J. Phys. D: Appl. Phys., Vol. 11, 1978. Printed in Great Britain
A calibrated capacitance transducer for the detection
of acoustic emission
C B Scrubyi and H N G Wadleyl
t Materials Physics Division, AERE, Harwell, Didcot, Oxon
4 Metallurgy Division, AERE, Harwell, Didcot, Oxon
Received 28 February 1978
Abstract. We describe a capacitance transducer for use as a calibrated detector of
energetic acoustic emission events. It is displacement-sensitive with a wide frequency
response, and typically has a rise-time of 20 ns. The electrical output of the transducer
has been calibrated as a function of displacement, and the device has been tested in a
broad-band acoustic emission system. It is envisaged that the transducer could either
be used to measure emission transients directly, or act as a reference against which
conventional piezoelectric transducers could be compared.
1. Introduction
Many experiments have been reported in recent years in which acoustic emission has been
observed during the deformation and fracture of a wide class of materials i~icluding
composites, ceramics and metals (for a review see Ying 1973). Because acoustic emission
is generated during the growth of a crack it has been used both as a technique for monitoring the behaviour of flaws in large engineering structures, and in laboratory experiments where it offers the possibility of dynamically following deformation and fracture
processes.
A central problem arising in all of these studies has, however, been the difficulty in
relating the features of individual acoustic emission signals to individual deformation
and fracture processes. Clearly, if the technique is to find general applicability for
monitoring deformation and fracture, it is necessary to be able to relate details of an
acoustic emission to the important features of the source event. This requires source
information to be retrieved from the recorded emission transient which can be directly
related to the physical process responsible for the transient.
In order to make progress it is essential that measurements are made using standardised
techniques, and that calibrated systems are used, so that results from different laboratories
can be compared directly. It is also very important that this standardisation of approach
be combined with systematic studies of well-characterised deformation and fracture
processes.
A critical component in any acoustic emission system is the transducer, and it is
essential for its response to be carefully calibrated if the problems presented above are
to be overcome. In this paper we describe a capacitance transducer which assists with
standardisation and which gives calibrated values for the motion of the test-piece surface
that can be related to source events.
0022-3727/78/0011-1487 $01-00
01978 The Institute of Physics
1487
1455
C B Scruby and H N G Wudley
2. Requirements for a transducer to measure acoustic emission
An ideal transducer for acoustic emission measurements should have the following
properties :
Sufficient sensitivity to detect emission of the energy normally encountered in
acoustic emission tests.
( 2 ) Sufficient bandwidth to cover the full frequency range of the emission source.
(3) Reproducibility, i.e. its transfer function must be independent of the test.
(4) A design which is compatible with most common testing configurations.
( 5 ) Be amenable to calibration so that the relation between the input signal, in terms
of absolute surface displacement or velocity, and the output signal be determined.
( 1)
The piezoelectric transducers generally employed for acoustic emission measurement
have complex transfer functions, and they monitor either displacement or velocity or a
combination of both depending on the frequency of the signal. Their frequency response
is narrow in comparison with the bandwidth of typical acoustic eemission signals, and
they need to be attached to the test-piece by a couplant such as silicone grease, whose
thickness is difficult to control and causes variable coupling efficiency. This irreproducibility, combined with limited bandwidth and complex transfer characteristics, make
piezoelectric transducers unsuitable for a calibrated system. Their chief advantage
however is high sensitivity.
One alternative, an air-gap capacitance transducer (Breckenridge et a1 1975), has been
found to fulfil all the requirements reasonably satisfactorily. Its most serious disadvantage
is that its sensitivity is typically an order of magnitude less than that of a piezoelectric
device. It can therefore only detect the more energetic sources of emission. The main
advantages of the capacitance transducer are that it is a displacement-sensitive device
over a wide bandwidth, so that its output can be calibrated, and that it does not require a
couplant.
3. Transducer design
The physical principles upon which a capacitance transducer is based are well established
(see for instance Kinsler and Frey 1962, Bordoni and Nuovo 1958, Curtis 1974). The
device used here consists of two parallel plates of area A , separated by a sinal1 air gap E.
