# Achieving basal texture in pure titanium: Process implementation and mechanical property evaluation

Mélaine Tournay, Jean-Sébastien Lecomte*, Christophe Schuman, Yudong Zhang, Éric Fleury

Université de Lorraine, CNRS, Arts et Métiers, LEM3, F-57000 Metz, France

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

## ARTICLE INFO

### Keywords:

Titanium

Cold-rolling

Annealing

In-situ heating

Twinning

Texture

## ABSTRACT

The strong crystallographic texture in titanium sheets leads to anisotropic mechanical properties, complicating forming processes. In this article, we outline a straightforward industrial thermomechanical process to achieve a basal texture in commercially pure titanium. This process involves cold rolling followed by annealing, without needing to modify the sheet's initial grain size or its mechanical properties (E, Rm, ε%). Notably, while the basal texture is seldom intentionally produced in titanium sheets, it is well-documented in magnesium alloys, where it promotes isotropic properties within the sheet plane. Tensile tests, aided by image correlation, confirm that planar isotropy and an improved deep-drawability (measured by the Lankford coefficient) are attained. Initial EBSD analysis determined the optimal temperature and annealing time. The article will detail the rolling-annealing protocol necessary to achieve this desirable basal texture.

## 1. Introduction

Commercially pure titanium (cp-Ti) is extensively utilized in industrial applications owing to its favorable properties, including low density, excellent biocompatibility, and strong corrosion resistance [1]. However, under large deformation at room temperature, cp-Ti, with its hexagonal close-packed (hcp) crystal structure, demonstrates greater anisotropy and more complex plastic deformation behavior than cubic metals. Crystallographic anisotropy during thermomechanical processing significantly affects the deformation behavior of cp-Ti [2,3], with the most pronounced anisotropy arising from the sheet texture [4].

During rolling, cp-Ti develops two conventional texture components, depending on the temperature and mode of rolling. When rolled at 800 °C, a Basal/Transverse (B/T) texture forms, with *c*-axes inclined at ±40° to the transverse direction (TD). At 950 °C, a Transverse (T) texture forms, with *c*-axes aligned along the TD. Both textures result in significant planar anisotropy, posing challenges for sheet formability [5]. It is important to note that the rolling temperature of 950 °C mentioned in [5] is not applicable to CP-Ti, as it would be above the β-transus temperature, leading to different texture developments compared to those discussed in this study. A study by Jia et al. [6] demonstrated that textural anisotropy can lead to early fractures, particularly at high-angle grain boundaries (HAGB).

Huang et al. [7] studied a cp-Ti sheet with a T-texture and 45 µm grain size, which was cold-rolled and annealed at temperatures between 0.42 Tm and 0.47 Tm. Their findings showed a clear textural evolution toward the B/T texture and a reduction in grain size (from 45 µm to 12 µm), which they attributed to basal slip activity. A temperature of T ≥ 0.5Tm is necessary for recrystallization to occur [8,9], replacing the cold-worked microstructure with new grains (T ≥ 700 °C for cp-Ti).

Zhao's study on cp-Ti with ultrafine grains (0.44 µm) and a B/T texture identified dislocation glide as the primary deformation mechanism during rolling. Meanwhile, Liu [10] and Tournay [11], using EBSD analyses, showed that both twinning and slip accommodate deformation during rolling. Given the limited number of slip systems in cp-Ti, mechanical twinning is often significantly activated [12,13]. Twinning is highly sensitive to microstructural factors, particularly grain size, lattice orientation, and deformation rate, as shown by statistical studies by Beyerlein et al. [14,15]. Recent studies have also shown that twinning is active at low cold rolling reduction rates [16–18], but beyond a certain reduction rate (between 0.3 and 0.8 according to [17]), twinning is suppressed and replaced by ⟨c + a⟩ slip.

Bozzolo et al. [19] studied cp-Ti with a 3.3 µm grain size and a B/T texture, identifying three sub-textures: tA (B/T texture), tB (a hybrid texture characterized by a primary orientation {11013}⟨11210⟩ or by {0°, 35°, 30°} angles in Euler space), and tC (T texture). After annealing, the tA grains remained stable, the tC grains disappeared, and the tB

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: jean-sebastien.lecomte@univ-lorraine.fr (J.-S. Lecomte).</footnote>
grains grew. They also observed that CSL grain boundaries had no significant impact on grain growth. Wang et al. [20] further explored the phenomenon of preferential grain orientation during growth, referring to it as oriented growth. Barrett [21] first proposed that the growth potential of a given nucleus or grain depends on the orientation difference across the migrating recrystallization front. It is evident that the fastest-growing nuclei contribute to the final recrystallization texture. Several studies [22–24] on aluminum have shown that nuclei with a misorientation of approximately 40° around a common (111) axis grew the fastest, though the preferential growth advantage depends on the material in question.

