The
Extended interfaces An extended interface is defined as a region of acoustic mismatch between two media, the area of which is larger than the area of the cross-section of the ultrasonic beam. There are two problems. Firstly, finding the position and mapping the region of acoustic mismatch which may vary in depth below the accessible surface, and secondly, measuring its properties in terms of the degree of mismatch which may vary from place to place over the interface. The contribution of ultrasonic spectroscopy to the problem of characterization of extended interfaces is shown below to be twofold. Firstly, the availability of wideband techniques is an aid to generation of high resolution short pulses
126mm 1
i-
~tl=o%Wtl Fig.4
t2=205mm
Demonstration
/, =3mm
/2
q6mm
test piece
Fig.3 Frequency dependence of back-scattering by CFRP. Horizontal scale: distance along the central axis of a CFRP plank approximately 100 mm. Vertical scale: energy integrated over each frequency range (all curves are at the same amplification). Bottom traces: integrated energy in the ranges 1-3 MHz and 4-6 MHz from a virgin plank. Middle trace: integrated energy in the 4-6 MHz range from a plank fatigued to 50% of expected life. Top trace: integrated energy in the range l-3 MHz from the same plank fatigued to 50% of expected life
204
ULTRASONICS.
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Transducer
I I
-
Distance
Fig.5 Detection of debonds in the test piece: a - top trace shows echo from a well bonded area, bottom trace shows corresponding spectrum; b - top trace shows echoes from a debonded area, bottom trace shows corresponding spectrum; c - bottom trace shows spectrum of a with water/metal surface reflection gated out, top trace shows corresponding time-domain signal; d 2 bottom trace shows spectrum of b with water/metal surface reflection gated out, top trace shows corresponding time-domain signal (time 1 ps per division: amplitude linear; frequency 0.5 MHz per division: amplitude linear)
A good bond is a region of good acoustic match and little incident energy is returned from the glue/metal interfaces. The simulated debonds, however, are regions of large acoustic mismatch and give large reflections. If the test piece had been sufficiently thick these reflections could have been resolved in the time domain from reflections from the other interfaces. Fig.S shows what is in fact observed when a pulse-echo test is carried out by a water immersion technique using ultrasound with approximately uniform spectral content in the range 0.5-8 MHz. In Figs 5a and b, the top traces of which show the echoes from a well bonded and a debonded area respectively, the first peak is the response from the water/metal interface and this is followed by a series of waveforms set up by multiple reflections within the plate thickness. The lower traces in each case show the corresponding spectra: that in FigSa is similar to the transducer spectrum but shows modulations corresponding in frequency to the reciprocals of times between reflections. The lower trace of FigSb shows the spectrum corresponding to a debonded region: here the modulation is at a higher frequency corresponding to the shorter distance from the water/metal interface to the debonded interface. Considerable simplification of these spectra is obtained if the signal gate is set so as just to exclude the water/metal surface reflection. These are shown in the lower traces of Figs 5c and d with their corresponding time domain signals above them. Referring to the spectrum in Fig.Sd, the first small maximum corresponds to a reflection from the back surface of the test piece and the height of this maximum is a measure of the amount of energy by-passing the debond and reflected from the back surface. When the width of the debond 1 is comparable with the beam width, the maximum is small as shown, but increases as I decreases. This suggests a testing procedure wherein the
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Scan
along test
piece
-+
IIOmm
Display with a section of test piece superposed on it. The Fig.6 linear scales are equal
d
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signal gate is set to exclude the water/metal interface reflection and the spectrum analyser is set to filter out only the first spectral maximum due to the debond. A display with the horizontal axis representing distance along the test piece and the vertical axis representing the time integral of the output of the spectrum analyser will then allow debonded regions to be easily identified. Fig.6 shows such a display with a section of the test piece superposed on it on the same linear scale: the spacing of the debond maxima is correct and their heights correspond to their extent. If the specimen is scanned by successive sweeps of the interrogating beam this display technique can readily be converted to B-scan. While in Fig.6 the debond pattern is clearly resolved, this in fact sets a new problem, for a naive picture of what is happening would predict that debond regions spaced apart by distances less than the width of the ultrasonic beam should not be resolved. In fact it is clear from Fig.6 that a much closer spacing of debond strips could have been resolved. A more sophisticated approach to ultrasonic resolution is required which takes account, perhaps, of coherence across the beam and different frequency contents of different areas of its cross-section. A practical illustration of this new technique is shown in Fig.7 which comes from a bonded-honeycomb aircraft structure. Here the spectrum analyser has been set, as described above, to pick out the resonance due to the reverberation set up in the glue of each cell of the honeycomb. The spacing of the honeycomb is clearly resolved and the height of each peak measures the thickness of the glue coating which apparently varies from cell to cell. At the right hand end of the component there is a region where the metal honeycomb has been removed leaving the metal skin coated on its inner surface with a layer of glue imprinted with the honeycomb pattern. The reverberation peaks from this region are lower since the glue is now backed by water instead of air (the honeycomb structure is watertight). Adhesion
and cohesion
Ultrasonic spectroscopy, as shown previously, has the ability to distinguish features separated in time but not resolved in conventional time-domain displays. This ability
Transducer
Variation
[water coupkdl
-Scan
lo”,,
along test piece IOYmm
Fig.7
Testing honeycomb
interface
bonds
provides a means of distinguishing between poor adhesion at glue/metal interfaces and poor cohesion within the glue .layer itself. The technique is shown schematically in Fig.& A metal sandwich with a glued interface is interrogated at normal incidence by broadband ultrasound exactly as described before. Reflections from the top surface, the first metal/glue interface, the subsequent glue/metal interface and the back surface arrive separated in time and can be resolved by the frequency analysis technique. Fig.8 (due to Lloyd) is a convenient way of demonstrating what is observed: the trick is to treat the ultrasonic axis as if it were tilted relative to the normal tr, the surface. In this way reflections from features at various depths, which are separated in time, appear separated as shown. In particular, since the speed of sound in glue is only about one tenth of that in metal, the two glue interface reflections are clearly resolved. The heights of the responses from these interfaces measure the state of adhesion at each individually, exactly as discussed before. The bonus is that the time separation between these responses depends on the speed of sound in the adhesive which is a measure of its state of cure and this is, in turn, a measure of cohesive strength. Moreover, if the adhesive has actually cracked so that adhesion has been locally lost, the time resolution of the technique is often adequate to show up the internal cracks.
