## 4 Results and Discussion
### Attenuation Behavior of Fiber-Reinforced Materials
The fit to the Biwa relation for the T-spectrum is better, with R\({}^{2}\) = 0.984. For G50 CFRC, \(\mathrm{C_{d}}\) values ranged from 100 to 148 dB/m/MHz for the L and S directions, showing low attenuation ratios of 1.3-1.5. In terms of the damping factor (\(\eta\)) values of these two CFRCs, the fiber (L) direction gave \(\eta\) values of 0.031 to 0.046 and the off-fiber direction gave \(\eta\) values of 0.013 to 0.036. The \(\eta\) values in the L direction were higher than the corresponding values in pultruded GFRC, reflecting higher wave velocity. The off-fiber \(\eta\) values were comparable between CFRC and GFRC, implying the dominance of the matrix properties. Figure 19: Attenuation spectra of uni-directional carbon-fiber-reinforced composite (UD-CFRC) with AS-4 fibers. Blue: L direction with linear fit (dotted line); red: T direction with Biwa relation fit (dashed curve) and linear fit (dotted line). For AS-4 CFRC, [PERSON] et al. [107] reported \(\eta\) values of 0.012 to 0.024 in the L direction, which were about a half of the present data. On the other hand, the \(\eta\) values for off-fiber directions ranged from 0.038 to 0.14, which exceeded the current results. While these were the only data available in the L direction, more attenuation measurements in the S direction have been reported. [PERSON] et al. [96] obtained \(\mathrm{C_{d}}\) = 234 dB/m/MHz (\(\eta\) = 0.026) for a CFRC with Mitsubishi TR30 fibers (0.6 volume fraction). From the data of [PERSON] and [PERSON] [108], \(\mathrm{C_{d}}\) values in the S direction were found to be 153, 128, and 307 dB/m/MHz for UD and QI epoxy CFRCs, woven epoxy CFRC, and woven polyimide CFRC, respectively. These corresponded to the lowest void contents below 1.2%. These were comparable to the present test results. On the other hand, the \(\eta\) values for CFRCs based on the complex elastic moduli measurements [104; 105; 7] were always higher. These complex moduli studies omitted detailed material descriptions, making meaningful assessment difficult. AS-4 CFRC with a polyimide (PMR-15) matrix had higher attenuation in comparison to the epoxy matrix CFRCs, especially in the off-fiber directions. The Biwa relation was found in both T and S directions. Studies on this high-temperature resin matrix CFRC are rare, even for usual mechanical properties, meaning ultrasonic attenuation data cannot be compared. The next group of CFRCs uses T700 fibers with 2501 epoxy. Both UD and QI layups were used, but the UD samples contained 3% and 10% cross piles at approximately 5 mm intervals to increase resistance against splitting. These will be referred to as UD(3) and UD(10), respectively. Attenuation values in the L direction were 69 and 95 dB/m at 1 MHz for UD(3) and UD(10), respectively, similar to other UD samples in the present study, including GFRCs. The much higher attenuation values in the off-fiber directions for this T700 CFRC are noteworthy. Here, \(\alpha\) values at 1 MHz ranged from 825 to 1733 dB/m. The difference in \(\alpha\) values from the L direction is expected to come from the matrix properties of the 2501 epoxy resin used in the T700 CFRC, similar to how the tough matrix resin in the PMR15 polyimide provided higher off-fiber attenuation. These higher attenuation levels can be easily recognized in the damping factor column as well, especially in the QI samples. Only one prior attenuation work on T700 CFRC seems to exists. [PERSON] et al. [109] examined porosity effects on UD and XP composites, and gave attenuation spectra for UD composites with various void contents (1.7 to 10%). For the 1.7% porosity sample, the \(\mathrm{C_{d}}\) value was 400 dB/m/MHz, which increased to 600 dB/m/MHz at 2.75% porosity. It appears that the Datta-Kinra relation [50; 51; 52] starts to take over above 6.7% porosity, probably resulting in scattering effects from voids. It is assumed that the measurements were made in the S direction, since the test configuration is not given. Their \(\mathrm{C_{d}}\) values were lower than in tests R27, R28, or R30.