This is the second chapter of an eleven part article on Ultrasonics by John Drury, the Author of Ultrasonic Flaw Detection for Technicians. This article was first published in INSIGHT magazine throughout 2004/5. The chapters can be downloaded in PDF for you to build into a complete series.

To access the other chapters please use the navigation at the bottom of this page.

J.C. Drury ' BACK TO BASICS - ULTRASONICS'

Chapter2.
PROPERTIES OF SOUND WAVES

VELOCITY

Sound travels at different speeds through different materials. This is noticeable when, for example, a railroad worker is observed from a distance striking a rail with a hammer. Since the speed of light is much faster than that of sound, the observer first sees the hammer strike the rail. If the observer is also close to the rail, the next event is the sound of the blow coming out of the rail and finally the airborne sound is heard.

This tells us that the speed of sound in the rail is faster than the speed of sound in air. It is true that sound travels faster in liquids than in gasses and faster in metals than in liquids. However, it is also true that sound travels at different speeds in different metals. There is a distinct speed of sound for each material and in ultrasonics this is called the VELOCITY of sound for that material. This being so, it would be useful to have an understanding of the reasons for the difference.

Imagine two pairs of identical steel balls, one pair joined by a strong compression spring and the other pair by a weak spring. If one of each pair is moved towards its partner at a constant speed, the spring joining the pair will start to compress. Eventually there will be enough compression in the spring to overcome the inertia of the second ball and it will start to move. As shown in figure 1, the second ball will move sooner for the pair connected by the stronger spring.

Fig. 1

In the analogy, the balls represent the particles of solid, liquid or gas through which the sound wave is propagating and the springs represent Young’s Modulus of elasticity ‘E’. The suggestion made by the analogy is that the disturbance will pass more quickly from one particle to the next in a material having greater elasticity. In other words, the velocity of a compression wave will be higher for greater values of elasticity. This is generally the case but there is another main factor affecting velocity, and that is the density of the material.

Consider another situation in which pair of aluminium balls and a pair of lead balls replace the steel pairs in the above analogy but with each pair joined by springs of equal strength. The inertia of the lead ball is greater than that of the aluminium ball and this time it will take longer to get the lead ball moving. This suggests that the compression wave velocity will be lower for high-density materials than for low-density materials. Density and elasticity are the dominant factors affecting velocity and the expression for the compression wave velocity in a fine wire is taken to be: -

However, when we have a bulk of material, the sample is more rigid than a fine wire giving an effective increase in Young’s Modulus and we need to modify the expression to take account of Poisson’s Ratio. During a tensile test, to measure the strength of a metal sample, the diameter of the sample reduces as the sample is stretched. The change in diameter divided by the change in length is Poisson’s Ratio. Considering all these factors, the velocity of a compression wave in a bulk material can be calculated from the following formula: -

Where

= Compression wave velocity

= Young’s Modulus of Elasticity

= Material Density

= Poisson’s Ratio

Shear waves are able to exist in solids but they do not travel at the same velocity as the compression wave in a given material. This is because it is the Modulus of Rigidity, rather than Young’s Modulus, that dictates the velocity, and the modulus of rigidity is lower than the modulus of elasticity. This means that the shear wave velocity is always slower than the compression wave velocity in a material. In Liquids and gases, the value of the modulus of rigidity is so low that shear waves cannot propagate. As a rule of thumb, the shear wave velocity is roughly half the compression wave velocity. The velocity can be calculated from: -

Or, alternatively

Where

= Shear wave velocity

G = Modulus of Rigidity

= Material Density

= Poisson’s Ratio

Surface (Rayleigh) waves also have their own particular velocity, which is generally taken to be approximately 90% of the shear wave velocity.

Although the velocity for each of these modes of propagation can be calculated, it requires a precise knowledge of all the parameters, and these are not usually available to the ultrasonic practitioner. Parameters such as density and strength vary with alloying, heat treatment, casting, rolling and forging processes – all of which make it difficult to know that the correct values are being used. Instead, it is more normal to carry out a routine called ‘Calibration’ during the setting up procedure for an ultrasonic inspection. In the calibration procedure the flaw detector time-base is adjusted to give a convenient scale against a calibration sample of known thickness and made of the same material as the work to be tested . Table 1 at the end of this chapter lists the compression and shear wave velocities for a number of materials.

