This is the seventh 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'

Chapter7.
THE ULTRASONIC BEAM

The beam of sound waves emerging from an ultrasonic probe is rather like the beam of light from a torch. The beam will spread out into an elongated cone shape, and the further away you go from the source, the weaker will be the beam. So in order to know just how this beam affects our in­spection, we need to study the shape of the beam in detail, and to study the changes in intensity of the beam along its axis and across the beam.

As a general principle, we have said that the beam gets weaker as we get further from the transducer. This weakening, or decrease in intensity represents a loss of energy; we say that the beam is attenuated as it progresses through a material. The sound beam suf­ fers this attenuation for the following reasons: -

ABSORPTION - of the energy due to moving the vibrating molecules

SCATTER - of sound waves reflecting from the grain boundaries

INTERFERENCE EFFECTS - close to the transducer

BEAM SPREAD - the energy spreads over a larger area with distance

The amount of energy lost through ‘A bsorption’ depends upon the elastic properties of the material being tested so that steel and aluminium have less absorption than lead, or Perspex. ‘Scatter’ also depends upon the material being tested, the larger the grain size, the greater the scatter (see figure 1). Forged and rolled materials generally give less scatter than castings or forgings. Heat treatment may reduce grain size and therefore reduce scatter, making testing easier. Faced with a material that presents either, or both, high absorption and scatter, you have to resort to a lower test frequency to overcome the problem. We can either say attenuation (absorption and scatter) decreases as test frequency decreases, or penetration increases, as frequency decreases.

INTERFERENCE EFFECTS

Point Source: - If we consider a point source of sound energy, then the disturbance (sound wave) will radiate outwards from the point in an ever in­creasing circle, just like the ripples on a pond spreading out when you drop a stone into it. So sound radiates in all directions from a point source. (figure 2) .

Finitesource: - Our transducer, however, is not a point source, but a plate of piezoelectric material of finite dimensions. In order to appreciate the way in which sound spreads out from a finite source, and to help us understand interference effects we will use Huyghens principle, Huyghens said that you can consider a finite source to be made up of an infinite number of point sources. When you energise the transducer, sound will radiate out from each of these point sources, just as it did for the stone dropping into the pond. Figure 3 shows sound radiating from just one of these point sources and figure 4 shows sound radiating from several point sources.

It can be seen from figure 4 that a short time (t B 1 B ) after the finite source has been energised, the disturbances from each of the point sources will have moved outwards by the same amount. Along a line equal to the radius of the small circles, running parallel to the face of the transducer, these disturbances re-enforce each other to produce a wave front moving out from the transducer. Notice also, a little energy ‘diffracts’ around the edge of the transducer and is ‘lost’. A little while later (t B 2 B ), sound from each point source will have travelled a little further and reinforce at a new distance in front of the transducer, thus the sound wave progresses from the source (figure 5).

This wave front may represent the initial ex­pansion of the transducer as it starts to vibrate (a positive going half cycle). It will tend to push particles of the material away from the source. Shortly afterwards, the transducer will con­tract as part of its vibration, and a wave front, drawing particles into the source (a negative going half cycle) will follow on behind the initial wave front, followed by another push, then another pull and so on.

In the third article in this series, we discussed refraction of the beam as an angled incident wave meets an interface. The bottom edge of the beam reaches the interface first and takes up the new velocity. We can use Huyghens principle to explain what happens. As each point along the incident wave front reaches the interface, each in turn takes the new velocity and in the new material, the line of initial wave fronts will determine the direction of the refracted beam. Similarly, in the fifth article we mentioned phased array probes. The shape of the beam and beam angle will be determined by the wave front for which the individual wave fronts are in phase.

Now consider a point reflector ‘P’ just in front of the probe centre. Let us consider how this reflector is affected by just three of the point sources, one in the centre and one at each edge of the transducer (figure 6).

Fig 6

We energise the source, and a split second later sound from the middle point source reaches P, and gives it a push (figure 7). Notice that energy from the edges of the probe has not reached P yet. This will take longer because P is further from the edges than from the centre.

