# Review on Structural Health Evaluation with Acoustic Emission
## 2 Signal Attenuation
### Guided Wave Attenuation on Fiber-Reinforced Composites
Thus, the Castaings-Hosten determination of GFRP damping factors that averaged to 0.043 apparently suffers from overestimation of a factor of two or more. Attenuation and damping studies for carbon-fiber reinforced plastics (CFRP) have been conducted since the 1970s. In his exhaustive review, [PERSON] [93] showed that longitudinal damping factor in the fiber direction (\(\eta_{1}\)) was 0.001-0.005 for unidirectional CFRP with 0.6-fiber volume fraction. Transverse damping factor normal to the fiber direction (\(\eta_{2}\)) was approximately 0.01. CFRP data from [60] were similar to GFRP values given above and match with the [PERSON] values. A newer study confirmed these results [95]. These damping studies were made at low frequencies below 20 kHz using flexural bending of long beam samples. A recent work also verified \(\eta_{1}\) of \(\sim\)0.001 using a longitudinal resonance technique with pultruded 0\({}^{\circ}\) samples [96]. At 2 MHz, \(\eta_{1}\) or \(\eta_{2}\) of 0.01 corresponds to ultrasonic attenuation coefficient (\(a_{\rm P}\)) of 50 or 182 dB/m in the direction parallel or normal to fibers. Using quartz disc transducers, [PERSON] [97] evaluated \(a_{\rm P}\) and \(a_{\rm t}\) of UD-CFRP (XA-S/1138) including those along the fiber direction over 1.8 to 9 MHz. At a fiber fraction of 0.6 and 2 MHz, \(a_{\rm P}\) was 55 and 450 dB/m, parallel and normal to fibers, while \(a_{\rm t}\) exceeded 1050 dB/m. [PERSON] et al. [98] made theoretical and experimental studies of attenuation for UD-CFRP (TR30/340) with epoxy matrix varying fiber volume fractions up to 0.6. At 2 MHz, \(a_{\rm P}\) was 430 dB/m normal to fibers, about 10% higher than their theory. In both studies [97, 98], the values of \(a_{\rm t}\) were much higher than those of \(a_{\rm P}\). When the observed \(a_{\rm P}\) of 450 dB/m is converted to \(\eta_{2}\), we get \(\eta_{2}\) of 0.025, about twice the low frequency data. An earlier work by [PERSON] et al. [99] obtained \(\eta_{1}\) and \(\eta_{2}\) values of 0.014 and 0.049 along and normal to fibers at 2 MHz for a CFRP (AS/3501-6). They used multiple samples of square cross section (9.5 \(\times\) 9.5 or 12.7 \(\times\) 12.7 mm\({}^{2}\)) and 3.8- to 127-mm length to get their \(\eta_{1}\) and \(\eta_{2}\) values. Even ignoring a diffraction correction [100, 101], \(a_{\rm P}\) along fibers at 2 MHz is 70 dB/m and is only 27% higher than [PERSON] [97]. For \(a_{\rm P}\) normal to fibers, it is 892 dB/m without diffraction correction and is about twice those of [PERSON] [97] and [PERSON] et al. [98]. We also conducted an ultrasonic attenuation measurement at 2.25 MHz using an immersion method and obtained \(a_{\rm P}\) normal to fibers of 704 dB/m for CFRP (G50/F584) in a cross-ply layup, corresponding to \(\eta_{2}\) of 0.034. Along the fiber direction, the same CFRP yielded \(\eta_{1}\) of 0.02 at 0.5 MHz. This CFRP sample was from our earlier AE study [102]. The differences in attenuation among CFRP are partly due to fibers and resins used, but may also be from methods used. Thus, we expect \(\eta_{1}\) = 0.01-0.02 and \(\eta_{2}\) = 0.02-0.05 for UD-CFRP at low-MHz ultrasonic frequencies. Using a torsion pendulum method, [PERSON] [103] evaluated the damping \(\eta\) for single carbon fibers. For polyacrylamide (PAN)-based fibers, \(\eta\) was 0.0013, while pitch-based fibers (after stretching) had \(\eta\) of 0.0028. [PERSON] et al. [104] examined \(\eta\) for single carbon fibers of 13 different combinations of tensile strength and elastic modulus. These were newer fibers with improved properties and both PAN- and pitch-based fibers were tested for torsional damping. For the low \(\eta\) group, the values of \(\eta\) were about 0.025 for low strength fibers (under 2 GPa tensile strength). The middle \(\eta\) group had \(\eta\) = 0.035 \(\pm\) 0.003 and the tensile strength varied from 2.5 to 6 GPa, including both high strength PAN fibers and high modulus meso-phase pitch fibers.