# Measurement of Elastic Properties of Brittle Materials by Ultrasonic and Indentation Methods
## 3 Results and Discussions
The average [PERSON]'s modulus of the four samples from both ultrasonic and nanoindentation are also listed in Table 4 for ease of comparison. The average [PERSON]'s moduli measured from the glass samples are 72.58 and 70.57 (max error @1.1) GPa, which is in accordance with the ultrasonic measurement. The average [PERSON]'s modulus measured from the BMG is 119.70 (max error @0.1) GPa. Compared to 91.90 GPa from ultrasonic measurement the difference is 23.59%. The [PERSON]'s modulus measured from the CM247 LC superalloy is 235.68 (max error @0.1) GPa. Compared to 248.67 GPa from ultrasonic measurement the difference is 5.11%. The disparity of the results by the two methods for these two materials is quite substantial. However, the nanoindentation results are closer to previously published data. This indicates that the approach by which the elastic coefficient calculated from acoustic speed has to be cautiously examined. Different from that of conventional metals the atoms of metallic glasses are \"frozen\" in a random, disordered structure, rather than arranging themselves into repeating patterns of grains, just like glass. The metallurgical microscopic photo of BMG sample (500\(\times\)) is shown in Figure 8. In general, it is homogeneous and no well-defined grain boundary can be found, although there are sparse precipitate crystalline phases as indicated in the area enclosed by the red bracket. It may be regarded without question as poly-crystalline or even amorphous depending on the manufacturing process. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Sample \#**} & \multicolumn{2}{c}{**Young’s Modulus (GPa)**} \\ \cline{2-3}  & **Ultrasonics** & **Nano-Indentation** \\ \hline
1 (ITO-glass) & 72.507 & 70.568 \\
2 (ITO-glass) & 71.980 & 72.582 \\
3 (BMG) & 91.463 & 119.698 \\
4 (CM247 LC) & 248.377 & 235.679 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of elastic coefficient measured by ultrasonics and nanoindentation. Figure 8: Metallurgical microscopic photo of BMG sample (500\(\times\)). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Sample Number**} & \multicolumn{2}{c}{**Elastic Coefficient and Hardness**} \\ \cline{3-4}  & & **Young’s Modulus (GPa)** & **Hardness (Unload) (GPa)** \\ \hline \multirow{4}{*}{No. 3 (BMG)} & Test-1 & 119.63 & 7.87 \\  & Test-2 & 120.28 & 7.92 \\  & Test-3 & 119.19 & 7.71 \\  & mean & 119.70 & 7.83 \\ \hline \multirow{4}{*}{No. 4 (CM247 LC)} & Test-1 & 234.75 & 7.55 \\  & Test-2 & 235.54 & 7.86 \\ \cline{1-1}  & Test-3 & 236.75 & 7.48 \\ \cline{1-1}  & mean & 235.68 & 7.63 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._The metallurgical microscopic photo of CM247 LC sample (500\(\times\)) is shown in Figure 9. The dendrite structure can be seen with no pores. It is not refined or directionally solidified so that there is no unified grain growth although columnar grains i.e., polycrystalline [23] may exist in different directions with strong matrix gain boundary with carbide and \(\gamma\)-\(\gamma^{\prime}\) eutectic phase as indicated in the area enclosed by the red bracket. One common trait for both materials is the disordered structure and broken grain boundary. [PERSON] et al. [33] compared ultrasonics with the nanoindentation method on titanium alloy material and concluded that elastic modulus can be measured more accurately by the ultrasonic method. The reason cited by them is that the accuracy of elastic modulus measurement using nanoindentation technique depends on more issues while ultrasonic method is directly related to the elastic property and density of the material. Both methods have some potential sources of errors. Factors that can lead to misleading results of nanoindentation include frame compliance, area function, tip sharpness, piling-up, unloading analysis, and specimen Poisson's ratio [10; 11]. However, determination of the elastic moduli matrix is rather complicated for non-homogeneous and anisotropic materials by ultrasonic method.