Article DOI:10.1557/s43578-025-01519-5 Dynamic recrystallization behavior of TC21 titanium alloy Rui Deng1, Song Xue1,a), Minglong Xu1, Zenong Li1, Shaoxiang He1, Ying Zhang1, Rongchao Li1, Qiankun Li1 1 School of Manufacture Science and Engineering, Key Laboratory of Testing Technology for Manufacturing Process, Ministry of Education, Southwest University of Science and Technology, Mianyang 621010, China a) Address all correspondence to this author. e-mail: xuesong2004@126.com Received: 12 July 2024; accepted: 2 January 2025 Vol.:(0123456789) © The Author(s), under exclusive licence to The Materials Research Society 2025 2025 Over the past 20 years, titanium alloys have been successfully applied to fuselage products such as aircraft, aircraft engines, and rocket engines due to its excellent performance, contributing significantly to the structural integrity of the majority of military aircraft [1–3]. TC21 titanium alloy is widely used in the aerospace field due to its superior comprehensive mechanical properties, including high strength, high toughness, low density, high damage tolerance, and low crack growth rate. It is increasingly replacing TC4 titanium alloy and has already become one of the key materials for manufacturing critical components of aircraft [4, 5]. Therefore, these components require excellent mechanical properties, which are influenced by the evolution of the material’s microstructure. The dynamic recrystallization occurring inside metal materials can effectively refine the grain structure, thereby obtaining uniform and fine equiaxed structure is critical [6–8]. Mironov et al. [9] investigated microstructure evolution during warm working of Ti–6Al–4V with a colony-a microstructure by EBSD technique, the research result indicates that changes in strain path may be beneficial in promoting globalization during warm working. Lin et al. [10] investigated the softening mechanism behavior of Ti-55511 alloy during thermal compression, mainly the spheroidization of lamellar α phase and recrystallization of β phase, the results indicate that the degree of spheroidization of the layered α phase is closely related to the deformation temperature and strain rate. The spheroidization fraction of lamellar α phases begins to drop at about 700 °C as the strain rate is higher than 0.01 ­s−1. Luo et al. [11] investigated the microstructure evolution and rheological stress behavior of TC17 titanium alloy in the dual-phase region, and they believed that the spheroidization rate of the α phase would increase slightly with the increase of strain and deformation temperature. By observing the trend of the rheological stress curve, it is concluded that the greater the degree of spheroidization of the α phase, the more favorable it is to reduce the rheological stress. Ma and Zhang [12] investigated the spheroidization behavior of cast Ti–6Al–4V alloy after rolling by spheroidization process of coupling pulsed electric, the spheroidization process mainly formed needle-like or equiaxed α phase, significantly improving the mechanical properties of the Ti–6Al–4V alloy. Li et al. [13] conducted microstructural studies on TC18 titanium Journal of Materials Research Introduction www.mrs.org/jmr This study investigated the dynamic recrystallization behavior of TC21 titanium alloy in the dual-phase region (850–930 °C) through thermal compression tests, analyzed the softening mechanism behavior through the stress–strain curve and microstructure, and then calculated the hot deformation activation energy of the material. Kinetics model was established. Dynamic recrystallization simulation was conducted using DEFORM-3D finite element software. The dynamic recrystallization of TC21 titanium alloy occurred in the dual-phase region was revealed by combining microstructure analysis and the value of thermal deformation activation energy. The predicted values of the dynamic recrystallization volume fraction model show a correlation coefficient of 0.967 with experimental values. By comparing grain size, the simulation and experimental results indicated that the grain size error is approximately 10.8%, demonstrating a certain level of reliability for kinetics model. Under the deformation conditions of deformation temperature is 890 °C and strain rates of 0.1 and 1 ­s−1, relatively uniform and fine microstructure can be obtained. Article Stress–strain curve Figure 1 is the true strain–stress curve obtained based on the thermal