# Measurement of Elastic Properties of Brittle Materials by Ultrasonic and Indentation Methods
## 3 Results and Discussions  
The ultrasonic measurement provides both the longitudinal and shear elastic constants, thus is discussed first for clarity. On the other hand, the nanoindentation measurement can only deliver longitudinal data and is discussed subsequently for comparison. The samples of the three different materials underwent both methods. Three ultrasonic measurements are performed for each sample and the average values are taken. In each measurement, three data points were taken, and the average values were recorded. Shown in Figures 3-6 are the of results from the ultrasonic measurement where the horizontal-axis is time (ns) while the vertical-axis is the amplitude of signals (mV). The values of the echo amplitude and arrival time and are read from a cursor provided by the data acquisition software. Once the cursor is moved to the selected point, a pair (time, amplitude) is shown on the screen and recorded. For example, round-trip travel time (\(\Delta t=t_{1}-t_{2}\)) in Figure 3a is 380 ns for the longitudinal waves. Similarly, the round-trip travel time is calculated as 631 ns for the transverse waves in Figure 3b. The attenuation of acoustic waves is weak so that the echo signals can be easily recognized for glass samples. However, the attenuation of acoustic waves is strong for the CM247 LC superalloy sample and the echo signals are more difficult to identify, especially in the case of traverse waves. Proper adjustment of impulse energy was made to make sure no ambiguity in picking up the arrival timings. Examples of the selection of the data points for calculation e.g., \(t_{1}\), \(t_{2}\), \(A_{0}\), and \(A_{1}\) are depicted in the Figures. The average elastic moduli, longitudinal attenuation and Poisson ratios obtained by the ultrasonic measurement are tabulated in Table 2. The variation of data is very low, and the measurement precision is quite good as the mean values of measurement are listed. Figure 4: The ultrasonic pulse-echo signal of the ITO-glass sample #2: (**a**) Longitudinal; (**b**) Transverse Wave. Figure 3: The ultrasonic pulse-echo signal of the ITO-glass sample #1: (**a**) Longitudinal; (**b**) Transverse Wave. The Young's modulus of different common types of glass ranges from 51 (high-lead glass) to 88 GPa (aluminosilicate glass) and 69 GPa for the most commonly used soda-lime glass. The average [PERSON]'s moduli measured from the glass samples are respectively 72.52 (max error @1.94) and 72.67 (max error @0.602) GPa, which is consistent with the previous published data. The Poisson ratio of different types of glass ranges from 0.2 to 0.25 according to [29] while a consistent value of 0.22 is obtained in the results. The ultrasonic pulse-echo method performed very satisfactory in measuring the elastic constants of homogeneous and amorphous glass material. The measured average [PERSON]'s modulus and Poisson ratio of BMG samples are 91.90 (max error @0.9) GPa and 0.38. There is no published data related to BMG material with the same Zr-Cu-Ni-Al constitution. The elastic properties of Cu-Zr-Ti BMG was investigated by the electromagnetic acoustic resonance (EMAR) technique [29]. The Young's modulus and Poisson ratio shown are about 125 GPa and 0.36, which are reasonably close to the values in current study. Furthermore, the amorphous structure of the BMG in this study is slightly different from the poly-crystalline structure BMG in [29]. The measured average Young's modulus and Poisson ratio of CM247 LC superalloy sample are 248.67 (max error @0.6) GPa and 0.26. According to the data published in [20] the Young's modulus and Poisson ratio of CM247 LC-EA superalloy at ambient temperature are 196.7 GPa and