Quantitative structural health monitoring using acoustic emission Paul D. Wilcox*1, Chee Kin Lee1, Jonathan J. Scholey2, Michael I. Friswell2, Michael R. Wisnom2 and Bruce W. Drinkwater1 1 Department of Mechanical Engineering, 2Department of Aerospace Engineering, Queen’s Building, University of Bristol, University Walk, Bristol, BS8 1TR, UK ABSTRACT Acoustic emission (AE) testing is potentially a highly suitable technique for structural health monitoring (SHM) applications due to its ability to achieve high sensitivity from a sparse array of sensors. For AE to be deployed as part of an SHM system it is essential that its capability is understood. This is the motivation for developing a forward model, referred to as QAE-Forward, of the complete AE process in real structures which is described in the first part of this paper. QAE-Forward is based around a modular and expandable architecture of frequency domain transfer functions to describe various aspects of the AE process, such as AE signal generation, wave propagation and signal detection. The intention is to build additional functionality into QAE-Forward as further data becomes available, whether this is through new analytic tools, numerical models or experimental measurements. QAE-Forward currently contains functions that implement (1) the excitation of multimodal guided waves by arbitrarily orientated point sources, (2) multi-modal wave propagation through generally anisotropic multi-layered media, and (3) the detection of waves by circular transducers of finite size. Results from the current implementation of QAE-Forward are compared to experimental data obtained from Hsu-Neilson tests on aluminum plate and good agreement is obtained. The paper then describes an experimental technique and a finite element modeling technique to obtain quantitative AE data from fatigue crack growth that will feed into QAE-Forward.
1. INTRODUCTION Acoustic emission (AE) is well known as a highly sensitive technique to detect various types of damage, such as fatigue crack growth, corrosion, impacts, delaminations and so forth1-3. This sensitivity coupled with the small number of sensors required potentially makes AE very attractive for structural health monitoring (SHM) applications. Although ambient acoustic noise may be high during in-service monitoring, the fact that monitoring can be performed over extended periods of time means that AE based SHM can exploit the repetitive nature of events that may occur in each loading cycle4,5. AE testing methodology tends to fall into one of two categories1: deterministic and probabilistic. In the deterministic methodology, suitable models of the AE process are used to analyze AE data, whereas, in the probabilistic methodology, a variety of techniques are employed to identify empirical trends in experimental data. While the probabilistic approach is well suited to repetitive testing of similar components, it is the belief of the authors that this approach is much less suitable for monitoring limited numbers of complex, high value, safety-critical structures of the type likely to be encountered in SHM. The authors believe that for AE to be used as the basis for an SHM system with quantifiable performance it is necessary have a deterministic model of the complete AE process from source to received waveform. In the first part of this paper, progress on the development of a modular framework (referred to as QAE-Forward) for quantitative forward modeling of the complete AE process in real structures is presented. The purpose of QAE-Forward is to predict the actual AE waveforms received from sensors when an AE event occurs anywhere in a structure. QAE-Forward is comprised of a growing number of separate functions that model different aspects of the AE process, such as wave generation at AE sources, wave propagation and transduction. The modular framework enables a high degree of complexity to be introduced gradually into the overall model. It should be stressed that the underlying mathematical modeling of QAE-Forward is not new but drawn together from a number of existing guided wave
*
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Smart Structures and Materials 2006: Smart Structures and Integrated Systems, edited by Yuji Matsuzaki, Proc. of SPIE Vol. 6173, 61731K, (2006) · 0277-786X/06/$15 doi: 10.1117/12.658510 Proc. of SPIE Vol. 6173 61731K-1
modeling techniques6-10. At present QAE-Forward can predict the waveforms obtained in isotropic or anisotropic planar structures from in-plane or out-of-plane point forces and includes the effects of dispersion, multi-modal propagation, reflections from simple boundaries and signal reception by transducers with finite spatial aperture and frequency response. Some types of AE sources, such as the Hsu-Neilson (lead break) simulate sources can be implemented as analytical functions in QAE-Forward. For other sources, such as fatigue crack growth, analytical models are not yet available and empirical data is required that can be used as the input to QAE-Forward. The second part of the paper shows the results of some of the experimental and finite element modeling studies that are being performed to provide supporting data for QAE-Forward.
