## 5 Results and Discussion
### Aluminum Alloys
#### 5.2.1 Al-1100-H18
In this case, the slow S\({}_{0}\) segment around the velocity minimum at 390 kHz was included in the attenuation plot. The A\({}_{\rm o}\) mode contribution was negligible with the two-side summation processing. The observed \(\alpha\)-S data matched well with the calculated \(\alpha\)-S\({}_{0}\) curve, indicating that \(\alpha\)-S\({}_{0}\) was measured. The maximum deviation was 4.7 dB/m, or 79%, of the calculated value at 286 kHz. Figure 6: (a) \(\alpha\)–S\({}_{\rm o}\) values for Al-1100 sheet of 2.1-mm thickness in blue symbols. \(\alpha\)–S\({}_{\rm o}\) values plotted in dots used PAC Pico as Tx and + symbols KRN-BB-PCP as Tx. Both Tx’s were attached on the end face. KRN-BB-PC was Rx for both. Calculated values of \(\alpha\)–S\({}_{\rm o}\) are plotted in a solid blue curve. \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\): Blue and red dash lines. Vertical bar shows 2 \(\times\) dev. (b) Four sets of \(\alpha\)–A\({}_{\rm o}\) values for Al-1100 sheet of 2.1-mm thickness are plotted in red symbols. Data with + symbols used NDT C16 Tx at 60\({}^{\circ}\) incident angle, dot, diamond and triangle symbols used surface-mounted KRN-BB-PCP Tx, located near edge, which allowed firm clamping and two-surface detection approach. The dot data used 200-kHz sinewave pulse, while the rest used short-pulse excitation. KRN-BB-PC was Rx for all four. Calculated \(\alpha\)–A\({}_{\rm o}\) (solid red curve), \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\) (blue and red dashed lines) are plotted as in Figure 5b. Vertical bar shows 2 \(\times\) dev. Figure 7b gives \(\alpha\)-A values and calculated values of \(\alpha\)-A\({}_{\rm o}\) in a solid red curve plus the dashed blue and red lines for \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\). The velocity range of these datasets was from 3.3 to 1.8 mm/us, excluding the faster S\({}_{\rm o}\) mode. Differences of the two-sided signals were used to minimize the symmetric components. The \(\alpha\)-A attenuation data followed the calculated \(\alpha\)-A\({}_{\rm o}\) (red curve), which almost overlaps the red-dashed \(\alpha_{\rm T}\) line. The observed attenuation values ranged from 130 to 500 kHz. These deviated from the predicted values by as much as 2.61 dB/m, or 24%, of the calculated value at 381 kHz. In order to evaluate the accuracy of attenuation values obtained, deviation and percent deviation were calculated. For this Al plate, the predicted \(\alpha\)-S values were fitted sectionally to third and fourth order polynomials in frequency, and \(\alpha\)-A 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 (\%) & Data Count \\ \hline Symmetric case: & 2.29 & 21.6 & 42 \\ \hline Asymmetric case: & 1.01 & 11.5 & 27 \\ \hline \end{tabular}   
Figure 7: (a) \(\alpha\)–S\({}_{\rm o}\) values for Al 1100 plate of 6.4-mm thickness plotted in blue squares used Olympus V101 as Tx and KRN-BB-PC as Rx. Calculated \(\alpha\)–S\({}_{\rm o}\) (solid blue curve), \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\) (blue and red dashed lines) are also plotted. Vertical bar shows 2 \(\times\) dev. (b) \(\alpha\)–A\({}_{\rm o}\) values for Al 1100 sheet of 6.4-mm thickness plotted in red dot symbols, using short-pulse excited NDT C16 Tx at 60\({}^{\circ}\) incident angle and KRN-BB-PC Rx. Calculated \(\alpha\)–A\({}_{\rm o}\) (solid red curve), \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\) (blue and red dashed lines) are also plotted. Vertical bar shows 2 \(\times\) dev. Obtained deviation values are similar to the results of the thinner Al, but larger values were found for the symmetric case. For the 6.4-mm Al-1100 plate, Lamb-wave attenuation is also found to match the theoretical prediction. Agreement was comparable to the case of the 2-mm Al sheet given above.