**2. Basic Properties**

Prior to the introduction of the application of Fe-SMA, it is necessary to have a comprehensive understanding of its basic characteristics. Typical physical properties of Fe-SMA together with other important steel types are listed in Table 1. The Fe-SMA presented in the table is Fe-17Mn-5Si-10Cr-4Ni-1(V,C) (mass%), which is one of the most typical classes. Other classes will be expressed in the form of their compositions when they are discussed.


**Table 1.** Physical properties for SMAs and conventional structural steels [5,11–13].

## *2.1. Metallographic Transformation in Fe-SMA*

When a metallic substance is subjected to an external force, metallographic transformation process is triggered. At the micro-level, the crystal lattice matrix is rearranged and the atoms move in a particular way. The accumulated movements of the atoms on the microscopic scale directly leads to deformation of the metal on a macroscopic scale [5]. Fe-SMA has three types of metallographic phases, i.e., γ-austenite (face-centered cubic structure, fcc), ε-martensite (hexagonal close-packed structure, hcp), and α'-martensite (body-centered tetragonal structure, bct). Schematic illustrations of these crystal lattices

are shown in Figure 1. The metallographic transformation between γ-austenite and εmartensite (so-called 'martensitic transformation') occurs when the material is under an applied force and/or a temperature change, and thus the martensitic transformation of Fe-SMA can be categorized into stress-induced martensitic transformation and thermalinduced martensitic transformation.

**Figure 1.** Micro-structure of crystal lattices: (**a**) γ-austenite; (**b**) ε-martensite; (**c**) α'-martensite.

The principle of thermal-induced martensitic transformation and its reverse process can be readily understood by the following description. As seen in Figure 2, four typical phase-transformation temperatures, i.e., martensite start temperature (*M*s), martensite finish temperature (*M*<sup>f</sup> ), austenite start temperature (*A*s), and austenite finish temperature (*A*<sup>f</sup> ), are representative ones related to the start and finish of martensitic transformation or its reverse process. When the initial temperature is high and it decreases to *M*s, the transformation from γ-austenite to ε-martensite starts and then the ε-martensite fraction in Fe-SMA increases gradually. When the temperature drops below *M*<sup>f</sup> , the transformation process is completed and the ε-martensite fraction in Fe-SMA reaches its maximum value (i.e., ζ in Figure 2). For the reverse transformation, when the rising temperature reaches *A*s, the ε-martensite starts to transform into the γ-austenite phase, and this process continues until the temperature increases beyond *A*<sup>f</sup> , where the ε-martensite is transformed into γaustenite completely. Table 2 gives the measured results of the critical phase-transformation temperatures of typical SMAs.

**Figure 2.** Schematic definition of thermal-induced martensitic transformation of Fe-SMA. ζ denotes the maximum martensite fraction, and 0 < ζ < 1.

**Table 2.** Phase-transformation temperatures of SMAs.


The martensitic transformation of Fe-SMA has two characteristics which directly promote its unique mechanical behavior: (1) The stacking fault energy required for martensitic transformation is low, which makes the martensitic transformation easy to occur [5], (2) The martensitic transformation is a diffusionless phase transformation process (i.e., it creates a new crystal structure without introducing any compositional change) [5], making its reversible martensitic transformation possible. The former gives the basis on why the transformation between γ-austenite and ε-martensite would take place first when Fe-SMA is exposed to external force and the latter explains the basic mechanism of pseudo-elasticity & shape memory effect (this part will be further described in Section 2.3). More detailed descriptions of the martensitic transformation from a perspective of crystallography can be found elsewhere [5,17].

## *2.2. Monotonic Loading Property*

Figure 3 compares the typical monotonic stress-strain curves of Fe-SMA with those of other structural steel, i.e., austenitic stainless steel S30408, low point steel LYP100, mild steel Q355, high-strength steel Q690 and aluminum alloy 7A04-T6. The stress-strain responses of Fe-SMAs seem to be similar to that of stainless steel, although the strength of the former is higher. Since there is no yield plateau in Fe-SMA, 0.2% proof stress is considered as an equivalent yield strength. The comparison of the basic mechanical properties between Fe-SMA and other metals is summarized in Table 3. The Young's moduli of the Fe-SMAs are generally comparable to, and may be slightly lower than, those of steel (except for aluminum alloy). High ultimate strengths (*f* <sup>u</sup> > 700 MPa) and remarkable ductility are observed in the Fe-SMAs, characteristics which are encouraging for seismic application. The yield to ultimate strength ratio of Fe-SMA is around 0.4, indicating a pronounced strain hardening behavior. Fracture of Fe-SMA occurs soon after reaching the ultimate strength, indicating an inadequate necking process. This feature can be more clearly reflected when compared with conventional structural steel (such as mild steel Q355) where a significant localized shrinkage appears before fracture, as shown in Figure 4. This phenomenon also indicates that the ductility of Fe-SMA is mainly derived from its evenly distributed plasticity rather than localized necking. Apart from these characteristics, Fe-SMA is also reported to possess a higher yield strength at higher strain rates [18], which may make Fe-SMA an ideal material for blast-resistant structures, but no such study is currently available.

