oco1_61M)81’0201-0?99102000
QUANTITATIVE ACOUSTIC EMISSION SOURCE
CHARACTEZRISATION DURING LOW TEMPERATURE
CLEAVAGE AND INTERGRANULAR FRACTURE
H. N. G. WADLEY, C R SCRUBY and G. SHRIMPTON
AERE, Harwell. Oxfordshire OX1 1 ORA, U.K.
fReceiued
26 June 1980)
AU-The
basic physical relationships between fracture processes and the acoustic emission waveforms accompanying them, have been ex.amined to show that dynamic information about the magnitude
and time-scale of fracture events can be deduced from measured waveforms. These findings have been
tested by measuring the acoustic waveforms from cleavage and intergranular microcrack formation in
mild steel and electrolytic iron at 77 K. The microcrack lengths deduced from acoustic emission
measurements were consistent with fractographic observations. The velocity of microcrack growth
deduced from the acoustic emission measurements indicated the existence of a limiting microcrack
speed, in both materials, of about half the shear wave speed.
Rbm&-Nous
avons itudit les relations physiques fondamentales entrc la rupture et l’imission acoustique qui l’accompagne, afin de montrer qu’on peut obtenir une information dynamique sur la grandeur et
I’&hdk de temps des phCnomtnes de rupture, B partir des formes d’ondcs mesurCcs. Nous avons v&i%2
cette idbe en mesurant la forme des ondes acoustiques &n&es au tours du c&age et de la formation de
rni~o~~ur~ inter~~ulair~
dans l’acier doux et le fer ilectrolytique B 77 IL Les longueurs de microfissures d&h&a des mcsures d’imission acoustique sont en accord avec ies observations fracto~aphiques.
La mesure de Ia vitesse dcs microiissu:es d partir des mcsures d’imission acoustique montre I’existence
d’une vitesse iimite, &gale ii la moitit environ de la vitesse de I’onde de cisaillement.
Zaammenfa~Die
physikalischen Zusammenhiinge zwischen Bruchprozessen und der SchwinBungsform der damit zusammenhlngenden
akustischen &mission werden untersucht. Es wird gezeigt.
da0 aus einer Analyse gemessener Schwingungsformen dynamische Informationen iiber CirBL3eund
Ablauf der Bruchereignisse abgekitet werden kiinnen. Die SchluDfolgerungcn wurden mit Messungen
der akustischen Schwingungsformen gepriift, die bei Spaltung und bei Bildung intragranularer Mikrorisse in Weichstahl und in elektrolytischem Eisen bei 77 K auftreten. Die aus den akustischen Emissionen
abgeleitetcn RiOtingen sind vertriiglich mit fraktografischen Beobachtungen. Die abgeleitete Geschwindigkeit der RiBausbreitung deutcte auf eine Grenzgeschwindigkeit in beiden Materialien hin, die etwa
die HIilfte der ~herwelIengeschwindi~eit
bet&&.
1. INTRODUCTION
Acoustic emission is the term used for the transient
elastic waves generated in a solid by rapid, usually
localised, stress (or strain) relaxations accompanying
for example, the propagation of dislocations or the
growth of cracks. In a metal under load, acoustic
emissions may be generated by a wide range of deformation and fracture proaases. The study of these
unissions has enabkd the development of techniques
for detecting and locating defects in structural components; it oouf& in printipk, also improve our
understanding of &formation and fracture dynamics,
since dynamical information about the sour= event is
contained in the elastic waves. This paper is concerned primarily with this latter application of acoustic emission.
Until quite recently, studies of acoustic emission
from metals were qualitative and only empirical
results were obtained (see for instance the review of
Lord [I]). Whilst these amply demonstrated the generation of detectabk elastic waves by many different
deformation/fracture processes they failed to give
quantitative information about the mechanism of
each process. This has been attributed in part to the
use of inadequate detection instruments, but also to a
poor understanding of the physical processes involved
during both the generation and propagation of acoustic emissions [23.
In the first successfulattempt to probe the physical
principles of acoustic emission, Breckenridge et al. [3]
applied the Pekeris solution for the response of an
elastic half-space due to a point force step [4], to
interpret the acoustic emission waveforms generated
by a simulated emission source (the fracture of a glass
capillary). The experiments were carried out under
carefully controlled conditions, and a capacitance
transducer was used to measure the emission. More
recently, theoretical studies have extended the calculation of waveforms to infinite plates [SJ, and excellent
agreement between theoretical and measured waveforms due to simulated sources has been found by
Hsu ef af. 163.
399
400
WADLEY
et nl.:
ACOUSTIC
EMISSION
DURING
In a parallel study, the authors have developed an
approach to the measurement and interpretation of
real, rather than simulated, acoustic emission waveforms. This technique also relies on the use of a capacitance transducer and calibrated detection instrumentation {7]. combined with a specimen geometry
to which the transfer functions of a half-space can be
applied [8].
The technique was used to record for the first time
relatively undistorted waveforms from fracture events
in steel [8,9]. These waveforms resembled that
from a force dipole. Recently a theoretical study has
modelled a microcrack event as combinations of force
dipoles, rather than as a monopole as in the case of
the simulated emissions [lo]. This fundamental study
showed clearly the potential of the approach for the
dynamic characterisation of deformation and fracture.
Here, we shall apply this quantitative acoustic
emission approach to the study of two distinct fracture processes: the formation of cleavage microcracks
in mild steel at 77 K. and the formation of inter~~ular microcracks in electrolytic iron also at 77 K.
Applying the theoretical model outlined in the following section, the data are used to derive crack growth
parameters which are then compared with indpendent
measurements.
2 THEORETICAL
ASPECTS
The problem is to determine the relationship
between the dynamics of dislocation motion or crack
growth and the acoustic emission signal measured at
a point on the surface of the material, so that each
measured waveform can then be inverted to give a
physical meaningful source function. This scheme is
shown schematically in Fig. 1. It is a difficult problem
because in general we have a poor understanding of
the following:
(a) the mechanisms by which a moving dislocation
or growing crack radiate elastic waves, ie. the source
function
LOW TEMPERATURE FRACTURE
(b) the way in which these waves are modified as
they propagate through a bounded attenuating specimen to the transducer, ie. the specimen transfer function.
