**1. Introduction**

Titanium (Ti) and its alloys been used extensively for biomedical applications due to their excellent combined properties of low elastic modulus, high specific strength, excellent corrosion resistance, complete inertness to body environment and superior biocompatibility [1,2]. Among the mechanical properties essential for implant materials, elastic modulus, whose value should be as close as possible to that of human bone, is of considerable importance [3]. Although the elastic modulus of the widely used pure Ti and Ti-6Al-4V is lower (104 GPa and 110 GPa, respectively) than that of other conventional metallic biomaterials such as 316 L stainless steel and cobalt–chromium alloys (higher than 200 GPa), it is still much higher than that of natural human bone (10–30 GPa) [4]. The modulus mismatch between implants and surrounding human bones can lead to a stress shielding e ffect, resulting in bone resorption and premature failure of the implant [5]. Additionally, the release of toxic Al and V ions from Ti-6Al-4V is associated with long-term health problems, such as Alzheimer disease, neuropathy and ostemomalacia [6]. Consequently, this has led to the development of β-type Ti alloys that consist of non-toxic alloying elements and process lower modulus than that of α- and (α + β)-type Ti alloys [7–9].

The β-type Ti alloys can exhibit a martensitic transformation from the body centered cubic (bcc) β phase (space group, Im-3m) to the orthorhombic α" phase (space group, Cmcm) [10,11]. The martensitic transformation temperature decreases with the increase in the concentration of alloying elements, and the single β phase can be kept to room temperature upon quenching when the concentration exceeds a critical value [12,13]. It has been well recognized that the elastic modulus of β phase in Ti alloys is closely related their phase stability, with lower modulus corresponding to lower phase stability [14]. Therefore, the concentration of β stabilizers in most low modulus β-type Ti alloys was carefully designed to be as low as possible while being slightly higher than the critical concentration, in order to stabilize the single β phase against α" martensitic transformation [15]. These alloys with low phase stability (i.e., low modulus) also have various deformation mechanisms, e.g., stress-induced martensitic transformation (SIMT), deformation twinning, dislocation slip, etc. [16–19]. The various deformation mechanisms enable the alloys to possess unique mechanical properties involving shape memory e ffect [20], superelasticity [21], high strain hardening rate [22], large recoverable strain [23], and nonlinear elastic-like behavior [24]. Among these properties, nonlinear elasticity has attracted considerable attention, since it exists in several multifunctional Ti alloys including the Gum Metal and Ti24Nb4Zr8Sn alloy [25,26]. Although several reversible deformation mechanisms such as lattice distortion [27], nanodisturbance [28], dislocation loops [29], and strain glass transition [30], were proposed, it was generally accepted that SIMT plays an important role in this kind of peculiar deformation behavior [31,32].

Due to the reversibility of SIMT after the release of the stress, in-situ experiments provide a very efficient method to explore the deformation mechanism of metastable β-type Ti alloys. Currently, in-situ conventional X-ray di ffraction (XRD) has been employed to detect stress-induced α" martensite in Ti13Nb4Mo and Ti26Nb alloys [33,34]. However, the volume fraction of stress-induced α" martensite is usually very low in Ti alloys with nonlinear elasticity, which makes it di fficult or even impossible to characterize the SIMT through conventional XRD. Furthermore, it is di fficult to separate the main peaks of the β phase and α" martensite, as the laboratory X-ray sources have relatively grea<sup>t</sup> wavelength and the Ka1 and Ka2 wavelengths coexist. Especially, the identification of β phase and α" martensite from conventional XRD patterns will become even harder for alloys subjected to severe cold deformation because of the broadening of di ffraction peaks. By contrast, synchrotron X-ray di ffraction (SXRD) technique can trace the formation of a small volume fraction of phases during deformation due to the combination of short wavelength, good monochromaticity, high penetration, low absorption, and high resolution [35–37]. In-situ SXRD have been used to study the nonlinear deformation behavior of the Ti24Nb0.5O (at.%), Ti24Nb4Zr8Sn and Gum Metal, and it is demonstrated that SIMT, to a small extent, really exists during loading and contributes to the nonlinear elasticity [38–40].

