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# Anisotropy in tensile properties of a high strength metastable β titanium alloy

Tiphaine Giroud*, Patrick Villechaise, Azdine Naït-Ali, David Mellier, Samuel Hémery*

Institut Pprime, ISAE-ENSMA, Université de Poitiers, CNRS UPR 3346, Téléport 2, 1 avenue Clément Ader, BP 40109, Futuroscope-Chasseneuil Cedex 86961, France

## ARTICLE INFO

### Keywords:

Titanium alloys

Mechanical properties

Anisotropy

Strain localization

Fracture mechanisms

## ABSTRACT

High strength metastable β titanium alloys are widely employed in the aircraft industry due to their outstanding strength-to-weight ratio. While components can endure complex in-service mechanical loading, the anisotropy in tensile properties has been the subject of limited attention. In this study, its origin was investigated focusing on the role played by millimeter scale β grains as they were recently identified as a source of heterogeneous deformation. Tensile properties of Ti-10V-2Fe-3Al processed via different thermomechanical routes were assessed using multiple sampling directions. In particular, elongation values were observed to vary significantly depending on the testing direction. A combination of SEM, EBSD, μ-CT and in-situ DIC during tensile tests was employed to clarify the underlying causes of this behavior. Substantial differences in strain heterogeneity and localization were found related to features of β grains, including their crystallographic and morphologic orientations. Furthermore, multiple fracture mechanisms were observed to derive from the differences in deformation behavior, and eventually compete to trigger specimen failure. Elongation values are then determined by both the degree of strain heterogeneity and the operating fracture mechanisms. These findings provide a new understanding of the role of the microstructure in the tensile behavior of high strength metastable β titanium alloys.

## 1. Introduction

High strength metastable β titanium alloys are widely employed for structural applications in the aerospace industry due to their outstanding strength-to-weight ratio at room temperature [1]. In particular, Ti-10 V-2Fe-3Al (Ti-10-2-3) alloy has been successfully used for various aircraft components, such as in the landing gear structure of the Boeing 777 [2]. A wide range of mechanical properties can be achieved depending on the thermo-mechanical route applied to tailor microstructural features [3,4]. For example, ultimate tensile strengths higher than 1.8 GPa can be obtained utilizing precursor metastable ω phase to generate ultra-fine α lamellae embedded in β phase [5]. However, bimodal microstructures exhibit the optimal balance of mechanical strength and ductility for numerous applications [6–10]. This notably results from the competitive effect of microstructural features including primary α, secondary α, grain boundary α and β grain size on mechanical properties [11,12]. Anisotropy in tensile properties is a major concern for this class of alloys. Several examples have been reported in prior studies for different microstructures [13–18].

Aspect ratios of β grains have been acknowledged as a key feature

governing the anisotropy in ductility [19]. Also, β grain size reduction generally enables to increase the elongation to fracture [20,21]. These trends pertain, at least partially, to localized plastic deformation along continuous α layers at β grain boundaries. In particular, the orientation of grain boundary α layers with respect to the tensile axis generates a substantial anisotropy for microstructures with elongated β grains [14]. While established several decades ago for metastable β titanium alloys, this feature was frequently invoked and studied in the more recent additive manufacturing framework [22,23]. Bimodal microstructures, obtained through processing in the α + β field, are often preferred to avoid the presence of continuous α layers at β grain boundaries, which is detrimental to ductility [24]. To the best of the authors’ knowledge, the origin of the anisotropy in elongation has not been clarified for such microstructures [25].

Regarding the anisotropy in yield strength, the orientation dependence was ascribed to a texture effect [14,25]. However, a restricted amount of comprehensive studies is available for dual phase titanium alloys with a high fraction of β phase retained at room temperature [26]. A significant contribution may pertain to the individual behavior of constitutive phases, which display a significant anisotropy in the elastic

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: tiphaine.giroud@yahoo.fr (T. Giroud), samuel.hemery@ensma.fr (S. Hémery).</footnote>
and plastic deformation regimes [6,19,26–28]. In particular, the texture of the α phase is known to generate a substantial tensile anisotropy in α and α + β alloys [19,29–31]. This feature results from the orientation dependent mechanical response of the α phase, which involves the competition between different slip and twinning systems displaying various critical resolved shear stress magnitudes. The situation is more complex in metastable β alloys as operating mechanisms, including transformation and twinning induced plasticity, depend on the degree of stability of the β phase [32–35]. While this topic has been the focus of intense research efforts over the past decades, a more restricted amount of studies was devoted to deformation anisotropy in stable β phase, such as found in most engineering components [36]. In particular, a pronounced elastic anisotropy of the β phase has been reported [26,37,38], but the poor knowledge of elastic constants to employ for a given material is still a challenge to overcome. This topic has recently drawn an increasing interest as elastic incompatibility stress driven by the elastic anisotropy of β phase and arising at α/β interfaces and β grain boundaries are known to influence the onset and the development of plasticity [26,39–41].

Cooperative deformation of α and β phases generates an anisotropic
deformation behavior at the mesoscale. This feature was highlighted in
single colonies owing to the operation of a variety of slip transmission
processes across α/β interfaces [38,42,43]. This behavior results from
Burgers orientation relationships, which also enable dislocation slip to
extend over large microstructural units, including multivariant α
structures or α colonies [44]. Consequences are expected on damage
evolution as well since void nucleation has been frequently reported to
occur at α/β interfaces due to plastic strain incompatibilities [48–51].
Features of β grains such as the crystallographic orientation and their
aspect ratio are then likely to govern tensile properties of metastable β
titanium alloys and the associated anisotropy. However, mesoscale
characterization of deformation and fracture mechanisms is still rarely
reported in these alloys in spite of the established role of large micro-
structural units in near – α and α + β Ti alloys [44–47]. In particular, a
recent study highlighted heterogeneous deformation in relation to β
grains [38]. Unfortunately, consequences on tensile properties and
fracture mechanisms have not been documented in the existing litera-
ture to the best of the authors’ knowledge.

In the present study, the tensile anisotropy of a high strength meta-
stable β titanium alloy was examined with a special emphasis on the role
of β grains in deformation and fracture processes. For this purpose, the
tensile properties of Ti-10-2-3 with a bi-modal microstructure were
characterized in three dimensions using multiple loading directions.
Two materials with different thermo-mechanical processing histories
but a similar heat treatment sequence were employed to consider
different aspect ratios of β grains alongside a similar population of α
precipitates. Origins of the differences in strength and ductility were
clarified using fractography and *in situ* tensile tests combined with dig-
ital image correlation (DIC). Strain fields were interpreted considering
microstructural information collected using scanning electron micro-
scopy (SEM) and electron back-scattered diffraction (EBSD) to unveil
features of mesoscale deformation and fracture processes. Complemen-
tary characterization using X ray micro-computed tomography (μ-CT)
was also carried out during interrupted tests to monitor damage evo-
lution. The origin of the anisotropy in tensile properties is finally dis-
cussed based on the analysis of deformation and fracture processes in
relation to β grains.