(c) how the vibrations of the specimen surface.
caused by the arrival of these waves are converted
into a fluctuating electrical signal by a transducer and
then recorded, ie. the detection system transfer function.
These will now be considered in turn.
2.1. The sourcejunction
A mathematical
description is required for the
deformation or fracture process of interest, in terms
of local changes in stress or strain. The description
can be in terms of the time-varying distributions of
forces which have to be applied to a perfect body to
produce the same elastic disturbance as the process of
interest [I 11. or in terms of notional dislocation
loops [ 123 The latter is more readily related to deformation and fracture events, but the two schemes are
formally related through the elastic constants.
Metal fracture processes usually comprise complex
combinations of crack extension and plastic flow over
non-planar surfaces, but no attempt will be made here
to model sources of such complexity. We shall,
instead, restrict attention to the creation and growth
of an infinitesimal planar elastic microcrack, the
strains from which under Mode I loading, are equivalent to an edge dislocation loop of strength b&4,
where b is the Burger’s vector and 6.4 the vector loop
area [12]. Thus b corresponds to the crack opening,
ii,4 to its area, and b&l to its volume. The dislocation
loop may in turn be represented by the sum of three
orthogonal. force dipoles of strength Dij since from
Burridge and Knopoff [ 113.
Dij = Cij,,b,JA,
(1)
where Cijkt are the elastic constants. The advantage of
such a representation is that it conveniently fits into
ElECTON
SYSTEM TRANSFER fWCllU4
4
MATERIAL
REmRED
mIssioN
WAVEFORM
Fig. 1. Schematic repr~ntation
of the relationship between recorded emission waveforms and the
fracture events that generate them.
WADLEY
er al.:
ACOUSTIC
EMISSION
DURII\;G
the Green’s function formalism used to evaluate the
transfer function.
A more complex source could be modelled as a
combination of dislocation loops or by expanding the
source function as a series of higher order multipolar
com~nents
(dipole, quadrupole. octapole, etc). For
reasons which will be given below. measurements of
acoustic emission waveforms were restricted to the
epicentre (the surface point vertically above the
source) for all tests. In this configuration single
measurements of normal displacement can only detect
Mode I opening (a shear source is invisible) and one
orientation parameter. the inc~nation of the crack to
the horizontal. The other orientation parameter. and
the two other time dependent amplitudes can only be
determined by a multi-transducer array.
2.2 Specimen transfer function
To calculate the transfer function from source to
specimen surface is, for any but the simplest of bodies,
a complex and, at present, impossible task. However.
for simple bodies such as an elastic half-space [4,13-J
and infinite plates [YJ transfer functions have been
evaluated. For a point force source and surface displacement measurement, the transfer function takes
the form of a Green’s function so that the displacement ui(f, x) at point x in response to a force
at
x’ is given by
Pj6(1)
Ui(t,Xl
=
G,j(r:
XZ X’)Pj
(2)
where G,j(r; x; x’) is the Green’s function.
For a half-space the Green’s function has closed,
analytic form at the epicentre and this is one reason
for choosing this position for waveform measure-
LOW
FRACTURE
I~,,&:x) = GEi, (I: x: x’)CijL,bkd.4,
(3)
where G"(t
:x ; x’) is for a source with Heaviside (step
function) time dependence H(r). obtained by integration of G(r
;x; x’).
For a horizontal dislocation loop source of strength
b&A. the normal displacement at the epicentre. Fig. 2.
comprises a singularity 6(r - (.xS!ccI))when the longitudinal wave arrives. followed by a low frequency
‘wash” whose amplitude increases until the direct
shear wave arrives. The strength of the singularity. A.
(the &function area) is proportional to the source
strength MA.
A =-
b6A
(4)
tns3c,
where c, and c1 are respectively the longitudinal (L)
and shear (S) wave speeds, In reality acoustic emission
sources are found to operate over a finite time. The
waveforms generated by these slower sources are
found by convolution of the Green’s function with
their time-history. The width of what then becomes a
pulse at the L arrival time is a measure of the time
over which the source operated.
2.3 Defecfion srsrem nnn.$er jii~rctioa
The detection system. which includes the transducer and recording instrumentation.
converts the
EXPERIMENT
OF
WAVE
PROPAGATIG~
THROUGH
MATERIAL
401
ments. The transfer function can be readily obtained
for a range of multipolar sources with either 60) or
N(t) time dependence, by suitable combinations of derivatives of the Green’s function. Thus for a dislocation loop of volume ~~~~,~(r). which can he
expressed as a sum of 3 orthogonal dipoles.
THEORY
SURFA:E
SPECiMEN
TEMPERATURE
coNvoLuTloN
WlTH
GREEN.S
FUNCTION
CONVOlUftON
GREEN
WITH
INVERSE
S FUNCTION
EDGE 515LOtATION
LOOP SOURCE.
EOUlVALEhT
?G
NORMALLY
LOADED
MlCRDCRACK
DEPTH
,X3
At
Fig 2. Showing the dislocation loop model for the microcrack emission source; the vertical surface
diiplaamcnt corresponding to a point source ‘switched on’ at t = 0 is given by the Green’s function: the
inverse Green’s function is used to obtain the source volume from the measured displacement.
402
WADLEY er al.:
ACOUSTlC
EMISSION DURING
normal surface displacement into an electrical signal
V(t)which can be recorded in either analogue or digital form. This electrical signal can be expressed as a
convolution of the displacement, a(t). with a detection
system transfer function. S(t), ie.
4!
S(t - ~)~(~)d?
