## 3 Test Results with Discussions
### Recovery Capacity of NiTi Foam Subjected to Dynamic Load with Discussions  
For each specimen in the SHPB test, the thickness and diameters of the specimen before loading, after loading, and after recovery, as well as the velocity of the striker bar, are recorded in Table 3. It is worth noting that the recovery is effective, but the efficiency is not 100%, implying that the foam undergoes plastic deformation in the present study. Figure 7 shows the relationship between the dynamic nominal stress (force over the undeformed specimen's cross-section area) and nominal strain (shortening over undeformed specimen thickness) of a specimen subjected to 1.0 MPa of gas gun pressure and recovery three times. In addition to the original readings, smoothed trend lines with a high frequency signal filtered are drawn to show the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Test No.**} & \multirow{2}{*}{\begin{tabular}{c} **Pressure** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Striker** \\ **Velocity** \\ **(m/s)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Before Test** \\ **(m/m)** \\ \end{tabular} } & \multicolumn{2}{c}{**After Test**} & \multicolumn{2}{c}{**After Recovery**} \\ \cline{3-10}  & & & & **Thickness** & **Diameter** & **Thickness** & **Diameter** & **Thickness** & **Diameter** \\ \hline
1-1 & 1.0 & 14.133 & 8.84 & 25.00 & 7.71 & 25.15 & 7.95 & 25.13 \\
1-2 & 1.0 & 13.414 & 7.95 & 25.13 & 7.51 & 25.41 & 7.81 & 25.35 \\
1-3 & 1.0 & 13.922 & 7.81 & 25.35 & 7.13 & 25.48 & 7.29 & 25.39 \\
1-4 & 1.0 & 13.904 & 7.29 & 25.39 & 7.00 & 25.52 & 7.05 & 25.52 \\
2-1 & 1.5 & 16.696 & 10.80 & 25.00 & 8.89 & 25.65 & 9.15 & 25.53 \\
2-2 & 1.5 & 16.467 & 9.15 & 25.53 & 7.79 & 26.47 & 8.14 & 26.10 \\
3-1 & 1.5 & 16.206 & 9.42 & 25.00 & 7.62 & 25.83 & 7.86 & 25.53 \\
3-2 & 1.5 & 16.727 & 7.86 & 25.53 & 6.75 & 25.92 & 6.93 & 25.94 \\
4-1 & 2.0 & 24.812 & 10.44 & 25.00 & 7.55 & 26.96 & 7.63 & 26.88 \\ \hline \hline \end{tabular} Note: the first digit of the test no. is specimen number, and the second digit of the test no. is the loading number for a certain specimen.  
\end{table} 
Table 3: Loading and recovery of specimens in SHPB tests. Figure 6: Specim after quasi-static failure test: (**a**) plan view; (**b**) side view. dynamic relationship. It is interesting to find that the strength of the foam increases as the number of loading and recovery cycles increases. In particular, the increase in the first loading and recovery is remarkable. The mechanism is that although the NiTi foam can recover when heated, it cannot recover to its original undeformed state. For the same reasons as the compression/recovery, the relative density of the foam increases with the test number for the same specimen, hence the increased dynamic stress-strain relationship. Subjected to 1.5 MPa of gas gun pressure, the increase in the foam strength is also observed for both specimens tested. Strain rate is defined as the derivative of strain with respect to time. It is a measurement of loading speed: the higher the loading speed, the higher the strain rate. It is the property of a material (especially the strength) under dynamic loading, and is often characterized by the Cowper-Symonds relationship:  
\[\sigma_{\text{d}}=\sigma_{\text{y}}\Bigg{[}1+\left(\frac{\dot{\epsilon}}{D} \right)^{\frac{1}{q}}\Bigg{]} \tag{1}\]  
where \(\sigma_{\text{d}}\) and \(\sigma_{\text{y}}\) are the dynamic and quasi-static strength; \(\dot{\epsilon}\) is the strain rate; and \(D\) and \(q\) are Cowper-Symonds coefficients. The \(D\) and \(q\) of steel are 600 and 5, implying that the steel is rate-sensitive while the \(D\) and \(q\) of aluminum are 6500 and 4, respectively, meaning that aluminum is rate-insensitive. As to the NiTi foam behavior indicated in Figures 7a and 8a of the current study, the gas gun launching pressures of 1.0 MPa and 1.5 MPa generates a striker velocity of 14.1 m/s and 16.7 m/s, respectively.