**Figure 3.** Typical full stress-strain curves of Fe-SMA and other typical structural steels [19–24].


**Table 3.** Mechanical properties of different metallic materials under quasi-static monotonic loading tests.

Notes: *E*<sup>0</sup> refers to Young's modulus; *f* <sup>y</sup> refers to yield strength; f<sup>u</sup> refers to ultimate tensile strength (UTS); *f* u2 refers to fracture stress; *ε*<sup>u</sup> refers to the strain corresponds to UTS; *ε*u2 refers to the strain till fracture; *EL* refers to elongation after fracture.

**Figure 4.** Macroscopic fracture behavior of (**a**) Q355 and (**b**) Fe-SMA under monotonic loading.

The evolution law of metallographic transformation during monotonic loading process [29–34] can be described as follows: the initial phase of Fe-SMA specimen can be considered pure γ-austenite since it is annealed during manufacturing, a process which is equivalent to the reverse transformation mentioned above. As the stress (or strain) increases, part of the parent γ-austenite gradually transforms into ε-martensite (see Path 1 in Figure 5), and this leads to a deviation of the monotonic stress-strain curve from the linear relationship [5,35]. As the stress further increases (see Path 2 in Figure 5), α'-martensite, whose structure is formed through the lattice expansion of fcc and hcp structures, is discovered in the field of γ-austenite and ε-martensite [5,9]. This transformation process continues until fracture. It is highlighted that when the material is loaded under a high service temperature, the formation of stress-induced ε-martensite may be strongly hindered, and this process is replaced by a direct transformation from parent γ-austenite to α'-martensite (see Path 5 in Figure 5).

**Figure 5.** Evolution law of metallographic transformation for Fe-SMA under different thermalmechanical states.

#### *2.3. Pseudo-Elasticity and Shape Recovery Property*

Hooke's law holds true for normal steel during both the loading and unloading stages. However, a nonlinear spring-back curve deviating from the linear path exists in Fe-SMA upon unloading (see Figures 6 and 7a). This unique phenomenon is called pseudo-elasticity [36–42], which is associated with the partial reverse transformation of the previously formed stressinduced ε-martensite. However, due to the limited fraction of stress-induced ε-martensite, the phenomenon of pseudo-elasticity is limited, i.e., much less significant than Nitinol [21,23,43,44]. In any case, the moderate pseudo-elasticity could still benefit residual deformation control during dynamic shakedown, as discussed later in Section 2.4.

**Figure 6.** Pseudo-elasticity phenomenon of Fe-SMA.

**Figure 7.** Schematic diagram of (**a**) activation process of shape recovery property, and (**b**) generation of recovery stress.

Shape recovery property, also known as shape memory effect (SME), is activated by heating the deformed material. The aforementioned thermal-induced ε→γ transformation contributes to the SME of Fe-SMA elements. Considering a Fe-SMA bar which is subjected to axial elongation and subsequently unloaded, residual deformation occurs, like normal steel. If the residual deformation of this bar is constrained, recovery stress (pre-stress) is generated after heating and cooling. Figure 7b illustrates the development of recovery stress (corresponding to path 4 in Figure 5). In the initial heating stage, stress relaxation is observed due to thermal expansion (path A→B). When the temperature reaches *A*s, thermal-induced ε→γ transformation is triggered and the recovery stress starts to coun-

teract thermal expansion. This process continues until the temperature increases to the predefined maximum temperature (path B→C). During the cooling stage (e.g., air cooling), a tensile stress is generated due to contraction and thus further recovery stress is induced, which first increases linearly with decreasing temperature (path C→D). As the tensile stress increases to a threshold of the minimum value for triggering the stress-induced martensite transformation, Fe-SMA again enters into the plastic stage. Consequently, a 'yield' phenomenon is observed (point D) and the stress-temperature curve becomes nonlinear (path D→E). Point E is the final recovery stress produced in this process. It is noteworthy that the preload level (i.e., path 1 in Figure 5) should be controlled within a moderate range to avoid the formation of α'-martensite, since the reverse transformation process cannot be realized when the material is in the α'-martensite state [9]. In other words, α'-martensite is responsible for the irreversible plasticity, i.e., unrecoverable plastic strain or permanent deformation.