## 2. Materials and experiments

### 2.1. Material and specimen preparation

Ti-10V-2Fe-3Al employed in the present study was provided by TIMET Savoie, France. Samples were machined from 280 and 125 mm diameter billets resulting from different thermo-mechanical processing routes in the α + β field. These billets will be denoted as LB and SB

respectively in the following. A reference frame established using the
billet geometry is shown in Fig. 1. L, R and T directions are used
throughout the article for designations of anisotropic properties. They
denote the longitudinal (L), radial (R) and transverse directions (T). The
measured chemical compositions are given in Table 1. Both SB and LB
materials were applied a solution treatment at 770 °C for 2 h followed by
air cooling. An aging treatment at 500 °C was then applied for 8 h and
followed by air cooling.

## 2.2. Microstructure characterization

For microstructural characterization, samples were first ground using SiC paper up to 4000 grade. Rough polishing was then applied using a 9 µm diamond suspension. A mixture of 90 % colloidal silica solution containing 40 nm SiO₂ particles and 10 % hydrogen peroxide was used for the final polishing step. This procedure was applied for EBSD and SEM characterization of the microstructure. To allow micro-structure observation using optical microscopy, chemical etching was applied after the preparation steps listed previously. The employed Kroll reagent solution consisted of 100 mL water, 3 mL HF, and 6 mL HNO₃.

Different characterization techniques were used to comply with the
different length scales of the microstructures composed of millimeter
large β grains as well as a few tens of nanometers thick secondary α (αs)
laths. Optical micrographs were acquired using a Zeiss Imager Vario Z2
microscope in dark field mode. SEM micrographs were acquired using a
JEOL 7000F microscope. The thickness of αs laths was estimated using
back-scattered electron micrographs. Crystallographic orientations were
characterized using a JEOL 6100 SEM equipped with a Hikari detector
provided by EDAX. A 3 µm step size was applied to characterize β grains.
Dimensions of β grains were determined along different directions using
the intercept method applied to EBSD data. To ensure the consideration
of reliable data points, pixels with a confidence index lower than 0.2
were excluded from texture analysis of the β phase. Maps showing the
local crystallographic orientations of β phase were generated using the
MTEX program for Matlab [52]. A confidence index higher than 0.1 was
considered for this purpose. Missing or mis-indexed pixels were subse-
quently replaced with data from surrounding pixels. Smaller EBSD maps
were collected using a 0.2 µm step size to assess the equivalent diameters
of primary α grains (αp) and β sub-grains. The area fraction of primary α
grains was derived from these datasets as well.

## 2.3. Mechanical testing

Monotonic uniaxial tensile tests were carried out to characterize
tensile anisotropy. Specimens were tested along different directions
represented in Fig. 1. Three sampling planes, T-R, L-R and L-T were
defined. Specimens were machined to assess tensile properties at 0°, 30°,

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Schematic representation showing the L, R and T reference frame defined according to the billet geometry. The L-T sampling procedure is also displayed with specimens machined 0°, 30°, 45°, 60° and 90° from the L direction in the LT plane.</figcaption></figure>
<table><caption>**Table 1**
Chemical composition of Ti-10-2-3 used in the present study (wt%).</caption><thead><tr><th>Elements</th><th>Al</th><th>Fe</th><th>V</th><th>O</th><th>C and N</th></tr></thead><tbody><tr><td>LB</td><td>3.1</td><td>1.9</td><td>9.6</td><td>0.11</td><td>Traces</td></tr><tr><td>SB</td><td>3.1</td><td>1.9</td><td>9.5</td><td>0.09</td><td>Traces</td></tr></tbody></table>

45°, 60° and 90° from L, R or T in the three planes. The inclination is relative to the direction first mentioned in the designation. Four specimens were tested per direction. Cylindrical specimens with a gage length of 13 mm and a gage diameter of 4.3 mm were used. Uniaxial tensile tests were performed on an INSTRON 8862-MT testing machine equipped with a 50 kN load cell. Displacement control was used for loading at a nominal strain rate of $10^{-3} s^{-1}$ at room temperature. The initial strain rate was about $4 \times 10^{-4} s^{-1}$. An extensometer was used for strain monitoring.

## 2.4. In-situ monitoring of strain localization and fracture mechanisms

Tensile tests were also carried out *in-situ* in an optical microscope to study deformation and fracture at the mesoscale. Dogbone shaped specimens with a gage length of 10 mm, a gage width of 2 mm and a gage thickness of 1 mm were used for these tests. For a quantitative study of strain localization, strain fields on the surface of the specimens were obtained by digital image correlation (DIC) over the whole gage length. The methodology used in [38] and [53] was applied in this work. The reader interested in more details may refer to these studies, although important features are briefly summarized in the following. After grinding and polishing using the procedure described in the 2.2 section, the tensile specimen was etched using Kroll's reagent. The apparent microstructure was used as a speckle.

The *in-situ* tensile tests were carried out using a DEBEN miniaturized tensile testing machine equipped with a 5 kN load cell. The loading direction is referred to as X throughout the article. The uniaxial tensile tests were performed at room temperature with an applied displacement rate of 0.05 mm/min. The displacement was stopped for different macroscopic strain levels. Optical micrographs used for digital image correlation were captured using a ZEISS Imager Vario Z2 in dark field mode. The XY plane was observed during the *in-situ* tests. The whole gage length was mapped using 2452 x 2056 pixels² tiles with a 20 % overlap. The spatial resolution was 1.46 pixels/µm. Acquired micrographs were then stitched using the “Grid/Collection stitching” routine from the Fiji software [54,55]. The NCORR open source program for Matlab was employed for DIC [56]. The subset radius was set to 25 pixels and the subset spacing to 5 pixels. The strain radius was set to 15 points. The effective shear strain ($\gamma_{eff}$) was calculated from the in-plane strain tensor, as described in Equation (1) to consider all in-plane strain components [57].

$$ \gamma_{eff} = \sqrt{\left(\frac{\epsilon_{xx} - \epsilon_{yy}}{2}\right)^2 + \left(\frac{\epsilon_{xy} + \epsilon_{yx}}{2}\right)^2} \quad (1) $$

With $\epsilon_{xx}$ the strain in the loading direction, $\epsilon_{yy}$ the strain normal to the loading direction and $\frac{(\epsilon_{xy}+\epsilon_{yx})}{2}$ the in-plane shear component.