with frequency
There are three characteristic regions. Firstly, the region on the left where the response rises steeply towards 0 dB corresponds to a square-law dependence of cross-section on frequency. This is called the Rayleigh region after Lord Rayleigh 9 who worked out the equivalent of this curve as long ago as 1871 and showed that the coefficient of a2 is proportional to the volume of the target. Secondly, at high frequencies the trend is for the response to be independent of frequency: this corresponds to specular reflection and measures the geometrical cross-section of the target as seen by the plane transducer. It is to this response that the scale has been normalized. The third intermediate frequency region, characterized by a series of maxima and minima, contains the shape information we want. In the simple case shown, the spacing of the maxima is inversely proportional to a or more accurately to I/AT where AT is the time for an ultrasonic wave to travel round the circumference to the equatorial plane and back, a distance of na. Fig.9b corresponds to the more realistic material case where the target is penetrable by ultrasound. For the calculation of this figure, the acoustic impedance of the sphere pc, has been taken as 90% of the acoustic impedance of the matrix pc,. While the three characteristic regions listed above are clearly visible, the intermediate region has become discouragingly complex; the spacing of the maxima has been reduced by a factor of 4/n corresponding to the new importance of the far side of the sphere, distant 2a from the front. The energy return in the frequency region immediately above the Rayleigh region has been enhanced because of focussing effects. Artificial
defects
complexity of theoretical analysis of even the simplest targets has led to concentration on a more empirical approach. Thus Gericke 2 began by simply connecting a commercial spectrum analyser to commercial ultrasonic test equipment. His results, recently re-analysed in detail,2 can be summarized as demonstrating the diagnostic possibilities of the better collimation of high frequencies relative to low frequencies. The spectral response of a known target could be explained on this basis, but there was no claim to be able to characterize an unknown target from its spectral response. The
incident beam
Discrete features The detection and characterization of discrete defects is the commonest application of ultrasound in the testing of structural components. Conventionally, in the pulseecho technique the presence and importance of the defect is assessed by the operator on the basis of the magnitude of the echo. Any additional quantitative information about the size, shape, orientation and other physical properties, to add to what he infers from his skill and experience is thus acceptable. A simple demonstration due to Lloyd * shows that at least some of the required information is available in the echo spectrum.
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cross-section
Fig.9a shows the calculated scattering cross-section for a hollow sphere of radius a in a metal matrix where the ultrasonic velocity is c. The cross-section has been plotted as a function of wa/c where w is the angular frequency and the calculation has assumed that the spherical void is not penetrated by the ultrasound.
ATuminium alloy outer skin
Distance
of scattering
First rnetd Second metd
t Time axis Fig.8
I Mhesiw
Testing adhesive bonded joints
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Lloyd,4 in a series of experiments with more ambitiouslyshaped targets than those used by Gericke, was again able to e,xplain their spectral response in terms of their known geometry. Thus Fig.10 shows the amplitude and spectral response of a series of brass stubs interrogated end-on to the transducer axis using water immersion at a depth of 75 mm. As the diameter of the stub is reduced, low frequencies become preferentially attenuated and high frequencies become lifted exactly as would be expected if the better-collimated high frequencies are directly reflected back to the transducer.
Lloyd’s smaller stubs, however, show a new complication: this is an apparent modulation which is evident on the spectrum of the response from the 1.25 mm diameter stub and very marked on that from the 1 .15 mm stub. The reason for this has been traced to phase relationships between the various parts of the cross-section of the beam. If the area of the beam sampled by the target is large enough, these modulations cancel out but can, as comparison of Figs 1Ob and c shows, appear suddenly with a 20% reduction of sampled area. This is a warning that transducer design is crucial for practicable interpretation of echoes from small targets and that sophisticated data processing is required to separate transducer properties from target properties. The results of similar experiments on 2.0 mm stubs with conical shaped tops are shown in Figs 1 la, b and c. Once again, different parts of the frequency spectrum are treated differently. In particular, a series of frequencies eliminated from the spectrum of the flat-topped stub can be interpreted in terms of the sonic transit time from the lip to the apex of the cones. Attempts at a theory
O
a
I
I
I
8
4 Frequency
parameter
12
16
wok
+2c
In the introductory paragraph to this paper, ultrasonic spectroscopy was justified as adding a little colour to a monochrome image. Further justification has since been produced by showing that some properties of bulk crystals are frequency dependent. Again, in the case of quasitwo-dimensional interfaces, the spacings between them in the direction of the beam may be difficult to measure unless the pulse extension is much less than the spacing between them; the spacing may, however, appear clearly resolved as peaks in the frequency spectrum as in Fig.5. Further understanding of why one goes to the trouble of obtaining a spectrum can best be seen by going back to first principles. This approach due to Lloyd &lo will also show why the technique, so successful in two dimensions, has yielded so little in three. If we could generate an infintely short delta-function pulse of ultrasound and receive its echo by perfect (infinite bandwidth) electronics we could distinguish between target features at different distances, however closely spaced, from the transducer by the difference in time of arrival of the echoes.
-4c
-
I 8
I
4
b
I 12
Frecptency parameter
W/C
a - Response of a spherical cavity of radius a in a metal Fig.9 matrix; b - response of a solid sphere of radius a in a metal matrix (PCs/PC, = 0.9)
16
In practice, of course, the interrogating pulse has the form g(t) where g(t) is made up of all the delta-functions we would like to have generated. The function g(t) incorporates all the transducer characteristics, the driving waveform, the effect of coupling, and the effect of the medium on the pulse. In fact everything except the effect of the echoproducing target. Similarly, the effect of a target feature
Fig.10 Amplitude and spectral responses of fiat-topped cylinders of various diamters: time domain signals, 1 MS per division; upper traces: spectra, 1 MHz per division)
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a - 2.0 mm; b -
1.25 mm; c -
1.15 mm flower traces:
density) and the logarithm of that (the log mod spectrum) are still difficult to interpret.
of complex shape can be described by a function h (t) where h(t) is a continuous function incorporating all the discrete features we might have hoped to resolve. The echo pulse f(t) is then g(t) modified by h(t) in the form
In the case of simple targets like the spheres which gave rise to Figs 9a and b, the spectra in one form or another show a clear modulation interval. For more complex targets the modulation intervals, though obviously there, are spread over a wide spectral range. The problem is to pick them out. One ossible way of doing this has been investi. a srm y hfied model for ultrasonic gated by Lloyd. E Using scattering due to Freedman,l he accounts for the modulation of the spectrum in terms of AT, the time for an ultrasonic wave to go between two important scattering features of the target. In the case of Fig.9a, these turned out to be the near point and equatorial plane of the sphere. In the case of Fig.9b where the sphere was penetrable, the significant features were the near and far points of the sphere. In either case a modulation interval of ~/AT arises, the depth of modulation being a measure of the mismatch at the two features. A more complex target with three significant features 1,2 and 3 would have a threeterm modulation corresponding to A712, Ar23 and Ar13. While the Freedman approach shows that the number of ‘features’ in a real target may not be as large as might be feared, it is clear that even in quite simple targets there must be a number of such modulation intervals. The problem is still to pick them out.
f(t) = g(t)*h(t) where the asterisk denotes a convolution of delta-functions, ie,
or infinite
sum
+oo
f(t) =
J-co
g(T)h(t- T)d7
Inprinciple the convolution could be unravelled by digitizing the echo pulse and feeding it to a computer. The snag, apart from the time required to obtain the result, is that g(t) has to be known and this varies with the conditions of the test (the modulation observed with the smaller stub targets in Fig.10 was ag(t) property not an k(t) property). A much more hopeful approach is to try to separate g(t) from h(t) and this is exactly what fourier transforms do. Gating out f(t) and frequency analysing it or, as electronic spectrum analysers do, taking its power spectral density gives IW412
= IG(w)IW(w)l2
‘Cepstroscopy’
One possible way of doing this is the cepstral l2 technique adapted from seismology. This involves treating the spectrum as if the abscissa were time rather than frequency (as it is when displayed on an oscilloscope) and re-Fourier analysing it. The result is called a cepstrum. This and other jargon l2 terms have been taken over from seismology.