Our experimental protocol builds on the previous PhD work of Serghat [25], who achieved a B/T texture in cp-Ti using a three-step cold rolling process. In his research, the sheet thickness was reduced from 6 mm to 1 mm over three rolling steps with intermediate annealing, resulting in a nearly basal texture.

This article demonstrates that twinning, particularly T1 twinning, plays a crucial role in achieving the basal texture, emphasizing that grains must reach a critical size to activate twinning. We will also show that slightly exceeding 0.5 Tm is necessary for grain recrystallization. Furthermore, we will demonstrate that to obtain this twinning-induced ND basal texture, low reduction rates (20 %) are required at each pass to allow the microstructure to regenerate through static recrystallization. The experimental protocol for obtaining the basal (B) texture, which to the authors' knowledge has never been intentionally produced, will be discussed in detail.

## 2. Experimental methods

The material used in this study is a commercially pure titanium (cp-Ti) sheet (ASTM grade 2) with a thickness of 5 mm, sourced from Baoji Titans Metal Co. (China). The chemical composition is given in Table 1.

The cp-Ti sheet was rolled down to 1 mm in thickness by 7 passes. The reduction per pass was 20 % as shown in the Fig. 1. The annealing heat treatments (or HTR: Heat treatment Recrystallization) were carried out in a BMICRO furnace from B.M.I, operating under primary vacuum and allowing argon quenching. The furnace enclosure is 45 cm deep with a diameter of 30 cm. The primary vacuum allows pressures of approximately $10^{-3}$ mbar to be reached.

RD, TD and ND represent the rolling direction, transverse direction, and normal direction of the as-received (annealed) sheet.

The cut samples were subjected to unidirectional rolling along either the RD (Conventional) or TD (Cross Rolling) at room temperature (see Fig. 2). For rolling, it was performed unidirectionally with a thickness reduction of 20 %, using a laboratory rolling mill, with rollers of 58 mm in diameter and a rotating speed of 36 mm/s.

The microstructure and texture of the deformed samples were examined using SEM imaging and EBSD. The SEM used was an In-lens Schottky Plus field emission gun (JSM-F100) equipped with a CMOS EBSD detector (Oxford Instruments) and the AZtec acquisition software package (Oxford Instruments). The samples were manually polished with SiC papers with grits from 1200 # to 4000 #. Then, electrolytic polishing was performed for 30 s using a solution of 20 % perchloric acid and 80 % methanol at 30 V and at 5 °C. The grain size distribution, grain boundary characters and twinning activity were analyzed based on the EBSD measurements using the MTEX v5.10 toolbox for MATLAB® [26]. Orientations were represented in pole figures on the RD-TD plane of the initial reference system and plotted with the ATEX software [27]. The area size mapped by EBSD to obtain the pole figures was 5 mm × 5 mm, which is sufficient to capture the significant grain size and ensure

<table><caption>**Table 1**
Chemical composition (wt%).</caption><thead><tr><th>Elements</th><th>C</th><th>Fe</th><th>H</th><th>N</th><th>O</th><th>Ti</th></tr></thead><tbody><tr><td>wt. %</td><td>0,08</td><td>0,3</td><td>0,015</td><td>0,03</td><td>0,25</td><td>Balance</td></tr></tbody></table>

adequate statistics.

The initial cp-Ti sheet has an equiaxed microstructure with a grain size of 45 µm and a poorly textured with a T-Texture (see Fig. 3b). The sampling scheme, drawing and dimensions of the test pieces are shown in the Fig. 4. The specimens were cut with an LDSA WJA II water jet cutting machine at a pressure of 3800 MPa and a speeds of 100 mm/min. In this study, the tensile tests are carried out on a Zwick/Roell tensile machine with a maximum capacity of 100 kN. The imposed movement speed is constant and the tests were carried out at ambient temperature until rupture, the deformation rate is $\dot{\epsilon} = 10^{-2}s^{-1}$.

Deformation was analyzed with digital image correlation (DIC) (see Fig. 5). The speckle images were processed using a commercial digital image correlation (DIC) algorithm (VIC 2D by Correlated Solutions Inc.) using a facet size of 15 pixels and spacing of 4 pixels.

Nanoindentation tests were conducted using the nanoindenter UNHT from Anton Paar equipped with a continuous stiffness measurements modulus and Berkovich tip indenter (142.3°). The indentation hardness (HIT) and plane strain modulus (E*) were extracted from the unloading part of load-depth curves by using Oliver and Pharr model [28].

## 3. Results

### 3.1. Mechanical properties as received

Uniaxial tensile tests were performed along 0°/RD, 30°/RD, 60°/RD, and 90°/RD on the as-received cp-Ti, and the results are presented in Fig. 6. For each loading orientation, the test was performed on three specimens to ensure reproducibility.

