# Dynamic Viscosity and Transverse Ultrasonic Attenuation of Engineering Materials
## 3 Results and Discussion
### Attenuation Behavior of Non-Ferrous Metals and Alloys
A peculiar feature of the longitudinal attenuation of Cu and brass was the prevalence of the frequency-squared dependence of attenuation coefficient, \(\alpha\). This behavior also exists in the transverse mode. In addition to Cu and brass, the frequency-squared dependence also appeared in a Cu-Zr alloy and Inconel 718, as well as frequency-cubed dependences in C260 (cartridge) brass (Tests N41, N42). Most of these squar \(\times\) or cub \(\times\) dependences can be fitted to the Mason-McSkimin relation, which combines low damping and large Rayleigh scattering terms. In all cases with a good power-law fit, their elastic anisotropy is high and grain boundary scattering is strong. No Al alloys and steels exhibited the frequency-squared dependence out of \(\sim\)140 tests. Finding Al and steels in the same group is strange as Al is isotropic but steels are not. Additional studies are needed to ascertain whether the power-law behaviors truly represent the attenuation of these alloys, especially by varying microstructures and cold working. Comparison of different Cu and its alloys can be made when C\({}_{\text{dt}}\) values can be assigned with the linear or Mason-McSkimin spectra. In OFHC Cu, C110 Cu (tough pitch grade) and C260 brass, annealed conditions generally produced high attenuation of more than 100 dB/m/MHz. Two-phase C280 brass also had high C\({}_{\text{dt}}\) values. With cold working or with second phase additions, C\({}_{\text{dt}}\) values decreased, sometimes down to the level comparable to the corresponding C\({}_{\text{d}}\) values. Both pure Mg and AZ61 Mg alloy (6% Al, 1% Zn) showed low attenuation. In pure Mg, the transverse mode C\({}_{\text{dt}}\) values increased over C\({}_{\text{d}}\) by a factor from 2.4 to 4.1, while AZ61 Mg alloy gave approximately comparable attenuation between the two modes at 2 to 4 dB/m/MHz. No scattering contribution was visible. An early work on AZ31 Mg alloy with 3% Al [16] gave \(\alpha_{\text{t}}\) (4.1 dB/m at 10 MHz) being 40% less than \(\alpha\). Both values were small, and when the diffraction correction is made, attenuation becomes nondetectable. Thus, our data is slightly higher. Low frequency damping data [42] listed \(\eta\) for pure Mg at 0.014-0.06 (\(f=60\)-400 Hz) or more than ten times the \(\eta\) or \(\eta_{\text{t}}\) values in Table 3. These \(\eta\) values were taken at strain amplitudes higher than \(10^{-4}\) and activated large scale dislocation glide. In pure Ni (grade 200), effects of cold work and magnetic field were significant. The effects were stronger for the transverse mode. In the annealed condition (Test N70), the C\({}_{\text{dt}}\)/C\({}_{\text{d}}\) ratio is 5, with C\({}_{\text{dt}}\) reaching 300 dB/m/MHz. This dropped to about \(\frac{1}{2}\), when two strong magnets were placed on the sides of the Ni sample (32 mm diameter). The magnets were F \(\times\) Nd-B type with the surface magnetic field of 5.6 kGauss (size: 25.4 mm diameter, 19 mm thick). C\({}_{\text{d}}\) also decreased by 20% and further decreased to \(\frac{1}{2}\) of the unmagnetized condition when one more magnet was applied. C\({}_{\text{dt}}\) was unaffected by the additional magnetic field. In cold-worked Ni (Test N72), both C\({}_{\text{dt}}\) and C\({}_{\text{d}}\) were approximately 20 dB/m/MHz and were unaffected by magnetic fields. Such effects were  
Figure 7: Three types of transverse attenuation spectra observed in Cu and its alloys: Linear (blue curve), Mason-McSkimin (red), and frequency-squared (green). expected [44; 45], but were insignificant in iron or steel. Large effects on the transverse attenuation of Ni were surprising. Reported attenuation values for Ni (grade A, equivalent to 200 grade) were C\({}_{\rm d}\) of 38.3 and C\({}_{\rm dt}\) of 120 dB/m/MHz [46]. These were 30 to 60% lower than Test N70. Since cold-work effects are strong, slight straining can cause such reduction.