Accelerated flow softening and dynamic transformation of Ti-6Al-4V alloy in two-phase region during hot deformation via coarsening α grain

1. Introduction

Hot deformation, i.e., hot rolling or forging in β single-phase and α + β two-phase regions, is essential in the industrial production of titanium alloys. Flow softening during deformation with the coupled functions of dynamic recovery and dynamic recrystallization is well studied [[1], [2], [3]]. More recently, dynamic transformation (DT) is proposed to be another important flow softening mechanism [4]. The DT is always associated with transformation from harder phase into softer phase during hot working, which contributes to a flow softening and significantly impacts on the microstructure and performance of products. In addition, decrement of β transus owing to DT can reduce production energy consumption and has great industrial application potential. Since the pioneering works on DT of austenite to ferrite above Ae₃ reported by Matsumura and Yada [5], it has been receiving increasing attentions because of its practical significance in the processing of high performance materials [6,7]. The thermodynamics mechanisms of DT were then investigated by many researchers in terms of stored energy, stress activation and phase softening models [4]. Subsequently, DT was also observed in hexagonal alloys, for instance in titanium alloys [[8], [9], [10], [11], [12], [13], [14]]. Koike et al. [8] found the stress-induced α to β phase transformation in a Ti-5.5Al-1.5Fe alloy during hot tensile testing, which served as additional stress accommodation mechanism for superplastic elongation [12]. Further, Guo et al. [[9], [10], [11]] confirmed the occurrence of DT in titanium alloys over a wide range of strains, strain rate and temperatures during hot compression and torsion. And the detailed mechanisms were also discussed on the basis of thermodynamics evaluation [13].

The α grain size is of vital importance in mechanical performance and microstructural evolution during hot deformation of titanium alloys. Luo et al. [15] reported that the increased α grain size could decrease flow stress and impact on the local efficiency maxima regions and unstable regions in processing maps. However, the underlying effect of primary α grain size on DT was not examined yet. In this work, a more evident flow softening owing to an accelerated DT of Ti-6Al-4 V alloy in two-phase region during hot deformation was observed via coarsening α grain. Microstructural evolutions were quantified from scanning electron microscope (SEM) and qualitatively examined by utilizing electron backscatter diffraction (EBSD) and transmission electron microscope (TEM). Further, thermodynamics evaluation and crystallographic analyses based on a phase reconstruction method [16,17] were also employed to reveal the in-depth mechanisms of DT.

2. Experimental

A commercial Ti-6Al-4V alloy with main chemical compositions (wt%) of 5.98Al, 3.85V, 0.19Fe, 0.027Si and balance Ti was employed in this work. The transus temperature from β region to α+β region of this alloy was determined to be approximate 995 °C by a dilatometer testing. The as-received alloy rod with diameter of 10 mm owned fine grain (FG) of about 3 μm. To increase the average α grain size, the alloy was annealed at 960 °C for 12 h in an argon atmosphere which had coarse grain (CG) of †10 μm. Both FG and CG alloys were then machined into specimens with length of 9 mm and diameter of 6 mm for hot deformation. Compression testing was performed on a 100 kN MTS servohydraulic compression machine equipped with a radiation furnace. The samples were heated to the testing temperature of 950 °C with heating rate of 2 °C/s and held for 15 min in argon atmosphere prior to deformation. During hot deformation, specimens were lubricated by applying a suspension of boron nitride in ethanol to the top and bottom surfaces [10,13,18]. The compression tests were performed to true strains of 0.1, 0.5, 0.9, 1.2 with a strain rate of 0.01 s^-1, and then water quenched after deformation, where delay prior quenching was approximate 2-3 s. Deformed samples were cut along longitudinal section on a wire cutting machine for SEM, EBSD and TEM micrographs examinations after common sample preparation processes [[8], [9], [10], [11], [12], [13], [14], [15]].

