Ultrasound (Overview)

Paul Schuler, January 2019

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Sound waves with frequencies above the audible range of the human hearing are referred to as ultrasound. This range of frequencies extends from 20 kHz to 1 GHz [1]. In the field of non-destructive testing, ultrasound is used to detect material defects and to characterize materials.

Fundamentals of sound waves

Sound waves are elastic waves in fluid, gaseous and solid material, generated by oscillations of atoms and molecules around their position of rest. The periodicity of the oscillations is described by the frequency $//<![CDATA[ \begin{array}{l}f \, \left (\text{s}^{-1} \right )\end{array} //]]>$. Due to the elastic property of the medium, the movement is passed to neighbouring atoms and particles and the elastic wave propagates at a characteristic speed of sound $//<![CDATA[ \begin{array}{l}v \, \left ( \text{m} \cdot \text{s}^{-1} \right )\end{array} //]]>$. Hereby only energy and no matter is transported by the wave. The spatial periodicity of the wave in the medium is described by the wavelength , which is the smallest distance between particles in an equal vibrational state: ^[2]

$//<![CDATA[ \begin{array}{l}\lambda = \frac{v}{f}\end{array} //]]>$.

An important quantity describing the propagation of sound in a medium is the acoustic impedance (or wave impedance) $//<![CDATA[ \begin{array}{l}Z \, \left ( \text{kg} \cdot \text{m}^{-2} \cdot \text{s}^{-1} \right )\end{array} //]]>$, which is defined as the product of the density of the medium $//<![CDATA[ \begin{array}{l}\rho \, \left ( \text{kg} \cdot \text{m}^{-3} \right )\end{array} //]]>$ and the speed of sound $//<![CDATA[ \begin{array}{l}v\end{array} //]]>$: ^[2]

$//<![CDATA[ \begin{array}{l}Z=\rho \cdot v\end{array} //]]>$.

A material with high acoustic impedance is called acoustically hard, a material with a low acoustic impedance is called acoustically soft ^[1]. Some Examples are given in the shown table.

Acoustic impedances at $//<![CDATA[ \begin{array}{l}p_0=10^5 \, \text{bar}\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}T=25^°\, \text{C}\end{array} //]]>$ ^[2]

The acoustic energy of a plain wave, which is transported through an area per time, is referred to as acoustic energy $//<![CDATA[ \begin{array}{l}I \, \left ( \text{W} \cdot \text{m}^{-2} \right )\end{array} //]]>$. It is calculated using the acoustic pressure $//<![CDATA[ \begin{array}{l}p\end{array} //]]>$ and the impedance $//<![CDATA[ \begin{array}{l}Z\end{array} //]]>$: ^[2]

$//<![CDATA[ \begin{array}{l}I = \frac{p^2}{2\cdot Z}\end{array} //]]>$.

Types of waves

For a distinction of elastic waves, the direction of motion of the particles in relation to the wave propagation direction is considered. A transverse (shear / S-) wave is characterized by an oscillation of the particles perpendicular to the propagation direction of the wave. If the particles oscillate parallel to the wave propagation direction, the wave is called longitudinal (pressure /P-) wave. While P-waves can propagate in fluid, gaseous and solid material, S-waves are limited to solid material, as fluids and gases hardly resist to shear stress ^[2]. The speed of sound, and thus the propagation velocity, of the S-wave is smaller compared to the P-wave. For steel, the speed of sound of the S-wave is about half the value of the P-wave. Following that, the S-wave allows to detect smaller reflectors compared to the equivalent P-wave ^[3]. In a non-continuous solid medium other wave types occur, so called surface waves and plate waves. They consist of longitudinal or transverse waves or as superposition of the two wave types.

Sound propagation

During its propagation, a sound wave loses energy even in a homogenous medium. This is caused mainly by two material-dependent properties, absorption inside the material (i.e. heating of the material) and scattering of the sound waves at smaller inhomogeneities inside the material. While absorption occurs more or less in every material, scattering is found in crystalline, e.g. metallic or fiber-reinforced materials such as GRP. As absorption and scattering in solid bodies increase with the frequency $//<![CDATA[ \begin{array}{l}f\end{array} //]]>$, the wavelength $//<![CDATA[ \begin{array}{l}\lambda\end{array} //]]>$ should be large enough to not be affected by the scattering of the inhomogeneities inside the material.^[2]

Behavior of sound at interfaces

When a sound wave reaches a surface between two phases $//<![CDATA[ \begin{array}{l}1\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}2\end{array} //]]>$, one part of the acoustic energy is reflected and another part is transmitted. This behavior is described by two corresponding factors, the reflection factor

$//<![CDATA[ \begin{array}{l}R=\frac{Z_2-Z_1}{Z_2+Z_1}\end{array} //]]>$

and the transmission factor ^[2]

$//<![CDATA[ \begin{array}{l}T=\frac{2\cdot Z_2}{Z_2+Z_1}\end{array} //]]>$.