Recently, our group developed several TiNb-based alloys with the β stabilizer concentration below the critical value [41,42]. These alloys consist of β and α" phases in solution treated and quenched states, suggesting the intrinsic low β phase stability. Upon cold rolling plus subsequent short time annealing treatment, single β phase was nearly obtained due to the suppression of martensitic transformation. Furthermore, the precipitates formed during annealing treatment did not result in a detectible increase in β stabilizers in residual β matrix, and thus the β stabilizer concentration of β matrix after thermo-mechanical treatment is identical to that in solution treated state [43]. As a result, even lower elastic modulus was realized in these alloys, e.g., 46 GPa for the Ti36Nb5Zr alloy and 36 GPa for the Ti33Nb4Sn alloys [41,43]. Interestingly, the Ti36Nb5Zr alloy subjected to cold rolling plus annealing treatment exhibits a nonlinear deformation behavior [44], similar to that of Ti24Nb4Zr8Sn and Gum metal. Since the Ti36Nb5Zr alloys have lower β phase stability than the low modulus Ti alloys with chemical composition above the critical concentration, SIMT might occur during loading and contribute to its deformation behavior. However, α" martensite has not been observed by conventional XRD and the underlying mechanism for the peculiar deformation behavior remains ambiguous.

In this paper, in situ SXRD experiments during uniaxial tensile loading were performed to explore the deformation mechanisms in the Ti36Nb5Zr alloy. The one-dimensional (1D) and two-dimensional (2D) SXRD patterns were obtained from in situ measurements to characterize the microstructural evolution of the alloy during in situ loading. Special attention was focused on the evolution of lattice strains and relative integrated di ffraction peak intensities of both the β and α" phases as functions of macroscopic applied strain. Our results indicated that the peculiar deformation behavior was closely related to various kinds of deformation mechanisms including elastic deformation, SIMT and plastic deformation, which were activated at di fferent external strains.

#### **2. Materials and Methods**

An ingot with a nominal composition of Ti36Nb5Zr (wt.%) was fabricated by arc melting in an argon atmosphere using high purity Ti (99.99%), Nb (99.95%) and Zr (99.95%). The ingot was re-melted four times in the furnace to obtain chemical composition homogeneity. The as-cast ingot was hot forged to a billet with a thickness of 8 mm and width of 60 mm, and then homogenized at 1223 K for 5 h in vacuum, followed by water quenching. The homogenized billet was cold rolled into a plate of approximately 1 mm in thickness with a final reduction ratio of 87.5%. The tensile specimens with the rolling direction parallel to the loading axis were cut from the cold rolled plate using an electro-discharge machine. These tensile specimens were annealed at 698 K for 20 min and finally quenched into water. Uniaxial tensile tests were conducted at a strain rate of 1 × 10<sup>4</sup> s<sup>−</sup><sup>1</sup> on an Instron 5982 machine using specimens with a gage length of 30 mm and a cross section of 1 × 1.46 mm2. In order to ensure accuracy of strain, a strain extensometer was used to record the stress–strain curves.

