# Characterization of the stress-induced martensitic transformation in a Ti-Zr-Nb-Sn biomedical alloy manufactured by laser powder bed fusion

Hugo Schaal, Philippe Castany, Thierry Gloriant

► To cite this version:

Hugo Schaal, Philippe Castany, Thierry Gloriant. Characterization of the stress-induced martensitic transformation in a Ti-Zr-Nb-Sn biomedical alloy manufactured by laser powder bed fusion. Materialia, 2026, 45, pp.102670. 10.1016/j.mtla.2026.102670. hal-05512565

HAL Id: hal-05512565

https://hal.science/hal-05512565v1

Submitted on 17 Feb 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
<figure><img src="image_2.png" /></figure>

# Characterization of the stress-induced martensitic transformation in a Ti-Zr-Nb-Sn biomedical alloy manufactured by laser powder bed fusion

Hugo Schaal<sup>a,b,✉</sup>, Philippe Castany<sup>a,✉</sup>, Thierry Gloriant<sup>a,*</sup>

## ARTICLE INFO

**Keywords:**

Additive manufacturing

Stress-induced martensitic transformation

Titanium alloy

## ABSTRACT

A new potentially biocompatible Ti-22Zr-7Nb-2Sn (at.%) alloy was prepared by laser powder bed fusion (L-PBF) directly from pure elemental powders (in situ alloying). The manufactured alloy was characterized in its as-fabricated state by cyclic tensile tests, X-ray diffraction (XRD), transmission electron microscopy (TEM) observations and electron back-scattered diffraction (EBSD). The as-fabricated microstructure is dual-phased, composed of both β and α'' phases, with a majority of β phase. Cyclic tensile tests show high strain-hardening, with a maximum strain-hardening rate of approximately 14 GPa. The post deformation microstructure is studied to highlight the deformation mechanisms of the present alloy and exhibits a large fraction of stress-induced martensitic α'' phase, which formed from the parent β phase according to the standard orientation relationship (OR) during tensile test. The identification of the martensitic variants, their interfaces with the parent phase and the twinning relationships between them are reported in this study based on crystallographic investigations. In view of all these results, a deformation sequence of the Ti-22Zr-7Nb-2Sn (at.%) alloy is proposed.

## 1. Introduction

β and metastable β-titanium alloys are perfect candidates for biomedical applications [1–4]. These alloys have been developed to overcome the controversies around the currently used Co-Cr and Ti-6Al-4 V alloys made from potential cytotoxic elements [5–7], and leading to “stress-shielding” effect [8–10] that causes bone resorption. β-titanium alloys display adapted Young’s modulus for biomedical applications due to the stabilisation of the β-phase and can be obtained with perfectly biocompatible elements such as Zr, Nb, Ta, Mo and Sn [11–14]. They can also undergo stress-induced martensitic transformation from the body-centered-cubic (bcc) β phase to the orthorhombic α'' phase, leading in a shift in the deformation mechanisms of such alloys [15–19].

In such alloys, plasticity depends on the chemical stability of the β phase, as it can be driven by dislocation slip [20–22] or mechanical twinning [23–25]. Stress-induced martensitic transformation can also occur as a primary deformation mechanism [26–29], leading to a superelastic effect if the transformation is reversible [30–34]. β-titanium alloys can also exhibit a combination of these different mechanisms, resulting in complex deformation sequences [35,36].

From a fundamental perspective, six different orientations of α'' phase are forming according to the standard Orientation Relationship (OR) {−110}β // (001)α''; <111>β // [110]α'' [37] for a given crystallographic orientation of β phase. Such orientations are called lattice correspondence variants, and are referred to as “CVs” (from CV1 to CV6). Metastable β-titanium alloys containing low concentrations of β-stabilizers can exhibit martensitic transformation during quenching treatments, or following the application of an external mechanical stress. The latter mechanism is referred to as stress-induced martensitic transformation (SIMT). On one hand, α'' martensite formed from a single orientation of the parent β phase during quenching treatments exhibits the six different CVs in an equivalent way. Such a martensitic structure is referred to as “self-accommodated” martensite due to the compensation of the shear induced by the transformation of the β phase into each of the different CVs, resulting in the minimisation of the shape variation of the initial β grain. The obtained self-accommodated microstructure is organised in a characteristic way [23,38,39]. On the other hand, stress-induced α'' martensite is formed from the parent β phase based on the variant selection of the most preferentially oriented CVs to accommodate the applied strain. Reports have rationalized the preferentially oriented CVs as the martensitic variants exhibiting the highest Schmid

<footnote><sup>a</sup> University of Rennes, INSA Rennes, CNRS, ISCR UMR 6226, 35000 Rennes, France</footnote>

<footnote><sup>b</sup> SLS France, 32 Boulevard de la Haie des Cognets, 35136 Saint-Jacques-de-la-Lande, France</footnote>

<footnote>* Corresponding author.
E-mail address: thierry.gloriant@insa-rennes.fr (T. Gloriant).</footnote>
factor or the largest lattice transformation strain with respect to the local crystallographic stress direction [17,28,38].

The rise of additive manufacturing (AM) processes, and especially the powder bed-based ones, represents a great opportunity for biomedical applications, due to the ability of these processes to produce patient-specific devices [40]. Most of the research on laser powder bed fusion (L-PBF) of titanium alloys is currently focused on pre-alloyed powders elaboration of α+β dual-phase Ti-6Al-4 V alloy, its microstructures and mechanical properties [41–47]. Reports on L-PBF processing of β-titanium alloys are more discrete [48–51], in most cases using pre-alloyed powders and only a few of them reporting clear evidences of SIMT [52,53]. One of the key factors explaining the lack of studies on L-PBF β-titanium alloys is the lack of availability and diversity of pre-alloyed powders, which are mainly commercial aerospace alloys. From a prospective point of view, going for gas atomization of ingots in order to obtain pre-alloyed powders of a desired composition is ineffective, as the cost of such operation is not worth obtaining alloys with microstructure or chemical composition that could not lead SIMT.

In *situ* elaboration has been developed to overcome the difficulties of the powder supply chain by promoting the use of a mixture of commercially pure elemental powders, alloying the different elements during laser scanning. This method has led to promising results in the elaboration of β-titanium alloys [53–59], but also highlights the difficulty of completely melting the high melting point alloying elements such as Ta, Mo and Nb, which are usually used as the main β-stabilisers in biomedical β-titanium alloys. Design of experiments (DOE) proved to be efficient in optimising the processing conditions of exotic materials [54,58], reducing both the porosity and the fraction of unmelted high melting point alloying elements. Control of these quantities is critical in AM parts, as porosity determines the static and dynamic mechanical strength of such parts [60], and the amount of unmolten particles determines the local chemical homogeneity of the parts. Even assuming the ability of the *in situ* elaboration method to obtain new and original alloys, there are only a few reports on *in situ* L-PBF β-titanium alloys that exhibit mechanical properties (superelasticity, shape memory effect, TRIP effect) attributed to a SIMT. As this phase transformation has been shown to be important in improving the mechanical properties of metastable β-titanium alloys, the L-PBF processing of such alloys is a subject of interest.

In this work, a new Ti-22Zr-7Nb-2Sn (at. %) metastable β-titanium alloy is prepared by the *in situ* L-PBF process. This composition is derived from the initial Ti-22Zr-11Nb-2Sn (at. %) which was also prepared by *in situ* L-PBF in the same research unit and showed no evidence of SIMT, even after quenching treatment [61]. Investigation on the influence of the chemical composition on the mechanical stability of the β phase have led to the elaboration and characterization of the Ti-22Zr-9Nb-2Sn [53], which exhibits a SIMT after quenching treatment in the β-phase temperature domain, but not in the as-built state. Such a result was expected as the niobium is the main β-stabilizer in the chemical composition. The reduction of the niobium content in the chemical composition aims to induce the SIM transformation during the mechanical test, as the zirconium concentration aims to compensate for such a low amount of β-stabilisers to retain the β phase after processing. Even if zirconium is considered to have a weak influence on the stability of the β phase of titanium, reports suggest that it can be considered as a β-stabiliser when combined with another β-stabiliser such as Mo and Nb [62,63]. Tin has proven to be effective to hinder the β to ω phase transformation during quenching treatments [64], which is detrimental for the mechanical properties of the alloy. Tin is then added to avoid detrimental ω phase formation during the process. The present studied composition, i.e. Ti-22Zr-7Nb-2Sn, aims to decrease again the amount of β-stabilizing elements in order to try to promote the SIMT in the as-fabricated state of the alloy.

The present study focuses on the characterisation of the as-fabricated (AF) state of this new β-titanium alloy, with particular interest in the relation between the microstructure and the mechanical properties of

the alloy.

