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Microstructure of Materials
{001}〈101〉 Texture Evolution by Preferential Dynamic Grain Growth in Ti–37 mol%Nb Alloy under Plane Strain Compression at High Temperatures
Osamu UmezawaYujiro HayakawaIvo SchindlerHiroshi Fukutomi
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2024 年 65 巻 3 号 p. 282-291

詳細
Abstract

{001}⟨101⟩ texture evolution in Ti–37 mol%Nb (Nb–46.5 mass%Ti) alloy was determined under plane strain compression at the temperatures of 800°C, 950°C, and 1100°C, in which preferential dynamic grain growth (PDGG) took place. At lower temperature and higher strain rate such as 800°C–10−2/s, almost no grain growth occurred in the transverse direction (TD), and the α-fiber + near {111}⟨110⟩ in the γ-fiber texture was developed, which was a stable orientation as deformation texture. At higher temperature and lower strain rate such as 1100°C–10−3/s, the grain growth along the TD remarkably appeared by grain boundary bulging, and an extremely high pole density of the texture near the α-fiber, especially the rotated cube {001}⟨101⟩, evolved. A planar dislocation structure with pile-ups appeared and individual dislocations were uniformly distributed in the grains. The rotated cube texture fulfills the conditions of the deformation stability and the low Taylor factor in accordance with the PDGG mechanism. The essential aspect of the mechanism is the preferential growth of grains with a stable orientation for deformation and a low Taylor factor in the given deformation mode.

Fig. 13 Schematic illustration of deformation stability (a) and Taylor factor distribution (b)6) given by the φ2 = 45° section of the Euler space.

1. Introduction

Ti–Nb based β-type titanium alloys exhibit high specific strength and superior biocompatibility; therefore, they have been adopted as biomaterials. Furthermore, the reduction of their Young’s modulus has been promoted,1) because the gap in Young’s modulus between an implant device and a natural human bone causes bone degradation and absorption by the stress shielding.2) The Young’s modulus depends on the crystal orientation. The lowest was calculated as ⟨001⟩ from the elastic stiffness in Ti–Nb–Ta–Zr alloy.3) In the previous study,4) the {001} texture in the Ti–37 mol%Nb alloy was enhanced during high-temperature uniaxial compression. A sharp {001} fiber texture evolution was achieved by extensive grain boundary migration to increase the specific orientations in binary solid solution alloys (body-centered cubic (BCC)). In particular, the grain boundary migration of {001} grains into {111} grains is consistent with the preferential dynamic grain growth (PDGG) mechanism.5) However, the mechanism of texture evolution could not be studied in detail, because the deformation was performed in the uniaxial compression mode, which does not provide sufficient information to discuss whether the changes in microstructure and texture can be attributed to the PDGG mechanism.

The PDGG mechanism, which has been proposed to explain the texture change accompanying the microstructure change during high-temperature deformation, has been determined theoretically and experimentally on solid solution alloys with face-centered cubic (FCC) and BCC structures under two deformation modes, uniaxial compression and plane-strain compression.5,6) The PDGG mechanism occurs when all three conditions are satisfied.5) Namely, the homogeneous distribution of dislocations due to solute atmosphere dragging enhances the orientation dependence of stored energy during the deformation. The grains with a low Taylor factor orientation can grow preferentially and stably for the high temperature deformation. As mentioned above, the {001} fiber texture evolution in the alloy is in consistent with the PDGG mechanism. However, the elastic interaction between dislocations and solute atoms due to the atomic size effect may be less responsible for the mechanism of the alloy because the atomic size misfit parameter in the Ti–Nb binary solid solution (Ti: 1.47 Å and Nb: 1.46 Å) is very small, as approximately 0.007. Therefore, it is expected that the homogeneous distribution of dislocations is achieved by the mechanisms other than the solute atmosphere dragging. It is necessary to study the texture formation process by the deformation modes other than uniaxial compression and the dislocation structure by transmission electron microscopy (TEM) observation to discuss whether the behavior of Ti–Nb alloy can be understood in terms of PDGG mechanism.

In the present study, the microstructural evolution of Ti–37 mol%Nb alloy during high-temperature plane-strain compression (HTPSC) is evaluated, and the PDGG mechanism in the alloy, where the {001} grains are stable against deformation and have a low Taylor factor, is discussed.

