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Although developed initially as a tool for sizing cracks whose location was already known, the Time-of-Flight Diffraction technique has usually been applied in practice to detect the defects as well. This is made possible by use of the B-scan presentation aided by the excellent sensitivity of the human eye and brain for spatial coherence.

The spatial coherence in the B-scan image takes the form of signal arcs generated as the transducers approach and recede from the defect. It is clear that, with the defect symmetrically between transmitter and receiver, crossing the plane passing through both transmitter and receiver and normal to the inspection surface, the transit time of the pulse is at a minimum. As the transducers move away from this position, along a scan line perpendicular to the plane of the defect, the transit time will increase.

Hence, if the transducers are scanned from one side of the symmetrical position to the other, the transit time of the diffracted signal will reduce to a minimum and then

2.3. Time-of-Flight Diffraction in Isotropic Media 39

increase again, forming an arc on the B-scan presentation. Such an arc is clearly visible in Figure 2.2 for a scan over a buried side-drilled hole.

In order to illustrate some of the properties of these arcs we consider a simplified situation in which the transmitting and receiving transducers located on a flat plate surface and we calculate the time-of-flight for a pulse scattered by a small spherical pore at a depth d. This defect is essentially a point scatterer. To calculate the effect of scanning the transducers, it is easier to fix the transmitter and receiver and let the defect move along some line parallel to the plate surface. The time-of-flight can then be obtained as a function of the distance of the defect along its scan direction from some arbitrary origin. The origin of coordinates is taken to lie in the surface and we fix the transmitter at (−S,0,0) and the receiver at (S,0,0). Let the defect position be (x, y,−d), then the time-of-flight t is given by

t= 1 where C is the appropriate signal velocity. This equation is for a fixed position of the small pore. If we simulate a transducer scan by allowing the defect to move along a path parallel to the surface given by a straight line such as

y= mx + constant

then we get an equation which is not of any well known form. There is, however, one special case, when the transducers scan parallel to the y-axis with the defect symmetrically placed between them (a D-scan). In this case, x= 0 and

C²t² 4k² −y²

k²= 1 (2.31)

where y gives the scan position and k²≡ S²+ d² is a constant. Equation 2.31 is recognised as the equation of a hyperbola. This has two branches; in the one of physical interest, t is at a minimum at the point where the scattering point lies in the plane defined by the two beam axes and it increases as the point moves away from that plane. From physical arguments it is clear that signal loci, although hyperbolic only in the special case referred to above, will be of the same general shape for all scan paths in this simple geometry. In particular, the signal loci for a scan parallel to the plane defined by the beam axes (a B-scan) will look very like hyperbolae for deep defects but will appear increasingly flattened near the minimum as the surface is approached (see Figure 5.5).

When the defect is well away from the beam axes of the transducers even simple defects can yield complex patterns of arcs. These arise because signals generated at the separate transducer edges can travel to the defect and back to the receiver as distinct wavepackets without interference, making it appear as though for each pair of probes there were in fact two transmitters and two receivers giving four possible arcs for each defect extremity. These effects are only striking in the near field of the transducers. Figure 2.13 shows schematically the geometry used in the following

Tx Rx

Displacement of probe pair from symmetrical position (mm)

Transittime(microsec)includingtimespentinshoe

Fig. 2.13 Multiple arcs produced by the inside and outside edges of the transmitter and receiver probes. The probes are 15 mm in diameter, have a beam angle of 60^◦and are separated by 150 mm; the defect tip is located 50 mm below the surface.

2.3. Time-of-Flight Diffraction in Isotropic Media 41

discussion of the origin of these multiple arcs and shows predictions of their shape for probes of diameter 15 mm, separated by l50 mm, scanning over a point defect 50 mm below the surface. For a crack, there would be a similar pattern of arcs for both the top and bottom crack edges, provided the defect through-wall dimension was greater than the pulse length, or bigger than about 2λ.

In the geometry shown in Figure 2.13 the probes are separated by 2S as usual, each probe is of diameter 2p, the defect is at depth z, and x denotes the horizontal distance of the defect from the plane midway between transmitter and receiver, i.e.

the offset of the probes from the position of minimum signal travel time. If the full geometry of the probe shoes and the Snell’s Law refraction at the workpiece surface is included in the analysis, a solution can only be obtained numerically and that is the way the curves in Figure 2.13 have been calculated. However, an approximate solution can be obtained by using a construction due to Coffey and Chapman [1983], in which the probes and shoe assemblies are replaced by virtual probes of radius p= a(cosθ/cosψ), where a is the true probe radius and θ and ψ are the beam angle and shoe angle respectively. The virtual probes are centred at the index points on the workpiece surface, and aligned normal to the beam axes. Paths from these probes to points in the interior of the workpiece are treated as lying entirely within the workpiece material; i.e. the surface is deemed to have been removed.

We define u= psinθ and v = pcosθ. Then, with these changes, the travel times become t_i, with i= 1,2,3,4, given by calculated from these formulae agree very closely in shape with the ones shown in Figure 2.13, but, because the time spent by the ultrasound in the probe shoes has been ignored, they are displaced on the time axis by a constant amount to earlier time.

The arcs themselves show the differences in travel time along the different paths but when considering the effect on the observed signals, the effect of the pulse shape has to be considered. In general, pulses travelling by different paths will overlap and interfere with each other so that the received pulse shape is modified. The precise effects will depend on the fundamental frequency of the pulse and the shape of its envelope. We here assume a typical pulse with an approximately Gaussian envelope centred on 5 MHz. In the particular case which Figure 2.13 illustrates, pairs of arcs are almost coincident over much of their length, so the effect is to split the signal into two arcs each with a pulse shape which differs from the basic pulse shape only in having frequency components which are well above the centre frequency somewhat attenuated. However, where all four arcs cross in the centre, the effects are more severe. Here, destructive interference occurs at the fundamental frequency, leaving a severely distorted pulse with a dominant low frequency component.

These characteristics are borne out in Figure 2.14 which shows such arcs recorded from a block containing side-drilled holes. The upper picture shows the signals ob-tained from 15 mm diameter transducers. The multiple arcs from the upper surface of the holes reduce the accuracy of depth measurement and the signals from the lower surface of the holes are obscured. A solution, for immersion probes, is to mask the transducer faces with absorbent material such as polytetrafluoroethylene (PTFE) leaving only a small aperture. The aperture can be circular or, to allow more energy through, slot-shaped, with the long axis aligned perpendicular to the plane containing the beam axes. The aperture width defines the transducer width for the calculation of near-field distance and so can be chosen to ensure that the defects of interest are effectively in the far field. The results of masking the transducers with 3 mm wide slots are shown in the lower part of Figure 2.14. The signal arcs from the upper surfaces of the holes are now single and, for the left hand hole, the signal from the lower surface is now clearly defined.

The conclusion is that, for sizing defects at short range, masking the transducer faces will bring improved sizing accuracy, equivalent to the use of smaller diameter transducers. We can go further and state as a general principle that, for best accuracy, the smallest diameter transducers that will provide adequate signal strength should be used.