The true stress-strain curves reveal less pronounced work hardening at 30° and 60° relative to the rolling direction (RD) compared to 0°/RD. For the specimen tested at 90°/RD, the elastic limit is higher than those of the other orientations. The macroscopic behavior curve exhibits slight hardening near the elastic limit. Table 2 summarizes the mechanical properties for the four different loading directions. The material's stiffness shows little sensitivity to the stress direction, with Young's modulus (E) values around 105 GPa.

The ultimate tensile strength (UTS) ranges from 613 MPa to 716 MPa, with a minimum at 60°/RD, while the yield stress (YS).increases from 333 MPa at 0°/RD to 422 MPa at 90°/RD. The elongation at break (ε) varies minimally with loading direction, averaging around 22.5 %.

The Lankford coefficient, r(α) (the methodology is detailed in the appendix), for the initial state of the sheet was measured to range between 0.7 and 1.7 (Table 3). BenMhenni et al. [29] studied the evolution of the Lankford coefficient in a 1.6 mm cp-Ti sheet initially textured using a grid method. The r(α) values obtained ranged from 2.2 at 0°/RD up to 4.9 at 90°/RD, with a peak value of 5 at 60°/RD. The evolution of r(α) as a function of the loading orientation follows a similar trend to the results obtained here using DIC, showing an increase in r(α) from 0°/RD to 60°/RD, followed by a slight decrease at 90°/RD. Wronski et al. [30] measured r(α) values of 1.13 and 3.01 in a cp-Ti sheet subjected to tensile testing along the RD and TD directions, respectively.

The differences between the measured r(α) values in this study and those reported in the literature are likely due to variations in the mechanical properties of the sheets studied (see Fig. 7). Crystallographic texture and texture intensity can significantly affect the anisotropy coefficient. In our study, the cp-Ti sheet exhibits weak texture, with a texture index of 1.5 and a maximum intensity of 3.9 on the {0002} pole figure (Fig. 3b), while BenMhenni et al.'s [29] study shows a higher maximum intensity of 6.24 on the {0002} pole figure.

### 3.2. Annealing temperature and annealing time

Before proceeding, we must first define the terminology used in this paragraph. To characterize intergranular misorientations, we will differentiate between two types in this study: small-angle
<figure><img src="image_2.png" /><figcaption>Fig. 1. Cold rolling is done by 7 passes and after each pass there is an annealing at 720° for 1 h in a primary vacuum of 10⁻³mbar</figcaption></figure>

<figure><img src="image_3.png" /></figure>

<table><caption></caption><thead><tr><th>Rolling step</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th></tr></thead><tbody><tr><td>Thickness (mm)</td><td>5</td><td>4</td><td>3,2</td><td>2,56</td><td>2,04</td><td>1,63</td><td>1,31</td><td>1</td></tr><tr><td>Accumulative reduction (%)</td><td>0</td><td>20</td><td>36</td><td>48.8</td><td>59.2</td><td>67.4</td><td>73.8</td><td>80</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>Fig. 2. RD and Cross (=TD) Cold Rolling.</figcaption></figure>

misorientations (ranging from 2° to 10°), referred to as LAGB (Low Angle Grain Boundary), and misorientations with angular values greater than 10°, referred to as HAGB (High Angle Grain Boundary).

The analysis of intragranular misorientations allowed us to evaluate the recrystallization state of the microstructure after thermal treatment. For this purpose, we used the grain orientation deviation criterion, known as GOS (Grain Orientation Spread). To calculate the GOS, the reference orientation deviation within a grain, called GROD (Grain Reference Orientation Deviation), must first be measured. GROD is defined as the misorientation between each pixel of a grain and the average orientation of that grain. Therefore, for each orientation on an EBSD map, there is an axis and a corresponding GROD angle. The average of the GROD angles within a grain represents the GOS. In this study, a grain is considered recrystallized if its GOS is less than 1°.

For reference, the two types of twins found in the deformed microstructures, along with their orientation relationships with the parent crystal and twinning parameters, are provided in Table 4.

Recrystallization begins at approximately 0.5 Tm, as many authors have established [8,9], corresponding to T ≥ 700 °C for cp-Ti. An in-situ heating test showed rapid grain growth at a slightly higher temperature

of 720 °C, although technical issues prevented us from obtaining reproducible and usable results. Nevertheless, we chose 720 °C (or 0.51 Tm) for our annealing temperature.

A study on the effect of annealing time was conducted to observe the evolution of the microstructure's recrystallization at 720 °C, as shown in Fig. 8. The sample had previously undergone rolling with a reduction of 59.2 % (corresponding to step 4 of the process). After 15 min of annealing (Fig. 8.a), the fraction of twin boundaries decreased slightly compared to the deformed state, and some regions of the microstructure began to recrystallize, forming equiaxed grains.