In situ SXRD experiments were conducted during tensile loading on the 11-ID-C beamline at the Advanced Photon Source, Argonne National Laboratory. High-energy X-rays with an energy of 115 keV, wavelength of 0.10798 Å and beam size of 0.4 × 0.4 mm<sup>2</sup> were used in transmission geometry, as shown in the schematic set-up in Figure 1. A PerkinElmer large area detector (PerkinElmer Inc., Waltham, MA, USA) of 2048 × 2048 pixels with a spatial resolution of 200 μm (pixel size) was placed behind the sample to collect the 2D di ffraction patterns. The loading direction (LD) and the beamline are parallel to the rolling direction (RD) and the normal direction (ND) of the rolled plate, respectively. The azimuth angles ( ϕ: 0–360◦) at the Debye rings are defined to be 0◦ and 90◦ at the transverse direction (TD) and the longitudinal direction (parallel to LD), respectively. Fit2d software was employed to process the 2D di ffraction images, and standard CeO2 powder was used for calibration. The 1D SXRD spectrums were obtained by integrating along specific azimuth angles over a range of ±10◦ in the 2D di ffraction patterns. The positions and areas of 1D di ffraction peaks were determined by Gaussian fit. The evolution of the interplanar spacing (*d*-spacing) with respect to the initial state is indicated by the lattice strain, i.e., εhkl = (*d*hkl − *d*0hkl)/*d*0hkl, where *d*hkl is the interplanar spacing of the (hkl) crystal plane with an external stress. The *d*0hkl is determined from the *d*-spacing of stress-free sample for the β phase, and from the *d*-spacing of sample subject to the stress that is high enough to resolve the accurate position of the martensite peak for the α" phase. The relative intensity is defined as the ratio of the integrated area of a peak to that at the strain-free state for the β phase and to that at the maximum applied strain for the α" phase, respectively.

**Figure 1.** Schematic set-up of in situ synchrotron X-ray experiments.

## **3. Results**

#### *3.1. Microstructure and Macroscopic Mechanical Behavior*

The microstructural evolution of Ti36Nb5Zr alloy during thermo-mechanical treatment has been described in detail in our previous work [41,44]. In brief, the Ti36Nb5Zr alloy after cold rolling and short time annealing treatment consists of a dominant β phase and a trace of a nanosized α phase. The annealing treatment did not result in significant recrystallization due to the low annealing temperature and short duration. The existence of high density of dislocations and grain boundaries suppressed the formation of α" martensite in thermo-mechanically treated alloys, although the solution treated alloy consisted of dual (β + α") phases. Figure 2a,b present the 2D SXRD pattern and 1D SXRD spectrum obtained by integrating over the entire 360◦ of the Ti36Nb5Zr alloy before tensile testing. It can be seen that the intensity of peaks for the α phase is very weak in comparison to that for the β phase, verifying that the volume fraction of α phase is very low and thus its precipitation should not result in obvious chemical stabilization of the residual β matrix.

**Figure 2.** Structural analysis of the Ti36Nb5Zr alloy before tensile loading. (**a**) Two-dimensional SXRD pattern of the alloy. (**b**) One-dimensional SXRD spectrum integrated over the entire 360◦. Inset shows the enlarged view of the boxed area in the spectrum. (**c**) Intensity distributions of the {110}β and {200}β di ffraction peaks along the azimuth angle.

The uneven intensity distribution of the 2D SXRD pattern along di fferent azimuth angles indicates that the alloy has a clear preferential orientation. The intensity distributions of the {110}β and {200}β di ffraction peaks were plotted against the azimuth angle, as shown in Figure 2c. The maximum of the di ffraction intensity for the {110}β peak appears at ϕ values of 0◦, 90◦, 180◦ and 360◦, suggesting the existence of α-fiber texture components (i.e., grains with <sup>&</sup>lt;110>β crystal direction parallel to RD). The azimuth angle of maximum di ffraction intensity between the {110}β and {200}β peaks can be determined to be 46◦ ± 2◦. Combined with the fact that the angle between the {110}β and {200}β crystal planes for bcc structure is 45◦, it can be demonstrated that the texture component of the cold rolled and annealed Ti36Nb5Zr alloy is {001}<110> [36]. This kind of texture is commonly observed in β-type TiNb-based alloys subjected to cold rolling/annealing or warm rolling/annealing treatment, and is closely related to the martensitic transformation behavior [38,45].

