Flow behavior and dynamic transformation of titanium alloy Ti62A during deformation at different temperatures and strain rates

The effect of deformation temperature and strain rate on the hot deformation behavior and dual-phase microstructure evolution of the titanium alloy Ti62A was examined using electron backscatter diffraction. In general, the activation energy of Ti62A during steady-state deformation in the (α + β) phase is 295 kJ mol−1. The primary recovery mechanisms of the β phase during hot deformation are dynamic recovery and dynamic recrystallization (DRX). Moreover, discontinuous DRX occurs at low temperatures and high strain rates, whereas continuous DRX occurs at high temperatures and low strain rates. Furthermore, high strain rates in the (α + β) phase and high deformation temperatures are advantageous to dynamic phase changes during dynamic transformation (DT). The β phase penetrates the lamellar α s phase, causing fragmentation and spheroidization of the α s phase. Finally, DT begins more easily in the fine α s phase than in the coarse α p phase.


Introduction
Damage-tolerant titanium alloy [1] is a low-density, high-strength, high-toughness alloy, and the demand for its strength and toughness is increasing with the application of damage-tolerance design criteria in aerospace and aviation. The titanium alloy Ti62A was developed via composition optimization based on Ti-62222S, and its nominal composition is Ti-6Al-3Mo-2Sn-2Zr-1Cr-1 V. Ti62A has high specific strength, corrosion resistance, a high fatigue-crack-growth threshold, and a low fatigue-crack-growth rate. Therefore, Ti62A has been extensively utilized [2,3]. Controlling the mechanical characteristics of Ti62A during hot forming is important for producing high-quality products, and therefore the hot deformation behavior of Ti62A should be examined.
The mechanical properties of dual-phase Ti alloys are particularly sensitive to hot deformation parameters and mechanisms [4,5], with work hardening (WH), dynamic recovery (DRV), and dynamic recrystallization (DRX) occurring during high-temperature deformation. The main microstructure evolution mechanisms during the thermal deformation of dual-phase titanium alloys are DRV and DRX. DRX is divided into two types: discontinuous DRX (DDRX) and continuous DRX (CDRX). A gradual transition from low-angle grain boundaries (LAGBs; 15°) to high-angle grain boundaries (HAGBs; >15°) with increasing strain is typical during CDRX [6,7]. Many researchers have been examining this field for decades and have a good grasp of the hot deformation behavior of dual-phase titanium alloys. For example, Huang et al [8] examined the titanium alloy Ti-5.5Al-3Nb-2Zr-1Mo in the (α + β) phase and reported that the major softening mechanism of the β phase during thermal deformation was DRX and that a large number of fine β recrystallization grains and HAGBs formed at the boundaries of deformed grains. Xie et al [9] investigated the titanium alloy TC21 and reported that the DRV mechanism intensified and the DRX mechanism weakened with an increase in deformation temperature and a decrease in strain rate. Sun et al [10] observed the recrystallization mechanism of the β phase of TC17; its DRX mechanism was primarily CDRX, and rotational recrystallization occurred at the local location, coordinating the deformation of the surrounding α phase. Jia et al [11] analyzed the equiaxed behavior of the lamellar α of the titanium alloy TC17. The lamellar α s first generated a dislocation substructure during DRV, and the fragmented α phase globularized the lamellar α s via diffusion migration with an increase in deformation. Li et al [12] examined the microstructure evolution of the titanium alloy TA19, and the lamellar α shifted to a curved morphology in which internal DRV and DRX occurred. In summary, the impact of deformation factors differs during the microstructure development of (α + β) titanium alloys.
Thus, this study aims to examine the influence of strain rate and deformation temperature on the Ti62A grain morphology, particularly its β, equiaxed α, and lamellar α phases, via optical microscopy (OM), scanning electron microscopy (SEM), and electron backscatter diffraction (EBSD), with focus on DRX and DT. The evolution behavior of DRV and DRX is used to discuss the evolution process of the Ti62A microstructure.

