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Research Papers

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

[+] Author and Article Information

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

Victor Giurgiutiu

Professor
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

## Abstract

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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## Figures

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

Fig. 2

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

Fig. 3

AE propagation and detection by a sensor installed on a structure

Fig. 4

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

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

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

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

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

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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