Figure 3a shows the cyclic tensile stress–strain curves at an interval of 0.5% to a total strain of 3.5%. The loading and unloading curves to a strain of 1% are overlapped, and the 1.5% loading strain is almost fully recovered during unloading with a residual strain of only 0.03%. The recoverable strain increases with increasing applied external strain, e.g., 2.01% and 2.11% are achieved at a loading strain of 2.5% and 3.5%, respectively. It is worth noting that a nonlinear deformation behavior is clearly observed when the loading strain exceeds the linear elastic range limit of ~0.6%. The peculiar nonlinear deformation behavior as well as large recoverable strain might be attributed to the low β phase stability of the Ti36Nb5Zr alloy, since such a phenomenon is usually observed in metastable β-type Ti alloys [25,46]. Figure 3b present the tensile stress–strain curve during in situ SXRD experiment, and 2D di ffraction patterns were taken at each block on the curve. The nonlinearity of the stress–strain curve upon in situ tensile loading is similar to that upon cyclic loading in Figure 3a. Furthermore, the in situ stress–strain curve can be divided into several stages by points O to D. OA (<0.67% strain) is undoubtedly the initial linear elastic deformation, while the mechanism of other stages will be discussed later. It is worth noting that no strain extensometer was used during the in-situ experiment, leading to overestimation of strains in Figure 3b. Therefore, the linear elastic range limit (~0.67%) in Figure 3b is slightly higher than that in Figure 3a (~0.6%).

**Figure 3.** Mechanical behavior and SXRD patterns of the Ti36Nb5Zr alloy during tensile loading. (**a**) Cyclic stress–strain curves with 0.5% strain step. (**b**) Uniaxial tensile stress–strain curve during in situ SXRD experiment. The 2D SXRD patterns at di fferent applied strains as noted in (**b**): (**c**) 4.13% (point D), (**d**) after fracture (point E). LD, TD and SD in (**<sup>c</sup>**,**d**) are abbreviations of loading direction, transverse direction and specific direction, respectively.

The 2D SXRD patterns of points D (corresponding to the maximum of external strain of 4.13%) and E (corresponding to the sample after fracture, i.e., the release of external strain) are shown in Figure 3c,d. Di ffraction spots ascribed to the (021) crystal plane of α" martensite can be clearly observed in di ffraction rings at an applied strain of 4.13%, demonstrating the existence of SIMT. Moreover, the angle between the (021)α" di ffraction spots and the loading direction is about 24◦, and this will be explained by the preferred selection of martensitic variants during SIMT in the next section. Therefore, the specific direction (SD) with an azimuth angle of 66◦ (i.e., 24◦ from loading direction) as well as the loading direction (LD, azimuth angle: 90◦) will be selected to clarify the microscopic mechanisms of deformation for the present Ti36Nb5Zr alloy. After the release of applied strain, the α" martensite disappeared and the 2D SXRD pattern was almost same with that before the tensile test (Figure 2a), indicating the complete reversibility of SIMT.

#### *3.2. In Situ SXRD Characterization along the LD and SD*

Figure 4a,b show the 1D SXRD spectrums during in situ tensile loading obtained by integrating along the longitudinal direction ( ϕ: 80–100◦) of the 2D SXRD patterns. Upon loading, the di ffraction peaks of the β phase shift slightly towards lower Bragg angles, demonstrating a tensile elastic deformation in the LD. The (021)α" and (222)α" di ffraction peaks are present at an applied strain of 0.88% and 1.28%, respectively. With the increase in external strain, the di ffraction peaks of α" martensite intensified, indicating a progressive transformation.

**Figure 4.** In situ SXRD analysis of the microstructural characteristics of the Ti36Nb5Zr alloy along LD. (**a**) One-dimensional SXRD spectrums. (**b**) Enlarged views of the boxed areas in (**a**). Evolution of the (**c**) lattice strains and (**d**) relative integrated diffraction peak intensities of the (110)β, (200)β, (211)β and (021)α" crystal planes as functions of the macroscopic applied strain. A, B and C in (**<sup>c</sup>**,**d**) represent the different macroscopic strains noted in Figure 3b.