The dot is now a simple multiplication which can, if desired, be removed by taking the logarithm, again electronically In IF(w)1 = In IG(o) I + In W(w) I Whether or not the logarithm is taken, the properties of the target have been thus partially separated from those of the interrogating pulse. In an ideal case if the interrogating pulse, while band limited, had a truly flat spectrum within the range accessible to the apparatus, then G(w) would be a constant and would drop out of consideration. Frequency analysis is thus an attempt to isolate the characteristics of the effect investigated from the notoriously variable characteristics of the investigating apparatus. This is a step forward bat the spectrum, its modulus (the power spectral
a
rl
b
An example of the use of this technique to identify the periodic modulation of a log mod spectrum has recently been published by Lloyd 8 who digitzed the time-domain signals from known targets and showed by digital computation that time-unresolved features could be identified in the cepstra, separated from transducer and coupling information. The inverse process is not, as yet, possible. For the record, Lloyd’s published cepstra were noisier than they need have been because of an unsatisfactory digitization process. For this reason, an example of a cepstrum will be delayed till a later section when it will be shown that, if
M
Amplitude and spectral response of 2.0 mm diameter cylindrical targets with flat and conical tops: b and c are 8 and 21 dB below a Fig.1 1 respectively (lower traces: time domain signals, 1 ~1sper division; upper traces: spectra, 1 MHz per division)
208
ULTRASONICS.
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1973
the geometry of the problem can be effectively reduced to two dimensions, the cepstral technique gives very encouraging results. The Rayleigh
analysis
An alternative approach, also proposed by Lloyd 8plo, l3 and based on Rayleigh’s original 1871 work on light scattering, is to obtain a polynomial fit to the log mod spectrum. Thus lnlF(w)(
=A,
+Alw
+. . . +A,d
+A2w2
Dividing the measured In lF(w) I by the computed term in a2 leaves a series which certainly contains shape information separated from the size information. Experience with the interpretation of discrete target data obtained by wideband ultrasonoscopy leaves no doubt that the response of known targets can be accounted for. Characterization of unknown targets by this method of data processing is not yet in sight. ultrasonic
b
+. . .
The Rayleigh analysis, which is similar to that discussed at the beginning of the section on a theoretical analysis, requires that A o = A 1 = 0 and that A 2 should be proportional to the volume of the target. The additional coefficients A,. describe the shape and other features of the target and can in fact l3 be obtained directly from the time domain response either digitally or electronically without having to obtain the spectrum. This approach has had some success with artificial targets with the same total volume, but different shapes or disposition can be shown to have similar values of A 2.
Practical
a
data processing
To sum up this section, the original aim of ultrasonic spectroscopy was to characterize discrete targets in a threedimensional matrix. Theory gave hope that this could be done. Now that apparatus has been constructed and experiments carried out, it has been confirmed that theory correctly describes the scattering properties of known targets but that derivation of target characteristics from the observed ultrasonic responses is still some way off. Against this, it has been shown that, when the problem
Fig.13 Ultrasonic responses from the slot shown in Fig.12: a - time-domain response from the whole slot; b - time-domain response from the leading (‘referee point’) corner; c - spectra (solid line is the spectrum of a, dotted line is the spectrum of b)
can be reduced to variation of material properties in two dimensions, ultrasonic spectroscopy is almost always successful. The next section will discuss a case where characterization of a discrete defect has been successfully carried out by ultrasonic spectroscopy, precisely by reducing the problem to one in two dimensions. Surface waves It has often been proposed to use ultrasonic surface (Rayleigh) waves for the detection and characterization of surface flaws in metals. A critical literature survey of previous attempts to do so has recently been prepared by Miss Jennifer Tolley I4 of the City University Centre for Information Science. Although this lists 132 references it shows that few positive results have been obtained. However, L. L. Morgan l5 appears to have made a breakthrough by using broadband surface wave transducers and the application of ultrasonic spectroscopy. Characterization
of a surface crack
A finger transducer interrogates the surface of an aluminium block with pulses of broadband (0.5-10 MHz) ultrasonic Rayleigh waves. In the surface of the block is a milled slot simulating a surface crack and having the dimensions shown in the upper part of Fig.12. Pulses reflected from the slot reveal its presence and position and are shown in Fig. 13a. Fig. 13b shows the echo signal from the leading corner only, carefully gated out from the signal from the whole slot. Comparison of Figs 13a and b shows that the smaller responses which arise from the other corners of the slot are not resolved in the time domain so that no inference can be drawn about the slot dimensions.
Time I/.4 Fig.12 Cepstral analysis of ultrasonic pulses from a slot. Top: cross-sectional view of the milled slot; bottom: cepstrum in which amplitude is dependent on the intensity of the feature
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Fig. 13c shows the frequency spectra of the responses from the whole crack (solid line) and the leading corner (dotted line). The effect of the internal structure of the slot is seen to be to modulate the leading corner spectrum which itself contains unwanted information about the transducer, its coupling to the surface and the properties of the surface
209
between transducer and slot. Extraction and interpretation of this modulation has been the first success of the cepstral method of data processing. At present this processing is carried out digitally: the reflected pulse in Fig.13a is digitized and its spectrum obtained by digital computation. The spectrum of that part of the pulse which comes from the leading corner of the slot is similarly obtained. Comparison of these spectra isolates the modulation due to the internal structure of the slot and eliminates the effects of variability of transducer, coupling and surface transmission between transducer and slot. The final stage is to obtain the spectrum of the comparison spectrum. This second spectrum is the cepstrum described earlier. The typical result is shown in Fig.12 where the peaks in the cepstrum (directly photographed from the computer print out) show that clear resolution of features separated in transmission time by less than 0.1 ~_lscan be obtained. Features in this case are regions of the surface where curvature is large and heights of the cepstral peaks are a measure of the angle through which the surface turns. Of particular interest is the cepstral peak at approximately 0.8 ps which is due to the ledge in the trailing vertical face of the slot. This was produced by a machining error and was only discovered when a reason for this peak was sought by subsequent sectioning of the metal. The size of the peak suggests that the actual ledge, before sectioning, was rather more ragged than is shown in Fig. 12. This is consistent with the nature of the machining error.
In non-destructive testing applications it is not practicable to avoid the contradiction by using separate transmitting and receiving transducers (the space and manoeuvrability restrictions in sonar applications may be much less stringent). Partial solutions have been obtained by development of finger transducers l&l7 and multi-element transducers.8>18 These and more recent developments will be the subject of a later article.
Acknowledgements This review relies heavily on work as yet unpublished. In particular, that of my colleagues at The City University, E. A. Lloyd, L. L. Morgan, D. G. Tasker and J. P. Weight who deserve thanks for allowing me to use their results. Also to be thanked are the committee headed by the late Richard Eborall of the British Non-Ferrous Metals Research Association who arranged for financial support from a consortium comprising the BNFMRA, the Central Electricity Generating Board, Rolls Royce Ltd, Henry Wiggin Ltd and the Ministry of Technology (Air).
References 1 2
Generation
and reception of wideband ultrasound
Early work with wideband ultrasound was done using conventional transducers with their properties modified by damping. Thus, in Gericke’s early experiments * conventional, heavily-damped transducers with pulse-excitation gave spectra with a series of humps separated by nulls at regular frequency intervals f These spectra were similar to the wellknown spectrum of a rectangular pulse of duration l/f:
6 I
For the experiments on grain size and collimation effects described earlier the multi-peak spectrum was not really a serious disadvantage; indeed it may even have helped interpretation of results by focussing attention on the behaviour of a few marked peaks. But for more sophisticated targets, such as extended interfaces, the nulls are a real disadvantage since the interfacial echoes also modulate the spectrum at well defined frequencies. For three-dimensional targets, the analysis attempted earlier shows that a really flat spectrum is essential: only such can be called true wideband transducers. Wideband
transducers
The problems of fabrication and excitation of wideband ultrasonic transducers have recently been reviewed by Lloyd * and by Mitchell,16 the most significant feature being Lloyd’s lo demonstration that the requirement for a satisfactory wideband transmitting transducer is a thick crystal (42 mm for 10 MHz bandwidth) while, in the reception mode, a thin (350 pm for the same bandwidth) crystal is necessary. If these contradictory requirements have apparently not been made before, it may be because traditionally the effects of the two functions are combined in the observed loop-response spectrum.