If the acoustic wave does not hit the surface perpendicularly, mode conversion occurs. In this case, the acoustic wave partly transforms into another wave type: A longitudinal wave reaching a solid body is not only split into reflected and transmitted parts of the longitudinal wave, but also partly transformed into a transverse wave. ^[2]

Ultrasonic testing

Ultrasonic test device

The unit to excite or receive ultrasonic waves is called ultrasonic probe or ultrasonic transducer ^[4]. Several ways exist to excite and detect ultrasonic waves. In the field of non-destructive testing, mainly the piezoelectric effect is used. To excite an ultrasonic signal, a short electric impulse, triggered by a pulse generator, is applied to the piezoelectric material and causes it to vibrate with its resonance frequency. The resonance frequency – and thus the test frequency – is dependent from its geometry and design. The right choice of a suited transducer for a specific application is essential for the measurement result. ^[2][4]

Other physical effects than the piezoelectric effect are sometimes used to avoid the need for mechanical contact to the medium to be tested. The energy is then transmitted by electrical or magnetic fields and the conversion into or from acoustic energy takes place in the medium to be tested and not in the transducer itself. The laser based ultrasonic testing for example uses short pulses of laser beams. When the coherent light of the laser hits a metal test object, a part of its electromagnetic energy is absorbed and transformed into heat. This takes place in a very thin layer of the test object’s surface which expands due to the heating – and cools down again. The expansion generates an elastic wave which is described by an oscillation of the particles parallel to the surface of the test object. Using higher laser intensity, atoms near the surface evaporate and cause a mechanic repulsion on the surface. Consequently, an elastic wave perpendicular to the surface is generated. Vice versa, ultrasonic vibrations on the surface of the test object can be detected using a laser interferometer. ^[2][5] In material with high electrical conductivity, high-frequency electric currents can be induced by externally applied current-carrying coils. The induced Lorentz force causes charge carriers in the test object to vibrate. The vibration is transferred to adjacent particles and ultrasonic vibration in the corresponding frequency is obtained. Ultrasonic transducers working according to this principle are called EMAT (electromagnetic acoustic transducers). ^[2] Complex geometries, where the shape of the test object limits access, complicate the use of ultrasound in non-destructive testing. For this application, the ultrasonic testing using phased arrays offers advantages. A phased array ultrasonic consists of many small ultrasound transducers. Are these elements small compared to the wavelength, every transducer can be considered as point source of sound from which the sound propagates in a sphere. The superposition of single waves results in a beam of sound wave. The single transducers can vibrate with a time difference and a so-called synthetic sound field in the test object can be generated. The direction of propagation in the test object can be defined by an angle or the sound beam can be focused to a pre-defined range. This testing method offers also fast inspection as more than one scan can be performed with different angles from one single sensor position. ^[2][6] Dedicated imaging techniques are required to process the captured signals.

Coupling of transducer and medium

As mentioned before, a considerable fraction of the ultrasonic energy is reflected, if two media at an interface differ significantly in impedance. As the impedance of air is much lower than the impedance of material like concrete or steel, an air gap between the transducer and the surface of the medium should be avoided. This is achieved by a couplant with an impedance similar to that of the test object. Besides the usually used fluid couplant (e.g. water) also dry couplants exist for purposes, where for example the medium to be tested would change its properties if wetted with a fluid. ^[2] In some cases, also air-coupled ultrasonic testing is possible. The high amplitude dampening due to high impedance differences is a challenge in this application. ^[6] In the construction sector, coupling the transducer for a large amount of measurements is time consuming. For this purpose, couplant-free ultrasonic arrays exist which enable time-efficient scanning of larger areas of, for example, concrete. These arrays consist of a large number of spring-loaded transducers. ^[7]

Ultrasonic testing methods

Two main categories of ultrasonic testing methods exist. The Transmission-Method and the Pulse-Echo-method.

