**1. Introduction**

NiTi Shape Memory Alloys (SMAs) are the most widely used in the shape memory material family, and have important applications in electronic components, medical devices, shock absorption devices, etc., thanks to their unique thermomechanical behaviors [1–4]. Reliable and predictive simulations of NiTi SMA wires under high strain rates are always required for actuation and auxiliary control. An example of a hybrid device with SMA wires is shown in Figure 1, which is designed for anti-seismic structure to restrict the strain within 6% [5]. These growing demands push investigations on both quasi-static and dynamic responses of NiTi SMAs [6–10].

Researchers have conducted experiments on NiTi SMAs at a wide range of strain rates and most experiments have been under uniaxial loads [11]. While the SMA specimens could be bars, wires, or plates depending on the specific experiments, general observations and mechanisms could be extracted and summarized regardless of the shape and size of specimens. The stress responses and temperature evolutions during transformation have varied depending on the strain rate. At a very low strain rate . < 10−4s−1, the stress and temperature scarcely changed since the latent heat dissipated to surroundings sufficiently [11–13]. As the strain rate rises to 10−4s−<sup>1</sup> <sup>&</sup>lt; . < 10−1s−1, the stress and temperature increases with increasing strain rate because part of the heat by transformation is left in the material [11,14–16]. The heat exchange rate between the specimen and the environment is found to be greatly influenced by the temperature rise in this strain rate range, as demonstrated in a comparison test by Shaw and Kyriakides [11] between water-enclosed and air-enclosed NiTi SMA wires. In the medium range of strain rate <sup>10</sup><sup>−</sup>1s−<sup>1</sup> <sup>&</sup>lt; . < 103s−1, the stress stopped increasing but the temperature increased quickly since an adiabatic process was reached [17–21]. A quickly-recovered residual strain was reported by Chen et al. [17] around 81~750 s<sup>−</sup>1, which was ascribed to the significant thermal

**Citation:** Wang, Z.; Luo, J.; Kuang, W.; Jin, M.; Liu, G.; Jin, X.; Shen, Y. Strain Rate Effect on the Thermomechanical Behavior of NiTi Shape Memory Alloys: A Literature Review. *Metals* **2023**, *13*, 58. https:// doi.org/10.3390/met13010058

Academic Editor: Lara Righi

Received: 28 November 2022 Revised: 16 December 2022 Accepted: 19 December 2022 Published: 25 December 2022

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

hysteresis as a result of an adiabatic process. In strain rates between 103s−<sup>1</sup> <sup>&</sup>lt; . < 104s−1, a sudden rise of the critical transformation stress takes place, and this can be attributed to the drag effect of dislocations surrounding the phase interface [22]. Nemat-Nasser et al. [23–25] observed considerably increased rate sensitivity and curved interfaces of martensite in TEM micrographs. The final strain rate range was . > 104s−1, in which plastic deformation occurs in austenite without martensitic transformation because martensitic transformation no longer satisfies the demand of quick deformation [24,26–28].

**Figure 1.** (**a**) Hybrid device with SMA wires and (**b**) different configurations of the proposed device [5]. (Reprinted from Ref. [5], Figure 21.1, 2021, with permission from Elsevier.)

Furthermore, the nucleation and propagation of phase transformation under various strain rates have also been investigated by many researchers [11,29,30]. When the strain rate is very low, the martensite nucleates at a few locations and then extends to all fields [11,29,31]. As the strain rate increases, the number of nucleation locations grows, and martensitic transformation domains propagate in a parallel mode rather than entirely [30,31].

Compared to uniaxial tests, experiments under shear and indentation have been conducted less frequently [32]. Simple shear tests on NiTi SMAs were performed early by Manach and Favier [33], while a more comprehensive study within a wider range of strain rates from 10−<sup>4</sup> s−<sup>1</sup> to 103 s−<sup>1</sup> was accomplished by Huang et al. [34]. As for indentation tests, Amin et al. [35] and Shahirnia et al. [36] both pointed out that the maximum indentation was influenced by the loading rate. In cases of cyclic loading, superelasticity degeneration and temperature variations have been found to be strongly dependent on the strain rate [37,38].

Besides the loading mode, microstructure also has an important impact on the ratedependent behaviors of NiTi SMAs [25,39–41]. The influences of R-phase, precipitated phase, and grain size on the strain rate responses of general SMAs have been explored in many studies [39,40,42,43]. The influence of R-phase transformation on the strain effect sensitivity has been investigated by Helbert et al. [39] on NiTi SMA wires. The precipitation evolution of Ni4Ti3 and transformation behaviors have been studied and characterized by Fan et al. [42] in quasi-static loading and Yu et al. [43] in impact loading. The grain size influenced the amount of transformable martensite and heat generation, and therefore influenced the temperature field and transformation stress [40]. For porous and composite SMAs, higher strain rates brought in a greater transformation stress similar to general NiTi SMAs [25,41].

Modeling the strain rate effect of NiTi SMAs at low and medium strain rates is focused on characterizing and qualifying the thermal effect during transformation, where the latent heat plays an important role. Thermal source models were proposed to represent the strain rate effect as extra heat sources added to the energy equation [44–47]. The thermodynamic potential is usually adopted in thermal source models to derive the temperature evolution equation, and can be obtained either empirically or theoretically [48,49]. Many simulations have been performed at strain rates ranging from very low to medium on the basis of the thermal source models, and their predictions have matched well with experiments at corresponding strain rates [50–55]. However, the drag effect surpasses the thermal effect at high strain rates. By considering the kinetic effect and adding a resistance force into the constitutive relationship, thermal kinetic models have been extended from thermal source models to describe the thermomechanical behaviors of NiTi SMAs at high strain rates [56–58].

Multiple studies have conducted experiments and developed models for the deformation behaviors of NiTi SMAs under various strain rates. However, there is hardly any systematic analysis of the strain rate effect, except for some subsections touching on the strain rate effect in general reviews for NiTi SMA microstructure evolution and thermodynamic behaviors [59–61]. Therefore, this paper aims to present a comprehensive review and summarize the common physical mechanisms of the strain rate effects in a wide strain-rate range from quasi-static to dynamic loading. The strain rate effect under uniaxial loads will be elaborated in the first place since the number of uniaxial tests is the largest. The rate effect under other loading modes, such as shear, indentation, and cyclic loading, will be discussed later. A brief summary of the dependence of the strain rate effect on microstructure is presented at the end of Section 2. Section 3 recapitulates the main constitutive models capturing the strain rate effect. The approach is to construct the thermal source model which will first be introduced and then followed by a discussion of thermal-source components. Thermal kinetic models will be discussed next. Simulation examples will be given in both models. Final remarks with future research directions are given in Section 4.