Comparisons of local strain values in different specimens were generally carried out considering similar macroscopic strain. However, the displacement control of the tensile stage led to differences typically about +/- 0.2 %. The effective shear strain values were normalized to alleviate related biases. They were divided by the average effective shear strain in the gage length for this purpose. This procedure defines the normalized effective shear strain.

## 2.5. 3D characterization of damage evolution and fracture surfaces

The presence of internal cracks was characterized in 3D using µ-CT. A

tomograph manufactured by RX Solution equipped with a Hamamatsu sealed type microfocus X-ray tube operating at 40–150 kV / 0–500 µA, within a maximum power of 75 W, was used for this purpose. A 5 µm resolution was reached in this work, with an accelerating voltage of 100 kV and a beam current of 59 µA. This X-ray detector consists in an X-ray CsI scintillator screen which is settled on an amorphous silicon layer. For 3D reconstruction, X-ray images were acquired from 1120 rotation views over 360° of rotation (approximately 0.32° rotation step). The reconstruction was performed using an algorithm based on the filtered back-projection procedure for Feldkamp cone beam geometry.

The 3D geometry of the fracture surfaces was characterized using the Alicona InfiniteFocus G5 optical microscope. For the applied conditions, the out-of-plane and in-plane spatial resolutions are 0.5 and 8 µm respectively.

# 3. Results

## 3.1. Microstructure

Optical micrographs obtained after etching using Kroll's reagent are shown in Fig. 2 for LB and SB respectively. Both billets contain millimeter sized β grains elongated in the L direction. Backscattered electron micrographs displayed in Fig. 2 reveal the presence of primary α phase located at β sub-grain boundaries. These precipitates are equiaxed and homogeneously distributed within β grains. Secondary α lamellas embedded in β phase are shown in Fig. 2. The observation of α lamellas with various orientations suggests no significant variant selection in the investigated materials. EBSD characterization in a restricted region confirmed the presence of the 12 crystallographic variants (not shown in the article for clarity purposes). The size of the various microstructural features is summarized in Table 2. Values demonstrate that features of α phase are similar for SB and LB. The main differences then pertain to β grains, which are shorter along T and R in SB than in LB. Their average length along L is similar, possibly due to grain fragmentation during more severe deformation applied during processing for SB. Thus, β grains exhibit a higher aspect ratio in SB. The distribution of crystallographic orientations is plotted on pole figures in Fig. 2. More than 200 β grains were considered for each material. Maximum values are approximately 2.1 and 3.2 for LB and SB respectively. This reveals that the texture of the β phase is weak although stronger for SB. However, the position of the main poles is similar for both billets.

## 3.2. Tensile properties

The Young's modulus (E), the 0.2 % proof stress (YS), the ultimate tensile strength (UTS) and elongation (El%) were extracted from the stress–strain curves. The average tensile properties obtained along the 12 loading directions are shown in radar plots displayed in Fig. 3. Significant differences in stiffness, strength and ductility exist depending on the considered direction in a given billet. For example, considering LB, average E spans a range between 108.1 GPa and 111.7 GPa. Minimum and maximum YS values are 1078 MPa and 1129 MPa respectively. The UTS is between 1134 MPa and 1193 MPa. The minimum elongation value is 4.7 % while the maximum is 16.3 %. The most notable anisotropy thus pertains to El%. Regardless of the considered billet, specimens tested along the L direction show superior elongation values. Specimens from LB and SB display average elongations of 16.0 % and 20.3 %, respectively. Tests of specimens extracted 45° to both the L and T directions resulted in minimum elongation values, with 4.7 % and 5.9 % for LB and SB, respectively. Elongation values for a given direction are then higher for SB than for LB.

Fracture surfaces of all tested specimens were observed using SEM. Examination of fracture surfaces revealed significant differences. The main characteristics are exemplified using two specimens showing different behaviors. Fig. 4 (a) shows engineering stress – strain curves obtained at room temperature for specimens from LB tested along the T
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Microstructures in LB (a.) and SB (b.) illustrated with i. micrographs showing similar features of α precipitates for both materials, ii. inverse pole figure maps of the β phase revealing the higher aspect ratio of β grains in SB, and iii. {001}, {110} and {111} pole figures indicating a weak texture of the β phase although stronger in SB.</figcaption></figure>

<table><caption>**Table 2**
Average microstructural features in studied materials.</caption><thead><tr><th>Material</th><th>α<sub>p</sub> fraction (%)</th><th>Equiaxe α<sub>p</sub> diameter (μm)</th><th>Lamellas thickness (μm)</th><th>β sub-grains diameter (μm)</th><th>β grains size along R (mm)</th><th>β grains size along T (mm)</th><th>β grains size along L (mm)</th></tr></thead><tbody><tr><td>LB</td><td>21</td><td>2.4</td><td>0.08</td><td>5</td><td>0.47</td><td>0.46</td><td>1.70</td></tr><tr><td>SB</td><td>18</td><td>2.0</td><td>0.08</td><td>5</td><td>0.30</td><td>0.26</td><td>1.43</td></tr></tbody></table>

and L directions. These specimens are referred to as specimens A and B in the following paragraphs. Elongation values are 5.2 % and 19.3 %, respectively. The Young's moduli are similar with 108.2 GPa for specimen A against 107.3 GPa for specimen B. The YS and UTS are 1087 MPa and 1142 MPa respectively for specimen A, versus 1089 MPa and 1149 MPa for specimen B. In spite of major differences in ductility, differences in macroscopic response are more subtle until the UTS is reached. The low strain hardening rates result in low uniform elongation values as predicted by the Considère criterion (i.e., typically ~ 2 % plastic strain). Despite the early onset of necking, specimen B withstood a high macroscopic strain, while specimen A did not. Fig. 4 (c) shows 3D views of fracture surfaces of specimens A and B. They display very different morphologies. The planar fracture surface of specimen A, which is inclined 45° to the loading axis, suggests a shear dominated fracture process. The height difference between the lower and the upper point of the fracture surface is about 4.4 mm. In contrast, the fracture surface of specimen B exhibits a reduced cross-sectional area alongside a cup and

cone morphology, which are typical of ductile fracture. The height difference between the upper and the lower point of the fracture surface is about 1.4 mm. It was measured on fracture surfaces of each tested specimen. The resulting values are plotted in the insert of Fig. 4 (b) as a function of elongation. The associated linear regression reveals that elongation is negatively correlated with the height of the fracture surface. SEM micrographs of the fracture surfaces of specimens A and B are reported in Fig. 4 (c). These surfaces are covered with dimples in certain locations. However, different topographies are observed in other regions. For specimen A, large regions with dimensions typical of a β grain exhibit a low roughness, which suggests fracture involving a limited or localized plastic activity. For this reason, such features will be denoted as "facets" in the following. For specimen B, a pit is present in addition to dimples covered regions. It contains a planar area covered with stretched dimples, which is inclined to the loading direction. These features suggest extensive plastic activity and a shear loading in this region. The characteristic dimensions are also typical of the β grain size.
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Radar plots showing the Young's modulus (E), the yield strength (YS), the ultimate tensile strength (UTS), and the elongation (Elongation) values as a function of the test direction. Reported values are the average of 4 tests.</figcaption></figure>

According to these observations, different fracture mechanisms seem operating and likely govern the anisotropy in ductility found in this material.