## 2. Materials & methods

### 2.1. L-PBF additive manufacturing

Gas atomised titanium, zirconium and niobium powders were obtained from ECKART TLS and H.C. Starck for the preparation. Tin powders were mechanically ground and obtained from Sigma Aldrich. Details of the different powders, such as particle size distribution, D50 (μm) and purity are given in Table 1. The different powders were mixed using a Turbula T2F device for 2 h at 34 rpm. Fig. 1 shows a secondary and a back-scattered electron image of the powder mix.

The different specimens were produced using a SLM 125 HL (SLM Solutions Group AG, Germany) equipped with a 400 W laser. The manufacturing chamber was filled with an Ar atmosphere and the oxygen level was maintained below 500 ppm during fabrication to prevent oxidation. *In situ* elaboration parameters must be carefully selected, as this type of fabrication tends to exhibit porosity and unmelted particles of high melting point elements, such as Ta, Mo, Nb. Literature examples of *in situ* elaboration of Ti-Ta [56,57] and Ti-Nb [54,55] binary systems show that the amount of such particles remaining in the metallic matrix tends to decrease with the correct manufacturing parameters. Furthermore, design of experiments (DOE) has proven to be a useful tool in narrowing the processability window of L-PBF process, and especially for *in situ* elaboration [61]. Ti-Zr-Nb-Sn titanium alloys have already been produced using the *in situ* technique by the same research group [53,61]. Optimised processing parameters shown in Table 2, were found using incremental DOE, giving a final density of >99.3 %, and unmolten Nb particles of about 0.04 % of the sample volume. In this table, *P* is the laser power, *v* the scanning velocity of the laser, *h* is the hatch-space, and *e* is the layer thickness of a powder layer. Both defects (porosity and unmelted particles) were characterized using micro-X-Ray tomography. However, some of the alloys previously designed did not show SIM transformation [61], due to the mechanical stability of the β phase. A decrease in the niobium content leads to a direct decrease in the stability of the β phase, and a shift in the mechanical properties of the alloy, since Nb is the main β-stabilizer in the chemical composition [53]. It can therefore be assumed that the elaboration of a titanium alloy of the same family, the Ti-22Zr-7Nb-2Sn (at. %), can be carried out with the same processing parameters, resulting in the same defect quantities (both unmelted particles, and porosity).

The macrostructure along the building direction of the *in situ* L-PBF Ti-22Zr-7Nb-2Sn (at. %) obtained alloy is shown in Fig. 2, and displays the typical scale-shaped melt pools which are very characteristics of L-PBF materials. The chemical composition of the samples is measured using energy dispersive spectroscopy (EDS). Examples of EDS analyses are presented in the supplementary file. Despite the presence of Nb inclusions, the measured chemical composition of the metallic matrix is consistent with the desired one within the experimental range, as the measured quantities (at. %) were respectively 70.3 ± 0.9 for Ti, 21.2 ± 0.6 for Zr, 6.8 ± 0.7 for Nb and 1.7 ± 0.1 for Sn. It can therefore be assumed that the obtained samples are macroscopically homogeneous, and that the quantity of inclusions in the metallic matrix should not significantly affect the macroscopic mechanical properties of the alloy.

Two different types of specimens were prepared for the mechanical

<table><caption>**Table 1**

Ti-22Zr-7Nb-2Sn (at. %) elemental powders properties.</caption><thead><tr><th>Element</th><th>Size distribution (μm)</th><th>D50(μm)</th><th>Purity</th><th>Morphology</th><th>Melting T (°C)</th></tr></thead><tbody><tr><td>Ti</td><td>15–45</td><td>35.7</td><td>>99.7</td><td>Spherical</td><td>1668</td></tr><tr><td>Zr</td><td>10–45</td><td>32</td><td>>99.7</td><td>Spherical</td><td>1855</td></tr><tr><td>Nb</td><td>10–45</td><td>29.9</td><td>>99.9</td><td>Spherical</td><td>2469</td></tr><tr><td>Sn</td><td>&lt; 45</td><td>-</td><td>>99.9</td><td>Irregular</td><td>232</td></tr></tbody></table>
<figure><img src="image_3.png" /><figcaption>Fig. 1. Secondary (a) and back-scattered (b) electron images of the Ti-22Zr-7Nb-2Sn powder mix.</figcaption></figure>

<table><caption>**Table 2**

Optimized building parameters for *in situ*elaboration of the Ti-22Zr-7Nb-2Sn alloy.</caption><thead><tr><td>P (W)</td><td>v (mm.s<sup>-1</sup>)</td><td>h (mm)</td><td>e (µm)</td></tr></thead><tbody><tr><td>200</td><td>305</td><td>0.06</td><td>20</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>Fig. 2. Optical micrograph of the Ti-22Zr-7Nb-2Sn alloy. Unmelted Nb particles are highlighted with white arrows.</figcaption></figure>

and microstructural characterisation. 10 × 10 × 10 mm³ cubes were used for microstructural characterisation and flat dog-bone tensile specimens with a gauge section of 3 × 1 mm² and a gauge length of 15 mm were extracted by electrical discharge machining from horizontal 50 × 5 × 2 mm³ parallelepipeds for mechanical characterisation. Dimensions of the specimens fit the ASTM E8 standard. No thermal treatment was performed after in order to maintain the microstructure in its as-fabricated (AF) state.

## 2.2. Microstructural & mechanical characterisations

The microstructure of the new Ti-22Zr-7Nb-2Sn (at. %) alloy is characterized using X-ray diffraction (XRD), electron back-scattered diffraction (EBSD) and transmission electron microscopy (TEM). Specimens for EBSD analysis are mechanically polished using SiC papers and a polishing colloidal silica suspension mixed with H₂O₂ to achieve a “mirror finish”. EBSD analyses are performed on a JEOL JSM 7100F scanning electron microscope with a 0.1 µm step and an accelerating voltage of 20 kV. EBSD data are presented as IPF maps and are also used to construct the stereographic projections of each crystal of interest directly from the experimental Euler angles values. TEM specimens are prepared by a three-step ion milling process using 4 keV, 2 keV and 0.5

keV argon ions on a Gatan PIPS II instrument. Observations of such foils are made on a JEOL JEM 2100 LaB6 microscope operating at 200 kV.

Optical microscopy observations are made on the “mirror finish” condition of the alloy, with a chemical etching using HF/HNO₃ aqueous solution. Mechanical characterisation is carried out on an Instron tensile instrument with a 5 kN load cell. Cyclic tensile tests are carried out at a strain rate of 10⁻⁴s⁻¹ using an extensometer and according to the ASTM E8 standard. It should be noted that there is a strong anisotropy in AM parts due to the processing conditions and epitaxial growth of the microstructure. Such anisotropy controls the preferential texture of the microstructure in the building and transverses directions, and therefore the mechanical properties. In the case of our tensile specimens, the tensile direction is orthogonal to the building direction. Five different specimens are tested to failure and the mechanical properties are presented as the mean value of all the different tests along their standard deviation.

# 3. Results & discussion

## 3.1. Microstructure and mechanical properties

Fig. 3 gives an overview of the microstructure of the AF alloy. The inverse pole figure (IPF) EBSD map along the building direction (Fig. 3a) shows elongated grains along the building direction. Such map displays the usual characteristics of body-centered cubic (bcc) L-PBF-built materials, i.e. columnar grains obtained thanks to the layer-by-layer building promoting epitaxial growth, and a strong <100>β texture along the building direction [53,54,61]. Approximately 98 % of the EBSD map was successfully indexed as β phase. This is due to the fact that the α'' phase is very thin in size and could not be indexed by the acquisition step used (0.1 µm). BD corresponds to the building direction and TD to the tensile direction. On the other hand, the diffraction pattern of the AF alloy (Fig. 3b) shows the typical diffraction peaks of the bcc β phase, with a measured lattice parameter of aβ = 0.337 nm. Along with the β phase peaks, other peaks are also visible and indexed as the orthorhombic α'' phase, with measured lattice parameters of aa'' = 0.308 nm, bα'' = 0.514 nm, and ca'' = 0.478 nm. From the relative intensity of the different phase peaks, it can be qualitatively assumed that the microstructure of the AF-Ti-22Zr-7Nb-2Sn alloy seems mostly composed of the β phase, at least to some extent.