WAVELENGTH

While the particles are completing each cycle of their oscillation, the sound wave is moving outwards in the direction of propagation at the characteristic velocity for that material. It follows that during the time taken to complete one cycle of vibration, the sound wave will move a certain distance depending on the velocity in that material. For a given sound frequency, this distance is relatively small for liquids and gasses compared to that in metals, because velocities are higher in metals. The distance travelled by the sound wave during one cycle of vibration is called the WAVELENGTH. In general, if the maximum dimension of a reflecting surface is equal to or greater than half a wavelength, the reflection will be detectable. It follows that calculation of the wavelength will help in the choice of test frequency for a specific application.

Wavelength is given the Greek symbol (lambda) and for any material and sound frequency, wavelength can be calculated from the equation: -

Where = wavelength

V = Velocity

f = frequency

At ultrasonic frequencies, the wavelength of sound in metals is relatively short and so it is usual to express the wavelength in millimetres. This is done at the start of the calculation by changing the velocity from meters to millimetres a second by multiplying the value in M/sec by 1,000.

Example

Calculate the wavelength of a 5MHz compression wave in steel (V c = 5960 m/sec).

ACOUSTIC IMPEDANCE

Acoustic impedance of a material is the product of the material’s density and velocity. At the interface between two materials, the acoustic impedances either side of the interface will determine what proportion of the incident sound wave will reflect and what proportion will transmit into the second material. The symbol allocated to acoustic impedance is ‘Z’ and for a given material,

REFLECTION

Fig. 2

Figure 2 shows the interface between two materials whose acoustic impedances are Z 1 and Z 2 respectively. In the example, part of the energy is transmitted into Material 2 and part is reflected back into Material 1. The percentage of the incident energy that is reflected can be calculated from the equation: -

Where: -

RE is the reflected energy

Z 1 & Z 2 are the acoustic impedances

Example 1

Calculate the percentage of the incident energy that would be reflected at a ‘steel to water’ interface given that Z steel = 46.7 and Z water = 1.48.

Note that the remaining 12% is transmitted into the water.

If the example had been given as a ‘water to steel’ interface, the second line of the calculation would have shown a negative value inside the brackets. However, the square term outside the bracket would restore the answer to a positive value and the answer would have been the same 88% reflected, this time in the water, and 12% would have been transmitted into the steel.

When the interface is between two solids, as in the case of a brazed joint between two pieces of steel, the reflected energy is much smaller, most of the energy passing across the braze and into the second steel layer. There are also examples of two very different materials that have the same acoustic impedance such as Ro-cee rubber and water. Sound travelling through water and then encountering this particular rubber compound will carry on through the rubber as if the interface did not exist. Table 1 shows the acoustic impedance for a number of materials.

COUPLANT

Acoustic impedances for metals tend to have high values whereas those for gasses are low. From the above example it is clear that at a solid to gas interface, the proportion of energy reflected is going to be very high and the proportion transmitted will be very low. That is useful because it means that a discontinuity such as a crack or a void in a metal object will reflect almost all the sound back to the test surface. However, it is also a nuisance because it means that air between the ultrasonic probe and the test surface will prevent the sound from entering the component. A couplant is a liquid or paste used between the probe and the test surface to try to match the acoustic impedance of the probe to that of the test material. It is not a very efficient process because the best couplants, for example glycerine, only allows about 15% of the sound to enter the component, and only the same proportion of any energy coming back to the test surface can enter the probe to give an echo. At best, then, only a little over two percent of the energy generated at the probe ever gets back to the display.

There are specially formulated couplants for use in flaw detection as well as water, oils, greases, glycerine and pastes such as wallpaper paste. The most important considerations when choosing a couplant are firstly that it is not hazardous to the individual and secondly that it will not adversely affect the component.

References: -

 ‘Ultrasonic Flaw Detection for Technicians’ - Third Edition, June 2004 by J. C. Drury

‘Ultrasonic Flaw Detection in Metals’ – Banks Oldfield & Rawding – ILIFFE 1962