compression test data. It can be observed that the flow stress exhibits a decreasing trend with increasing deformation temperature across various strain rates. The main reason is that with increasing deformation temperature, more heat energy is obtained inside structure. The motion between atoms becomes © The Author(s), under exclusive licence to The Materials Research Society 2025 When the deformation temperature is 850 °C, as shown in Fig. 2(a), compared with the original structure, it was observed that in the microstructure after thermal compression deformation, many small dynamic recrystallization (DRX) grains appeared between equiaxed α phase, indicating that TC21 titanium alloy has started to undergo dynamic recrystallization at 850 °C. As depicted in Figs. 2, 3 and 4 that when the strain rate is between 0.01 and 1 ­s−1, with increasing deformation temperature, number of α phase decreases firstly, part of α phases merge and grow with each other, as shown in Fig. 2(c); overall, www.mrs.org/jmr Microstructure analysis 2025 Result and discussion unstable, and the atomic motion becomes more active, accelerating the speed of grain boundary slip and grain growth, both of which are manifestations of dynamic recrystallization. Therefore, the accumulation of dislocations and work hardening generated by thermal compression will be partially offset by the softening mechanism of dynamic recrystallization [16–18]. In addition, as increasing deformation temperature, α phase inside alloy gradually decreases, but β phase gradually increases due to the proximity to the phase transformation temperature. Because α phase belongs to hard phase, but β phase belongs to phase with better processing plasticity [19, 20]. So, as the deformation temperature increases, the flow stress shows a decreasing trend. The flow stress of TC21 titanium alloy first reaches a peak quickly, then begins to decrease slowly, and gradually tends to a stable value, this is because at the beginning of hot deformation, dislocations gradually accumulate and work hardening occurs, at this stage, the true stress–strain curve shows a straight line rise. When the dislocations accumulate to a certain extent, reaching the critical strain value for dynamic recrystallization, then material begins to experience dynamic recrystallization. When the curve reaches its peak, due to the interaction between softening mechanism and work hardening, the flow stress begins to decline and gradually tends to dynamic equilibrium [21–23]. As depicted in Fig. 1, it is evident that the flow stress of the alloy rises with increasing strain rate at same deformation temperature. This phenomenon arises due to the increasing hot deformation compression, leading to the increasing dislocation accumulation within the structure, consequently inducing work hardening; moreover, higher strain rates correspond to shorter time of hot deformation. The dislocation slips and climbing inside the structure are difficult to carry out, and the mobility between atoms has also become difficult, therefore, there is not enough time to undergo dynamic recovery and dynamic recrystallization, mitigating the hardening phenomenon induced by hot compression becomes difficult. At the macro level, there is an increase in deformation resistance and a decrease in plasticity, therefore, at same temperatures, an increasing strain rate corresponds to a great flow stress [24, 25]. Journal of Materials Research alloy produced by laser additive manufacturing at different hot working temperatures, after double annealing treatment, the degree of spheroidization of the α phase was highest when the temperature was below 750 °C. Pu et al. [14] in order to study the dynamic recrystallization behavior of TC4 titanium alloy under isothermal compression test, they used the Poliak Jonas method to obtain the critical strain value for dynamic recrystallization and then analyzed the thermal deformation behavior of the material based on the rheological stress curve. Yi and Pan [15] studied the dynamic recrystallization behavior of TC4 titanium alloy through thermal compression test and established a dynamic recrystallization model, the results showed that the grain size and volume ratio of TC4 titanium alloy increased with increasing temperature and decreasing strain rate. Most scholars have conducted research on the hot behavior of metal materials, mainly including phase transitions and different softening mechanisms, the