Materials and experiments
The following are the chemical components (wt.%) of the as-received Ti62A alloy: 6.1Al-3.1Mo-3.1Zr-1Cr-1V-0.2Fe-(bal.)Ti. This alloy's β transformation temperature was 969°C ± 5°C, as determined via the continuous heating metallographic method. The approximate β transformation temperature was calculated as 969°C using the chemical composition calculation method. The experimental temperatures were set to 964°C, 969°C, and 974°C and the phase transition point was determined as 969°C ± 5°C according to the Ti62A microstructure.
Deformation tests were performed using a Gleeble 3800 mechanical system. Figure 1 shows the experimental flow. Cylindrical specimens (Φ 8 mm × 12 mm) were cut from forging stock, heated to the experimental temperatures (820°C, 860°C, 900°C, and 940°C) at a rate of 10°C s −1 , and held for 8 min to guarantee their temperatures. The specimens were compressed at four strain rates (0.001, 0.01, 0.1, and 1 s −1 ) to achieve a 65% deformation reduction. After the deformation tests, the samples were air-cooled, because the sample size of Ti62A titanium alloy is relatively small, and actual argon quenching rate is similar to that of air cooling. All experiments were performed under safe conditions to avoid oxidation. Their microstructures were observed by slicing them along the deformation axis. Three samples were taken for each set of data in this paper, and the average value of each set was obtained for data analysis.
The distorted samples were sectioned parallel to the deformation axis, and the center portion of each section was examined via OM, SEM, and EBSD. The OM samples were ground to 600 mesh, 1500 mesh, and 2000 mesh for approximately 2 min and then polished using polishing liquid (20 vol.% H 2 O 2 , 80 vol.% SiO 2 ) for approximately 7 min Grinding and polishing were conducted using an automatic polishing-grinding machine. A Kroll reagent (2 vol.% HF, 6 vol.% HNO 3 , 92 vol.% H 2 O) was used after etching. Optical microstructure investigations were performed using a Zeiss AX10 optical microscope. SEM was conducted using a Phenom Pro machine. EBSD characterization was performed using an Oxford NordlysMax3 machine. EBSD mapping was conducted at operational voltages ranging from 10 to 20 kV for a thorough examination. HKL Channel 5 was used for data collection and processing. The orientation data from EBSD mapping were used to differentiate the β and α phases below Tβ.  Figure 2 shows the initial microstructure of the Ti62A alloy. Equiaxed α p (black) is distributed equally across the β zone (light) in figure 2(a). Image-Pro Plus determined the volume fractions of the α p , α s , and β phases (figure 2(a)) to be 31.5%, 52.3%, and 16.2%, respectively. The average thicknesses of α p and α s are 11 and 1 μm, respectively. In figure 2(b), the α phase displays a 〈11-20〉 orientation, which may be attributed to the forging stock [13]. The β phase is oriented to 〈100〉 + 〈111〉. Pole figure (PF) maps of the phases with maximal texture strengths of 30 and 14 are shown in figure 1(d). Figure 3 shows the Ti62A flow curves at various temperatures and strain rates. Flow stress increases as strain rate increases and temperature decreases. In general, the dislocation multiplies, which results in an immense growth in flow stress until the peak stress, with WH as the primary cause. The real stress-true strain curves show two deformation processes. The flow curves show a flow softening behavior as flow stress decreases with an increase in strain at the lowest deformation temperature of 820°C (figure 3(a)), which has been confirmed in several other titanium alloys. The flow curves exhibit a constant flow behavior at the higher deformation temperatures of 900°C and 940°C, and flow stress does not vary with an increase in strain; this flow behavior is attributed to the balance between DRV and WH during deformation [14]. The stress curve exhibits a noticeable characteristic at the strain rate of 0.01 s −1 and temperature of 940°C. The peak stress emerges in the low-strain region at the beginning of deformation; then, stress quickly declines, and the flow curve exhibits a concave trend, which is a discontinuous yield phenomenon [15], as seen in Ti-55531, Ti-6Cr-5Mo-5V-4Al, and Ti-55511 [16][17][18]. The mobility and fast multiplication of the movable dislocations at the grain boundaries possibly cause this phenomenon.

Constitutive relationships
Given the constitutive connection devised by Sellars and McTegart [13], the following equation contains the flow stress, deformation temperature, and strain rate [19] in stationary hot deformation: where e  is the strain rate (s −1 ), A is the material constant, Q is the steady-state deformation activation energy (kJ/mol), R is the gas constant (8.314 J (mol·K) −1 ), and T is the deformation temperature (K). In the preceding .