2. Experimental Procedure

2.1 High-temperature plane-strain compression test

The details of the test material were described in the previous study.4) A 20-mm-diameter bar was cold-rolled into a 12-mm-thick plate and annealed at 950°C for 1.2 ks, followed by water cooling. The test material consisted of a β phase without α and ω precipitates, and its β-transus temperature is approximately 637°C. A rectangular specimen of 10 mm height (ND), 15 mm width (RD), and 20 mm length (TD) was cut from the plate by electric discharge machining. The height and length directions were parallel to the normal and the rolling directions of the plate, respectively.

The HTPSC tests were carried out at different temperatures and constant true strain rates using a dynamic thermal-mechanical test simulator, Gleeble-3800 (Dynamic Systems Inc.), as shown in Fig. 1(a). A 5-mm-wide anvil (made of tungsten carbide) was inserted into the rectangular specimen. Undeformed areas of the sample acted as free ends (Fig. 1(b)), limiting the metal flow in the transverse direction (TD). A thermocouple welded to the specimen surface controls the test temperature. The direct resistance heating system is capable of heating specimens in an Ar gas atmosphere and by Ar gas cooling. The specimens were heated to test temperatures of 800°C, 950°C, and 1100°C (0.51 Tm ∼ 0.65 Tm, where Tm is the melting temperature), at a rate of 10°C/s. The test temperature was maintained for 180 s to homogenize its distribution, after which the specimen was isothermally compressed along the normal direction (ND) for a reduction of 40% (true strain, ε = −0.5), 50% (ε = −0.7), 60% (ε = −0.9), or 75% (ε = −1.4) at a constant true strain rate of 1.0 × 10−3/s or 1.0 × 10−2/s, respectively. True strain and true stress values were calculated from the load-stroke measurements by assuming uniform and constant volume deformation.

Fig. 1

Schematic diagram of the thermomechanical treatment (a), high-temperature compression in a dynamic thermal-mechanical test simulator (b), and illustration of analysis area (hatched) for SEM-EBSD in the samples (c).

2.2 Microstructure analyses

Electron backscattered diffraction (EBSD) using scanning electron microscopy (SEM) was employed to evaluate the microstructural evolution during high temperature deformation in the β-region. Data sets of point analyses with every 5 mm beam scanning yielded image analyses, e.g., orientation by a tiled standard stereographic triangle. The X-ray texture analysis agreed with the EBSD analysis in the previous study,4) so that the texture was evaluated by the EBSD technique in the present study due to the limited analysis area. The analyzed samples were taken from the central position in the sections of the compressed specimens normal to the ND and TD planes, as shown in Fig. 1(c). In terms of texture representation, the {φ1, Φ, φ2} Euler angles are as defined by Bunge,7) and the computed orientation distribution function (ODF) is defined as 0° ≤ φ1 ≤ 90°, 0° ≤ Φ ≤ 90°, and 0° ≤ φ2 ≤ 90°. The thin disk for TEM was sectioned from the central position in the TD section (Fig. 1(c)).

Figure 2 shows the EBSD orientation map representing microstructure of the annealed material. The microstructure consists of equiaxed β grains with an average grain diameter of approximately 45 µm. The compressive directions (ND) are indicated by the colors given in the standard stereographic triangle. The EBSD measurement revealed that the ⟨111⟩//ND preferred orientation developed.

Fig. 2

Orientation map representing microstructure of the annealed material on the ND plane. The orientation of the ND plane normal is expressed by the colors given in the standard stereographic triangle. The black lines are large angle boundaries higher than 15 deg.

3. Results

3.1 True stress-true strain curves

In the HTPSC tests, the flow stresses of the material increased as the test temperature was lowered from 1100°C to 800°C and the strain rate was increased from 10−3/s to 10−2/s. Figure 3 shows the true stress–true strain (flow) curves of the materials, which showed softening after an initial peak and a steady state at strains between −0.2 and −1. Namely, the so-called work softening is observed independently of the test temperature and strain rate and corresponds to the microstructural evolution dominated by dynamic recrystallization.8) The flow stress in the HTPSC (Gleeble) test was higher than that in the uniaxial compression test at approximately 20–30 MPa, which may be due to the deformation constraints along the TD, which are different from those in the uniaxial compression test.