2. MODELLING THE ACOUSTIC EMISSION PROCESS IN REAL STRUCTURES 2.1. Motivation and methodology QAE-Forward is a forward model of the AE process from source to detection. The goal is to be able to simulate the timedomain signal that is received from a transducer when an AE even occurs anywhere in a structure. Such a model has great importance for the development of AE SHM systems since it can be used to, for example: 1.
Optimize sensor placement and spacing to achieve a desired level of sensitivity,
2.
Perform probability of detection (POD) and false call ratio (FCR) simulations, and
3.
Support safety cases based on the use of AE in a complex structure.
QAE-Forward is based on a modular linear systems architecture using frequency-domain transfer functions and is implemented within Matlab (The MathWorks, Inc., Natick, MA). A fundamental aspect of QAE-Forward is that the modular architecture enables the source, propagation and detection of AE signals to be separated. This has important implications for the design of experiments to obtain data to input to the three parts of QAE-Forward which will be discussed later. The overall architecture of QAE-Forward is illustrated schematically in Fig. 1. Where possible, the building blocks of QAE-Forward are developed from existing analytic models, in particular those related to guided wave excitation and propagation. This is based on the observation that a wide range of structures are made up of plate-like elements, through which AE signals will propagate as guided waves. However, it is recognized that there are no analytic solutions to some aspects of the AE process, such as wave propagation through complex geometries, and here the plan is to link QAE-Forward to transfer functions obtained either experimentally or through numerical finite element (FE) models.
Source
Propagation
Detection
Source characteristics Frequency content Stress tensor (orientation, amplitude etc)
Wave propagation model Phase and group velocity Attenuation Interaction with features
Transducer characteristics Frequency response In-plane/out-of-plane response Spatial aperture
Excitability model Modal amplitudes Radiation pattern
Figure 1:
Received waveform
Noise Discrete acoustic sources Acoustic signal reflections Random acoustic noise Random electrical noise
Block diagram showing the main components of QAE-Forward.
The overall model for the frequency spectrum, H(ω), of a received time-domain signal, excluding noise terms, can be expressed as a single equation:
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H (ω ) =
∑
All rays and modes
⎡ ⎤ ⎢ E (ω )P(ω )BA(ω )R X (ω ) RC (ω ) TC (ω )⎥ ⎢⎣ All reflections All transmissions ⎥ ⎦
∏
∏
(1)
where E(ω) is the modal excitability at the source, P(ω) is the delay due to propagation, A(ω) is attenuation, B is beam spreading, RX(ω) is the sensitivity of the receiver, RC(ω) is the reflection coefficients of all features at which the ray is reflected and TC(ω) are the transmission coefficients of all features that the ray has traversed. The final received timedomain signal is the inverse Fourier transform of H(ω). The outer summation is performed over all possible ray paths of all possible wave modes from source to receiver. The following subsections describe the nature of the terms in Eq. 1 in more detail. 2.2. Source QAE-Forward begins at the AE source which is characterized by a frequency dependent radiation pattern of guided wave energy partitioned between various modes, the so-called source function, E(ω). In the past, the mechanism of AE signal generation by a variety of sources has been well studied in the case of sources buried in an infinite medium1. What has received much less attention due to its inherent complexity is the case of sources in finite media, such as plates, which has much greater applicability to practical testing. The types of source functions that can currently be obtained analytically for plate-like structure are those for transient point loads either on the surface or embedded within the structure. Such sources including Hsu-Neilson lead breaks, used by many workers to simulate AE events, which can be modeled as an out-of-plane force applied to the surface of the plate. Fig. 2 shows source functions computed at 200 kHz for a 3 mm thick plate for various combinations of source orientation and plate material. In the case of an isotropic aluminum plate subjected to an out-of-plane surface force, the source function in Fig. 2(a) shows that the only modes excited are the fundamental Lamb wave modes A0 and S0 and there is no angular dependence. However when a 3 mm thick cross-ply composite plate is subjected to the same type of force the graph in Fig. 2(b) shows that three fundamental guided wave modes are excited and that there is a strong angular dependence. In this particular case, the mode labeled SH0 has the interesting property of having multiple components in certain directions. Fig. 2(c) shows the effect of applying an in-plane force in the 0° direction to the surface of an isotropic aluminum plate. In contrast to the case of an out-of-plane force, there is now an angular dependence on modal amplitude. It is thought, although not yet proven, that the source function for the guided waves emitted from sudden crack growth may be closely related to this case.
