**4. Discussion**

#### *4.1. Variant Selection of Stress-Induced Martensite*

To further explore the detailed scenarios of SIMT, the 2D SXRD patterns at di fferent applied strains (corresponding to points O–E in the macroscopic stress–strain curve in Figure 3b) were unrolled along the full azimuthal circle (0◦–360◦) and presented in Figure 6. The di ffraction lines of the β phase are non-uniform and even discontinuous at zero external strain (O), indicating the existence of strong texture as described above. The di ffraction lines curved into "banana" shapes with increasing the applied strain (A–D), indicating that the specimen experiences maximum tension and compression in the longitudinal direction ( ϕ: 90◦ and 270◦) and the transverse direction ( ϕ: 0◦ and 180◦), respectively. Faint shadows ascribed to (021)α" appeared at the applied strain corresponding to point A, and evolved into di ffraction spots at specific azimuth angles with the increase in external strain (B–D), implying the progressive SIMT during loading. By contrast, the di ffraction spots of (222)α" formed at higher applied strain and are weaker than those of (021)α". In addition to the di ffraction spots of (021)α" and (222)α", no α" di ffraction spots can be identified from the unrolled 2D SXRD images. Furthermore, it should be emphasized that the intensity of α" martensite is much lower than that of the parent β phase even at the maximum applied strain (point D), which is evidenced by the 1D SXRD spectrums integrated over the entire 360◦ shown in Figure 7. This suggests the transformed fraction of the β phase is very low, which might be the reason why a nonlinear deformation instead of a yielding plateau is observed during loading of the present Ti36Nb5Zr alloy.

**Figure 6.** The unrolled 2D SXRD images along the azimuthal circle (0◦ to 360◦) at di fferent applied strains corresponding to points O–E in Figure 3b.

**Figure 7.** One-dimensional SXRD spectrums integrated over the entire 360◦ at different applied strains corresponding to points O–E in Figure 3b. Inset shows the enlarged view of the boxed area in the spectrums.

Figure 8 shows the intensity distribution of the (021)α" diffraction peak along the azimuth angle at different applied strains corresponding to points O–E in Figure 3b. The curves at applied strains corresponding to points O and E are overlapped, demonstrating the complete reversibility of SIMT in the present alloy. Moreover, the overlap of curves corresponding to points C and D reveals that SIMT did not further occur when the external strain exceeded point C in the local area under SXRD study. The angle between (021)α" diffraction peaks and the LD is determined to be 24◦ ± 3◦ at the maximum applied strain (corresponding to point D). From the energetics of β→α" transformation, the critical stress of SIMT depends on the initial orientation of β grains, and the minimum critical stress can be realized in the β grains that are orientated with a <110> direction along the tensile direction [40]. Moreover, it has been reported that a variant selection operates during SIMT process and only the variants that give a maximum of transformation strain can be formed [36,47]. As mentioned above, the present Ti36Nb5Zr alloy has a texture <110> fiber texture component, i.e., <sup>&</sup>lt;110>β is parallel to the rolling direction/LD. Therefore, SIMT will first occur in the β grains with <110> parallel to the tensile axis due to their having the lowest critical stress. Furthermore, only one martensitic variant that gives the maximum transformation is activated. The [100]α*"*, [10]α*"* and [1]α*"* crystal orientation of this specific variant are parallel to [1]β, [110]β and [1–10]β, respectively. This implies that the (110)β and (020)α*"* peaks will appear in the LD of the 2D SXRD patterns and the positions of other α" peaks can be calculated according to the lattice parameters. As only two α" peaks were observed in our measurements, the lattice parameters of α" martensite cannot be calculated for the present alloy. As a solution, the lattice parameters of Gum Metal, which has a similar Nb and Zr content with the Ti36Nb5Zr, were used here, i.e., a = 3.250 Å, b = 4.853 Å and c = 4.740 Å [32]. Based on this assumption, the angle between [20]α*"* and [21]α*"* is calculated to be 26◦, i.e., the angle between the (021)α" peaks and the LD in 2D SXRD diffraction patterns is 26◦, which is consistent with the experimental value (24◦ ± 3◦).

As mentioned before, the present Ti36Nb5Zr alloy did not experience complete recrystallization during the annealing process, thus the existence of large amount of defects such as dislocations and grain boundaries resulted in the broadening of β diffraction peaks. Furthermore, the volume fraction of α" martensite is much lower than that of the β phase. Consequently, most α" peaks were either overlapped with β peaks or too weak to be identified from diffraction patterns. According to the PDF card (No. 17-0102), the (021)α" peak is one of the second strongest peaks of the α" phase, and the distance between the (021)α" peak and the β diffraction peaks is relatively large. This might be the reason why only (021)α" diffraction peaks of martensite transformed from β grains with <110> parallel to the tensile axis were observed. In the case of (021)α" peaks along the LD and (222)α" peaks along both the LD and SD, these martensite variants were transformed from β grains whose <sup>&</sup>lt;110>βdirection

is not parallel to the tensile axis. Therefore, higher critical stresses for SIMT are required, which agrees well with the experimental results that the first appearance of these martensitic peaks occurred at higher external strain than the (021)α" peak along the LD. Furthermore, the intensities of these peaks are relatively weaker due to the α-fiber texture component in the original β grains.

