The use of simulated and controlled acoustic emission signals forms the basis of a powerful tool for the detailed study of various deformation and wave interaction processes in materials. The results of experiments and signal analyses of acoustic emission resulting from point sources such as various types of indentation-produced cracks in brittle materials and the growth of fatigue cracks in 7075-T6 aluminum panels are discussed. Recent work dealing with the modeling and subsequent signal processing of an extended source of emission in a material is reviewed. Results of the forward problem and the inverse problem are presented with the example of a source distributed through the interior of a specimen

Chen, C. P.

Kim, K. Y.

Sachse, W.

English

NASA Technical Reports Server

STUDIES OF ACOUSTIC EMISSION FROM POINT AND EXTENDED SOURCES
Wolfgang Sachse, Kwang Yul Kim, and C.P. Chen
Cornell University
Ithaca, New York 14853
The use of simulated and controlled acoustic emission signals forlns the basis of a
powerful tool for the detailed study of various deformation and wave interaction processes in
materials. We report the results of experiments and signal analyses of AE resulting from point
sources such as various types of indentation-produced cracks in brittle materials and the growth
of fatigue cracks in 7075-T6 aluminum panels. Furthermore, we describe our recent work
dealing with the modeling and subsequent signal processing of an extended source of emission in
a material. Results of the forward problem and the inverse problem are presented with the
example of a source distributed through the interior of a specimen shown.
INTRODUCTION
The use of acoustic emission (AE) signals for real-time structural integrity monitoring
applications has long been sought. Developments over the last several years have gone far
towards obtaining a better understanding of the AE process in actual structural components
(Refs. l-5). These include the development of a model consisting of a repeatable source of
known type, a structure for which the propagation of transient elastic waves can be computed,
sensors whose transfer characteristics are either known or can be determined experirnentally
and the development of new signal processing algorithms for analyzing the detected signals.
The associated problem, sometimes called the "inverse source problem", has as its aim the
characterization of a source in terms of its location in the structure, its type, specified in
terms of force or moment tensor components, its spatial distribution, if the source is extended,
and its temporal or dynamic characteristics. This paper gives an overview of the work recently
completed in our laboratory on aspects of this topic.
THEORY AND WAVEFORM PROCESSING
The displacement signals uk detected at a receiver location, x) in a structure from an
arbitrary source f(x',t) located at x' having source volume V° can be written as
Uk = I fj(x',t) * Gjk(X/X',t) dV (1)oV -
where the term Gjk represents the Green's function of the structure. Insight into this
formulation can be "obtained if one makes a Taylor series expansion of the Green's function
about the source point, _', located at, say 0, to give
Uk(X't)= [v_(O't)*Gjk(X/O't)dV + I xifj(0't)*Gjk, i(x/0't) dv' (2)Vo
49
https://ntrs.nasa.gov/search.jsp?R=19860013494 2020-03-20T15:03:09+00:00Z
Tne first term in this equation, representing the monopole contribution, can be rewritten in the
form
u_m) : { [vfj(0,t) dV} * Gjk[X/0,t)Q
OF
u(m) = Sj(t) * Gjk(X/0,t) (3)
The second term in Eq. (2), representing the dipole contribution, can be rewritten in a similar
fashion as
u(kd)= { I x'i fj(x',t) dr' } * Gjk,i(x/0,t)
Vo
or
u_d) = Mij(t)* G'jk,i(x/0,t)_ (#)
The term, M.. , called the moment tensor of the source,can be used to represent any
combination ot_Jdoubleforces([_ef.3) to model the source. Itcan be shown that the moment
tensorcan be writteninterms of the crack'sdisplacementjump and itsarea in a material(Ref.
6). If each of the components of the moment tensor of the source have the same time
dependence, then the spatialand temporal characteristicsof the source are separable. Thus,
the moment tensorcan be writtenas a product of the moment densitytensor,mij, and the and
tilesource-timefunction,S(t),
M.. = S(t) "m.. (5)
ij Ij
In recovering the characteristics of a dipolar source from the measured signals, u , one usesz
knowledge of the Green's function G and inverts Eq. (#) to recover S(t) and the components
m U . In the most complicated deformation processes and for an arbitrary crack orientation, all
six Jcomponents of the moment density tensor may need to be evaluated. As of now, this has
not yet been done. Here we show the results obtained for several simpler cases.