The microstructure is further investigated by TEM observations. Fig. 4 shows bright-field TEM observations of the microstructure, highlighting thin and long laths of the α'' martensitic phase within the β-grains (Fig. 4a). These laths are approximately 25 nm thick and a few micrometres long. As the size of the martensitic phase is smaller than the step size used for the EBSD acquisition, such martensitic laths were not detected using EBSD. The associated electron diffraction pattern (Fig. 4b) shows intense β phase spots along the [111]β zone axis. However, additional and less intense spots are also visible on the
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** IPF-EBSD map along the building direction (vertical direction) (a) and XRD pattern (b) of the as-fabricated Ti-22Zr-7Nb-2Sn alloy.</figcaption></figure>

diffraction pattern (Fig. 4b): spots located at 1/2{110}β are identified to arise from double diffraction after tilting to non-axial conditions [65], while others are related to α'' phase. These α'' spots are attributed to the presence of the α'' self-accommodated martensite and are indexed based on the standard OR between the β and the α'' phase, i.e. {110}β // {001}α''; <111>β // <101>α''. Two dark field images of the same area at higher magnification are provided in Fig. 4c-d. The Fig. 4c is obtained with the (-110)β//({002}α'' spot, thus highlighting both the β phase and the variant of α'' which is indexed in the Fig. 4b and keeping the other variants of α'' in dark. On the other hand, the Fig. 4d is obtained with the (110)α'' spot and only highlights this same variant of α'' martensite. Such a microstructure is typical of water-quenched metastable β-titanium alloys with low β-stabilisers content, which causes the β phase to partially or completely decompose into the α'' martensite phase during quenching. In our case, the combination of the designed chemical composition and the high cooling rate of the L-PBF process (~10⁵ K/s [66]) promoted the formation of the martensitic phase during the elaboration of the alloy. Bright-field TEM observation also highlights different orientations of the martensitic phase (Fig. 4a), which is consistent with the self-accommodating nature of the martensite, as each different CVs should form in an equiprobable manner. For clarity

purposes, only one of the present CVs is indexed on the corresponding selected area electron diffraction (SAED) pattern (Fig. 4b). Moreover, it is well-known that all neighbouring CVs share a self-accommodating twinning relationship, selected from type I {111}α'', type II <211>α'' or compound {011}α'', depending on CVs pairs [37].

Fig. 5a shows the cyclic engineering tensile stress/strain curve of the AF-Ti-22Zr-7Nb-2Sn alloy. Mechanical properties are obtained from 5 tensile tests. From these tensile tests, average values of Young's modulus, elongation, yield and tensile strength are measured to be 49.2 ± 0.1 GPa, 10.2 ± 0.4 %, 530 ± 34 MPa and 1093 ± 18 MPa respectively. The absence of the characteristic hysteresis during the mechanical unloading of the alloy (Fig. 5a) leads to the conclusion that the present alloy does not exhibit a superelastic effect. However, high strain-hardening can be observed, as the difference between yield and the tensile strength is significant (~560 MPa). Fig. 5b shows the true stress/strain curve derived from the engineering stress-strain curve along the strain-hardening rate $d\sigma/d\epsilon$. To perform such calculation, the instantaneous method is used. On the same curve are represented the different strain-hardening stages, highlighting the multi-step hardening of the alloy during deformation: at first, elastic deformation of both β and α'' phases occurs, causing the strain-hardening rate to decrease rapidly (stage I), then the strain-hardening rate increases as the alloy begins its transition from the elastic regime to the plastic regime (stage II), reaching a maximum value of about 14 GPa. In the last stage of deformation (stage III), the strain-hardening rate decreases until the alloy exhibits a second yield just prior to specimen rupture.

Mechanical properties of the other Ti-Zr-Nb-Sn alloys along other titanium alloys obtained through additive manufacturing in literature are presented in Table 3. Mechanical properties such as yield strength (Ys), tensile strength (σm), maximum strain-hardening rate (n) and the difference between the tensile and yield strength (σm - Ys) are presented.

The Ti-22Zr-11Nb-2Sn alloy exhibits poor strain hardening, which is attributed to the absence of twinning or SIMT in both as-built and 700 °C water quenched states. Decreasing the niobium content leads to a more unstable β phase in the Ti-22Zr-9Nb-2Sn alloy, that promotes SIMT after annealing at 700 °C and water quench and, in turn, increases outstandingly the strain hardening rate. The present Ti-22Zr-7Nb-2Sn alloy exhibits mechanical properties that are comparable with the former Ti-22Zr-9Nb-2Sn alloy. However, there are two main differences that have a direct influence on the mechanical properties: the dual-phased microstructure of the Ti-22Zr-7Nb-2Sn alloy increases the yield strength and the present alloy exhibits such mechanical properties in its as-fabricated state, whereas the Ti-22Zr-9Nb-2Sn alloy has been water quenched from 700 °C after 30 min. In both cases, the mechanical properties exhibit similar mechanical behaviour, with a post deformation microstructure which is very much alike, solely constituted of different variants of α'' martensite. Such a feature can also be found in the other alloys extracted from the literature and presented in Table 3. These alloys also exhibit a SIMT that is supported with a high strain hardening, as shown with the difference σm - Ys. The triggering of the SIMT is the key to obtain important TRIP effect, and an increase in the strain hardening of these alloys.

Fig. 6a shows the XRD pattern of the fractured Ti-22Zr-7Nb-2Sn alloy, showing diffraction peaks of both α'' and β phases. One can note the difference in the relative intensity of the stress-induced martensitic α'' peaks with the AF state (Fig. 3b), indicating that the deformed microstructure now consists mainly of the α'' phase. The lattice parameters of both phases are determined to be aβ = 0.337 nm, aα'' = 0.309 nm, bα'' = 0.517 nm, cα'' = 0.479 nm. These parameters are consistent with those previously obtained from the AF XRD pattern (Fig. 3). Fig. 6b shows an optical micrograph of the fractured microstructure, in which columnar grains can be observed along the building direction. Such an elongated morphology is typical of the as-fabricated states of L-PBF parts, as the layer-by-layer building promotes epitaxial growth. A complex sub-structure of thin martensitic laths can be observed within
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Bright-field TEM image of the AF-Ti-22Zr-7Nb-2Sn alloy where the α'' phase is highlighted (a), along its corresponding indexed diffraction pattern (b) and dark-field images at higher magnification obtained from the (−110)$_{\beta}$//(002)α'' spot (c) and the (110)α'' spot (d).</figcaption></figure>

these grains, delimited by the grain boundaries of the columnar grains. These laths are a few micrometres thick, and a hundred micrometres long. Different orientations of the laths can be seen within the different grains, which could mean that these orientations are dependent on the initial orientation of the parent β phase. The combination of the XRD profile of the fractured specimen and the optical microscopy observations suggests that stress-induced martensitic transformation (SIMT) occurs in the present AF-Ti-22Zr-7Nb-2Sn alloy during tensile test. The difference in dimensions between the observed stress-induced martensite (Fig. 6b) and the self-accommodated martensite (Fig. 4) highlights the stress-induced nature of the later martensite. The transition observed between stages I and II of the strain-hardening rate curve (Fig. 5b) can then be identified as the triggering of such martensitic phase transformation.

Orientation maps of the fractured alloy obtained by EBSD, such as the IPF in the building direction, along band contrast and phase maps are shown in Fig. 7. The rather poor overall quality of the orientation maps obtained is due to the deformed microstructure (>10 % strain), which causes non-indexed areas due to the high local density of dislocations. Even considering the step used to perform the analysis (<0.1 µm), details about the deformed microstructure should not be considered relevant at this scale. However, several regions of such maps remain useful for orientation analysis, and the investigation of such alloy deformation mechanisms. Particularly, the indexed regions are uniformly indexed, meaning the absence of martensitic features smaller than the step size. Otherwise, this would lead to superimposed Kikuchi patterns that could not be indexed. The phase map (Fig. 7c) is consistent

with both XRD pattern and optical micrograph (Fig. 6) obtained on the fractured specimen, highlighting the important amount of α'' martensitic phase formed during the tensile test. IPF in the building direction map (Fig. 7b) shows different grains composed of α'' martensite and residual β phase. It also implies that for one orientation of the residual parent β phase, more than one orientation of the α'' martensitic phase was formed during deformation.

These orientations of martensite are more thoroughly investigated in the following section, with a focus on the crystallographic relationships between the stress-induced martensite and the residual β phase, and between the different orientations of martensite.

## 3.2. *Variant selection analysis*

As shown in the previous section, the L-PBF Ti-22Zr-7Nb-2Sn alloy exhibits interesting mechanical properties, correlated with a massive SIMT observed by post deformation analysis. To the best of the authors' knowledge, the observation and characterisation of such deformation mechanism for in situ L-PBF elaborated β-titanium alloys are not reported in the literature. This section aims to characterise the phase transformation through analysis of crystallographic orientation relationships, twinning relationships and crystallographic interfaces between α'' martensite and parent β phases. As mentioned in the previous section, six different orientations (CVs) of the α'' phase can be obtained from an initial orientation of the β phase. These variants can be identified by the standard OR between β and α'' phases, as shown in Table 4.

