Research Papers

A Helmholtz Potential Approach to the Analysis of Guided Wave Generation During Acoustic Emission Events

[+] Author and Article Information
Mohammad Faisal Haider

Department of Mechanical Engineering,
University of South Carolina,
300 Main Street, Room A237,
Columbia, SC 29208
e-mail: haiderm@email.sc.edu

Victor Giurgiutiu

Fellow ASME
Department of Mechanical Engineering,
University of South Carolina,
300 Main Street, Room A222,
Columbia, SC 29208
e-mail: victorg@sc.edu

1Corresponding author.

Manuscript received May 4, 2017; final manuscript received September 28, 2017; published online October 27, 2017. Assoc. Editor: Paul Fromme.

ASME J Nondestructive Evaluation 1(2), 021002 (Oct 27, 2017) (11 pages) Paper No: NDE-17-1005; doi: 10.1115/1.4038116 History: Received May 04, 2017; Revised September 28, 2017

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.

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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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Roberts, T. , and Talebzadeh, M. , 2003, “ Acoustic Emission Monitoring of Fatigue Crack Propagation,” J. Constr. Steel Res., 59(6), pp. 695–712. [CrossRef]
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. [CrossRef]
Lamb, H. , 1917, “ On Waves in an Elastic Plate,” Proc. R. Soc. London A: Math., Phys. Eng. Sci., 93(648), pp. 114–128. [CrossRef]
Helmholtz, H. , 1858, “ Uber Integrale der Hydrodynamischen Gleichungen, Welche den Wirbelbewegungen Entsprechen,” J. Reine Angew. Math., 1858(55), pp. 25–55. [CrossRef]
Achenbach, J. D. , 2003, Reciprocity in Elastodynamics, Cambridge University Press, Cambridge, UK.
Giurgiutiu, V. , 2014, Structural Health Monitoring With Piezoelectric Wafer Active Sensors, 2nd ed., Elsevier, Amsterdam, The Netherlands.
Graff, K. F. , 1975, Wave Motion in Elastic Solids, Clarendon Press, Oxford, UK.
Viktorov, I. A. , 1967, Rayleigh and Lamb Waves: Physical Theory and Applications, Plenum Press, New York. [CrossRef]
Landau, L. D. , and Lifschitz, E. M. , 1965, Teoriya Uprugosti, Nauka, Moscow, Russia [Theory of Elasticity, 2nd ed., Pergamon Press, Oxford, UK (1970)].
Love, A. E. H. , 1944, A Treatise on the Mathematical Theory of Elasticity, Dover Publications, New York.
Aki, K. , and Richards, P. G. , 2002, Quantitative Seismology, Vol. 1, University Science Books, Sausalito, CA.
Vvedenskaya, A. V. , 1956, “ The Determination of Displacement Fields by Means of Dislocation Theory,” Izv. Akad. Nauk SSSR, 3(27), pp. 227–284.
Nabarro, F. R. N. , 1951, “ The Synthesis of Elastic Dislocation Fields,” Philos. Mag., 42(334), p. 313.
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.
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. [CrossRef]
Rice, J. R. , 1980, “ Elastic Wave Emission From Damage Processes,” J. Nondestr. Eval., 1(4), pp. 215–224. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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
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
Johnson, L. R. , 1974, “ Green’s Function for Lamb’s Problem,” Geophys. J. Int., 37(1), pp. 99–131. [CrossRef]
Roth, F. , 1990, “ Subsurface Deformations in a Layered Elastic Half-Space,” Geophys. J. Int., 103(1), pp. 147–155. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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
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
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. [CrossRef] [PubMed]
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
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. [CrossRef]
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
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.
Pao, Y. H. , 1978, “ Theory of Acoustic Emission,” Transactions of the 23rd Conference of Army Mathematicians, Hampton, VA, May 11–13, p. 389.
Ohtsu, M. , 1995, “ Acoustic Emission Theory for Moment Tensor Analysis,” J. Res. Nondestr. Eval., 6(3), pp. 169–184. [CrossRef]
Fischer-Cripps, A. C. , 2000, Introduction to Contact Mechanics, Springer, New York.
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.
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.
Jackson, J. D. , 1999, Classical Electrodynamics, Perseus Books, Reading, MA.
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. [CrossRef]
Jensen, F. B. , Kuperman, W. A. , Porter, M. B. , and Schmidt, H. , 1994, Computational Ocean Acoustics, American Institute of Physics, Woodbury, NY.
Remmert, R. , 2012, Theory of Complex Functions, Vol. 122, Springer Science & Business Media, New York.
Cohen, H. , 2010, Complex Analysis With Applications in Science and Engineering, Springer Science & Business Media, New York.
Krantz, S. G. , 2007, Complex Variables: A Physical Approach With Applications and MATLAB, CRC Press, Boca Raton, FL.
Watanabe, K. , 2014, Integral Transform Techniques for Green’s Function, Springer, Cham, Switzerland. [CrossRef] [PubMed] [PubMed]
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


Grahic Jump Location
Fig. 1

(a)–(d) Plate with existing crack length 2a, energy release rate with crack length, time rate of energy from a crack, and total released energy from a crack

Grahic Jump Location
Fig. 2

Plate of thickness 2d in which straight-crested Lamb waves (P + SV) propagate in the x direction due to concentrated potentials

Grahic Jump Location
Fig. 8

Higher-order Lamb waves (S1 and A1) modes at 500 mm distance in 6 mm 304-steel plate for (a) pressure potential excitation and (b) shear potential excitation (peak time = 3 μs) located at midplane

Grahic Jump Location
Fig. 9

(a) Effect of pressure excitation potential and (b) effect of shear excitation potential: variation of out-of-plane displacement (S0, A0, and bulk wave) with propagation distance in 6 mm 304-steel plate for source (peak time = 3 μs) located at the midplane

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Fig. 3

AE propagation and detection by a sensor installed on a structure

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Fig. 4

Excitation profile: (a) time rate plot and (b) cumulative plot

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Fig. 5

Lamb waves (S0 and A0 modes) and bulk waves propagation at 500 mm distance in 6 mm 304-steel plate for (a) pressure potential excitation and (b) shear potential excitation (peak time = 3 μs) located on top surface

Grahic Jump Location
Fig. 6

Lamb waves (S0 and A0 modes) and bulk waves propagation at 500 mm distance in 6 mm 304-steel plate for (a) pressure potential excitation and (b) shear potential excitation (peak time = 3 μs) located at 1.5 mm depth from top surface

Grahic Jump Location
Fig. 7

Lamb waves (S0 and A0 modes) and bulk waves propagation at 500 mm distance in 6 mm 304-steel plate for (a) pressure potential excitation and (b) shear potential excitation (peak time = 3 μs) located at midplane




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