When Fe-SMA is employed as a measure of prestressing, the amount of prestress is the property of most concern to engineers. With the aim of increasing the shape recovery properties, many research groups across the world have been devoted to developing improved production and manufacturing processes, including but not limited to thermal mechanical training, adjusting the chemical compositions and heat treatment [45–71]. These efforts greatly enhance the reliability of Fe-SMA as an emerging prestressing strategy. For engineering practice, a satisfactory prestress level can be achieved by pre-loading and heating the Fe-SMA in an appropriate way. Table 4 summarizes the reported recovery stress (*f* <sup>R</sup>) of Fe-SMA generated from different activation conditions. A pre-strain level of 2–4% seems to be an optimum range to achieve a satisfactory recovery stress (300–450 MPa) when the activation temperature is below 200 ◦C [14,21,41,72]. It is also interesting to find that concurrently applying a higher activation temperature (350 ◦C) and a larger prestrain level (6–8%) is beneficial for producing a larger recovery stress (which is almost 30% higher than that activated at 200 ◦C) [73]. An increase in the activation temperature may cause problems to concrete but is acceptable for steel structures [74]. Instead of applying monotonic pre-strain, researchers have also examined the recovery stress of Fe-SMA upon heating after experiencing tension-compression strain cycles, where the shape recovery capability is decreased [75]. One possible reason is that the compression history worsens the micro-structural environment for the reverse martensitic transformation process.

## *2.4. Cyclic Behavior, Low Cycle Fatigue and Energy Dissipation Capacity*

The potential of Fe-SMA as energy-dissipating material was not recognized until 2006, when its stable hysteretic behavior and excellent low cycle fatigue resistance were first identified by Sawaguchi et al. [77]. For seismic application, it is essential to clarify the mechanical behavior of Fe-SMA under cyclic loading [78–94]. In this section, some basic properties of Fe-SMA under cyclic loading are discussed.

#### 2.4.1. Hysteretic Behavior

Obtaining the hysteretic behavior under symmetrical cyclic loading is often a first and standard procedure to understand the basic performance of a member or material during earthquakes [95–100]. Figure 8a shows typical stabilized hysteretic loops (taken from half-life cycle response) of Fe-SMA and steel, where the curves are divided into the elastic (linear) part, transition part and hardening part. It is found that the loop shape of the Fe-SMA is slightly narrower than that of the mild steel. An early spring-back phenomenon, which results from the aforementioned pseudo-elasticity, is displayed during the unloading process, leading to a smaller elastic region. In addition, Fe-SMA shows a more obvious strain hardening response, whereas the mild steel shows little hardening with an almost flat stress-strain curve in the hardening part. It is reasonable to deduce that the residual deformation of structures with Fe-SMA-based components would be reduced during earthquake conditions, since the spring-back self-centering trend, together with a relatively large post-yield hardening, could effectively promote a self-centering capability of the system under dynamic shakedown [101,102]. Figure 8b further presents the full incremental stress-strain responses as well as the skeleton curves (obtained from connecting the peak stresses of the hysteretic loops) of Fe-SMA and mild steel.


1 'SP' refers to the sheet plate specimen, and is expressed in the form of 'thickness <sup>×</sup> width'; <sup>2</sup> The pre-strain process is performed under room temperature environment; <sup>3</sup> '*f* <sup>R</sup>' refers to the recovery stress of Fe-SMA.

**Figure 8.** Comparison of (**a**) Decomposed hysteretic loops; and (**b**) Skeleton curves obtained from stabilized hysteretic loops of Fe-17Mn-5Si-10Cr-5Ni and mild steel (Q235).

Researchers have reported that the hysteretic loops of Fe-SMA can quickly saturate regardless of the strain range so that the peak stress is stable until failure [23]. However, according to the findings reported by Rosa et al. [26], a slight cyclic softening behavior (i.e., decrease in peak stress) appears when the strain rate reaches 0.08/s, which is an expected strain rate considering a real earthquake excitation [103]. Further research opportunity exists in comprehensive understanding of the rate effect of the material, especially in the context of seismic application.