### 3.3. *Strain localization*

Dog-bone specimens machined along the R direction of SB and LB were tested in *situ* in the optical microscope. As the T-R plane was observed, the major axis of β grains (L) is normal to the surface. Fig. 5 shows the crystallographic orientations of the β phase along the loading direction and the effective shear strain maps obtained from DIC. The macroscopic strain was approximately 2 % for both specimens. The examination of strain fields revealed a highly heterogeneous deformation, which appears dependent on the crystallographic orientations of β phase. In particular, shear strain localization is suggested in β grains with a [001] direction parallel to the loading direction. This configuration is denoted as [001] oriented β grain in the following. To confirm this qualitative observation, the distribution of the effective shear strain was plotted in Fig. 5 (e) and (f) as a function of the crystallographic orientation of β grains. Three orientation domains were defined based on the alignment of [001], [110] and [111] directions of the β phase with the tensile direction. A maximum misorientation angle of 20° was used to assign pixels to a given orientation domain. The plot demonstrates that the effective shear strain is higher in [001] oriented β grains. In LB, the maximum frequency was reached for a shear strain of 0.018 or 0.026 in [001] oriented β grains while it was 0.016 and 0.012 in [110] and [111] oriented β grains respectively. In SB, the maximum frequencies are reached for shear strains of 0.018, 0.011, and 0.009 for [001], [110] and [111] oriented β grains, respectively. Similar trends thus arise for both materials.

As shown in Fig. 5, in-plane dimensions of β grains differ significantly for the specimens from LB and SB. Fig. 6 (a) shows the distribution of effective shear strain values for the specimens examined in Fig. 5. The plot reveals a more homogeneous strain distribution in the specimen from SB as compared to the specimen from LB. The maximum value of normalized effective shear strain is about 3.0 in the former versus about 4.3 in the latter. This feature being possibly related to both the β grain size and the crystallographic texture, the normalized effective shear strain was averaged over the different crystallographic orientation domains of the β phase defined in the previous paragraph. The resulting values are plotted in Fig. 6 (b). The difference between minimum and maximum values is higher for LB than for SB. This result suggests that smaller β grains favor a more homogeneous distribution of plastic strain. Interestingly, a lower elongation was obtained for the specimen from LB than for the specimen from SB, with values of approximately 8 % and 15 %, respectively. This suggests a negative correlation between strain localization and ductility, which is examined further in the following paragraphs.

Strain localization was also investigated as a function of the morphologic orientation of β grains. For this purpose, *in situ* tensile tests were carried out using three different loading directions in the L-T plane. Specimens from SB were tested along L, T and 45° to the L and T directions. Fig. 7 (a) shows the effective shear strain maps obtained for a macroscopic strain about 2.5 %. Qualitative observations of the strain fields reveal that strain localization is related to the morphology of β grains. The effective shear strain is homogeneously distributed over the gage length of the specimen tested along the L direction, which is parallel to the major axis of β grains. In contrast, specimens with elongated β grains oriented 45° and 90° to the loading direction show a more spatially heterogeneous distribution of the strain. Deformation bands
<figure><img src="image_6.png" /><figcaption>Fig. 4. (a) Engineering stress – strain curves of specimens A and B from LB tested along the T (blue) and L (green) directions, respectively, which illustrates the anisotropy in ductility, (b) fracture surface height plotted as a function of El% for all specimens, and (c) 3D views of the fracture surfaces alongside SEM micrographs showing the fracture surface of specimens A and B.</figcaption></figure>

are oriented 45° to the tensile direction for β grains with their major axes oriented 45° to the L and T directions, while they are oriented 90° to the loading direction for β grains with their major axes oriented 90° to the loading direction. The distributions of the normalized effective shear strain values are reported in Fig. 7 (b). The maximum values are about 1.9 for β grains with their major axis aligned with the loading direction (i.e., L). In contrast, they reach 4.8 and 4.2 when the major axis is rotated by 45° and 90°, respectively. Different elongation values were also measured for these three specimens. For the specimens tested along the L direction, the T direction and 45° to the L and T directions, elongation values are 11.9 %, 5.9 % and 2.1 % respectively. High local shear strain values at low macroscopic strain appear correlated with a low ductility.

### 3.4. Fracture mechanisms

To clarify the variety of behaviors and features highlighted in section 3.2, fracture mechanisms were studied using *in situ* tensile testing. Complementary information including strain fields and crystallographic orientations was obtained using DIC and EBSD, respectively. Specimens were tested along different directions to highlight the competition of multiple fracture mechanisms and the relation with strain localization. For clarity purposes, representative examples are reported in the following paragraphs.

#### 3.4.1. *Intergranular cracking mechanism*

A set of specimens showed the presence of facets on fracture surfaces. This feature was frequent when the loading direction was oriented 45° to L and T directions. However, it was also occasionally observed for other directions, as shown in Fig. 4c for a specimen tested along the T direction. Facets are illustrated in the SEM micrographs displayed in Fig. 8 (a), which show the fracture surface of a specimen from SB tested *in situ* 45° to L and T directions. The associated elongation value was about 0.7 %. All facets were inclined relative to the loading axis. The total area of facets was manually measured on fracture surfaces and plotted as a function of elongation in Fig. 8 (b). An increase in the area of facets is associated with a decrease in elongation. A linear regression was applied to the data. The correlation coefficient value, i.e., about 0.996, indicates a high correlation between the total facet area and the ductility. An increase in facet area by 0.1 mm² leads to a reduction in elongation of about 1.7 %. These observations confirm the detrimental effect of their formation on ductility.