210
8
9 10
11 12 13 14 15 16
17
18
Gericke, 0. R. Ultrasonic spectroscopy, US patent 3538753 (10 November 1970) Gericke, 0. R. Paper number 1 in The Future of Ultrasonic Spectroscopy, edited by P. M. Reynolds, British NonFerrous Metals Research Association, London (1971) Gericke, 0. R. Encyclopedic Dictionary of Physics Supple ment 4, Pergamon Press, Oxford (1971) 502 Lloyd, E. A. British Non-Ferrous Metals Research Association paper S150/30/13 (1972) to be published Bhatia, A. B. Scattering of high-frequency sound waves in polycrystalline materials, Journal of the Acoustical Society ofAmerica 31 (1959) 16 Samain, D. Ultrasonic Techniques in Biology and Medicine, edited by B. Brown and D. Gordon, Iliffe, London (1967) 145 Weight, .I. P. Instrumentation associated with the development of wideband ultrasonic techniques (ultrasonic spectroscopy), M Phil thesis, The City University (1972) Lloyd, E. A. Paper number 2 in The Future of Ultrasonic Spectroscopy, edited by P. M. Reynolds, British NonFerrous Metals Research Association, London (1971) Lord Rayleigh, The Theory of Sound, volume 2 chapter XVII, McMilIan, London (1896) Lloyd, E. A. A heuristic approach to the scattering cross section of targets at ultrasonic frequencies and the development of wideband ultrasonic techniques, PhD thesis. The City University (1973) Freedman, A. Mechanism of acoustic echo formation, Acustica 12 (1962) 10 Brown, A. F. Physical problems in a technological university, Quest 9 (1969) 24 Lloyd, E. A. British Non-Ferrous Metals Research Association paper (1971) to be published Tollcy, J. Ultrasonic Rayleigh and Lamb waves in NDT, The City University Centre for Information Science (1972) Morgan, L. L. Crack size evaluation using ultrasonic surface wave spectroscopy, PhD thesis, The City University (1973) Mitchell, R. F. Paper number 5 in The Izuturc of Ultrasonic Spectroscopy, edited by P. M. Reynolds, British NonI:errous Metals Research Association, London (197 1) Van der Pauw, L. J. The planar transducer ~- a new type of transducer for exciting acoustic waves, Applied I’/??~ics Letters9 (1966) 129 British Non-Ferrous Metals Research Association, Improvements relating to piezoclectric transducers, I!K patent application 149869 (1969)
ULTRASONICS.
SEPTEMBER
1973
Ultrasonic spectroscopy is a development of the pulse-echo technique which uses broadband (0.5-10 MHz) ultrasound and analyses the spectra of the echo pulses. It has already proved its value in cases where the geometry is essentially two-dimensional. Examples include the determination of grain size in metals and quality control in carbon-fibre composites and glued joints, while a new development has opened up the possibility of measuring the depth and width of surface cracks down to sub-millimetre size. When the problem is essentially three-dimensional, as in characterization of discrete defects in metals, full interpretation of the echo signal cannot as yet be achieved except in a few special cases. This paper is the first of two reviews on ultrasonic spectroscopy. the generation and reception of wideband ultrasound.
Introduction The name ‘ultrasonic spectroscopy’ seems to have been first used by 0. R. Gericke who devised and patented 1 a device whereby ultrasonic echo pulses from internal discontinuities in a test specimen could be displayed on an oscilloscope alon with their frequency spectra. Basically the idea is simpl$ : in . conventional ultrasonic inspection techniques the ultrasonic frequencies are limited to a narrow band, so the information has to be deduced solely from amplitude variations. Broadband techniques, by analogy with visual inspection with white light, give additional information corresponding to the colour of the inspected item. The experimental difficulties of producing and receiving pulses of ultrasound of the desired bandwidth are formidable since transducers of a new type have to be made and excited. Provided the signals they receive can be converted to broadband ac, commercial spectrum analysers are ,available, but at such a price as to make them unattractive for routine testing. While the development of practicable equipment (wideband transducers and their excitation sources, wideband amplifiers, spectrum analysers and spectrum-free gates) has been an essential part of the development of ultrasonic spectroscopy, this review will do little more than refer to them and will concentrate on their applications to materials testing. Furthermore, the discussion will be confined to the pulse-echo method of ultrasonic testing: for other methods, in particular sweptfrequency techniques and through-transmission techniques, the reader is referred to a recent article by Gericke.3 Professor A. F. Brown is in the Department of Physics, The City University, London, UK. He is currently a visiting professor in the Department of Physics, Western Australian Institute of Technology, South Bentley, Australia. Paper received 12 February ,1973.
202
The second will cover
There are three main fields in which ultrasound is used in materials testing. These are the detection and characterization of discrete defects, the study of extended interfaces and the investigation of the properties of bulk materials. Although all are interrelated, it is profitable to discuss them, and the application of ultrasonic frequency analysis to them, separately. Properties of the bulk material Grain
size determination
The use of ultrasonic spectroscopy in grain size determination has been illustrated by Gericke 2 who interrogated metal plates with broadband ultrasound. In these experiments the loop response of the transducer, as measured with an aluminium test plate, showed a frequency characteristic with two well defined humps centred on frequencies of about 3.5 and 6 MHz respectively. The corresponding loop frequency responses of steels of varying grain sizes showed that, as the mean grain size increased from 0.05 to 0.10 mm, the ratio of the heights of the two frequency humps changed, the higher frequency being preferentially attenuated by coarser grained material. Comparison of relative attenuation of more closely-spaced frequencies ~ for example by attempting to account for changes in the shape of each hump in Gericke’s published spectra ~ does not yield such a simple law. Presumably this is because such detailed structure is affected by the distribution of grain size around the mean and explains why a wide spectrum of frequencies is needed to give an unequivocal measurement of the mean. Lloyd 4 has attempted to construct a mathematical model to describe the frequency dependence of grain boundary scattering. The model, which is similar mathematically to
ULTRASONICS.
