# Measurement of Elastic Properties of Brittle Materials by Ultrasonic and Indentation Methods
## 3 Results and Discussions
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample Number**} & \multicolumn{2}{c}{**Longitudinal**} & \multicolumn{2}{c}{**Transverse**} & \multicolumn{2}{c}{**Attenuation Coefficient**} & \multicolumn{2}{c}{**Poisson**} & \multicolumn{1}{c}{**[PERSON]’s**} \\  & \(\mathbf{t}\) **(ns)** & \(\mathbf{V_{L}}\) **(m/s)** & \(\mathbf{t}\) **(ns)** & \(\mathbf{V_{T}}\) **(m/s)** & **Longitudinal** & **Transverse** & \(\mathbf{\
u}\) & **GPa** \\ \hline No. 1 (ITO-glass) & 380 & 5836.8 & 632 & 3509.4 & 0.35 & 1.1 & 0.22 & 72.67 \\ No. 2 (ITO-glass) & 377 & 5867.3 & 634 & 3488.9 & 0.17 & 0.91 & 0.23 & 72.52 \\ No. 3 (BMG) & 881 & 4790.0 & 1970 & 2142.1 & 0.58 & 2.79 & 0.38 & 91.90 \\ No. 4 (CM247 LC) & 1174 & 5940.3 & 2056 & 3392.0 & 5.51 & 5.64 & 0.26 & 248.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Ultrasonic measurement results and derived elastic coefficients. Longitudinal and shear attenuation were measured at 20 MHz and 5 MHz respectively. Figure 5: The ultrasonic pulse-echo signal of the BMG sample: (**a**) Longitudinal; (**b**) Transverse Wave. Figure 6: The ultrasonic pulse-echo signal of the CM247 LC superalloy sample: (**a**) Longitudinal; (**b**) Transverse Wave. 0.15. The discrepancy of the data is substantially at about 25%. Although it may be due to the difference of material and sample preparations, the validity of the ultrasonic data has to be examined by other modality. The ultrasonic longitudinal attenuation coefficients of the two glass samples are 0.35 and 0.17 dB/mm at 20 MHz. The transversal attenuation coefficients of the two glass samples are 1.1 and 0.91 dB/mm at 5 MHz. As the glass is fully amorphous and homogeneous, the low attenuation is reasonable and predictable. The ultrasonic longitudinal and transversal attenuation coefficients of BMG sample are 0.58 (20 MHz) and 2.79 dB/mm (5 MHz). The longitudinal and transversal attenuation coefficients of the CM247 LC superalloy sample are 5.51 dB/mm (20 MHz) and 5.64 dB/mm (5 MHz), respectively. As the material constitution and structure get more complicated the acoustic attenuation is raised accordingly. Notably, the attenuation coefficients of CM247 LC superalloy is much higher than normal metals [28; 30; 31] e.g., steel, homogeneous alloy,... which normally lies within 1 dB/mm. The measured transverse attenuation coefficients follow the same trend. This is a unique property not usually found in commonly used metal and ceramic materials. Current findings of high ultrasonic attenuation are similar to what [PERSON] et al. [32] have reported, at 1.0 dB/mm (15 MHz) from the family of Ni\({}_{3}\)Si intermetallic materials previously. Three nanoindentation measurements are performed for each sample and the average values are taken. The original (loading-unloading) and deduced loading (\(P\)) versus square of displacement (\(h^{2}\)) (loading-unloading) diagrams of metallic glass (sample #3) sample in the nanoindentation test are shown in Figure 7 as an example. The elastic coefficient and hardness measured by nanoindentation are calculated with assumed Poisson ratio and tabulated in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Sample Number**} & \multicolumn{3}{c}{**Elastic Coefficient and Hardness**} \\ \cline{3-4}  & & **Young’s Modulus (GPa)** & **Hardness (Unload) (GPa)** \\ \hline \multirow{4}{*}{No. 1 (ITO-glass)} & Test-1 & 71.76 & 7.33 \\  & Test-2 & 70.39 & 7.04 \\ \cline{1-1}  & Test-3 & 69.55 & 6.81 \\ \cline{1-1}  & mean & 70.57 & 7.06 \\ \hline \multirow{4}{*}{No. 2 (ITO-glass)} & Test-1 & 72.79 & 7.87 \\ \cline{1-1}  & Test-2 & 72.15 & 7.75 \\ \cline{1-1}  & Test-3 & 72.81 & 7.85 \\ \cline{1-1}  & mean & 72.58 & 7.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Elastic coefficient and hardness measured by nanoindentation. Figure 7: The (**a**) original loading-unloading loading vs. displacement and (**b**) \(P\)-\(h^{2}\) relation curve by the nano-indentation measurement from BMG sample.