An optical micrograph displayed in Fig. 8 (d) shows a crack observed prior to fracture. The macroscopic strain was about 1.7 %. Post-mortem observations confirmed that this crack resulted in a facet. The comparison of optical micrographs with crystallographic orientations of the β phase shown in Fig. 8 (e) revealed that cracking occurred along a β grain boundary. The strain field obtained before crack opening in Fig. 8 (f) demonstrates that intense and highly localized deformation precedes
<figure><img src="image_7.png" /><figcaption>Fig. 5. Crystallographic orientations of β phase relative to the loading direction (R) and effective shear strain maps for dog-bone specimens from LB (a-b) and SB (c-d). Effective shear strain distribution frequencies in [001], [110] and [111] oriented β grains in LB (e) and SB (f).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6. (a) Distribution of normalized effective shear strain values for specimens from SB and LB tested along the R direction, and (b) normalized effective shear strain averaged over [001], [110] and [111] oriented β grains as a function of the elongation.</figcaption></figure>

facet formation. The crystallographic orientations of the β phase on either side of the grain boundary are plotted on an inverse pole figure in Fig. 8 (c). The analysis was repeated on another facet in a different specimen. The corresponding orientations are indicated by blue points in Fig. 8 (b) and (c). For a given specimen, the points are connected and the same color was used. It is interesting to note that the orientations are not favoring early yielding and strain localization as discussed in section 3.3 (i.e., [001] oriented β grains).

Fig. 9 (a) shows an optical micrograph of the microstructure before crack formation and specimen failure. A long slip band extends across several $\alpha_p$ precipitates located at the β grain boundary. Crystallographic orientations displayed in Fig. 9 (b) confirm the presence of the β grain boundary. Fig. 9 (c) shows optical and SEM micrographs of the microstructure after fracture occurred. *In situ* monitoring confirmed that cracking occurred along the slip band located at the β grain boundary. Both the fracture plane and slip traces are parallel to a prismatic plane in $\alpha_p$ particles, which is associated with a Schmid factor of 0.49 in the example of Fig. 9 (c). Crystallographic orientations of several $\alpha_p$ particles located along the cracked β grain boundary are plotted in Fig. 9 (d). They show a high maximum Schmid factor for prismatic slip systems.

Thus, the crystallographic orientation of $\alpha_p$ precipitates located at the cracked grain boundary is favorable to slip activity. This feature is likely important for early and intense deformation to develop along the β grain boundary.

### 3.4.2. Shear dominated cracking mechanism

Planar areas covered with elongated dimples, which suggest local shear loading, were observed on the fracture surfaces of dog-bone specimens. An example is shown in Fig. 10 (a) for a specimen from LB tested *in situ* along the L direction. They are similar to those found in pits located on the fracture surface of the specimen with a high elongation and shown in Fig. 4 (c) (i.e., specimen B). *In situ* testing revealed that they correspond to early crack formation in [110] oriented β grains, which eventually triggers specimen failure. Crystallographic orientations of the β phase along the loading direction and the effective shear strain map for a macroscopic strain about 2.8 % are shown in Fig. 10 (b). The major axis of β grains is parallel to the loading direction. In agreement with strain fields shown in Fig. 7 (a) for a similar configuration, the effective shear strain is homogeneously distributed over the gage length, without noticeable localization along β grain boundaries. SEM
<figure><img src="image_9.png" /><figcaption>Fig. 7. (a) Effective shear strain maps and (b) normalized effective shear strain distribution frequencies for specimens from SB tested along different directions in the L-T plane.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 8. (a) SEM micrographs of the fracture surface of a specimen showing a facet. The specimen was taken from SB and tested 45° to the L and T directions. El % is 0.7 %. (b) Cumulative area of the facets found on the fracture surface as a function of the elongation. All dogbone specimens exhibiting facets are represented in this plot. (c) Crystallographic orientations of the β phase on both sides of cracks plotted relative to the loading direction on an inverse pole figure. Facets found in two different specimens are reported. The black dots correspond to the specimen in Fig. 8 (a). The blue dots correspond to a specimen taken from LB and tested along the T direction. (d) Optical micrograph showing a crack for a macroscopic strain about 1.7 %. (e) Crystallographic orientations of the β phase along the loading direction in the same region as (d). (f) Strain field along the loading direction (x) for a macroscopic strain about 1.4 % (i.e., before crack opening).</figcaption></figure>

micrographs of the specimen surface shown in Fig. 10 (c) and (d) reveal the presence of slip traces extending over several hundreds of micrometers in the [110] oriented β grain containing the first crack. The slip bands thus developed through several microstructural elements although they were restricted to a single β grain. The crack is oriented parallel to these slip bands. Given the length of the slip traces, they were compared to potential slip plane traces of the β phase. They match a {112} < 111 > slip system with Schmid factor of 0.48. However, one must keep in mind that the wavy slip traces and the numerous potential slip planes in BCC metals make this identification uncertain. The crack shown in Fig. 10 (c) and (d) eventually triggered failure of the specimen.

Strain localization is often linked with early damage. However, β
grains prone to strain localization (i.e., with a [001] orientation) were
not presently found associated with cracking. Deformation was studied
in β grains with different crystallographic orientations to clarify the

specific behavior of [110] oriented β grains. Fig. 11 (a) shows SEM
micrographs in three β grains with [001], [110] or [111] directions
within 20° from the loading direction and located in the region sub-
jected to necking. The high strain in the [001] oriented β grain appears
diffuse as no slip step was clearly visible based on repeated observations.
In the [111] oriented β grain, slip steps were visible in the αp grains and
at the interface between the transformed β regions and αp grains. Some
αs lamellas presented slip traces, which seemed to be restricted to in-
dividual lamellas. In the [110] oriented β grain, steps resulting from
localized slip activity were observed in transformed β region. They were
mostly located within αs lamellas. According to an analysis using EBSD
data, slip traces correspond to prismatic planes and the associated slip
systems display a high Schmid factor as exemplified in Fig. 11 (b). Ev-
idence of slip transfer across α/β interfaces is also observed. It is likely
due to the good alignment between the prismatic slip system active in
<figure><img src="image_11.png" /><figcaption>**Fig. 9.** (a) Optical micrograph obtained *in-situ* showing a slip trace located at the β grain boundary. (b) Crystallographic orientations along the loading direction in the same region. (c) Optical and SEM micrographs in the same region after fracture. Prismatic slip plane traces are indicated in red and the one with the highest Schmid factor (SF) is highlighted in white. (d) Crystallographic orientations of the fractured αₚ particles plotted on an inverse pole figure. Orientations are relative to the loading direction. Maximum Schmid factor *iso-contours* for prismatic slip are also indicated.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 10.** (a) SEM micrographs of the fracture surface of a specimen from LB tested *in situ* along the L direction. (b) Crystallographic orientation of the β phase relative to the loading direction (L) and effective shear strain map for a macroscopic strain about 2.8 %. Elongation reached 13.5 % at the end of the test. (c) and (d) SEM micrographs of the crack leading to failure. The trace of the {112} plane matching the slip traces is indicated in (c). The Schmid factor (SF) of the associated slip system is also reported.</figcaption></figure>