3. Results

3.1. Flow stress and dynamic softening behaviors

The true stress-strain curves of both FG and CG alloys deformed at the temperature of 950 °C and strain rate of 0.01 s^-1 are presented in Fig. 1(a). It is observed that the initial peak stresses are almost identical. With increased strain, the flow stress of CG alloy decreases faster than that of FG specimen owing to more dynamic softening during hot deformation [10]. At larger strain, dynamic softening is gradually suppressed. The dynamic softening after the peak stress can also be quantitatively estimated by relative softening (RS) [19,20]:

RS=$\frac{(σ_{ p } -σ)}{σ_{ p }}$ (1)

where σ_p is the peak stress and σ is the instantaneous stress at corresponding strains. The calculated results of both alloys by utilizing Eq. (1) are shown in Fig. 1(b). With increasing strain levels, it is observed that RS values in both alloys gradually increase at lower strain and reach a plateau later. At lower strain levels, slight difference of dynamic softenings is observed between both alloys. However, CG sample owns a more remarkable increase of RS with the increament of strain levels. The mechanisms for such differences on flow stress and dynamic softening behaviors of both alloys will be further discussed in the following sections with the evaluations of microstructural evolution.

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Fig. 1.   (a) True stress-strain curves of both FG and CG specimens deformed at temperature of 950 °C and strain rate of 0.01 s^-1. Deformed samples at various strain levels for microstructural observation are marked with dotted lines; (b) relative softening-strain curves of both FG and CG specimens corresponding to the true strain-stress curves in (a).

3.2. Evolution of α phase fraction

The processes of DT in both alloys are revealed by selected SEM micrographs at strains of 0, 0.5 and 1.2, as shown in Fig. 2. In Fig. 2(a) and (d), different grain sizes of α phase with little difference on phase fraction are exhibited. Mean grain size of FG samples is approximate 3 μm, while that of CG samples is about 10 μm. With the increment of strain, α phase gradually transforms to β phase. At strain of 1.2, notably, full β phase is shown in CG alloy (Fig. 2(f)) which indicates that all α phase transforms into β phase during hot deformation. While in FG alloy, retained α phase is still observed in Fig. 2(c).

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Fig. 2.   Typical SEM microstructures at strains of 0, 0.5 and 1.2, where dark areas indicate α phase: (a-c) FG alloys; (d-f) CG alloys.

Fig. 3 shows the evolution of α phase fraction during hot deformation, which is quantified from SEM micrographs (Fig. 2). It is indicated that the fraction of α phase in CG alloy decreases more rapidly than that in FG alloy, though slight difference is observed in non-deformed samples. These results coincide with the flow stress behaviors in Fig. 1. It is also noted that little α phase († 0%) is presented in CG sample at strain of 1.2.

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Fig. 3.   Quantified evolution of α phase fraction with increased strain during hot deformation.

3.3. EBSD and TEM observations

Fig. 4 shows the EBSD microstructures in deformed samples at various strain levels. The DT processes observed in Fig. 2, Fig. 3 are further demonstrated. EBSD microstructure agrees well with SEM results on the evolution of α phase fraction. Typical microstructure of CG sample (Fig. 4(a)) prior to deformation (ε = 0) is displayed with equiaxed α grains and acicular α′ martensitic microstructure. More α′ phases with longer strip morphology are gradually exhibited with increased strain. Full α′ phase microstructure is presented at strain of 1.2 in CG sample, as shown in Fig. 4(e). In FG alloy (Fig. 4(f)-(g)), the sizes of both α and α′ phases are smaller. At strain of 1.2, some α phases are still revealed in FG alloy (Fig. 4(g)). Microstructures of non-deformed samples (ε = 0) are under equilibrium state attributing to the sufficient time of isothermal holding prior deformation. When deformation is carried out, primary α phase dynamically transforms into metastable β phase [[8], [9], [10], [11], [12], [13], [14], [15]]. It is interesting to note that a certain amount of coupled parallel laths, i.e. typical Widmanstätten α phase, are clearly shown in Fig. 4(b)-(d). In general, Widmanstätten α microstructures are observed in the over-saturated β phase and distribute along a specific direction of Burger’s relationship [21,22]. In the present work, the DT metastable β phase also leads to the formation of Widmanstätten α phase.