As shown by the TEM observations of the AF microstructure
<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Engineering cyclic tensile curve (a) and the associated true stress-strain and strain-hardening (dash-line) curves (b) of the AF-Ti-22Zr-7Nb-2Sn alloy.</figcaption></figure>

<table><caption>**Table 3**

Mechanical properties of additively manufactured β-Ti alloys.</caption><thead><tr><th>Alloy</th><th>Y<sub>S</sub><br>(MPa)</th><th>σ<sub>m</sub><br>(MPa)</th><th>n<br>(GPa)</th><th>σ<sub>m</sub> - Y<sub>S</sub><br>(MPa)</th></tr></thead><tbody><tr><td>Present Study</td><td>530</td><td>1093</td><td>14</td><td>563</td></tr><tr><td>As fabricated + 400 °C water-quenched Ti-22Zr-11Nb-2Sn [61]</td><td>986</td><td>1111</td><td>/</td><td>125</td></tr><tr><td>As fabricated + 700 °C water-quenched Ti-22Zr-11Nb-2Sn [61]</td><td>737</td><td>835</td><td>/</td><td>98</td></tr><tr><td>As fabricated Ti-22Zr-11Nb-2Sn [61]</td><td>788</td><td>822</td><td>/</td><td>34</td></tr><tr><td>As fabricated + 700 °C water-quenched Ti-22Zr-9Nb-2Sn [53]</td><td>421</td><td>1049</td><td>14.6</td><td>628</td></tr><tr><td>Ti-6246 [67]</td><td>932</td><td>1400</td><td>13</td><td>468</td></tr><tr><td>Ti-1023 [68]</td><td>375</td><td>895</td><td>10</td><td>520</td></tr><tr><td>Ti-1023 [69]</td><td>400</td><td>950</td><td>20</td><td>550</td></tr><tr><td>Ti-14Mo [70]</td><td>448</td><td>1046</td><td>/</td><td>598</td></tr></tbody></table>

(Fig. 4a), the self-accommodated martensite can be obtained by the combination of low concentration of β-stabiliser elements and rapid cooling. During this specific martensitic transformation, every CVs of the α'' phase (c.f. Table 4) are formed. However, in the case of stress-induced α'' martensite, variant selection occurs. Crystallographic orientation relationships between the β phase and the martensitic α'' phase can be used to deduce the activation of the different CVs with respect to the local crystallographic tensile direction [38,71–73]. Thus, the lattice deformation matrix can be obtained based on the lattice parameters of

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** XRD pattern of the ruptured state of the Ti-22Zr-7Nb-2Sn alloy(a), along an optical micrograph of the ruptured microstructure of the AF-Ti-22Zr-7Nb-2Sn alloy highlighting the columnar aspect of the microstructure and the stress-induced martensitic structure (b).</figcaption></figure>

both α'' and β phases, and the principal strain η₁, η₂ and η₃ can be obtained from these lattice parameters:

$$η_1 = \frac{a_{α''} - a_{β}}{a_{β}}$$

$$η_2 = \frac{b_{α''} - \sqrt{2}a_{β}}{\sqrt{2}a_{β}}$$

$$η_3 = \frac{c_{α''} - \sqrt{2}a_{β}}{\sqrt{2}a_{β}}$$

Where a_β, α'', bα'' and cα'' are the lattice parameters of both β and α'' phases. Lattice strain transformation along the tensile direction for each CV is then calculated following the formulae εᵢ = T''ε⁽ᵏ⁾T where T'' is the column vector corresponding to the local tensile direction of the considered β grain, and ε⁽ᵏ⁾ the lattice deformation matrix of each different CV. As an example, such deformation matrix for CV1 is given by:

$$ε^{(1)} = \begin{pmatrix} \eta_1 & 0 & 0 \\ 0 & \frac{\eta_2 + \eta_3}{2} & \frac{\eta_2 - \eta_3}{2} \\ 0 & \frac{\eta_2 - \eta_3}{2} & \frac{\eta_2 + \eta_3}{2} \end{pmatrix}$$

The prediction of the activated CVs is based on the maximisation of the lattice deformation of a given CV through the β to α'' phase
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Band contrast (a), IPF along the building direction (vertical direction) (b) and phase (c) EBSD maps of the ruptured AF-Ti-22Zr-7Nb-2Sn alloy. White colour on both (b) and (c) corresponds to unindexed pixels.</figcaption></figure>

transformation. In other words, CVs with the highest values of such lattice transformation strain are expected to be preferentially formed when a tensile stress is applied. Fig. 8 shows the superposition of the band contrast and IPF along the building direction maps obtained from EBSD analysis. Residual β phase grains (β1 and β2) and their stress-induced martensitic α'' phases (M1 to M5) are highlighted (Fig. 8). Stereographic projections of both β and α'' crystals are shown (Fig. 9& 10) and are constructed from the Euler angles extracted from the EBSD data of each crystal shown in Fig. 7b The stereographic projections of both β

<table><caption>**Table 4**
Lattice correspondence variants derived from the β→α'' phase transformation [37].</caption><thead><tr><th>Variant</th><th>[100]<sub>α''</sub></th><th>[010]<sub>α''</sub></th><th>[001]<sub>α''</sub></th></tr></thead><tbody><tr><td>CV<sub>1</sub></td><td>[100]<sub>β</sub></td><td>[011]<sub>β</sub></td><td>[011]<sub>β</sub></td></tr><tr><td>CV<sub>2</sub></td><td>[100]<sub>β</sub></td><td>[011]<sub>β</sub></td><td>[011]<sub>β</sub></td></tr><tr><td>CV<sub>3</sub></td><td>[010]<sub>β</sub></td><td>[101]<sub>β</sub></td><td>[101]<sub>β</sub></td></tr><tr><td>CV<sub>4</sub></td><td>[010]<sub>β</sub></td><td>[101]<sub>β</sub></td><td>[101]<sub>β</sub></td></tr><tr><td>CV<sub>5</sub></td><td>[001]<sub>β</sub></td><td>[110]<sub>β</sub></td><td>[110]<sub>β</sub></td></tr><tr><td>CV<sub>6</sub></td><td>[001]<sub>β</sub></td><td>[110]<sub>β</sub></td><td>[110]<sub>β</sub></td></tr></tbody></table>

<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Superposition of the EBSD band contrast and IPF along the building direction (vertical direction) maps of the deformed Ti-22Zr-7Nb-2Sn alloy. CVs and residual β phase grains are highlighted.</figcaption></figure>

grains show the crystallographic loading direction for β1 and β2, [−301]β and [−9 −9 10]β respectively. The combination of these directions and the lattice parameters of both phases measured following post deformation XRD (Fig. 6a) allows the calculation of the lattice transformation strain of β1 and β2 at each different CVs, as shown in Table 5.

One should note that some CVs exhibit negative lattice deformation, corresponding to a contraction of the lattice following the phase transformation, which is not expected under tensile loading. However, such CVs may form to some extent during tensile loading to locally accommodate the strain in the initial grain due to the formation of other CVs. Comparison of the stereographic projections of the initial β grain β1 and its stress-induced martensite products M1 and M2 (Fig. 9) can lead to the identification of the CVs for this particular grain: M1 (100)α'', (010)α'' and (001)α'' poles correspond to β1 (001)β, (110)β and (1–10)β respectively, while M2 (100)α'', (010)α'' and (001)α'' poles correspond to β1 (010)β (−101)β and (101)β respectively. According to Table 4, M1 and M2 can be identified as CV5 and CV4.

Regarding the β2 grain, the M3 (100)α'', (010)α'' and (001)α'' poles correspond to the (010)β, (−101)β, and (101)β poles, M4 (100)α'', (010)α'' and (001)α'' poles correspond to the (100)β, (0–11)β, and (011)β poles and M5 (100)α'', (010)α'' and (001)α'' poles correspond to the (001)β, (110)β, and (1–10)β poles. M3, M4 and M5 can then be identified as CV4, CV2 and CV5 respectively. In the case of β1 grain, the dominant CV in the deformed microstructure is M2, which results in a lattice deformation of about 6.9 % (CV4) and is the most important of the 6 different CVs. Orientation M1 leads to a lattice deformation of about 3.2 % (CV5) and is therefore less present in the deformed microstructure than M2. In the case of β2 grain, M3 and M4 lead to the same lattice deformation of 3.2 % (CV4 and CV2) and appear to form in an equivalent manner in β2 grain. As for M5, the associated lattice
<figure><img src="image_12.png" /><figcaption>Fig. 9. Stereographic projections of the β₁ grain (a) and its deformation α'' products M₁ (b) and M₂ (c).</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 10. Stereographic projections of the β₂ grain (a) and its deformation α'' products M₃ (b), M₄ (c) and M₅ (d).</figcaption></figure>

deformation is about 2 % (CV5), and this CV is observed in a more discrete manner than for M3 and M4.

