**1. Introduction**

Shape memory alloys (SMAs) are insightful types of materials that is designed to undertake the phase transformation of martensitic phase once the thermomechanical loads are employed, and also in a position to restore their initial form as soon as heated up above particular temperatures [1–3]. A couple of symmetries take place for the structural morphologies within this kind of the materials; high symmetry at high-temperature is known as austenite and also a low symmetry at lower temperatures known as martensite. The martensitic transformation that starts for the transformation of austenite (high temperature phase) ⇄ martensite (low temperature phase), is the principal characteristic in charge of shape memory alloys features. Furthermore, this transformation is prominent as diffusionless solid-state step of transformation which is presented by means of nucleation, accompanied by the formation route of the relative austenitic phase [4, 5]. Due to the pseudo-elasticity and shape memory effect (SME) properties, the shape memory alloys have been remarkably distinguished compared to other types of materials [6–8], in which they are completely related the incidence of martensitic phase transformation. The variant crystal structure disparities take place during the phase transformation of a cubic structure (austenite) transferred to a monoclinic structure (martensite).

These sorts of martensite forms have the ability to be organized independently in a self-accommodation approach by the mechanism of twinning throughout the inadequacy of the practiced stresses, with the consequence that virtually no shape transform can certainly be realized. The results of martensitic phase deformation are able to be detwinned into a single variant corresponded to the applied loads, and consequently a large inelastic strain happened [9, 10]. Heating the deformed alloys to a certain temperature above the austenite temperature will turn the inelastic strain to be recovered through transferring the existed martensite to austenite, this kind of feature is known as shape memory effect (SME) [9]. On the other hands, the pseudo-elasticity (PE) is caused by transferring the twinned martensitic phase into detwinned phase and obtained the shape recovery under the austenite starts temperature; in other words, the deformation of loading and unloading will be occurred in the austenite phase. This kind of structure transfer will be resulted in a large inelastic strain and a consequence of the phase reverse transformation, the initial shape will be restored upon the unloading process. Therefore, these types of materials such as Ti-based, Cu-based, and Fe-based SMAs are capable to demonstrated SME and PE [11–13]. Generally, there are two groups of martensitic transformation, thermoelastic and non-thermoelastic [14]. The thermoelastic martensitic transformations happen during the mobile interfaces between the martensite phase and parent phase. These types of interfaces are able to move during the reverse martensitic transformation as an alternative to the nucleation of the parent phase, which leads to a crystallographically reversible transformation [1]. On the other hand, the non-thermoelastic martensitic transformations are mainly found in ferrous alloys, which are related to the non-mobile interfaces of the martensitic parent phase pinned by permanent defects leading to a successful nucleation and growth. As a result of the austenite re-nucleation during the reversible martensitic transformation, these kinds of transformations are crystallographically nonreversible, in which the martensite phase is not able to return to original phase [15].
