This paper addresses the predictive simulation of acoustic emission (AE) guided waves that appear due to sudden energy release during incremental crack propagation. The Helmholtz decomposition approach is applied to the inhomogeneous elastodynamic Navier–Lame equations for both the displacement field and body forces. For the displacement field, we use the usual decomposition in terms of unknown scalar and vector potentials, Φ and H. For the body forces, we hypothesize that they can also be expressed in terms of excitation scalar and vector potentials, A* and B*. It is shown that these excitation potentials can be traced to the energy released during an incremental crack propagation. Thus, the inhomogeneous Navier–Lame equation has been transformed into a system of inhomogeneous wave equations in terms of known excitation potentials A* and B* and unknown potentials Φ and H. The solution is readily obtained through direct and inverse Fourier transforms and application of the residue theorem. A numerical study of the one-dimensional (1D) AE guided wave propagation in a 6 mm thick 304-stainless steel plate is conducted. A Gaussian pulse is used to model the growth of the excitation potentials during the AE event; as a result, the actual excitation potential follows the error function variation in the time domain. The numerical studies show that the peak amplitude of A0 signal is higher than the peak amplitude of S0 signal, and the peak amplitude of bulk wave is not significant compared to S0 and A0 peak amplitudes. In addition, the effects of the source depth, higher propagating modes, and propagating distance on guided waves are also investigated.

References

References
1.
Harris
,
D. O.
, and
Dunegan
,
H. L.
,
1974
, “
Continuous Monitoring of Fatigue-Crack Growth by Acoustic-Emission Techniques
,”
Exp. Mech.
,
14
(
2
), pp.
71
81
.
2.
Han
,
B. H.
,
Yoon
,
D. J.
,
Huh
,
Y. H.
, and
Lee
,
Y. S.
,
2014
, “
Damage Assessment of Wind Turbine Blade Under Static Loading Test Using Acoustic Emission
,”
J. Intell. Mater. Syst. Struct.
,
25
(
5
), pp.
621
630
.
3.
Tandon
,
N.
, and
Choudhury
,
A.
,
1999
, “
A Review of Vibration and Acoustic Measurement Methods for the Detection of Defects in Rolling Element Bearings
,”
Tribol. Int.
,
32
(
8
), pp.
469
480
.
4.
Roberts
,
T.
, and
Talebzadeh
,
M.
,
2003
, “
Acoustic Emission Monitoring of Fatigue Crack Propagation
,”
J. Constr. Steel Res.
,
59
(
6
), pp.
695
712
.
5.
Bassim
,
M. N.
,
Lawrence
,
S. S.
, and
Liu
,
C. D.
,
1994
, “
Detection of the Onset of Fatigue Crack Growth in Rail Steels Using Acoustic Emission
,”
Eng. Fract. Mech.
,
47
(
2
), pp.
207
214
.
6.
Lamb
,
H.
,
1917
, “
On Waves in an Elastic Plate
,”
Proc. R. Soc. London A: Math., Phys. Eng. Sci.
,
93
(
648
), pp.
114
128
.
7.
Helmholtz
,
H.
,
1858
, “
Uber Integrale der Hydrodynamischen Gleichungen, Welche den Wirbelbewegungen Entsprechen
,”
J. Reine Angew. Math.
,
1858
(
55
), pp.
25
55
.
8.
Achenbach
,
J. D.
,
2003
,
Reciprocity in Elastodynamics
,
Cambridge University Press
,
Cambridge, UK
.
9.
Giurgiutiu
,
V.
,
2014
,
Structural Health Monitoring With Piezoelectric Wafer Active Sensors
,
2nd ed.
,
Elsevier
,
Amsterdam, The Netherlands
.
10.
Graff
,
K. F.
,
1975
,
Wave Motion in Elastic Solids
,
Clarendon Press
,
Oxford, UK
.
11.
Viktorov
,
I. A.
,
1967
,
Rayleigh and Lamb Waves: Physical Theory and Applications
,
Plenum Press
,
New York
.
12.
Landau
,
L. D.
, and
Lifschitz
,
E. M.
,
1965
, Teoriya Uprugosti, Nauka, Moscow, Russia [
Theory of Elasticity
,
2nd ed.
,
Pergamon Press
,
Oxford, UK
(1970)].
13.
Love
,
A. E. H.
,
1944
,
A Treatise on the Mathematical Theory of Elasticity
,
Dover Publications
,
New York
.
14.
Aki
,
K.
, and
Richards
,
P. G.
,
2002
,
Quantitative Seismology
, Vol.
1
, University Science Books, Sausalito, CA.
15.
Vvedenskaya
,
A. V.
,
1956
, “
The Determination of Displacement Fields by Means of Dislocation Theory
,”
Izv. Akad. Nauk SSSR
,
3
(27), pp.
227
284
.
16.
Nabarro
,
F. R. N.
,
1951
, “
The Synthesis of Elastic Dislocation Fields
,”
Philos. Mag.
,
42
(334), p.
313
.
17.
Maruyama
,
T.