V(t) (5)
i -P
It is, however, dificult to determine S(r) for many
transducers, so that the alternative approach of using
a detection system whose transfer function reduces to
a constant, ie. V(r)= ku(t),is to be preferred.
3. EXPERIMENTAL PROCEDURE FOR
ACOU!!$TlCEMISSION MEASUREMENT
The theoretical studies have shown that in order to
deduce a physical description of the source from a
recorded waveform, a number of stringent requirements must be satisfied by the specimen and detection
system (transducer and recording instrumentation).
3.1 Specimen geometry
LOW TEMPERATUREFRACTURE
tudinal and shear waves. Emission sources are constrained to lie within a narrow, short gauge section,
thus keeping the relative positions of source and
transducer
fixed to within fL5mm
so that the
transfer function is approximately constant for all
source events. The waveforms measured at this position have been shown in earlier work [It31 to bear a
close resemblance to calculated dipole waveforms,
@ving confidence in the continued use of this geemetry.
The presence of boundaries at the gauge does cause
problems; they have been found to cause small ‘echo’
pulses at the epicentre. However, earlier work has
shown conclusively that because the most useful information about the crack growth process is contained at the leading edge of the signal, echo effects
can be eliminated from the interpretation [lo]. In the
specimens used here the source-transducer distance
was small (- 17mm) and this served to reduce both
the attenuation of high frequency components by
scattering and the loss of signal amplitude by geometrical spreading
ideally the specimen must be both suitable for 3.2 The transducer
The transducer must be able to measure surface
inducing microcrack events by simple mechanical
loading in Mode I and yet sufficiently like an elastic displacement over the full bandwidth of the emission
half-space to allow valid application of the above source. For sources of -c 10m size, its bandwidth
theory. One such ~mpromi~ specimen, the Yobell, should be sufficient to record accurately pulses of durFig. 3, has already been designed for uniaxiai tensile ation -50ns and its sensitivity sufficient to detect
tests. At the epicentre, the specimen approximates to displa~ments of z 10”” m or less. Ideally the output
a half-space until after the arrival of both direct iongi- of the transducer should be propo~ional to the dis-
~-SURFACE
DISPLACEMENT
THROUGH
WAvEFRoNTs
PROPAGATING
SPECIMEN
ACOUSTIC
EMISSION
YOBELL
SOURCE
SPECIMEN
Fig. 3. Showing the Yobell specimen geometry. The acoustic emission sour= (eg. a microcrack event) is
constrained within the short gauge section. Elastic waves from the propagating microcrack radiate
spherically and when they reach a surfaa cause a transient displacement. At the ~mtre of the top fact.
this displacement is initially due to L and S wavefronts that have experiencedno major reflections.
WADLEY er al.:
ACOUSTIC
EMISSION
DURING
LOW TEMPERATURE
i 10
INPUT CHARGE
SIGNAL FROM
TRANSDUCER
403
DISC
TRANSIENT
RECORDER
FILTER
FRACTURE
STORAGE
121
t
lx
,003l4HZL5
;I
TRANSIENT
RECORDER
11 I
POPOE
MlNl
COMPUTER
Fig. 4. Schematic diagram of the acoustic emission recording system. With the exception of gain, the
two transient recorders had the same setting. Triggering was controlled by transient recorder (1).
placement so that its transfer function is a constant,
and it should not change the boundary conditions at
the surface.
A piczoelectric transducer satisfies only the sensitivity criterion. However, a capacitance transducer
can be made to satisfy all the criteria and has been
successfully used to detect acoustic emissions [3,7].
The transducer works by making the surface of the
specimen act as one plate of a parallel plate capacitor.
The other plate, of area A, is positioned a distance d
above the surface to leave a narrow air gap (dielectric
constant 4) and a potential V is maintained across the
plate. Thus, a displacement, dx,, of the specimen surface induces a charge dq on the capacitor, and the
sensitivity is given by
ds
-=
d+
--
EVA
d2
(6)
The transducer used for these experiments had a plate
area of 28.3 mm2 at a potential of 50 V. The plates
were highly polished, and a separation of 2-3 jun was
set up for each test using a differential micrometer.
Taking l = 8.85 x lo-” Fm-‘, gives the sensitivity
dq/dx3 = 3.13 x 10m3Cm-’ for d = 2 pm.
Transducer bandwidth is controlled by phase
coherence across the specimen surface under the
transducer plate. At normal incidence this loss of
coherence is due only to wave front curvature; the
phase difference across the plate rapidly increases for
increasingly oblique angles of incidence. This was a
further reason for restricting measurements to the epicentre. For the transducer used in these tests a longitudinal wavefront with H(t) time dependence emanating from a point 17 mm below the transducer would
appear as a ramp function of rise time -2Ons
(cl = 596Oms-‘)[7], and this imposes a bandwidth
limit on all measurements. Thus, the transfer function
of the transducer was a constant up to this bandwidth
limit.
For the experiments reported here few if any of the
detected signals appeared to be bandwidth limited.
However, this was only achieved at the sacrifice of
sensitivity. Noise limited the minimum detectable signal. Thus it was of paramount importance to mmimise extraneous electrical noise. Radio frequency
interference was reduced by performing the experiments within a screened enclosure. Insulation in the
specimen grips prevented ground-loop coupled noise
from being injected into the sensitive charge amplifier.
4.Y.29
2-J
For the experiments performed at 77 K the minimum
detectable signal was 1O- ’ * m.
3.3 Recording instrumentation
The purpose of the instrumentation was to transfer,
with the minimum of distortion, the charge fluctuation of the transducer onto a recorder for later
analysis. This was achieved, Fig 4, first by coupling
the transducer to a wideband low-noise charge amplifier. The voltage output of this amplifier was bandpass filtered at 30 kHz and 45 kHz to reduce noise
from the environment and to avoid antialiasing errors
associated with later digital recording. The signal was
further amplified and digit&d using a Biomation
8100 transient recorder of 10ns sampling interval
and with a maximum precision of 8 bits. The recording instrumentation
had a flat response from
80 kHz to 25 MHz, and over this frequency range
had an effectively constant transfer function of
2.1 x 10”Vm-‘.
