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 PhD
thesis: Defect detection in plates using guided waves
Introduction
Technical machinery, systems, and
components, e.g., airplanes, cars, pumps, and pipes in refineries, are subject
to varying or cyclic service loads and environmental influences. Such operation
conditions can lead to wear, corrosion, and damaging of the components. The
problem is relevant in aircraft industry, where a common maintenance problem is
the development of fatigue and corrosion cracks in aircraft fuselage and wings.
Due to stress concentration and the contact of different materials, fastener and
rivet holes are frequently sources of crack growth. The longer service life span
of aircraft increases the need to periodically check the structure for damage. Manual scanning around each rivet hole is time-consuming and therefore cost-intensive, as it increases the downtime of the
plane. Much might be gained by being able to perform such checks automatically
over large parts of the structure with the use of guided waves. Placing a
transducer on the specimen, a guided wave can be excited that interrogates
complete lines of rivets. Due to the rather low cost of piezoelectric
transducers one could also think about integrating the transducers into the
structure. This way a smart structure may be fabricated, performing the damage
checks while the structure is in service.
Mechanical waves as used in ultrasonic testing (UT) have a well established
performance for the detection of defects. Guided waves result from multiple reflections of the
bulk waves over the specimen cross section, such that a standing wave mode
through the thickness and a propagation direction along the structure is obtained. From the measurement of the
guided wave at a few points on the surface of the structure it is possible to
detect defects in a large area with a fast and cost-effective method. The
method has been used successfully for the detection of corrosion and cracks in tubes
and pipes, which are widely used in oil and chemical industries and for water
supply and distribution. The problem arising from the use of guided waves is the
fact that the wavelength is usually of the order of magnitude or larger than the
thickness of the structure, and hence large compared to the typical crack size
one aims to detect. The large ratio between wavelength and defect length reduces
the sensitivity and makes an accurate study of the scattering characteristics
necessary, to determine experimental constraints and gain a well-founded
theoretical understanding of the interaction between wave and flaw. The model
system investigated in this thesis is a circular through hole in an aluminum
alloy plate with a notch at an arbitrary angle. This interesting theoretical
problem has only partially been discussed in literature. Analytical solutions
can be found for the geometrically simpler problem of the scattering of guided
waves at a circular cavity. Only few, mostly numerical, studies exist on the
scattering characteristics of Lamb waves at a notch or crack in the plate.
Two types of Lamb wave modes
can exist in isotropic, homogeneous plates, either symmetric or antisymmetric.
In
contrast to the bulk waves used in UT, the propagation of these modes is
dispersive, i.e., wavelength and propagation velocity depend on the frequency.
For the scope of this thesis, the wave mode was selected as the first
antisymmetric mode A0. This mode can be excited rather easily by means of a
piezoelectric transducer and measured using a heterodyne interferometer. As this
mode is highly dispersive in the frequency range of interest, it is usually
avoided. However, applying Fourier transform for the data evaluation and
studying amplitude and phase variations instead of time of flight measurements,
this poses no problem. The displacement of the antisymmetric mode A0 is a
transversal movement of the plate. For low frequencies this out-of-plane
displacement is a pure bending mode. Going to higher frequencies, the effects of
shear and rotatory inertia have to be taken into account. Different
approximate theories exist, describing the propagation and scattering of the
flexural waves. Defects at or close to the surface have a larger influence on
the bending stiffness of the plate than anomalies in the center, and can
therefore be more easily detected. As fatigue cracks usually start to grow at
the surface corner of the holes, the antisymmetric mode is very sensitive to
this kind of defect.
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