TYPES OF ULTRASONIC WAVES AND THEIR APPLICATIONS

Ultrasonic waves are classified on the basis of the mode of vibration of the particles of the medium with respect to the direction of propagation of the waves, namely longitudinal, transverse, surface and lamb waves. The major differences of these four types of waves are discussed below:

2.3.1. Longitudinal or Compressional Waves

In this type of ultrasonic wave alternate compression and rarefaction zones are produced by the vibration of the particles parallel to the direction of propagation of the wave. Figure 2.5 represents schematically a longitudinal ultrasonic wave.

FIG.2.5. Longitudinal wave consisting of alternate rarefactions and compressions along the direction of propagation.

Because of its easy generation and detection, this type of ultrasonic wave is most widely used in ultrasonic testing. Almost all of the ultrasonic energy used for the testing of materials originates in this mode and is then converted to other modes for special test applications. This type of wave can propagate in solids, liquids and gases.

2.3.2. Transverse or shear waves

This type of ultrasonic wave is called a transverse or shear wave because the direction of particle displacement is at right angles or transverse to the direction of propagation. It is schematically represented in Figure 2.6.

The transmission of this wave type through a material is most easily illustrated by the motion of a rope as it is shaken. Each particle of the rope moves only up and down, yet the wave moves along the rope from the excitation point.

FIG.2.6. Schematic representation of a transverse wave.

For such a wave to travel through a material it is necessary that each particle of material is strongly bound to its neighbours so that as one particle moves it pulls its neighbour with it, thus causing the ultrasound energy to propagate through the material with a velocity which is about 50 percent that of the longitudinal velocity.

For all practical purposes, transverse waves can only propagate in solids. This is because the distance between molecules or atoms, the mean free path, is so great in liquids and gases that the attraction between them is not sufficient to allow one of them to move the other more than a fraction of its own movement and so the waves are rapidly attenuated.

2.3.3. Surface or Rayleigh waves

Surface waves were first described by Lord Rayleigh and that is why they are also called Rayleigh waves. These type of waves can only travel along a surface bounded on one side by the strong elastic forces of the solid and on the other side by the nearly non-existent elastic forces between gas molecules. Surface waves, therefore, are essentially non-existent in a solid immersed in a liquid, unless the liquid covers the solid surface only as a very thin layer. The waves have a velocity of approximately 90 percent that of an equivalent shear wave in the same material and they can only propagate in a region no thicker than about one wavelength beneath the surface of the material. At this depth, the wave energy is about 4 percent of the energy at the surface and the amplitude of vibration decreases sharply to a negligible value at greater depths.

FIG. 2.7. Diagram of surface wave propagating at the surface of a metal along a metal-air interface.

In surface waves, particle vibrations generally follow an elliptical orbit, as shown schematically in Figure 2.7.

The major axis of the ellipse is perpendicular to the surface along which the waves are travelling. The minor axis is parallel to the direction of propagation. A practical method of generating surface waves is given in Section 2.4.2.2.

Surface waves are useful for testing purposes because the attenuation they suffer for a given material is lower than for an equivalent shear or longitudinal waves and because they can travel around corners and thus be used for testing quite complicated shapes. Only surface or near surface cracks or defects can be detected, of course.

2.3.4. Lamb or plate waves

If a surface wave is introduced into a material that has a thickness equal to three wavelengths, or less, of the wave then a different kind of wave, known as a plate wave, results. The material begins to vibrate as a plate, i.e. the wave encompasses the entire thickness of the material. These waves are also called Lamb waves because the theory describing them was developed by Horace Lamb in 1916. Unlike longitudinal, shear or surface waves, the velocities of these waves through a material are dependent not only on the type of material but also on the material thickness, the frequency and the type of wave.

Plate or Lamb waves exist in many complex modes of particle movement. The two basic forms of Lamb waves are (a) symmetrical or dilatational and (b) asymmetrical or bending. The form of the wave is determined by whether the particle motion is symmetrical or asymmetrical with respect to the neutral axis of the test piece. In symmetrical Lamb (dilatational) waves, there is a longitudinal particle displacement along neutral axis of the plate and an elliptical particle displacement on each surface Figure 2.8.

FIG.2.8.Lamb wave Modes.

This mode consists of the successive thickening and thinning in the plate itself as would be noted in a soft rubber hose if steel balls, larger than its diameter, were forced through it. In asymmetrical (bending) Lamb waves, there is a shear particle displacement along the neutral axis of the plate and an elliptical particle displacement on each surface Figure 2.8. The ratio of the major to minor axes of the ellipse is a function of the material in which the wave is being propagated. The asymmetrical mode of Lamb waves can be visualized by relating the action to a rug being whipped up and down so that a ripple progresses across it.

2.3.5. Velocities for longitudinal, transverse, and surface waves

The velocity of propagation of longitudinal, transverse, and surface waves depends on the elastic modulus and the density of the material, and in the same material it is independent of the frequency of the waves and the material dimensions.

Velocities of longitudinal, transverse and surface waves are given by the following equations.

(2.10) 𝑣 = 𝐸(1 − 𝜇)

𝜌 (1 + 𝜇)(1 − 2𝜇)

(2.11)

𝑣 = 𝐺

2𝜌 (1 + 𝜇)

(2.12)

𝑣 = 0.9 𝑣

Where

𝑣 = velocity of longitudinal waves 𝑣 = velocity of transverse waves 𝑣 = velocity of surface waves E = Young's modulus of elasticity G = modulus of rigidity

ρ = density of the material μ = Poission ratio

For steel

𝑣 /𝑣 = 0.55 (2.13)

The velocity of propagation of Lamb waves depends not only on the material density but also on the type of wave itself and on the frequency of the wave.

Table 2-I gives the velocities of longitudinal and transverse waves in some common materials.