purpose is to obtain a uniform microstructure to improve the mechanical properties of metals. The research material of this article is TC21 titanium alloy, which is a typical dual-phase titanium alloy. Currently, there is relatively little research on the dynamic recrystallization of TC21 titanium alloy in the dual-phase region. Due to the crucial role of grain size in the evolution of metal forming process, the dynamic recrystallization model is an effective research tool; therefore, this article mainly analyzes the dynamic recrystallization evolution of TC21 titanium alloy in the dual-phase region through the changes of grain size. This article studies the dynamic recrystallization evolution of TC21 titanium alloy in the dual-phase region through a dynamic recrystallization model, mainly by grasping the changes in grain size to study the evolution of its microstructure. Thermal compression tests were conducted on TC21 titanium alloy using the Gleeble-3800 thermal simulator, subsequently, the stress–strain curve and microstructure obtained from the test were analyzed for work hardening and softening behavior. Dynamic recrystallization kinetics model was established based on experimental data, we conducted thermal compression simulations using this model and analyzed the simulation results and verified the reliability of the model by comparing experimental and simulated values of grain size. 2 Article 120 (a) 160 140 80 /MPa /MPa 100 850℃ 60 890℃ 40 930℃ 20 120 100 850℃ 80 60 890℃ 40 930℃ 20 0 0.0 200 (b) 180 0.2 0.4 0.6 0.8 0 0.0 1.0 (c) 300 0.2 0.4 0.6 0.8 1.0 (d) 150 850℃ /MPa /MPa 250 890℃ 100 0 0.0 850℃ 150 890℃ 100 930℃ 50 200 930℃ 50 0.2 0.4 0.6 0.8 1.0 0 0.0 0.2 0.4 0.6 0.8 1.0 © The Author(s), under exclusive licence to The Materials Research Society 2025 2025 in Fig. 4(d). As shown in Fig. 4(b), with increasing deformation temperature, part of α phase in microstructure is broken, and many fine equiaxed α grains appear at the grain boundary. In summary, the dynamic recrystallization of TC21 titanium alloy occurred in the range of 850–930 °C, but when the strain rate is 10 ­s−1, it is mainly dynamic recovery. At same deformation temperature, recrystallized grain size tends to grow with decreasing strain rate, especially at deformation temperature of 850 and 890 °C and in strain rate range of 0.01–1 ­s−1, some recrystallized grains appear to aggregate and show a chain shape at grain boundary, as shown in Fig. 3(b), this is because there is sufficient deformation time, and the dislocations caused by plastic deformation caused by compression are eliminated by slip and climb. Because dislocation density determines the number of nucleation sites of recrystallized grains, dislocation density is lower at this time, resulting in a decrease in nucleation rate of recrystallized grains, and the driving force of dynamic recrystallization decreased; therefore, slight recrystallized grains are easily stacked in a chain shape. When Journal of Materials Research the number of α phases shows a decreasing trend, while their size increase, especially at 930 °C. This is because that the temperature approaches phase transition temperature, leading to a greater transformation of α phase into β phase, the presence of β phase in microstructure surpasses that of α phase. With the rise in deformation temperature, atomic activity increases, accelerates grain boundary migration speed, and the condition of recrystallized grain growth is carried out by grain boundary migration. Therefore, recrystallized grains will undergo growth, at the same strain rate, it can be observed that the nucleation of fine grains gradually decreases. At deformation temperature of 930 °C and strain rate of 0.01 ­s−1, grown recrystallized grains were observed, as shown in Fig. 4(a); as strain rate is 10 ­s−1 and deformation temperature is 930 °C, from the observation of the metallographic structure, it was found that most of the grains were elongated and flattened; at the same time, due to the high strain rate, the nucleated grains did not have sufficient time to grow, resulting in the appearance of many fine grains, which are typical characteristics of dynamic recovery [19], as shown www.mrs.org/jmr Figure 1: True stress–strain curves at various strain rates. (a) 0.01 ­s−1; (b) 0.1 ­s−1; (c) 1 ­s−1; and (d) 10 ­s−1. 