-20 -40
S0
-60 -80 30 60 Angle (o)
90
(c)
0
-20
A0
-40 S0 -60 -80
-100 0
SH0 30 60 Angle (o)
90
Amplitude (arbitrary dB scale)
A0
-100 0
Figure 2:
(b)
0
Amplitude (arbitrary dB scale)
Amplitude (arbitrary dB scale)
(a)
0 -20 -40
A0 S0
-60 -80
-100 0
30 60 Angle (o)
90
Angular dependence of source functions, E, at 200 kHz for (a) an out-of-plane force on a 3 mm thick aluminum plate, (b) an out-of-plane force on a 3 mm thick composite plate and (c) an in-plane point force applied at the surface of an isotropic plate.
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2.3. Propagation, attenuation and beam spreading Once the amplitude of a mode in a particular direction is known it is straightforward to simulate its propagation as a guided wave through uninterrupted structure by applying an appropriate phase delay: P(ω ) = exp[− ik (ω )d ]
(2)
where i is √-1, k(ω) is the wavenumber of the wave mode and d is the propagation distance. Note that if k is not proportional to ω then the mode is dispersive. The energy spreading in time due to dispersion is implicitly accounted for in this equation. In a plate-like structure, the guided wave rays from a point source such as an AE event diverge in two dimensions. For conservation of energy, this requires that the amplitude of guided waves decays with the square root of propagation distance. This is the basis of the beam spreading term: B=
1
(3)
d
Material attenuation and energy leakage into surrounding media appear as exponential decays in signal amplitude with distance that can be represented by one exponential function: A = exp[− α (ω )d ]
(4)
where α is the attenuation in Nepers m-1, which is, in general, a function of both mode and frequency. The data required to implement the propagation and attenuation functions are the wavenumber and attenuation characteristics of possible guided wave modes in the structure in the propagation direction of interest. Both of these quantities are, in general, functions of frequency. For most single and multi-layered planar structures, the phase velocity dispersion relationships can be computed using established techniques from the material stiffness and density. For structures where the material properties are unknown there are experimental techniques available to measure the phase velocity dispersion data experimentally. More importantly, experimental data is essential for accurately determining the attenuation, which is much more difficult to calculate due to uncertainties in the governing material properties. 2.4. Detection Practical detection of AE signals is almost invariably performed using some sort of surface mounted piezoelectric transducer, although in the laboratory other methods such as laser interferometry are available. As a first approximation, it can be assumed that a surface mounted piezoelectric transducer is primarily sensitive to out-of-plane surface displacement. However, the output from the transducer will not be an exact replica of the out-of-plane displacement at a point on the surface of the plate for a number of reasons. Firstly, the transducer has its own frequency response function which can be readily included in the transfer function model if it can be measured. A typical frequency response spectrum for a commercial AE transducer is shown in Fig. 3(a). For accurate transducer simulation, the amplitude and phase of the frequency response is required. This is particularly important in the case of transducers with high sensitivity over a wide bandwidth, where the sensitivity is achieved by a transducer design with multiple lightly damped resonances that overlap over a range of frequencies. Such transducers are high-sensitivity but are not high-fidelity in terms of replicating the surface displacement of the structure on which they are mounted.
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(a) 1
(b) 1
Sensitivity
Sensitivity
0
0
100
200
300
400
0
S0
A0
0
1
2
3
4
Frequency (kHz) Figure 3:
(a) Typical frequency response of a commercial transducer; (b) wavelength, λ, response of a circular transducer with diameter D. The points marked correspond to the sensitivity of a 10 mm diameter transducer to the A0 and S0 Lamb wave modes on a 3 mm thick aluminum plate at 250 kHz.
