**1. Introduction**

The phenomenon of shape memory is characteristic of some alloys based on titanium, iron, copper, or manganese. Particular attention to materials with the shape memory effect (SME) is associated with their ability of recovering significant inelastic deformations when heated. The most famous representative of such materials is titanium nickelide. Its unique properties are widely used in world industries and in medicine [1,2]. The SMEs in titanium nickelide are caused by the B2–B19' thermoelastic martensitic transformations (MTs) occurring in the temperature range close to room temperature [1–4]. The cycle of martensitic transformations upon cooling and heating leads to the generation of dislocations in the crystal lattice. Understanding the nature of the influence of multiple cycles of "cooling and heating" below and above the points of martensitic transformation—thermal cycling (TC)—on the structure and properties of materials is of great importance, particularly for TiNi alloys and their products. The phenomenon of phase hardening (PH)—the accumulation of dislocations during martensitic transformations—does not seem trivial in the case of martensitic transformation with a reversible motion of martensitic boundaries. The term "thermoelastic transformation" in the strict sense does not imply irreversible changes in the structure. At the same time, in real metallic materials, including TiNi alloys, a certain increase in the dislocation density occurs during multiple MT cycles, which, in turn, is accompanied by a change in the martensitic transformation temperature and an increase in the dislocation yield strength of the alloys under mechanical loading [5–7].

The design of products with SME makes certain demands on the physico-mechanical and functional properties and their stability. The properties in alloys with shape memory can be further improved by forming an ultrafine-grained (UFG) state using severe plastic deformation (SPD) methods, in particular, equal channel angular pressing (ECAP) [8–13]. Because TiNi system alloys are the most common in

technological applications and have the best set of properties among alloys with a shape memory effect, the effect of thermal cycles (TCs) on their structure and properties has been studied for many years. In TiNi alloys, the transformation of B2 into B19 is characterized by the incompatibility of lattice deformation, which contributes to the emergence of local stresses at the phase boundary, and stress relaxation leads to the accumulation of plastic deformation and, as a consequence, irreversible changes in the kinetics of martensitic transformations with each thermal cycling cycle [14]. The first works [5,6] were devoted to the influence of TCs on the structure and characteristic temperatures of martensitic transformations, and the mechanical characteristics in the TiNi alloy. It was previously shown that thermal cycling through the interval of martensitic transformations leads to a change in the staging of the transformation [15–19]. Alloy Ti50.0Ni50.0 undergoes B19 → B2 transformation upon cooling. However, after several thermal cycles during cooling, the alloy begins to experience a multi-stage B2→R→B19 transformation. At the same time, other studies report slightly different dependences of the transformation temperatures upon thermal cycling under an applied load [20,21]. There are additional studies of the "thermocyclic training" of TiNi alloys to enhance memory effects [20,22–24]. However, the studies were carried out mainly on alloys in a coarse-grained (CG) state, or in states with a small degree of deformation, and there is a limited number of studies on the processes of accumulation of dislocations and change in properties during thermal cycling of TiNi alloys in UFG and nanocrystalline (NC) states [25]. In addition, the conducted studies did not determine how many cycles were required to obtain optimal characteristics of the properties in these alloys. The studies in this work were aimed at determining the optimal number of thermal cycles necessary to obtain stability of the structure and the physico-mechanical properties of the TiNi alloy in coarse-grained and ultrafine-grained states.
