# Dynamic Viscosity and Transverse Ultrasonic Attenuation of Engineering Materials
## 3 Results and Discussion
### Attenuation Behavior of Iron and Ferrous Alloys
This distribution differed from an expectation of much higher \(\mathrm{C_{dt}}\) over the entire tests. This expectation came from the previous transverse attenuation results of metals and polymers, reviewed in [13], and Q values of rocks and the Earth [1,6]. The ratio of damping factors, \(\mathrm{\eta_{t}/\eta_{t}}\), was smaller than \(\mathrm{C_{dt}/C_{d}}\) ratios, with their average equaling 0.65 and only 20% exceeded unity ratio. The observed similarities of \(\mathrm{\eta}\) and \(\mathrm{\eta_{t}}\) values for a given sample are consistent with the dislocation bow-out mechanism of damping, proposed in [13]. Structural steels from 1020 to 1 Cr-1 Mo-V turbine rotor steels in Table 2 showed low transverse attenuation with \(\mathrm{C_{dt}}\) values below 20 dB/m/MHz except for two cases. These were modestly higher than the corresponding \(\mathrm{C_{d}}\) values. \(\mathrm{C_{dt}}\) values for high alloy steels were higher, but most of them were less than 50 dB/m/MHz. Of these, A286 steel showed exceptionally high \(\mathrm{C_{d}}\) and \(\mathrm{C_{dt}}\) values of 72 and 142 dB/m/MHz (note that previous results for A286 steels had to be moved to the Ni-base alloy category due to mislabeling. This A286 sample is a new addition.) The 300-series austenitic stainless steels exhibited slightly higher attenuation than low alloy steels, but cold working reduced transverse attenuation to low levels as was the case for longitudinal attenuation (see Tests F84, F85, F90). These three cold-worked stainless steels showed no damping term (\(\mathrm{C_{dt}}=0\)) and the transverse attenuation, \(\mathrm{\alpha_{t}}\), followed a 4 th-power frequency dependence, indicating Rayleigh scattering. Another cold-worked 302 stainless steel (Test F83) with lower hardness showed the usual Mason-McSkimin relation, but also with low \(\mathrm{C_{dt}}\) value of 1.4 dB/m/MHz. The Mason-McSkimin relation that includes the 4 th-power frequency dependent term was found in more cases for transverse attenuation. The coefficient, \(\mathrm{C_{RT}}\), was always higher than the corresponding \(\mathrm{C_{R}}\) term of the same sample. The increase was 9-fold in 304L stainless steel (Test F89), and 7.5-fold in 1020 steel (Test F11), while \(\mathrm{C_{RT}}\) appeared in some steels for which \(\mathrm{C_{R}}\) was absent (HSLA, A533B, 1 Cr-1 Mo-V steels, and 321 stainless steel, Tests F58, F66, F68, F91). Figure 3 shows a comparison of the longitudinal and transverse attenuation spectra of 1020 steel (Test F11). The initial slopes differed only 50%, but the two curves diverged with increasing frequency. Three samples showed especially high scattering effects. These were A286 and 304 stainless steels in the thickness direction and a low-C steel (Tests F99a, F89, F12). Both stainless samples had large \(\mathrm{C_{R}}\) values also. The low-C steel sample (Test F12) showed a frequency-squared dependence previously, which now appears to come from scattering as in the case of transverse attenuation. Observed results in steels indicate that the scattering effects of transverse waves are stronger from grain boundaries, second phases, and non-metallic inclusions. Figure 3: Attenuation coefficients vs. frequency. Transverse attenuation spectrum of 1020 steel is plotted in blue curve with the Mason-McSkimin fitted dashed curve. Corresponding longitudinal attenuation spectrum from [13] is shown in red, also with the Mason-McSkimin fitted dashed curve. The transverse attenuation spectra of six austenitic stainless steels are compared in Figure 4. These include Type 301 (blue curve), 302 (red), 304 (purple), 304L (dark red), 316 (dark blue), and 321 (green). Of these steels, 301 had nearly linear spectrum with the lowest scattering, while 304L showed the strongest Rayleigh scattering. Type 316 (in cold-worked condition) only had the scattering term. In all cases, the transverse attenuation was moderate below 5 MHz.