Figure 9 presents the stabilized hysteretic loops at different strain amplitudes by moving their compressive corners to the same coordinate origin. If the ascending curves of these hysteresis loops coincide, i.e., a master curve can be drawn in accordance with the ascending curves, the material is deemed to possess Masing behavior. Previous research [84] reported that Masing behavior can be observed in Fe-SMA when the strain amplitudes are less than ±2%, as shown in Figure 9a. However, when the strain amplitude increases, the ascending branches of the saturated hysteresis loops deviate from the master curve and represent a non-Masing behavior (Figure 9b). Microstructural observations reveal that the adaptability of Fe-SMA to Masing behavior is related to its micro-deformation patterns. When the strain amplitude is moderate (e.g., not exceeding ±2%), the strain-induced martensitic transformation accompanied by a planar slip of Shockley partial dislocations in austenite is the main deformation mode [84]. However, when the strain amplitude advances to a larger range, the micro-deformation pattern is dominated by the formation of mechanical-twinning [90].

**Figure 9.** Adaptability of Fe-SMA to Masing behavior under (**a**) small strain ranges [84]; and (**b**) large strain ranges [23].

#### 2.4.2. Low Cycle Fatigue (LCF) Behavior

Large-size Nitinol elements are often criticized for their brittle fracture behavior and poor LCF resistance [104–107]. Figure 10 and Table 5 summarize the LCF lives of some typical steels. It can be seen that Fe-SMA possesses significantly longer LCF life than conventional steels. This remarkable property results from the evolution of cyclically deformation-induced ε-martensitic transformation, in contrast to dislocation-based plasticity with irreversible slip in normal steels. As demonstrated in Figure 11, the parent γ-austenite phase partially transforms into a tension-induced ε-martensite during the loading process. During the unloading stage, the tension-induced martensite gradually diminishes and returns back to γ-austenite. When subjected to compression towards negative strain, compression-induced ε-martensite is generated in the field of γ-austenite [77,78]. The phase transformation of the re-loading stage is similar to that of the aforementioned unloading stage, and the repeated tension-compression cyclic loading process induces alternate formation and disappearance of stress-induced ε-martensite. The repeated phase transformation is beneficial in reducing the internal stress concentration caused by cyclic loading and inhibiting local accumulation of dislocations and hence the initiation and propagation of fatigue cracks [88].

**Figure 10.** Comparison of fatigue lives between Fe-SMA and other typical metals [23,108,109].

**Table 5.** Numbers of cycles to failure of different metals.


**Figure 11.** Phase transformation during cyclic tension-compression process for Fe-SMA.

#### 2.4.3. Energy Dissipation

The equivalent viscous damping ratio (EVD), as defined in Equation (1), is considered to evaluate the energy dissipation capacity of Fe-SMA specimens under fully reversed cyclic loading.

$$\text{EVD} = \frac{1}{2\pi} \frac{E\_D}{E\_S} \tag{1}$$

In the equation, *E<sup>D</sup>* is the area within the inelastic force-displacement response curve, and *E<sup>S</sup>* is the recoverable elastic strain energy stored in an equivalent linear elastic system [110]. The EVDs of different metals under half-life cycle are plotted in Figure 12a. It can be seen that the EVDs of Fe-SMA are lower (decreased by about 20%) than that of conventional steel. This is mainly attributed to its strain hardening behavior, resulting in a narrower hysteresis loop shape. The early spring-back behavior also decreases the *E<sup>S</sup>* of Fe-SMA to some degree. On the other hand, the absolute energy dissipation *WD*, which is calculated by the area of the stabilized stress-strain curves, shows that Fe-SMA could be have more energy dissipation, especially at larger strain amplitudes (see Figure 12b). More importantly, due to the excellent LCF resistance, the total energy dissipation (accumulation of *ED*) of Fe-SMA is much larger than that of normal steel with the same geometric size.

**Figure 12.** Parameters for evaluating energy dissipation capacity under different strain amplitudes: (**a**) EVDs; and (**b**) Absolute energy dissipation at half-life cycle. Results are re-produced from [23,25].

#### **3. Research and Potential Engineering Applications**

Early application of Fe-SMA in civil engineering began in the 1990s, where focus was mainly on special connections, such as railway fishplates, crane rail joint plates, and pipe connection devices for tunnel construction [5,9,17,111]. These connections are tightened via the SME of Fe-SMA. The SME-triggered tightening method greatly simplifies the construction/prestressing process.

Recent research and development activities enable a wider use of Fe-SMA in the construction industry. In particular, the research and application of Fe-SMA over the past 10 years can be mainly divided into two fields: (1) SME-induced prestressing technique for repairing and strengthening structures [112–139], and (2) seismic damping [23,28,75].