The simplest case is that of a point source of known type for which only the temporal
aspects of the source are to be recovered from the detected signals. [n that case, Eq. (3) can
be rewritten as a simple convolution equation in time
u(t) = S(t) * G[t) (6)
This equation has been modified to include the transfer characteristics of a non-displacement
transducer, whose response is band-limited. Recovery of the source function, 5(t) , then
involves two measurements, one of which is a calibration experiment using a known step
excitation source applied at the source position. Examples of processing near-field and far-
field signals from an axisymmetric source have been published previously (Refs. 7-9).
For the case described by Eq. (#) in which both the time-function and moment-density
tensor components of a source are to be recovered, several processing algorithms have been
developed. One of these is based on an algebraic scheme in which the amplitudes of particular
ray arrivals in the detected signals are directly related to the amplitudes of the Green's
function (Ref. 10). Once these are determined, the source time-function can be recovered as
before. The problems related to this scheme result principally from the amplitude
50
measurement precision required of specific features on a waveform. An alternative is a double
iterative scheme demonstrated by Michaels and Pao (Ref. 9). The procedure is initiated with a
guess o5 the moment tensor magnitudes from which a solution of the source time-function is
obtained. This solution is used, in turn, to evaluate a new set of moment tensor amplitudes, and
so on. The iteration process is continued until the results obtained in the iterations converge to
a final answer. The procedure appears to be initial guess dependent and it may also converge
slowly for certain configurations of the source moment tensor. It has been found that an
appropriate initial guess for the double-iterative scheme can be obtained by making use of the
results obtained from the algebraic processing scheme.
RESULTS
Demonstration of any signaianaiysisprocedure for AE source characterizationmust begin
with a controlled deformation process in a material. Reproducible, deformation-related AE
sources whose location is known precisely, include indentation-produced cracks in brittle
materials and fatigue-generated cracks in thin specimens and these were investigated in this
work.
a. Fatigue Cracks
In detailed fatigue experiments, conventional test parameters were recorded in
combination with electrical crack length measurements and a total of five AE waveforms,
detected at points around the crack region. Two sample signals recorded equidistant from the
crack front are shown in Figure I. The four equivalent forces or moment tensor components by
which an arbitrary dipolar source in a thin specimen can be modelled are shown schematically in
Figure 2. It is found that the dynamic Green's functions corresponding to the M_ and M_l
source components exhibit a non-zero signal amplitude between the P- and S-wa_'e arrival_.
From observations as this, each corresponding to an event, it is concluded that only two signals
are needed to determine without ambiguity the characteristics o5 the source. It was found that
some of the events could be adequately described in terms of only two double forces, i.e.; MII
and M_. Other events required also a contribution from the M,_ and M_. components. Tabl'_
I show_Zthe results obtained for two events one of each type. _ore th_ thirty-eight signals
were processed in a typical test. In Figure 3 is the recovered source-time function obtained
with the double-iterative processing scheme. It appears that the crack displacement profile had
a risetime of approximately t_00 nsec. The risetime may actually be shorter than this, since the
recovered value corresponds to the upper bandwidth limit of the transducer/amplifier system.
b. Indentation Cracks
The pressing of an Indentor onto the surface of a flat plate results in a stress field
configuration which depends on the shape of the indenter and the mechanical properties of the
plate specimen. If the specimen is a brittle material, cracks of specific shape form when and in
those regions where the stress field exceeds the fracture strength of the material. The dynamic
force released in forming the crack is emitted as an AE signal. A typical epicentral AI5 signal
obtained with a spherical-tipped indenter is shown in Figure 4(a). Typical Hertzian cone cracks
are obtained when such indenters are pressed against a specimen. It has been shown that the
associated dynamic source is equivalent to a vertical axisymmetric force acting on the
structure (Ref. I I). On unloading, one or more lateral vent cracks may form whose associated
AE signals exhibit completely different characteristics as shown in Figure t_(b). In some cases,
these may be adequately modelled by a single horizontal dipole acting near the surface of the
plate. This appears to be the case, when only one lateral vent crack forms. The detected AE
5]
signals resemble those obtained when a conical indenter is pressed against the specimen. In the
latter situation) a single penny=shaped crack is formed. Evaluation of the stress field under the
conical indenter, obtained from the Boussinesq solution (Ref. 12), shows regions of tensile and
compressive hoop stresses. The crack is generated in the region of tensile hoop stresses whose
contours resemble a penny.
