Experimental detection of cracks at rivets using structural wave propagation
M. B. SAYIR
ETH Zürich, Switzerland
- International Symposium on NDT Contribution to|
the Infrastructure Safety Systems, 1999 NOV 22-26 Torres,
published by UFSM, Santa Maria, RS, Brazil
Technical structure components like aeroplane fuselage, often consist of thin aluminium face sheets, connected through rivets or containing holes which are sources of stress concentration and crack formation at their boundaries. We propose an experimental method for the detection of such cracks based on low frequency structural wave propagation with wavelengths larger than the structure (plate) thickness, and hence much larger than the typical crack dimensions. The waves are excited by means of a piezoelectric or electromagnetic acoustical transducer producing a transverse force with a time function corresponding to a narrow-band signal. Due to the fact that only large wavelengths are represented in the narrow-band spectrum, the main direction of propagation is parallel to the plate faces. Furthermore, the strong dispersive character of structural waves is an advantage, since useful information can be collected from the frequency dependency of the signal without losing too much amplitude in the propagating narrow-band signal.
When the wave hits a discontinuity like a hole, a typical scattered displacement field is obtained and can be analysed quite accurately both in theory and in experiment. A crack at the boundary of the hole changes the scattered field corresponding to an undamaged plate. In our laboratory experiment, a laser-interferometer has been used to measure the scattered field around a hole before and after a notch was introduced at the boundary. Experimental constraints like the adequate choice of the narrow frequency band and the minimal detectable crack length are discussed. The experimental results are compared to theoretical calculations and the practical applicability of the method is discussed.
Keywords: Nondestructive Testing, Structural Waves, Crack Detection
The need for Non-destructive Testing of ageing aircraft structures is widely acknowledged. Several methods have been developed for this purpose and are currently used in industry . Especially, applications of ultrasonic methods have been widely studied, and their efficiency has been improved. Two main obstacles remain: The need for scanning (manually or using devices) and the necessity of a coupling fluid. Recently, the use of leaky Lamb waves (LLW) has been proposed in this context. LLW are plate waves with symmetric or anti-symmetric modes with a frequency content lower than classical ultrasonic waves, allowing for travelling along the structure. The use of LLW for the detection of small rivet cracks has been studied very recently and was shown to give good results for this case .
In this paper, we move one step further away from classical ultrasonic testing and use structural transversal waves, whose frequency content is limited to a narrow band around central frequencies f0. The values of f0 are chosen in the interval 10 to 200 [kHz], corresponding to wavelengths l of 31 to 7 [mm]. These wavelengths are a factor 31 to 7 larger than the thickness of the plate tested in the experiments. To allow for detection of small cracks around the hole, the wavelengths should not be too large. This gives the lower limit of the frequency interval for the choice of f0. The upper limit is derived from the condition that the wavelength remains sufficiently large compared to the plate thickness, thus allowing for the theoretical modelling of the propagation and scattering by simple approximate theories, like thin plate theory, Mindlin's theory of plates  or asymptotically developed theories .
In the scope of this paper, the experimental set-up and measurement results will be described, while referring the interested reader to forthcoming publications on a theoretical treatment of this problem  and a more detailed description of the method . Experimental results are given for the case of a hole in a flat plate, considered to be a simple model for a rivet hole in an aeroplane fuselage. The results are compared to numerical calculations and an outlook is given on how this method could be used for the detection of initial corrosion cracks.
In the experiment, an aluminium alloy plate (Anticorodal 110, size 1.0 ´ 1.0 [m]) of 1.0 [mm] thickness with a hole of 10 [mm] radius is vertically suspended above an optical table, to avoid static bending and facilitate the measurements. A piezoelectric transducer is glued to the plate at 300 [mm] distance from the hole to excite a bending wave. The plate is chosen large enough, so that the reflections from the borders of the plate do not interfere with the measurements of the incident wave and the wave scattered at the hole.
The generated wave pulse corresponds in the time domain to a sinus in a Hanning-window. This gives the above-mentioned signal with a narrow bandwidth. The pulse is defined on the PC and transmitted to a signal generator, where it is converted to a voltage signal and amplified to 200 Vpp using a power amplifier. As the central frequency of the pulse is way below the first resonance frequency of the piezo, its transfer function can be assumed to be nearly constant for each frequency band around f0. The flexural wave propagates radially outwards. At a distance from the source which is large with respect to the diameter of the hole, the wavefront can be assumed to be plane for the evaluation of the scattered wave. Driving the piezo well below its first eigenfrequency leads to small amplitudes of a few micrometers, so that the measurements have to be very accurate.
Fig 1: Experimental Set-up
A laser interferometer is fixed to a positioning system, so that the transverse velocity of the plate along a measurement grid around the hole can be measured. The signal from the interferometer (voltage proportional to the velocity) is band-pass filtered around f0 and stored in a digital oscilloscope. The wave is excited repetitively in the plate, and at each measurement point 25 measurements are averaged in the oscilloscope to reduce noise. The data is then transferred to the PC and analysed using a code written in Matlab. After time-windowing which discards the reflections from the border of the plate, the time series of each measurement point is Fourier transformed using a FFT-algorithm and the amplitude and phase at the central frequency f0 are extracted. The amplitude can be compared directly to other measurements and theoretical calculations, allowing only for a constant factor of the excitation amplitude.