In addition to a frequency response curve, a transducer of finite size also has a wavelength response curve to incident guided waves. This is a significant effect as the diameter of a typical AE transducer is around 10 mm, which is of similar order to the wavelength of guided waves in the frequency range of interest. Currently in QAE-Forward, the frequency and wavelength responses are assumed to be uncoupled and the wavelength response of a transducer is estimated by integrating out-of-plane surface displacement over its aperture. In the case of circular transducers, this gives rise to a wavelength response, RX(λ), in the following form: R X(λ ) (ω ) =
⎛ πD ⎞⎤ πD 2 ⎡ ⎛ πD ⎞ ⎟ + J 2 ⎜⎜ ⎟⎟⎥ ⎢Jo ⎜ 4 ⎣ ⎜⎝ λ (ω ) ⎟⎠ ⎝ λ (ω ) ⎠⎦
(5)
where D is the diameter of the transducer, λ is wavelength, and J0 and J2 are zeroth and second order Bessel functions of the first kind respectively. This function is plotted in Fig. 3(b) and the points corresponding to the A0 and S0 Lamb wave modes in a 3 mm thick aluminum plate at 250 kHz detected by a 10 mm diameter transducer are highlighted. It can be seen that at this frequency the transducer is around 2.5 times more sensitive to the S0 mode than the A0 mode. 2.5. Interaction with features The interaction of guided waves with simple straight features, such as edges, can be readily modeled using a simple raytracing approach, and requires the length of all possible ray paths that pass through a sensor location over a given time period to be calculated. This is achieved by calculating the position of virtual receivers, which are reflections of the actual receiver position about the edges of the structure, and then computing the distance between the actual source and each of the virtual receivers. This is shown schematically in Fig. 4. This shows the construction of the possible ray paths for direct transmission, one reflection and two reflections in a simple rectangular plate. In this figure, and in QAE-Forward currently, mode conversions are ignored and reflection coefficients for all modes are assumed to be unity for all incident angles. In the future, the possibility of including mode conversions and reflection coefficients that are functions of frequency and incident angle can be added, subject to the availability of data.
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Physical plate Direct path One reflection paths Two reflection paths Source Physical receiver Virtual receiver
Figure 4:
Ray paths for the direct transmission and first two reflections for an AE event in a rectangular plate.
2.6. Example results for a Hsu-Neilson source in aluminum plate The simplest AE source that has been considered is the standard Hsu-Neilson source that is widely used to simulate AE signals. This consists of a pencil lead being broken on the surface of the structure and can therefore be regarded as a step force applied to the surface in the out-of-plane direction. The excitability function, E(ω), for guided waves excited by such a force can be obtained analytically as noted previously and the time-domain signals recorded by a remote transducer can therefore be predicted. Fig. 5 shows a comparison between the simulated and experimental time-domain signals and it can be seen that good agreement is achieved. The discrepancies between the two signals, in particular the slight tails on each signal that are observed experimentally, have been attributed to inaccurate modeling of the frequency response function of the transducer.
(a)
(b)
0
Figure 5:
100 Time (µs)
200
300
0
100 Time (µs)
200
300
(a) Experimental recorded time-trace and (b) time-trace simulated using QAE-Forward for HsuNeilson source 300 mm away from transducer on 3 mm thick aluminum plate.
It should be noted that there is an important reason why the Hsu-Neilson source and other point forces can be modeled analytically. The reason is that in these cases, a force is applied to the surface of an otherwise uniform structure and can therefore be modeled using knowledge of wave propagation in a uniform structure. This is not true in the case of genuine
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AE sources, where the exciting force comes from within the structure and originates at a discontinuity such as a crack. However, this does not preclude the use of the QAE-Forward away from the immediate locality of the source provided that an excitability function can be obtained by other means. This is the motivation for the ongoing experimental and finite element modeling program discussed in the following section which seeks to characterize the modal excitability functions for genuine AE sources in different structures.
3. EXPERIMENTAL AND FINITE ELEMENT WORK 3.1. Experimental characterization of acoustic emission from fatigue crack growth in large plate The AE from a fatigue crack growing in the centre of a large aluminum plate has been studied experimentally. The experimental set-up is shown in Fig. 6. It should be stressed that this experiment is designed to characterize the AE source itself so that this information can be input into QAE-Forward. The size of plate is necessary to allow separation in the time-domain of the A0 and S0 mode signals from the crack and from the edge reflections. The teardrop shaped cut-out in the center of the plate is designed to provide the necessary stress concentration to initiate fatigue crack growth from its tip.