Experiments were carried out with an eight=channel AE system consisting of point
piezoelectric transducers with a 1.2 mm active area situated at various angles at a distance
approximately 2h (h = plate thickness) from the indenter. Sensors whose response was nearly
uniform in amplitude were selected for the array. The signals were amplified by 60 dB with.
preamplifiers whose bandwidth ranged from i0 kHz to 2 MHz. They were subsequently
digitized in transient waveform recorders operating at a smnpling rate of 30 MHz with 10-bit
resolution.
Evaluation of the moment tensor components of the penny-shaped crack via one of the
procedures listed in the previous section often did not yield reliable results, as they were
strongly initial guess dependent. It was clear) however, when comparing the detected
waveforms to synthesized AE signals, that the model of a tensile crack given in terms of three
orthogonal dipoles of strength, _, + 2 B ) ), and ), ) where _, and ]J are the Lame constants,
may not be appropriate to model an indentation=produced crack in a small specimen as
described here.
An alternative approach for recovering the ratios of the moment tensor components
involves measurement of the radiated field of the AE signal from the source. The radiated
amplitude measured at a distance R from a dipolar source, can be written in terms of the
displacement amplitude) Uz) and this is expected to be of the form
Uz(R,t)= al(t)+ a2(t)cos2 0 (7)
where 8 is the orientationof the normal to the crack. For a singlehorizontaldipolesource,
alignedparallelto the crack normal) the term al(t)is expected to be near zero. For three-
dipolecrack model, il;svalue isexpected to be approximately 0.28. Eq. (7)can be rewritten to
account for an arbitrarycrack orientationrelativeto the sensor array
Uz(R ,t)=al(t)+a2(t)cos 2(8- Oc) (8)
where Oc isthe orientationof the normal of the crack relativeto the orientationof the sensor
array.
By a proper choice of angular distribution of sensors around the indenter, an eight-channel
AE system is adequate to determine the field characteristics of the indentation-generated
cracks. Each channel of the entire system was calibrated simultaneously by breaking a glass
capillary 0.05 mm in diameter a% the crack position on the specimen. The result was an
axisymmetric step excitation source. The amplitudes of both the first P- and S-wave arrivals
were measured. The corresponding amplitudes in the crack-generated signals were normalized
with the calibration amplitudes. The result obtained after one indentation is shown in Figure 5.
The solid and dashed lines correspond to the results produced from a non=linear least-square fit
of Eq. (8) to the measured data. From the curve fit) the parameters of the radiated field can be
extracted. Once these are.known, the measured amplitudes at each transducer can be re_lected
across the various symmetry planes to generate image data points with the results obtained
shown in Figure 6. Inspection of the amplitude ratio al/a 9 shows that the tensile cracks
produced by the conical indenter are best modelled as'regulting principally from a single
52
horizontal dipole. The orientation of the crack, relative to the array configuration, is
recovered immediately when Eq. (8) is fit to the amplitude data. The difference between the
observed and recovered crack orientation angle from seven indentations was always less than
6° and on average less than 3° .
The radiated field of the signals emitted from lateral vent unloading cracks was also
measured. It was found that the formation of multiple cracks results in a radiated field which
radiate more uniformly in all directions and clearly, the radiation does not resemble that of a
single crack.
It is possible to process an epicentral displacement signal with the double-iterative
processing scheme to recover the individual magnitudes of the moment tensor as well as their
time function. Figure 7 shows the recovered source time function for an incientation crack.