In order to extend the limited dynamic range of the transient recorder for acoustic
emission studies, a second recorder was used in
parallel with the first with ten times the input range.
With this arrangement the working dynamic range for
recording was 44 dB.
During a tensile test the recorded waveforms and
the load at which each was emitted were recorded on
magnetic disc using a PDP/8 minicomputer.
4 MATERIALS PREPARATION
AND TESTING
4.1 Materials
The two processes chosen for study both involved
brittle fracture at low temperature (77K) to reduce
the complicating effects of plasticity. The first was
cleavage fracture of quenched mild steel and the
second was intergranular fracture of a high oxygen
electrolytic iron.
The mild steel was supplied in the form of 70mm
diameter bar, and Yobell specimens were prepared
with the tensile axis parallel with the cylindrical axis
of the bar. The chemical composition of the bar was
determined by a range of techniques including X-ray
fluorescence and emission spectroscopy, and the
results are shown in Table 1.
Ten Yobell specimens of mild stal were austenitised in the range 840-1200°C and quenched into
404
WADLEY er al:
ACOUSTIC
EMISSfONDURING LOW TEMPERATURE
FRACTURE
Table 1. Chemical composition of the materials
Element
Mild steel
(wt”,)
Electrolytic
iron (wt ppm)
C
0
0.25
-
24
430
N
P
S
Mn
0.08 0.017 0.039 0.72
12
50
<SO
80
Si
Ni
MO Cu
Fe
0.07 0.017 <0.01 0.019 Balt
100
I5
7
Bal$
70
t Other elements: AL Ti. Nb. V. Cr less than O.Olk.
$ Other elements: As. Sn. Sb. Al. Cr less than 50 ppm.
water at room temperature. This resulted in a martensitic microstructure within the gauge with no evidence of carbide precipitation (precipitates were
observed in thicker sections of specimens where the
cooling rate was much slower). The object of varying
the austenitising conditions was to produce specimens
~di~er~t prior austenite grain size and hence martensite lath packet size, Table 2. The grain sizes were
measured by the usual line intercept technique. No
account was taken in the calculations of mean values
of gram size and lath packet size of the sampling error
associated with the line intercept method of grain size
estimation, The actual sizes were some poorly-defined
fraction larger ( - 30%).
Intergranular fracture was studied in a specially
prepared Japanese electrolytic iron containing a high
oxygen concentration, Table 1. Yobeil specimens with
~mensions identical to those of the mild steel were
prepared from bars that had been produced by hot
extrusion to 80 mm diameter and further cold rolling
to 63 mm diameter. The tensile axis of the specimens
was again parallel to the cylindrical axis of the
bar.
The seven specimens were recrystallised by annealing in argon atmosphere furnaces in the temperature
range 700-710°C. The annealing time was systematically varied in an attempt to vary the ferrite gram
size, but little variation was obtained once the specimens had fully recovered, Table 3 shows that the
specimens had a constant grain size of 45 w. Once
again the grain size was measured using a line intercept and no account of the under-estimation of grain
size by this technique was made,
Annealing at 700°C followed by air cooling was
found, by Auger spectroscopy, to result in a high concentration of sulphur within a few atom layers of
grain boundaries [I43. No oxygen segregation was
detected,
During heat treatment oxide layers formed on the
surface of all the specimens. Since the cracking/
del~jnation of this layer is known to be a copious
source of emission, all the oxide was carefully removed by electropolishing prior to testing
4.2 Mechanical resting
All the Yobell specimens were tested to faiiure in
Table 2.
Temperature
(‘C)
Specimen
MS1
MS2
MS3
MS4
MS5
MS6
MS7
MS8
MS9
MS10
Treatment
Prior
Austenite
grain size/pm
Lath packet
size/pm
.
850
I BWQ
30
890
950
1060
1080
1140
If.50
1 h-WQ
1 h-WQ
1 h-WQ
1 h-WQ
1 h-WQ
1 h-WQ
45
90
105
123
127
131
:
100
90
1130
1 h-WQ
176
95
30
3s
80
Table 3. Heat treatment and mean grain sire for electrolytic iron
Temperature
Specimen
CC)
EIl
710
E13
El2
E14
EIS
EI6
E17
710
700
700.
710
700
Treatment
40 mirkair cool
160
80 min-air
322 &n-air
750 n&-air
1450 min-air
5760 mm-air
cool
cool
cool
cool
cool
Nominal fracture
stress/
MNmm2
1470
1800
1340
1570
1020
1610
1680
1750
1750
I190
specimens
Mean grain size
Nominalfracture
cun
Stress,MNm c z
36
170
43
45
60
45
46
47
2::
156
325
156
99
WADLEY er ah:
ACOUSTIC
EMISSION
DURING
LOW TEMPERATURE
FRACTURE
405
TO LOAD CELL
ATTACHED
To CROSSHEAD
DIFFERENTIAL
MICROMETER
ELECTRICAL
INSULATOR
TRANSDUCER
PLATE
TO HEAD AMPLIFIER
VOBELL
SPECIMEN
VACUUM
LIQUID
NITROGEN
AT 77K
Fig. 5. Schematic diagram of low temperature testing rig. designed for installation below the crosshead
of an Instron 1195 machine. Not shown are the insulation inserted in the neck of the dewar and the
transfer tube for introducing liquid nitrogen into the dewar.
an Instron 1195 screwdriven machine at a constant
crosshead speed of 0.1 mm/min. Apparatus. shown
schematically in Fig. 5, was designed for low temperature testing, in which the specimens were cooled by
immersion in liquid nitrogen held in a Dewar. Additional insulation was packed around the top of the
rig, which also reduced ice crystal formation by
excluding moist air. The liquid nitrogen level was
continuously adjusted in order always to cover the
gauge but to be below the polished face of the specimen to avoid disturbing the transducer. During initial
cooling diff&ntial thermal contraction caused separation of the plates. This effect could be monitored by
measuring the transduar capacitance and was used
to determine when thermal equilibrium had been
attained. It took about 90min to reach equilibrium,
when the specimen temperature was assumed to be
77K.