In the case of linear dependence, the slope yields an n of 1.159 ( figure 4). The fitting slope k for the constant is 23,400, and Q is determined as 295 kJ mol −1 using the slope of the Arrhenius plot (figure 5). The Q value discovered in the (α + β) phase exceeds the stated figure for α-Ti (150 kJ mol −1 ) [21]. This difference in activation energy is associated with the microstructural development (DRV and DRX) of the β phase, recovery of the lamellar α, and transition of the lamellar α into equiaxed α [22].
The microstructure of titanium alloys with strain during hot deformation is affected by the deformation temperature and strain rate. In this study, the strain rate and deformation temperature are coupled in the form of a function during hot deformation based on the Zener-Hollomon hot deformation conclusion, and the Z  parameter [23] is introduced. After temperature adjustment, the physical meaning of the Z parameter is the strain rate factor [24]. Equation (3) shows the formula for the Z parameter.
In this study, the microstructure of Ti62A after hot deformation is studied by combining it with the Z parameter.
3.4. Microstructure evolution 3.4.1 Microstructure evolution of α phase figure 6 shows the OM morphology at a strain rate of 0.01 s −1 at temperatures of 820°C-940°C. The microstructure is mostly formed throughout the β phase, α p , and some fractured lamellar α s after deformation at 820°C. At the deformation temperatures of 900°C and 960°C, the microstructure mostly comprises the α p and equiaxed β grains; it has nearly no α s . The α p percentages of the  alloy at the strain rate of 0.01 s −1 at the different deformation temperatures are 26.4%, 23.4%, 10.6%, and 5.7%, at a strain rate and different deformation temperature as shown in figure 7. Correspondingly, as the temperature increases, the α p phase progressively drops in volume fraction and slowly converts into the β phase. Furthermore, the β phase has distinct grain boundaries, and its orientation distribution shifts. Figure 8 shows the SEM morphology of the hot deformation microstructures at 860°C at the varied strain rates. In figure 8(a), certain α s phases are bent to some degree (shown by the yellow circle) at the strain rate of 1 s −1 , whereas some α s phases are sufficiently globularized, forming globular α grains and short α laths (marked by the red circle). Nearly all α s phases are changed into β phases in figure 8(b), and the few residual α s and α p phases are divided into small pieces or particles; the α p phases display necking and elongation. The frequency of α p rises with the strain rate. In figure 9, the α p volume fractions of Ti62A at 860°C at the strain rates of 0.001, 0.01, 0.1, and 1 s −1 are 19.6%, 23.4%, 25.1%, and 30.6%, respectively. In figures 2(a) and (a), the α p volume fractions are 30.3% and 31%, respectively. In particular, the drop in α s shows that α s undergoes major deformation during hot deformation, whereas the size and shape of α p change very slightly in the absence of sufficient strain. Thus, the α s phase is entirely converted in figure 8(b).   respectively, at the deformation temperature of 860°C. At the deformation temperature of 900°C, the frequencies of the LAGBs and HAGBs become 90.08% and 9.52%, respectively, and at 940°C, they become 76.59% and 22.37%, respectively. At the different deformation temperatures, the high frequencies of the LAGBs confirm that the main recovery mechanism is the DRV of the β phase. Nevertheless, the frequencies of the HAGBs are higher at the deformation temperature of 820°C than at the other temperatures. This phenomenon may be because the α phase is a hexagonal close-packed (HCP) crystalline structure with a few active slip systems, whereas the β phase is a body-centered cubic (BCC) crystalline structure with many active slip systems. During deformation, the β phase is more prone to deformation compared with α p , and little deformation is observed in α p ( figure 7(a)). Hence, deformation primarily occurs in the β phase, and the main softening mechanisms are DRV and DRX.  