The continuing growth of computer resources, in particular high-speed parallel processing and large RAM memories, has made it possible to implement finite element modeling of acoustic emission source dynamics and wave propagation from positions near the source out to considerable distances from the source. Thus we developed and validated this approach. Also we have used finite element modeling to create extensive databases of AE signals.

The finite element method offers some additional capabilities that were not previously available for past modeling efforts of acoustic emission signals. Finite samples with their inherent boundary reflections (e.g., plates that are not infinite) have been successfully modeled with the finite element approach. Further we expect in the future to be able to model complex geometries more typical of actual experimental acoustic emission setups. Also, the finite element technique can provide the three displacement components as a function of position at a given time. This procedure can be repeated for a series of incremental times to provide "movies" of the motions of the displacement fields as a function of time. Since the finite element approach provides the displacement fields seamlessly from very near the acoustic emission source out to significant distances from the source, the examination of near-field and far-field results does not require different analytical approaches. Modeling of acoustic emission displacement signals can conveniently provide high signal-to-noise ratio modeled data that can be used to develop useful advanced signal processing and analysis techniques, which one could apply to real AE data. This modeling approach compared to working with real acoustic emission signals has the huge advantage that for each acoustic emission event the researcher knows exactly the source location, source type, source orientation, and source time history of the AE signal. This situation is not the case with empirically measured real AE signals.

We have validated both two- and three-dimensional finite element codes for both surface sources as well as buried monopoles and dipoles. The modeled signals that are computed can be easily frequency filtered after computation to correspond to the frequency response sensitivity of the experimental wideband conditions. Thus, a comparison of a finite element reference "library" with experimental results can be facilitated. In addition, the effects of changing source parameters, such as source rise time and location of the source through the thickness of a sample, can be studied. Optimal sensor locations can also be determined for use in subsequent real world experiments. Of further significant importance, the differences between real acoustic emission sources occurring in a typical small laboratory sample versus a real world large sample have been now examined.

The titles, abstracts, references and in some cases additional information from our relevant papers in this subject area are listed below.

In Part 2, the same finite-element-generated database of acoustic emission (AE) signals was used, as in Part 1: Source Identification, to examine the application of a wavelet transform (WT) to improve the accuracy of AE source location. These signals represented the top surface out-of-plane displacement versus time from buried dipole sources in aluminum plates 4.7 mm thick. The method utilizes a WT result to select AE signal-arrival times for a single group velocity from energetic modes. The cases of both the large plate without edge reflections and the small plate (coupon) with multiple edge reflections were examined. The arrival time of a specific frequency of an energetic fundamental mode of the far-field signals was determined from the WT. Using these arrival times at three propagation distances, a group velocity was determined for comparison with the appropriate group velocity based on dispersion curves. Both filtered narrow-band (100 to 300 kHz) and wideband (40 kHz high-pass) signals were examined. In addition, in the large-plate case, experimental sensor/ preamplifier electronic noise was added to the AE signals to examine the effect of noise on the determination of accurate arrival times as a function of signal-to-noise (S/N) ratios. Results for the large plate indicate that very accurate arrival times can be determined that correspond to a particular group velocity. In the coupon case, the results indicate significant distortions in the arrival times due to the multiple edge reflections. The perturbation due to the presence of electronic noise was relatively small for the case of the wideband signals in the large plate until signal-to-noise ratios reached levels where an AE hit would likely not be recorded.

A. Source Location-Large Plates

• Excellent straight-line correlations of propagation distance versus the WT-based arrival times of the fundamental modes at fixed frequencies indicate that source location in large plates can be significantly enhanced by use of WT results compared to that possible with fixed thresholds and an assumed constant group velocity.
• Since the amount of energy in a particular mode depends on the source depth, it will be necessary to first select the mode with the dominant energy in each AE signal. Then WT-based arrival times of the maximum WT magnitude of the experimental AE signals can be obtained from that mode at a selected frequency.
• In experimental situations, carefully applied pencil-lead breaks can be used to determine the key frequency to use for each dominant mode. Then only the WT-based arrival times and peak magnitudes at these frequencies need to be extracted. The source location can then be directly calculated from the arrival times for the mode with the dominant peak magnitude. The group velocity for the calculation could be taken from dispersion curves for the selected mode and frequency or from a WT-based group velocity obtained during pre-experiments with careful pencil lead breaks.
• The technique for extraction of WT-based arrival times corresponding to a single group velocity was found to be applicable for both wideband and narrow-band signals.
• In the wideband case, the extraction of single-velocity arrival times was found to be robust in the presence of electronic noise even for signal-to-noise ratios as low as 1:1.