After failure the specimens were rapidly warmed to
room temperature to minimise oxidation of the frac-
ture surfaces. Each specimen was then examined by
optical and scanning electron microscopy to characterise both the microstructure and fracture mode.
5. EXPERIMENTAL
RESULTS
5.1. Mild steel
Representative graphs of nominal stress as a function of crosshead displaccmcnt are shown in Fig. 6,
with the acoustic emission data superimposed. The
non-linearities in the stress-displacement curve at
low stress were due to the high compliance of the
electrical insulation within the grips; otherwise the
specimens exhibited nominal elastic behaviour. The
specimens fractured at a range of loads, from which
fracture stresses were calculated using the initial
gauge section area (Table 2). The nominal fracture
stresses appeared to be independent of prior austenite
grain size.
WADLEY et al.: ACOUSTlC EMISSION DURING LOW TEMPERATURE FRACTURE
406
-FAILURE
CROSSHEAD
IO)
0
lb1
SPECIMEN
0 25
CROSSHEAD
SPECIMEN
DISPLACEMEW
-200
fmm
238
OS
0 75
DlSPLACEMENTlmm
242
/
Genuine acoustic emissions. with characteristic high
and low frequency components, were recorded from
all the specimens of both materials.
The parameter chosen to represent the genuine
emission in Fig. 6, was the longitudinal component
peak amplitude. This parameter is system independent and Fig. 6 shows that the emission usually
occurred towards the end of test, during the period
when subcritical microcrack formation would have
been expected. These emission waveforms. Fig. 9(a)
were in good agreement with that calculated for a
dislocation loop source. Variations in the amplitude
and width of the L component pulse of measured
waveforms were thought to reflect the variability of
the emission soura: process. The presence of oscillation between the L and S arrivals was in part due to
the presence of the gauge surfaces close to the source.
The distance from the epicentre to the fracture
surface was measured with a mjcrometer. Since the
fracture path was not smooth, this distance represented an approximate mean source depth. These
resulting errors in source depth introduce only a
small error during later deconvolution of the waveform.
5.2 Ekctrolytic iron
CROSSHEAD
ICI
SPECIMEN
DISPLACEMENT
/mm
265
Fig 6. Nominal stress versus crosshead d~spla~ment for
mild steel specimens MSl, MS5 and MS8. Non-linearity at
low stress was due to distortion of electrical insulation
within the grips. The figures also show the amplitude of
each recorded emission as a function of displacement.
All ten specimens fractured by cleavage, and low
~~ifi~tion
observations suggested that increasing
the prior austenite grain-size and hence the lath
packet size, resulted in a coarsening of the fracture.
This coarsening was observed at higher magnifications to result from an increase in length of individual
cleavage facets, Fig. 7. Optical metallography of settioned specimens, Fig, 8, revealed the presence of sub<*i&al cracking in the vicinity of the main crack path.
‘l&se subcritical cracks extended over a compkte
lath packet and were apparently arrested by lath
packet boundaries rather than lath boundaries.
Numerous acoustic emission signals were detected
and recorded as a function of load during each tensile
test. Some of the signals were found, on later examination, to be low frequency, due either to nitrogen boiling, grip noise or long duration ‘ringing of the specimen folIo~ng an emission, and were discarded.
The dependence of nominal stress upon crosshead
displacement is shown for two specimens in Fig. 10.
Again the specimens deformed elastically (with the
exception of the strain due to low compliance of the
gripping system) up to fracture. Specimens fractured
at a range of loads and the nominal fracture stress for
each is given in Table 3. The fracture stress was not a
function of grain size or mnealing time.
These specimens fractured by a mixture of cleavage
of individual ferrite grains and intergranular cracking,
Fig. 11. The intergranular cracking may from Auger
spectroscopy measurements be associated with the
presence of an appreciable concentration of sulphur
on the grain boundaries [143. The degree of cleavage
varied from specimen to specimen but was usually
less than the degree of intergranular cracking. Optical
metallo~aphy
revealed the presence of subcritical
cleavage and intergranular microcracks and deformation twins all close to the main crack path, Fig. 12.
The cleavage microcracks were arrested at ferrite
boundaries and, in some cases, at twin boundaries.
The intergranular cracks were, apparently, less easy to
arrest and were oftm 10 or 12 facets in length, only
being halted when reaching a strong triple point
which caused a major d&e&on of overall crack
path.
The dependence of emission activity upon nominal
stress for two typical tests is shown in Fig. 10. In these
specimens, the emissions were first detected at a lower
fraction of the failure stress than for the mild steel.
The emission waveforms, Fig. 13, were again similar
in form to those calculated for a dislocation loop
source.
WADLEY
cr al.:
ACOUSTIC
EMISSION
DURING
LOW TEMPERATURE
FRACTURE
407
J
I
t00gm
Fig. 7. Fracture surface of mild steel specimen MS9: crack growth occurred by successive cleavage of
lath packets.
4 ~~TERPRETA~O~
AKD DISCCSSION
6.1 Inrersion of ~ure~~rms
In section 2.2 there was described the calculation of
the transfer function R(f) which enabled the epicentral
surface displacement u(t) to be determined from the
volume-time history. L(r). of a microcrack modelled
as an edge dislocation loop.
ThUS
3
u(r) =
R(t
--5
-
T)V(TJ
dr
(7)
where R(r) is also a function of crack depth and
orientation, and is derived from the Green’s function
of equation (I ).
If the inverse function R - ’ (t ) can be calculated from
R(t), then the volume of any crack can be calculated
from the measured surface dispfacement U(r) by convolution with R-‘(r), i.e.
s
3:
V(t) =
--5
R_‘(f - r)U(t)ds
(8)
In practice discrete sampled representations of the
experimental data are used, so that R(r) becomes a
matrix. R-t(r) is obtained by matrix inversion, and
the integrals are replaced by summations.