One plate is the polished surface of the test-piece, and this is earthed (figure 1). The other
plate in the transducer is maintained at a potential V . Thus oscillation of the surface due
to the arrival of an elastic wave causes the capacitance C of the transducer to change.
Provided the potential difference between the plates is kept constant, then a charge 6y
must be induced on the plates, which is given by
sq=
Since
vsc.
(1)
(2)
C= CA/(
where E is the permittivity of the gap we can write
6q= - E VA@/(Z.
The sensitivity of the transducer to surface displacement is thus
dq/d[=
EVA/[^.
(4)
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A colibrated capacitance transducer
To charge
amplifier
Induced charge b q
Plate area A
Plate potential V
Gap C
____--
displacement 6 E
////////// / / /// /
/
Earthed
specimen
7
-
Elastic
wave
Acoustic emission
source
Figure 1. Schematic diagram of a capacitance transducer, showingits mode of operation.
0
From equation (4) it can be seen that the sensitivity is increased by increasing plate
area, decreasing plate separation, and increasing the potential difference between the
plates. The plate area, however, is limited by bandwidth considerations. It can readily
be shown that, if the source of an ultrasonic pulse is at a depth 12 vertically below a
transducer plate of radius a, i.e. on the axis of the transducer, the path difference between
waves reaching the circumference and the centre of the transducer is given by
611 =a2/2h
(5)
provided a < / I . Thus, if the wave velocity is v, the difference in transit times is given by
6t =a2/2vh.
(6)
For a source 20 mm vertically below a transducer of radius 3 mm, and a longitudinal
wave velocity typically of 6000 ni s-1 for steel, 6t is 37 ns. The conventionally defined
rise-time of a transducer in response to a step-function pulse generating a spherical wave
front can then be calculated to be 23 ps. This clearly imposes a bandwidth limit which is
shown from equation (6) to be inversely proportional to the plate area, and thus to the
sensitivity of the transducer. Consequently, greater sensitivity by means of increased
plate area can only be obtained at the expense of bandwidth. In order to satisfy the
bandwidth requirement for which the transducer was principally developed, the plate
diameter was chosen to be 6 mm.
It should be noted that the position of the source with respect to the axis of the
transducer also places a limit on bandwidth. For a depth of 20 mm, perpendicular displacement of the source away from the axis must be less than about 1 mm to avoid a
significant reduction in bandwidth due to coherency loss across the transducer facc.
Maintaining the air gap as small as possible improves the bandwidth of the transducer as well as maximising sensitivity because the resonance frequency of the air gap is
inversely proportional to the plate separation. For a 2 pm gap, the lowest resonance
frequency is about 80 MHz, and this is much higher than the limits placed by other
factors on the bandwidth. A particularly important requirement for this transducer is
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C B Scruby and H N G Wudley
-
that a small area (i.e. 1 cm2) of the test-piece surface, which forms one plate of the
capacitor, must be ground flat and polished so that a small air-gap can be obtained to
maximise the sensitivity. For non-metallic test-pieces a conducting layer must be plated
on to the surface. Tests have shown that gaps of 2 pm or less can be achieved and maintained, provided both plate surfaces are accurately flat, parallel, clean and well polished,
at least to ? 0.25 p i . A differential micrometer adjustment enables the centre plate of
the transducer to move perpendicular to the specimen surface over a traverse of 2 mm
(figure 2). It also enables the gap to be set to any value within about 0.25 pm, although it
cannot be used to measure the gap with this accuracy due to backlash. The determination
of the plate separation is made from a measurement of the transducer capacitance using
an AC bridge technique. Edge effects can be neglected for the capacitor since the ratio
of plate separation to diameter is less than 10-3.
Plate
--
block
Figure 2. Cut-away drawing of capacitance transducer, showing the difyerential micrometer used to adjust the plate separation.
With regard to the requirement to maximise the potential difference applied across
the plates, it has been found by experiment that an electric field of about 35 V pm-1 can
be applied before there is any measurable discharge or breakdown. This is, however,
critically dependent on the cleanliness and smoothness of the two plate surfaces.