deformed α phase and a {112}[111] slip system of the β phase. The m' parameter, which was defined by Luster and Morris [58], allows to assess the geometric compatibility of two slip systems. A value of 1 indicates a perfect alignment between incoming and outgoing slip systems. In the examples shown in Fig. 11 (b), the m' values are higher than 0.8. This feature highlights conditions favorable for slip transfer [43,59]. Differences in deformation behaviors as a function of the crystallographic orientation of the β phase were confirmed with a statistical significance based on multiple observations. Long slip bands in [110] oriented β grains thus emerge from α variants provided (i)

prismatic slip activity occurs due to a high resolved shear stress, and (ii) the geometric compatibility with a {112}[111] slip system of the β phase is good enough to allow slip transfer. Fig. 11 (c) shows the density of slip traces in transformed β regions as a function of the crystallographic orientation of the β grain for different loading steps. Two dog-bone specimens from LB were tested along the L direction for this purpose. The local strain along the tensile direction was extracted from the DIC data. [110] oriented β grains show higher densities of slip traces in transformed β regions than other orientations. For a strain around 8 %, [110] oriented β grains display a minimum density about 0.005 mm⁻²
<figure><img src="image_13.png" /><figcaption>**Fig. 11.** (a) SEM micrographs showing surface topography due to deformation in [001], [110] and [111] oriented β grains located in the necking region. (b) Crystallographic orientations of α and β phases in a deformed [110] oriented β grain. Slip traces in the α phase match a prismatic slip plane associated with a high Schmid factor (SF). Slip traces also match {112} slip planes of the β phase, which are associated with a high Schmid factor. (c) Density of slip traces in the transformed β regions for [001], [110] and [111] oriented β grains as a function of the local strain. Two dog-bone specimens tested along the L direction from LB were considered for this plot. (d) Elongation values as a function of the normalized effective shear strain in the [110] oriented β grain where crack initiation was observed.</figcaption></figure>

while it is around 0.0025 mm⁻² and 0.001 mm⁻² for [111] and [001] oriented β grains respectively. Plastic deformation then seemingly develops differently as a function of the crystallographic orientation of the β phase.

Specimens showing evidence of cracking in a [110] oriented β grain were found associated with elongations spanning a wide range of values. To clarify the role of strain localization in this feature, the maximum effective shear strain was assessed in the [110] oriented β grain where the crack was observed to initiate during *in situ* monitoring. Before being carried out to failure, all *in situ* tests were interrupted at a targeted macroscopic strain of 2.5 % to collect surface strain fields via DIC, which ensures comparable deformation level. With this approach, local strain values provide indications about the degree of strain localization in the

fracture process zone. Fig. 11 (d) displays the elongation values as a function of the normalized effective shear strain in the [110] oriented β grains where cracks were initiated. A decrease in elongation is observed with increasing local shear strain values. A linear regression displays a negative slope of -5.98 and a high correlation coefficient of 0.83. This reveals that the degree of strain localization in [110] oriented β grains determines the ductility of the specimen.

### 3.4.3. *High local strain induced fracture*

The operation of fracture mechanisms described in the previous paragraphs relies on high strains in [110] oriented β grains or at β grain boundaries. An additional condition was used to study the competition between crack initiation mechanisms if the microstructure is

<figure><img src="image_14.png" /><figcaption>**Fig. 12.** (a) Crystallographic orientation of the β phase relative to the loading direction (T) and effective shear strain map at 2.4 % macroscopic strain for a specimen taken from SB and tested along the T direction. Elongation reached 5.9 %. (b) SEM micrographs showing the surface topography and the microstructure near the fracture surface before and after mechanical sectioning parallel to the surface. (c) Elongation plotted as a function of the normalized effective shear strain in the β grain where cracks initiated. The average crystallographic orientations of β grains where fracture is initiated are plotted in an inverse pole figure. The orientation is relative to the loading direction. The blue point corresponds to the specimen shown in (a) and (b).</figcaption></figure>
unfavorable to these mechanisms. In particular, specimens tested along the T direction satisfy none of the requirements as the number of [110] oriented β grains is low and most of the β grain boundary length is normal to the loading direction. These features are illustrated in the inverse pole figure map shown in Fig. 12 (a). The strain field obtained from DIC reveals that deformation is mostly localized in [001] oriented β grains, as expected from previous observations. The orientation of the major axis of β grains, which is normal to the loading direction, and their size, which is comparable to the cross section area of the specimen, lead to a composite like behavior, with little influence of neighboring β grains. Post mortem observations showed no presence of [110] oriented β grains or 45° oriented β grain boundary in the fracture region. Instead, fracture occurred within a near [001] oriented β grain experiencing a high strain magnitude. Little inclination of the fracture plane was suggested from the micrographs shown in Fig. 12 (b). Surface examination reveals that slip traces are visible in αp grains while the topography in the transformed β regions do not show evidence of localized deformation. Mechanical sectioning parallel to the surface showed the presence of voids, underneath the fracture surface. Voids were observed up to 120 µm away from the fracture surface. They appear to be formed in αp grains, or at the interface between αp grains and β phase. Damage then seems related to αp grains instead of transformed β regions in [110] oriented β grains. Two specimens were tested with similar conditions. The normalized effective shear strain magnitudes assessed in the β grains involved in fracture are plotted as a function of the elongation value in Fig. 12 (c) alongside points already discussed in the 3.4.2 paragraph. While elongation values are similar, higher maximum normalized shear strain magnitudes are reached. This reveals a higher resistance to fracture of β grains with a near [001] orientation. For an elongation about 6 %, the normalized shear strain values are higher than 5 versus less than 3 for [110] oriented β grains induced fracture.