The EBSD grain boundary diagram at the temperature of 940°C at the strain rate of 0.01 s −1 is shown in figure 11. In figures 11(a)-(c), the white areas are the α phases. In figure 11(b), the white and black lines represent the LAGBs and HAGBs, respectively. In figure 11(c), the blue components represent recrystallized β phases, the yellow parts represent the β phases' substructures, and the red parts represent deformed β phases. In figure 11(d), the blue areas are the β phases, and the red parts are the α phases. Some LAGBs and HAGBs exist inside the β grains, which proves the occurrence of DRV and DRX. In particular, the substructures indicated by the black arrows are similar in color to adjacent structures. LAGBs are observed near the substructures by the black arrow in figure 11(b). The occurrence of recrystallization is confirmed in figure 11(c), which shows that the LAGBs of the β phase gradually transform into HAGBs, which is a typical characteristic of CDRX. Therefore, CDRX occurs at the deformation temperature of 940°C. In brief, the main recovery mechanism is the DRV of the β phase with the CDRX mechanism. Figure 12 shows EBSD grain boundary diagrams at the strain rates of 0.001, 0.01, 0.1, and 1 s −1 at the deformation temperature of 860°C. The frequencies of the LAGBs and HAGBs of the β phase are 93.24% and 6.17%, respectively, at the strain rate of 0.001 s −1 ; 95.45% and 3.66%, respectively, at the strain rate of 0.01 s −1 ; 89.61% and 9.19%, respectively, at the strain rate of 0.1 s −1 ; and 73.36% and 25.68%, respectively, at the strain rate of 1 s −1 . The frequencies of the LAGBs of the β phase vary from 70% to 100% at the various strain rates, which indicates that the significant restoration mechanism is the DRV of the β phase. Moreover, the frequency of the LAGBs reduces as the strain rate increases, which may be linked to the occurrence of DDRX in the β phase; DDRX will considerably consume the substructures containing LAGBs. Furthermore, the smaller volume portion of HAGBs suggests that DDRX is in its early stages.

Dynamic transformation of α phase
DT is a common diffusion-controlled process in Ti alloys, indicating that the higher energy storage and a higher diffusion rate would facilitate DT [25]. Lie et al [26] demonstrated that DT is influenced by temperature and strain rate and may benefit from increases in temperature and time. Moreover, the major α phase even vanishes in some situations. Therefore, the DT mechanism associated with α phase size and morphology is investigated below.  (a-c), the white areas are the α phases. In (b), the white and black lines represent the LAGBs and HAGBs, respectively. In (c), the blue areas are recrystallized β phases, the yellow parts are the β phases' substructures, and the red parts are deformed β phases. In (d), the blue areas are the β phases, and the red parts are the α phases.
Increases in deformation temperature, energy storage, and stress aid in diffusion of element [27]. At high strain rates, the deformation time is relatively short, and the element diffusion time is insufficient, which is unfavorable for lattice conversion when the α phase is not easily converted into the β phase. Thus, diffusion theory is used for the DT process associated with α phase size and morphology.
where D is the diffusion coefficient and T is the deformation time with the influence of ΔT added. Because Al is a powerful α phase stabilizer in Ti alloys, the L of DT is roughly regarded to represent the diffusion and migration distance of Al in the β phase [28]. Tables 1 and 2 show the diffusion coefficient (D Al ) and diffusion distance (L Al ) of Al in the β phase. This method can be used to characterize DT; the technique for estimating D Al for titanium alloys follows equation (5) [29], and the ΔT for diffusivity follows equation (6) [26].  / According to tables 1 and 2, with an increase in temperature, both D Al and L Al increase, and with an increase in strain rate, D Al increases and L Al decreases. This is because increasing the deformation temperature provides enough energy for atomic diffusion, thereby increasing D Al [27], and longer distances prolong the time, thus increasing the deformation duration and D Al . This result shows that increasing the temperature and extending the deformation time are beneficial for DT.