Fig 7

By the time sound from the edges of the transducer reaches P (figure 8) and tries to push P away from the transducer, the energy from the centre may be on the opposite half cycle of vibration, and be pulling P back towards the transducer. The resultant force acting on point P will be the vector sum of the forces acting from all parts of the crystal. In our example, the result is that P doesn't move at all (i.e. the sound intensity=0). The distance between the solid arc (positive peak) and the dotted arc (negative peak) is half a wavelength. If a different frequency had been used, it may have been that the second positive half cycle from the centre of the crystal reached point P at the same time as those from the edges of the crystal. In that case, the forces would have reinforced and point P would have been given an extra hard ‘push’.

Fig. 8

When two solid arcs cross, the forces from those two parts of the crystal are both ‘pushing’ at the intersecting point and when two dotted arcs cross the forces from that part of the crystal are both ‘pulling’ at the intersecting point. In both cases we call the effect ‘constructive interference’. When a solid arc cuts a dotted arc, the forces are in opposition and we call the effect ‘destructive interference’. Of course point P will not always be exactly a multiple of half wavelengths away from the center and the edges, and constructive interference happens when the relevant point sits anywhere within the same half cycle. Destructive interference happens when the relevant point is in dissimilar half cycles.

‘Interference’ occurs whenever energy arrives at different phase (wavelength) intervals at a particular point. Whether the interference is constructive, or destructive, is determined by the path difference between P and the centre, and P and the edges. As P gets further away from the front of the transducer, this path dif ference becomes negligible compared to the wavelength (figure 9) and interference problems become insignificant.

Fig 9

Where, NF = Near Field Distance .

D = Crystal Diameter.

l = Wavelength

Example 1.

Calculate the Near Field distance for a 10mm diameter, 5MHz crystal transmitting into steel (Velocity 5960m/sec. \ l = 1.192mm).

This means that for this probe, in steel, we can expect fluctuations in intensity of sound for the first 21mm of steel depth due to interference effects. As a result, it is unwise to rely solely on amplitude as the criterion for acceptance or rejection of the part for discontinuities that are in the near field region.

The last item on our list of factors affecting attenuation of the sound as it travels through a material is the ‘Beam Spread’. Because the beam spreads out into a conical shape, intensity follows the inverse square law just as it would for a beam of light or X-rays. If you double the distance from the probe, the intensity drops to one quarter of its original value because of beam spread. Of course, it will actually fall to less than a quarter, because we have to add any ab­ sorption, scatter losses to the beam spread losses. We can now plot a graph of intensity against distance from the probe, to sum­ marise the previous discussions. Figure 10 show amplitude on the vertical axis and distance on the horizontal axis. Distance is shown in multiples of the near field distance.

Fig. 10

The beam profile shown in figure 11 is very much a ‘theoretical’ beam spread. Alongside there are three ‘slices’ through the beam showing that the highest sound intensity is in the centre of the beam. The sound gradually fades away towards the edge of the beam until there is no sound left. It is often more convenient to define the beam to a theoretical edge where the intensity of sound has fallen to one half (-6dB), or sometimes one tenth (-20dB) of the intensity at the beam centre. We can consider three theoretical edges; one defining the absolute edge of the beam, another defining the 6dB edge and the third defining the 20dB edge. These three edges can be expressed mathematically: -

_{Defines the 6dB edge}

_{Defines the 20dB edge}

It is often convenient to use the theoretical beam shape shown in figure 11 in order to explain some concepts in ultrasonic flaw detection. However it is not good practice to use a calculated beam shape for sizing discontinuities by one of the intensity drop methods. This is because practical beam shapes seldom match the theoretical model closely enough.

Example 2.

Calculate the 20dB beam spread angle for a 5MHz compression wave in steel from a 10mm diameter crystal.

q = U14.8UPU^oU

We have used three terms connected with the beam of sound in the test material, namely ‘Dead Zone’, ‘Near Field’, and ‘Far Field’. The dead zone is that part of the timebase occupied by the initial pulse when using a single crystal contact probe. The near field is the distance in the material that suffers from interference effects and the far field is the rest of the beam beyond the near field. The trace shown in figure 12 is calibrated for 100mm of steel return path using a single crystal 5MHz compression wave probe. The three zones are shown on the trace.

Reference: -

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