# 4. Discussion

## 4.1. Anisotropy in strength

Tensile tests performed at room temperature revealed a significant anisotropy in tensile properties. The yield strength and the ultimate tensile strength were less sensitive to the loading direction than elongation. However, significant variations were noticed, as also reported in different metastable β titanium alloys [14,25]. Although no comprehensive study was reported, Sauer and Lütjering suggested a texture effect [14]. The study of strain localization reported in section 3.4 revealed high strains in [001] oriented β grains. This feature suggests a lower strength of β grains with a [001] direction parallel to the loading direction. Incompatibility stresses arising from the high elastic anisotropy of β phase may play a key role [38]. A significant contribution may also pertain to the α phase texture developed from the β → α transformation and its evolution during subsequent thermo-mechanical processing. In particular, a substantial influence of orientation distributions resulting from the Burgers orientation relationships commonly adopted between α and β phases was suggested in additively manufactured Ti-6Al-4 V [60]. A simple analysis was performed to confirm the contribution of the volume fraction of [001] oriented β grains to the observed strength anisotropy. A multi-linear regression was applied to yield strength values considering the area fraction of [001] and [111] oriented β grains. A term was also added to account for differences in β grain size in SB and LB. The corresponding equation is reported below:

$$YS = A_0 + A_1 f_{[001]} + A_2 f_{[111]} + \frac{A_3}{\sqrt{D}} \qquad (2)$$

With YS the yield strength, A₀, A₁, A₂, A₃ fitting constants, f[hl] the area fraction for [hl] oriented β grains and D the average slip length in β grains. D was calculated as the average length of segments contained in a single β grain and oriented 45° to the loading direction (i.e., the directions of maximum shear stress with the approximation of a global

stress state). For this purpose, β grains were considered as spheroids with dimensions given in Table 2. A 20° threshold was used to assign pixels to either [001], [111], or the remaining orientation domains. As this very simple approach cannot account for sample to sample variations in a given direction, the average yield strength was considered for each tested direction. The following values were obtained after fitting: A₀ = 1019.5MPa, A₁ = -0.8MPa, A₂ = 1.4MPa and A₃ = 49.7MPa.m⁻⁰.⁵. Yield strength values calculated using Equation (2) are plotted as a function of the experimental measurements in Fig. 13. The regression coefficient is about 0.6, which suggests a significant correlation between the texture of the material and the tensile strength. Increasing the fraction of [001] oriented β phase leads to a substantial decrease in strength, while increasing the fraction of [111] oriented β phase leads to an increase. This feature provides new insights into texture engineering for tailoring mechanical properties. As the low strength of [001] oriented β grains notably arises from the elastic anisotropy of the β phase, alloy design strategies to develop β phase with a reduced anisotropy may lessen the texture sensitivity of this class of alloys [61].

## 4.2. Anisotropy in ductility

Major differences in ductility were observed depending on the loading direction. In situ characterization suggested an important role of strain localization in ductility. In particular, the β grain size was found to be an influential parameter, with a small β grain size leading to a more homogeneous strain distribution and a higher elongation. The morphologic orientation of β grains was observed to be influential as well. Loading directions leading to a lower strain heterogeneity, such as the L direction, were observed to be associated with high elongation values. However, the maximum strain magnitude was found insufficient to predict the ductility. In particular, the strain was found mainly localized in [001] oriented β grains although they were rarely identified as preferred sites for fracture initiation.

Features of fracture surfaces were found characteristic of the elongation displayed during the tensile tests. Facets, pits and dimples covered regions have been identified in specimens used to assess the anisotropy in tensile properties. Facets and pits correspond to crack initiation sites leading to low and high elongation values, respectively, while dimples covered regions likely pertain to final fracture. Details of the fracture mechanisms were investigated using in situ testing. Low elongation values, such as recorded for specimens tested 45° from the L direction in the L-T plane for example, were associated with inclined fracture surfaces displaying no evidence of necking, in agreement with the stress strain curves. Planar facets with a low roughness are characteristic features. In situ tensile testing revealed that they resulted from cracking along β grain boundaries, which was preceded by intense shear localization at these locations. No thick and continuous α layer was present at the β grain boundaries. This observation highlights that its absence is not sufficient to rule out early damage in such locations [14]. Indeed, necklaces of αp phase well oriented for prismatic slip seemingly permit slip localization along β grain boundaries. When operating, this mechanism is very detrimental to ductility. However, specific conditions are required. It was only observed when a substantial fraction of the β grain boundary length was subjected to a high shear stress and served as a path for the formation of long shear bands (e.g., for loadings 45° from the L direction, which corresponds to the major axis of β grains). Details of the underlying mechanism remain to be clarified, including the contributions of the sub-micron scale microstructure configurations at the β grain boundary, such as thin but continuous α phase layers, and the specific stress state reached locally.

The abovementioned conditions were not satisfied for specimens showing superior elongation values. In this case, fracture surfaces displayed no such facet, and conventional cup and cone fracture surfaces were observed. However, pits, with an inclined and planar region showing evidence of ductile shearing, were identified. They result from transgranular crack initiation in [110] oriented β grains due to intense
<figure><img src="image_15.png" /><figcaption>Fig. 13. (a) Experimentally measured values of yield strength (YS) versus values obtained from Equation (2), and (b) Orientation domains used to calculate the area fractions for [001] and [111] orientations and defined such as a [001] or [111] direction is within 20° from the loading direction.</figcaption></figure>

slip activity. The development of long slip bands involves coarse slip in transformed β regions. In particular, prismatic slip nearly parallel to the habit plane of α/β interfaces was observed in α_s lamellas. This configuration allows a high mean free path for dislocation glide and an easy transmission to surrounding β phase. A significant correlation between local strain magnitudes and the resulting macroscopic elongation was noticed. Interestingly, elongation values associated with crack initiation involving severe strain localization in [110] oriented β grains overlapped with failures due to facet formation. Specific microstructure configurations were found critical for crack initiation. As illustrated in the examples reported in Fig. 10 (b) and 11 (b), the [110] oriented β grain associated with the development of the main crack was generally surrounded by [100] oriented β grains. Based on the findings from the present study, the critical character of this microstructural arrangement can be explained as follows. [100] oriented β grains are locations of high strain magnitudes due to their low strength highlighted in the previous paragraphs. As a consequence, the adjacent [110] oriented β grain is imposed a high strain magnitude due to compatibility across grain boundaries. Early cracking eventually occurs in the [110] oriented β grain as a result of the strain state imposed by the surrounding microstructure. Indeed, [100] oriented β grains can withstand high strain magnitudes without detectable damage, while [110] oriented β grains experience damage at much lower strain levels.

