## 4 Results and Discussion
### Attenuation Behavior of Ferrous Alloys
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Test** & **Material \({}^{\star}\)** & \(\rm C_{d}\) & \(\rm C_{R}\) & \(\alpha\) at 5 MHz & **Velocity** & **Thickness** & **Vickers HN** & **Notes** \\ \hline F70 & Tool steel W1 & \(<\)2 & & – & 5.89 & 52.1 & 293 & \\ F71 & Tool steel M2 (T) & 68.9 & & 344.5 & 5.78 & 12.7 & 785 & \\ F72 & Tool steel T8 (T) & 56.7 & & 283.5 & 5.75 & 12.7 & 850 & \\ F73 & Hardness block1 & 25.3 & & 126.5 & 5.92 & 14.8 & 460 & \\ F74 & Hardness block2 & 27.0 & \(1.69\times 10^{-2}\) & 145.6 & 5.92 & 14.8 & 666 & \\ F75 & Hardness block3 & 25.7 & & 128.5 & 5.92 & 14.8 & 434 & \\ F76 & Hardness block4 & 28.4 & & 142.0 & 5.92 & 14.8 & 695 & \\ F77 & Hardness block5 & 37.2 & & 186.0 & 5.92 & 14.8 & 659 & \\ F78 & 301 & 6.7 & & 33.5 & 5.92 & 25.4 & 214 & Magnetic \\ F79 & 301 & 5.9 & \(3.05\times 10^{-3}\) & 31.5 & 5.92 & 101.5 & 214 & Magnetic \\ F80 & 301 & 5.6 & \(3.34\times 10^{-3}\) & 30.2 & 5.92 & 25.4/101.5 & 214 & Magnetic, TDM-1 \\ F81 & 301 & 5.0 & \(3.28\times 10^{-3}\) & 27.7 & 5.92 & 25.4/76.2 & 214 & Magnetic, TDM-1 \\ F82 & 302 & 18.6 & & 93.0 & 5.87 & 43.7 & 251 & \\ F83 & 302 (T) & 33.2 & \(1.99\times 10^{-2}\) & 178.4 & 5.75 & 60.2 & 213 & \\ F84 & 302 & 4.0 & \(1.00\times 10^{-3}\) & 20.8 & 5.73 & 77.4 & 339 & Magnetic \\ F85 & 304 & 1.5 & \(1.10\times 10^{-3}\) & 8.1 & 5.72 & 479.0 & 321 & Magnetic \\ F86 & 304 & 21.2 & \(7.78\times 10^{-3}\) & 110.9 & 5.75 & 77.0 & 193 & \\ F87 & 304 (T) & 22.0 & \(9.98\times 10^{-3}\) & 116.2 & 5.72 & 50.1 & 193 & Same as F86 \\ F88 & 304 (S) & 38.2 & \(8.92\times 10^{-3}\) & 196.6 & 5.83 & 19.0 & 193 & Same as F86 \\ F89 & 304L (S) & 23.4 & \(1.36\times 10^{-2}\) & 125.5 & 5.65 & 25.6 & 199 & \\ F90 & 316 & 11.9 & \(2.33\times 10^{-3}\) & 61.0 & 5.69 & 26.8 & 368 & \\ F91 & 321 & 61.8 & & 309.0 & 5.78 & 34.0 & 196 & \\ F92 & 321 (S) & 49.3 & & 246.5 & 5.67 & 25.3 & 295 & \\ F93 & 321 (S) & 39.7 & & 198.5 & 5.65 & 25.2 & 145 & \\ F94 & 430 & 9.9 & & 49.4 & 5.81 & 24.3 & 312 & \\ F95 & 440A (S) & 39.5 & & 197.5 & 5.85 & 19.0 & 541 & \\ F96 & A286 (S) & 170.9 & & 854.5 & 6.29 & 11.2 & 146 & Solution-treated \\ F97 & A286 & 18.5 & \(1.57\times 10^{-1}\) & 190.8 & 5.72 & 101.5 & 319 & Aged \\ F98 & A286 (T) & 41.6 & \(1.25\times 10^{-1}\) & 285.9 & 5.73 & 46.4 & 319 & Same as F97 \\ F99 & A286 (S) & 98.7 & \(7.88\times 10^{-2}\) & 542.8 & 5.62 & 15.2 & 319 & Same as F97 \\ F100 & 17-4 PH & 9.0 & \(4.19\times 10^{-3}\) & 47.6 & 6.10 & 238.3 & 360 & Solution-treated \\ F101 & 17-4 PH & 34.7 & & 173.5 & 5.84 & 25.4 & 412 & Aged at 480 \({}^{\circ}\)C, 2 h \\ \hline \multicolumn{8}{c}{\({}^{\star}\) L direction when no direction is given. \(\rm C_{d}\), damping coefficient; \(\rm C_{R}\), Rayleigh scattering coefficient; \(\alpha\), attenuation coefficient; WQ, water quenched; OQ, oil quenched; ESR, electro-slag remelted; HSLA, high strength low alloy; HN, hardness number.} \\ \end{tabular}
\end{table} 
Table 2: _Cont._The attenuation data from [PERSON] et al. [17,73] is also plotted in this figure in green circles, with the fitted expression given as  
\[\alpha\left(\text{dB/m}\right)=16.0\text{ f}+0.03\text{ f}^{4}. \tag{18b}\]  
These data are for a medium-C steel (C = 0.38%) with a ferritic-pearlitic microstructure. The ferrite grain size was 56 to 60 \(\upmu\)m and pearlite content was 27%. This data further reinforces the viability of the Mason-McSkimin relation, which combines damping and Rayleigh scattering [8]. The next examples are shown in Figure 11b. The material is A286 austenitic stainless steel (UNS S66286), which can be precipitation-hardened. Both solution-treated and hardened conditions were tested. This steel showed the highest and second highest attenuation among the ferrous group. The solution-treated A286 showed linear dependence (blue curve), while hardened A286 showed combined linear and f\({}^{4}\) dependence (red curve).