V, = ~(R-‘)i,Vj
j
Fig. 8. Optical micropraph of area adjacent to fracture surface of mild steel specimen MS9: secondary
cleavage cracking can be seen. Major crack path changes occur at lath packet boundaries.
(9)
WADLEY et al.:
408
5
;
ACOUSTIC EMISSION
LOW TEMPERATURE
20-
FRACTURE
500 -
Y
J
?I
0%
DURING
6
7
-lO-
250
“E
3
w
-
o-255-
5
i
z
-560
-
-750-1090
-
E
LI
$j
I
w
Y
2
g
200-
! 000
loo-
6
,
0,
3
-loo&
r
7
2550
“E
t
I
vg\/l-/
0
:
e
0
1
2
3
‘
0
1
2
3
L
- 2500
- 5000
- 7500
:
7500 h
- 10,000
5,000
t
:
0
2500
2
5
- 5ow
-7500
“E
Ial
SURFACE
DISPLACEMENT
2,500 !1::-I;
- 1 0,000
!bl
CRACK
VOLUME
Fig. 9. (a) Surface displacement as a function of time/ps for three emission transients recorded from
specimen MS5 (b) Corresponding crack volume time histories calculated as described in the text.
FAILURE-
,300
g
ii
?
-200
z
3001
SURFACE
z
d
:
$
5
DISPLACEMENT
5
0
:
CROSSHEAD
ial
SPECIMEN
DISPLACEMENT
/mm
E13
OFF
SCALE
FAILURE
SURFACE
DISPLACEMENT-
CROSSHEAD
Ibl
SPECIMEN
DISPLACEMENT
I mm
EI 7
Fig. 10 Nominal stress versus crosshead displacement for
Japanese electrolytic iron specimens E13 and E17. The nonlinearity at low ioads was due to distortion of electrical
insulation within the grips. The figures also show the
amplitude of each recorded emission as a function of
displacement.
It is noted that in this case the inversion
step is relatively straightforward
because the Green’s Function is
front-loaded. The inversion of other types of transfer
function may be more difficult. This inversion pro-
cedure was applied to all the recorded emission waveforms, so that the volume-time history was obtained
for each detected microcrack. The derived crack
volumes are given for typical emission transient waveforms from mild steel in Fig. 9, and from electrolytic
iron in Fig. 13. The fall in source volume after the
attainment of a maximum value was due to a combination of the 30 kHz high-pass filter and the reduced
response of the main amplifier below 80 kHz. In order
to reduce errors due to this and due to the presence
of oscillations following the L arrival from some of
the waveforms, the source volume was measured by
doubling the value attained when the L component
displacement was at its peak value, as illustrated in
Fig. 14. For similar reasons the other parameter
measured, source lifetime was taken as twice the time
taken for the displacement to rise from 10% to 90%
its peak value (Fig. 14).
The volume and lifetime were measured for every
recorded waveform, the mean values computed for
each sample tested and the results tabulated in Tables
4 and 5. The standard deviation is given as a measure
of the scatter in the values for each sample, although
there was no evidence of a normal distribution.
A few signals overloaded the recording system, and
because of the large errors which would be introduced
WADLEY tar al.: ACOUSTIC EMISSION DURING LOW TEMr’ERAWRE FRACTURE
409
J
I
1001.tm
Fig. 11. Fracture surface of electrolytic iron specimen E17; crack growth occimed by a mixture of
inter~ranu~ar and cleavage fracture
by ignoring them. their source volumes and lifetimes
were estimated by direct comparison with a signal of
similar shape which had over-loaded the more sensitive recorder, but had been captured by- the less sensitive.
6.2 Elastic crack model
The inversion procedure described above resulted
in a source description in terms of a time dependent
crack volume. However. it is more usual to consider
the crack length for each source. as this is the parameter most readily related to crack growth mechanisms. Since the waveform insersion gives a one-parameter source description the problem is underdetermined and we can only obtain crack length by
using a further simple model. We assume that the
acoustic emission source was the creation and growth
of a horizontal. circular. brittle crack under Mode I
Fig. 12, Optical micrograph of electrolytic iron specimen Ef6. area adjacent to fracture surface: secondary inter-granular cracking. cleavage cracking and deformation twinning can be seen close to the main
crack path.
410
WADLEY et al.:
I al
ACOUSTIC
SURFACE
EMISSION DURING
LOW TEMPERATURE
DISPLACEMENT
tb)
CRACK
FRACTURE
VOLUME
Fig. 13. (a) Surface displacement as a function of time&s for three emission transients recorded from
specimen EI6. (b) Corresponding crack volume time histories calculated as described in the text.
300
E,
;-
200 [
w
:
I
::
1ooc
i:
‘”
0
8
o
iz
2
-1oo-
1
26’
I
I
I
I
VI
t
2 V PEAK
i 2 T PEAK
Fig. 14. Showing how the crack volume (V) and lifetime (z) are measured from the crack volume time
history.
WADLEY et al.:
Table
ACOUSTIC
EMISSION
DURING
4. Mean values (with standard deviations) of the parameters
specimen
No. of
Specimen
MS1
MS2
us3
Volume/~m3
2080 2
700 +
480 +
2170 +
1450 +
2340 k
24,190 I
4120 +
450 +
134Oi---
10
11
33
;z
MS6
MS7
MS8
MS9
MS10
Lifetime/m
3480
570
670
3350
2290
3920
30,400
3210
280
122 & 37
110+30
106&46
113 k 30
106k46
120 + 63
205 + 115
124 f 13
104+ 18
130&--
elastic loading Under a uniform applied stress, u, the
crack faces will open a distance 2x given by:
2(1 - ?)a
x=
E
(f0)
’
where v is Poisson’s ratio, u is the radius of the
crack and E is Young’s modulus (151. The crack has
an ellipsoidal geometry with volume
43dX
P-j
(11)
Substituting for x in this expression then gives a
relation between crack volume and crack radius
8n(l - v’l)cr
a3
P
TEMPERATURE
defining
(12)
=
3E
from which the crack length 2~; or crack area rcu* or
crack opening x may be deduced.
