## 3 Mechanical Performance of Fe-SMA
### Cyclic Mechanical Properties  
When reinforcing structures, the mechanical properties of Fe-SMA under cyclic load, such as pseudo-static and fatigue load, are noteworthy and crucial. In this regard, the Empa Institute has carried out some relevant studies, in which the alloy elements are Fe-17 Mn-5 Si-10 Cr-4 Ni-1(V,C).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Alloys** & **Elastic Modulus** & \(\sigma_{\text{y,0,2}}\) & **Ultimate Strength** & **Ultimate Strain** & **References** \\  & **(Gpa)** & **(MPa)** & **(MPa)** & **(MPa)** & **(\%)** & **References** \\ \hline \multirow{6}{*}{Fe-17 Mn-5 Si-10 Cr-4 Ni-1(V,C)} & 194 & 476 & 950 & 45 & [15] \\  & 184 & 450 & 950 & 54 & [31] \\  & 160 & 535 & \(\approx\)1000 & 47 & [67] \\  & 173 & 546 & 1015 & 54.9 & [83] \\  & 200 & 310 & 993 & 15.4 & [84] \\ \hline Fe-Mn-Si alloys & 133 & 463 & 863 & 12.4 & [79] \\ \hline Fe-Mn-Si alloys & 186 & 490 & 894 & 35.5 & [82] \\ \hline Fe-17 Mn-5 Si-5 Cr-0.3C-1T & 125 & 599 & 1140 & 22.56 & [85] \\ \hline Fe-17 Mn-5 Si-5 Cr-4 Ni-0.1C & 123 & 410 & 1080 & 39.51 & [85] \\ \hline Fe-15 Mn-4 Si-10 Cr-8 Ni & 184 & 260 & 676 & 74 & [86] \\ \hline Fe-Mn-Si alloys & 172 & 298 & 774 & 48.05 & [87] \\ \hline \hline \end{tabular}
\end{table}
Table 4: Mechanical properties of Fe-SMA.  
Figure 5: Stress–strain curves of Fe-SMA [15; 79; 80; 81; 82].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Materials** & **Density** & **Elastic Modulus** & **Thermal Expansion** & **Poisson Ratio** & **Elongation** & **Ultimate Strength** \\  & **(kg/m3)** & **(GPa)** & **(K-1)** & **Poisson Ratio** & **(\%)** & **(MPa)** \\ \hline Fe-SMA & 7200–7500 & 170 & 16.5 \(\times\) 10\({}^{-6}\) & 0.359 & 16–30 & 680–1000 \\ \hline Steel–Q235 & 208 & & & 25 & 467 \\ Steel–Q355 & 7860 & 206 & 11–13 \(\times\) 10\({}^{-6}\) & 0.294 & 25 & 533 \\ Steel–Q690 & 218 & & & 7 & 990 \\ \hline Concrete & 1950–2500 & 32.5 & 12 \(\times\) 10\({}^{-6}\) & 0.18–0.21 & — & — \\ \hline \hline \end{tabular}
\end{table}
Table 3: Physical parameters of Fe-SMA, steel, and concrete [32; 74; 75; 32].  
[PERSON] et al. [83] studied the pseudo-static performance of Fe-SMA with a 1% strain increment, and the loading curves are presented in Figure 6a. The hardening of Fe-SMA occurs under cyclic load, due to the corresponding stress in the pseudo-static process being higher than that in the static tensile process. According to the study by [PERSON] et al. [84], the stress corresponding to the pseudo-static tensile strain of 9% is about 60 MPa higher than that in the static tensile test. Additionally, owing to the pseudo-elasticity of Fe-SMA, the unloading process of hysteresis curves does not follow Hooke's law, and this discovery is of great significance for the energy dissipation capacity of Fe-SMA.  
The fatigue properties of Fe-SMA were investigated by [PERSON] et al. [84]. When a fatigue stress of \(\pm\)230 MPa was applied based on 300 MPa pretension stress, the Fe-SMA members could withstand a fairly high number of loading cycles without fatigue fracture. The fatigue limit of Fe-SMA under 2 \(\times\) 10\({}^{6}\) loading cycles is 450 MPa, much higher than its yield strength (\(\sigma_{y0.2}\) = 371 MPa), and the transition stress between high-cycle and low-cycle fatigue is about 500 MPa. [PERSON] et al. [83] studied the fatigue performance of Fe-SMA after activation. Based on the recovery stresses of 359-372 MPa, fatigue load with strain amplitudes (\(\Delta\varepsilon\)) of 0.035% and 0.07% was applied to the Fe-SMA members (as shown in Figure 6b), and the alloy did not undergo fatigue fracture after 2 \(\times\) 10\({}^{6}\) loading cycles. The above fatigue properties of Fe-SMA shall be considered in the design of structural reinforcements.