After 30 min of annealing, the fractions of twin boundaries C1 and T1 decreased to 6 % and 3 %, respectively (Fig. 8.b). The proportion of LAGB decreased from 19 % after 15 min to 10 % after 30 min, while the fraction of grains with a GOS greater than 1° dropped from 22.3 % to 16.0 %.

At 45 min, twins were no longer observed, and the microstructure was fully equiaxed. The amounts of LAGB and grains with a GOS greater than 1° were reduced to 6 % and 2.6 %, respectively, marking the microstructure as recrystallized. After 60 min of annealing, the LAGB content decreased further to 4 %, while the fraction of grains with a GOS
<figure><img src="image_5.png" /><figcaption>Fig. 3. a) Equiaxed grain microstructure of the as-received cp-Ti sheet. b) Associated pole fig. (B/T -T texture). c) Histogram of grain sizes and the associated table. The average grain size is approximately 45 µm. d) Histogram of disorientation angle.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. a) cutting out specimens from sheet b) draw and c) Dimensions of the tensile specimen.</figcaption></figure>

greater than 1° was reduced to 0.5 %.

A study on the recrystallization of rolled cp-Ti by [10] reported similar results when annealed at 550 °C for 5 to 60 min. However, they noted that their microstructure was not fully recrystallized, which is not the case in our study.

### 3.3. Influence of rolling and annealing cycles

#### 3.3.1. Influence of the number of cold-rolled passes before annealing

Highly cold-rolled tests with an 80 % reduction were conducted (see Fig. 9). The sheet was reduced from a thickness of 5 mm to 1 mm through multiple passes, each with a thickness reduction not exceeding 20 %, to achieve the total reduction of 80 %. Afterward, the sample underwent annealing at 720 °C for 1 h. The final texture displayed a typical rolling texture, characterized by a TD-split basal texture in which

the $\vec{c}$-axes of most grains were tilted by 25°-35° from the RD toward the TD.

#### 3.3.2. Microstructural and textural evolutions

The average grain diameter after each of the seven annealing steps is summarized in Table 5. Annealing 720 °C for 1 h makes it possible to keep an average grain diameter between 33 µm and 44 µm throughout the rolling and annealing cycles.

To avoid overloading the paper, we will present only the results from Step 1 and Step 7, focusing on both the RD and TD orientations. Each step was analyzed using EBSD in both the rolled and annealed states. The remaining results, including EBSD maps, angular distribution profiles, and pole figures for Steps 2 through 6, are provided in the **supplementary material**.

A strong activation of C1 and T1 twins is observed, with maxima at
<figure><img src="image_7.png" /><figcaption>Fig. 5. (a) Speckle pattern of a tensile specimen, (b) mounting the specimen with extensometer and camera, and (c) determination of the area of interest.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6. Tensile test curves of the as-received cp-Ti at 0°, 30°, 60° and 90° / RD at $\dot{\epsilon} = 10^{-2}s^{-1}$. The curves shown here represent the average of 3 tests.</figcaption></figure>

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

Mechanical properties of the as received cp-Ti.</caption><thead><tr><th></th><th>E (GPa)</th><th>YS (MPa)</th><th>UTS (MPa)</th><th>ε (%)</th></tr></thead><tbody><tr><td>0°/RD</td><td>101</td><td>333</td><td>647 ± 20</td><td>25 ± 2</td></tr><tr><td>30°/RD</td><td>97</td><td>385</td><td>618 ± 14</td><td>20 ± 2</td></tr><tr><td>60°/RD</td><td>96</td><td>384</td><td>613 ± 2</td><td>18 ± 1</td></tr><tr><td>90°/RD</td><td>112</td><td>422</td><td>716 ± 30</td><td>27 ± 1</td></tr></tbody></table>

65° and 85° on the angular misorientation profiles shown in Fig. 10c and f. The EBSD maps also reveal the presence of secondary twinning, where primary C1 twins coexist with secondary T1 twins, especially in the TD-

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

Values of r(α) of cp-Ti in initial state measured by DIC ($\dot{\epsilon} = 1.0 \times 10^{-2}s^{-1}$)).</caption><thead><tr><th>Angle/RD</th><th>r(α)</th></tr></thead><tbody><tr><td>0°/RD</td><td>0.74 ± 0.03</td></tr><tr><td>30°/RD</td><td>1.05 ± 0.02</td></tr><tr><td>60°/RD</td><td>1.75 ± 0.01</td></tr><tr><td>90°/RD</td><td>1.68 ± 0.01</td></tr></tbody></table>

rolled sample (Fig. 10d). The primary C1 and T1 twins appear to be activated in parent grains with specific orientations. The morphology
<figure><img src="image_9.png" /><figcaption>Fig. 7. Lankford coefficient for as-received cp-Ti: Comparison with references [29,30].</figcaption></figure>