Furthermore, if the source lifetime, z, corresponds
approximately to the time taken for the crack to
attain its final shape, then an average crack growth
rate, t/r, may also be deduced for a single microcrack. This expression for the average growth rate
assumes that at one point on its circumference the
crack was s~tion~y, modelling for example, a crack
which initiated at a grain boundary and which grew
to cover the grain. It also ignores Doppler effects and
(2a):rm
an average
56 + 27
42 +_ 12
42 + 13
55 + 15
63 k31
53 + 32
113 f 76
71 f 33
37 f 8
70 * -
rate/ms-
411
FRACTURE
microcrack
Deduced crack
Growth
Length
Measured crack
emissions
LOW
’
480 * 200
390 f 90
440 k 140
470 + 170
620 +- 170
450 & 180
510 + 120
580 + 270
370 + 100
540+-
for each mild
steel
Prior
austenite
Lath
packet
grain size/pm
sizerpm
30
30
45
90
105
123
127
131
176
176
-30
-30
35
::
90
100
90
95
95
the time taken to reach equilibrium for very fast
cracks. Alternatively, if the oentre of the circular crack
were stationary, modelling for instance, a crack initiated at the centre of gram, the mean growth rate
would be a/r.
Using this analysis, the crack length and the crack
growth rate were calculated for each emission waveform. The data were condensed by calculating the
mean values for every test, which are presented in
Tables 4 and 5. The standard deviation is also given
again as a measure of the scatter of the results.
6.2.1 Mild steel. None of the microcrack parameters
in Table 4 shows a strong dependence on the prior
austenite grain size, which steadily increases from
about 30 m to - 180 m. In particular, the correlation coefficient, R, between deduced crack length
and gram size is only 0.3. There is, however, a slightly
better correlation between crack length and lath
packet size (R = 0.S). The mean lath packet size
remained approximately constant for the last four
tests at -95 arm and whilst the mean crack lengths
fluctuated considerably, due partly to the poor statistics for these tests, the mean for the four tests was
h 75 m suggesting that the cracks propagated over
single lath packets. For the first two specimens the
lath packet size could not be measured accurately, but
was 530~.
The apparent crack length of 4 50 m
would, at Grst sight appear to be a contradictory
result. This apparent discrepancy is thought to be a
Table 5. Mean values (with standard deviations) of the parameters defining an average microcrack for each electrolytic
iron specimen
Specimen
No. of
emissions
El1
EI2
El3
El4
El5
El6
El7
2
26
22
7
14
:
Measured
Volume/~m3
1810 f 1460
1280
2240
3870
13,090
1550
6280
f
*
f
*
+
&
2460
4300
4460
19,610
1s90
31,700
crack
Lifetimelns
132 f 19
142
15s
197
202
162
138
f
f
f
f
f
f
SE
52
44
103
95
63
Deduced
Length
crack
Growth
(2a)~~
tate/ms-’
Ferrite grain
tie (d)/~rn
1000 + 250
loo0 + 230
740 * 210
890 it 260
7SOf260
900 f 280
980 f 350
36
45
43
60
45
46
47
137
139
113
172
157
131
140
f 51
& 62
f 54
f 58
+ 104
+43
i 119
2a$
3.8
3.1
2.6
2.9
3.5
2.9
3.0
412
WADLEY
et al.:
ACOUSTK
EMlSSiON
DURING
LOW
TEMPERATURE
FRACTURE
dependent. At 77 K. when the fracture mode was cieavage, there was a range of terminal velocities from
-0.3 c2 up to a maximum of -0.6 c2. Theoretical
work on brittle crack propagation, using a quasistatic
model [19] also indicates the existence of a terminal
velocity of 0.38c,, (equivalent to 0.69~~ in mild
steel). A dynamical calculation, reviewed by Erdogan [20], indicates that the Rayleigh speed (10.92 c2
in steel) is the maximum crack velocity, whilst the
m~imum energy dissipation rate occurs at a speed of
0.6~~. The data for cleavage fracture in mild steel
show a lower average crack growth rate than either
the theoretical calculations or the data for tungsten [18] ; the measured velocities ranged from
0.05 c2 to 0.3 c2 as shown in Fig. 15. The apparent
lower velocities in the steel may, in part, be due to the
different crack growth mechanism, the presence of the
laths being expected to reduce the crack speed. However, account must also be taken of ail the assump
tions made in the calculation of crack growth rate
from the emission data, since these could give rise to
appreciable systematic errors.
6.2.2 Ekctrolytic iron. Three processes may have
generated acoustic emission signals during the testing
of electrolytic iron specimens, namely the creation of
deformation twins, cleavage microcrack formation
and subcritical intergranular cracking. The waveforms
were compared with a waveform computed for the
formation of a deformation twin (J. E. Sinclair,
unpublished work). The calculated amplitudes were
so small and other waveform differences so marked
that twin formation could not have been the source of
the majority of the emissions. It was not possible to
consequence of the limited transducer sensitivity.
With the transducer sensitivity used small crack
lengths ($20 pm) were undetectable in this experiment. Consequently, the crack lengths sampled by the
acoustic emission measurements were only a fraction
of the complete crack length population for a test.
When the most likely crack length was close to the
detection threshold the mean crack length deduced
from acoustic emission measurements would be an
overestimate. However, for a mean length large compared to the detection threshold, a much better estimate of the population mean would be expected.
Extensive fractographic studies in the past have
shown the crack length population mean to be the
average lath packet size [l&17] so that the results
above are in good agreement with these observations.
