Quantitative acoustic emission source characterisation during low temperature cleavage and intergranular fracture

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.

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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.

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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.

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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.

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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

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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


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

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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.

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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 1. A. E. Lord, Physical Acoustics (Edited by W. P. Mason and R. N. Thurston) Vol. 11, Ch. 6, Academic Press, New York (1975). 2. H. N. G. Wadley, C. B. Scruby and J. Speake, Inr. metoll. Rec. 2, 41 (1980). 3. F. R. Breckenridge, C. E. Tschiegg and M. Greenspan, J. aco~st. Sot. Am. 57, 626 (1975). 4. C. L. Pekeris and H. Lifson, J. ocousr. Sot. Am. 29, 1233 (1957). 5. Y. H. Pao, R. R. Gajewski and A. N. Ceranoglu, J. acoust. Sot. Am. 65.96 (1979). 6. N. N. Hsu, J. A. Simmons and S. C. Hardy, Mater. Eocll. 35. 100 (1977). 7. C. B. &ruby and H. N. G. Wadley. -. J. Phvs. _ D 11. 1487 (1978). 8. C. B. Scruby, J. C. Collingwood and H. N. G. Wadley. J. Ph. D 11. 2359 (1978). 9. H. N.-G. Wadley and C. B. Scruby, Acta metall. 27, 613 (1979). 10. C. B. &ruby, H. N. G. Wadley and J. E. Sinclair. Proc. Con& Periodic Inspection for Presswised Components. Inst. Mechanical Engineering, London 8-10 May (1979). 11. R. Burridge and L. Knopoff. Bull. seism. Sot. Am. 54, 1875 (1964). 12. J. E. Sinclair, J. Phys. D 12, 1309 (1979). 13. L. R. Johnson, Geophys. J. R. astr. Sot. 37,99 (1974). 14. H. N. G. Wadley and B. C. Edwards, to be published. 15. J. F. Knott, Fundamentals of Fracture Mechanics p. 58, Butterworths, London (1973). 16. P. Brozzo, G. Buzzicheh, A. Mascanroni and M. Mirabile, Metals Sci. 123 (1977). 17. J. P. Naylor and P. R. Krahe, Metal/. Trans. A. 6, 594 (1975). 18. D. Hull and P. Beardmore, ht. J. Fract. Mock 2, 468 (1966). 19. D. K. Roberts and A. A. Wells, Engineering 178, 820 (1954). 20. F. Erdogan Fracture: An advanced treatise, (Edited by H. Liebowitz) Vol. II. p. 497, Academic Press, New York (1968).