SEPTEMBER
1973
that used to describe the response of discrete targets in a later section, adds up the time domain responses of many small grains randomly distributed throughout the matrix. While the model is probably more applicable to the case of a dispersed precipitate than to that of grains which fill up the whole volume of the matrix, two predictions of the theory have been confirmed by experiment. The first of these is that the back-scattered spectral response from coarse-grained material should have a lower-frequency cutoff than that from fine-grained material: this is demonstrated by experiments on gunmetal shown in Fig.1. Here the frequency characteristics of the transducer were uniform in the range shown and the curves were obtained under identical conditions of amplification. The second prediction of the theory is that the amplitude of the response at a given frequency should be proportional to the product of the number of scattering centres and their reflectivity. The first inference of this second prediction is that the back-scattered response will be low for very coarse material, increasing as the grain size decreases. The correctness of this is also shown by Fig.1 but a second inference is that the increase in response will come to a maximum and fall again as the material becomes very fine grained. This predicted maximum has not yet been observed but it is doubtful if the model can be taken, without further consideration, to apply to very large grains from which, as mentioned below, a collimated beam can be specularly reflected. A dark-field
ultrasonic
Y Transducer
a
Specular reflectionfrom
-face
technique
Free surface
A useful technique in ultrasonic examination of bulk material has been developed by following up a theoretical observation of Bhatia 5 who calculated the polar diagrams for scattering by systems of discrete centres. Applied to the problem of detection of sub-surface scattering centres such as the metal grains described above, theory suggested that maximum back-scattered energy would be in the direction straight back to the transducer while the surface would behave more like a mirror. Thus with the transducer axis normal to the free surface (Fig.2a), echoes from subsurface features are superposed on echoes from the surface. However, if the transducer axis is inclined at an angle 6 to the surface, response from sub-surface features is still preferentially directed back to the transducer but the sur-
\\\\\\\\’
11’
\\\\“\‘\““”
Dark-field ultrasonics. Polar diagrams for reflection from Fig.2 sub-surface feature: a - normal incidence; b - angle-probe technique
face echoes are specularly directed away from the transducer. The dark-field technique shown in Fig.2b with 0 - 25 degrees provides an alternative to electronic gating for removing the effect of a noisy surface, and is more delicate than gating in allowing study of immediate sub-surface features. The technique has been used for the grain size experiments described previously and for the experiments on carbon fibre reinforced plastics described below. Carbon
2 MHz Fig.1 Variation of frequency response with grain size for two specimens of gunmetal. Top trace: fine grain (-1 mm). Middle trace: coarse grain (-5 mm). Bottom trace: frequency calibration, the peaks are at 2 MHz and 6 MHz
ULTRASONICS.
SEPTEMBER
1973
fibre reinforced
plastics (CFRP)
CFRP is a difficult material to test because the large specular return from the surface in water swamps the response from sub-surface features. This difficulty has been overcome by use of the dark-field or angle-probe technique described above. In Fig.3 back-scattered energy in the frequency ranges l-3 MHz and 4-6 MHz has been integrated and displayed
203
on an x-y plotter against distance along the central axis of a test piece of CFRP. All traces were made with identical geometrical set-up and amplification. The two lowest traces show responses in these two frequency ranges from a virgin specimen of high-quality material. The topmost curve shows the total energy back-scattered in the l-3 MHz range from a similar specimen after torsional fatigue to an estimated 50% of fatigue life. The next highest curve similarly shows the total energy in the 4-6 MHz range from the same specimen. There was no visible indication of fatigue damage. In terms of Lloyd’s model for scattering from grains or precipitates in a matrix, these four curves may be interpreted as follows: in virgin specimens there are few scattering centres; back scattering is of small amplitude and all frequencies are treated alike. Fatigue damage leads to nucleation and growth of distributed scattering centres and to reduction in high-frequency response relative to low frequency. A complication arises with high damage for then the scattering centres become large enough to reflect the better collimated high frequencies directly back to the transducer.
and the maintenance of their shape after passage through the specimen. Secondly, the frequency analysis part of ultrasonic spectroscopy is an aid to measurement of transit times between features when these times are comparable to, or even less than, the normal pulse length. Pulse shaping by wideband
techniques
Conventional pulse-echo equipment tends to be monochromatic, the pulse of nominal length At being generated by a few cycles of ac at a high frequency which might typically be about 5/At. Using wide bandwidth techniques, however, a square pulse of length At can be generated by use of a band of frequencies the highest of which need not exceed 1/At. When the pulse is required to go deep into the medium, the higher frequencies in the band are preferentially absorbed, which is equivalent to lengthening the pulse. Resolution can, however, be restored by differential amplification of the higher frequencies. This is the sweptgain technique.6 Bonded structures
application of ultrasonic spectroscopy to quality testing of interfacial bonds is conveniently introduced by consideration of some structures devised by Weight 7 who made up a test piece consisting of two sheets of aluminium glued together (Fig.4). A number of simulated debonds were introduced by milling slots of various widths I and about 2.50 pm deep into one surface as shown. The
Extended interfaces An extended interface is defined as a region of acoustic mismatch between two media, the area of which is larger than the area of the cross-section of the ultrasonic beam. There are two problems. Firstly, finding the position and mapping the region of acoustic mismatch which may vary in depth below the accessible surface, and secondly, measuring its properties in terms of the degree of mismatch which may vary from place to place over the interface. The contribution of ultrasonic spectroscopy to the problem of characterization of extended interfaces is shown below to be twofold. Firstly, the availability of wideband techniques is an aid to generation of high resolution short pulses
126mm 1
i-
~tl=o%Wtl Fig.4
t2=205mm
Demonstration
/, =3mm
/2
q6mm
test piece
Fig.3 Frequency dependence of back-scattering by CFRP. Horizontal scale: distance along the central axis of a CFRP plank approximately 100 mm. Vertical scale: energy integrated over each frequency range (all curves are at the same amplification). Bottom traces: integrated energy in the ranges 1-3 MHz and 4-6 MHz from a virgin plank. Middle trace: integrated energy in the 4-6 MHz range from a plank fatigued to 50% of expected life. Top trace: integrated energy in the range l-3 MHz from the same plank fatigued to 50% of expected life
204
ULTRASONICS.
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1973
Transducer
I I
-
Distance
Fig.5 Detection of debonds in the test piece: a - top trace shows echo from a well bonded area, bottom trace shows corresponding spectrum; b - top trace shows echoes from a debonded area, bottom trace shows corresponding spectrum; c - bottom trace shows spectrum of a with water/metal surface reflection gated out, top trace shows corresponding time-domain signal; d 2 bottom trace shows spectrum of b with water/metal surface reflection gated out, top trace shows corresponding time-domain signal (time 1 ps per division: amplitude linear; frequency 0.5 MHz per division: amplitude linear)
A good bond is a region of good acoustic match and little incident energy is returned from the glue/metal interfaces. The simulated debonds, however, are regions of large acoustic mismatch and give large reflections. If the test piece had been sufficiently thick these reflections could have been resolved in the time domain from reflections from the other interfaces. Fig.S shows what is in fact observed when a pulse-echo test is carried out by a water immersion technique using ultrasound with approximately uniform spectral content in the range 0.5-8 MHz. In Figs 5a and b, the top traces of which show the echoes from a well bonded and a debonded area respectively, the first peak is the response from the water/metal interface and this is followed by a series of waveforms set up by multiple reflections within the plate thickness. The lower traces in each case show the corresponding spectra: that in FigSa is similar to the transducer spectrum but shows modulations corresponding in frequency to the reciprocals of times between reflections. The lower trace of FigSb shows the spectrum corresponding to a debonded region: here the modulation is at a higher frequency corresponding to the shorter distance from the water/metal interface to the debonded interface. Considerable simplification of these spectra is obtained if the signal gate is set so as just to exclude the water/metal surface reflection. These are shown in the lower traces of Figs 5c and d with their corresponding time domain signals above them. Referring to the spectrum in Fig.Sd, the first small maximum corresponds to a reflection from the back surface of the test piece and the height of this maximum is a measure of the amount of energy by-passing the debond and reflected from the back surface. When the width of the debond 1 is comparable with the beam width, the maximum is small as shown, but increases as I decreases. This suggests a testing procedure wherein the
SEPTEMBER
Scan
along test
piece
-+
IIOmm
Display with a section of test piece superposed on it. The Fig.6 linear scales are equal
d
ULTRASONICS.