Finally, the sensitivity is also proportional to the dielectric constant. It is not possible
to increase this appreciably when the dielectric is a gas. Introducing a solid or liquid into
the gap, however, increases the dielectric constant, but seriously reduces the compliance,
and may also lead to low-frequency resonances.
4. Calibrating the transducer
In order to calibrate the transducer response to acoustic emission it is necessary to know
the relationship between the output signal from the transducer and the displacement of
the specimen surface. For a capacitance transducer this involves relating the change in
A calibrated capacitance transducer
1491
charge on the plates to the change in plate separation. This can be done theoretically
using equation (4) or experimentally by measuring the capacitance of the transducer as a
function of plate separation. It is then possible, knowing the initial separation, to evaluate
the transient change in displacement due to an emission event from the recorded change
in capacitance. Using capacitance measurement for the determination of plate separation
has the advantage of being rapid without disturbing the experimental configuration. The
technique also minimises any errors due to surface flatness.
The transducer response was therefore calibrated by measuring the capacitance for
independently measured plate separations. The stray shunt capacitance from leads and
connectors was determined first by setting up a very large gap, and was found to be 28.1
pF. Two methods were used to obtain known air gaps. First the differential micrometer
(20 turns per mm travel) was used to adjust and measure the gap over a range of 50 pm,
these measurements being made in one direction only to reduce backlash. Second, the
transducer was set up to have a very small gap, and then metal foil shims, 5pm thick, were
inserted so as to increase the plate separation by known increments. The capacitance of
the air gap was obtained by subtracting the stray capacitance from the measured value,
and it was found to be inversely proportional to plate separation. Both methods gave
50
I
I
I
100
150
203
Measured capacitance IpFl
Air gap Ipm I
Figure 3. ( U ) Transducer air gap as a function of the capacitance measured at the output
of the transducer; (6) transducer sensitivity as a function of air gap for different plate
voltages.
1492
C B Scrtrby a d 11 N G Wadley
the following relationship :
,C=248/(C- 28.1)
(7)
where the plate separation ,C is measured in pm and the measured capacitance C in pF.
This result agrees well with calculation for parallel circular plates of 6 mm diameter, i.e.
from equation (2)
E=
EAICgap
(8)
= 250*3/Cgap.
(9)
Figure 3 shows the calibration curves for plate separation and transducer separation
based on equation (7) and (4).
5. Incorporation into a detection system
During a test the transducer plates are maintained at a constant potential difference so
that surface displacements are converted into changes in induced charge. The transducer
must therefore be coupled directly to a low-noise charge-sensitive head amplifier as shown
in figure 4. The transducer impedance is very high (capacitance typically 120 pF, resistance > 10 GQ),so that the input impedance of the head amplifier needs also to be high.
,
Pencil
elad<,
Aluminium
transfer
block
Capacitance
t ransdu cer
Transient
recorder
Load cell
amplifier
Load cell-Chart
recorder
Figure 4. Schematic diagram of the experimental arrangements for recording acoustic
emission transients from the fracture of pencil leads. L longitudinal wave, S shear wave,
arrival time.
It is also important to minimise the cable length linking the transducer to the amplifier,
since the cable adds to the shunt capacitance and increases the input noise level. The head
amplifier must also have at least the bandwidth of the transducer, as well as the capability
of providing a constant polarising potential for the transducer.
The remainder of the system, to which the head amplifier is coupled, needs to incorporate further wide-band amplification, and possibly some fikering (depending on ambient
noise level), prior to data recording.
A calibrated capacitance transducer
1493
6. Detection of acoustic transients
The transducer has been used to detect stress wave transients from the fracture of glass
capillaries and 0.3 mm diameter pencil leads, following the work of Breckenridge et al
(1975).
A slowly increasing load is applied either to a capillary or pencil lead, the end of which
is in contact with the transfer block vertically above the transducer (figure 4). The applied
load was measured using a load cell and the fracture load for the pencil lead was typically
about 3 N. The sudden load relaxation on fracture generates an elastic wave which
causes the surface of the transfer block to experience a point force step, whose rise-time
depends on the time taken for the crack to propagate across the lead, which was typically
about 300 11s. The fracture of the pencil leads was preferred to the glass capillaries,
because of greater reproducibility in the magnitude of the force step.