In both cases (β1 and β2 grains), formed CVs can be identified according to the standard OR between β and α'' phases, highlighting no evidence of deformation twinning during deformation. The obtained CVs can also be correlated with the lattice deformation calculation, as

they were formed to maximise the lattice transformation deformation during SIMT. These observations have been reproduced in other grains and systematically lead to the formation of the CV that exhibits the largest lattice deformation in a major way, along with minor CVs that also tend to form under tensile loading, but in a less significant way. The dominant CV induced during deformation is therefore always the one
<table><caption>**Table 5**
Calculated lattice transformation strain for each CV in the case of β₁ and β₂ grains.</caption><thead><tr><th></th><th>CV<sub>1</sub></th><th>CV<sub>2</sub></th><th>CV<sub>3</sub></th><th>CV<sub>4</sub></th><th>CV<sub>5</sub></th><th>CV<sub>6</sub></th></tr></thead><tbody><tr><th>β<sub>1</sub></th><td>-7.30 %</td><td>-7.30 %</td><td>2.10 %</td><td>6.88 %</td><td>3.18 %</td><td>3.18 %</td></tr><tr><th>β<sub>2</sub></th><td>-2.30 %</td><td>3.18 %</td><td>-2.30 %</td><td>3.18 %</td><td>1.96 %</td><td>-2.97 %</td></tr></tbody></table>

with the highest value of transformation strain. The formation of multiple CVs during deformation could explain the high strain-hardening observed during tensile test (cf. Fig. 5), since the formation of these martensitic variants represents new interfaces that could hinder dislocation glide, and highly contribute to the strain-hardening of the alloy.

It can be noted that the laths of martensite observed after deformation (Fig. 7 and Fig. 8) are here attributed to SIMT, i.e. the nucleation of new martensite laths, instead of the growth of the pre-existing nano-scale martensite (Fig. 4) since the latter cannot lead to strain-hardening. Indeed, if the observed martensite after deformation was due to the growth of pre-existing martensite, no new interfaces would be created to impede dislocation glide. Consequently, no strain-hardening would be observed as the martensite growth would be due to the extension of pre-existing α''/β interfaces. The possible movement of pre-existing self-accommodating twin boundaries (type I {111}α'', type II <211>α'' or compound {011}α'') can also be neglected in terms of mechanical properties for the same reason.

### 3.3. Orientation relationships analysis

The previous section showed that the stress-induced martensite in the AF-Ti-22Zr-7Nb-2Sn alloy is formed according to the standard OR, with no evidence of deformation twinning. In this section, the orientation relationship between the parent β phase grains and their stress-induced martensitic products is investigated through the identification of the crystallographic interface between the two phases along with the identification of the self-accommodation twinning relationship between stress-induced martensitic products. Such an analysis provides information on the consistency of the interfaces predicted for such alloys in the literature.

The interface between α'' martensitic laths and the initial β grain can also be described as a continuous, unrotated and undistorted interface plane usually referred to as the habit plane [71,72,74,75]. In the case of SIMT, such habit planes are predicted to be {755}β planes between the β and the α'' phase based on the invariant plane strain theory [37]. Two different habit planes are predicted for each CV. The identification of the different habit planes is based on the stereographic projection of the two β crystals, in which the {755}β planes corresponding of each observed CV are plotted (cf. Fig. 9a & 10a). The angle between the trace of each {755}β plane and the local tensile direction is then reported and compared with the experimental angle between the tensile direction and the interface between the β and α'' phases.

In our case, the interfaces between the stress-induced martensitic products M1 and M2 and the initial parent β1 grain are (557)β and (-575)β respectively, and the interfaces between M3, M4, M5 and β2 are (-575)β, (7-55)β and (557)β, respectively. One can conclude that the stress-induced martensitic products formed from the initial β grains according to one of the two different predicted habit planes for each CV.

Studies of martensitic transformation in materials such as NiTi alloys [76-78] or metastable β-Ti alloys [37,38] clearly suggest twinning relationships between the different CVs, which are different from deformation twinning. In the case of martensitic transformation occurring in β-titanium alloys, three different self-accommodation twinning relationships can be observed among the CVs, which are reduced as follows: type I {111}α'', type II <211>α'' and compound type {011}α'', respectively. Compound type {011}α'' twinning is the exclusive twinning relationship between only CV1 and CV2, CV3 and CV4 or CV5 and CV6. Any other twinning relationship between CVs should be {111}α'' type I

or <211>α'' II. The infinitesimal deformation approach [78] used to calculate the various twinning relationships for this kind of alloys also suggests that any twinning mode other than these later does not transform one CV into another CV. Consequently, other twinning modes commonly observed in such alloys after deformation, such as the compound {130}<310>α'' [16,17,23,24,35,36], are generally referred to as deformation twinning in opposition to the former self-accommodation twinning modes.

In our case, since the different α'' martensitic laths formed according to the classical OR do not show twinning during deformation, the twinning relationships between the observed CVs can be clarified using the stereographic projections of the different α'' martensitic crystals, and by comparing them after a 180° rotation around {111}α'' and {011}α'' poles, or <211>α'' directions. If the obtained crystal is identical to one of the other martensitic crystals, it can be concluded that both crystals are in a twinning relationship. As the {111}α'' poles are close to the <211>α'' directions on the stereographic projection of a α'' crystal, it can be difficult to formally identify a type I or type II twinning relationship. In our case, we chose the twinning relationship that matches the best the different crystals.

The initial β1 grain has two different deformation products, M1 and M2. Fig. 11 shows the stereographic projections of the stress-induced martensitic crystal M1 (Fig. 11a), its (111)α'' type I twinned crystal (Fig. 11b) and the observed stress-induced martensitic crystal M2 (Fig. 11c). The correspondence between the different poles of the stereographic projection of M2 (Fig. 11c) and M1 after (111)α'' twinning (Fig. 11b) is close to 1.5°, whereas the correspondence with M1 after <211>α'' twinning (not shown) is beyond 5° It can therefore be concluded that M1 and M2 are in type I (111)α'' twinning relationship. The identification of the twinning relationship for the β2 crystals also highlight the exclusive type I twinning between all the different deformation products (M3, M4 and M5, respectively).

Finally, only {111}α'' self-accommodation twinning relationship between martensite domains is observed and no deformation twinning modes, such as the classical {130}<310>α'', are observed. This confirms that the strain-hardening is due to the formation of new α''/β interfaces from SIMT, rather than the growth of pre-existing martensite, as no other sources of strain-hardening, such as deformation twinning, are observed in this material.

### 3.4. Influence of this mechanism on the mechanical properties: an alloy comparison

The design and characterisation of the present alloy is based on the Ti-Zr-Nb-Sn system, and other alloys studied by the same research group [53,61]. The aim of this new alloy is to reduce the concentration of β-stabilisers concentrations in the chemical composition in order to promote SIMT. Such a deformation mechanism has already been reported in the case of the study of the mechanical properties of the heat treated Ti-22Zr-9Nb-2Sn (at. %) alloy [53], whereas the Ti-22Zr-11Nb-2Sn (at. %) alloy didn't show any evidence of SIMT [61]. The present Ti-22Zr-7Nb-2Sn (at. %) alloy exhibits a SIMT in its as-fabricated state, as demonstrated during this study. Initially, its microstructure is β+α'' dual-phased. According to XRD analysis, the microstructure of this alloy is assumed to be mostly composed of β phase. During tensile deformation, the alloy undergoes elastic deformation until the stress reaches the critical stress required for the SIMT to occur. After reaching the critical stress triggering the SIMT, α'' martensitic laths are formed in the initial columnar β grains (Fig. 6b) according to the classical OR. At this stage of deformation, CVs of martensite with the highest lattice transformation strain are formed in β grains. These different variants of martensite form along the {755}β theoretical interfaces between β and α'' phases, and the twinning relationships between the CVs of the same β grains appeared to be predominantly {111}α'' type I, based on the EBSD acquisitions. This combined formation of major and minor CVs in the initial β grains
<figure><img src="image_14.png" /><figcaption>Fig. 11. Stereographic projections of the initial $M_1$ deformation product of $\beta_1$ (a), the $(1\bar{1}1)\alpha''$ twinned $M_1$ crystal (b), and the $M_2$ deformation product (c).</figcaption></figure>

represent a large source of new interfaces which can hinder the dislocation glide during plastic deformation, causing the stress to gradually increase as the deformation proceeds (Fig. 5), generating more and more martensite, and a dynamic strain-hardening effect. The post deformation analysis of the microstructure indicates no evidence of deformation twinning of the $\alpha''$ phase during deformation, meaning that the observed mechanical properties are most likely due to the phase transformation from the $\beta$ phase to the $\alpha''$ phase and the interaction between the dislocations and the stress-induced martensite. The maximum strain-hardening rate measured was approximately 14 GPa, which is close to the maximum strain-hardening rate measured for the heat-treated Ti-22Zr-9Nb-2Sn alloy [53]. As the texture of the different alloys is the same, the proportion of martensite formed during deformation is expected to be the same for these two alloys and is based on the stability of the $\beta$-phase. For the Ti-22Zr-11Nb-2Sn, it appears that the $\beta$-phase is mechanically stable, even after heat treatment [61], which is not the case for the Ti-22Zr-9Nb-2Sn, which requires quenching treatment for the SIMT to occur [53]. The present study's alloy does not require heat treatment for the $\beta$-phase to become mechanically unstable, which allows for a high strain hardenability of the alloy in its as-fabricated state.