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Fig. 4.   EBSD micrographs of the studied samples deformed at temperature of 950 °C and strain rate of 0.01 s^-1: CG samples at strains of (a) 0, (b) 0.1, (c) 0.5, (d) 0.9 and (e) 1.2; FG alloys at strains of (f) 0.5 and (g) 1.2.

Fig. 5 presents typical TEM microstructures of CG specimens deformed at various strains. Well-formed acicular α′ martensites and high density of dislocation are observed in non-deformed samples with subsequent water quenching in Fig. 5(a) [23]. No residual primary β phase is observed. After hot compression (Fig. 5(b) and (c)), similar microstructure with typical α′ phase and high dislocation density is observed as well. Meanwhile, a large number of stacking faults are formed within a substructure accompanying with lath α′ phases, as confirmed in Fig. 5(d)-(f). The presence of streaking (Fig. 5(e)) in selected area electron diffraction (SAED) indicates the existence of stacking faults [24]. The stacking faults are further observed under high resolution transmission electron microscope (HRTEM, Fig. 5(g)-(h)) in which an obvious stacking faults is illustrated by light lines and the light arrow indicates the stacking faults plane. In addition, Widmanstätten α phase is also observed under TEM (illustrated by dashed line in Fig. 5(c)) which can be distinguished from α′ martensites with little dislocation and coupled parallel laths.

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Fig. 5.   TEM bright field images of CG specimens deformed at strains of (a) 0, (b) 0.5 and (c) 0.9, respectively; (d, f) observed lath α′ phase coupled with stacking faults and the corresponding (e) SAED pattern and (g, h) HRTEM images.

4. Discussions

Generally, when deformed at high temperature, the flow softening of titanium alloy is associated with dynamic recovery (DRV), dynamic recrystallization (DRX) [2,25], as well as DT [4,10]. For instance, Sheppard and Norley [25] found that DRV was the operative mode when deformed in the β-region, while DRX predominated in the α+β-region based on extensive optical and electron microscopy examinations. According to Furuhara et al. [2], some discontinuous dynamic recrystallization could also occur along β grain boundaries in the β single-phase region. Meng et al. [26] studied the flow behavior of an ATI425 titanium alloy and found that the variation tendency of power dissipation factor had positive correlation with the examined fraction of recrystallized grains. In addition, DT was also found to affect the flow behaviors in titanium alloys remarkably [8,[11], [12], [13], [14]]. In the present titanium alloy specimens with different α grain sizes, approximate volume fraction of α phase in non-deformed samples was observed (Fig. 2, Fig. 3). On the other hand, the hardness of α phase is higher than that of β phase [27,28]. Hence, though DRV/DRX in β phase should contribute to flow softening by balancing the rate of hardening by generation of dislocations and the rate of softening due to dislocation annihilation, DT is the primary interpretation for the different flow softening behaviors in the present titanium alloy specimens with different α grain sizes (Fig. 1). Owing to quenching effect, i.e. β phase transfers to α′ martensitic microstructure, the deformation mechanisms in β phase could not be observed in the present microstructural examinations. According to microstructural examinations (Figs. 2, 4 and 5), main difference on α phase during hot deformation is the volume fraction. The flow stress during deformation is also related to the hardness of both phases [[9], [10], [11]]. As confirmed by SEM and EBSD microstructures, less residual α phase remains in CG samples indicating more DT of the harder α phase transformed into the β phase during hot deformation. Therefore, more DT in CG samples contributes to the faster flow softening, as shown in Fig. 1. When DT is gradually finished, flow stress tends to reach steady states at higher strain levels (RS plateau in Fig. 1(b)).

