## 1 Introduction  
Ti-Zr-Nb shape memory alloys (SMAs), initially niobium- and lately zirconium-enriched, are promising materials for bone implants [1, 2, 3, 4, 5, 6, 7, 8, 9]. This is primarily due to their high biomechanical and biochemical compatibilities. Their biomechanical compatibility is a result of their relatively low Young's modulus (\(\leq\)50 GPa) and non-linear superelastic mechanical behavior, which is similar to that of bone tissue [1, 2, 3, 10, 11, 12, 13, 14]. Their biochemical compatibility is due to the presence of only biocompatible elements in their composition [15, 16, 17]. The basic purpose of constructing Ti-Zr-Nb SMAs is to identify their superelastic behavior at operating temperature, i.e., human body temperature, as a result of reversible stress-induced \(\beta\)+\(\alpha\)* martensitic transformation [2, 7, 18, 19]. Previous studies have shown that zirconium as an alloying element in combination with niobium is quite effective for increasing the crystallographic limit of recovery strain (\(\epsilon_{r}\)\({}^{max}\)) [19]. Thus, the amount of Zr is optimized to achieve superelastic behavior at human body temperature. Historically, all Ti-Zr-Nb SMAs have been classified into three groups: (1) low-Zr alloys (Ti-22 Nb-6 Zr, for example); (2) medium-Zr alloys (Ti-18 Zr-15 Nb), and (3) high-Zr alloys (Ti-41 Zr-12 Nb) (all in at.%). Low-Zr alloys: The Ti-22 Nb-6 Zr shape memory alloy is an evolution of the binary Ti-22 Nb SMA [2; 20]. Besides increasing the crystallographic limit of recovery strain and realizing superelastic behavior at human body temperature, the addition of zirconium helps to control \(\omega\)-phase precipitation upon cooling in the course of heat treatment [21; 22]. However, this alloy has a relatively low crystallographic limit of recovery strain of about 3%, which limits the maximum superelastic strain and functional fatigue resistance. Medium-Zr alloys: The Ti-18 Zr-(14-15)Nb SMA is a highly developed and promising second-generation Zr-rich alloy [15; 23; 24]. This alloy has a higher crystallographic limit of recovery strain of about 5.5% due to its higher zirconium and lower niobium content, which positively affects the maximum superelastic strain and number of cycles to failure during functional cycling tests [24; 25]. High-Zr alloys: Further Zr enrichment and transition to Ti-(40-44)Zr-(10-12)Nb are expected to increase the crystallographic limit of recovery strain to 7-8% [19; 23; 26]. These alloys hold promise for the third generation of Ti-Zr-Nb-based SMAs. All functional properties of Ti-based SMAs are structure-sensitive. Therefore, to obtain optimal functional properties, it is necessary to optimize the structural/phase state and crystallographic texture of the alloy [25; 27; 28; 29]. Grain and/or subgrain refinement, down to submicrometer and nanometer sizes, drastically increases the dislocation yield stress, which in turn increases the difference between the dislocation and transformation yield stresses. This leads to an improved realization of recovery strain or recovery stress and enhances superelasticity and shape memory effect characteristics [30; 31]. Furthermore, shape recovery properties are also sensitive to the crystal lattice orientation. The maximum recovery strain in \(\beta\)-titanium SMAs can be achieved in the \(\langle 001|_{\beta}\)\(<\)110\(>_{\beta}\) crystallographic orientation of tensile stress [32]. The Young's modulus is only about 35 GPa in the \(<\)001\(>_{\beta}\) orientation, while in other orientations it can be twice as high. For example, it is about 75 GPa in \(<\)111\(>_{\beta}\) and 55 GPa in the \(<\)110\(>_{\beta}\) orientation [32; 33]. This all underscores the importance of crystallographic texture in polycrystalline alloys. Thermomechanical treatment (TMT), which includes cold plastic deformation and post-deformation annealing (PDA), is an effective method for controlling the grain and subgrain structure [34; 35]. The effect of TMT conditions on the structure and functional properties varies depending on alloy composition.