## 5 Results and Discussion
### Aluminum Alloys
#### 5.2.2 Al-6061-T6  
A large 12.7-mm thick plate (G3a) of 1.22 \(\times\) 1.2 m was used for this part. Because of the increased thickness, the frequency range of the low-dispersion S\({}_{0}\) mode is limited to about 100 kHz, and its attenuation level was low, as this alloy has low bulk-wave attenuation (see Table 1). The calculated \(\alpha\)-S\({}_{0}\) curve is plotted in Figure 8a, indicating \(\alpha\)-S\({}_{0}\) values of less than 1 dB/m below 140 kHz and reaching only 3.8 dB/m at the 200-300 kHz segment, where the S\({}_{0}\) velocity is near the minimum. Lamb-wave intensity near the velocity minimum is often low, preventing \(\alpha\)-S\({}_{0}\) measurements. For these reasons, short-pulse excitation methods used in all other tests failed to produce a consistent S\({}_{0}\)-mode attenuation dataset. In order to enhance Lamb-wave intensity at lower frequencies, sinewave pulses (or tone bursts) of 100 or 200 kHz center frequency and 40 \(\upmu\)s duration (with 12 \(\upmu\)s rise time to the maximum, followed by 0.8 dB/\(\upmu\)s decay) were generated using an acoustic emission simulator (AES-1, AE Associates, Laguna Beach, CA, USA). The output was set at \(\pm\)10 V, which was fed to an AET FC500 transducer mounted to the plate edge. This set-up was similar to the other tests as described in Section 3. Because of the size and weight of the plate, only one-side detection was used. With this procedure, \(\alpha\)-S\({}_{0}\) values were determined from 90 to 280 kHz and are plotted in Figure 8a. Blue + symbols are for the data with the 100-kHz excitation, whereas blue dots used 200-kHz excitation. The observed values are two to three times the calculated \(\alpha\)-S\({}_{0}\) values to 170 kHz, but these become comparable to the calculated value at higher frequencies. The low frequency data can hardly be considered to agree to theory, but the values at 220 to 270 kHz can be treated as being matched to the prediction. In this case, the detected waveforms (taken from 100 to 600 mm distances in 100-mm steps using a point-contact KRN receiver) consisted of the S\({}_{0}\) mode only. For the 100-kHz excitation, fast S\({}_{0}\) mode (5.6 to 2.1 mm/\(\upmu\)s) was strong (see Figure 9a), whereas slow S\({}_{0}\) mode (2.5 to 1.0 mm/\(\upmu\)s) was strong using 200-kHz excitation (Figure 9b). As the limit of \(\alpha\)-S\({}_{0}\) measurements appears to be at 1 to 2 dB/m, large deviations are unavoidable. Still, the observed \(\alpha\)-S\({}_{0}\) values are in the same general range as predicted, and an increasing trend with frequency is revealed. For the \(\alpha\)-A attenuation measurements, the usual short-pulse excitation method was used using an AET FC500 transducer through a wedge as a transmitter. Again, the one-sided detection method was used, but the S\({}_{0}\) mode was weak and removed during the WT analysis procedures. Measured \(\alpha\)-A attenuation data are plotted with red dots in Figure 8b, together with the calculated \(\alpha\)-A\({}_{0}\) attenuation (red curve). Agreement between measured and calculated values is moderately good. In order to assess the accuracy of attenuation values obtained, deviation and percent deviation were calculated. For this Al plate, the predicted \(\alpha\)-S\({}_{0}\) values were fitted to third and fifth order polynomials in frequency, and \(\alpha\)-A\({}_{0}\) values were fitted to a linear equation. Averaged results are as follows: \begin{tabular}{c c c c} \hline Wave Mode & Deviation (dB/m) & Percent Deviation (\(\upmu\)s) & Data Count \\ \hline Symmetric case: & 0.81 & 66.6 & 46 \\ \hline Asymmetric case: & 0.75 & 17.7 & 34 \\ \hline \end{tabular}   
Obtained values are similar to the results of the thinner Al for the asymmetric case, but a larger percent deviation value was found for the symmetric case. This resulted from the limitation of the \(\alpha\)-S\({}_{0}\) measurements in this work because the attenuation was low. The maximum deviation of \(\alpha\)-S\({}_{0}\) reached 2.38 dB/m (and 260%) at 130 kHz.