(a)
(b)
Channel 1 Channel 2
Fatigue machine grip area
Channel 3 300 mm
Channel 4
Figure 6:
(a) Photograph of experimental set-up to characterize acoustic emission from fatigue crack growth in aluminum plate and (b) schematic of plate area. The plate is 1000 mm wide by 1200 mm high.
To date, two plate specimens have been fatigued to failure and some initial qualitative results have been obtained that indicate the direction for future testing. The two plate specimens were cyclically loaded in tension from 225 kN to 275 kN at frequency of 1 Hz. A four channel AE system (PCI-2, Physical Acoustics Corp., Princeton Jct, NJ) was used to record the full AE waveform from all sensors whenever an event was detected on any sensor. A typical waveform is shown in Fig. 7(a). Each waveform was then post processed in Matlab to determine the amplitude of the A0 and S0 Lamb wave modes. Example results are shown in Fig. 7(b). Although more data is required, some initial trends can be observed. Firstly, it can be seen that there is a steady increase in both the average amplitude and rate of AE events as the test progresses. Secondly, the ratio between the amplitudes of the A0 and S0 Lamb wave modes remains reasonably constant over the duration of the tests. As yet there is insufficient data to draw conclusions about the angular distribution of energy, although this has been addressed by the finite element modeling described in the following section. In subsequent tests it is planned to use eight transducers arranged in a circle around the crack tip and to measure the precise crack growth rate which will then be correlated with the received signals. Because of the difficulty in obtaining experimental data, it is intended that finite element numerical simulations will be used to provide more extensive parametric data which is then backed up with experimental data from a limited number of validation cases.
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Amplitude (arb.)
(b)
Amplitude (arb.)
(a)
0 Figure 7:
200
400 Time (µs)
600
0
0.4
0.8 1.2 Time (hours)
1.6
(a) Typical experimentally obtained time-trace from AE event during fatigue loading of plate; (b) amplitude of A0 (asterisks) and S0 (open circles) Lamb wave modes recorded during the course of the fatigue test.
3.1.1. Finite element modeling of acoustic emission from crack growth Two- and three-dimensional time-marching finite element (FE) models have been used to investigate the nature of the AE wave field produced by crack growth in plates. The modeling has been performed using the ABAQUS platform (ABAQUS Inc., Providence, RI) with post-processing in Matlab. The basic modeling procedure is as follows: 1.
An appropriate mesh is generated. The nodes along the desired line of crack growth are split into two and tied together. The mesh may also include nodes that are split but not tied together to simulate the presence of an existing pre-crack.
2.
The model is statically loaded in tension using ABAQUS-Standard.
3.
The tied nodes along the desired line of crack growth are released from each other and the model imported into ABAQUS-Explicit - the explicit time-marching part of the ABAQUS platform.
4.
The subsequent elastic wave propagation away from the source is then modeled in ABAQUS-Explicit.
5.
The surface displacement time history is recorded at a number of appropriate locations and imported into Matlab for post-processing.
6.
The time histories are frequency filtered to the range of interest and the results processed to extract the contributions from different modes.
Typically, the out-of-plane surface displacement is recorded at pairs of points at the same positions but on opposite sides of the plate. In the frequency range where only fundamental Lamb wave modes are present this allows the signals to be separated into those from the symmetric S0 mode and the anti-symmetric A0 mode by addition or subtraction of the signals from opposing points. The SH0 mode is also excited, but in an isotropic plate, this has no out-of-plane surface displacement and is therefore not detected. For example a three-dimensional model of fatigue crack growth is presented here, the geometry of which is shown in Fig. 8. The material is 3 mm thick aluminum plate, the crack growth is assumed to be at the end of an existing crack. The crack growth in this example occurs over a rectangular region, 3 mm long in the crack direction and for four different values of depth through the thickness of the plate, the remaining thickness of the plate remaining intact in each case.
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3 mm
3 mm
Crack growth Pre-crack
θ
150 mm
Depth
toring points Moni
Applied force Figure 8:
Schematic diagram of FE model.