Fig. 3

True stress-true strain (flow) curves of the materials compressed at (a) 800°C, (b) 950°C, and (c) 1100°C.

3.2 Deformation microstructure

Figures 4, 5 and 6 show the orientation maps in the ND or TD plane for samples compressed with ε = −1.4. The test temperatures and true strain rates affected the microstructure evolution. The equiaxed grains shown in Fig. 2 were elongated along the rolling direction (RD). The coarsening along the ND and TD of the pancake-shaped grains depended on the temperature and strain rate. Since the deformation along the TD is constrained by HTPSC, the grains cannot be plastically elongated along the TD. In addition, the pancake grains are compressed along the ND. Therefore, grain coarsening along the ND and TD is due to grain boundary migration. At lower temperatures and higher strain rates, such as 800°C–10−2/s, grain growth along the TD is not apparent, but grain boundary bulging is often seen (Fig. 4(a)), indicating that grain boundary bulging occurs depending on the diffusion rate and strain rate up to ε = −1.4. On the other hand, higher temperatures and lower strain rates drive the extensive grain growth along ND and TD, where the {001}⟨101⟩ grains are particularly large (Figs. 4(f), 6(e) and 6(f)). Large grain boundary bulges develop between the {001}⟨101⟩ grains and their neighboring grains.

Fig. 4

Orientation maps in the ND section of the materials compressed up to ε = −1.4 at (a), (d) 800°C, (b), (e) 950°C, and (c), (f) 1100°C with the strain rates of 10−2/s (a)–(c) and 10−3/s (d)–(f). The orientations on ND are expressed by the colors given in the standard stereographic triangle. The black lines are large angle boundaries higher than 15 deg.

Fig. 5

Orientation maps in the TD section of the materials compressed up to ε = −1.4 at (a), (b) 800°C, (c), (d) 950°C, and (e), (f) 1100°C at a strain rate of 10−2/s. The orientations on ND (a), (c), (e) and RD (b), (d), (f) are expressed by the colors given in the standard stereographic triangle. The black lines are large angle boundaries higher than 15 deg.

Fig. 6

Orientation maps in the TD section of the materials compressed up to ε = −1.4 at (a), (b) 800°C, (c), (d) 950°C, and (e), (f) 1100°C at a strain rate of 10−3/s. The orientations on ND (a), (c), (e) and RD (b), (d), (f) are expressed by the colors given in the standard stereographic triangle. The black lines are large angle boundaries higher than 15 deg.

The test temperatures and true strain rates also affect the texture evolution. The pancake-shaped grains were mostly oriented to {111} or {001} on the ND plane (Fig. 4). Although the fraction of {001} grains was almost the same as that of {111} grains at 800°C–10−2/s (Figs. 4(a) and 6(a)), it increased as the test temperature was increased from 800°C to 1100°C or lower strain rate. At 1100°C with strain rates of 10−2/s and 10−3/s, {001} grains were mostly developed (Figs. 4(c), 4(f), 5(e), and 6(e)).

In the central part of the thickness, most of the grains were oriented as ⟨101⟩//RD as shown in Figs. 5 and 6, where the crystal rotation during HTPSC deformation for the grains oriented as {001}⟨110⟩, $\{ 111\} \langle \bar{1}01\rangle $, $\{ 121\} \langle \bar{1}01\rangle $, and $\{ 111\} \langle 11\bar{2}\rangle $ appeared along ⟨101⟩//RD.

