Keywords: acoustic emission, quantitative source characterisation, numerical methods, transient finite element analysis, band-limited Green's function, ball impact, pencil lead break.

On the onset of damage in materials, strain energy is suddenly released generating transient elastic waves known as acoustic emission (AE). These waves propagate away from the source giving rise to small surface displacements that can be detected using piezoelectric AE sensors. The measured AE signals contain information about the micro-mechanisms of sources, the structure through which the waves propagate, and the characteristic response of the sensor and the detection electronics. Ideally a technique is needed that would uncouple these effects from the measured AE signals in order to extract quantitative information about the AE sources.

The AE measurement chain can be modelled using a linear time-invariant system described by two transfer functions. The first transfer function describes the effects of wave propagation. This provides the relationship between the source and the measured surface displacement. The second transfer function describes the characteristic response of the recording system, which includes the response of the sensor and the detection electronics. If both transfer functions are known, then it becomes possible to determine the source function by deconvolution.

The transfer function of the recording system can be determined by an absolute system calibration. This provides the relationship between the mechanical displacement input and the recorded electrical waveform output. The effects of wave propagation are usually studied using a Green's function approach. The Green's function predicts the response of a body due to a unit impulse (delta function) loading at some point in the body. It has been shown that AE sources, such as cracks, can be represented by "equivalent" volume forces that produce the same wave field as that of the crack [1]. If the equivalent volume forces of a crack are known, it becomes possible to predict the displacement response at some other location in the body by convolution of the source function with the appropriate Green's functions.

Analytical expressions of the Green's function have been found for a number of simple geometries, including an isotropic infinite space, an isotropic half space, a layered half space and an isotropic plate with an infinite lateral dimension [2]. These solutions are very accurate and have been used for the calibration of AE sensors [3] and for the characterisation of AE sources in carefully designed experiments [4]. Obtaining analytical solutions of the Green's function for more complicated geometries becomes mathematically intractable. This is one of the main reasons why the application of the quantitative AE approach has been restricted to laboratory based analysis.

In this paper a numerical approach is used to predict the Green's function. The approach is based on a transient finite element analysis which predicts a limited bandwidth solution of the Green's function. The advantage of the method is that it can be used to model arbitrary geometries that cannot be treated analytically. The aim of this paper is to validate the proposed numerical band-limited Green's function approach. First, exact analytical solutions of an isotropic infinite plate subjected to a point source loading have been used to validate the numerical solutions in the near-field and for short signal durations. Second, experimental measurements are used to validate far-field and long signal durations of AE responses on a circular glass plate subjected to two known artificial AE sources: ball impact and pencil lead-break sources.

1

Burridge, R., Knopoff, L., "Body force equivalents for seismic dislocations", Bulletin of the Seismological Society of America, 54, pp. 1875-1914, 1964.

2

Pao, Y.-H., "Elastic waves in solids", Journal of Applied Mechanics, 50, pp. 1152-1164, 1983.

3

Breckenridge, F.R., Tschieff, C.E., Greenspan, M., "Acoustic emission: some applications of Lamb's problem", Journal of Acoustical Society of America, 57, pp. 626-631, 1975. doi:10.1121/1.380478

4

Michaels, J.E., Michaels, T.E., Sachse, W., "Application of deconvolution to acoustic emission signal analysis", Materials Evaluation, 39, pp. 1032-1036, 1981.

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