[water coupled]
1973
signal gate is set to exclude the water/metal interface reflection and the spectrum analyser is set to filter out only the first spectral maximum due to the debond. A display with the horizontal axis representing distance along the test piece and the vertical axis representing the time integral of the output of the spectrum analyser will then allow debonded regions to be easily identified. Fig.6 shows such a display with a section of the test piece superposed on it on the same linear scale: the spacing of the debond maxima is correct and their heights correspond to their extent. If the specimen is scanned by successive sweeps of the interrogating beam this display technique can readily be converted to B-scan. While in Fig.6 the debond pattern is clearly resolved, this in fact sets a new problem, for a naive picture of what is happening would predict that debond regions spaced apart by distances less than the width of the ultrasonic beam should not be resolved. In fact it is clear from Fig.6 that a much closer spacing of debond strips could have been resolved. A more sophisticated approach to ultrasonic resolution is required which takes account, perhaps, of coherence across the beam and different frequency contents of different areas of its cross-section. A practical illustration of this new technique is shown in Fig.7 which comes from a bonded-honeycomb aircraft structure. Here the spectrum analyser has been set, as described above, to pick out the resonance due to the reverberation set up in the glue of each cell of the honeycomb. The spacing of the honeycomb is clearly resolved and the height of each peak measures the thickness of the glue coating which apparently varies from cell to cell. At the right hand end of the component there is a region where the metal honeycomb has been removed leaving the metal skin coated on its inner surface with a layer of glue imprinted with the honeycomb pattern. The reverberation peaks from this region are lower since the glue is now backed by water instead of air (the honeycomb structure is watertight). Adhesion
and cohesion
Ultrasonic spectroscopy, as shown previously, has the ability to distinguish features separated in time but not resolved in conventional time-domain displays. This ability
Transducer
Variation
[water coupkdl
-Scan
lo”,,
along test piece IOYmm
Fig.7
Testing honeycomb
interface
bonds
provides a means of distinguishing between poor adhesion at glue/metal interfaces and poor cohesion within the glue .layer itself. The technique is shown schematically in Fig.& A metal sandwich with a glued interface is interrogated at normal incidence by broadband ultrasound exactly as described before. Reflections from the top surface, the first metal/glue interface, the subsequent glue/metal interface and the back surface arrive separated in time and can be resolved by the frequency analysis technique. Fig.8 (due to Lloyd) is a convenient way of demonstrating what is observed: the trick is to treat the ultrasonic axis as if it were tilted relative to the normal tr, the surface. In this way reflections from features at various depths, which are separated in time, appear separated as shown. In particular, since the speed of sound in glue is only about one tenth of that in metal, the two glue interface reflections are clearly resolved. The heights of the responses from these interfaces measure the state of adhesion at each individually, exactly as discussed before. The bonus is that the time separation between these responses depends on the speed of sound in the adhesive which is a measure of its state of cure and this is, in turn, a measure of cohesive strength. Moreover, if the adhesive has actually cracked so that adhesion has been locally lost, the time resolution of the technique is often adequate to show up the internal cracks.
with frequency
There are three characteristic regions. Firstly, the region on the left where the response rises steeply towards 0 dB corresponds to a square-law dependence of cross-section on frequency. This is called the Rayleigh region after Lord Rayleigh 9 who worked out the equivalent of this curve as long ago as 1871 and showed that the coefficient of a2 is proportional to the volume of the target. Secondly, at high frequencies the trend is for the response to be independent of frequency: this corresponds to specular reflection and measures the geometrical cross-section of the target as seen by the plane transducer. It is to this response that the scale has been normalized. The third intermediate frequency region, characterized by a series of maxima and minima, contains the shape information we want. In the simple case shown, the spacing of the maxima is inversely proportional to a or more accurately to I/AT where AT is the time for an ultrasonic wave to travel round the circumference to the equatorial plane and back, a distance of na. Fig.9b corresponds to the more realistic material case where the target is penetrable by ultrasound. For the calculation of this figure, the acoustic impedance of the sphere pc, has been taken as 90% of the acoustic impedance of the matrix pc,. While the three characteristic regions listed above are clearly visible, the intermediate region has become discouragingly complex; the spacing of the maxima has been reduced by a factor of 4/n corresponding to the new importance of the far side of the sphere, distant 2a from the front. The energy return in the frequency region immediately above the Rayleigh region has been enhanced because of focussing effects. Artificial
defects
complexity of theoretical analysis of even the simplest targets has led to concentration on a more empirical approach. Thus Gericke 2 began by simply connecting a commercial spectrum analyser to commercial ultrasonic test equipment. His results, recently re-analysed in detail,2 can be summarized as demonstrating the diagnostic possibilities of the better collimation of high frequencies relative to low frequencies. The spectral response of a known target could be explained on this basis, but there was no claim to be able to characterize an unknown target from its spectral response. The
incident beam
Discrete features The detection and characterization of discrete defects is the commonest application of ultrasound in the testing of structural components. Conventionally, in the pulseecho technique the presence and importance of the defect is assessed by the operator on the basis of the magnitude of the echo. Any additional quantitative information about the size, shape, orientation and other physical properties, to add to what he infers from his skill and experience is thus acceptable. A simple demonstration due to Lloyd * shows that at least some of the required information is available in the echo spectrum.
206
cross-section
Fig.9a shows the calculated scattering cross-section for a hollow sphere of radius a in a metal matrix where the ultrasonic velocity is c. The cross-section has been plotted as a function of wa/c where w is the angular frequency and the calculation has assumed that the spherical void is not penetrated by the ultrasound.
ATuminium alloy outer skin
Distance
of scattering
First rnetd Second metd
t Time axis Fig.8
I Mhesiw
Testing adhesive bonded joints
ULTRASONICS,
SEPTEMBER
1973
Lloyd,4 in a series of experiments with more ambitiouslyshaped targets than those used by Gericke, was again able to e,xplain their spectral response in terms of their known geometry. Thus Fig.10 shows the amplitude and spectral response of a series of brass stubs interrogated end-on to the transducer axis using water immersion at a depth of 75 mm. As the diameter of the stub is reduced, low frequencies become preferentially attenuated and high frequencies become lifted exactly as would be expected if the better-collimated high frequencies are directly reflected back to the transducer.
Lloyd’s smaller stubs, however, show a new complication: this is an apparent modulation which is evident on the spectrum of the response from the 1.25 mm diameter stub and very marked on that from the 1 .15 mm stub. The reason for this has been traced to phase relationships between the various parts of the cross-section of the beam. If the area of the beam sampled by the target is large enough, these modulations cancel out but can, as comparison of Figs 1Ob and c shows, appear suddenly with a 20% reduction of sampled area. This is a warning that transducer design is crucial for practicable interpretation of echoes from small targets and that sophisticated data processing is required to separate transducer properties from target properties. The results of similar experiments on 2.0 mm stubs with conical shaped tops are shown in Figs 1 la, b and c. Once again, different parts of the frequency spectrum are treated differently. In particular, a series of frequencies eliminated from the spectrum of the flat-topped stub can be interpreted in terms of the sonic transit time from the lip to the apex of the cones. Attempts at a theory
O
a
I
I
I
8
4 Frequency
parameter
12
16
wok
+2c
In the introductory paragraph to this paper, ultrasonic spectroscopy was justified as adding a little colour to a monochrome image. Further justification has since been produced by showing that some properties of bulk crystals are frequency dependent. Again, in the case of quasitwo-dimensional interfaces, the spacings between them in the direction of the beam may be difficult to measure unless the pulse extension is much less than the spacing between them; the spacing may, however, appear clearly resolved as peaks in the frequency spectrum as in Fig.5. Further understanding of why one goes to the trouble of obtaining a spectrum can best be seen by going back to first principles. This approach due to Lloyd &lo will also show why the technique, so successful in two dimensions, has yielded so little in three. If we could generate an infintely short delta-function pulse of ultrasound and receive its echo by perfect (infinite bandwidth) electronics we could distinguish between target features at different distances, however closely spaced, from the transducer by the difference in time of arrival of the echoes.
