Maximilian Hilbck winter semester 2021/2022

The Rayleigh wave ultrasonic method is mostly used for component inspection through the use of so-called Rayleigh waves, which belong to the category of surface waves.

Fundamentals

Ultrasonic testing is an important tool in the field of non-destructive testing of components. In ultrasonic testing, material properties or defects can be made visible by the external introduction of ultrasound waves into a component and by recording the travel times of the reflected waves. A wide range of materials can be inspected using this method. So-called volume ultrasound waves are most commonly used for bulk insprection. These constitute longitudinal and transverse waves.

For surface inspection, so-called Rayleigh waves can be used for ultrasonic testing. They belong to the category of surface waves and are characterised by their high energy in the area of the near surface.

Due to the high energy of the Rayleigh wave in the near surface region, it is possible to detect the smallest surface discontinuities and to inspect components with complex curvatures and geometries for defects.[11]

Rayleigh-waves

Rayleigh waves are surface acoustic waves used in both seismic and component testing.

Rayleigh waves belong to the category of elastic waves and were first discovered by Lord Rayleigh in 1885. They propagate on the surfaces of elastic solids. They are composed of longitudinal and transverse particle displacements. Their penetration depth into the body on which the waves propagate is about one wavelength and their amplitude decreases with increasing penetration depth. In addition to the decrease in the direction of penetration, the amplitude in the far field (the area further away from the source where the ultrasound beam is relatively uniform) decreases as a result of the two-dimensional propagation with the mathematical relationship formula in (1‑1), where s is the sound path. Rayleigh waves are particle motions which follow an elliptical path and also move in the vertical plane (see Figure 1).[1][13]

$//<![CDATA[ \begin{array}{l}\frac{1} {\sqrt{s}}\end{array} //]]>$                                                                                                        (1-1)

In addition to Rayleigh waves, where particles move perpendicularly to the surface plane, there is a second type of surface wave, the Love wave. In contrast to the Rayleigh wave, the Love wave oscillates in the surface plane at right angles to the direction of propagation. (see Figure 2)

Applications

Rayleigh waves are used in a variety of applications. These include component testing and seismology.

Component testing

One application of Rayleigh waves, as described above, is Rayleigh wave ultrasonic testing. It is particularly suitable for crack depth measurement as well as for the highly sensitive surface inspection of complex components.

Cracks in parts and components still represent a major failure criterion today. It is therefore all the more important to detect them in order to determine the remaining service life, test intervals and permissible limits of the component.

In the test procedure, Rayleigh waves in the ultrasonic range are applied to the component. There are three different methods, which are briefly described below.

1.Sokolinskii comb device
2.Optical generation of acoustic surface waves.
3.Use of angle probes that convert longitudinal waves into Rayleigh waves.

The Sokolinskii comb device is based on a comb-like structure. The grooves of the comb are arranged to correspond to the wavelength of the desired Rayleigh wave. The comb-like structure is glued to the test object on one side and connected to the transducer on the other side. The method is characterised by a high spectral purity.[10]

In the method of optically generated surface acoustic waves, these are generated by a pulsed laser source. The method is characterised by the contactless generation of Rayleigh waves and the avoidance of coupling conditions.[10]

In the method using the angle probe, as shown in Figure 3, the probe is placed on the component. The angle probe converts longitudinal waves into Rayleigh waves. This method is the most widely used in the industry, resulting in a large commercial selection of different angle probes. Advantages of this method are that the same wedge can be used with probes of different frequencies and can produce a large deflection.[2] [10]

In order to detect the resulting sound field, a detection device is needed that picks up the sound waves. Different methods are suitable for this purpose, two of which are described in more detail below.

1. Laser interferometry
2. Transmitter-receiver arrangement with a point-shaped piezo transducer

Laser interferometry:

In laser interferometry, a laser beam is split by a semi-transparent mirror. One of these split laser beams hits a mirror so that the phase of the laser beam is kept stable. The other part of the split laser beam hits the component (represents the second mirror), whose position, acceleration or speed can change. The laser beam is also reflected by this component and subsequently reunited with the reference laser beam. Due to the different paths of the laser beams, an interferometry pattern is created. [9][11]

The disadvantage of this method is that the surface of the component must reflect very well, otherwise there is considerable interference noise. In addition, this method is very costly in terms of equipment.[1][2]

Transceiver arrangement with a point-like piezo transducer:

When using the piezo transducer, the reflected waves are detected and converted into electrical voltages. Reflections of the Rayleigh waves can be analysed and used to detect and locate cracks or defects, for example by deviations in the transit-times. The connection of the piezo transducer to the surface of the test object is problematic, as an air layer would lead to falsified measurement results due to surface roughness. Wax, for example, is suitable as a coupling medium. The advantage of this method is not only the good resolution when using coupling agents, but also the lower costs of the apparatus.

The relationship of the Rayleigh wave speed (approximate) is described in formula (1‑2). Here v describes the Poisson ratio and β the propagation speed in an unbounded medium. It should be noted that the test method is very sensitive and even the smallest surface disturbances, such as scratches, roughness and weld spatter, are detected and can falsify the measurement results.