,
1963
, “
On the Force Equivalents of Dynamical Elastic Dislocations With Reference to the Earthquake Mechanism
,”
Bull. Earthquake Res. Inst., Tokyo Univ.
,
41
, pp.
467
486
.
18.
Lamb
,
H.
,
1903
, “
On the Propagation of Tremors Over the Surface of an Elastic Solid
,”
Proc. R. Soc. London
,
72
(477–486), pp.
128
130
.
19.
Rice
,
J. R.
,
1980
, “
Elastic Wave Emission From Damage Processes
,”
J. Nondestr. Eval.
,
1
(
4
), pp.
215
224
.
20.
Miklowitz
,
J.
,
1962
, “
Transient Compressional Waves in an Infinite Elastic Plate or Elastic Layer Overlying a Rigid Half-Space
,”
ASME J. Appl. Mech.
,
29
(1), pp.
53
60
.
21.
Weaver
,
R. L.
, and
Pao
,
Y.-H.
,
1982
, “
Axisymmetric Elastic Waves Excited by a Point Source in a Plate
,”
ASME J. Appl. Mech.
,
49
(4), pp.
821
836
.
22.
Ono
,
K.
, and
Ohtsu
,
M.
,
1984
, “
A Generalized Theory of Acoustic Emission and Green’s Functions in a Half Space
,”
J. Acoust. Emiss.
,
3
, pp.
27
40
.http://adsabs.harvard.edu/abs/1984JAE.....3...27O
23.
Ohtsu
,
M.
, and
Ono
,
K.
,
1986
, “
The Generalized Theory and Source Representations of Acoustic Emission
,”
J. Acoust. Emiss.
,
5
(
4
), pp.
124
133
.http://adsabs.harvard.edu/abs/1986JAE.....5..124O
24.
Johnson
,
L. R.
,
1974
, “
Green’s Function for Lamb’s Problem
,”
Geophys. J. Int.
,
37
(
1
), pp.
99
131
.
25.
Roth
,
F.
,
1990
, “
Subsurface Deformations in a Layered Elastic Half-Space
,”
Geophys. J. Int.
,
103
(
1
), pp.
147
155
.
26.
Bai
,
H.
,
Zhu
,
J.
,
Shah
,
A. H.
, and
Popplewell
,
N.
,
2004
, “
Three-Dimensional Steady State Green Function for a Layered Isotropic Plate
,”
J. Sound Vib.
,
269
(
1
), pp.
251
271
.
27.
Liu
,
G. R.
, and
Achenbach
,
J. D.
,
1995
, “
Strip Element Method to Analyze Wave Scattering by Cracks in Anisotropic Laminated Plates
,”
ASME J. Appl. Mech.
,
62
(3), pp.
607
613
.
28.
Jacobs
,
L. J.
,
Scott
,
W. R.
,
Granata
,
D. M.
, and
Ryan
,
M. J.
,
1991
, “
Experimental and Analytical Characterization of Acoustic Emission Signals
,”
J. Nondestr. Eval.
,
10
(
2
), pp.
63
70
.
29.
Ono
,
K.
,
2011
, “
Acoustic Emission in Materials Research—A Review
,”
J. Acoust. Emiss.
,
29
, pp.
284
309
.http://www.ndt.net/article/jae/papers/29-284.pdf
30.
Wisner
,
B.
,
Cabal
,
M.
,
Vanniamparambil
,
P. A.
,
Hochhalter
,
J.
,
Leser
,
W. P.
, and
Kontsos
,
A.
,
2015
, “
In Situ Microscopic Investigation to Validate Acoustic Emission Monitoring
,”
Exp. Mech.
,
55
(
9
), pp.
1705
1715
.
31.
Momon
,
S.
,
Moevus
,
M.
,
Godin
,
N.
,
R’Mili
,
M.
,
Reynaud
,
P.
,
Fantozzi
,
G.
, and
Fayolle
,
G.
,
2010
, “
Acoustic Emission and Lifetime Prediction During Static Fatigue Tests on Ceramic-Matrix-Composite at High Temperature Under Air
,”
Composites, Part A
,
41
(
7
), pp.
913
918
.
32.
Haider
,
M. F.
,
Giurgiutiu
,
V.
,
Lin
,
B.
, and
Yu
,
L.
,
2017
, “
Irreversibility Effects in Piezoelectric Wafer Active Sensors After Exposure to High Temperature
,”
Smart Mater. Struct.
,
26
(9), p.
095019
.
33.
Cuadra
,
J. A.
,
Baxevanakis
,
K. P.
,
Mazzotti
,
M.
,
Bartoli
,
I.
, and
Kontsos
,
A.
,
2016
, “
Energy Dissipation Via Acoustic Emission in Ductile Crack Initiation
,”
Int. J. Fract.
,
199
(
1
), pp.
89
104
.
34.
Khalifa
,
W. B.
,
Jezzine
,
K.
,
Grondel
,
S.
,
Hello
,
G.
, and
Lhémery
,
A.
,
2012
, “
Modeling of the Far-Field Acoustic Emission From a Crack Under Stress
,”
J. Acoust. Emiss.
,
30
, pp.
