# Dynamic Viscosity and Transverse Ultrasonic Attenuation of Engineering Materials
## 3 Results and Discussion
### Attenuation Behavior of Iron and Ferrous Alloys
Two high hardness steels (T8 tool steel and a hardness block, Tests F72 and F76) showed moderate levels of C\({}_{\rm dt}\) values (37-38 dB/m/MHz), which were lower for T8 and higher for the block than their respective C\({}_{\rm d}\) values. Their high hardness conditions (VHN of 1155 and 847) reflect dispersed carbides and martensitic microstructures that impede dislocation motion. Yet, their damping is higher than much softer cold-worked 302 and 304 stainless steels (VHN of 362 and 321). This remains to be a topic for further study. Anisotropic directionality effects observed in longitudinal attenuation were examined for three steel plates of 4340, HSLA, and 304 (Tests F38-40, F58-60, F86 = 88). Previously, the thickness (S) direction showed the highest (or next highest) attenuation. For transverse attenuation, the same behavior was only found in the 4340 plate, for which C\({}_{\rm dt}\) for the S direction was more than three times higher than either the longitudinal (L) or transverse (T) direction. In the L or T direction, C\({}_{\rm dt}\) was comparable to C\({}_{\rm d}\). In the HSLA steel plate, C\({}_{\rm dt}\) showed no directionality as three values were essentially identical. Spectral responses of this hot-rolled HSLA steel block (JIS-SM50 grade, Nippon Kokan, Kawasaki, Japan: 0.15% C, 0.29 Si, 1.29 Mn) are shown in Figure 5. The purple and light green curves represent \(\alpha\) term of the longitudinal (L) and short-transverse (S) orientations without scattering contributions. The transverse attenuation spectra in the three orientations are plotted in blue (L), red (transverse or T), and green (S) curves, each with some scattering effects. The spread of these three \(\alpha_{\rm t}\) curves are smaller than the two for \(\alpha\). In contrast, an opposite anisotropic effect was found in the 304 stainless steel plate. That is, the S direction showed the lowest attenuation. The scattering contribution was similar in the three directions in both wave modes. Since the microstructures varied in these plates (tempered bainitic, ferritic-pearlitic, and annealed austenitic, respectively), no clear cause can be suggested for the observed results. However, directionality effects need to be considered when one needs to utilize published attenuation data. Figure 4: Transverse attenuation coefficients vs. frequency for six austenitic stainless steels. The attenuation spectra of five stainless steels fitted to Mason-McSkimin relations are plotted in dark red (304L), purple (304), green (321), dark blue (316), and red (302), respectively. The 301 stainless steel showed a linear spectrum, given in blue. Previously published transverse attenuation (\(\alpha_{\rm t}\)) data is limited, but two cases may be compared. [PERSON] et al. [39; 40] used a resonance method with an electromagnetic transducer and obtained \(\alpha_{\rm t}\) values of 0.15% C and 1 Cr-1 Mo-V steels at 5 MHz. Converting the data, their C\({}_{\rm dt}\) values became 23.2 and 6.6 dB/m/MHz. These can be compared to C\({}_{\rm dt}\) values of a low-C steel (Test F12) and 1 Cr-1 Mo-V steel (Test F68), which are 16.9 and 5.9 dB/m/MHz. These are in good agreement. A separate part of Table 2, the last four rows, provide the attenuation data of four cast iron samples. These represent three types of cast iron, gray, ductile, and malleable. Test I3 was on gray cast iron of class 20, which is of the lowest strength grade (minimum tensile strength of 150 MPa). Test I8 was on class 60 gray iron (minimum tensile strength of 430 MPa). Test I18 was on ductile iron 80-55-06 grade (minimum tensile strength of 552 MPa). Test I21 was on ferritic malleable iron. The transverse attenuation spectra of these four samples are plotted in Figure 6. Gray iron showed attenuation with frequency-squared dependence for both longitudinal and transverse modes, but the attenuation coefficients were about twice larger in the transverse mode. The steeply rising blue curve is for class 20 gray iron and the next red curve is for class 60 gray iron.