EXTENDED SOURCE
Both the forward and inverse problems of the extended source have been solved using
synthetic data. A series of examples dealing vcith two source types and several linear
distributions on the surface or through the interior of a plate specimen have been computed
(Ref. 13). In Figure 8(a) is shown the case of a distribution of horizontal dipole sources,
extending to 0.75h into the interior of the plate and whose time function was a Heaviside step
function. It has been proposed that such a source may be used to model the interaction of
intense synchrotron=generated pulses of x=rays striking a specimen and penetrating into its
interior (Refs. 14-15). Figure 8(b) shows a comparison between the signal from a single dipole
very close to the top surface of the specimen and the signal synthesized from forty source
points whose strength distribution along the z=axis was given by e =0._z. After only ten
iterations in the double=iterative processing schemed the input source function was recovered
from the synthetic input data within a percent and the corresponding recovered source time
function was indistinguishable from the input.
CONCLUSIONS
Acoustic emission signals detected from cracks formed during indentation and fatigue
loading experiments have been processed to recover the moment tensor components of the
crack source and their time function. Several signal processing schemes were demonstrated
including one based on ray amplitude measurements, a double=iterative processing scheme and
an AE radiation pattern analysis method. A signal processing algorithm was also demonstrated
with synthetic AE waveforms corresponding to an extended source of emission by which the
signals can be processed to recover both the spatial extent of the source and its time function.
ACKNOWLEDGMENTS
This work was supported by the National Science Foundation through grants to the
Materials Science Center and to the College of Engineering at Cornell University. A significant
portion of the equipment used in the experiments described was acquired through a DoD
Instrumentation Grant awarded through the Office of Naval Research.
53
REFERENCES
(1) R. F. Breckenridge, C. E. Tschiegg and M. Greenspan, "Acoustic Emission: Some
Application of Lamb's Problem", 3. Acoust. Soc. Am., 57, 626-631 (1975).
(2) N.N. Hsu, 3. Simmons and S. C. Hardy, "An Approach to Acoustic Emission Signal
Analysis - Theory and Experiment", Marls. Eval, 35.._(10),100-106 (1977).
(3) Y.H. Pao, "Theory of Acoustic Emission", in Elastic Waves and Non-destructive Testing
of Materials, Y. H. Pao, Ed., AMD-Vol. 29, Am. Soc. Mech. Engrs, New York (1978), pp.
107-128.
(#) N.N. Hsu and S. C. Hardy, "Experiments in Acoustic Emission Waveform Analysis for
Characterization ol AE Sources, Sensors and Structures", in Elastic Waves and Non-
destructive Testing of Materials, Y. H. Pao, Ed., AMD-Vol. 29, Am. Soc. Mech. Engrs.,
New York (1978), pp. 8_-106.
(.5) H. N. G. Wadley and C. B. Scruby, "Quantitative Acoustic Emission Studies during
Deformation and Fracture: A Review", Report AERE - R 10353, AERE Harwell,
Oxfordshire (1981).
(6) K. Aki and P. G. Richards, Quantitative Seismology, Vol. 1) w. H. Freeman and Co., San
Francisco (1980), Chapt. #.
(7) 3. E. Michaels) T. E. Michaels and W. Sachse) "Applications ol Deconvolution to Acoustic
Emission Signal Analysis", Materials Evaluation, 39(11), 1032-1036 (1981).
(8) P.N. Hsieh and W. Sachse, "Far-lield Signals Irom Axis-symmetric Sources in Elastic
Plates", in Ultrasonics International '83 - Conlerence Proceedings, Butterworth and Co.
Publ., Sevenoaks, Kent, UK (1983), pp. 388-39#.
(9) 3. E. Michaels and Y. H. Pao) "Deconvolution of Source Time Functions of the Moment
Density Tensor", in Review of Progress in Quantitative NDE, D. O. Thompson and D. E.
Chimenti, Eds., Plenum Press, New York (198#), pp. 707-715.
(10) C. P. Chert, "Acoustic Emission Source Characterization of Fatigue Cracks in 7075-T6
Aluminum Alloy Thin Plate", Ph. D. Dissertation, Cornell University, Ithaca, NY (1985).