Dynamic globularization (DG) of α phase
The globularization of α s primarily occurs through two mechanisms [30,31] in titanium alloys: grain boundary separation and end migration. The grain boundary separation mechanism refers to the occurrence of DRV and DRX in the α s phase during deformation. The α s phase forms grain boundaries, and the β phase passing through α s along these grain boundaries results in the globularization of the lamellar α s . The end migration mechanism refers to the globularization of α s because of the inward migration of chemical elements from the end of α s during deformation. By continuously exploring the globularization mechanisms of α s , researchers have explained the influence mechanism of process parameters on its globularization behavior [32,33]. Figure 13 shows a schematic of the α s phase deformation and the behaviors of DT and DG. In figure 13(a), the lamellar α s and α p are in the β phase matrix before deformation, and the β and α phase dislocation densities are low. With an increase in strain, the slip system of the β phase is activated, and the dislocation density increases greatly. Moreover, the β phase wedges into the α s phase, and the α s phase further separates into two parts. The α s phase undergoes bending/fragmentation, as indicated by the yellow circle in figure 8. Therefore, DG is the major deformation mechanism of α s , because it may enlarge the interface of the α and β phases, thereby benefiting DT. Finally, as strain increases, α s spheroids form, α p dissolves, and DT considerably increases, as shown in figure 13(c). Finally, the α s fragments are more readily transformed into β phases than the coarser α p fragments.
4.3. DRX mechanism of β phase DRV and DRX play important roles in the microscopic development of the β phase, according to deformation behavior and microstructure studies [34,35]. The microstructures of titanium alloys depend on the Z parameter after heat deformation [36]. Moreover, the Z parameter modulates cell and subgrain structures and hence DRX. The CDRX process occurs at the highest Z parameter. CDRX is often preceded by dislocation formation, DRV, and LAGB formation [37], whose process is distinguished by an increase in the rotation of subgrains and the appearance of a noticeable misorientation gradient [38]. The subgrains are numbered 1 to 4 in figure 14(a), and the crystal orientations of the grains and similar hues reflect a progressive shift. Hence, these results show a common CDRX process. A similar phenomenon was discovered in Ti5321 by B Gu et al [30].
The CDRX mechanism can be demonstrated by misorientation. The cumulative misorientation from A to B in figure 14(a) exceeds 15° [37,39], and the point-to-point misorientation in figure 14(c) is over 7°(within 5 μm), which is typical of CDRX. These findings suggest the gradual rotation of subgrains in grains [39]. The point-to-origin misorientation from A to B in figure 14(a) has numerous platforms, indicating that the orientation between neighboring subgrains is fairly big and relatively stable within the grains. Thus, subgrain rotation enhances misorientation, leading to a misorientation gradient [40,41]. To summarize, the DRV mechanism is the primary deformation mechanism of Ti62A, and CDRX also occurs, as seen in such titanium alloys as Ti-5321 and Ti-10V-2Fe-3Al. Finally, the β phase's DRX mechanism is more likely to be CDRX at a higher Z parameter.
The typical DDRX process occurs at the lowest Z parameter, as indicated in figure 15. Subgrain borders separate some subgrains in figure 15(a). In figure 15(b), the different colors of DRX grains 1 to 9 prove the randomness of the DDRX mechanism and DDRX grain orientations. In figure 15(a), the variation in the pointto-point misorientation along MN is <2.5°. Furthermore, the overall misorientation is considerably lower than 15°. In other words, the principal recovery mechanism is the β phase's DRV, whereas the β phase's DRX mechanism is primarily DDRX at a low Z parameter.
More than one DRX mechanism exists, but one of these mechanisms is dominant. The CDRX and DDRX mechanisms differ in their form of expression, but both are processes of deformation energy storage consumption. New DRX grains form through dislocation proliferation, slippage, and structural changes in cellular organization. In the DDRX, certain dislocations proliferate as strain increases, and the grain boundaries bend after coordination because of dislocation proliferation. However, DRX grains consume considerable energy through DRV and generate significant numbers of fine DRX grains at grain borders as dislocation density increases. Furthermore, as dislocation improves and cross-slip may occur entirely during CDRX, the dislocation density in the crystal significantly decreases.

Conclusion
Flow stress highly depends on deformation temperature and strain rate. The flow behavior is mostly governed by WH, the DRX of the β phase, the DT and DG of the α phase, and the deformation heat at high strain rates.
During the deformation of the Ti62A dual-phase region, the hot deformation activation energy Q is 295.297 kJ mol −1 . The main recovery mechanism of the β phase is DRV. The DRX mechanism is primarily DDRX (CDRX) at a high (low) Z parameter.  High strain rates and high deformation temperatures promote DT. Furthermore, the lamellar α s phase undergoes bending/fragmentation, thereby possibly enlarging the interface of the α and β phases and benefiting DT. Finally, DT begins more simply in the fine α s phase than in the coarse α p phase.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).