B. Source Location-Small Coupon Specimens

• The inherent multiple side-edge reflections present in small-coupon specimens complicate the use of the WT for the purpose of obtaining accurate source locations.

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A database of wideband acoustic emission (AE) modeled signals was used in Part 1 to examine the application of a wavelet transform (WT) to identify AE sources. The AE signals in the database were created by use of a validated three-dimensional finite element code. These signals represented the out-of-plane displacements from buried dipole sources in aluminum plates 4.7 mm thick and of small and large lateral dimensions. The surface displacement signals at three far-field distances were filtered with a 40 kHz high-pass filter prior to applying the WT. The WTs were calculated with AGU-Vallen Wavelet, a freeware software program. The effects of propagation distance, AE source type, and the depth of the AE source below the plate surface were examined. Specifically, a ratio of the WT magnitude (WT coefficient) from the fundamental anti-symmetric mode to that from the fundamental symmetric mode was studied for correlation with the AE source type. The WT magnitudes were those corresponding to a particular group velocity and signal frequency for each mode. For sources in the large plate located at the same depth, the ratios were able to distinguish different source types and exhibited only small changes with increasing propagation distance. But, when the variable of depth of the source was introduced, the ratios did not uniquely classify the AE source type. In the case of the small coupon plate specimen, reflections from the specimen edges distorted and complicated the WTs. Since the current coupon database excludes (except for one case) the parameter of changes in the distance of the source from the coupon sides, a full examination of these complications was not possible.

A. Source Identification-Large Plates

• For the 4.7 mm aluminum plate thickness of the current FEM database, a potentially useful parameter for source identification has been found. Using a separate selected frequency and approximate group velocity for each fundamental mode, the WT coefficients (usually local maxima for the frequency and group velocity) can be combined to form an Ao/So magnitude ratio. This ratio was found to distinguish different source types when the sources were all centered at the same depth below the plate surface and with the same propagation distance.
• But, since the values of this ratio overlap for different source types at different depths, it is not possible to uniquely identify the source type with this small set of WT-based data.
• The current database indicates that the value ranking of the Ao/So magnitude ratio for different source types remains in the same order as a function of source depth. Since this result is for a single radiation direction, it is to be expected that obtaining this ratio for other radiation directions will supplement the WT-based data with possibly sufficient information to uniquely classify the AE source type even with changing source depth. This expectation is based upon the fact that different source types have different AE-energy radiation patterns. Thus a series of WT-based magnitude ratios from a total number, n, of different radiation angles (e.g., (Ao/So)1, (Ao/So)2, (Ao/So)n) could form an input vector to an artificial intelligence (AI) software program that would determine the AE source type. The AI program could be initially trained using a FEM-generated database.

B. Source Identification-Small Coupon Specimens

• The inherent multiple edge reflections present in small coupon specimens complicate the use of WT coefficients for source identification. Since the current small coupon FEM database does not include (except for one case) the important parameter (relative to edge reflection effects) of changes in specimen side-to-side position of the source, the current database did not allow a full examination of these complications.

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With a validated three-dimensional finite element code, the out-of-plane displacements corresponding to acoustic emission (AE) model sources were calculated in aluminum plate samples of two different lateral dimensions. Both samples were 4.7 mm thick. The lateral dimensions were 480 mm by 25.4 mm, which represented a laboratory-size coupon, versus 1000 mm by 1000 mm, which represented a larger field-size sample. The displacement signals were calculated for positions of the receiver on the top plate surface at several different distances (in the far-field) from the source’s epicenter. The signals were predicted for the same propagation distances of source-to-receiver in both the large and small samples. Models of both point-like sensors as well as sensors with a large aperture were used. The signals were filtered with either a 40 kHz high pass filter or a 100 to 300 kHz bandpass filter. The AE sources were modeled as either a point single dipole (both in-plane and out-of-plane) or a point multi-dipole located at different depths within the plate thickness. Analysis of the simulated AE signals shows that the superposition of edge reflections on the arrivals of the direct signal significantly distorts and amplifies AE signals in the laboratory-size coupon relative to a larger field-sized sample. This results in significantly larger AE signal features such as amplitude, duration, and energy in the laboratory-sized sample. Edge reflections also distort the frequency spectrum of signals in the small sample.

