## 4 Results and Discussion
### Attenuation Behavior of Non-Ferrous Alloys
The quadratic behavior was also observed in 60-40 brass (tests N46,N47; UNS C28000). These 60-40 brass samples were heavily cold-worked, showing twice the Vickers hardness of annealed alloy. In the present study, it is shown that quadratic attenuation spectra were found in cold-worked plates of steel, Cu, and brass, suggestive of a common dislocation damping mechanism from the KGL formulation [33; 34; 35; 36; 37]. These Cu and brass plates also exhibited anisotropic directional effects similar to those of ferrous plates. The directional anisotropy was also found in two plates of Al 7075 (tests N19-N24; UNS A97075) and in Inconel 625 (tests N77,N78; UNS N06625). In all cases, the S direction had higher attenuation. Flattened grain microstructures in Al 7075 are known to cause exfoliation corrosion damages [86] and act as large effective grain sizes in the S direction. Similar microstructures were not documented in Cu and brass, but are plausible as the processing methods are similar. These flattened microstructures lead to higher attenuation. Attenuation behavior due to anisotropic distribution of inclusions was studied by [PERSON] et al. [28; 29; 30], as noted earlier. Aluminum alloy samples showed low attenuation of less than 10 dB/m at 1 MHz in 19 of 24 tests. These low \(\alpha\) values were always for hardened conditions of T3 and T6 temper. Two higher \(\alpha\) values were found in annealed 6061 alloy (UNS A60610), while 6061-T6 showed lower \(\alpha\) values by a factor of 3 to 5. One 2024-T6 sample (test N8) was annealed (at 370 \({}^{\circ}\)C, 1 h), after which the \(\alpha\) value more than doubled (test N13). While the sample count is small, it appears that annealed Al alloys have higher \(\alpha\) values in comparison to the hardened conditions. This hardening originated from precipitation, but the attenuation behavior is common with the type-n CW effect discussed in the previous section. The effects of annealing were evaluated using two sets of cold-worked brass 360 samples (UNS C36000, tests N48-N55). In the hardened conditions, \(\alpha\) values were high (e.g., tests N48 and N53 (Vickers values of 149 and 124) had \(\alpha\) values of 43.8 and 61.6 dB/m, respectively, at 1 MHz). With annealing, both \(\alpha\) values and hardness decreased, as plotted in Figure 13 (in purple triangles), exhibiting the type-p CW effect. This finding seems to imply that higher dislocation densities in cold-worked conditions contribute to more damping, increasing the \(\alpha\) values. As seen in Table 3, C\({}_{\mathrm{R}}\) terms are zero, except in one case (test N49), indicating Rayleigh scattering has no influence on cold-working effects in brass. Some samples of Cu, Ni, and a beta-Ti alloy (Beta-III, UNS R58030) also received cold working and showed increased hardness values with low \(\alpha\) values (type-n behavior). Two Cu samples were annealed to reduce hardness, allowing direct comparison between the two states. Higher \(\alpha\) values resulted, again showing the type-n CW effect. For three cold-worked Ni 200 samples (UNS N02200) plus one Ni 211 sample (UNS N02211), a clear trend was visible of low \(\alpha\) values with high hardness. In beta-III Ti (UNS R58030), 10% cold working increased the hardness and reduced \(\alpha\) values by nearly a factor of four (test N91). In contrast with the brass tests given above, these were not as systematic, yet a clear trend emerged. Table 4 summarizes the available data, albeit with limited data counts. This observed trend was opposite to the annealing effects found in brass, where \(\alpha\) values decreased with decreased hardness of the test samples. The type-n behavior is more difficult to rationalize in terms of the dislocation damping, since it is difficult to rationalize the fact that more dislocations cause less damping. At this stage, no plausible mechanisms exist and new explanations or mechanisms must be found for both types of cold work effects. The last group of six tests examined the attenuation behavior of three metal matrix composites (MMCs).