0
I
3
I
I
I
1
2
3
1
2
3
L
5
T l m l ips1
Figure 5. Surface displacement of two aluminium blocks of different thickness, in
response to the fracture of a pencil lead vertically above the detector. Source strength
3N, depth 10.5 mni: (a) experimental, (b) theoretical. Source strength 3.2 N, depth
20 mm:( c ) experimental, ( d ) theoretical. The experimental values were measured using
the capacitance transducer, and the calculated values were from a theoretical model
based on Pekeris and Lifson (1957). The time is measured from the arrival of the
longitudinal pulse.
Figure 5 shows typical transients recorded when the thickness of the transfer block
was 10.5 m m and 20 mm. For both these tests a plate separation of 5 pni and voltage
of 5 0 V were used. The theory for a point source buried within a semi-infinite solid
(Pekeris and Lifson 1957) shows that the height of the compression wave step should be
inversely proportional to the source-transducer distance. The present results are in
general agreement with this theory (figure 5). The diffetent transit times for the two blocks
account for the differences in the shear wave arrival times.
When pencil lead fracture was used as a reproducible source and the plate separation
varied (using the micrometer adjustment on the transducer) the height of the resulting
1494
C B Scruby and H N G Wadley
surface displacement step was found to be inversely proportional to the square of the
plate separation, which is consistent with equation (4). Results could also be reproduced
after xemounting the transducer on the block and resetting the plate separation, provided
the surfaces were polished and clean.
The transducer appears to be linear in response, and tests have shown that its sensitivity to surface displacement is of the order of 10-12 m (0.01 A). The transducer should
have a flat frequency response over a wide bandwidth. The use of a laser interferometer
(Drain et al 1977) to determine this will be reported later. Other tests currently in progress show that the transducer can detect surface pulses with rise-times at least as short
as 20 ns, which is the limit imposed by the amplification and a signal processing.
7. Summary
We have reported the construction and testing of a transducer which fulfils the proposed
criteria, set out in $2, for a standard or reference device. The use of the differential
micrometer for adjusting the air gap gives the transducer flexibility and enables it to be
used with constant sensitivity on different test-pieces. Two uses are envisaged for the
capacitance transducer. Firstly, it is ideal for incorporation into a calibrated, broadband
detection system for acoustic emission, provided only energetic events are studied. A
capacitance transducer has already been used in this context (Scruby et nZ1978), to obtain
calibrated information about the deformation and fracture events which generate
acoustic emission. Its broadband response has made it possible to obtain information
about acoustic emission events over ten times the frequency range of other published work.
Secondly, preliminary tests suggest that it can be used as a reference transducer for
more conventional systems. Using a standard test-piece and source of emission [such as
the fracture of a pencil lead) measurements could be made first with the conventional
piezoelectric transducer and then compared with the capacitance transducer, which had
been set up on the test-piece in a symmetrical position to the first. This would enable the
output from the conventional transducer to be related back to the actual surface displacement of the test-piece.
Acknowledgments
We wish to thank J C Collingwood, G J Curtis, B L Eyre and A B Johnson, for many
helpful discussions during the development of this work.
References
Bordoni P G and Nuovo M 1958 Acustica 8 351
Breckenridge F R, Tschiegg C E and Greenspan M 1975 J. Acoust. Soc. Am. 57 626
Curtis G J 1974 (April) Non-Destructive Testing p 82
Drain LE, Speake J H and Moss B C 1978 Proc. 1st Europ. Congr. on Optics Applied to Metevology to be
published
Kinsler L E and Frey A R 1962 Fundamentals of Acoustics 2nd edn (New York: Wiley) pp 298-303
Pekeris C L and Lifson H 1957 J. Acoust. Soc. Am. 29 1233
Scruby C B, Collingwood J C and Wadley H N G 1978 AERE Rep. 8915
Ying S P 1973 CRC Crit. Reo. Solid St. Sei. 4 85