137
152
.http://www.aewg.org/jae/JAE-Vol_30-2012.pdf
35.
Hamstad
,
M. A.
,
O’Gallagher
,
A.
, and
Gary
,
J.
,
1999
, “
Modeling of Buried Monopole and Dipole Sources of Acoustic Emission With a Finite Element Technique
,”
J. Acoust. Emiss.
,
17
(
3–4
), pp.
97
110
.https://www.nist.gov/publications/modeling-buried-monopole-and-dipole-sources-acoustic-emission-finite-element-technique
36.
Hill
,
R.
,
Forsyth
,
S. A.
, and
Macey
,
P.
,
2004
, “
Finite Element Modelling of Ultrasound, With Reference to Transducers and AE Waves
,”
Ultrasonics
,
42
(
1
), pp.
253
258
.
37.
Hamstad
,
M. A.
,
2010
, “
Frequencies and Amplitudes of AE Signals in a Plate as a Function of Source Rise Time
,”
29th European Conference on Acoustic Emission Testing
, Vienna, Austria, Sept. 8–10, pp. 1–8.http://www.ndt.net/events/EWGAE%202010/proceedings/papers/20_Hamstad.pdf
38.
Sause
,
M. G.
,
Hamstad
,
M. A.
, and
Horn
,
S.
,
2013
, “
Finite Element Modeling of Lamb Wave Propagation in Anisotropic Hybrid Materials
,”
Composites, Part B
,
53
, pp.
249
257
.
39.
Michaels
,
J. E.
,
Michaels
,
T. E.
, and
Sachse
,
W.
,
1981
, “
Applications of Deconvolution to Acoustic Emission Signal Analysis
,”
Mater. Eval.
,
39
(
11
), pp.
1032
1036
.http://pwp.gatech.edu/ece-quest/wp-content/uploads/sites/484/2012/11/Michaels_MatEval1981_AE.pdf
40.
Hsu
,
N. N.
,
Simmons
,
J. A.
, and
Hardy
,
S. C.
,
1978
, “
Approach to Acoustic Emission Signal Analysis-Theory and Experiment
,” Nondestructive Evaluation, La Jolla, CA, July 17–21, p.
31
.
41.
Pao
,
Y. H.
,
1978
, “
Theory of Acoustic Emission
,”
Transactions of the 23rd Conference of Army Mathematicians
, Hampton, VA, May 11–13, p.
389
.
42.
Ohtsu
,
M.
,
1995
, “
Acoustic Emission Theory for Moment Tensor Analysis
,”
J. Res. Nondestr. Eval.
,
6
(
3
), pp.
169
184
.
43.
Fischer-Cripps
,
A. C.
,
2000
,
Introduction to Contact Mechanics
,
Springer
,
New York
.
44.
Haider
,
M. F.
, and
Giurgiutiu
,
V.
,
2017
, “
Full Derivation of the Helmholtz Potential Approach to the Analysis of Guided Wave Generation during Acoustic Emission Events
,” University of South Carolina, Columbia, SC, Report No. USC-ME-LAMSS-2001-101.
45.
Wolski
,
A.
,
2011
, “
Theory of Electromagnetic Fields
,” CAS - CERN Accelerator School: RF for Accelerators, Ebeltoft, Denmark, June 8–17, Paper No.
15
http://pcwww.liv.ac.uk/~awolski/teaching/cas/ebeltoft/theoryemfields.pdf.
46.
Jackson
,
J. D.
,
1999
,
Classical Electrodynamics
, Perseus Books, Reading, MA.
47.
Uman
,
M. A.
,
McLain
,
D. K.
, and
Krider
,
E. P.
,
1975
, “
The Electromagnetic Radiation From a Finite Antenna
,”
Am. J. Phys.
,
43
(
1
), pp.
33
38
.
48.
Jensen
,
F. B.
,
Kuperman
,
W. A.
,
Porter
,
M. B.
, and
Schmidt
,
H.
,
1994
,
Computational Ocean Acoustics
, American Institute of Physics, Woodbury, NY.
49.
Remmert
,
R.
,
2012
,
Theory of Complex Functions
, Vol.
122
,
Springer Science & Business Media
,
New York
.
50.
Cohen
,
H.
,
2010
,
Complex Analysis With Applications in Science and Engineering
,
Springer Science & Business Media
,
New York
.
51.
Krantz
,
S. G.
,
2007
,
Complex Variables: A Physical Approach With Applications and MATLAB
,
CRC Press
,
Boca Raton, FL
.
52.
Watanabe
,
K.
,
2014
,
Integral Transform Techniques for Green’s Function
,
Springer
,
Cham, Switzerland
.
53.
Haider
,
M. F.
,
Giurgiutiu
,
V.
,
Lin
,
B.
, and
Yu
,
Y.
,
2017
, “
Simulation of Lamb Wave Propagation Using Excitation Potentials
,”
ASME
Paper No. PVP2017-66074.https://www.researchgate.net/publication/318541093_SIMULATION_OF_LAMB_WAVE_PROPAGATION_USING_EXCITATION_POTENTIALS
You do not currently have access to this content.