*2.1. Strain Rate Effect under Uniaxial Loads*

The uniaxial experimental tests have been conducted by either tension or compression. Tensile test experiments are more common and frequent at low and medium loading rates, while the quantity of compression tests under shock conditions with the split Hopkinson bar are more numerous [18,26,32,62]. Compared to those in tension, stress-strain curves in compression tests have less recoverable strain, a steeper transformation slope, and higher critical stress. Tension-compression asymmetry is strongly dependent on the level of strain rate and temperature [63,64].

Under the uniaxial loading mode, the critical transformation stress is an important indicator of the strain rate effect on NiTi SMAs. To better explain the rate effects on the transformation stress over a wide range of strain rates, the transformation stress is constructed as a function of the strain rate by this review in Figure 2, based on the previous work by Nemat-Nasser et al. [23–25,65] and Zurbitu et al. [20,21]. On the whole, at a temperature below the maximum temperature for stress-induced martensite formation, the martensitic transformation stress (*σt*) and the austenite yield stress (*σy*) increase with strain rate. Specifically, at . < 10<sup>4</sup> s<sup>−</sup>1, stress-induced martensitic transformation always happens devoid of austenite yielding as *σ<sup>y</sup>* > *σt*, where *σ<sup>y</sup>* can be obtained using tensile experiments under high temperature. In shock conditions where . > 10<sup>4</sup> s<sup>−</sup>1, austenite yields without any martensitic transformation as now *σ<sup>y</sup>* < *σt*.

**Figure 2.** A general plot of the martensitic transformation stress (*σt*) and the austenite yield stress (*σy* ) as functions of the strain rate.

The features for the deformation mechanisms of NiTi SMAs at various strain rates can be classified into categories in five strain ranges separated by four critical strain rate values, which are 10−<sup>4</sup> s<sup>−</sup>1, 101 s<sup>−</sup>1, 103 s<sup>−</sup>1, and 104 s<sup>−</sup>1.


Experimental results and deformation mechanisms in all these five strain-rate ranges will be elaborated individually in the next section.

2.1.1. Less Than 10−<sup>4</sup> s−<sup>1</sup>

Isothermal processes are always observed in NiTi SMA experiments under very low loading rates. This is because the heat energy generated by transformation dissipated sufficiently into the environment [11–13]. In the last century, researchers measured the strain rate threshold, below which the sample temperature and transformation stress only changed in a negligible small range [11–13]. The threshold value is finally given around 10−<sup>4</sup> s<sup>−</sup>1.

According to the experimental results obtained by Shaw and Kyriakides [11], martensite nucleates at few locations and subsequently extends to all NiTi crystallites when the strain rate is below 10−<sup>4</sup> s<sup>−</sup>1. They installed four strain sensors on the wire to monitor the nuclear situation of the martensite during transformation in 70 °C water. The locations of four sensors are shown in Figure 3.

**Figure 3.** Photograph of a NiTi wire specimen with four extensometers [11]. (Reprinted from Ref. [11], Figure 8, 1995, with permission from Elsevier.)

Based on the temperature, stress, and strain histories obtained with four sensors (Figure 4a), the propagation path can be captured by connecting the transformation points between austenite and martensite along the time, as shown in Figure 4b. The stress level was not sufficient to drive multiple phase fronts in this very slow loading test; therefore, only one front propagates from one side to the other during loading and unloading. The symbol A and M represent, respectively, the region of austenite and martensite. Note that small temperature jumps were recorded (depicted with T1 squares in Figure 4a) when the A/M interface crossed the thermocouple at the middle point of the wire. The two temperature jumps peak during loading and valley during unloading, indicating rapid local loss and gain of heat, respectively, which confirms the isothermal hypothesis. It can be seen from Figure 4a that the stress roughly changes with the strain in both forward and reverse transformation under this very low strain rate.

**Figure 4.** (**a**) Temperature, stress, and strain histories at four sensor positions under a strain rate of <sup>4</sup> <sup>×</sup> <sup>10</sup><sup>−</sup>5s−1; (**b**) Location-time diagram of significant events [11]. (Reprinted from Ref. [11], Figure 11, 1995, with permission from Elsevier.)