3.3 Texture evolution

Figure 7 shows the {001}, {101}, and {111} pole figures after deformation up to ε = −1.4 at (a) 800°C–10−2/s and (b) 1100°C–10−3/s, respectively. Pole densities were projected onto the compressive (ND) plane with an average of 1.0. The pole figures suggest that {001}⟨101⟩ oriented grains (rotated cube) are highly distributed at 1100°C–10−3/s as pole densities greater than 12, although ⟨001⟩//ND is an unstable orientation except for {001}⟨101⟩.9) Alternatively, no {111} oriented (⟨111⟩//ND) grains (γ-fiber) were detected at 1100°C–10−3/s, although the grains were partially dispersed at 800°C–10−2/s. The ⟨101⟩//RD (α-fiber) texture, which is stable against the HTPSC deformation as well as γ-fiber,10) is highly developed in both pole figures. Figure 8 shows the ODFs (φ2 = 45° section) for the samples compressed to a strain of ε = −1.4 at 800°C, 950°C, and 1100°C with strain rates of 1.0 × 10−2/s and 1.0 × 10−3/s, respectively. Orientation densities were also drawn as contour maps with an average of 1.0. Although the γ-fiber is highly present in the initial material (Fig. 8(a)), the texture evolution from {001} + {111} to {001} is remarkable due to the compressive deformation at high temperatures and low strain rates. The deformation texture at 800°C–1.0 × 10−2/s shows an intensified distribution along the α-fiber and in the γ-fiber (Fig. 8(b)). At higher temperatures or lower strain rates, the orientation densities of the γ-fibers were significantly reduced, and a part of the α-fibers evolved as a strong component. In particular, the orientation densities of the rotated cube corresponding to the maximum are greater than 100 at 1100°C, with strain rates of 1.0 × 10−2/s and 1.0 × 10−3/s (Figs. 8(f) and 8(g)).

Fig. 7

{001}, {101}, and {111} pole figures of the materials compressed up to ε = −1.4 at (a) 800°C with a strain rate of 10−2/s and (b) 1100°C with a strain rate of 10−3/s.

Fig. 8

φ2 = 45° sections of ODFs showing the textures for (a) initial material and samples compressed up to ε = −1.4 at (b), (c) 800°C, (d), (e) 950°C, and (f), (g) 1100°C with strain rates of 1.0 × 10−2/s (b), (d), (f) and 1.0 × 10−3/s (c), (e), (g). Marked orientations correspond to the strong orientation densities.

Figure 9 shows the orientation maps for the samples compressed at 1100°C with 10−3/s up to true strains of ε = −0.5, −0.7, and −0.9. The fraction of {001} grains increased as the true strain increased, while the fraction of {111} grains decreased. In other words, the true strain also affects the texture evolution. Figure 10 shows the ODFs (φ2 = 45° section) for the samples compressed at 1100°C with 10−3/s up to true strains of ε = −0.5, −0.7, and −0.9, respectively. At strains of ε = −0.5 and −0.7 (Figs. 10(a) and 10(b)), both α-fiber and γ-fiber textures are developed, and high orientation density regions are detected at not only in the rotated cube orientation, but also in ⟨001⟩//ND orientations. At a strain of ε = −0.9 (Fig. 10(c)), most of the α-fibers are distributed, especially in the rotated cube orientation. The {001}⟨101⟩ component develops and the {111} component weakens with increasing true strain, consistent with the orientation maps shown in Fig. 9.

Fig. 9

Orientation maps in the ND (a), (d), (g) and TD (b), (c), (e), (f), (h), (i) sections of the materials compressed at 1100°C with a strain rate of 10−3/s up to the true strains of (a)–(c) ε = −0.5, (d)–(f) ε = −0.7 and (g)–(i) ε = −0.9. The orientations on ND (a), (b), (d), (e), (g), (h) and RD (c), (f), (i) are expressed by the colors given in the standard stereographic triangle. The black lines are large angle boundaries higher than 15 deg.

Fig. 10

φ2 = 45° sections of ODFs showing the textures for the materials compressed at a temperature of 1100°C with a strain rate of 10−3/s up to the true strains of (a) ε = −0.5, (b) ε = −0.7, and (c) ε = −0.9. Marked orientations correspond to the strong orientation densities.

The orientation density distributions shown in Figs. 8 and 10, analyzed from EBSD data with less statistical confidence than X-ray diffraction, are not inconsistent with the textures reported in the literature.47,9,10) Therefore, during HTPSC deformation at higher temperatures and lower strain rates, the {001}⟨101⟩ (rotated cube) texture evolved with grain coarsening and equiaxing, as shown in Fig. 4(f).