3 Article Hot deformation activation energy The deformation activation energy denotes the energy required for atomic transition, serving as an indicator of the alloy’s © The Author(s), under exclusive licence to The Materials Research Society 2025 2025 deformation difficulty. Typically, when the hot deformation activation energy of a titanium alloy approaches the self-diffusion activation energy of the α phase in pure titanium, which is 242 kJ/mol, it indicates that the alloy’s softening mechanism primarily involves dynamic recovery. Conversely, if the hot deformation activation energy significantly exceeds the self-diffusion activation energy of the α phase in pure titanium, the alloy’s softening mechanism is predominantly attributed to dynamic recrystallization. The former is because during the dynamic recovery process, migration, rearrangement, and annihilation of defects such as vacancies and dislocations in the material are all achieved through the diffusion mechanism; so, the diffusion activation energy is similar to the self-diffusion activation energy of α phase in pure titanium. The dynamic recrystallization of the latter is realized by nucleation and growth of grains, which requires more energy than the vacancy diffusion, therefore, activation energy required for dynamic recrystallization process is much larger than the self-diffusion activation energy of α phase in pure titanium [26]. The dynamic recrystallization of alloy belongs to hot activation process, that is, with the continuous accumulation of dislocations in alloy. When reached critical strain, the alloy will begin to undergo dynamic recrystallization. Hot deformation Journal of Materials Research deformation temperature is 930 °C and strain rate is in the range of 0.01–1 ­s−1, due to the high temperature, the energy provided for atomic diffusion increases, resulting in acceleration of atomic migration; therefore, at this temperature, recrystallized grains are more dispersed, and there are some broken fine equiaxed α grains, as shown in Fig. 4(b). When strain rate is 10 ­s−1, due to large strain rate, softening mechanism is mainly dynamic recovery and deformation time is shortened, the deformation mode is mainly dislocation slip and climbing. However, grain growth will be hindered due to difficulty of dislocation slips and climb and can only participate in the compression deformation inside structure by changing its own shape; therefore, it can be seen that recrystallization grains are elongated and flattened. Increasing dislocation density elevates both the number of nucleation sites and the nucleation rate of grains; however, due to short deformation time, recrystallization grains cannot fully grow up, so recrystallized grain size is more refined [20, 21], as shown in Fig. 4(d). www.mrs.org/jmr Figure 2: Microstructure of different strain rates at 850 °C. (a) 0.01 ­s−1; (b) 0.1 ­s−1; (c) 1 ­s−1; and (d) 10 ­s−1. 4 Article Figure 3: Microstructure of different strain rates at 890 °C. (a) 0.01 ­s−1; (b) 0.1 ­s−1; (c) 1 ­s−1; and (d) 10 ­s−1. ε̇ = A2 exp(A3 σ ) ασ ≥ 1.2, (2) Q ασ for all, ε̇ = A[sinh (ασ )]n exp − RT (3) where ε̇ is the strain rate, α is the stress level constant, σ is the peak stress, Q is the hot deformation activation energy, R is the molar gas constant, its value is 8.314 J/(mol K), T is the deformation temperature, and A1, A2, A3, and A are constants related to materials. According to deformation temperature, strain rate, and stress–strain curve data, the values of n1 and A3 were fitted to obtain 6.486 and 0.05063, respectively. The value of hot deformation activation energy Q can be expressed as Eq. (4): ∂ ln ε̇ Q=R ∂ ln[sinh ασp ] ∂ ln[sinh ασp ] . ∂(1/T) © The Author(s), under exclusive licence to The Materials Research Society 2025 (4) Kinetic model Critical strain equation When the material undergoes dynamic recrystallization, traditional concept believes that it begins at the peak of stress–strain curve, with more and more research later, and it is found that dynamic recrystallization of the material has occurred before the peak strain, which is called the critical strain of the material [29, 30]. However, the true stress–strain curve cannot directly obtain the critical strain value of material, so it is impossible to know the degree of material deformation to which dynamic recrystallization will occur. Therefore, this paper uses method of work hardening rate [31] to process stress–strain curve, and critical strain www.mrs.org/jmr (1) 2025 ε̇ = A1 σ n1 ασ ≤ 0.8, The hot activation energy Q = 395.463 kJ/mol of TC21 titanium alloy in dual-phase region was obtained by fitting the parameters in Eq. (4), and the hot activation energy is much larger than self-diffusion activation energy of α phase in pure titanium 242 kJ/mol, so it can be inferred that the TC21 titanium alloy has dynamic recrystallization in dual-phase region, and the metallographic diagram of the microstructure can also prove the accuracy of this inference. Journal of Materials Research activation energy can be described by Eqs. (1)–(3), which are applicable to the relationship between flow stress and strain rate at low stress level, high stress level, and so on [27, 28]. 