Vol.20 No.

1 (Jan 2015) - The e-Journal of Nondestructive Testing - ISSN 1435-4934

www.ndt.net/?id=16996

Photoelastic Visualisation _ Phased Array Sound Fields

Part 18 – 45° shear plane wave from refracting wedge

Ed GINZEL 1
1
Materials Research Institute, Waterloo, Ontario, Canada
e-mail: eginzel@mri.on.ca

Keywords: Photoelastic visualisation, ultrasonic, phased array

The video to this article can be seen here: www.ndt.net/search/docs.php3?id=16996&content=1

1. Introduction
This technical note is Part 18 of a series in NDT.net.

Most weld inspection by PAUT is carried out using the angled transverse mode. In order to
avoid the initial compression mode entering the test piece, refracting wedges are used.

The associated video in this article uses the same probe and equipment as used in Part 17 with
the addition of a refracting wedge mounted to the probe. It is made of cross-linked
polystyrene (trade name Rexolite) with a machined incident angle of 36.5°. The intent of the
incident angle at 36.5° is to produce a refracted angle of about 55° in most common steels.
This refracted angle also provides a useful median value for the phased array probe to be able
to generate a range of angles ± 15° from that median value.

It will be noted that there are no markings on the sides of the wedge apart from the irrigation
grooves with 10mm spacing along the bottom of the wedge. In 2003 RD/Tech provided the
author with the refracting wedge used in the video. At that time the intent was to use this
wedge with the photoelastic system to examine the incident and reflected paths in the wedge.
This required annealing of the wedge after fabrication. Plastics are prone to retaining residual
stresses from the casting and machining processes. These residual stresses can be so
pronounced that the cross polarised light required in the photoelastic method is unable to
achieve a uniform null. In order to allow the pulse be seen in the wedge, it was annealed to
reduce the residual stresses. Although there are still small bands of stress seen in the wedge,
the pulse can now be seen as it approaches the wedge/glass interface.

Cross-linked polystyrene has a compression mode velocity of about 2400m/s and a density of
approximately 1.04 g/cm3. This makes a good acoustic impedance match to the soda-lime
glass block specimen (compression mode velocity 5840m/s, transverse velocity 3450m/s,
density 2.5g/cm3).

It is the intent of the video to demonstrate how the incident pulse formed in the wedge
advances to form a 45° refracted transverse mode in the glass. The active aperture in the
demonstrations uses 16 elements starting at element #2.

Figure 1 illustrates the configuration used.

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Figure 1 16 element aperture 45° transverse mode using refracting wedge

2. Comments on the Video

Since the wedge is made with a 36.5° angle, Snell’s Law allows us to calculate that the beam
emitted from the probe must be 7.7° less than the natural incident angle (i.e. 28.8° incident
angle) in order for the refracted beam to be 45° in the glass. These angles are illustrated in
Figure 2.

Figure 2 Wedge angle and incident angles required for 45° beam in glass

The video begins with the pulse seen in the wedge approximately 6mm before entering the
glass at the midpoint of the pulse. An image of the 28.8° incident angle is overlaid during the
video with a line parallel to the wavefront. The pulse location is indicated in Figure 3.

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 Pulse

Figure 3 Pulse location in wedge

As seen in previous videos in this series, the ends of a plane wave pulse are characterised by
pronounced diffraction arcs. Due to the high attenuation of the cross-link polystyrene, the arc
shapes at the ends of the pulse are difficult to see in the wedge. However, as the pulse enters
the glass, the lower arc can be seen to contribute to a compression mode in the glass. This is
due to it having components with incidence at angles less than the first critical angle.

The faint compression mode arc is indicated in Figure 4.

Compression
mode arc

Figure 4 Compression mode arc in glass

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As the pulse advances and the transverse mode clearly established in the glass, a reflected
component can be seen in the wedge. The bulk transverse mode and reflected compression
mode are indicated in Figure 5.

Reflected
Compression

Refracted
Transverse

Figure 5 Reflected compression and refracted transverse modes

To indicate that the 45° angle computed is actually being generated in the glass, another
images is overlaid indicating the 45° refracted angle with a line parallel to the wavefront.
This is illustrated in Figure 6.

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Figure 6 Confirmation of refracted transverse angle

Computation of the delays required to generate a simple plane wavefront were introduced in
Part 16 of this series where a direct contact probe was used to form a 30° compression mode.

The same approach can be used with the wedge. Snell’s law was used above to calculate that
the incident beam in the wedge had to make a 28.8° angle from the normal in order to make
the 45° angle in glass. Since there was already a natural 36.5° incident angle machined on the
wedge, this required the beam be steered -7.7°. In the demonstration, elements 2-17 are used
and a negative steering is achieved when the furthest element (#17) is fired first.

Using 16 elements with 0.6mm pitch results in 9mm from the centre of element 2 to the centre
of element 17. This distance represents the hypotenuse of the triangle. The distance that the
first wavelet arc must travel is the distance that would make the line back to the last firing
element 7.7°. The distance required is 1.2mm (i.e. sin 7.7° x 9mm). These dimensions are
indicated in Figure 7.

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Figure 7 Calculating delays for a 7.7° beam with a 16 element aperture

Dividing the 1.2mm distance by the acoustic velocity in the wedge (2.4mm/µs) indicates the
first arc must advance 0.502µs at 2.4mm/µs. With 15 steps along the array from the first to
last fired element this indicates that there will be approximately 33.5ns time difference
between the firing of each adjacent element.

The tabulated values from the software used indicate the following delays starting at time zero
for element #17 which is the first element fired.

Element 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2
Delay 0 34 67 101 134 168 201 235 268 302 335 369 402 436 469 502
(ns)

For more information about the photoelastic system see www.eclipsescientific.com.

The video to this article can be seen here: www.ndt.net/search/docs.php3?id=16996&content=1

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