4. Discussion

4.1 Deformation behavior

Plastic deformation in BCC metals and alloys is controlled by kink-pair nucleation and kink migration processes along screw dislocations.11) This is the motion of 1/2{110}⟨111⟩ screw dislocations between local energy minima under thermally activated process. Nucleation of the kink-pair is along an initial long straight screw dislocation. The migration along the screw dislocation is estimated as the distance between dislocation junctions/jogs. In general, solutes reduce the nucleation barrier and increase the kink migration barrier. In particular, the kink migration barriers are high at low stress and high temperature.

At high temperatures, various phenomena such as dislocation motion dragging solute atmosphere, grain boundary sliding, and dynamic recrystallization operate, depending on temperature, grain size, strain rate, and amount of strain. These mechanisms produce microstructures, dislocation structures and textures that are different from those formed by room temperature deformation. Therefore, TEM observation was done to discuss the mechanisms that affect the development of both microstructure and as texture. The TEM images shown in Figs. 11 and 12 represent the deformation structures of the Ti–37Nb alloy compressed at a strain rate of 1.0 × 10−2/s to the true strain of −0.9.

Fig. 11

TEM bright-field images of the materials compressed at 800°C with a strain rate of 1.0 × 10−2/s up to ε = −0.9: (a) straight screw dislocation substructure, (b) dislocation bowing out, (c) kinks and dislocation network, and (d) slip bands and twinning. The beam direction is near $[\bar{1}11]$ (a)–(c) or [011] (d).

Fig. 12

TEM bright-field images of the materials compressed at 1100°C with a strain rate of 1.0 × 10−2/s up to ε = −0.9: (a) dislocation pileups, and (b) slip bands. The beam direction is near $[\bar{1}11]$.

Since extensive grain boundary migration does not occur at 800°C, the intensified orientation distribution along the α-fiber and in γ-fiber appears as shown in Fig. 8(b). Figure 11 shows the dislocation substructures in γ-fiber developed at 800°C, where individual dislocations are uniformly distributed in the grains. The activation of the slip systems as well as the multiplication and movement of the dislocations resulted in straight screw dislocation substructure (a), dislocation bowing out (b), kinks and dislocation network (c) in the microstructure. Regular dislocation networks are directly built up on dislocation forests by dislocations during deformation, and low-energy hexagonal dislocation network forms a subgrain boundary when the temperature is high enough to allow rapid climbing.12,13) However, the subgrain boundaries and dislocation cell structures shown in Figs. 11(a) and 11(d) were hardly observed. In addition, slip bands and {112}⟨111⟩ twinning were confirmed in one grain as shown in Fig. 11(d), where the dislocation density in the grain was higher than that of the other grains.

On the other hand, the grains in the α-fiber, especially the rotated cube orientation, were intensified at 1100°C as shown in Fig. 8(f). Figure 12 shows the dislocation substructures of near {111} grains developed at 1100°C. Individual dislocations are uniformly distributed in the grains as at 800°C. Therefore, dynamic recovery is not a main restoration mechanism, although the high stacking fault energy of the BCC crystal structure promotes the recovery of the β-phase at high temperatures.14) Viscous motion of the dislocation is expected and supports the operation of the PDGG mechanism.5) The planar dislocation configuration shows that the kink migration barrier at 1100°C is higher than that at 800°C. Plastic deformation in BCC metals and alloys is controlled by kink-pair nucleation and kink migration processes along screw dislocations. Generally, solutes reduce the nucleation barrier, and increase the kink migration barrier. In particular, the kink migration barriers are high at low stress and high temperature, because kinks move and annihilate. Then, kink motion becomes the rate-limiting step, leading to slow dynamics and large kink lateral pileups. Screw dislocation glide in the alloy is achieved by a high temperature kink-pair mechanism. The dislocation arrays show not only planar structure but also three-dimensional arrays of dislocations as shown in Fig. 12(a). A few bands were detected and were seen together with planar arrangements of primary dislocations as shown in Fig. 12(b). The dislocation density within these bands is very high and the activity of local cross slip is visible.

