Diffraction around 90° cracks

Figure 6.1 shows maps of the out-of-plane displacement in a chosen area of two samples,

at different times t during propagation of the wave. Each sample contains a 90° crack

located at the centre of the sample transverse to the incident wave, at 130 mm on the scan distance as indicated in the figure. The cracks have different widths; 10 mm and 20 mm. The maps of the displacements at different times for each crack are shown in two columns. The left column shows the maps for the 10 mm wide crack and the right column shows the maps for the 20 mm wide crack. Descending down the column, the

time increases from t1 shortly after generation of the wave to t5, after the wave has

interacted with the crack. At t1and t2, the Rayleigh wave approaches the crack from

the left end of the maps. At t3, the Rayleigh wave has reached the crack. At t4, the

Rayleigh wave is about to pass the crack, and diffraction can be observed. Finally, the

Rayleigh wave has fully passed the crack at t5.

The laser receiver measurements give an images of resolution 1 mm by 1 mm. The distance across the width of the aluminium bar is shown by the y-axes, where the origins (0 mm) indicate the position of the centre of the bar, and the distance is given as the offset from the centre. The x-axes show the scan distance of the laser receiver relative to the centre of the coil in the EMAT transmitter. Thus, the position of the crack is at 130 mm on the scan distance axes (x-axes), and this is inidcated in Figure 6.1 at time

t=t1 as a black line.

The Rayleigh wave approaches the cracks with a wavefront that is approximately a

line near the centre, but curved at the edges, shown in Figure 6.1 at times t1 and t2.

The shape of the wavefront is determined by two factors here; firstly, the size of the coil in the EMAT transmitter, and secondly the directionality of the ultrasound wave generated. The EMAT transmitter consists of a 35 mm wide coil, covering the area from -17.5 mm to 17.5 mm on the maps. Within this region, the wavefront can be seen in the figure as approximately a line. Meanwhile, outside this region, the wavefront starts to curve slightly due to the small spread in the ultrasound wave generated. The spreading of the generated wave has been discussed in Section 3.1, and limited when using this EMAT designs.

Figure 6.1: Diffraction on 5 mm deep, 90° cracks of 10 mm width (left) and 20 mm width (right).

The reflection of the Rayleigh wave from the left end of the bar (shown in Fig-

ure 3.12) starts to appear in this window at time t2, as indicated in Figure 6.1, and it

becomes more prominent at timet3. Att4, the reflection from the crack can be observed

clearly to appear in front of the crack. This is in addition to the earlier reflection from the left end of the bar.

The interaction of the Rayleigh wave with the crack, leading to signal enhancement,

starts to take place at time t3. It can be seen that, for both cracks, the magnitude

of the Rayleigh wave as indicated by the colour scale increases in front of the crack (before scan distance =130 mm). The wider crack 20 mm, shows a greater area with the increased magnitude shown by the colour scale, compared to the 10 mm wide crack. The diffraction of the Rayleigh wave at both cracks of different widths is shown at

time t = t4. It is very clear that the diffraction is different for 10 mm and 20 mm

wide cracks. The diffraction caused by the 10 mm wide crack shows that the crack is still detectable although its size is smaller than the width of the EMAT coil. At time

t =t4, the incoming Rayleigh wave reached the cracks, and diffracted at both ends of

the cracks edges. The smaller crack, 10 mm wide, diffracts the incoming wave causing it to bend around the edges. In the meantime, some of the Rayleigh wave is transmitted underneath the crack. Since the path length for the this transmission is longer than for the wave diffracted around the crack edges on the surface, the arrival time of the transmitted wave will be slightly later. Similar diffraction and transmission occurs to the Rayleigh interacting with the 20 mm wide crack, except in this case the shadow behind the crack is larger, according to the crack width.

At timet =t5, Rayleigh wave has propagated far enough from the cracks to be con-

sidered in the far-field. The transmitted portion of the Rayleigh wave that propagated underneath the crack has fully recovered from the interaction. The wavefront of the Rayleigh wave can be seen to regain an approximate to their original shape, but with a smaller displacement magnitude at the centre, where the crack has blocked some of the Rayleigh wave from passing through.