The amplitudes of the A0 and S0 Lamb wave modes detected over a range of angles for the four different crack growth depths are shown in Figs. 9(a) and (b) respectively. (a)
(b) 2.625 2.625
1.875
1.875
1.125
1.125
0.375
0.375
Figure 9:
Polar plots of angular mode amplitude for various depths of crack growth: (a) A0 mode; (b) S0 mode. The angular, θ, datum is in the direction of the pre-crack and the radial scale is the same on both figures. The numbers in boxes refer to the depths of the new crack surface as shown in Fig. 8.
It can be seen that the A0 mode is always of higher amplitude than the S0 mode for a given crack depth and this is consistent with the earlier experimental results. Furthermore, it can be seen that radiation pattern of both modes exhibits a strong angular dependence. This has obvious implications for the detectability of crack growth and the estimation of growth rate in AE monitoring. The spikes visible in the θ = 0° direction for the A0 mode have been attributed to an extra edge wave mode propagating along the edge of the pre-crack.
4. CONCLUSION An overview of a systematic modeling framework, QAE-Forward, for simulating the AE process in real structures has been presented. Good simulations of experimentally received waveforms have been achieved using analytical functions to represent AE sources, wave propagation in finite plate structures and reception by finite sized transducers. Initial
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results from controlled experimental measurements and finite element simulations have been used to show how different types of AE sources may be characterized in a manner which will enable them to be incorporated into QAE-Forward. The next phase of the research program is to begin to use the model to perform probability of detection (POD) studies for various sensor configurations. The procedure will be to use QAE-Forward to simulate received waveforms from a series of possible source locations, orientations and amplitudes and measure the proportion of these which satisfy some predefined detection and/or localization criteria.
ACKNOWLEDGEMENT This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) through the UK Research Centre in NDE and by Airbus, Rolls-Royce and Nexia Solutions. Jonathan Scholey is funded through an Industrial CASE studentship with Airbus.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
C. B. Scruby and D. J. Buttle, “Quantitative Fatigue Crack Measurement by Acoustic Emission”, pp. 207-287 in Fatigue Crack Measurement: Techniques and Applications, eds. K. J. Marsh, R. A. Smith, and R. O. Ritchie, Engineering Materials Advisory Service Ltd, 1991. K. Ono, “Acoustic Emission”, pp. 173-205 in Fatigue Crack Measurement: Techniques and Applications, eds. K. J. Marsh, R. A. Smith, and R. O. Ritchie, Engineering Materials Advisory Service Ltd, 1991. M. Fregonese, H. Idrissi, H. Mazille, L. Renaud and Y. Cetre, “Initiation and Propagation Steps in Pitting Corrosion of Austenitic Stainless Steel: Monitoring by Acoustic Emission”, Corros. Sci., 43, pp. 627-641, 2001. L. M. Rogers, “Structural and Engineering Monitoring by Acoustic Emission Methods - Fundamentals and Applications”, Lloyd’s Register Technical Investigation Department, 2001. E. W. O'Brien, “An Experimental Mechanics approach to Structural Health Monitoring for Civil Aircraft”, pp. 727-736 in Recent Advances in Experimental Mechanics, ed. Emmanuel E. Gdoutos, Kluwer Academic Publishers, 2002. A. N. Ceranoglu, and Y. H. Pao, “Propagation of Elastic Pulses and Acoustic-Emission in a Plate: Parts 1 to 3”, J. Appl. Mech., 48(1), pp. 125-132, 1981. M. R. Gorman, “Plate Wave Acoustic Emission”, J. Acoust. Soc. Am., 90(1), pp. 358-364, 1991. M. R. Gorman and W. H. Prosser, “Application of normal mode expansion to acoustic emission waves in finite plates”, J. Appl. Mech., 63(2), pp. 555-557, 1996. A. K. Maji, D. Satpathi and T. Kratochvil, “Acoustic Emission Source Location Using Lamb Wave Modes”. J. Eng. Mech., 123(2), pp. 154-161, 1997 W. H. Prosser, M. A. Hamstad, J. Gary, and A. O’Gallagher, “Reflections of AE Waves in Finite Plates: Finite Element Modeling and Experimental Measurements”, J. Acoust. Emiss., 17(1-2), pp. 37-47, 1999.
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