The user of AE technology who does not understand the effects of nearby specimen edges can make incorrect conclusions. On one hand, a field practitioner testing a large sample without nearby edges may not detect damage-indicating AE events. These same events may have been easily detected in small laboratory coupons due to edge reflections that amplify the direct signal. Further, if events are detected in the field case, the field practitioner may underestimate their significance. The reason is that the events will not have the amplitude, energy and duration levels associated with the same original source amplitude in the results for laboratory coupons. On the other hand, the materials scientist attempting to use AE techniques to identify certain types of damage in a small laboratory coupon may become frustrated with the lack of consistency in source identification using features such as the hit peak amplitude, energy, duration, and frequency content. In addition, the materials scientist may find that the distorted frequency spectra make it difficult or impossible to distinguish one type of source from another. Finally, we believe the development of AE technology could experience a much larger payoff in the practical application of the technology to large samples if associated laboratory research were regularly carried out on larger samples.

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The requirements for dynamic finite-element modeling of the source dynamics and wave propagation of buried acoustic-emission point sources were examined. Maximum permissible source and cell sizes for point sources were determined as a function of the minimum wavelength for frequencies of interest. These wavelengths were calculated from the source rise-times. For both buried monopoles and dipoles, finite-element predictions for both plates and half-spaces were compared with published results obtained from other approaches. The modeled signals were evaluated from the epicenter to a distance of 15 plate thicknesses for plates with a thickness of <25 mm. The finite-element method provided accurate results and a practical means to analyze finite specimens, unlike most alternate approaches.

Key finite element parameters have been determined for finite element modeling of buried monopole and dipole AE point sources with a "cosine bell" source: l_m/s and l_m/(cs). Here, l_m (l=lambda) is the minimum wavelength of interest, s is the source size, and cs is the cell size. Our study indicated that adequate results can be obtained for l_m/s >2 and l_m/(cs) >15. Very good results can be obtained if both of these numbers are doubled.

Comparisons with independent methods show that the FEM results are accurate. Results also demonstrate that three-dimensional cases (with a 2.3 µs rise time and a 25.4 mm thick plate) can be effectively modeled with the FEM code to obtain displacements up to a distance of 15h by using our current computing resources.

The capability of a three-dimensional dynamic finite element method for predicting far-field acoustic emission signals in thin plates of finite lateral extent, including their reflections from the plate edges, was investigated. A lead break (Hsu-Neilsen) source to simulate AE was modeled and used in the experimental measurements. For the thin plate studied, the signals were primarily composed of the lowest order symmetric (S₀) and antisymmetric (A₀) Lamb modes. Experimental waveforms were detected with an absolutely calibrated, wideband, conical element transducer. The conditions of lead fractures both on the surface of the plate as well as on the edge of the plate were investigated. Surface lead breaks preferentially generate the A₀ mode while edge lead breaks generate the S₀ mode. Reflections of developed plate waves from both normal and oblique incidence angles were evaluated. Particularly interesting for the case of the lead break on the plate edge were S₀ waves produced by the interaction of a Rayleigh wave with the plate corner and by a bulk shear wave mode converting at the side edge. The Rayleigh wave, in this case, propagated along the specimen edge. For all cases considered, the experimental measurements were in good agreement with the predictions of the finite element model.

The results of this study validate the three-dimensional dynamic finite element method (DFEM) for predicting AE waveforms in finite plates including reflection components. Simulated AE sources (lead breaks) were modeled and used for the experimental confirimation. Lead breaks on both the surface and the edge of thin aluminum plates were considered. In thin plates, surface lead breaks preferentially generate the A₀ Lamb mode while those on the edge near the midplane of the plate preferentially generate the S₀ mode. It was demonstrated theoretically and experimentally that the edge break source also generates a Rayleigh wave which propagates along the plate edge. This Rayleigh wave interacts at the plate corner to produce a mode converted S₀ wave. Also observed theoretically and experimentally was a mode converted reflection caused by shear waves generated by the edge break source. Upon reflection, these waves mode converted at the sides of the plate to longitudinal waves which then propagated through the thin plate as the S₀ mode. An absolutely calibrated, wideband sensor was used for all experimental measurements. In all cases, good agreement was obtained between the DFEM predictions and experimental measurements.

