PhD thesis: Defect detection in plates using guided waves

Starting from a specific problem, the detection of fatigue cracks at fastener holes in aircraft, a general experimental and theoretical study of the underlying problems was performed, employing guided waves. The model system investigated was the scattering of the first antisymmetric Lamb wave mode A0, a flexural wave, at a circular hole with a notch at an arbitrary angle. With the insight gained from this fundamental research, the developed measurement method was re-applied to the specific problem. In collaboration with the fatigue engineering center of RUAG Aerospace, Emmen a monitoring system for the crack length in tensile specimens was implemented and found to allow the reliable detection of defects. However, the nondestructive testing method is usable for a much broader range of problems. Almost all technical systems contain thin-walled structures like plates and shells, connected with joints, at which stress concentration and damage development can occur. Guided waves allow a fast measurement of large areas of the structures, and therefore a significant cost reduction compared to conventional testing methods can be achieved.

With the chosen measurement method, the excitation and measurement of flexural waves in plates was performed with good accuracy and repeatability. Piezoceramic and electromagnetic acoustical transducers were used as excitation transducers, allowing the excitation of waves in a broad frequency spectrum with a linear transfer function and sufficient amplitude. Line excitation was achieved by using custom cut piezoelectric ceramic plates, resulting in waves with a nearly plane wavefront in the strip-like tensile specimen. Since the excitation transducer is fixed to the structure, the repeatability of the measurements is excellent. This allows an averaging over several measurements, improving the signal-to-noise ratio and canceling out spurious influences that can occur in a harsher environment, like an aircraft hangar. The cost of the piezoceramics is rather low, permitting the integration into the structure for a permanent on-line monitoring.
The scattered field was measured using a heterodyne laser interferometer, mounted on a positioning system and moved parallel to the plate. This allows an automated, non-contact, pointwise measurement of local variations of amplitude and phase in the scattered field, that can not be achieved with most contact-type transducers. The whole scattered field on a measurement grid around obstacles like a hole with and without a defect was measured, gaining an understanding of the geometry of the scattered waves. The evaluation of the measured time series by FFT gives the local values of amplitude and phase and allows the direct comparison to the theoretical calculations. Even more complicated signals, like multi-mode signals could be evaluated using the appropriate digital signal processing.
The study in this thesis was confined to the first antisymmetric Lamb wave mode A0. Good experimental experience and know-how for this mode exists. The measurement of changes in the amplitude and phase of the scattered field overcomes the problems associated with the dispersive propagation characteristics. The A0-mode below the cutoff frequencies of the higher wave modes is easily excited using piezoelectric transducers, as the main displacement is out-of-plane. The energy transferred to the symmetric mode and shear mode is negligible. It would be interesting to apply the measurement with a laser interferometer to other wave types, like Rayleigh waves, possibly improving the sensitivity to small defects, as very local variations of the wave propagation and scattering characteristics can be observed.

In the context of Lamb waves in homogeneous, isotropic plates, the approximate theories for the description of flexural waves were reviewed. The scattering at a circular hole in a plate was calculated analytically and the different approaches using classical plate theory, Mindlin’s theory, and an asymptotic expansion were compared to experimental results. Excellent agreement between the measurements and the analytical calculations was obtained. Care has to be taken concerning the validity of the different approximations, as not only the ratio from wavelength to plate thickness, but also the ratio of hole radius to plate thickness define the validity of the approximations.
The combined scattered field at a hole with a crack at its boundary was calculated numerically, using finite difference methods to discretize Mindlin’s equations on a staggered Cartesian grid. Through explicit time integration a fast and stable algorithm was achieved. The crack was modeled as a through notch, without considering the sharp edge and effects like crack closure. For the model system of a through notch at a hole in a large plate, good agreement with experiments was achieved for the whole range of parameter variations. The effect of a fatigue grown crack on the scattered field around a hole in a tensile specimen was also well predicted. The complicated geometry of tensile specimens with multiple scattering at the hole and specimen boundaries poses no problem. Accurate predictions on the detectability of a defect were made. Conducting a numerical study for a variation of all geometrical parameters, it was found that the main influence on the detectability is the ratio from wavelength to defect size.

In cooperation with the fatigue engineering center of RUAG Aerospace, Emmen the applicability of the measurement method for the detection of fatigue cracks in aluminum specimens was investigated. The substantial geometric relation between hole radius and specimen thickness was selected as in a fighter plane. Fatigue cracks at circular holes were generated by cyclic tensile loading in a servo-hydraulic material testing machine. The scattered field around the damaged holes was measured and found to be well described by the numerical model using finite difference methods. An on-line monitoring of the crack length during the cyclic tensile loading was implemented experimentally. Good correlation between measured and calculated change in signal and the optically measured crack length was found, allowing a sizing of the defect. However, the variation in the measured signal due to noise and external influences was still rather high, making a reliable detection of cracks at an early stage of the damaging process impossible. Higher excitation frequencies and the use of other wave types, e.g., Rayleigh waves, would allow the detection of smaller defects.

Insight on the mechanics of the scattering of flexural waves at defects was gained. From the exact measurement of the complex magnitude of the scattered field, the influence of the defect could be accurately described and modeled theoretically. Further fundamental research would be necessary for an analytical model, allowing a faster calculation and possibly a solution of the inverse problem, i.e., the localization and sizing of the crack from a remote measurement. By the use of higher excitation frequencies and the solution of the resulting experimental obstacles, smaller cracks could be reliably detected. Alternatively, different wave modes might be employed, applying the exact measurement of amplitude and phase variations for an improved resolution of small defects. Building on the knowledge gained from the fundamental research, the nondestructive testing of real aircraft or other technical systems can now be approached.