## 5 Results and Discussion
### Aluminum Alloys
#### 5.2.3 Al-7475-H18  
A fully cold-worked Al-7475 alloy sheet was tested for Lamb-wave attenuation. This alloy was derived from Al 7075 by reducing Si and Fe impurities, which gives 40% higher fracture toughness. Cold-working is rarely used for structural Al alloys, but was utilized for superplasticity studies. Because of this special circumstance, no comparable material with adequate thickness for bulk-wave attenuation tests was available, even in the Al-7075 alloy. For comparison, \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\) values of the 7075-T6 plate were used (cf. Table 1). Figure 10a,b show \(\alpha\)-S and \(\alpha\)-A for the 2.7-mm thick sheet from two-sided tests in blue and red symbols, respectively. In Figure 10a, a set of \(\alpha\)-S values are plotted in dot symbols from 250 to 500 kHz, and calculated values of \(\alpha\)-S\({}_{\rm o}\) are plotted in a solid blue curve; also shown are dashed lines for \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\). The velocity range of the dataset was from 5.6 to 3.0 mm/us. In this case, the slow S\({}_{\rm o}\) segment around the velocity minimum at 870 kHz was well beyond the attenuation test range, limited to 500 kHz. This limit was mainly imposed by the arrival of reflected signals at longer propagation distances due to the sheet size. The A\({}_{\rm o}\)-mode contribution was cut off in the WT analysis procedures. The observed \(\alpha\)-S\({}_{\rm o}\) data matched moderately with the calculated \(\alpha\)-S\({}_{\rm o}\) curve. The maximum deviation was 1.4 dB/m (41% of the calculated value) at 458 kHz. Figure 10b gives \(\alpha\)-A\({}_{\rm o}\) values and calculated values of \(\alpha\)-A\({}_{\rm o}\) in a solid red curve plus the blue and red dashed lines for \(\alpha_{\rm L}\) and \(\alpha_{\rm T}\). The velocity range of these datasets was from 3.0 to 2.2 mm/us, excluding the S\({}_{\rm o}\) mode. The observed \(\alpha\)-A\({}_{\rm o}\) values were two to three times larger than the calculated ones. Lines for 2 \(\alpha_{\rm T}\) and 3 \(\alpha_{\rm T}\) (drawn in red dots and dash-dots) encompassed 10 out of 12 data points between them. This difference is apparently due to a lower \(\alpha_{\rm T}\) value used in  
Figure 9: (**a**) Received signal and its WT spectrogram of \(\alpha\)–S\({}_{\rm o}\) test for Al-6061 plate of 12.7-mm thickness with 100-kHz excitation at 400 mm from the source. Transform start time was shifted by 75 \(\mu\)s. Red and blue represent high and low WT intensities. Dispersion curves for S\({}_{\rm o}\), A\({}_{\rm o}\) and A\({}_{\rm 1}\) modes are also plotted. (**b**) Received signal and its WT spectrogram of \(\alpha\)–S\({}_{\rm o}\) test for Al-6061 plate of 12.7-mm thickness with 200-kHz excitation at 400 mm from the source. Transform start time was shifted by 185 \(\mu\)s. Red and blue represent high and low WT intensities. Dispersion curves for S\({}_{\rm o}\) and A\({}_{\rm 1}\) modes are also plotted. the calculation. When \(\alpha_{\rm T}\) is taken to be 2.5 times, or 30.6 dB/m/MHz, agreement between observed and calculated becomes fair, giving a correct trend. This level of \(\alpha_{\rm T}\) value is similar to that of cold-worked Al-1100-H18. However, Al-1100 is three times softer in terms of Vickers hardness due to large alloying additions to Al-7475. Additionally, an increased \(\alpha_{\rm T}\) also increases \(\alpha\)-S\({}_{\rm 0}\) prediction. Further testing is needed to clarify the cause of the \(\alpha\)-A\({}_{\rm o}\) discrepancy. Lamb-wave attenuation tests on Al-7475 showed that the observed \(\alpha\)-S\({}_{\rm o}\) and \(\alpha\)-A\({}_{\rm o}\) values are in the same ranges as the calculated values. Because of large differences in \(\alpha\)-A\({}_{\rm o}\) values, however, improved testing is required before these tests on Al-7475 can be used for the verification of theory. Underestimate of \(\alpha_{\rm T}\) is another likely cause. Enlargement of sheet width is one of the steps for refinement.