## 4 Results and Discussion
### Relationship between Transverse Wave Velocity and Stress  
To analyze the correlation between the transverse wave velocity and the loading stress, the average wave velocities of specimens #A-1, #A-2, and #A-3 were calculated, as well as the average wave velocities of specimens #B-1, #B-2, and #B-3. Then, the average values of the transverse wave velocity corresponding to the stress applied are demonstrated in Figure 11, in which the compressive stress is labeled with a negative sign, and tensile stress is labeled with a positive sign.  
In Figure 11, it was found that the relationship between the transverse wave velocities \(V_{v}\) or \(V_{p}\) and the stress \(\sigma\) follow linear variation, and two linear fitting lines \(V_{v}\)-\(\sigma\) and \(V_{p}\)-\(\sigma\) can be plotted. The correlation coefficients \(R^{2}\) of the linear fitting line \(V_{v}\)-\(\sigma\) and \(V_{p}\)-\(\sigma\) are 0.94 and 0.96, indicating a significant linear correlation between the transverse wave velocity and the stress. Therefore, the acoustoelastic effect of transverse waves in GIS composites is verified. Moreover, it was found that the velocities of ultrasonic transverse waves increase linearly with the compressive stress and decrease linearly with the tensile stress.  
In Figure 11, it can be found that the slopes (\(k_{v}\) and \(k_{p}\)) of the linear fitting lines \(V_{v}\)-\(\sigma\) and \(V_{p}\)-\(\sigma\) are \(-0.20\) m/s/MPa and \(-0.33\) m/s/MPa, respectively, as shown in Table 1. Substituting the slopes above into Equation (5), the acoustoelastic coefficient of transverse waves with polarization vertical to stress \(K_{v}\) is \(-1.18\)\(\times\)\(10^{-4}\)/MPa, and the acoustoelastic coefficient of transverse waves with polarization parallel to stress \(K_{p}\) is \(-1.96\)\(\times\)\(10^{-4}\)/MPa, as shown in Table 1. For comparison, the line slope and acoustoelastic coefficients of longitudinal waves in the previous study are also demonstrated in Table 1[2].  
\begin{table}
\begin{tabular}{c c c} \hline
**Ultrasonic Waves to Measure** & **Linear Fitting Line Slope** & **Acoustoelastic Coefficient \(K\)** \\
**Tangential Internal Stress** & **\(k\) (m/s/MPa)** & **(\(\times 10^{-4}\)/MPa)** \\ \hline Transverse waves with & \(-0.2\) & \(-1.18\) \\ polarization vertical to stress & & \\ \hline Transverse waves with & \(-0.3\) & \(-1.96\) \\ polarization parallel to stress & & \\ \hline Longitudinal waves [2] & \(0.141\) & \(0.456\) \\ \hline \end{tabular}
\end{table}
Table 1: The linear fitting line slope and acoustoelastic coefficients of transverse waves with polarization vertical to stress and transverse waves with polarization parallel to stress and longitudinal waves.  
Figure 11: The linear fitting line of \(V_{v}\)-\(\sigma\) and \(V_{p}\)-\(\sigma\) in the range of 0–100 MPa compressive stress and 0–50 MPa tensile stress.  
It can be found that \(k_{p}\) is larger than \(k_{p}\) and \(K_{p}\) and is larger than \(K_{p}\). This finding is consistent with the studies on acoustoelastic coefficients in metals [21]. Moreover, it can be found that the absolute slope and acoustoelastic coefficient of transverse waves with polarization parallel to stress is the largest. Considering that the slope of the linear fitting line is defined as the ratio of wave velocity change to stress change, and the acoustoelastic coefficient refers to the stress-velocity sensitivity, according to Equation (1), it can be concluded that the transverse wave with polarization parallel to stress shows the highest velocity-stress sensitivity.