In the experiments, as a first step, the scattering around the undamaged hole in the plate is measured and compared to numerical calculations. Then, at a 45° angle to the propagation direction of the incident wave, a notch through the thickness of the plate with a length of 1 [mm] is sawed with a thin sawblade (0.3 [mm] thick) starting from the hole. Afterwards, the scattered field is measured again and then the length of the cut is increased to 2 [mm] and a third measurement is made.
For the discussion of the experimental results, the amplitude of the scattered field around the hole is displayed in a quasi-three-dimensional plot as a colour-coded surface. The colour represents the pulse amplitude at the central frequency (FFT) of the interaction field between incident and scattered waves. The surface patch at a location is lighter, when the measured or calculated amplitude at this location of the measurement grid is higher. In all plots, the amplitude has been scaled by a constant factor, so that the amplitude of the incident wave is one. For example, in figure 2a, the measurement field around the hole without a crack is given at the central frequency of 50 [kHz] (l = 14 [mm]). The incident wave propagates from top to bottom. At the front of the hole the amplitude is high (light colour). Behind the hole a shadow area develops, since only very little of the incident energy can reach this area. Around the hole the incident and scattered wave interfere constructively and destructively to develop a characteristic hill and valley pattern (high and low amplitude / light and dark). The dark spots on the innermost radius and at discrete spots throughout the measurement grid are errors in the measurement, which result from poor reflection of the laser beam at these positions. A theoretical calculation of the combined incident and scattered field with thin plate theory at an undamaged hole (described in [4, 5]), confirms the measurements (compare figures 2a and 2b). For higher frequencies Mindlin's theory of plates  can be used to predict the measurements.
Fig 2: Scattered field (amplitude) around the hole (r = 10 [mm]) at f = 50 [kHz]
a) Measurement b) Theoretical calculation
To evaluate the influence of a small notch on our measurements, the amplitudes for the damaged case (with a notch length of 1 respectively 2 [mm]) are deducted from the amplitudes measured at the undamaged hole for a central frequency of 50 [kHz]. Directly in front of the notch position (at a 45° angle to the vertical on the innermost measured radius, shown with an arrow), a marked increase of the amplitude can be seen in figure 3a. At larger distances from the notch a new hill and valley pattern can be seen, which results from a shift of the original pattern for the undamaged case and allows the detection of such a crack from a measurement at some distance from the hole. When the notch length is increased from 1 to 2 [mm], the same pattern can be seen in figure 3b, only much clearer and with a distinctively higher difference in amplitude, reaching approximately 20% of the amplitude of the incident wave.
Fig 3: Difference of the amplitude at f = 50 [kHz]|
a) Notch length 1 [mm]
b) Notch length 2 [mm]
Fig 4: Difference in amplitude for a 2 [mm] Notch|
a) f = 20 [kHz]
b) f = 100 [kHz]
As a next step, we discuss the adequate choice of the central pulse frequency. Using a lower excitation frequency, e.g. 20 [kHz] instead of 50 [kHz], increases the wavelength l to 22 [mm] and reduces the possibility to resolve small defects. In figure 4a the difference in amplitude of the scattered field for a 2 [mm] notch is given at a central frequency of 20 [kHz]. Compared to figure 3b, a markedly smaller influence of the notch is visible (ca. 10% difference in amplitude). The notch, which was clearly discernible at 50 [kHz] is rather hard to detect, although still visible. On the other hand, increasing the central frequency to 100 [kHz] decreases the wavelength l to 10 [mm] and increases the influence of the notch to about 40% of the amplitude of the incident wave, as can be seen in figure 4b. In this case, it is even possible to visually detect the influence of the notch on the scattered field in the display of the amplitude without taking the difference between the damaged and undamaged patterns (not displayed). However, at such high frequencies higher order theories, e.g. Mindlin's theory of plates, must be used to accurately describe the scattered field numerically and make predictions [4, 5].
The method described in this paper and employing structural bending waves travelling along a plate, allows the detection of small defects in structures. For the case of a small notch at a hole in a plate, experimental considerations are shown and discussed. The central frequency of the pulse can be chosen to either allow an easy comparison to theoretical calculations or to maximise the influence of the crack on the measurement. A measurement at a point some distance from the hole before and after a notch is cut, shows a difference in amplitude of up to 40% and allows the detection of a crack.
We would like to thank Georgios Kotsalis for his work on the theoretical description of the scattering of a transversal wave at a hole and Joachim Lackner for his help in carrying out the experiments.
/DB:Article /SO:NDTISS /AU:Fromme_P /AU:SAYIR_M /CN:CH /CT:UT /CT:lamb_wave /CT:aerospace /ED:2000-06
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