# Dynamic Viscosity and Transverse Ultrasonic Attenuation of Engineering Materials
## 2 Experimental Methods
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Test Method** & **C\({}_{dt}\)** & **R\({}^{2}\)** & **v\({}_{t}\)** & **Damping Factor** & **Thickness** \\ \hline \multicolumn{5}{c}{**dB/m/MHz**} & **mm/μs** & **m\({}_{t}\)** & **mm** \\ \hline TDM-1 & 211 & 0.999 & 1.41 & 0.0109 & 17.95, 5.25 \\ TDM-1 & 260 & 0.992 & 1.39 & 0.0132 & 17.8, 9.11 \\ TDM-1 & 236 & 0.994 & 1.40 & 0.0121 & 9.11, 5.25 \\ TDM-1 & 231 & 0.992 & 1.39 & 0.0118 & 17.8, 5.25 \\ TDM-1 & 238 & 0.994 & 1.40 & 0.0122 & 9.11, 5.25 \\ TDM-1 & 259 & 0.994 & 1.41 & 0.0134 & 17.95, 5.25 \\ TDM-1 & 260 & 0.992 & 1.41 & 0.0134 & 17.95, 9.11 \\ TDM-1 & 251 & 0.993 & 1.40 & 0.0129 & 11.75, 5.25 \\ TDM-1 & 249 & 0.993 & 1.39 & 0.0127 & 27.3, 5.25 \\ TDM-1 & 248 & 0.992 & 1.39 & 0.0126 & 27.3, 9.11 \\ TDM-1 & 260 & 0.992 & 1.39 & 0.0132 & 27.3, 11.75 \\ TDM-1 & 263 & 0.993 & 1.38 & 0.0133 & 24.64, 5.25 \\ TDM-1 & 261 & 0.992 & 1.38 & 0.0132 & 24.64, 9.11 \\ TDM-1 & 260 & 0.992 & 1.38 & 0.0131 & 24.64, 11.75 \\ TDM-1 & 270 & 0.993 & 1.40 & 0.0139 & 24.77, 5.25 \\ TDM-1 & 274 & 0.991 & 1.40 & 0.0141 & 24.77, 9.11 \\ TDM-1 & 274 & 0.989 & 1.40 & 0.0141 & 24.77, 11.75 \\ Average & 253.2 & 0.9928 & 1.395 & 0.0129 & \\ Std dev & 16.5 & 0.0020 & 0.010 & 0.0008 & \\ TDM-2 & 211 & 0.997 & 1.41 & 0.0109 & 17.95 \\ TDM-2 & 240 & 0.997 & 1.39 & 0.0122 & 17.80 \\ TDM-2 & 219 & 0.998 & 1.40 & 0.0112 & 9.11 \\ TDM-2 & 244 & 0.997 & 1.41 & 0.0126 & 17.95 \\ TDM-2 & 224 & 0.996 & 1.40 & 0.0115 & 11.75 \\ TDM-2 & 253 & 0.996 & 1.39 & 0.0129 & 27.30 \\ TDM-2 & 259 & 0.995 & 1.38 & 0.0131 & 24.64 \\ TDM-2 & 259 & 0.995 & 1.40 & 0.0133 & 24.77 \\ Average & 238.6 & 0.9964 & 1.40 & 0.0122 & \\ Std. dev. & 18.6 & 0.0011 & 0.010 & 0.0009 & \\ Quartz TDM-1 & 223 & 0.953 & 1.38 & 0.0113 & 9.11, 5.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test results of transverse attenuation coefficients, \(\alpha_{t}\), of PMMA. longitudinal damping factor. The ratio of these two damping factors is 1.62 and matches well with the damping factor ratio at lower frequencies found in the literature. As reviewed in [13], the ratio was 1.6 from 0.2 to 20 kHz. Thus, the value of Cdt in this work and those of [35; 36; 37] fit the decreasing trend of PMMA damping with increased frequency. At the low MHz range, however, the damping factor becomes a constant, as indicated by the good linearity of \(\alpha_{\text{t}}\). Table 1 also lists a representative result of Cdt measurements using quartz disk transducers. Two 9.5-mm diameter, AC-cut crystals of 5-MHz center frequency were bonded for through-transmission tests for the TDM-1 method using two thicknesses of PMMA plates. Linear fitting of the obtained spectrum was poor with R\({}^{2}\) = 0.953. Cdt was 20% lower than the average PMMA Cdt value. Due to a narrow high-sensitivity band, effects of spectral shifts made rational analysis difficult. Several other materials were tested similarly, but reproducibility was low. This reproducibility issue with the quartz tests was likely due to the lack of adequate forces that can be put in thin quartz disks as suitable solid bonding methods were unavailable. It appears that the puls x echo mode with tuned excitation may be beneficial. Unfortunately, equipment break-down prevented further attempts with puls x echo testing. The transducer to sample coupling is crucial in contact testing. In the present work, ultrasonic gel couplant was used (type 54T04, Sonotech, Glenview, IL, USA) under force of 200-250 N (corresponding to the maximum torque that can be applied by two fingers on a 12-mm diameter bolt). This force (which is approximately 0.7 MPa) was 5-8 times higher than that needed to establish a good contact in longitudinal wave testing [13]. The time to reach the stabilized condition was 8 to 10 times longer, typically needing 4 to 5 h at 25 \({}^{\circ}\)C. All the testing was done at 25 \(\pm\) 2 \({}^{\circ}\)C.  
Having shown the consistency of transverse attenuation measurements using TDM-1 and TDM-2, testing of various materials is next conducted. In most cases, TDM-2 will be utilized.