In titanium alloys, grain boundary sliding was found to occur preferably at α/β interfaces rather than at α/α or β/β boundaries for its much lower sliding resistance during hot deformation [29,30]. In the alloy with coarser α grain, the reduction on the fraction of α/β boundaries will lead to a higher grain boundary sliding resistance. In such situation, deformation accommodation by grain boundary sliding will be suppressed, and α grain has to accommodate more deformation. As a result, DT processes can be accelerated [4]. By utilizing TEM observation, Kim et al. [31] found that high density dislocations were developed in coarse α grain specimen († 11 μm) when deformed at 900 °C, while little dislocation in fine α grain alloy († 3 μm) but only some dislocations near the α/β boundaries were observed.

In addition, thermodynamic evaluations of DT in both alloys are also different. The actual driving force for DT is estimated by the difference between actual stress of α phase at various strains and the yield stress of β phase. In general, DT is considered to be a displacive nucleation and diffusion-controlled growth process [4,6,9,13]. Thus energy barrier opposing DT is composed of dilatation work, shear accommodation work and Gibbs energy difference [4]. The driving force and energy barrier can be expressed by the following equations:

DF_actual=σ_α-actual-σ_β-yield (2)

EB=W_dilatation+W_{shearaccommodation}+ΔG (3)

where σ_α-actual is actual flow stress of α phase at various strains and σ_β-yield is yield stress of β phase. The yield stress is taken by the 0.2% offset rule, and that for CG and FG alloy in this work is 18.1 MPa and 22.0 MPa, respectively. According to Guo et al. [13], both σ_α-actual and σ_β-yield could be calculated based on the law of mixtures. ΔG is Gibbs energy difference that increases with formation of DT β phases during deformation. The calculation of ΔG at various strains is based on α volume fraction changes. To unify the units of mechanical work and energy, an unit conversion is used here 1 MPa≈10.6 J/mol [9]. Wdilatation is dilatation work that can be estimated by:

W_dilatation=$\sqrt{ m }$×σ_α-critical×ε_dilatation (4)

where σ_α-critical is critical stress for further occurrence of DT, m is Schmid factor. A critical state that maximum resolved shear stress applies to habit plane is considered, so m is taken as 0.5 here. And ε_dilatation is dilatation strain associated with transformation of α to β phase taken as 1.7% as reported in Ref. [9]. Similarly, the shear accommodation work (W_{shearaccommodation}) can be calculated by :

W_{shearaccommodation}=m×σ_α-critical×ε_shear (5)

where ε_shear is the shear strain associated with transformation which is taken as 0.14 [9]. σ_α-critical is calculated in a critical state when the critical driving force equals to energy barrier, which can be expressed by:

DF_critical=σ_α-critical-σ_β-yield=EB (6)

The critical stress of α phase can be calculated by the reorganized Eqs. (3), (4), (5), (6):

σ_α-critical=$\frac{σ_{β-yield } +ΔG }{1-(\sqrt{ m }×ε_{ dilatation } +m×ε_{ shear }) }$ (7)

The relationships of estimated critical stress of DT (Eq. (7)) of both FG and CG alloys at various strains are summarized in Fig. 6(a). The relationships of corresponding energy barrier and actual driving force of DT (Eqs. (2), (3), (4), (5)) are presented in Fig. 6(b) and (c). In Fig. 6(a), it is indicated that critical stress for DT of FG alloys is higher than that of CG alloys. With strain increment, critical stress for DT gradually increases mainly owing to the increased DT β fraction which raises the chemical Gibbs energy (Fig. 6(b)) [9,13]. On the other hand, the actual driving force decreases gradually because of dynamic softening and decrement of α phase volume fraction. Notably, it is observed that the differences between actual driving force and total energy barrier in FG alloy are smaller and decrease more rapidly than that in CG specimen. After strain of 1.1, energy barrier exceeds driving force in FG alloy as illustrated in Fig. 6(c), which indicates that little drive force is retained for further DT. While in CG alloy, driving force is always higher than total energy barriers. Such difference reveals thermodynamically that larger driving force leads to an accelerated DT in samples with coarser primary α grain. As a consequence, more α phases transform to β phases in CG alloy during deformation, as shown in Fig. 2, Fig. 3, Fig. 4.