## 4. Conclusion

In the present study, a biomedical Ti-22Zr-7Nb-2Sn (at. %) alloy obtained by *in situ* L-PBF process from elemental powders is investigated in its as-fabricated state. The mechanical and microstructural properties are characterized by uniaxial cyclic tensile tests, EBSD, XRD, and TEM before and after deformation.

The as-fabricated state displays a $\beta+\alpha''$ dual-phase microstructure due to the quantity of $\beta$-stabilizers in the initial chemical composition. TEM observations highlighted a thin formation of self-accommodated $\alpha''$ martensite within initial $\beta$ grains. However, the XRD pattern implies that the microstructure is mainly composed of $\beta$ phase. An extremely high strain-hardening rate of about 14 GPa combined with a very high tensile strength of about 1100 MPa are shown from tensile experiments, and stress-induced martensite is evidenced in the microstructure from post deformation XRD and EBSD analyses.

The main conclusions of the study are summarized as follows:

* The post deformation microstructure is mainly constituted of $\alpha''$ martensitic phase with some residual $\beta$ phase.

* The $\alpha''$ stress-induced martensite formed accordingly to the standard orientation relationship. In the observed grains, the activated CVs are consistent with their respective lattice transformation strain, as the CV that exhibits the largest lattice transformation strain is always

the one observed in initial $\beta$ grains. Other CVs are also observed but in a more minor way. The formation of these new interfaces during deformation is the most probable reason of the high strain-hardening observed from tensile tests.

* The post deformation analysis and the investigation of the orientation relationships between the residual $\beta$ phase and the $\alpha''$ phase shows no evidence of deformation twinning.

* Each of the different observed CVs formed along the theoretical habit planes for this kind of phase transformation. In each studied grain, all CVs are in type I $(1\bar{1}1)\alpha''$ twinning relationship. No evidence of twinning in the $\beta$-phase was observed.

* *In situ* L-PBF process is perfectly fitted for the design of potentially biocompatible titanium alloys that exhibit SIMT and exceptional mechanical properties.

### CRediT authorship contribution statement

**Hugo Schaal:** Writing – original draft, Validation, Methodology, Investigation, Formal analysis. **Philippe Castany:** Writing – original draft, Validation, Supervision, Methodology, Investigation. **Thierry Gloriant:** Writing – review & editing, Supervision, Project administration, Investigation, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

The authors acknowledge the SCANMAT platforms of the University of Rennes and PLASSMAT platform of the IMN (Institut des matériaux de Nantes) for providing access to XRD, SEM and TEM facilities.

### Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.mtla.2026.102670.

### References

[1] M. Niinomi, Mechanical biocompatibilities of titanium alloys for biomedical applications, J. Mech. Behav. Biomed. Mater. 1 (2008) 30–42, https://doi.org/10.1016/j.jmbbm.2007.07.001.

[2] M. Long, H.J. Rack, Titanium alloys in total joint replacement-a materials science perspective, Biomaterials 19 (1998) 1621–1639, https://doi.org/10.1016/S0142-9612(97)00146-4.
[3] M. Niinomi, M. Nakai, J. Hieda, Development of new metallic alloys for biomedical applications, Acta Biomater. 8 (2012) 3888-3903, https://doi.org/10.1016/j. actbio.2012.06.037.

[4] D.M. Gordin, F. Sun, D. Laillé, F. Prima, T. Gloriant, How a new strain transformable titanium-based biomedical alloy can be designed for balloon expendable stents, Materialia (Oxf) 10 (2020) 100638, https://doi.org/10.1016/j. mta.2020.100638.

[5] C. Exley, J.D. Birchall, The cellular toxicity of aluminium, J. Theor. Biol. 159 (1992) 83-98, https://doi.org/10.1016/S0022-5193(05)80769-6.

[6] B.C. Costa, C.K. Tokuhara, L.A. Rocha, R.C. Oliveira, P.N. Lisboa-Filho, J.C. Pessoa, Vanadium ionic species from degradation of Ti-6Al-4V metallic implants: *in vitro* cytotoxicity and spectrophotometry evaluation, Mater. Sci. Eng. C 96 (2019) 730-739, https://doi.org/10.1016/j.msec.2018.11.090.

[7] S.G. Steinemann, Metal implant and surface reactions, Injury 27 (1996), https:// doi.org/10.1016/0020-1383(96)89027-9. S/C16-S/C22.

[8] R.B. Ashman, S.C. Cowin, W.C. Van Buskirk, J.C. Rice, A continuous wave technique for the measurement of the elastic properties of cortical bone, J. Biomech. 17 (1984) 349-361, https://doi.org/10.1016/0021-9290(84)90029-0.

[9] M. Geetha, A.K. Singh, R. Asokamani, A.K. Gogia, Ti based biomaterials, the ultimate choice for orthopaedic implants - A review, Prog. Mater. Sci. 54 (2009) 397-425, https://doi.org/10.1610/j.pmatsci.2008.06.004.

[10] B. Van Rietbergen, R. Huiskes, H. Weinans, D.R. Summer, T.P. Turner, J. O. Galante, The mechanism of bone remodeling and resorption around press-fitted THA stems, J. Biomech. 26 (1993) 369-382, https://doi.org/10.1016/0021-9290 (93)90001-U.

[11] Y. Okazaki, E. Gotoh, Comparison of metal release from various metallic biomaterials *in vitro*, Biomaterials 26 (2005) 11-21, https://doi.org/10.1016/j. biomaterials.2004.02.005.

[12] M. Niinomi, Mechanical properties of biomedical titanium alloys, Mater. Sci. Eng. A 243 (1998) 231-236, https://doi.org/10.1016/S0921-5093(97)00806-X.

[13] E. Bertrand, T. Gloriant, D.M. Gordin, E. Vasilescu, P. Drob, C. Vasilescu, S.I. Drob, Synthesis and characterisation of a new superelastic Ti-25Ta-25Nb biomedical alloy, J. Mech. Behav. Biomed. Mater. 3 (2010) 559-564, https://doi.org/ 10.1016/j.jmbbm.2010.06.007.

[14] Y.L. Hao, S.J. Li, S.Y. Sun, C.Y. Zheng, R. Yang, Elastic deformation behaviour of Ti-24Nb-4Zr-7.9Sn for biomedical applications, Acta Biomater. 3 (2007) 277-286, https://doi.org/10.1016/j.actbio.2006.11.002.

[15] J.J. Gao, I. Thibon, P. Castany, T. Gloriant, Effect of grain size on the recovery strain in a new Ti-20Zr-12Nb-2Sn superelastic alloy, Mater. Sci. Eng. A 793 (2020) 139878, https://doi.org/10.1016/j.msea.2020.139878.

[16] P. Castany, T. Gloriant, F. Sun, F. Prima, Design of strain-transformable titanium alloys, C. R. Phys. 19 (2018) 710-720, https://doi.org/10.1016/j. crhy.2018.10.004.

[17] E. Bertrand, P. Castany, Y. Yang, E. Menou, T. Gloriant, Deformation twinning in the full-α' martensitic Ti-25Ta-20Nb shape memory alloy, Acta Mater. 105 (2016) 94-103, https://doi.org/10.1016/j.actamat.2015.12.001.

[18] S. Miyazaki, H.Y. Kim, H. Hosoda, Development and characterization of Ni-free-Ti- base shape memory and superelastic alloys, Mater. Sci. Eng. A 438-440 (2006) 18-24, https://doi.org/10.1016/j.msea.2006.02.054.

[19] F. Sun, J.Y. Zhang, M. Marteleur, T. Gloriant, P. Vermaut, D. Laillé, P. Castany, C. Curfs, P.J. Jacques, F. Prima, Investigation of early stage deformation mechanisms in a metastable β titanium alloy showing combined twinning-induced plasticity and transformation-induced plasticity effects, Acta Mater. 61 (2013) 6406-6417, https://doi.org/10.1016/j.actamat.2013.07.019.

[20] P. Castany, M. Besse, T. Gloriant, *In situ* TEM study of dislocation slip in a metastable β titanium alloy, Scripta Mater. 66 (2012) 371-373, https://doi.org/ 10.1016/j.scriptamat.2011.11.036.

[21] M. Besse, P. Castany, T. Gloriant, Mechanisms of deformation in gum metal TNTZ- O and TNTZ titanium alloys: a comparative study on the oxygen influence, Acta Mater. 59 (2011) 5982-5988, https://doi.org/10.1016/j.actamat.2011.06.006.

[22] E. Farghadan, A. Zarei-Hanzaki, H.R. Abedi, D. Dietrich, M.R. Yadegar, T. Lampke, The coupled temperature-strain rate sensitivity of Ti-29Nb-13Ta-4.6Zr alloy, Mater. Sci. Eng. A. 610 (2014) 258-262, https://doi.org/10.1016/j. msea.2014.04.052.

[23] E. Bertrand, P. Castany, I. Péron, T. Gloriant, Twinning system selection in a metastable β-titanium alloy by Schmid factor analysis, Scripta Mater. 64 (2011) 1110-1113, https://doi.org/10.1016/j.scriptamat.2011.02.033.