<table><caption>**Table 4**

Characteristics of observed twins during cold-rolling of the CP-Ti-sheet.</caption><thead><tr><th>Name</th><th>Type</th><th>Mis. axis</th><th>Mis. Angle</th><th>Twinning shear</th><th>Colour</th></tr></thead><tbody><tr><td>T1</td><td>{1012} (1011)</td><td>(1210)</td><td>85.05°</td><td>0.173</td><td>Red</td></tr><tr><td>C1</td><td>{1122} (1123)</td><td>(1100)</td><td>64.38°</td><td>0.630</td><td>Green</td></tr></tbody></table>

and volume fraction of the twins vary depending on the twinning type, as illustrated in Fig. 10.

In the sample rolled along RD, the EBSD micrograph shows C1 twins with a fine, lenticular morphology, whereas T1 twins are wider and occur repeatedly within the same grain. These features are even more pronounced in the TD-rolled sample (Fig. 10d), where the repetition of T1 twinning is common across most grains that activate this type of twin. The lower volume fraction of C1 twins compared to T1 twins may be

<figure><img src="image_10.png" /><figcaption>Fig. 8. EBSD mappings and distribution of angular misorientations for annealing times of (a) 15 min (b) 30 min (c) 45 min and (d) 60 min at 720 °C.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 9. (a) cold rolling diagram, (b) (0001) and (11̄20) pole figures of the final texture.</figcaption></figure>

<table><caption>**Table 5**
Average grain diameter after annealing at each rolling step in cp-Ti.</caption><thead><tr><th>Step</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th></tr></thead><tbody><tr><td>Mean diameter (μm)</td><td>43.7</td><td>41.0</td><td>33.0</td><td>35.4</td><td>43.4</td><td>41.5</td><td>43.5</td></tr></tbody></table>

attributed to differences in shear stresses [31]. The statement that a smaller twin volume is sufficient to accommodate the same strain rate for C1 twins compared to T1 twins can be explained as follows: The twinning shear for T1 twins is 0.173, while for C1 twins it is 0.630, which is almost four times larger. Since the shear stress required for C1 twins is significantly higher, they can accommodate the same strain rate with a smaller volume of twins. This is because a higher twinning shear means that the material can accommodate more strain with a smaller volume of twin formation, compared to T1 twins, where a larger volume is required to achieve the same strain rate.

Fig. 11 shows examples of T1 twin morphology in the TD-rolled

sample. Multiple T1 twins are visible within a grain, growing until they coalesce, covering almost the entire parent grain.

After annealing at 720 °C for 1 h, the EBSD maps, along with the distributions of angular misorientations and grain diameters of cp-Ti, are presented in Fig. 12. The microstructure consists of equiaxed grains with a LAGB fraction of approximately 3 %. Post-annealing, no twins are observed, and the proportion of grains with a GOS greater than 1° is below 1 %, indicating complete recrystallization of the microstructure. The grain diameter distribution remains similar to the initial state, with average diameters of 47.4 ± 25.0 µm and 43.7 ± 22.6 µm after rolling and annealing along RD and TD, respectively.

Comparing Figs. 13f and 14d, at step 7, the texture is basal for rolling in RD and also for TD.

The activation of T1 twinning appears to explain the tilting of the c̄-axes, initially oriented in the TD direction, toward the ND direction, thereby forming a basal texture. This twinning arises either from primary T1 twinning or from secondary T1 twinning that is favorably activated within grains that have undergone primary C1 twinning. The

<figure><img src="image_12.png" /><figcaption>Fig. 10. EBSD maps of cp-Ti after 20 % cold rolling (a) RD with (b) Pole figure (c) associated distribution profiles of angular misorientations and (d) TD (e) Pole figure and (f) associated distribution profiles of angular misorientations.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Fig. 11. EBSD maps showing the morphology of T1 twins in the 20 % TD-cold-rolled cp-Ti sample. As we can observe, the T1 twin has developed in the grain and has almost completely replaced the grain.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 12. (a)-(b) EBSD maps for RD-rolled and TD-rolled, (c)-(d) distribution of angular misorientations and (e)-(f) distribution of grain diameter of cp-Ti sheet after 20 % cold rolling and annealing (720 °C - 1 h).</figcaption></figure>

intermediate anneals facilitated complete recrystallization of the microstructure, which in turn led to intense activation of both C1 and T1 twins during the subsequent rolling stage, thereby reinforcing the basal texture in cp-Ti.