The validation of the DFEM for predicting reflections of AE signals in plates is an important step toward making it a useful tool for predicting AE waveforms in real practical structures. In such structures, signal reflections often significantly contribute to the waveform because of structural complexities such as holes, free edges, welds, joints, etc. The effect of reflections on AE waveforms is even more pronounced in laboratory specimens such as coupons, which usually have very small lateral dimensions. Further work is necessary, however, to validate the model for predicting waveforms in other practical situations to include specimens with changes in thickness, welds, and varying and/or anisotropic material properties.

Using a dynamic finite element model, we studied the interrelationships between acoustic source rise-time and plate thickness in steel plates. The source was typically a midplane vertical dipole, and the out-of-plane displacement was obtained in the far-field, typically at a distance of 15 times the plate thickness. Results with the finite element approach were first obtained without considering practical experimental factors such as the bandwidth limitations of acoustic emission (AE) sensors. In addition, signal processing was applied to the displacement signals to more accurately simulate typical wideband experimental conditions. Analysis of the results indicates that practical measurement realities (bandwidth of contemporary wideband sensors) have a significant effect on the observed displacement signals when the same AE source (temporal characteristics) operates in plates of different thicknessess. The question of "scaling" of results with plate thickness was also addressed for typical AE rise-times. It was demonstrated that nearly correct results for thinner plates (with the same source rise-time) could be obtained by simple signal processing of results from a thicker plate. Experimental realities, which currently limit the full characterization of AE sources with fast rise-times, were pointed out. Also, the relationships between the multi-mode group velocity curves and the observed displacements were examined. The perspective taken in the examination of the modeled AE results was that of using the AE data in order to characterize particular AE sources.

1. FEM results demonstrate that with proper scaling (including the rise-time) exactly the same displacement results are obtained at the same number of plate thicknesses from the same type of AE source located in two plates with different thicknesses.
2. But experimental realities such as limited high-frequency wideband sensor response normally preclude observation of such results.
3. Further, real AE sources have rise-times that depend on the material rather than on plate thickness.
4. Experimental realities (bandwidth of current wideband sensors) also limit the ability to experimentally characterize the source rise-time character of AE sources having fast rise-times.
5. Dramatic differences appear in far-field out-of-plane displacements versus time for the same rise-time source operating in plates of different thickness. These differences are directly attributable to the excitation of additional modes shown in diagrams of group-velocity versus frequency times thickness for the thicker plate.
6. Simple signal processing (change of time scale and filtering) of FEM results from thick plates can generate fairly accurate results for thinner plates for the same source rise-time in both plates.
7. Experimental wideband displacement results from thick plates also can potentially be used to generate useful results for thinner plates (if the time scale is changed and filtering is applied to maintain the same rise-time).

This paper is concerned with the calculation of the acoustic emission wavefield in an isotropic elastic plate. The calculations are carried out by means of two methods: modal superposition (MSM) and finite elements (FEM). These two methods are complementary in the sense that modal superposition is very efficient in constructing the far field response while the finite element method is most efficient in the near field. It is shown that for the source-receiver distance, R, larger than five times the plate thickness, 2H, superposition of a small number of propagating modes gives virtually the same surface motion as that obtained through finite element analysis. For R approximately equal to H, MSM requires evaluation of the non-propagating modes and becomes computationally inefficient. For R >> H, the FEM requires enormous computational effort due to the large size of the discretized model while the computational efficiency of the MSM the same, or even improves. The two methods can be combined for efficient and accurate calculation of acoustic emission waveforms and analysis of AE data for source characterization.

The FEM approach to modeling guided-wave acoustic emission signals has both advantages and disadvantages. The FEM approach can provide results for small specimens where boundary reflections significantly contribute to the observe signals. In addition the FEM results allow the extraction of the spatial displacement distribution at a single fixed or a multitude of times. The FEM approach also gives the accurate results for both the near and the far-field (up to 20 plate thicknesses for a 25 mm thick plate using the 2-D code for axisymmetrical cases). In the case of 3-D problems the range of source rise times and plate sizes which can be exactly modeled is more limited due to the resolution limitations with current workstation resources. Conversion of the 3-D code to allow parallel processing is underway, but this approach will not be inexpensive. In contrast the strengths and weaknesses of the modal superposition approach are due to response close to resonance frequencies and damping coefficient included in the calculation. Modal superposition method, on the other hand, requires very little in computation resource. It is particularly efficient for the far field calculation, in which only a few Lamb wave modes are required. The computations in this paper were done on a lower-end PC, and it took only a few minutes.