[24] H. Tobe, H.Y. Kim, T. Inamura, H. Hosoda, S. Miyazaki, Origin of (332) twinning in metastable β-ti alloys, Acta Mater. 64 (2014) 345-355, https://doi.org/ 10.1016/j.actamat.2013.10.048.

[25] L. Lilenberg, Y. Danard, C. Brozek, S. Mantri, P. Castany, T. Gloriant, P. Vermaut, F. Sun, R. Banerjee, F. Prima, On the heterogeneous nature of deformation in a strain-transformable beta metastable Ti-V-Cr-Al alloy, Acta Mater. 162 (2019) 268-276, https://doi.org/10.1016/j.actamat.2018.10.003.

[26] M. Tahara, H.Y. Kim, H. Hosoda, S. Miyazaki, Cyclic deformation behavior of a Ti- 26 at.% Nb alloy, Acta Mater. 57 (2009) 2461-2469, https://doi.org/10.1016/j. actamat.2009.01.037.

[27] H.Y. Kim, Y. Ikehara, J.I. Kim, H. Hosoda, S. Miyazaki, Martensitic transformation, shape memory effect and superelasticity of Ti-Nb binary alloys, Acta Mater. 54 (2006) 2419-2429, https://doi.org/10.1016/j.actamat.2006.01.019.

[28] E. Bertrand, P. Castany, T. Gloriant, Investigation of the martensitic transformation and the damping behavior of a superelastic Ti-Ta-Nb alloy, Acta Mater. 61 (2013) 511-518, https://doi.org/10.1016/j.actamat.2012.09.065.

[29] S. Sadeghpour, S.M. Abbasi, M. Morakabati, Deformation-induced martensitic transformation in a new metastable β titanium alloy, J. Alloys Comps. 650 (2015) 22-29, https://doi.org/10.1016/j.jallcom.2015.07.263.

[30] M.F. Ijaz, H.Y. Kim, H. Hosoda, S. Miyazaki, Superelastic properties of biomedical (Ti-Zr)-Mo-Sn alloys, Mater. Sci. Eng. C. 48 (2015) 11-20, https://doi.org/ 10.1016/j.msec.2014.11.010.

[31] Y. Yang, P. Castany, M. Cornen, I. Thibon, F. Prima, T. Gloriant, Texture investigation of the superelastic Ti-24Nb-4Zr-8Sn alloy, J. Aloys Comps. 591 (2014) 85-90, https://doi.org/10.1016/j.jallcom.2013.12.207.

[32] J.J. Gao, I. Thibon, D. Laillé, P. Castany, T. Gloriant, Influence of texture and transformation strain on the superelastic performance of a new Ti-20Zr-3Mo-3Sn alloy, Mater. Sci. Eng. A. 762 (2019) 138075, https://doi.org/10.1016/j. msea.2019.138075.

[33] P.J.S. Buenconsejo, H.Y. Kim, H. Hosoda, S. Miyazaki, Shape memory behavior of Ti-Ta and its potential as a high-temperature shape memory alloy, Acta Mater. 57 (2009) 1068-1077, https://doi.org/10.1016/j.actamat.2008.10.041.

[34] H. Hosoda, Y. Kinoshita, Y. Fukui, T. Inamura, K. Wakashima, H.Y. Kim, S. Miyazaki, Effects of short time heat treatment on superelastic properties of a Ti- Nb-Al biomedical shape memory alloy, Mater. Sci. Eng. A. 438-440 (2006) 870-874, https://doi.org/10.1016/j.msea.2006.02.151.

[35] Y. Yang, P. Castany, Y.L. Hao, T. Gloriant, Plastic deformation via hierarchical nano-sized martensitic twinning in the metastable β Ti-24Nb-4Zr-8Sn alloy, Acta Mater. 194 (2020) 27-39, https://doi.org/10.1016/j.actamat.2020.04.021.

[36] J.J. Gao, P. Castany, T. Gloriant, Complex multi-step martensitic twinning process during plastic deformation of the superelastic Ti-20Zr-3Mo-3Sn alloy, Acta Mater. 236 (2022) 118140, https://doi.org/10.1016/j.actamat.2022.118140.

[37] Y.W. Chai, H.Y. Kim, H. Hosoda, S. Miyazaki, Self-accommodation in Ti-Nb shape memory alloys, Acta Mater. 57 (2009) 4054-4064, https://doi.org/10.1016/j. actamat.2009.04.051.

[38] T. Inamura, J.I. Kim, H.Y. Kim, H. Hosoda, K. Wakashima, S. Miyazaki, Composition dependent crystallography of α'-martensite in Ti-Nb-based β titanium alloys, Philos. Mag. 87 (2007) 3325-3350, https://doi.org/10.1080/ 14786430601003874.

[39] H. Tobe, H.Y. Kim, T. Inamura, H. Hosoda, T.H. Nam, S. Miyazaki, Effect of Nb content on deformation behavior and shape memory properties of Ti-Nb alloys, J. Alloys, Comps. 577 (2013) 435-438, https://doi.org/10.1016/j. jallcom.2012.02.023.

[40] M. Lowther, S. Louth, A. Davey, A. Hussain, P. Ginestra, L. Carter, N. Eisenstein, L. Grover, S. Cox, Clinical, industrial and research perspectives on powder bed fusion additively manufactured metal implants, Addit. Manuf. 28 (2019) 565-584, https://doi.org/10.1016/j.addma.2019.05.033.

[41] C.-L. Li, J.-K. Hong, P.L. Narayana, S.-W. Choi, S.W. Lee, C.H. Park, J.-T. Yeom, Q. Mei, Realizing superior ductility of selective laser melted Ti-6Al-4V through a multi-step heat treatment, Mater. Sci. Eng. A 799 (2021) 140367, https://doi.org/ 10.1016/j.msea.2020.140367.

[42] D. Zhang, L. Wang, H. Zhang, A. Maldar, G. Zhu, W. Chen, J.-S. Park, J. Wang, X. Zeng, Effect of heat treatment on the tensile behavior of selective laser melted Ti-6Al-4V by *in situ* X-ray characterization, Acta Mater. 189 (2020) 93-104, https://doi.org/10.1016/j.actamat.2020.03.003.

[43] N. Jin, Z. Yan, Y. Wang, H. Cheng, H. Zhang, Effects of heat treatment on microstructure and mechanical properties of selective laser melted Ti-6Al-4V lattice materials, Int. J. Mech. Sci. 190 (2021) 106042, https://doi.org/10.1016/j. imjecsci.2020.106042.

[44] L. Thijs, F. Verhaeghe, T. Craeghs, J. Van Humbeek, J.-P. Kruth, A study of the microstructural evolution during selective laser melting of Ti-6Al-4V, Acta Mater. 58 (2010) 3303-3312, https://doi.org/10.1016/j.actamat.2010.02.004.

[45] H. Gong, K. Rafi, H. Gu, T. Starr, B. Stucker, Analysis of defect generation in Ti-6Al- 4V parts made using powder bed fusion additive manufacturing processes, Addit. Manuf. 1-4 (2014) 87-98, https://doi.org/10.1016/j.addma.2014.08.002.

[46] A. Zafari, M.R. Barati, K. Xia, Controlling martensitic decomposition during selective laser melting to achieve best ductility in high strength Ti-6Al-4V, Mater. Eng. A 744 (2019) 445-455, https://doi.org/10.1016/j.msea.2018.12.047.

[47] G. Kasperovich, J. Haubrich, J. Gussone, G. Requena, Correlation between porosity and processing parameters in TiAl6V4 produced by selective laser melting, Mater. Des. 105 (2016) 160-170, https://doi.org/10.1016/j.matdes.2016.05.070.

[48] J.P. Luo, Y.J. Huang, J.Y. Xu, J.F. Sun, M.S. Dargusch, C.H. Hou, L. Ren, R.Z. Wang, T. Ebel, M. Yan, Additively manufactured biomedical Ti-Nb-Ta-Zr lattices with tunable Young's modulus: mechanical property, biocompatibility, and proteomics analysis, Mater. Sci. Eng. C. 114 (2020) 110903, https://doi.org/10.1016/j. msec.2020.110903.

[49] R. Ummethala, P.S. Karamched, S. Rathinavelu, N. Singh, A. Aggarwal, K. Sun, E. Ivanov, L. Kollo, I. Okulov, J. Eckert, K.G. Prashanth, Material 14 (2020) 100941, https://doi.org/10.1016/j.mtla.2020.100941.

[50] T. Ishimoto, K. Hagihara, K. Hisamoto, S.-H. Sun, T. Nakano, Crystallographic texture control of beta-type Ti-15Mo-5Zr-3Al alloy by selective laser melting for the development of novel implants with a biocompatible low Young's modulus, Scripta Mater. 132 (2017) 34-38, https://doi.org/10.1016/j. scriptamat.2016.12.038.