### 3.3.3. Evolution of mechanical behavior after rolling of cp-Ti

After the sequential treatments, the specimens were subjected to a tensile test to verify the mechanical behavior change. As expected, the mechanical behaviors of the tensile test in all directions are similar as shown in Fig. 15. This is explained by the basal texture with the **c**-axis of the grains into ND. A strain hardening after the elastic region is
<figure><img src="image_15.png" /><figcaption>**Fig. 13.** EBSD maps in the (a) 80% RD-cold-rolled cp-Ti sample and (b) annealed (c) and (d) misorientation angle distribution for (e) cold-rolled and (f) annealed. Associated pole Figure for (e) cold-rolled and (f) annealed.</figcaption></figure>

observed for all the loadings directions.

The difference in behavior between the initial (5 mm) and final state (1 mm) of the specimens is shown in Table 6 with the mechanical properties. In terms of ultimate tensile strength (UTS), the slight difference between 0°/RD and 90°/RD remains after the process of rolling. There is no loss of tensile strength after the thickness reduction. At the final state, the ultimate strength (UTS) increases and it is more homogeneous between the 0°/RD and 90°/RD loadings directions. The fracture elongation (e) is slightly lower for the final state than the initial state but the CP-Ti still shows a good ductility.

In the Fig. 16 are given the values r(α). A good drawability is obtained if r >> 1 and Δ(r) is very small: which is our case. We can therefore conclude that cp-Ti has good drawability.

## 4. Discussion

Ex-situ annealing tests clearly indicate that “basal” grains, with their $\vec{c}$-axes aligned along the ND, grow more rapidly than grains with other orientations. This finding contrasts with previous studies [19,32,33], which reported that grains with a {110} orientation grow the fastest. As the rolling process progresses, transverse grains ($\vec{c}$ // TD) are progressively eliminated, consumed by T1-twins. These twins rotate the $\vec{c}$-axis from the TD nearly into the ND, explaining the increasing

proportion of “basal” grains.

By annealing after each 20% rolling pass, the internal stresses generated during rolling are released, preventing the fragmentation of grains into sub-grains. According to previous studies, beyond a certain deformation level, twinning ceases and is replaced by shear bands and $\langle c + \alpha \rangle$ slip. Indeed, the shear bands formed cause an increase in sub-grains in the microstructure; some authors [12,14,15] have shown that grain size is an important factor in activating twinning; from a certain critical size, twinning is no longer active and is replaced by $\langle c + \alpha \rangle$-slip. However, in our case, twinning persists throughout all stages of the process, continuously resulting in the twinning-induced ND basal texture. Finally, since the grain size did not change during the process, the mechanical properties did not drop as in other studies (by Hall-Petch effect) [9,34]. A key hypothesis to explore is the stored energy within specific grains. As demonstrated by Humphreys and others [35–37], the driving force behind grain growth is primarily the stored energy. Wilkinson and Dingley [38] established a relationship between stored energy and the image quality (IQ) of Kikuchi diffraction patterns obtained via SEM. In the Channel 5 package, Band Contrast (BC) serves as an index reflecting image quality, with a theoretical range of 0–255. From this perspective, the BC value indirectly represents energy storage: the lower the BC value, the higher the stored energy. Choi [39] proposed a criterion linking BC to stored energy. Beyond BC, other parameters,
<figure><img src="image_16.png" /><figcaption>Fig. 14. EBSD maps in the (a) 80 % TD-cold-rolled cp-Ti sample and (b) annealed and the associated pole Figure for (c) cold-rolled and (d) annealed.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Fig. 15. True stress-strain curves of the 1 mm CP-Ti sheet subjected to cold cross-rolling and annealing. Tensile tests are carried out for different directions of loadings: 0°/RD, 30°/RD, 60°/RD, 90°/RD.</figcaption></figure>

<caption>**Table 6**</caption>

Mechanical properties of tensile tests carried out at 0°/RD and 90°/RD for the initial (5 mm) and final (1 mm) state of CP-Ti sheet after cross-rolling and annealing.

<table><thead><tr><th></th><th>UTS(MPa)</th><th>YS (MPa)</th><th>ε (%)</th></tr></thead><tbody><tr><td>Initial 0°/RD</td><td>482 ± 7</td><td>338 ± 8</td><td>33.5 ± 2.6</td></tr><tr><td>Initial 90°/RD</td><td>507 ± 0.1</td><td>427 ± 2</td><td>32.3 ± 1.9</td></tr><tr><td>RD-rolling 0°/RD</td><td>490 ± 6</td><td>433 ± 7</td><td>30.2 ± 3.6</td></tr><tr><td>RD-rolling 90°/RD</td><td>511 ± 7</td><td>450 ± 7</td><td>27.7 ± 0.9</td></tr></tbody></table>

such as Mean Angular Deviation (MAD) and Grain Orientation Spread (GOS), may also play a role.