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Fig. 6.   (a) Evolution of critical stress of DT with increased strain levels in FG and CG alloys, (b) evolution of energy barriers opposing DT with increased strain levels in both alloys and (c) relationship of total energy barriers and actual driving force of DT at various strains.

To further understand DT mechanisms, a phase reconstruction method [16,17] is adopted. The assumption is first employed that DT and martensitic transformation during water quenching in titanium alloy follow strict Burgers orientation relationship of (1 1 0)_β //(0 0 0 1)_α and [-11 -1]_β//[-2110]_α [[32], [33], [34]]. In EBSD maps, hexagonal close packed (hcp) α or α′ crystal orientation can be expressed in the forms of Euler angel rotation matrix Pα and the corresponding prior body centered cubic (bcc) β phase crystal orientation (Bliβ) as follows [16,17]:

$ B_{li}^{β}=D^{-1}S_{l}^{α} G_{i}^{α} P^{α} $ (8)

where D is the rotation matrix with Euler angles (135°, 90°, 154.74°) expressing Burgers relationship mathematically calculated by Humbert et al. [35], $ G_{i}^{α} $ is the six-fold symmetry operators to simplify hexagonal space with i=1…6, $ S _{l }^{α} $ is the rotated operators or rotational elements of hexagonal symmetry with Euler angles E (0,0,0), $ C_{6z +}^{α}$ (π/3,0,0), $ C_{3z+}^{α}$ (2π/3,0,0), $ C_{21+}^{α}$ (π,π,π), $ C_{22+}^{α}$ (π,π,π/3), $ C_{23+}^{α}$ (π,π,2π/3) corresponding to l=1…6. The operators for other variants can transfer to these six operators. A set of 6 possible orientations with Euler angle matrix $ B_{li}^{β} $ can be established via Eq. (8). All β orientations calculated from a prior β phase should have the same orientation. Therefore, to determine the approximate prior β phase orientation, all calculated β phases, if belong to one prior β phase, own a minimal misorientation. The misorientation between two neighboring β orientations matrix g_i,g_j(i,j=1…6) is gained from a misorientation matrix [16,17]:

(9)

And the misorientation is expressed by the equation as follows:

γ_ij=cos^-1[(Δg₁₁+Δg₂₂+Δg₃₃-1)/2] (10)

Finally, a minimal misorientation angle γ_min that is no more than a given tolerance (here we choose 4°) is used to determine the correct prior β orientation. Two typical EBSD microstructures of CG alloy deformed to strain of 0.5 with higher magnification are shown in Fig. 7(a) and (b), where particular points are illustrated by hexagonal wireframes. The original and reconstructed orientation relationships of such points are summarized in Fig. 7(c) and (d) within the hcp (0 0 0 1) and bcc (1 0 0) pole figures respectively. The primary α grains (i.e., A1 and B1) are transformed to bcc structure as well to gain the orientation relationship with their neighboring β grains. The calculated results for selected points via the phase reconstruction method (i.e., Eqs. (8), (9), (10)) are also listed in Table 1. The typical points with calculated bcc misorientations not exceeding the given tolerance are grouped together as shown in Table 1.

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Fig. 7.   (a, b) Two typical EBSD maps of CG alloy deformed to the same strain of 0.5 with higher magnification. The hexagonal wireframes of marked grains are also given. The (c) hcp (0 0 0 1) and (d) bcc (1 0 0) pole figures show the original and reconstructed orientation relationships of marked points in (a) and (b), respectively.

