## 3 Results
### Dynamic Mechanical Test Results
#### 3.2.3 Effects of Heat Treatment Temperatures on the Hysteresis Behavior of WMD  
Figure 12 illustrates the effects of heat treatment temperatures on the hysteresis behavior of WMDs. NiTi WMDs were heat-treated at 150 \({}^{\circ}\)C, 200 \({}^{\circ}\)C, and 250 \({}^{\circ}\)C for 30 min before being subjected to sinusoidal excitations at 1 Hz with amplitudes of 0.3 mm, 0.4 mm, 0.5 mm, and 0.6 mm. The shape of the symmetric hysteresis loop of the NiTi WMD hardly changes when the heat treatment temperature is below 200 \({}^{\circ}\)C. When the heat treatment temperature reaches 250 \({}^{\circ}\)C, the hysteresis loop takes a notable counterclockwise rotation, indicating a change in the loss factor and dynamic stiffness.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Relative Density**} \\ \cline{2-4}  & **0.25** & **0.31** & **0.38** \\ \hline Dynamic stiffness \(K_{\text{D}}\) (kN/mm) & 0.41 \(\pm\) 0.06 & 0.48 \(\pm\) 0.07 & 0.76 \(\pm\) 0.06 \\ Loss factor \(\eta\) & 0.49 \(\pm\) 0.01 & 0.44 \(\pm\) 0.01 & 0.33 \(\pm\) 0.01 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Dynamic performance parameters of NiTi WMD with different densities.  
Figure 11: Dynamic performance of NiTi WMDs with different densities. (**a**) Hysteresis curves of force versus displacement; (**b**) characterized dynamic stiffness and loss factor evolving with mesh density.  
As shown in Tables 7 and 8 and Figure 13, the dynamic stiffness and loss factors are calculated using Equations (2) and (6), then plotted as a function of displacement amplitude and heat treatment temperature, to better examine this phenomenon. On the one hand, the stiffness of the NiTi WMD first undergoes a drop and then increases to reach its maximum as the heat treatment temperature rises to 250 \({}^{\circ}\)C. An enormous increase in the stiffness appears when the heat treatment temperature increases from 200 \({}^{\circ}\)C to 250 \({}^{\circ}\)C, which corresponds to the spin observed from the hysteresis loop. On the other hand, the loss factor of the NiTi WMD initially decreases as it is heat-treated at 150 \({}^{\circ}\)C and subsequently climbs to its maximum when heat-treated at 200 \({}^{\circ}\)C. The damping capacity of the WMD deteriorates rapidly if a heat treatment temperature higher than 200 \({}^{\circ}\)C is used.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Amplitude**} & \multicolumn{4}{c}{**Heat Treatment Temperature (\({}^{\circ}\)C)**} \\ \cline{2-5}  & **25** & **150** & **200** & **250** \\ \hline
0.3 & 0.59 \(\pm\) 0.03 & 0.47 \(\pm\) 0.07 & 0.58 \(\pm\) 0.05 & 0.96 \(\pm\) 0.02 \\
0.4 & 0.51 \(\pm\) 0.06 & 0.45 \(\pm\) 0.03 & 0.52 \(\pm\) 0.04 & 0.86 \(\pm\) 0.01 \\
0.5 & 0.48 \(\pm\) 0.07 & 0.42 \(\pm\) 0.08 & 0.49 \(\pm\) 0.07 & 0.83 \(\pm\) 0.03 \\
0.6 & 0.45 \(\pm\) 0.11 & 0.40 \(\pm\) 0.01 & 0.47 \(\pm\) 0.02 & 0.83 \(\pm\) 0.04 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Dynamic stiffness parameters at different heat treatment temperatures.  
Figure 12: Effect of heat treatment temperature on the dynamic hysteresis behavior of NiTi WMDs with displacement amplitudes of: (**a**) 0.3 mm; (**b**) 0.4 mm; (**c**) 0.5 mm; (**d**) 0.6 mm.  
When adjusting heat treatment temperatures, there is a trade-off between the dynamic stiffness and the loss factor of the NiTi WMD. Raising the heat treatment temperature increases the WMD's stiffness while lowering the loss factor. Nevertheless, the lowest loss factor of NiTi WMD is still higher than that of the SS 304 WMD. As far as the loss factor is concerned, 200 \({}^{\circ}\)C appears to be an optimum heat treatment temperature. Temperatures above that limit may cause the rapid deterioration of the NiTi wire's damping mechanism.