# Review on Structural Health Evaluation with Acoustic Emission
## 2 Signal Attenuation
### Guided Wave Attenuation on Fiber-Reinforced Composites
The last group, or the high \(\eta\) group, showed high damping with \(\eta\) = 0.05 to 0.08 and possessed high strength of 3.8-6.3 GPa. This high damping in the newer high-performance carbon fibers is surprising since these \(\eta\) values are three to four times larger than epoxy matrix and nearing those of some elastomers. Earlier damping results from the 1980s were on CFRP with fibers of low to medium strength in today's classification. Thus, these fibers had values of \(\eta\) under 0.04 and in combination with epoxy (\(\eta\) = 0.022), resultant \(\eta_{2}\) is consistent with the observed \(\eta_{2}\) of 0.02-0.05. Another check can be made by measuring ultrasonic attenuation. If the high damping values of 0.05 to 0.08 persist at low MHz frequencies, we should expect \(\alpha_{\rm p}\) of 900-1500 dB/m at 2 MHz (2300-3600 dB/m at 5 MHz) of ultrasonic attenuation. This level of \(\alpha_{\rm p}\) was reported on CFRP with T700 fiber. [PERSON] et al. [105] measured \(\alpha_{\rm p}\) of 3300 dB/m at 5 MHz for 8-ply unidirectional CFRP, but with 1.7% porosity. Our recent preliminary measurement on a CFRP with T700 fiber (2-10 mm thickness, made from Toray 2501 prepregs; fiber fraction of 0.4) showed \(\alpha_{\rm p}\) = 72 or 600 dB/m at 0.45 MHz in the fiber direction or normal to fiber direction. These \(\alpha_{\rm p}\) values correspond to \(\eta_{1}\) and \(\eta_{2}\) of 0.05 and 0.13, respectively, and indeed imply that newer high-performance fibers have higher intrinsic damping in comparison to fibers made before the mid-1990s. The high damping behavior is beneficial for many engineering applications, but poses a challenge for SHM. [PERSON] et al. [104] related high torsional damping to amorphous carbon phase. Yet there seems to be no clear reason why newer high-performance carbon fibers possess high acoustic damping. Note that amorphous fused silica has very low damping. These ultrasonic studies should be repeated including the evaluation of neat resin and further research is needed for the origin of damping. Complex elastic moduli of CFRP plates have been measured with the Castaings method. Four sets of \(\eta_{\rm ij}\) values are tabulated in Table 1. Note that fibers are oriented along the 3-axis for [PERSON] et al. [61], but along the 1-axis for [PERSON] [62] and [PERSON] [63; 64]. In three cases for CFRP-UD samples, damping along the fiber axis averaged to 0.069 while shear damping normal to fibers 0.098. These damping values are again two or more times higher than \(\eta_{2}\) values of comparable CFRP-UD samples. The complex elastic moduli were then used with higher order plate theory to calculate attenuation coefficients for S\({}_{0}\) and A\({}_{0}\) modes. [PERSON] [63] obtained for a UD plate along the fibers (0\({}^{\circ}\)) \(\alpha_{\rm L}\) of 27 and 150 dB/m at 300 kHz (45 and 250 dB/m at 500 kHz) for S\({}_{0}\) and A\({}_{0}\) modes, respectively. Along the fiber normal (90\({}^{\circ}\)) direction, corresponding values were 75 and 108 dB/m at 300 kHz. These attenuation values are beyond geometrical spreading. A few other calculations resulted in much higher attenuation values [16; 61; 62] than Calomfirescu results. The S\({}_{0}\) value along 0\({}^{\circ}\) of Calomfirescu [63] was much higher than our measurements on AS4/3506-1 CFRP plates [106]. In our CFRP study, three types of lay-ups (unidirectional, cross-ply, and quasi-isotropic) were used and complex attenuation behavior was found when the wave propagation direction shifted from the fiber orientations. For the UD plate, S\({}_{0}\)-mode attenuation value along the fiber direction (0\({}^{\circ}\)) at 300 kHz was 4.8 dB/m, which was slightly less than that of Al plate (5.8 dB/m). Since geometrical spreading was not separated and receiver size was 8 mm, the same test was repeated using a KRN sensor of 1 mm size. Figure 6a gives attenuation data for S\({}_{0}\) and A\({}_{0}\) modes at 100 kHz, which are represented by attenuation coefficients of 20 dB/m for S\({}_{0}\) and 38 dB/m for A\({}_{0}\) mode.