The MAD represents the angular error between the experimental Kikuchi diffraction patterns and the calculated Kikuchi diffraction patterns; when the error is small, the experimental and theoretical Kikuchi diffraction patterns align closely. GOS, on the other hand, indicates the degree of disorientation within the grain. A perfectly recrystallized grain

<figure><img src="image_18.png" /><figcaption>Fig. 16. Lankford coefficient r(α) in RD-rolling case and in TD-Rolling case for the cp-Ti.</figcaption></figure>
will exhibit a very low GOS. Choi's approach can be expanded by incorporating not only BC but also MAD and GOS as additional indicators of stored energy.

$$H_i = \left( \frac{BC_i - BC_{min}}{BC_{max} - BC_{min}} \right) \left( 1 - \frac{MAD_i - MAD_{min}}{MAD_{max} - MAD_{min}} \right) \left( 1 - \frac{GOS_i - GOS_{min}}{GOS_{max} - GOS_{min}} \right) \quad (1)$$

The $H_i$ parameter ranges from 0 to 1. $BC_{max}$ and $BC_{min}$ represent the maximum and minimum BC values, respectively, while $GOS_{max}/GOS_{min}$ and $MAD_{max}/MAD_{min}$ denote the maximum and minimum values for GOS and MAD in the studied EBSD map. By combining these parameters, the goal is to highlight the “cleanest” grains. The grains selected should exhibit the highest BC, the lowest MAD, and the lowest GOS. Grains with an $H_i$ value of 1 represent those with minimal stored energy and will, therefore, grow preferentially of stored energy based on BC's factor.

A filter was applied to identify grains with the highest $H_i$ values (see Fig. 17a). Nearly half of the grains with a high $H_i$ were basal grains. While this parameter does not entirely explain basal grain growth through the $H_i$ factor alone, there is a strong correlation suggesting that stored energy could be the key factor driving the preferential growth of basal grains compared to others. The $H_i$ parameter is primarily governed by BC, with MAD and GOS providing additional but less significant distinctions. Finally, based on the histograms in Fig. 17b, the BC factor appears to be the most significant, while the GOS factor does not provide any clear distinction. Additionally, diffraction patterns are often binned to reduce digital processing time, which results in a loss of resolution. Using higher-quality (unbinned) EBSD data presents a promising direction for future studies. To further investigate the mechanism behind the development of the basal texture, we performed nanoindentation experiments to compare the hardness of T1 twins and their parent grains. The results, shown in Fig. 18, reveal that the T1 twins are less hard than the parent grains. This lower hardness indicates that the T1 twins have fewer dislocations and, consequently, lower stored energy compared to the parent grains. During recrystallization, grains with lower stored energy are energetically more favorable for growth. Therefore, the T1 twins, which are energetically more favorable, contribute significantly to the development of the basal texture.

Although this does not directly prove that basal grains grow faster, it provides indirect evidence that the T1 twins play a crucial role in the texture evolution observed in this study. Nanoindentation tests were performed in a twinned area after a 10 % conventional rolling. We selected an area containing both T1 and C1 twins. In Fig. 18a), we created a 10 × 10 indent matrix in this area. In Fig. 18b), we compared the indentations in a T1 twin and its parent grain. In Fig. 18c), we plotted the hardness as a function of the $\bar{c}$-axis inclination. The red circles represent the hardness values of the T1 twin ($\bar{c}$-axis // ND, angle close to zero) and the parent grain ($\bar{c}$-axis in TD, angle equal to 90°). We also superimposed the hardness results on commercially pure titanium ([40]). The mechanism behind the growth of twinned regions is that these regions, having lower stored energy due to fewer dislocations, grow during the recrystallization heat treatment and eventually take over the entire grain.

## 5. Conclusion

This study investigated the microstructural, textural, and mechanical evolution of a 5 mm commercially pure titanium (cp-Ti) sheet undergoing cold rolling and annealing. Initially, the cp-Ti sheet displayed equiaxed $\alpha$ grains with an average diameter of 45 µm and a transverse texture, where the $\bar{c}$-axes were aligned with the transverse direction (TD). This texture anisotropy resulted in heterogeneous mechanical behavior, particularly with variations in yield strength depending on the tensile test loading direction.

After seven rolling steps, each reducing the sheet thickness by 20 %, followed by 1 h of annealing at 720 °C, the cp-Ti sheet was reduced to 1 mm thick and achieved isotropy in mechanical properties. Throughout the rolling process, the $\bar{c}$-axis gradually reoriented toward the normal direction (ND), driven by the activation of both extension and compressive twins during deformation. Annealing facilitated the growth of the twinned regions, intensifying the basal texture. The final microstructure consisted of equiaxed grains with an average size of 40 µm, and the mechanical properties became isotropic, with reduced yield strength differences across different loading directions. The process significantly enhances planar isotropy, making cp-Ti sheets more suitable for forming

