This is the third 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'

Chapter3.
REFRACTION & MODE CONVERSION

Previous diagrams have shown the incident sound as if it were a single ray of energy, but of course it is really a beam that has some width, rather like a torch beam. If the incident beam is directed at an interface between water and steel at an angle other than normal, the angle taken up by the transmitted beam in the steel will be greater than the incident angle in water. The advancing wave front in a sound beam can be defined as the plane in which all the oscillating particles are ‘in phase’, or at the same position in their oscillating cycle. The bottom edge of the beam shown in figure 1 arrives at the interface first and immediately takes up the faster velocity of the steel. As the rest of the wave front reaches the interface, so the transmitted beam gradually takes up steel velocity. By the time that the top edge of the beam enters the steel, the sound from the bottom edge has already travelled four times further than it would have in water. Joining up the ‘in phase’ points on the wave front at the instant the top edge enters the steel shows the wave front advancing at a new angle. The beam of sound is said to have undergone ‘Refraction’ as it crossed the interface and the new angle is called ‘the angle of Refraction.

Fig. 1

The refraction occurs because of the difference in velocity on either side of the interface and the proportions of energy reflected in the water and transmitted into the steel remain the same as it would be for normal incidence. Figure 2 shows the incident, reflected and refracted angles. These angles are always measured from the Normal to the interface. In the diagram, ‘i’ is the angle of incidence, r o is the angle of reflection and ‘R’ is the angle of refraction.

Fig. 2

The angles and velocities are related and the relationship is expressed in Snell’s Law such that: -

Where: -

i = Angle of Incidence

r = Angle of Reflection

R= Angle of Refraction

V 1= Velocity in Medium 1

V 2= Velocity in Medium 2

MODE CONVERSION

If Medium1 is a liquid and Medium 2 a solid, some of the energy in the solid will change to the Shear Wave mode. This change is known as Mode Conversion. For small angles of incidence the proportion of energy changing to shear wave mode is small and can be ignored. However as the angle of incidence increases the proportion increases and the shear wave becomes significant so that there can be two types of wave in medium 2 at the same time, both of which can reflect from surfaces within the object. Since they both travel at different speeds, and Snell’s Law tells us that they will refract in different directions, the results can be very confusing. This was a restricting factor in ultrasonics until Sproule developed the first Shear wave angle probes in 1947. Until then it was unsafe to rely on angles of refraction greater than about 10 0 since echoes from the compression wave could not be discriminated from the shear wave reflections. Because of this ambiguity, ultrasonics tended to be restricted to the detection of discontinuities with surfaces parallel to the scanning surface such as laminations and cavities. Attempts to detect, for example, weld defects such as lack of sidewall fusion and root cracks by angling the beam were not reliable.

Sproule realised that the compression wave refracted angle would always be about double the shear wave refracted angle because the shear wave velocity is about half the compression velocity. Therefore if the angle of incidence were to be increased progressively there would be a critical angle of incidence at which the compression wave would refract through 90 0. Any increase in angle of incidence beyond this critical angle would leave only a shear wave in medium 2 and the compression wave would undergo total internal reflection in Medium1. With only a shear wave in medium 2 travelling at a known velocity and at a known angle, the field was open for many new applications of ultrasonics. The critical angle at which the compression wave is refracted through 90 0 is called the first critical angle. For a water to steel interface the first critical angle is about 15 0 and for a Perspex to steel interface the angle is about 28 0. At these critical angles, the remaining shear wave is at an angle of refraction just over 30 0. Increasing the angle of incidence above the first critical angle causes the compression wave to be totally reflected in medium 1 and the shear wave refracted angle to increase so that transducers can be produced at a suitable angle to detect particular defect propagation directions.