According to the dislocation structure mentioned above, a planar dislocation structure with pile-ups appears, individual dislocations are uniformly distributed in the grains, and no subgrain structure is developed in pure metals. While these dislocation configurations are different from a wavy dislocation structure in the solid solution alloys such as Al–Mg,1517) it is pointed out that the PDGG mechanism can work in the Ti–Nb alloy whenever effective stress is present. Here, it should be noted that the essence of the first condition is the uniform distribution of dislocations and not the solute atmosphere dragging of dislocations. In addition, the evolution of the {001}⟨101⟩ texture can be delayed because the diffusion rate decreases at lower temperatures such as 800°C, and higher strain rate results in shorter grain boundary migration time at the same strain.

Therefore, not only the dragging of solute atmosphere, but also the interaction forces between two parallel dislocations and mutual cutting of dislocations, such as the formation of jogs, elastic interaction between dislocations, and reaction between dislocations are a factor of work hardening.

4.2 Grain growth mechanism

The microstructure developed by HTPSC was similar to that developed by high-temperature uniaxial compression.4) The {001}⟨101⟩ texture evolution was pronounced at higher temperatures and lower strain rates during HTPSC deformation. Considering that the grains were coarsened at higher temperatures and lower strain rates, grain boundary migration was very active in this alloy. The grain boundary bulging due to the PDGG mechanism can result in the {001}⟨101⟩ grain microstructure with small-angle grain boundaries as shown in Figs. 4(f), 6(e) and 6(f). Here, a PDGG mechanism is considered to play an important role in the microstructural evolution of Ti–Nb alloys.

As discussed in section 4.1, a uniform dislocation distribution is achieved in Ti–Nb alloy (atomic size misfit parameter ≈ 0.007) whose atomic size effect seems to be small compared to the alloy systems such as Al–Mg (≈0.119) and Al–Cu (≈0.117). Therefore, two other conditions in the PDGG mechanism which are the preferential growth of grains with low Taylor factor orientation and the texture evolution by high-temperature deformation with stable low Taylor factor orientation should be satisfied in this alloy. Then, the microstructure evolution in this alloy is discussed from the viewpoints of these conditions as follows.

The hypothesis consists of two assumptions: (1) the texture transition associated with changes in microstructure results from the preferential growth of grains with specific orientations, such as {001}⟨101⟩ in the present study, and (2) the growing grains are stable for the deformation in the given deformation mode. To find the grains with low-stored energy, it is assumed that the Taylor factor is equal to the stored energy.5) Thus, the texture change can occur when a low Taylor factor orientation is stable for the deformation and different from the deformation texture. On the other hand, at the lower temperature and higher strain rate, serrated steps on the boundaries of the pancake grains were fitted to the {101} or {112} traces between the neighboring grains of {111} and {001},4) which may indicate the evolution of the deformation texture before the grain boundary migration.

The essential features observed in the pole figures (Fig. 7) and φ2 = 45° sections of the ODF (Figs. 8 and 10) are shown in Fig. 13. The dependence of the Taylor factor on the crystal orientation is shown by the φ2 = 45° section of the Euler space in Fig. 13(b). For the calculation of the Taylor factor,6) 48 slip systems with {011}, {112} and {123} slip planes are considered,18) and the main orientations are listed in Table 1. The Taylor factors of {111} and {001} in the compressive deformation of BCC metal by pencil glide are 3.182 and 2.121, respectively.19) HTPSC usually produces a texture consisting of α-fiber (⟨101⟩//RD) and γ-fiber (⟨111⟩//ND) as stable orientations in BCC solid solution alloys (Fig. 13(a)), such as Fe–Si alloys.6) The grains oriented as ⟨101⟩//RD (α-fiber) are stable against deformation. Their Taylor factors are between 2.1 and 3.7. On the other hand, the grains oriented as ⟨111⟩//ND (γ-fiber) are stable to deformation and have high Taylor factors between 3.5 and 3.7. Dynamic recrystallization to near $(111)[0\bar{1}1]$ in γ-fiber during isothermal compression was promoted with decreasing deformation temperature, increasing strain rate (as occurred at 800°C–10−2/s), and true strains of −0.7 (as shown in Fig. 10), while {001} grains became elongated, forming serrated grain boundaries. Dynamic recrystallization normally results in the elimination of a large number of dislocations by the migration of high-angle boundaries, and a single peak in flow stress signifies that grain refinement occurs.20) Therefore, the dislocation density of the {111} grains is higher than that of the {001} grains, which is consistent with the deformation structures shown in Fig. 11. A lower strain rate and higher temperature promoted the formation of the coarsened $(001)[1\bar{1}0]$ grains. Since the grains oriented as ⟨001⟩//ND are unstable to deformation except for the rotated cube orientation {001}⟨110⟩, the ⟨001⟩//ND grains should be accelerated to $(001)[1\bar{1}0]$ and $(001)[\bar{1}\bar{1}0]$ as shown in Fig. 8. Furthermore, the rotated cube orientation $(001)[1\bar{1}0]$ has the lowest Taylor factor in ⟨001⟩//ND as well as α-fiber (Fig. 13(b)). This sequence of texture evolution suggests that the {001} grains can reduce the stored strain energy prior to the {111} grains, leading to a difference in the stored strain energy between the {001} and {111} grains. Therefore, the grain boundary migration of $(001)[1\bar{1}0]$ grains in the α-fiber may result in the main component of the texture due to the PDGG mechanism with the reduction of the accumulated strain energy.