5 Article Figure 4: Microstructure of different strain rates at 930 °C. (a) 0.01 ­s−1; (b) 0.1 ­s−1; (c) 1 ­s−1; and (d) 10 ­s−1. Since work hardening rate is obtained by slope of the true stress–strain curve, that is, θ = dσ/dε. True stress–strain curve obtained from thermal compression test is not smooth, therefore it is necessary to fit the stress–strain curve to obtain the fitting equation and then the derivative of the fitting equation is used to obtain the slope of stress–strain curve under various deformation conditions, that is, work hardening rate θ, then the θ − σ curve is drawn, and critical strain value under different deformation conditions is determined from curves related to θ [32]. The specific method is illustrated by deformation temperature of 930 °C and strain rate of 0.01 ­s−1. Critical strain equation of dynamic recrystallization is expressed by Eq. (5): εc = kεp , © The Author(s), under exclusive licence to The Materials Research Society 2025 (5) (6) Because it is difficult to directly derive the fitting equation, in origin software, the fitting equation can be derived by fitting the stress–strain curve data and the value of work hardening rate under this deformation condition can be obtained; thus, the θ − σ curve can be drawn. Then, by taking the logarithm of the work hardening rate θ , the ln θ − ε curve is drawn, and at the same time, the polynomial third-order fitting of the ln θ − ε curve is performed; the third-order fitting equation is provided as Eq. (7): ln θ = 14.038 − 1040.99ε + 25391.496ε2 − 191952.98ε3 . (7) The inflection point of ln θ − ε curve is the critical strain value under this deformation condition. In order to obtain the value more accurately, the data of the ln θ − ε curve are derived www.mrs.org/jmr 1.26 × 10−5 + 0.041ε − 1.462ε2 + 598.326ε3 + 4735.481ε4 − 1407.352ε5 . 6.59 × 10−6 + 5.714 × 10−4 ε − 0.047ε2 + 13.565ε3 + 74.209ε4 + 113.202ε5 − 86.098ε6 2025 σ = where εc is the critical strain, k is the material-related constant, and εp is the peak strain. By processing the data of strain–strain curve, the fitting equation under this deformation condition was obtained as Eq. (6). Journal of Materials Research of material corresponds to the curve of work hardening rate and stress (θ − σ), ln θ − ε and ∂ ln θ/∂ε − ε. 6 Article 1.0 (a) 0.8 0.8 0.6 0.6 0.4 0.4 850℃ 890℃ 930℃ 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.0 1.0 (c) 0.8 0.8 0.6 0.6 0.4 0.2 0.4 0.6 0.8 1.0 1.2 (d) 0.4 850℃ 890℃ 930℃ 0.2 0.0 0.0 850℃ 890℃ 930℃ 0.2 Xdrx Xdrx 1.0 (b) Xdrx Xdrx 1.0 0.2 0.4 0.6 0.8 1.0 1.2 850℃ 890℃ 930℃ 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Figure 5: Dynamic recrystallization volume fraction curves under different deformation conditions. (a) 0.01 s­ −1; (b) 0.1 ­s−1; (c) 1 ­s−1; and (d) 10 ­s−1. εc = 0.575εp . © The Author(s), under exclusive licence to The Materials Research Society 2025 (8) Peak strain equation The peak strain equation of dynamic recrystallization can be expressed by Eq. (9): εp = a1 ε̇m1 exp(Q1 /RT). (10) The peak strain under various deformation conditions is obtained from stress–strain curve, fitting Eq. (10). The relevant parameters of Eq. (10) are fitted to obtain m1 = 0.09117 and Q1 = 34473.579 J/mol . The calculated m1 and Q1 are substituted into Eq. (10) to calculate the value of a1. The peak strain www.mrs.org/jmr (9) where a1, n1, and m1 are material-related constants, εp is the peak strain, d0 is the initial grain size, Q1 is the activation energy, R is the molar gas constant, its value is 8.314 J/(mol K), and T is the deformation temperature. Because the initial grain size is relatively uniform, it is neglected, therefore, Eq. (9) can be simplified to Eq. (10): 2025 εp = a1 d0n1 ε̇m1 exp(Q1 /RT), Journal of Materials Research for the second time to obtain the ∂ ln θ/∂ε − ε curve, and the critical strain