Strain localization along a path of [001] oriented β grains connecting across the section of specimens was reported in a prior study [38]. Such configuration is generally not available. A β grain with a different crystallographic orientation is likely present, which triggers fracture according to processes such as discussed in the previous paragraph (i.e., for [110] oriented β grains). However, a specific configuration involving the major axis of β grains oriented normal to the loading direction and a low probability of [110] oriented β grains in the gage section occurred for small dog-bone specimens tested *in situ* along the T direction, as illustrated in Fig. 12. Intermediate elongation values and intense strain localization were observed. *In situ* characterization confirmed that in spite of the high local strain values, damage tolerance is high in β grains with [001] orientations. Voids found deep under the fracture surface according to *post-mortem* analyses suggest that [001] oriented β grains could be responsible, at least in part, for dimples covered regions.

To summarize, the presently reported observations highlighted that the anisotropy in ductility is determined by the degree of strain localization and the operating fracture mechanisms. Both are governed by the crystallographic orientation and the morphology of β grains. In future investigations, quantitative assessments of the contributions of the various features identified in this study may be achieved using crystal plasticity simulations of carefully designed dual-phase microstructures. This methodology enables to dismiss limitations of experimental approaches related to the restricted range of configurations that can be considered.

### 4.3. Competition between fracture mechanisms, and resulting ductility

The analysis of strain localization and fracture mechanisms highlighted a complex interplay resulting in anisotropic ductility. Global trends can be summarized as follows. Specimens tested along the L direction generally exhibited a high ductility due to a low degree of strain localization and transgranular crack initiation. The limited fraction of grain boundaries oriented 45° from the loading axis is a key feature. In contrast, specimens tested ~ 45° from the L and T directions generally exhibited a very low ductility due to a high degree of strain localization and intergranular crack initiation promoted by the significant fraction of grain boundaries oriented 45° from the loading axis. The behavior of specimens from the R-T plane showed a significant scatter. The variable strain localization and the occasional presence of grain boundaries oriented 45° from the loading axis resulted in average elongation values indicating intermediate ductility. However, it was very low for specimens associated with facet formation, or very severe strain localization, and significantly higher in other cases. Tensile tests carried out along the T direction for the LB material supports this analysis. The 8 specimens tested along this direction resulted in an average elongation value about 9.8 % and the standard deviation was 4.2 %. In particular, sample A shown in Fig. 4 failed after less than 5.2 % total strain. In this specimen, the fracture surface exhibited a higher fraction of facets due to early intergranular fracture than other specimens. This observation highlights the key role of critical microstructure configurations highlighted in this study, and the random character of their distribution in the specimens.

The major role played by millimeter scale β grains identified in this work suggests that extrinsic size effects are likely important for laboratory scale testing procedures. In particular, significant differences were observed between *in situ* and conventional specimens considered in this study. While the first crack has always led to failure in the *in situ* analyses, this was not the case in conventional tensile tests. µ-CT characterization was carried out before fracture of several specimens. 3D views showing the cracks present before failure of the specimen are displayed in Fig. 14. Multiple cracks can co-exist, and be associated with different fracture mechanisms as suggested by the *post-mortem* observation of facets and pits on fracture surfaces. The total elongation thus appears governed by the competition between the different mechanisms, which can operate concurrently in relation to local microstructural configurations.

A restricted number of β grains is typically present in a cross sectional area of conventional laboratory specimens. This feature is likely related to the significant variability in ductility for a given test direction. Dimensions of specimens are then of utmost importance for the assessment of mechanical properties in metastable β Ti alloys, especially when used as a basis for component design. The dimensions of β grains being larger than typical microstructural configurations in other classes of alloys, specific approaches have to be considered. In particular, free surface
<figure><img src="image_16.png" /><figcaption>**Fig. 14.** (a) 3D views of cracks obtained using µ-CT for 8.9 % macroscopic strain applied to a specimen from LB tested along the R direction. El % was 9.4 %. (b) SEM micrographs of the fracture surface of the specimen. (c) 3D views of cracks obtained using µ-CT for 19.2 % macroscopic strain applied to a specimen from SB tested along the L direction. El % was 19.8 %. (d) SEM micrographs showing the fracture surface of the specimen. Inserts show the fracture surface and the underlying microstructure after mechanical sectioning parallel to the loading axis. A competition between different fracture mechanisms is evidenced.</figcaption></figure>

effects may influence strain localization and fracture mechanisms in a way that remains to be clarified, and would be exacerbated for small specimen sizes. This is under on-going investigation.

## 5. Conclusion

In this article, the anisotropy in tensile properties of Ti-10 V-2Fe-3Al was studied at room temperature. A special focus was put on the role of β grains using different techniques including in-situ optical microcopy tensile test, DIC, µ-CT and EBSD. The main conclusions can be drawn as follows:

- A significant anisotropy in tensile properties was noticed. While variations in strength were moderate, major elongation differences were found, with maximum values reaching up to 4 times the minimum values.

- In agreement with prior studies, the crystallographic orientation of the β phase governs strain localization. Indeed, high strain magnitudes were mainly associated with [001] oriented β grains. The analysis of the tensile responses suggests a lower strength for this orientation, which contributes to the observed strength anisotropy.

- Strain localization is also highly affected by geometric features of β grains. For example, small grains promote a spatially homogeneous distribution of deformation. The orientation of the major axis of β grains with respect to the loading direction is an important parameter as well.

- A competition between different fracture mechanisms was identified. Low elongation values mainly result from shear dominated cracking along β grain boundaries, even in the absence of coarse and continuous α layers. Higher elongation values were obtained when this mechanism was inactive and transgranular fracture was shear dominated in [110] oriented β grains. However, the elongation resulting from the operation of each of these mechanisms depends on the strain magnitude reached locally and the associated microstructural configurations.

- Overall, β grains play a major role in the mechanical properties of high strength metastable β titanium alloys. In particular, they are the cause of an intricate interplay between strain localization and fracture mechanisms, which results in the observed anisotropy in tensile properties. This finding provides guidelines for future improvements of mechanical properties in this class of alloys.

## CRediT authorship contribution statement

**Tiphaine Giroud:** Writing – original draft, Investigation, Formal analysis, Data curation. **Patrick Villechaise:** Writing – review & editing, Validation, Supervision, Project administration, Methodology, Conceptualization. **Azdine Naït-Ali:** Writing – review & editing, Visualization, Formal analysis. **David Mellier:** Writing – review & editing, Investigation, Data curation. **Samuel Hémery:** Writing – review & editing, Validation, Supervision, Project administration, Methodology, 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.

## Acknowledgements

Airbus, Aubert & Duval, Safran Tech and TIMET Savoie are gratefully acknowledged for financial support of the Continuum consortium. This work has been partially supported by the "Contrat de Plan Etat - Région Nouvelle-Aquitaine" (CPER) as well as the "Fonds Européen de Développement Régional (FEDER)".

## Data availability

Data will be made available on request.

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