In Fig. 7(a), A1 is a primary α grain without DT. The calculated orientations of A1-A7 reveal that A1 has divergent Burgers relationships with the neighboring β phases, which is indicated in the pole figure (Fig. 7(c)) and Table 1. In Fig. 7(b), lamellar microstructure B2 is a DT β phase transformed from B1. Interestingly, the calculated bcc orientation of B1 and B2 matches well with misorientation of solely 1.6° (Table 1). In addition, the calculated prior β orientations of surrounding B5-B9 also have close Burgers relationships with B1 (Fig. 7(d) and Table 1). Hence, it is presented that DT could be more likely to occur where a close Burgers relationship between primary α and neighboring β phase. In titanium alloys, dislocation slip transfer has been found to show strong dependence on Burgers orientation relationship between the α and β phases because of different resistances or resolved shear stress [36]. During hot rolling, Roy et al. [37] proposed that dislocation slip transfer at α/β interface became difficult if the Burgers relationship was broken particularly for prism or basal slip. A co-linearity Burgers orientation relationship would be helpful for dislocation slip transfer and ease the dislocation pile-up at α/β interface. Weak starting texture and easy slip transfer were indicated to accelerate dynamic α→β transformation. Therefore, particular α grains owing close Burgers relationships (Fig. 7(b)) with adjacent β phases could be preferred for DT at lower strains. As strain increasing, residual α grains (Fig. 7(a)) may rotate or dynamically recrystallize, and then transfer to a better Burgers relationship for DT at higher strain.

As confirmed by EBSD and TEM, Widmanstätten α phase is presented in deformed specimens. Ohmori et al. [21] suggested that the partitioning of alloying elements in Widmanstätten laths occurs mainly during the isothermal holding after their formation, and their habit planes lie close to the lattice invariant shear plane. In the present work (Fig. 5(c)), Widmanstätten α with width approximate 0.2-0.3 μm is observed in deformed spcecimen. When stress is removed, reverse transformation of metastable β phases may occur owing to the driving force (i.e. Gibbs energy differce of β→α transformation) exceeding the energy barriers (i.e. the shear accommodation and contraction work) [11,13]. During this process, the potential diffusion distances of aluminum and vanadium elements can be estimated by the following equation (Fick's second law) [13,38]:

$\bar{X}_{i} =\sqrt{ Dt } $ (11)

where t is time for diffusion and D is the diffusion coefficient. At 950 °C, the value of D for vanadium in β phase is 0.0486 μm²/s and for aluminum is 0.0782 μm²/s [39]. Under the maximum delay of 3 s prior quenching, the mean diffusion distances for vanadium and aluminum in these deformation conditions are estimated to be 0.38 μm and 0.48 μm. Hence, the diffusion distances are sufficient for a formation of Widmanstätten α with width about 0.2-0.3 μm. In addition, DT is a displacive nucleation and diffusion-concriled growth process [4]. This indicates that reverse transformation of newly DT β phase could be more likely in formate of Widmanstätten transformation for a closer element distribution and Burgers relationship orientation in a short time after the deformation. At lower strain, newly DT β phase may have a closer element composition to primary α phase. While the element distribution is tend to be uniform at higher strain ascribe to longer diffusion time for DT β phase formed at early stages. Therefore, most Widmanstätten laths are observed at lower strain (Fig. 4). When deformed to strain of 1.2, much fewer Widmanstätten α phases are found (Fig. 4(e)). Further, as suggested by Kherrouba et al. [40], the formation of Widmanstätten laths may obey the combined displacive-diffusional mode as well. Because of the predominant equilibrium β phases in all specimens, martensitic transformation is the main processes during water quenching, as indicated in Fig. 4, Fig. 5.

5. Conclusions

DT in Ti-6Al-4V alloy was studied by performing compression tests at temperature of 950 °C and strain rate of 0.01 s^-1. Main conclusions are summarized as following:

(1)The alloy with coarser α phase grain size indicated a more evident flow softening during hot deformation, which is attributed to an accelerated DT with greater decrement of α volume fraction. Full β microstructure was observed at strain of 1.2 while retained α phase was observed in fine α grain specimens.

(2)The accelerated DT in CG samples was attributed to more deformation accommodation and higher DT driving forces than that in FG alloys.

(3)Phase reconstruction showed that DT was more likely to occur where a close Burgers orientation relationship existed between primary α phase and neighboring β phase.

(4)Widmanstätten α phase was observed in deformed alloys which was reversely transformed from metastable DT β phase prior water quenching.

Acknowledgments

This work was supported financially by the National Natural Science Foundation of China (Nos. 51674111 and 51874127) and the Chinese Scholarship Council (No. CSC 201606130102).