Eventually a second critical angle of incidence will be reached at which the shear wave will be refracted through 90 0. The shear wave at this second critical angle will again mode convert, this time to become a Surface (Rayliegh) wave. This new wave travels at 90% of the shear wave velocity, only penetrates to a depth of about one wavelength, will follow the surface contour of the object and will only reflect at an abrupt change in surface direction such as a corner or a crack. If the angle of incidence is increased beyond the second critical angle, no sound will be transmitted into medium 2. Ultrasonic transducers having refracted angles between 0 0 and 10 0 are likely to be compression wave probes and those with refracted angles between 35 0 and 80 0 will be shear wave probes. Surface wave probes have a refracted angle of 90 0. Between 10 0 and 35 0, and 80 0 to 90 0 it would be possible to have two simultaneous modes existing in Medium 2 and so it is unusual to find transducers in these two ranges – exceptions to this rule will be discussed in a later chapter.

Fig. 3

Fig. 4

Figures 3 and 4 show the relationship between the incident angle and refracted angle for water to steel and Perspex to steel interfaces. The graphs show that the second critical angle for water to steel is about 28 0 and for Perspex to steel about 58 0. These values would be different if medium 2 were to be aluminium or some other solid than steel.

Example 1

An incident compression wave in water meets a steel interface at an incident angle of 19 0, calculate the shear wave refracted angle in the steel given that the compression wave velocity in water as 1480m/s and the shear wave velocity in steel as 3240m/s.

From Snell’s Law

Therefore: -

R = 45.46 o

From a practical point of view it is more usual to know the refracted angle needed in the test material in order to detect a particular discontinuity, and so the calculation would be to find the necessary angle of incidence, in water for immersion testing, or in Perspex for contact scanning. Example 2 shows this version of the application of Snell’s Law.

Example 2

Calculate the angle of incidence required in Perspex in order to produce 45 o Shear wave in steel given that the compression wave velocity in Perspex is 2680m/s and the shear wave velocity in steel is 3240m/s.

From Snell’s Law

Therefore: -

Incident angle = 35.8 o

REFLECTIVE MODE CONVERSION

Mode conversion also takes place when an ultrasonic beam reflects at internal surfaces in solids whether these are boundary surfaces, machined features, or discontinuities. The relationship between incident angle of a given beam and the relative amplitude of the reflected and mode conversion beams for steel is shown in the following graphs. They allow an assessment to be made of the potential confusion in any given situation and can be used to determine an alternative test angle to be chosen to avoid the problem.

A compression wave incident on a steel to air interface will reflect as a compression wave together with a mode converted shear wave. For example figure 5 shows that at an incident angle ( a) of 30 o we find that b is around 15 o but the relative amplitudes of the shear wave and compression wave are 90% and 70% respectively. Both will give strong signals if they reach the receiver. In the extreme case, where a is around 60 o and b around 30 o we find that the relative shear wave amplitude is 90% but the reflected compression wave amplitude has fallen to only about 10%. For greater angles of incidence than 60 o, the shear wave rapidly decreases in amplitude and the compression wave recovers. Clearly we need to take care in our interpretation of signals if we see that a compression wave in steel is likely to meet a known reflecting surface in that part of the graph where the shear wave amplitude is significant.

A shear wave will reflect as a shear wave together with a mode converted compression wave. Using the graph in figure 6 we can see that the most severe case is when the incident shear wave meets a steel to air interface at about 30 o. The reflected shear wave amplitude is very low and the mode-converted compression wave is very strong and almost perpendicular to the test surface.

If the incident shear wave grazes a surface, in other words the incident angle is around 90 o, there will be a mode conversion to Rayleigh wave. This can happen when a shear wave grazes the bore of a machined hole in the specimen. In that case the Rayleigh wave will follow the bore surface and will reflect if it encounters a sharp changes to the bore such as a keyway. If you are not aware of the possibility, you may assume that there is a discontinuity in a false position. An example is shown in figure 7 below. Of course, when you are aware of this phenomenon, you can use it to advantage to find a crack in an otherwise ‘blind’ position around a hole or radius.

Fig. 7

References: -

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

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