# Review on Structural Health Evaluation with Acoustic Emission
## 2 Signal Attenuation
### Survey of Ultrasonic Attenuation of Metallic Alloys  
Table 2 lists ultrasonic attenuation of engineering alloys, noting material parameters given in the original articles. This list attempted to cover all the attenuation data available for engineering alloys, but some data were omitted for obvious errors in methods used. Large variations are sometimes seen for similar alloys, but detailed reevaluation of measurement methods is needed to explore their causes [67]. For example, [PERSON] et al. [68] obtained \(a_{\mathrm{P}}\) of 60 dB/m at 5 MHz for an annealed 0.15%C steel with 20 \(\upmu\)m grain size, but later [PERSON] et al. [69] reported for a similar sample \(a_{\mathrm{P}}\) of 670 dB/m at 10 MHz. Papers from [PERSON] [70,71] also reported 500 to 1350 dB/m attenuation for annealed low C steels at 8-10 MHz. Such large differences in \(a_{\mathrm{P}}\) at 5 and 10 MHz may arise from the frequency dependence of \(a_{\mathrm{P}}\). However, these appear to be strange, since [PERSON] [29,72] obtained \(a_{\mathrm{P}}=12\) dB/m for annealed 4150 steel and below 10 dB/m for a tempered martensitic bearing steel (52100 steel) over 1 to 10 MHz. Serious evaluation of these diverging results has not been conducted so far, but [PERSON] data are more reliable as he used directly bonded quartz disc transducers, while later studies used damped ultrasonic transducers and water immersion [68, 69, 70, 71]. Magnetic effects could be a factor, but are less than 10 dB/m at 1 MHz and not large enough [73,74]. Most of the references dealt with the longitudinal wave attenuation. Recently, [PERSON], [PERSON], and [PERSON] [75, 76, 77, 78, 79] have measured shear wave attenuation using non-contact electromagnetic sensors. For example, they found \(a_{\mathrm{t}}=116\) dB/m at 5 MHz for 0.15%C steel with 49 \(\upmu\)m grain size, almost doubling [PERSON]'s \(a_{\mathrm{P}}\) data at 5 MHz cited above [68]. Their \(a_{\mathrm{t}}\) results in combination with longitudinal attenuation data allow one to estimate guided wave attenuation using the theories discussed in [PERSON] [20]. The number of engineering alloys examined for \(a_{\mathrm{t}}\), however, is still limited. In contrast to polymers, in which hysteretic effects due to molecular rearrangements are dominant [18], ultrasonic attenuation of crystalline metals and ceramics mainly comes from absorption, Rayleigh scattering, and stochastic scattering [26,80]. Absorption effect is similar to polymers with linear frequency dependence, though mechanisms are different. Both of the scattering contributions depend on frequency with a power law and the exponents are 4 and 2. Rayleigh scattering varies most with grain size. In Table 2, attenuation measurements that used low-loss quartz discs directly bonded to samples are marked with Q while non-contact electromagnetic measurements are marked with E. The rest utilized immersion, buffer rod, or direct contact methods. The unmarked group needs assumptions regarding signal loss at sample interfaces, where errors may be generated. [PERSON] [81] examined ultrasonic reflection coefficients and showed large variations and dependence on interface thickness and contact pressure. In view of low attenuation found in guided wave propagation dominated by the \(1/\surd\)x dependence, it is likely that most structural steels used in pressure vessels, tanks, and pipelines have low values of \(a_{\mathrm{P}}\) and \(a_{\mathrm{t}}\). Thus, high bulk wave attenuation of ultrasonic waves must be reexamined since high attenuation reports have mostly originated from immersion test procedures that included a plane-wave assumption in the analysis. This last point also needs further study because the sound fields ahead of a commonly used piston transducer suffer from divergence and diffraction [31,72].