(11) K. Y. Kim and W. Sachse, "Characteristics of Acoustic Emission Signals of Hertzian and
Unloading Cracks in Glass", 3. Appl. Phys., _ 28#7-2856 (198#).
(12) I. N. Sneddon, "Boussinesq's Problem for a Rigid Cone '), Proc. Cambridge Phil. Soc.,#__##,
#92- (19#8).
(13) C. Chang and W. Sachse, "Analysis of Elastic Wave Signals from an Extended Source in a
Plate", 3. Acoust. Soc. Am., 77, 1335-13#1 (1985).
(1#) K. Y. Kim and W. Sachse, "X-ray Generated Ultrasound", Appl. Phys. Letts., #3, 1099-
1101 (1983).
(15) W. Sachse and K. Y. Kim, "Observation of X-ray Generated Ultrasound", 1983 Ultrasonics
Symposium, Inst. Elect. Electr. Engs., New York (1983), pp. 677-680.
54
CHARACTERIZATION OF FATIGUE CRACKS IN 7075-T6
Eve_nt :_3+ ; HocleL: T_o Dou.b[el:io_-ces
AL_ebTe._.c.; C,: P-=z= I " o._.s8
Oou,bL_T-t:erc,.f.Co_,; C, " C==---I " o.2G(;
Event # 35 ,; _odeL" T_o Dou_bLol_o--rces,T_0S_Le CoupLes
Dou.bLeIsr.e_.'rc.,J._.o_; C," C,, :C_" £,_.=o.'_9_.'o,t,o,_:-o_'1:o._o9
Table I
55
FATIGUE CRACK SIGNALS IN 7075-T6
FRTIGUE CRRCK: SENSOR _i FRTIGUE CRRCK: SENSOR _2
6.00 S,O@
-5.00 -_.00
TIME (u_eo} TIME {useo)
Figure i
EQUIVALENT FORCES / MOMENT TENSOR COMPONENTS
3 3
Mtl Mr2 ld /
1 I
3 3
I 1
Figure 2
56
RECOVEREO SOURCE-TIME FUNCTION
1.00
C)
LU 0.50
C_
I---
e'e-
O.O0 .,;,/_: ._' : ._ I I I i l i i i i i i i i i i _ i i i
O.O 1,0 2.0 3.0 4.0 5.0
TIME {usec)
Figure 3
UNLOADING CRACK: 14.5NT/MAX: 35.3NT
1.0 IP
I0"0 t
IS 1P
I.iJ _ 3P 5P t 3P
_b_'-J o.o_-, _ ;51o_ io:o'q>'"li.d " "_ " _i_""l'-> ' ....... , _k'_'_.......',._"_,_,o.o
_ TIME <
(p.sec) (p.sec)
1.0 (a) o.0 ,s
Figure 4(a) Figure 4(b)
57
120° CONICAL INDENTER - DIPOLE RADIATION
90
Crack 4
13 ' 13
180 0
270
P - Wove
--- S - Wave9O
Figure 5
Y
_' \ \ _ nJr,, I / ," " I
'50 ',,_5 '_.0 '05 ;_lv 75 60 45 30 I
.4- I
o • o
"165 o o o 0o2 o • 15
-195 o 345
o . •
210 225 40 255 rO 285 300 315 330
f / I I _ \ % ",
•-RealDofopolnfs,o-lmagesocrossX,¥Axes;Ap=0.585(0.123+cos28)
Figure 6
58
RECOVERED SOURCE-TIME FUNCTION (CRACK 9)
I0.0
V)
,m
e,-
o
,u
_ 5.0
"0
e_
E
0
0
0 0.25 0.50 0.75 I.O0
Time (_sec)
Figure 7
DIPOLE SOURCES: EXPONENTIAL DISTRIB
1.00
HORIZONTAL DIPOLES
(o.o- o.75h)
Z
U
N 2.0 3.0 4.0
zX
Receiver -,.oo
NORMALIZED TIuE T = Cp%/h
Extended dipole source model Synthetic normal displacement signals
corresponding to several source
distributions
Figure 8(a) Figure 8(b)
59


Studies of acoustic emission from point and extended sources

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