-4c
-
I 8
I
4
b
I 12
Frecptency parameter
W/C
a - Response of a spherical cavity of radius a in a metal Fig.9 matrix; b - response of a solid sphere of radius a in a metal matrix (PCs/PC, = 0.9)
16
In practice, of course, the interrogating pulse has the form g(t) where g(t) is made up of all the delta-functions we would like to have generated. The function g(t) incorporates all the transducer characteristics, the driving waveform, the effect of coupling, and the effect of the medium on the pulse. In fact everything except the effect of the echoproducing target. Similarly, the effect of a target feature
Fig.10 Amplitude and spectral responses of fiat-topped cylinders of various diamters: time domain signals, 1 MS per division; upper traces: spectra, 1 MHz per division)
ULTRASONICS.
SEPTEMBER
1973
a - 2.0 mm; b -
1.25 mm; c -
1.15 mm flower traces:
density) and the logarithm of that (the log mod spectrum) are still difficult to interpret.
of complex shape can be described by a function h (t) where h(t) is a continuous function incorporating all the discrete features we might have hoped to resolve. The echo pulse f(t) is then g(t) modified by h(t) in the form
In the case of simple targets like the spheres which gave rise to Figs 9a and b, the spectra in one form or another show a clear modulation interval. For more complex targets the modulation intervals, though obviously there, are spread over a wide spectral range. The problem is to pick them out. One ossible way of doing this has been investi. a srm y hfied model for ultrasonic gated by Lloyd. E Using scattering due to Freedman,l he accounts for the modulation of the spectrum in terms of AT, the time for an ultrasonic wave to go between two important scattering features of the target. In the case of Fig.9a, these turned out to be the near point and equatorial plane of the sphere. In the case of Fig.9b where the sphere was penetrable, the significant features were the near and far points of the sphere. In either case a modulation interval of ~/AT arises, the depth of modulation being a measure of the mismatch at the two features. A more complex target with three significant features 1,2 and 3 would have a threeterm modulation corresponding to A712, Ar23 and Ar13. While the Freedman approach shows that the number of ‘features’ in a real target may not be as large as might be feared, it is clear that even in quite simple targets there must be a number of such modulation intervals. The problem is still to pick them out.
f(t) = g(t)*h(t) where the asterisk denotes a convolution of delta-functions, ie,
or infinite
sum
+oo
f(t) =
J-co
g(T)h(t- T)d7
Inprinciple the convolution could be unravelled by digitizing the echo pulse and feeding it to a computer. The snag, apart from the time required to obtain the result, is that g(t) has to be known and this varies with the conditions of the test (the modulation observed with the smaller stub targets in Fig.10 was ag(t) property not an k(t) property). A much more hopeful approach is to try to separate g(t) from h(t) and this is exactly what fourier transforms do. Gating out f(t) and frequency analysing it or, as electronic spectrum analysers do, taking its power spectral density gives IW412
= IG(w)IW(w)l2
‘Cepstroscopy’
One possible way of doing this is the cepstral l2 technique adapted from seismology. This involves treating the spectrum as if the abscissa were time rather than frequency (as it is when displayed on an oscilloscope) and re-Fourier analysing it. The result is called a cepstrum. This and other jargon l2 terms have been taken over from seismology.
The dot is now a simple multiplication which can, if desired, be removed by taking the logarithm, again electronically In IF(w)1 = In IG(o) I + In W(w) I Whether or not the logarithm is taken, the properties of the target have been thus partially separated from those of the interrogating pulse. In an ideal case if the interrogating pulse, while band limited, had a truly flat spectrum within the range accessible to the apparatus, then G(w) would be a constant and would drop out of consideration. Frequency analysis is thus an attempt to isolate the characteristics of the effect investigated from the notoriously variable characteristics of the investigating apparatus. This is a step forward bat the spectrum, its modulus (the power spectral
a
rl
b
An example of the use of this technique to identify the periodic modulation of a log mod spectrum has recently been published by Lloyd 8 who digitzed the time-domain signals from known targets and showed by digital computation that time-unresolved features could be identified in the cepstra, separated from transducer and coupling information. The inverse process is not, as yet, possible. For the record, Lloyd’s published cepstra were noisier than they need have been because of an unsatisfactory digitization process. For this reason, an example of a cepstrum will be delayed till a later section when it will be shown that, if
M
Amplitude and spectral response of 2.0 mm diameter cylindrical targets with flat and conical tops: b and c are 8 and 21 dB below a Fig.1 1 respectively (lower traces: time domain signals, 1 ~1sper division; upper traces: spectra, 1 MHz per division)
208
ULTRASONICS.
SEPTEMBER
1973
the geometry of the problem can be effectively reduced to two dimensions, the cepstral technique gives very encouraging results. The Rayleigh
analysis
An alternative approach, also proposed by Lloyd 8plo, l3 and based on Rayleigh’s original 1871 work on light scattering, is to obtain a polynomial fit to the log mod spectrum. Thus lnlF(w)(
=A,
+Alw
+. . . +A,d
+A2w2
Dividing the measured In lF(w) I by the computed term in a2 leaves a series which certainly contains shape information separated from the size information. Experience with the interpretation of discrete target data obtained by wideband ultrasonoscopy leaves no doubt that the response of known targets can be accounted for. Characterization of unknown targets by this method of data processing is not yet in sight. ultrasonic
b
+. . .
The Rayleigh analysis, which is similar to that discussed at the beginning of the section on a theoretical analysis, requires that A o = A 1 = 0 and that A 2 should be proportional to the volume of the target. The additional coefficients A,. describe the shape and other features of the target and can in fact l3 be obtained directly from the time domain response either digitally or electronically without having to obtain the spectrum. This approach has had some success with artificial targets with the same total volume, but different shapes or disposition can be shown to have similar values of A 2.