With the inclusion of a small imaginary part in frequencies in modal superposition method (MSM), all the proper sections of the Lamb wave dispersion curves for Fourier synthesis of Lamb wave modes are obtained automatically from the dispersion equation. Efficient and accurate calculations of the surface displacements at source-receiver distance over 5 plate thickness is demonstrated. The MSM is not very efficient at small source-receiver distances and it can not be applied to non-planar geometry. The DFEM can be used for arbitrarily complex geometry of the structures. But it demands extensive computational resources. As shown in this paper the two methods can be combined for efficient and accurate calculations of acoustic emission waveforms and analysis of AE data for source characterization in realistic structure.

We have performed a study to validate a three-dimensional dynamic finite element code for calculating expected dynamic displacement fields in the far field from various of acoustic emission sources. This work uses several approaches to complete the validation and to determine values for key parameters so that acoustic emission sources can be modeled. These parameters include the cell size, source diameter, and source rise time. Laboratory experiments using pencil-lead breaks on a large 25.4 mm thick steel plate were used to validate the three- dimensional code. Lead breaks were carried out both on the top surface of the plate and at various depths along one edge. Using a calibrated, wideband displacement sensor, the experimental out-of-plane displacements versus time were quantitatively compared to calculated displacements at distances of up to 366 mm from the source. In addition, certain interesting cases were examined with the code.

A 3-D dynamic finite element code has been validated on a 25.4-mm-thick steel plate as a means of accurately calculating the time dependence of far-field AE displacements. This validation was accomplished by quantitative comparison with experiments using a calibrated wideband sensor. To retain accurate frequency content up to the frequencies of Rayleigh waves, a cell size of about 0.13 to 0.27 mm was required. If providing good definition of the Rayleigh wave is not required, a cell size of about 0.53 mm can be used. To model AE sources that generate frequencies up to the Rayleigh wave frequencies, the source size must be less than about 3 mm diameter and have a rise time of less than about 1 µs. The 3-D code also showed the wide variations in AE waveforms as the depth through the plate thickness was changed for a pencil-lead break source on a plate edge.

The overall objective of this work is the study of the structure of Lamb waves produced in thin plates and the techniques used to measure such waves. Laboratory experiments were conducted using a lead break source on an aluminum plate. These experiments were used to validate a computer model for elastic waves in cylindrical symmetry. The computer model was used to study the influence of the characteristics of the source stress on the resulting waves. The rise time, source width, and the distribution of the stress over the source were all considered. The dependence of the results on the cell size used in the computer model was studied, and the computer requirements for an extension of this work to three dimensions were considered. The effect of aperture size on the signal fidelity from potential acoustic sensors was examined. Validation of the computer model allows the model to be used for the study of certain acoustic emission phenomena which are difficult or impossible to measure in the laboratory.

Our objective was to first validate our computer model against laboratory experiments, and then apply the model to study the structure and measurement of waves generated by a lead break. The reasonable agreement with the measured data indicates that the computer model at the high resolution reproduces the wave structure in the far field quite well. More importantly, the qualitative structure of the waves is reproduced well using only 5 cells across the plate. However, at the low resolution, the amplitude of the some of the peaks in the far field can differ by a factor of two or more from those obtained in the high resolution runs.

In the near field, the qualitative nature of the solution is affected by the resolution. We surmise that the higher resolution is needed in the neighborhood of the source in order to properly launch the wave. However, we can not determine why this resolution is required, nor have we been able to locate a problem in the finite element algorithm, which would explain the variation in the near field solution. Since we can obtain useful results using only 5 cells across the plate, three dimensional computations for thin plates should be possible on the powerful workstations that are now available. This means that many useful results should be obtained, at reasonable cost, on a small cluster of workstations or even on a single workstation.

In addition, there are conclusions from this study relevant to the application of AE technology. In particular, the rise time of the source has a very dramatic effect on the detection of the source. For detectability of sources with rise times up to 40 µs, the AE measurement system must have good response to relatively low frequencies. For typical AE monitors with little sensitivity below 100 kHz, the source rise time must be on the order of 10 µs is or less. Also, there is an important implication from these results concerning the maximum allowable sensor diameter. Clearly, for the waves considered here, the fidelity of the measured waves is not preserved for diameters above about 6 mm. Finally, the lack of large effects for changes in the source size, or a force increasing in area rather than intensity, is of considerable interest for AE studies of source effects on the resulting AE signals.

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