# Dynamic Viscosity and Transverse Ultrasonic Attenuation of Engineering Materials
## 5 Summary  
1. Methods of ultrasonic attenuation measurement for the transverse waves were implemented and verified using PMMA samples. These were transmission difference methods, similar to those used previously for the longitudinal waves [13]. 2. A total of 223 transverse attenuation measurements were completed together with 50 additional longitudinal attenuation measurements. The frequency dependence of the attenuation coefficients followed four patterns, linear, Mason-McSkimin (linear + f\({}^{4}\)), linear + f\({}^{2}\) (or f\({}^{2}\)), and linear + f\({}^{3}\) (or f\({}^{3}\)). The linear spectra were found in two-thirds of the tests, followed by Mason-McSkimin relation in a quarter of the cases. In only five cases, the linear component was absent. 3. The transverse damping factors, \(\eta_{\rm t}\), converted from the linear components, ranged from 0.004 for ferrous alloys to 0.065 for FRP. Corresponding longitudinal values of \(\eta\) were from 0.007 to 0.048. These \(\eta\) and \(\eta_{\rm t}\) for non-metals are higher than those of prototypically viscoelastic PMMA (\(\eta=0.008\) and \(\eta_{\rm t}=0.013\)). Even metallic values were within a factor of three, suggesting almost all engineering materials are viscoelastic. 4. The transverse attenuation coefficients, \(C_{\rm dt}\), were 1.5-times higher than the corresponding longitudinal attenuation coefficients, \(C_{\rm d}\), in 61% of the tests, while they were comparable or lower in 23 or 17%. In polymers and FRP, \(C_{\rm dt}>2C_{\rm d}\) in most cases. Figure 12: \(C_{\rm dt}\)/\(C_{\rm d}\) values vs. [PERSON]’s ratio of tested samples, grouped into four types, ferrous, non-ferrous, polymers, and ceramics and rocks. Note that the fraction of high \(C_{\rm dt}\)/\(C_{\rm d}\) is lower than in Table 8 because power-law fits were omitted for this data set. Low-alloy structural steels mostly showed low C\({}_{\rm dt}\) values below 20 dB/m/MHz, which were moderately higher than C\({}_{\rm d}\) values. C\({}_{\rm dt}\) values for high alloy steels were higher, but most of them were below 50 dB/m/MHz. 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. 6. Gray cast iron again showed frequency-squared dependence, while ductile and malleable iron had the Mason-McSkimin relation. The transverse attenuation was approximately twice than the longitudinal mode. 7. Aluminum alloys showed low transverse attenuation, giving C\({}_{\rm dt}\) in the range of 3 to 34 dB/m/MHz with C\({}_{\rm dt}\)/C\({}_{\rm d}\) ratios varying from 1.5 to 10.5. The average C\({}_{\rm dt}\)/C\({}_{\rm d}\) was 3.75. 8. A peculiar attenuation behavior of Cu and brass with the frequency-squared (and -cubed) spectra was again found in the transverse mode. 9. Both pure Mg and AZ61 Mg alloy showed low attenuation. In pure Mg, the transverse mode was 2.4 to 4.1 times higher, while AZ61 Mg alloy gave approximately comparable attenuation. No scattering contribution was visible. 10. In Ni, effects of cold work and magnetic field were stronger for the transverse mode. C\({}_{\rm dt}\) reached 300 dB/m/MHz in annealed Ni, but dropped to \(\frac{1}{2}\) with strong magnets. In cold-worked Ni, both C\({}_{\rm dt}\) and C\({}_{\rm d}\) were 20 dB/m/MHz with no magnetic effects. High-temperature Ni alloys, Ti alloys, and tungsten were also evaluated with varied responses. Isotropic W showed comparable C\({}_{\rm d}\) and C\({}_{\rm dt}\) values to those of most Al alloys. 11. Nine engineering polymers showed about three times higher transverse attenuation than longitudinal cases. Their spectra were always linear and C\({}_{\rm dt}\) values ranged from 253 to 1830 dB/m/MHz. 12. Eight fiber-reinforced plastics showed higher transverse attenuation than longitudinal cases with the average C\({}_{\rm dt}\)/C\({}_{\rm d}\) ratio of 4.45.