$//<![CDATA[ \begin{array}{l}c=\frac{0,87+1,12*v}{1+v}*β\end{array} //]]>$                                                                                              (1-2)

When the Rayleigh waves hit a crack they are transmitted, reflected and mode-converted. The crack depths can be determined using three different methods: by means of amplitude measurement, by means of propagation time and by means of spectral analysis.

The three different methods are briefly explained below and their suitability is determined.

Crack depth measurement by means of amplitude measurement:

For the amplitude-based measurement, the amplitude of reflected and transmitted Rayleigh wave at small crack can be correlated to the crack depth [1][12]. However, it should be noted that the curves are non-monotonic and are therefore not used to determine the crack depth, but rather to characterize the crack initiation.

Crack depth measurement by means of time-of-flight determination:

In crack depth measurement by means of time-of-flight determination, Rayleigh waves are generated and the runtime that a reflection needs to be picked up by the receiver provides information about the crack depth. The intensity of the reflection deviates significantly from the Rayleigh wave generated, shown in Figure 4. [12]

The mathematical relationship is represented by formula (1‑3).  describes the Rayleigh wave propagation speed.

$//<![CDATA[ \begin{array}{l}a=\frac{t_1_2 *C_R} {2}\end{array} //]]>$                                                                                                        (1-3)

In principle, the measurement accuracy can even be set to tenths of a millimetre. However, the accuracy depends on the frequency used.

The method of crack detection with the help of the run time is, however, limited to the detection of cracks that are deeper than 4mm. This is due to the resolvability of the reflection, as so-called crack closure effects do not always allow identification. [1][12]

Crack depth measurement with spectral analysis:

With this method, the resulting resonances of the scattered Rayleigh waves are measured and the propagation in crack depth and length and causative geometric factors are derived on the basis of this. [1][12]

Also problematic with this method are the crack closure effects, which no longer allow the detection of cracks.

Field of application in Seismic

In seismology (from the ancient Greek σεισμός seismós "[earth] shaking, earthquake"), Rayleigh waves are used to investigate large structures in the mantle surface and earth crusts. [6] Rayleigh waves are also the main cause of extreme destruction in earthquakes. They cause what is called "rolling motion" of the earth's surface. The rolling motion causes the ground to rise and fall, stretch and compress. [3] [4][5][13][14]

Literature

[1 ]Jürgen Pohl, Otto-von-Guericke-Universität Magdeburg, Institut für Werkstofftechnik und  Werkstoffprüfung, „Risstiefenmessung mit Ultraschall-Rayleighwellen“, Berlin, 21.-23. Mai 2001 -Berichtsband 75-CD, https://www.ndt.net/article/dgzfp01/papers/p04/p04.htm

[2] Donald O. Thompson and Dale E. Chimenti,”Review of Progress in Quantitative Nondestructive Evaluation” Volume 16A, 1997 Plenum Press, New York, ISBN: 0-306-45597-8, S.161, https://books.google.de/books?id=3etLzmHu6bQC&pg=PA161&redir_esc=y#v=onepage&q&f=false

[3] Joachim Herz Stiftung, Mechanische Wellen „Seismische Wellen“, https://www.leifiphysik.de/mechanik/mechanische-wellen/ausblick/seismische-wellen, 07.01.2022

[4] Bundesverband Geothermie, Rayleighwellen, September 2020, https://www.geothermie.de/bibliothek/lexikon-der-geothermie/r/rayleighwellen.html, 07.01.2022

[5] Bundesverband Geothermie, Seismik Aktive, September 2020, https://www.geothermie.de/bibliothek/lexikon-der-geothermie/s/seismik-aktive.html, 07.01.2022

[6] Hans Berckhemer, Frankfurt, Spektrum Akademischer Verlag, Heidelberg 1998, „Seismologie“, https://www.spektrum.de/lexikon/physik/seismologie/13138, 07.01.2022

[8] Larry Braile, Purdue University, “Love-wave Motion”, https://www.iris.edu/hq/inclass/animation/lovewave_motion, 07.01.2022

[9] Larry Braile, Purdue University , “Rayleigh-wave Motion”https://www.iris.edu/hq/inclass/animation/rayleighwave_motion, 07.01.2022

[10] Masserey, Bernard, ETH Zürich, https://www.research-collection.ethz.ch/handle/20.500.11850/25384, 24.01.22

[11]Felix Brand, „ Vergleich zwischen Lser-Doppler- und photorefrativem Interferometer zur Messung von akustischen Oberflächenwellen unter industriellen Bedingungen“ https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwj12sn3jNL1AhWDR_EDHRyFBEUQFnoECAMQAQ&url=https%3A%2F%2Fwww.ama-science.org%2Fproceedings%2FgetFile%2FZwZ4AD%3D%3D&usg=AOvVaw2MW4pmqXrLKtVa8xGabLLH, 24.01.22

[12] Jürgen Pohl, Risse mit Ultraschall- Rayleighwellen charakterisieren https://www.degruyter.com/document/doi/10.1515/mt-2001-4311-1208/html, 24.01.22

[13] Andreas Barth, Brückenkurs Geophysik – Oberflächenwellen https://publikationen.bibliothek.kit.edu/1000115500, 28.01.22

[14] BR-Wissen, Seismische Wellen im Detail
https://www.br.de/wissen/erdbeben-beben-plattentektonik-tsunami-seismische-wellen-100.html, 28.01.22

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