## 2 Material Properties of Fe-SMA
### SME and Activation Recovery Performance  
The SME is the result of the reversible martensite transformation [12]. The corresponding relationship between the temperature and martensite fractions is depicted in Figure 2. There are four characteristic temperatures in the transformation process from low to high: martensite finish temperature (\(M_{\rm f}\)), martensite start temperature (\(M_{\rm s}\)), austenite start temperature (\(A_{\rm s}\)), and austenite finish temperature (\(A_{\rm f}\)). The martensite transformation from fcc (\(\gamma\)-austenite) to hcp (\(\varepsilon\)-martensite) is induced when the temperature decreases lower than \(M_{\rm s}\). The martensite fraction increases with the decreasing temperature, and the martensite transformation is completed until the temperature is below \(M_{\rm f}\). Adversely, the reverse transformation from hcp (\(\varepsilon\)-martensite) to fcc (\(\gamma\)-austenite) is induced when the temperature increases beyond \(A_{\rm s}\) and the martensite fraction decreases until the reverse \begin{table}
\begin{tabular}{c c c} \hline
**Stage** & **Alloys (Composition in Mass \%)** & **Year** & **References** \\ \hline Fre-30 Mn-1 Si & 1982 & [28] \\ Fre-30 Mn-6 Si & 1984 & [29] \\ Fre-32 Mn-6 Si & 1986 & [58] \\ Fre-28 Mn-6 Si-5 Cr & & \\ Fre-20 Mn-5 Si-8 Cr-5 Ni & 1990 & [48] \\ First stage: & Fe-16 Mn-5 Si-12 Cr-5 Ni & & \\ optimization of alloy elements & Fe-30 Mn-6 Si & 1995 & [54] \\ Fre-28 Mn-6 Si-5 Cr & & 2001 & [46] \\ Fe-18 Mn-8 Cr-4 Si-2 Ni-0.36 Nb-0.36N & 2002 & [46] \\ Fe-30 Mn-6 Si & & \\ Fe-30 Mn-6 Si-5 Cr & 2002 & [51] \\ Fe-13 Mn-5 Si-12 Cr-5 Ni & & \\ Fe-25 Mn-6 Si-5 Cr-0.14N & 2006 & [53] \\ \hline Fre-28 Mn-6 Si-5 Cr-0.5(Nb,C) & 2001 & [55] \\ Fre-28 Mn-6 Si-5 Cr-1(V)N & 2004 & [56] \\ Fe-15 Mn-5 Si-5 Cr-5 Ni-(0.5-1.5)NbC & 2005 & [59] \\ Second stage: & Fe-28 Mn-6 Si-5 Cr-0.5(3 Nb)-0.06C & 2006 & [60] \\ introduction of fine precipitates & Fe-14 Mn-5 Si-8 Cr-4 Ni-0.16C & 2007 & [61] \\ Fre-17 Mn-5 Si-10 Cr-4 Ni-1(V,C) & 2009 & [57] \\ Fe-16 Mn-5 Si-10 Cr-4 Ni-1(V,N) & 2013 & [44] \\ Fe-19 Mn-4 Si-8 Cr-4 Ni-0.01C & 2021 & [35] \\ \hline \end{tabular}
\end{table} 
Table 1: The most significant Fe-Mn-Si alloys in the development history. transformation is completed with the temperature higher than \(A_{\rm f}\)[62; 63]. In Table 2, the characteristic temperatures in the phase transformation of several typical Fe-SMA are compared. Notably, in the absence of external force, the martensite transformation induced only by temperature change will not cause macroscopic deformation. The SME of Fe-SMA is illustrated in Figure 3a [67; 68]. Pre-stretching the alloy at ambient temperature (\(T<A_{\rm s}\)), it deforms macroscopically (Path 1). The macroscopic deformation includes four parts: elastic deformation, recoverable deformation, pseudoelastic deformation, and plastic deformation. After unloading, the elastic and pseudoelastic deformations can be recovered (Path 2). Then, with raising the temperature higher than \(A_{\rm s}\), the reverse martensitic transformation is induced, in which the recoverable deformation gradually diminishes until the temperature is beyond \(A_{\rm f}\) (Path 3). The residual deformation is only the plastic deformation. Without external force, the cooling stage does not experience macroscopic deformation (Path 4). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Alloys** & \(M_{\rm f}\) (\({}^{\circ}\)C) & \(M_{\rm s}\) (\({}^{\circ}\)C) & \(A_{\rm s}\) (\({}^{\circ}\)C) & \(A_{\rm f}\) (\({}^{\circ}\)C) & **Refs.** \\ \hline Fe-30 Mn-1 Si & — & 27 & 127 & — & [28] \\ Fe-28 Mn-6 Si-5 Cr & — & 20 & 120 & 180 & [64] \\ Fe-14 Mn-6 Si-9 Cr-5 Ni & — & 20 & 70 & 300 & [65] \\ Fe-17 Mn-5 Si-10 Cr-4 Ni-1(V,C) & \(-90\) & \(-75\) & 85 & 110 & [57] \\ Fe-17 Mn-5 Si-10 Cr-4 Ni-1(V,C) & \(-64\) & \(-60\) & 103 & 162 & [66] \\ Fe-19 Mn-4 Si-8 Cr-4 Ni-0.01C & \(-100\) & \(-38\) & 138 & 218 & [35] \\ \hline \end{tabular}
\end{table} 
Table 2: Martensite transformation temperatures of Fe-SMA.