<figure><img src="image_19.png" /><figcaption>Fig. 17. a) Pole figure of the best $H_i$ factor b) 4 histograms for BC, MD, GOS and $H_i$ for two categories: basal grains (B) (Basal grains were defined as grains with a $\bar{c}$-axis deviation of less than 15° from the ND direction) and others (the rest)).</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Fig. 18.** Nanoindentation results in a twinned area after 10 % conventional rolling. (a) 10 × 10 indent matrix in the twinned area. (b) Comparison of indentations in a T1 twin and its parent grain. (c) Hardness as a function of the $\bar{c}$-axis inclination ($\phi$). Red circles represent the hardness values of the T1 twin ($\bar{c}$-axis // ND, angle close to zero) and the parent grain ($\bar{c}$-axis in TD, angle equal to 90°). Superimposed hardness results on commercially pure titanium ([40], with kind permission from Elsevier). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

applications.

Two unidirectional rolling schemes were tested:

* Rolling along the initial rolling direction (RD-rolling)

* Rolling along the initial transverse direction (TD-rolling)

After seven steps of rolling and recrystallization, the basal texture was successfully developed. Two types of twinning, T1 and C1, were activated, with T1 twinning making the most significant contribution to the formation of the basal texture. During the early stages of deformation, TD-rolling proved more effective at activating T1 twinning compared to RD-rolling. Twinning was more intense when the twinning deformation aligned with the macroscopic deformation, underscoring the importance of compatibility between deformation modes and texture evolution.

## Author contributions

MT: Formal analysis, Data curation, Investigation, Methodology, Software, Visualization, Writing - original draft.

CS: Funding acquisition, Investigation, Methodology, Project administration, Supervision, Validation, Writing - review & editing.

YZ: Data curation, Investigation, Methodology, Resources, Visualization, Writing - review & editing.

EF: Methodology, Software, Validation, Writing - review & editing.

JSL: Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Software, Visualization, Writing - original draft.

## License

This research was funded, in whole or in part, by the National Research Agency (ANR). A [CC-BY public copyright license] has been applied by the authors to the present document and will be applied to all

subsequent versions up to the Author Accepted Manuscript arising from this submission, in accordance with the grant's open access conditions.

## CRediT authorship contribution statement

**Mélaine Tournay:** Writing – original draft, Methodology, Investigation, Formal analysis, Conceptualization. **Jean-Sébastien Lecomte:** Writing – review & editing, Writing – original draft, Validation, Supervision, Resources, Project administration, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Christophe Schuman:** Writing – review & editing, Supervision, Methodology, Formal analysis, Conceptualization. **Yudong Zhang:** Writing – review & editing, Validation, Supervision, Formal analysis, Data curation, Conceptualization. **Éric Fleury:** Writing – review & editing, Supervision, Formal analysis.

## 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 article.

## Data availability statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

## Acknowledgement

This work was supported by the ANR AFoTi project, grant ANR-20-CE08-0020-02 of the French Agence Nationale de la Recherche. We acknowledge the experimental facilities MicroMat from LEM3 (Université de Lorraine - CNRS UMR 7239). JSL thanks Dr. Nathalie Gey for carrying out the in-situ heating tests.
## Appendix A. Lankford coefficient calculation from DIC

The principle of Lankford coefficient r(α) determination is based on the measurements of dimension changes in length and width during uniaxial tensile test. Combination of width and length extensometer is extensively used as it is more automatic and with higher efficiency. The in-plane cumulative length strains (ε₁₁) and width strain (ε₂₂) is defined as:

$$ε_{11} = ln(\frac{l}{l_0}) \quad \text{and} \quad ε_{22} = ln(\frac{b}{b_0}) \qquad (A.1)$$

where l₀ and b₀ are the origin gauge length and width, and l and b are the gauge length and width after deformation, respectively. By following the law of constancy of volume, the r(α) is obtained from the strain components according to Eq. A.2:

$$r(\alpha) = \frac{\epsilon_{22}}{\epsilon_{33}} = - \frac{\epsilon_{22}}{\epsilon_{11} + \epsilon_{22}} \qquad (A.2)$$

the subscript 11, 22 and 33 represent the tensile direction, width direction, and thickness direction, respectively. For DIC, we will use the slope q = $-\frac{\epsilon_{22}}{\epsilon_{11}}$ to calculate r(α):

$$r(\alpha) = \frac{q}{1-q} \qquad (A.3)$$

Assuming that the work hardening of the material is isotropic, the slope q is measured over identical strain ranges for the different loading orientations. The measurement being imprecise at the beginning of the deformation part during the transition from the elastic domain to the plastic domain, the slope is measured from 5% longitudinal deformation and those up to a deformation of 20% for all the samples in the different orientations tested (see Fig. A.19).

<figure><img src="image_21.png" /><figcaption>Fig. A.19. Determination of the slope q for a deformation range from 5% to 20% (between the red dotted lines) here q = -0.4239 then r(α) = 0.735. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

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