Transmission-Method

The sound component transmitted through or to the side by the defect is used for the detection. One transmitter and one receiver are coupled to the test object on two opposite sides. For a known distance, the required time of flight is measured and wave speed is obtained. This allows the determination of (some) material properties (Ultrasound Transit Time Method). The testing is referred to as Ultrasound Intensity Method, if in addition also the intensity of the received signal is considered. The intensity depends on the distance of travel inside the material, material properties and also heavily of the coupling. The impulse intensity is much more sensible on defects in the materials than the time of flight but the strong influence of the coupling on the intensity causes difficulties for interpretable measurements in practice. ^[7] The ultrasonic frequency analysis uses a frequency analysis to determine the intensities of different frequency components of an impulse. As every construction material dampens several parts of the frequency range of an impulse regarding to its state, this method allows to characterize material states as e.g. the state of solidification of concrete. ^[7]

Pulse-Echo-Method

If the reflected part of the acoustic energy is used to detect and specify material defects, this is referred to as Pulse-Echo-method. In this case, transmitter and receiver are placed on the same side of the test object. Often, one single transducer performs both transmitting and receiving of the acoustic energy. The evaluation of the pulse propagation time and, optionally, intensity or frequency, allow statements to be made about the depth and dimensions of the reflector. This reflector can be either the backwall of the test object, a detachment, interface or crack in the component. ^[7][2]

Evaluation of ultrasonic testing results

The sound waves returning from or transmitted through the test object are converted into electrical signals. Sometimes, ultrasound signals are transferred from the time domain into the frequency domain to simplify the evaluation and further processing of the measurement results. ^[7] For the Transmission-Method, the exact determination of the first-arrival of the signal is crucial as the time of flight is used for the measurement. This can be done automatic using algorithms or visually by the inspector. The typical screen display is referred to as the A-scan and shows the amplitude of the returned sound waved over the sound transit time, which is connected to the depth in the material. The displayed result is called B-scan, if the transducer is moved along a line and several (or many) A-Scans are combined. Consequently, if the transducer is also moved in a second dimension on the surface of the test object, the result is called C-scan and shows a plan view of the test object. ^[7][3] For phased-array ultrasonic testing, Full-Matrix Capture (FMC) allows to obtain fully focused images at a high resolution with a high sensitivity to flaws. Each possible transmitter-receiver pair in the array is used to capture the corresponding time-dependent signal (A-Scan). The image is reconstructed from the quantity of single signals afterwards. ^[8] Another technique to enhance the image resolution is Synthetic Aperture Focusing Technique (SAFT). Here a B-Scan is computationally obtained from several previous recorded A-Scans. ^[2]

Applications of Ultrasonic testing

Ultrasonic testing is often used to determine elastic parameters, for example Young’s modulus, Torsion modulus or Poisson’s ratio, from the propagation velocities of the acoustic waves, sent to the medium to be tested ^[7]. Theoretically, small structures and defects inside the materials can only be resolved, if they are larger than half the wavelength. In practice however, the wavelength should be much smaller than half the structure to be detected. The downside of a small wavelength is, that a lot of the acoustic energy is reflected even at the heterogeneities of the material, i.e. the conditions for homogeneity are not given. A compromise must therefore be found. ^[7]

In the following, some applications of ultrasound in non-destructive testing are listed exemplary.

Where mechanical wall thickness measurement is not possible, the [[Schichtdickenmessung mit Ultraschall|thickness can be determined by ultrasound using the pulse-echo-method ^[3]. In the construction industry, ultrasonic testing allows to test the homogeneity of components and structures made of steel and prestressed concrete ^[7]. Ultrasonic testing can also be used to determine the quality of curing concrete, as parameters of interest (as the compressive strength and the young’s modulus) are linked to the ultrasound signal parameters ^[7]

. Puls-echo-method and transmission-method can both be used to detect flaws in wood – for example cracks or rot. To detect flaws in welding seams, ultrasonic testing using the pulse-echo-method can be used. The increasing use of carbon fiber reinforced plastic (CFRP) led to the need of suitable methods of non-destructive testing for CFRP. Due to their structure (e.g. sandwich structure composites) and the material mix, CFRP are challenging for non-destructive testing. Composite testing with lamb waves, for example using ultrasonic testing or the impact echo method, allows to detect damages and flaws inside the composite material.

Literature

1. Lerch, R.; Sessler, G. M.; Wolf, D.: Technische Akustik – Grundlagen und Anwendungen. 2009.
2. Deutsch, V.; Platte, M.; Vogt, M.: Ultraschallprüfung – Grundlagen und industrielle Anwendungen. 1997.
3. Schiebold, K.: "Zerstörungsfreie Werkstoffprüfung – Ultraschallprüfung". 2015.
4. Schuster, V., Lach, M.; Platte, M.: "Die Qual der Wahl: Welcher Prüfkopf für welchen Einsatz?". 2004.
5. Krautkrämer J.; Krautkrämer H.: "Ultrasonic Testing of Materials". 1990.
6. Olympus: Tutorial Phased Array .
7. Große, C.: "Zerstörungsfreie Prüfung". 2018.
8. Tremblay, P.; Richard, D.: Development and validation of a Full Matrix Capture Solution. 2012.