Fig. 13

Schematic illustration of deformation stability (a) and Taylor factor distribution (b)6) given by the φ2 = 45° section of the Euler space.

Table 1 Taylor factors for the plane strain compressive deformation at various orientations.6)


The PDGG mechanism in the HTPSC deformation of the Ti–Nb alloy is consistent with the above hypothesis. The essential aspect of the PDGG mechanism is the preferential growth of grains with a stable orientation for deformation and a low Taylor factor in the given deformation mode, which is also applicable to the high-temperature deformation of a pure metal if the installed deformation is sufficient for the driving force of its grain boundary migration.

5. Conclusions

{001}⟨101⟩ texture evolution in Ti–37 mol%Nb alloy was determined under plane strain compression at the temperatures of 800°C, 950°C, and 1100°C to characterize its high-temperature deformation and PDGG mechanisms.

  1. (1)    A steady-state deformation was confirmed in which the flow stress was constant at true strains between −0.2 and −1.0. A single peak in flow stress indicated that dynamic recrystallization occurred.
  2. (2)    The microstructural evolution depended on the deformation temperatures, strain rates and strains. At lower temperature and higher strain rate, such as 800°C–10−2/s, the α-fiber and near {111}⟨110⟩ in γ-fiber textures evolved as a deformation texture up to a strain of −1.4, where almost no grain growth along the TD was detected.
  3. (3)    At higher temperature and lower strain rate, such as 1100°C–10−3/s, the rotated cube {001}⟨101⟩ texture developed up to a strain of −1.4. Grain growth along the TD was evidenced by grain boundary bulging and a high pole density of the texture along the α-fiber, especially near the rotated cube.
  4. (4)    A planar dislocation structure with pile-ups appeared, and individual dislocations were uniformly distributed in the grains. Not only dragging of solute atmosphere, but also interaction forces between two parallel dislocations and mutual cutting of dislocations were a factor of work hardening.
  5. (5)    The rotated cube texture fulfilled the conditions of stable orientation against deformation and low Taylor factor, and was predominant in the orientation components of high-temperature compression.
  6. (6)    The microstructural evolution according to the PDGG mechanism was validated in the Ti–Nb alloy. The essential aspect of the PDGG mechanism is the preferential growth of grains with a stable orientation to deformation and a low Taylor factor in the given deformation mode, which is also applicable to the high-temperature deformation of metals and alloys if the installed deformation is sufficient for the driving force of their grain boundary migration.

Acknowledgements

We are grateful to Prof. Bohumír Strnadel, Dr. Daniel Bartoněk, and Mr. David Dvořák, Center of Advanced Innovation Technologies, Vysoká Škola Báňská - Technical University of Ostrava for their help. This paper was supported by projects No. CZ.02.1.01/0.0/0.0/17_049/0008441, “Innovative Therapeutic Methods of Musculoskeletal System in Accident Surgery”, and No. CZ.02.1.01/0.0/0.0/17_049/0008399, “Development of inter-sector cooperation of RMSTC with the application sphere in the field of advanced research and innovations of classical metal materials and technologies using modelling methods” within the Operational Programme Research, Development and Education financed by the European Union and by the state budget of the Czech Republic.

REFERENCES
 
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