Practical
a
data processing
To sum up this section, the original aim of ultrasonic spectroscopy was to characterize discrete targets in a threedimensional matrix. Theory gave hope that this could be done. Now that apparatus has been constructed and experiments carried out, it has been confirmed that theory correctly describes the scattering properties of known targets but that derivation of target characteristics from the observed ultrasonic responses is still some way off. Against this, it has been shown that, when the problem
Fig.13 Ultrasonic responses from the slot shown in Fig.12: a - time-domain response from the whole slot; b - time-domain response from the leading (‘referee point’) corner; c - spectra (solid line is the spectrum of a, dotted line is the spectrum of b)
can be reduced to variation of material properties in two dimensions, ultrasonic spectroscopy is almost always successful. The next section will discuss a case where characterization of a discrete defect has been successfully carried out by ultrasonic spectroscopy, precisely by reducing the problem to one in two dimensions. Surface waves It has often been proposed to use ultrasonic surface (Rayleigh) waves for the detection and characterization of surface flaws in metals. A critical literature survey of previous attempts to do so has recently been prepared by Miss Jennifer Tolley I4 of the City University Centre for Information Science. Although this lists 132 references it shows that few positive results have been obtained. However, L. L. Morgan l5 appears to have made a breakthrough by using broadband surface wave transducers and the application of ultrasonic spectroscopy. Characterization
of a surface crack
A finger transducer interrogates the surface of an aluminium block with pulses of broadband (0.5-10 MHz) ultrasonic Rayleigh waves. In the surface of the block is a milled slot simulating a surface crack and having the dimensions shown in the upper part of Fig.12. Pulses reflected from the slot reveal its presence and position and are shown in Fig. 13a. Fig. 13b shows the echo signal from the leading corner only, carefully gated out from the signal from the whole slot. Comparison of Figs 13a and b shows that the smaller responses which arise from the other corners of the slot are not resolved in the time domain so that no inference can be drawn about the slot dimensions.
Time I/.4 Fig.12 Cepstral analysis of ultrasonic pulses from a slot. Top: cross-sectional view of the milled slot; bottom: cepstrum in which amplitude is dependent on the intensity of the feature
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Fig. 13c shows the frequency spectra of the responses from the whole crack (solid line) and the leading corner (dotted line). The effect of the internal structure of the slot is seen to be to modulate the leading corner spectrum which itself contains unwanted information about the transducer, its coupling to the surface and the properties of the surface
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between transducer and slot. Extraction and interpretation of this modulation has been the first success of the cepstral method of data processing. At present this processing is carried out digitally: the reflected pulse in Fig.13a is digitized and its spectrum obtained by digital computation. The spectrum of that part of the pulse which comes from the leading corner of the slot is similarly obtained. Comparison of these spectra isolates the modulation due to the internal structure of the slot and eliminates the effects of variability of transducer, coupling and surface transmission between transducer and slot. The final stage is to obtain the spectrum of the comparison spectrum. This second spectrum is the cepstrum described earlier. The typical result is shown in Fig.12 where the peaks in the cepstrum (directly photographed from the computer print out) show that clear resolution of features separated in transmission time by less than 0.1 ~_lscan be obtained. Features in this case are regions of the surface where curvature is large and heights of the cepstral peaks are a measure of the angle through which the surface turns. Of particular interest is the cepstral peak at approximately 0.8 ps which is due to the ledge in the trailing vertical face of the slot. This was produced by a machining error and was only discovered when a reason for this peak was sought by subsequent sectioning of the metal. The size of the peak suggests that the actual ledge, before sectioning, was rather more ragged than is shown in Fig. 12. This is consistent with the nature of the machining error.
In non-destructive testing applications it is not practicable to avoid the contradiction by using separate transmitting and receiving transducers (the space and manoeuvrability restrictions in sonar applications may be much less stringent). Partial solutions have been obtained by development of finger transducers l&l7 and multi-element transducers.8>18 These and more recent developments will be the subject of a later article.
Acknowledgements This review relies heavily on work as yet unpublished. In particular, that of my colleagues at The City University, E. A. Lloyd, L. L. Morgan, D. G. Tasker and J. P. Weight who deserve thanks for allowing me to use their results. Also to be thanked are the committee headed by the late Richard Eborall of the British Non-Ferrous Metals Research Association who arranged for financial support from a consortium comprising the BNFMRA, the Central Electricity Generating Board, Rolls Royce Ltd, Henry Wiggin Ltd and the Ministry of Technology (Air).
References 1 2
Generation
and reception of wideband ultrasound
Early work with wideband ultrasound was done using conventional transducers with their properties modified by damping. Thus, in Gericke’s early experiments * conventional, heavily-damped transducers with pulse-excitation gave spectra with a series of humps separated by nulls at regular frequency intervals f These spectra were similar to the wellknown spectrum of a rectangular pulse of duration l/f:
6 I
For the experiments on grain size and collimation effects described earlier the multi-peak spectrum was not really a serious disadvantage; indeed it may even have helped interpretation of results by focussing attention on the behaviour of a few marked peaks. But for more sophisticated targets, such as extended interfaces, the nulls are a real disadvantage since the interfacial echoes also modulate the spectrum at well defined frequencies. For three-dimensional targets, the analysis attempted earlier shows that a really flat spectrum is essential: only such can be called true wideband transducers. Wideband
transducers
The problems of fabrication and excitation of wideband ultrasonic transducers have recently been reviewed by Lloyd * and by Mitchell,16 the most significant feature being Lloyd’s lo demonstration that the requirement for a satisfactory wideband transmitting transducer is a thick crystal (42 mm for 10 MHz bandwidth) while, in the reception mode, a thin (350 pm for the same bandwidth) crystal is necessary. If these contradictory requirements have apparently not been made before, it may be because traditionally the effects of the two functions are combined in the observed loop-response spectrum.
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11 12 13 14 15 16
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18
Gericke, 0. R. Ultrasonic spectroscopy, US patent 3538753 (10 November 1970) Gericke, 0. R. Paper number 1 in The Future of Ultrasonic Spectroscopy, edited by P. M. Reynolds, British NonFerrous Metals Research Association, London (1971) Gericke, 0. R. Encyclopedic Dictionary of Physics Supple ment 4, Pergamon Press, Oxford (1971) 502 Lloyd, E. A. British Non-Ferrous Metals Research Association paper S150/30/13 (1972) to be published Bhatia, A. B. Scattering of high-frequency sound waves in polycrystalline materials, Journal of the Acoustical Society ofAmerica 31 (1959) 16 Samain, D. Ultrasonic Techniques in Biology and Medicine, edited by B. Brown and D. Gordon, Iliffe, London (1967) 145 Weight, .I. P. Instrumentation associated with the development of wideband ultrasonic techniques (ultrasonic spectroscopy), M Phil thesis, The City University (1972) Lloyd, E. A. Paper number 2 in The Future of Ultrasonic Spectroscopy, edited by P. M. Reynolds, British NonFerrous Metals Research Association, London (1971) Lord Rayleigh, The Theory of Sound, volume 2 chapter XVII, McMilIan, London (1896) Lloyd, E. A. A heuristic approach to the scattering cross section of targets at ultrasonic frequencies and the development of wideband ultrasonic techniques, PhD thesis. The City University (1973) Freedman, A. Mechanism of acoustic echo formation, Acustica 12 (1962) 10 Brown, A. F. Physical problems in a technological university, Quest 9 (1969) 24 Lloyd, E. A. British Non-Ferrous Metals Research Association paper (1971) to be published Tollcy, J. Ultrasonic Rayleigh and Lamb waves in NDT, The City University Centre for Information Science (1972) Morgan, L. L. Crack size evaluation using ultrasonic surface wave spectroscopy, PhD thesis, The City University (1973) Mitchell, R. F. Paper number 5 in The Izuturc of Ultrasonic Spectroscopy, edited by P. M. Reynolds, British NonI:errous Metals Research Association, London (197 1) Van der Pauw, L. J. The planar transducer ~- a new type of transducer for exciting acoustic waves, Applied I’/??~ics Letters9 (1966) 129 British Non-Ferrous Metals Research Association, Improvements relating to piezoclectric transducers, I!K patent application 149869 (1969)
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