To validate the temperature compensated thickness extraction method, a pitch-catch measurement was performed. Two shear horizontal electromagnetic acoustic transducers
59 (EMATs) were placed at a fixed separation distance (0.367m) on a 10mm thick aluminium plate, in a configuration so that edge reflections were minimised (Figure 3.9). A 5 cycle Hann-windowed toneburst at a centre frequency of 200kHz1 was propagated between the
transducers, this excited both the SH0 (non-dispersive) and SH1 (dispersive) modes. The SH0 and SH1 modes had a wavelength of approximately 16mm and 27mm respectively.
Figure 3.9. a) Schematic of the experimental setup, b) configuration of Tx and Rx EMAT transducers on an aluminiu plate to reduce edge reflections
The toneburst was generated using a HandyScope HS3 Function generator/ADC (TiePie Engineering, Sneek, NL) connected to a laptop running MATLAB. The toneburst was input into a Yamaha AS500 Power Amplifier (Yamaha, Iwata, JP), which in turn drove the transmitting (Tx) EMAT. The guided wave packet excited by the Tx EMAT propagated to the receiving (Rx) EMAT. EMATs were custom built by the Imperial NDE group for the excitation of SH0 and SH1 at 200-300kHz. The signal detected by the Rx EMAT was amplified and fed into the HandyScope, which passed the resulting time trace on to the MATLAB code for post processing. The input signal was also collected, by the HandyScope, using a current sensor which consisted of a coil of wire through which the power amplified Tx EMAT signal passed. Multiple time traces of both the input (Tx) and output signals (Rx) were collected per measurement and averaged.
3.4.1 EMAT Construction, SH Signal and Beam Shape
EMATs (Electromagnetic Acoustic Transducers) are non-contact transducers which are able to generate and receive ultrasonic guided waves in electrically conductive media. EMATs generate ultrasonic waves via one of two methods: Lorentz forces or magnetostriction [84].
1 The centre frequency value was nearing the frequency response limit of the power amplifier, Yamaha AS500 Power Amplifier (Yamaha, Iwata, JP). The finite element simulations used a 250kHz, centre frequency thereby moving further away from the SH1 cut-off.
60 This project used PPM (permanent periodic magnet) EMATs which exploit the Lorentz force to excite the required guided wave modes in the plate.
Figure 3.10. PPM EMAT schematic from above showing the direction of the Lorentz force created and SH wave propagation direction
The Lorentz force is produced by inducing an eddy current J in the conductive material by using an alternating current flowing through a coil. When a static magnetic field, B, interacts with the eddy current the Lorentz volume force arises, F, whose magnitude and direction is governed by [85]:
𝑭 = 𝑱 × 𝑩 (3.4)
Figure 3.10 shows a schematic of the EMAT used for generating the SH modes in the experiments. It consists of a static magnetic field placed in the centre of a racetrack coil, with the static magnetic field perpendicular to the current in the wires. In this setup, the Lorentz force excites the SH0 and SH1 modes and the transducer creates a collimated beam propagating from either end of the EMAT. Figure 3.11 shows the simulated beam profile over a distance of 0.5m, which was constructed using a Huygen's model of wave propagation with a 50mm array of point sources (with 5 sources per SH1 wavelength, i.e. every 2mm). Figure 3.12 is an example of a time trace experimentally produced by the EMAT showing the windowed SH0 and SH1 signals.
61
Figure 3.11. Amplitude distribution (dB, relative to max) of the wavepacket emitted by a 50mm wide SH source when excited at 200 kHz with a 5 cycle Hann windowed toneburst with a shear velocity of 3260 m/s.
The width of the transducer is 50mm and all SH wave simulations and experiments were carried out for a 50mm wide transducer unless otherwise stated. Ideally the transducer's beam would have a constant width with as little spreading as possible, however, that would require a large aperture (i.e. large EMAT width) which increases size of the near field region and the beam width. A trade-off is therefore required between size of the near field, width of the beam and beam spread.
Figure 3.12. Experimental time trace produced by a single measurement with the SH transducer, showing the gated SH0 (red) and SH1 (green) modes. This was produced using a 200kHz 5 cycle Hann toneburst over a propagation distance of 500mm in a 10mm thick plate
3.4.2 Temperature Compensation Results
The experimental setup described above was placed in an environmental testing chamber (Vötsch VT3/VC3 - Temperature and Climate Test Chamber. Vötsch, Lindenstruth, DE). The chamber was heated to the required temperature and kept at that temperature for at least 30 minutes to ensure that the plate was in thermal equilibrium with the chamber. The environmental chamber was then switched off to improve the sensitivity of the measuring equipment whilst the thickness measurement was performed. Two hundred measurements were taken in quick succession (within 2 minutes), and averaged. Measurements were taken
62 at approximately 10°C intervals between 30°C-90°C, plus a measurement at room temperature (26°C).
Figure 3.13. The effect of temperature on a) the extracted thickness (blue) and the extracted thickness without temperature compensation is shown in green (cs= 3140m/s), b) the measured shear velocity (red) using the group velocity thickness extraction methods with SH waves in an aluminum plate. Error bars are 95% range in the extracted thickness values.
Figure 3.13b shows that as the temperature of the plate increased, the shear velocity of the metal decreased, as expected [41]. When the thickness extraction algorithm was applied, the expected thickness was approximately constant over the entire temperature range. In fact the extracted thickness (with temperature compensation) has significantly deviated away from the extracted thickness without temperature compensation (calculated by fixing the shear velocity value at 3140m/s). The mean error in the individual temperature compensated thickness measurements was found to be 0.04mm (95% range). The finite window width of the thickness algorithm means that the absolute value of extracted thickness is not exactly 10mm.