# Ultrasonic Attenuation of Ceramic and Inorganic Materials Using the Through-Transmission Method
## 4 Results and Discussion
### Other Ceramics, Mortars and Composites
The \(\alpha_{\text{1 IM}}\) -V relation and the \(f^{4}\)-dependence for the transverse attenuation agree with [PERSON] theory, Equation (15), but the \(\alpha_{\text{1M}}\)-V\({}^{2}\) relation and \(f^{2}\)- or \(f^{3}\)-dependence for the longitudinal attenuation have no theoretical basis at this time. The reduced effect of voids on \(\alpha_{\text{1M}}\) in the saturated state indicated that the longitudinal waves have less mismatch in the acoustic impedance since Z within the void increases from nil to 1.5 Mayl of water. Z for the mortar sample ranges from 3.5 to 7.3. For the transverse waves, \(\alpha_{\text{1M}}\) values were unaffected since both air and water cannot support this wave mode. This absence of water-saturation effect on the transverse attenuation appears to be unreported previously and should be confirmed by additional studies. The presence of the void affected the elastic moduli strongly, reducing E and G to 30-40% of the initial values of the sample. It is common to the behavior of hard ceramics as documented for alumina [6] and was confirmed in a recent data compilation on pervious concrete [85]. It is interesting to note that the void content of 23 to 31% is called optimum for pervious concrete [86], while it is less than 14% for normal concrete [79; 80]. When the sample thickness was reduced, E and G values increased by 3 to 7%, indicating that microstructural variation occurs within even a small-sized mortar sample, similar to the variation known for larger concrete [87]. This apparently caused large reduction in attenuation found in this study compared to the previous reports that used 50 mm cubes [43; 44]. The saturation of entrained voids also increased wave velocities, producing increases in E and G values (cf. Table 10). From the corresponding dry states, E values increased by 41 to 50% and G values by 49 to 68%. The study of acoustic wave propagation in media with voids and cracks filled with liquid has been an important and active field, based on the Biot theory [88; 89; 90]. The applications of the Biot theory to seismic exploration have yielded broad successes [89], but its extension to the ultrasonic frequency range has remained static. The Biot approach introduced damping terms into the elastic constant operators [88], but their interpretation in terms of void and liquid characteristics has not been developed. At higher frequencies, fluid flow within voids [90] can hardly be a factor in wave attenuation. Increases in the longitudinal wave velocity of concrete due to water saturation was reported  
Figure 11: Attenuation at 1 MHz (dB/m) vs. void content (%) of mortar samples. Blue dots and + are longitudinal attenuation and matched to the \(\alpha_{\text{1M}}\)-V\({}^{3}\) relation (blue line). Red dots are transverse attenuation, matching to the \(\alpha_{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{ \text  
in 1980 [91], continuing to the present [92]. However, no comparable studies on attenuation have been made. The observed increases in the longitudinal wave velocity (by 4.5 to 11.5%) and E (by 41 to 50%) from water-filled voids are consistent with the replacement of air with water, having 21.8-times higher bulk modulus than that of air. The observed increases in the transverse wave velocity and G from water-filled voids were 14.2 to 20% and 49 to 60%, respectively. It is difficult to attribute these increases to water-to-air replacement as both cannot support transverse waves. These changes and the absence of saturation effects on transverse attenuation require further study since no conceivable mechanisms can be suggested at this stage. Velocity and attenuation data for graphite plate samples (Test 20 to 25) showed orthotropic behavior. This is most clearly found in the Young's moduli of the three directions; 14.7-15.2 GPa for the L direction and 7.8 or 7.6 GPa for the T or S direction (cf. Table 11). The longitudinal attenuation data showed the frequency-squared dependence (cf. Table 6) and C\({}_{2}\) values increased from L to S to T directions.