The wide range of acoustic emission signal amplitudes, as exemplified by the large standard deviations
in Table 4, is thought partly a consequence of the
wide distribution of actual lath packet sizes within a
specimen.
Analysis of the emission waveforms indicated that
the detected microcracks took, on average, only
-_ 1lOns to reach their final size. There exists at
present no independent method of determining microcrack lifetime. However, we can compare the estimated average crack velocity during the growth of
a typical microcrack, -490 ms- ’ = 0.15 ~2. with
macroscopic measurements of crack velocities. Hull
and Beardmore [l S] studied fracture propagation in
spark notched tungsten single crystals over the temperature range 20-300 K. They found an average terminal velocity that was both temperature and stress
2000
0.6 C2
0
_____o__-------0
C-
_c--
_e--
_---
_00
0
0
04 c&y
C
._
__
Mm._
Fig. 15. Showing the crack diameter and growth rate for every emissiont recording during the two stries
of tests. Note that there is little overlap between data from the two fracture processes, and that the data
appear bounded by a maximum velocity. O-Cleavage fracture of mild steel, O-intergranular
fracture
of electrolytic iron.
t Except one (ElOpm, ZlSOms-I).
0.2 c2
WADLEY et oL: ACOUSTIC
EMISSlON
DURING
04
.w--Chow
03
rn
i?ocrvcm
mid steela~ 77K
. .
Fig 16. Histograms of crach diameter. lifetime and growth
rate for the two fracture processes.
distinguish unambiguously between intergranular and
cleavage cracks but since the latter would have been
only just detectable in this experiment, the measured
waveforms were mostly of reIatively large ~p~tude.
it is fair to conclude that int~~~ul~
cracking was
the predominant source of detected emission.
Using the same analysis procedure as for mild steel,
the crack length and crack growth rate were calculated for each emission event. The mean values for
each test are presented in Table 5 whilst Fig 15 shows
the scatter of crack length and growth rate for each
emission. The typical microcrack had a lifetime of
w 150 ns and during this period propagated over a
distance of - 140m at a velocity 930 ms- ’ (0.3 c,).
This crack length is around three times the grain diameter and might have corresponded to a microcrack
propagating over a length of around 8 gram facets.
There was considerable scatter (as shown by the large
standard deviations) in the lifetimes, microcrack
length and crack growth rate. This may be an indication of the variability in actual microcrack growth
process as sacks grow around larger or smaller than
average grains, and across a variable number of facets
before arrest. However, when averaged over all
emissions from a test, the number of grain diameters
LOW TEMPERATURE
FRACTURE
413
(a) traversed on average by a microcrack (2a,‘& is in
remarkably good agreement for all the tests (Table 5).
The mean crack velocity for each test also appeared
constant and independent of small differences in grain
size. The deduced crack velocity was around twice the
value obtained from the cleavage fracture of mild steel
and may be due either to the lower resistance offered
to a propagating crack by an embrittled grain boundary or the smaller cont~bution of crack acceleration
to the crack velocity for the longer cracks. Figure 15
shows that crack velocities in the electrolytic iron
ranged from -0.1 c2 to -0.6 cl. The figure also
shows limited correlation between crack length and
velocity. and that there is a limiting velocity of
5 0.5 cz reached only by some of the largest cracks.
These observations would tend to agree with the
theoretical studies of dynamic fracture (Erdogan
1968). However, care must be taken since the model
used of a planar, circular crack exp~ding equally fast
in all directions is only a very approximate representation of an intergranular crack whose length covers
many grain boundary facets.
Figure 15 shows clearly that the two deduced parameters of crack diameter and growth rate are very
effective at separating the data from the two fracture
processes with only a few percent of overlap. An alternative method is to present the data in the form of
histograms, Fig. 16. As Fig 16 shows, cleavage crack
growth in mart~site can be distinguish~ from intergranular cracking of iron by different crack length,
lifetime and velocity distributions. However, variability in each crack growth process is sufficient to
cause appreciable overlap of the histograms. It is thus
only possible to state a probability that a single
recorded emission was generated by one or other process.
Theoretical studies of dynamic fracture (Erdogan
1968) indicate that a propagating crack should accelerate to reach a terminal velocity, provided enough
time is allowed. The recorded emission data were
Fig. 17. Time dependence of microcrack diameter for transient 3 from specimen EIl. The crack is assumed to grow
as a self-similar circular elastic crack of elliptical crosssection. Note that the crack reaches a terminal velocity of
227.; shear velocity.
414
WADLEY et 01.: ACOUSTIC EMISSION
DURING
examined for evidence of terminal velocity by plotting
crack diameter as a function of time. Many of the
data showed a period of apparent acceleration followed by a period of growth at a constant velocity
prior to deceleration and an example is given in
Fig 17. The existence of an appreciable period of
apparent uniform velocity did not appear to correlate
well with either final crack length or average growth
rate.
In conclusion, these two series of tests have shown
that quantitative acoustic emission waveform analysis
can provide new insights into the dynamics of fast
fracture events. The parameters deduced from the experimental data, using a theoretical model based on
an elastic microcrack, are in good agreement with
independent measurements where comparison is possible. The ability to deduce a value for the crack velocity should prove important in future studies of fast
fracture, while the ability to determine the size of a
crack, and to distinguish, with a measure of confidence, one crack mechanism from another should
also prove important in the practical applications of
the technique, provided these measurements can be
successfully transferred to crack growth geometries
and more complex structural components.
Acknowledgements-We
wish to acknowledge the many
helpful discussions of this work with Drs. J. E. Sinclair,
B. L. Eyre, J. A. Hudson. G. J. Curtis, Mr. D. Birchon and
Mr. A. B. Joinson. The study was funded by the Ministry
of Defence (Procurement Executive) through the Admiralty
Marine Technology Establishment, Holton Heath, Dorset.
LOW TEMPERATURE
FRACTURE
REFERENCES
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and R. N. Thurston) Vol. 11, Ch. 6, Academic Press,
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_ D 11. 1487
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