# Dynamic Viscosity and Transverse Ultrasonic Attenuation of Engineering Materials
## 3 Results and Discussion
### Attenuation Behavior of Fiber-Reinforced Plastics
** & **Material** & **C\({}_{4}\)** & **C\({}_{5}\)** & **v** & **\(\eta\)** & **C\({}_{6}\)** & **C\({}_{7}\)** & **v\({}_{1}\)** & **v\({}_{1}\)** & **v\({}_{2}\)** & **C\({}_{6}\)** & **n/n** & **Thickness** & **Density** & **Notes** \\ \hline
**No** & & **d/n/n** & **d/n/n** & **mm** & **d/n/n** & **d/n/n** & **mm** & & & & & **mm** & **Mg/n\({}^{3}\)** & \\ \hline R1 & GRP rod /F & 74.6 & 4.96 & \(3.00\times 10^{-2}\) & 478 & & 1.71 & \(3.00\times 10^{-2}\) & 6.41 & 2.21 & 33.5 & 1.97 & & \\ R4 & GRP rod /N & 173 & 5.946 & 3.07 & \(5.72\times 10^{-2}\) & 952 & 1.64 & \(5.72\times 10^{-2}\) & 5.50 & 2.94 & 6.3 & 1.97 & \(\rm pol=\) \(\pm\)F \\ R4a & GRP rod & 173 & 5.946 & 3.07 & \(6.99\times 10^{-2}\) & 944 & 1.76 & \(6.09\times 10^{-2}\) & 5.46 & 3.13 & 6.3 & 1.97 & \(\rm pol=\) \(\pm\)F \\ R5 & GRP rod /F & 121 & 5.06 & \(4.29\times 10^{-2}\) & 660 & 1.80 & \(4.29\times 10^{-2}\) & 5.37 & 1.91 & 7.0 & 2.07 & \(\rm pul\) \(\rm\mu\)F \\ R13 & GRP rod /F & 202 & 4.15 & \(1.27\times 10^{-1}\) & 1740 & 1.99 & \(1.27\times 10^{-1}\) & 8.61 & 4.13 & 7.0 & 1.81 & \\ R14 & GRP rod /N & 441 & 2.84 & \(1.83\times 10^{-1}\) & 300 & 1.65 & \(1.83\times 10^{-2}\) & 6.87 & 3.99 & 2.2 & 1.81 & \(\rm pol=\) \(\rm\mu\)F \\ R15 & GRP rod /F & 91.0 & 9.32 & \(1.83\times 10^{-2}\) & 326 & 74.4 & 2.15 & \(3.15\times 10^{-2}\) & 3.58 & 1.02 & 5.4 & 1.53 & \\ R35 & GRP rod /N & 65.2 & \((0.0372.n-n)\) & 9.20 & \(1.10\times 10^{-2}\) & 9 & 140 & 2.15 & \(1.10\times 10^{-2}\) & 2.15 & 0.50 & 5.4 & 1.53 & \\ R16 & GRP rod /F & 267 & 4.938 & 3.16 & \(4.04\times 10^{-2}\) & 579 & 2.09  
One repeat test for a carbon fiber reinforced plastic (CFRP) with unidirectional (UD) AS-4 fibers (Test R15a) showed a linear attenuation spectrum plus a \(\rm C_{R}\) (the 4 th power of frequency) contribution in the orientation parallel to the fibers. This is one of the additional longitudinal tests and results are shown in Figure 10. In the previous work, the test was limited to 10 MHz and the \(\rm C_{R}\) part was not recognized, as shown in a blue curve. A new test extended the frequency limit to 16 MHz (by using Olympus V111 as a transmitter in place of an older V1030, though both are 10 MHz transducers). This spectrum (light blue curve) can be fitted to the Mason-McSkimin relation with a linear part plus \(f^{4}\) part. The fitted spectrum is plotted in a dashed curve. Additionally shown in Figure 10 for a comparison, is the longitudinal attenuation for the surface normal orientation (red curve), as noted above. Figure 11 gives the transverse attenuation spectra along the fiber direction (purple curve, Test R15a). The polarization was along the fibers. This is to be compared to the light blue curve, replotted from Figure 10, representing the Mason-McSkimin spectrum for the same orientation. The sample for the  
Figure 11: The transverse attenuation spectra of AS4 UD-CFRP. Purple curve: Transverse attenuation parallel to fibers. A linear + \(f^{2}\) fit (dashed curve) and a \(f^{2}\) fit (dash-dotted) are also plotted. Dark red: Transverse attenuation normal to fibers, with the polarization parallel to fibers. A linear fit is in the dotted line. A longitudinal attenuation spectrum from Figure 10 is shown in light blue with a Mason-McSkimin fit (dashed curve). Figure 10: The longitudinal attenuation spectra of a unidirectional (UD) carbon fiber reinforced plastic (CFRP) with AS4 fibers. Wave direction was parallel to fibers (blue curves, fitted to Mason-McSkimin or to linear + \(f^{4}\) relation) or normal to fibers (red curve, fitted to linear + \(f^{3}\) relation). Fitted curves in dashed plots (a red dotted line is for linear fit). transverse attenuation was cut from a longer sample used for the previous longitudinal test (Test R15). The transverse attenuation increased rapidly with increasing frequency and became more than ten times higher than the longitudinal value at 5 MHz and the difference expanded further as \(f\) increased. This attenuation curve has two possible fitting functions (shown as in purple dash and dash-dotted curves).