[51] Y.J. Liu, X.P. Li, L.C. Zhang, T.B. Sercombe, Processing and properties of topologically optimised biomedical Ti-24Nb-4Zr-8Sn scaffolds manufactured by selective laser melting, Mater. Sci. Eng. A. 642 (2015) 268-278, https://doi.org/ 10.1016/j.msea.2015.06.088.

[52] S.A. Mantri, M.S.K.K.Y. Martu, S. Dasari, A. Sharma, P. Agrawal, R. Salloom, F. Sun, E. Ivanov, K. Cho, B. McWilliams, S.G. Srinivasan, N.B. Dahotre, F. Prima, R. Banerjee, Suppression and reactivation of transformation and twinning induced plasticity in laser powder bed fusion additively manufactured Ti-10V-2Fe-3Al, Addit. Manuf. 48 (2021) 102406, https://doi.org/10.1016/j.addma.2021.102406.

[53] H. Schaal, P. Castany, T. Gloriant, Outstanding strain-hardening of a new metastable β-titanium alloy elaborated by *in situ* additive manufacturing L-PBF
process, Mater. Sci. Eng. A. 875 (2023) 145117, https://doi.org/10.1016/j.msea.2023.145117.

[54] M. Fischer, D. Joguet, G. Robin, L. Peltier, P. Laheurte, *In situ* elaboration of a binary Ti-26Nb alloy by selective laser melting of elemental titanium and niobium mixed powders, Mater. Sci. Eng. C 62 (2016) 852–859, https://doi.org/10.1016/j.msec.2016.02.033.

[55] D. Zhao, C. Han, J. Li, J. Liu, Q. Wei, *In situ* fabrication of a titanium-niobium alloy with tailored microstructures, enhanced mechanical properties and biocompatibility by using selective laser melting, Mater. Sci. Eng. C 111 (2020) 110784, https://doi.org/10.1016/j.msec.2020.110784.

[56] S.L. Sing, W.Y. Yeong, F.E. Wiria, Selective laser melting of titanium alloy with 50 wt% tantalum: microstructure and mechanical properties, J. Alloys. Compd. 660 (2016) 461–470, https://doi.org/10.1016/j.jallcom.2015.11.141.

[57] E.G. Brodie, A.E. Medvedev, J.E. Frith, M.S. Dargusch, H.L. Fraser, A. Molotnikov, Remelt processing and microstructure of selective laser melted Ti25Ta, J. Alloys. Compd. 820 (2020) 153082, https://doi.org/10.1016/j.jallcom.2019.153082.

[58] S. Huang, R. Lakshmi Narayan, J. Heang Kuan Tan, S.L. Sing, W.Y. Yeong, Resolving the porosity-unmelted inclusion dilemma during in-situ alloying of Ti34Nb via laser powder bed fusion, Acta Mater. 204 (2021) 116522, https://doi.org/10.1016/j.actamat.2020.116522.

[59] J.C. Wang, Y.J. Liu, P. Qin, S.X. Liang, T.B. Sercombe, L.C. Zhang, Selective laser melting of Ti-35Nb composite from elemental powder mixture: microstructure, mechanical behavior and corrosion behavior, Mater. Sci. Eng. A 760 (2019) 214–224, https://doi.org/10.1016/j.msea.2019.06.001.

[60] H. Gong, K. Rafi, H. Gu, G.D. Janaki Ram, T. Starr, B. Stucker, Influence of defects on mechanical properties of Ti-6Al-4V components produced by selective laser melting and electron beam melting, Mater. Des. 86 (2015) 545–554, https://doi.org/10.1016/j.matdes.2015.07.147.

[61] H. Schaal, P. Castany, P. Laheurte, T. Gloriant, Design of a low Young's modulus Ti-Zr-Nb-Sn biocompatible alloy by in situ laser powder bed fusion additive manufacturing process, J. Alloys Compds. 966 (2023) 171539, https://doi.org/10.1016/j.jallcom.2023.171539.

[62] K. Endoh, M. Tahara, T. Inamura, H. Hosoda, Effect of Sn and Zr content on superelastic properties of Ti-Mo-Sn-Zr biomedical alloys, Mater. Sci. Eng. A 704 (2017) 72–76, https://doi.org/10.1016/j.msea.2017.07.097.

[63] Y.L. Hao, S.J. Li, S.Y. Sun, R. Yang, Effect of Zr and Sn on Young's modulus and superelasticity of Ti-Nb based alloys, Mater. Sci. Eng. A 441 (2006) 112–118, https://doi.org/10.1016/j.msea.2006.09.051.

[64] F. Brumbauer, N.L. Okamoto, T. Ichitsubo, W. Sprengel, M. Luckabauer, Minor additions of Sn suppress the omega phase transformation in beta titanium alloys, Acta Mater. 262 (2024) 119466, https://doi.org/10.1016/j.actamat.2023.119466.

[65] J.W. Edington, Practical Electron Microscopy in Materials Science, Macmillan Philips Technical Library, 1975.

[66] D. Herzog, V. Seyda, E. Wycisk, C. Emmelmann, Additive manufacturing of metals, Acta Mater. 117 (2016) 371–392, https://doi.org/10.1016/j.actamat.2016.07.019.

[67] H. Peng, Y. Zhu, J. Wang, J. Zhu, J. Liu, K. Zhang, P. Lynch, H.L. Fraser, P. Hodgson, M. Heilmaier, N. Birbilis, Y. Wang, A. Huang, Achieving high strain hardening and strength in an additively manufactured titanium alloy, Nat. Commun. 16 (2025) 10224, https://doi.org/10.1038/s41467-025-65033-2.

[68] T. Ingale, A. Sharma, J. Tang, A. Chesetti, S. Kumar Sarkar, V. Soni, S. Aditya Mantri, Y. Zheng, F. Sun, N.B. Dahotre, F. Prima, R. Banerjee, Extending strain hardening to high yield strengths in additively manufactured Ti-10V-2Fe-3Al alloy via confined stress-induced transformations, Acta Mat. 298 (2025) 121437, https://doi.org/10.1016/j.actamat.2025.121437.

[69] J.F. Xiao, X.K. Shang, J.H. Hou, Y. Li, B.B. He, Role of stress-induced martensite on damage behavior in a metastable titanium alloy, Int. J. Plast. 146 (2021) 103103, https://doi.org/10.1016/j.ijplas.2021.103103.

[70] M. Duport, P. Lhuisser, J.-J. Blandin, R. Dendievel, M. Veron, F. Prima, G. Martin, Processing, microstructures and mechanical response of a β-metastable Ti-14Mo alloy fabricated by Electron Beam Powder Bed Fusion, Addit. Manuf. 61 (2023) 103340, https://doi.org/10.1016/j.addma.2022.103340.

[71] J.A. Klostermann, The concept of the habit plane and the phenomenological theories of the martensite transformation, J. Less Common Met. 28 (1972) 75–94, https://doi.org/10.1016/0022-5088(72)90170-1.

[72] E.G. Obbard, Y.L. Hao, R.J. Talling, S.J. Li, Y.W. Zhang, D. Dye, R. Yang, The effect of oxygen on α'' martensite and superelasticity in Ti-24Nb-4Zr-8Sn, Acta Mater. 59 (2011) 112–125, https://doi.org/10.1016/j.actamat.2010.09.015.

[73] S. Li, T. Nam, Superelasticity and tensile strength of Ti-Zr-Nb-Sn alloys with high Zr content for biomedical applications, Intermetallics 112 (2019) 106545, https://doi.org/10.1016/j.intermet.2019.106545.

[74] W.-Z. Zhang, G.C. Weatherly, A comparative study of the theory of the O-lattice and the phenomenological theory of martensite crystallography to phase transformations, Acta Mater. 46 (1998) 1837–1847, https://doi.org/10.1016/S1359-6454(97)00435-7.

[75] J.K. Mackenzie, J.S. Bowles, The crystallography of martensite transformations – IV body-centered cubic to orthorhombic transformations, Acta Metall. 5 (1957) 137–149, https://doi.org/10.1016/0001-6160(57)90018-4.

[76] O. Matsumoto, S. Miyazaki, K. Otsuka, H. Tamura, Crystallography of martensitic transformation in Ti-Ni single crystals, Acta Metall. 35 (1987) 2137–2144, https://doi.org/10.1016/0001-6160(87)90042-3.

[77] S. Miyazaki, K. Otsuka, C.M. Wayman, The shape memory mechanism associated with the martensitic transformation in Ti-Ni alloys-I. Self-accommodation, Acta Metall. 37 (1989) 1873–1884, https://doi.org/10.1016/0001-6160(89)90072-2.

[78] Y. Liang, H. Kato, M. Taya, T. Mori, Infinitesimal approach to the crystallography of martensitic transformation: application to Ni-Ti, Scripta Mater. 43 (2000) 535–540, https://doi.org/10.1016/S1359-6462(00)00465-6.