# Recovery Behavior of Fe-Based Shape Memory Alloys under Different Restraints
## 4 Result and Discussion
### Fe-SMA Behavior under Rigid Restraint  
#### 4.3.1 Effect of Pre-Straining  
The temperature-stress relations that rely on the alloy type, pre-strain and heating temperatures under rigid restraint are summarized in Table 2. Figure 7 shows the comparison of temperature-recovery stress curves by pre-strain under rigid restraint. The recovery stress at maximum temperature (\(\sigma_{m,T}\)) for the FSMA-A specimen with 0.02 to 0.06 of pre-strain was approximately 94 MPa. While the recovery stress within the range of 0.02 to 0.06 of pre-strain was slightly increased, the recovery stress at the maximum temperature in pre-strain specimen of 0.08 decreased to 73 MPa which is 22.8% lower. The final recovery stress (\(\sigma_{f}\)) for the FSMA-A specimen in the range of 0.02 to 0.04 of pre-strain were similar to each other. Subsequently, the recovery strain gradually grew 10 MPa in every 0.02 of the pre-strain increase. Also, the maximum recovery stress (\(\sigma_{m}\)) and final recovery stress (\(\sigma_{f}\)) in the range of 0.02 to 0.08 were analogous to each other and short-term relaxation was not involved.  
Figure 6: Comparison of temperature-recovery strain curves under free restraint.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type of SMA** & **Residual Strain** & **Strain at 200 °C** & **Strain after Activation** & **Recovery Strain** \\ \hline FSMA-A & 0.03033 & 0.02406 & 0.02077 & 0.00956 \\ \hline FSMA-B & 0.03214 & 0.02103 & 0.01769 & 0.01445 \\ \hline FSMA-C & 0.03234 & 0.01703 & 0.01257 & 0.01977 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Summary of activation test result under free restrains.  
Figure 7: \(Cont.\)In contrast to the FSMA-A specimen, the recovery stress at the maximum temperature (\(\sigma_{m,T}\)) steadily decreased 10 MPa for every 0.02 of pre-strain increase. However, the maximum recovery stress (\(\sigma_{m}\)) and final recovery stress (\(\sigma_{f}\)) were not affected by the increase of pre-straining in the FSMA-B specimen. This is because any pre-strain over 0.02 does not affect to the recovery stress in Fe-SMA [20]. With the same pre-strain level, the final recovery stress (\(\sigma_{f}\)) in the FSMA-B specimen was approximately 19% smaller than one in the FSMA-A specimen. This is due to the fact that the recovery stress depends on the yield strength rather than the recovery strain [2]. The maximum recovery stress (\(\sigma_{m}\)) and final recovery stress (\(\sigma_{f}\)) with 0.02 of pre-strain in the FSMA-B specimen are 381 MPa and 364 MPa. The short-term relaxation of the FSMA-B specimen is evaluated at 17.21 MPa. Afterward, the short-term relaxation gradually decreased as the pre-strain increased. The short-term relaxations in pre-strains of 0.06 and 0.08 are 0.4 MPa and 0.13 MPa.  
In a similar manner as the FSMA-B specimen, the recovery stress at the maximum temperature (\(\sigma_{m,T}\)) in the FSMA-C specimen decreased 11 MPa for every 0.02 of pre-strain increase. The recovery stress at the maximum temperature (\(\sigma_{m,T}\)) in the FSMA-C was 13% higher than the one in the FSMA-B at the same pre-strain. The magnitude of the pre-strain did not affect the maximum recovery stress (\(\sigma_{m}\)) and final recovery stress (\(\sigma_{f}\)). The maximum recovery stress (\(\sigma_{m}\)) and final recovery stress (\(\sigma_{f}\)). in the FSMA-C were different by 8.2% and 0.7% from the FSMA-B and the relaxation gradually decreased according to the increase in the pre-strain value. In the case of a pre-strain of 0.08, the short-term relaxation did not develop. However, short term relaxation of the FSMA-C, which had heating treatment, developed more than 50% when compared to the one in the FSMA-B.  
Figure 7: Comparison of temperature-recovery stress curves by pre-strain under rigid restraint.