**Figure 8.** Intensity distributions of the (021)α" diffraction peaks along the azimuth angle at different applied strains corresponding to points O–E in Figure 3b.

#### *4.2. Origin of the Recoverable Strain*

The cyclic tensile stress–strain curve in Figure 3a indicates that the cold rolled and annealed Ti36Nb5Zr alloy processes a maximum recoverable strain of 2.11%. This is much larger than that of most engineering materials (<0.5%) and is even similar to that of bulk metallic glasses [48–51], although it is lower than that of superelastic β-Ti alloys whose recoverable strain is mainly realized by SIMT [11]. Considering that the volume fraction of the transformed α" martensite is very low, the direct contribution of SIMT to the recoverable strain in the present alloy should be small. Figure 4c indicates that the lattice strains along the LD for the (110)β, (200)β and (211)β reached maximum values of 2.08%, 1.71% and 1.41% at applied strain of 2.62% (corresponding to point C in macroscopic stress–strain in Figure 3b). It is worth noting that the maximum lattice strain of the (110)β at point C is close to the macroscopic recoverable strain (2.01%) at a similar applied strain (2.5%) to those determined from the cyclic stress–strain curves in Figure 3a. Considering that the present alloy exhibits a strong <110> fiber texture (i.e., (110)β perpendicular to the LD), it is proposed that the recoverable strain of the present Ti36Nb5Zr alloy is mainly contributed by the elastic strain of the β phase. It has been reported that the martensitic transforming alloy can exhibit much larger elastic strain than the conventional dislocation slip alloy [52]. The possibility of SIMT implies the structural instability of the parent phase, and the uniform lattice distortion provided by martensitic transformation can suppress strain localization and damage accumulation [53]. These two characteristics enable alloys that can undergo SIMT to possess large elastic strain. The present Ti36Nb5Zr alloy was designed to have low β phase stability in order to realize low modulus, which provides the possibility of the occurrence of SIMT. In other words, the low β phase stability leads to the large elastic strain that dominated the large recoverable strain of the alloy.

#### *4.3. Microscopic Deformation Mechanisms at Di*ff*erent Macroscopic Applied Strains*

Based on the evolution of lattice strains and relative integrated diffraction peak intensities of both the β and α" phases, it is possible to elucidate the activation sequence of each deformation mechanism at different applied strains. This sequence can be summarized on the cyclic and in situ tensile stress–strain curves of the Ti36Nb5Zr alloy, as shown in Figure 9. In the stage of O–A, the deformation was only accommodated by the elastic deformation of the β phase, which corresponds to linear elastic range in the stress–strain curves. In the stage of A–B, SIMT progressively occurred with increasing external

strain and the onset of SIMT at point A corresponds to the start of nonlinearity in the stress–strain curves. Besides, the elastic deformation of the β phase continued during this stage. The elastic deformation as well as the reversible SIMT contributed to the fully recoverable strain of 1.5% in the cyclic tensile loading. In the stage of B–C, the SIMT process continued while the β exhibited elastic and plastic deformation simultaneously. These mechanisms provided a ~2.01% recoverable strain at an applied strain of 2.5% during cyclic tensile loading.

**Figure 9.** Domains of occurrence of different deformation mechanisms noted on conventional stress–strain curves for Ti36Nb5Zr alloy. "def" is the abbreviation of "deformation".

In the stage of C–D, the homogeneous plastic deformation evolved into inhomogeneous plastic deformation due to the lack of strain hardening, resulting in plastic strain localization. Romanova et al. have reported that the local strain in the subsection that is far from the one where a neck will form, ceases to develop as soon as plastic strain localizes [54]. Actually, the tensile specimens break near one of the movable grips rather than the center where the synchrotron X-ray beam penetrated into the sample. Therefore, it is believed the plastic deformation of the local area under SXRD study did not continue when the applied strain exceeded point C. That might be why the lattice strains and the relative integrated intensities of all crystal planes remain almost unchanged in the stage of C–D. Although the SXRD experiment was not carried out in the local area of neck formation, it is believed that the plastic deformation continued in this region. On the other hand, the reversible deformation mechanisms including elastic deformation and/or SIMT existed but contributed little to deformation behavior due to the slight increase in the recoverable strain in the stage of C–D. Therefore, it is proposed that plastic deformation dominated the process in the stage of C–D.