Figure 4c,d show the evolution of the lattice strains and relative integrated diffraction peak intensities in the LD for the (110)β, (200)β, (211)β and (021)α" peaks during in situ tensile loading. The *d*0021 of α" martensite is defined to be the *d*-spacing at an applied strain of 1.28%, since the (021)α" peaks at lower external strains are too weak to be fitted for accurate peak positions and it is also difficult to obtain the *d*-spacing of martensite under zero external stress due to the complete reversibility of SIMT in the present alloy. In the stage of O–A–B (applied strain range: 0–1.46%), the lattice strains of all β crystal planes increase linearly with the increase in external strain, implying a elastic deformation behavior; in the stage of B–C (applied strain range: 1.46–2.62%), the lattice strains of the β crystal planes continue to increase at a much reduced rate with further increase in the applied strain, indicating the commencement of plastic deformation; in the stage of C–D (applied strain range: 2.62–4.13%), the lattice strains of both the β and α" crystal planes remain almost constant, suggesting a complete stop of elastic deformation in the local area under SXRD study. The relative diffraction intensity reveals that progressive SIMT occurred with an external strain of up to 2.62% (point C), which can be demonstrated by the continuous increase in relative intensity of (021)α" at the expense of that of (110)β, (200)β and (211)β. It is worth noting that the nonlinear deformation behavior appears at a strain of 0.67% (point A) while the SIMT along LD is first observed at a strain of 0.88%. The martensitic variants characterized by the (021)α" peak along the LD might not form firstly during tensile loading; the examination of martensitic transformation along other azimuth angles should be considered.

Figure 5a,b show the 1D SXRD spectrums during in situ tensile loading obtained by integrating along a specific direction (SD, ϕ: 56–76◦) of the 2D SXRD patterns. The shift of the diffraction peaks of the β phase towards lower angles indicates that a tensile elastic deformation exits in the SD. The diffraction peaks ascribed to (021)α" and (222)α" started to appear at certain external strain values, and intensified with the increase in applied strain, demonstrating that gradual SIMT occurred during tensile loading. However, the applied strains for the first appearance of (021)α" and (222)α" diffraction peaks are 0.67% and 1.46%, respectively, which is different from the results of 1D XRD spectrums along the LD. This implies that the β phase grains with different crystal orientations have different critical stress for SIMT. Besides, the intensity of α" martensite is clearly greater in the SD than that in the LD, suggesting the preferred selection of martensite variants.

**Figure 5.** In situ SXRD analysis of the microstructural characteristics of the Ti36Nb5Zr alloy along SD. (**a**) One-dimensional SXRD spectrums. (**b**) Enlarged views of the boxed areas in (**a**). Evolution of the (**c**) lattice strains and (**d**) relative integrated diffraction peak intensities of the (110)β, (200)β, (211)β and (021)α" crystal planes as functions of the macroscopic applied strain. A, B and C in (**<sup>c</sup>**,**d**) represent different macroscopic strains noted in Figure 3b.

Figure 5 show the evolution of the lattice strains and relative integrated diffraction peak intensities for the (110)β, (200)β, (211)β and (021)α" as functions of applied strain in the SD. The *d*0021 of α" martensite is defined to be the *d*-spacing at an applied strain of 0.88% when the (021)α" diffraction peak is strong enough to be fitted for accurate peak position. The evolution of the lattice strains in the SD is similar to that in the LD. In brief, in the stage of O-A-B, the lattice strain–macroscopic applied strain curves are linear for the β phase, reflecting an elastic deformation; in the stage of B-C, the lattice strain–macroscopic applied strain curves deviate from the linearity and the slopes of the curves begin to decrease, indicating a elastoplastic deformation; in the stage of C-D, the lattice strains of all crystal planes remain almost unchanged, suggesting that elastic deformation disappears in the local area

under SXRD study. The evolution of the relative integrated intensity of the (021)α" di ffraction peak indicates that the onset of SIMT corresponds to point A in the tensile stress–strain curve in Figure 3b, which means the deviation from linearity observed in macroscopic stress–strain curve is coincident with the SIMT. This provides direct evidence that the nonlinear deformation behavior of the cold rolled and annealed Ti36Nb5Zr alloy could be attributed to the SIMT during loading.