value under this deformation condition can be accurately obtained by curve of ∂ ln θ/∂ε − ε, which is 0.04406. Similarly, the correlation curves under other deformation conditions can also be obtained; accordingly, critical strain values under various deformation conditions can be obtained. In the past, the correlation coefficient between critical strain and peak strain was obtained based on experience, but this test inevitably had errors. Therefore, the correlation coefficient between critical strain and peak strain can be obtained more accurately by this method, and the critical strain values of TC21 titanium alloy under various deformation conditions in the dualphase region can be obtained by above method. The peak strain values under various deformation conditions can be obtained by true stress–strain curve. Fitting with obtained values and peak strain values, the critical strain equation is provided as Eq. (8): 7 1.0 (a) 1.0 (b) 0.8 0.8 Predicted data Xdrx Article 0.6 0.4 0.2 0.0 0.0 Experimental value Predictive value 0.2 0.4 0.6 0.8 1.0 1.2 0.6 0.4 0.2 0.0 0.0 Data points Fitting line 0.2 0.4 0.6 0.8 1.0 Test data Figure 6: Under the conditions of deformation temperature of 930 °C and strain rate of 0.01 s­ −1. (a) Comparison between experimental and predicted volume fraction values; (b) correlation between experimental and predicted values. (11) Dynamic recrystallization model In the process of hot compression deformation, dynamic recrystallization occurs under the condition of the dislocation distortion energy existing in material. When dislocations accumulate to a critical strain, dynamic recrystallization grains will nucleate and grow up at grain boundary in microstructure with an equiaxed shape and slowly covering the original structure, forming a new structure composed of new equiaxed grains. Dynamic recrystallization transformation has no change in crystal structure and chemical composition, which is dynamic recrystallization; volume fraction of dynamic recrystallization is related to critical strain, strain rate, and deformation temperature. The Aviami equation [33] is used to establish dynamic recrystallization volume fraction model. Xdrx = 1 − exp −βd ε − εc ε0.5 kd , ε0.5 = a2 d0n2 ε̇m2 exp(Q2 /RT), (12) (13) where Xdrx is the dynamic recrystallization volume fraction, βd , kd , a2, and n2 and m2 are the material-related constants, ε is the strain, εc is the critical strain, ε0.5 is the strain at dynamic recrystallization volume fraction of 50%, d0 is the initial grain size, Q2 is the dynamic recrystallization activation energy, and R is the molar gas constant, its value is 8.314 J/(mol K). The formula for calculating volume fraction of dynamic recrystallization is provided as Eq. (14): © The Author(s), under exclusive licence to The Materials Research Society 2025 (14) where σsat is the saturation stress (MPa), σ is the instantaneous stress during hot compression (MPa), σss is the steady-state stress (MPa). σss and σsat can be obtained through the method of work hardening rate [31], and the critical strain values [32] under different deformation conditions have been calculated based on the work hardening rate method. Substituting corresponding parameters under various deformation conditions into Eq. (14), variation of dynamic recrystallization volume fraction curve with strain during hot compression under various deformation conditions can be obtained and is shown in Fig. 5. As depicted in Fig. 5, volume fraction of dynamic recrystallization increases roughly as an S-shaped curve with increasing hot compression strain. Due to the higher deformation temperature, the greater energy will be obtained inside the material and the activation of material itself will be enhanced. The dynamic energy of the atomic motion will be increased, so that dynamic recrystallization has sufficient driving force to occur; hence, the volume fraction of dynamic recrystallization will also increase with increasing deformation temperature. Due to uniform distribution of initial grain size, its impact on this study can be ignored, therefore, in Eq. (2), n2 = 0 , so Eq. (2) can be abbreviated as Eq. (15): ln ε0.5 = ln a2 + m2 ln ε̇ + Q2 /RT. (15) According to dynamic recrystallization volume fraction curve, the strain at a volume fraction of 50% under various deformation conditions can be obtained, the corresponding parameters are fitted to obtain m2 = 0 and Q2 = 20,330.94 J/ www.mrs.org/jmr exp(34473.579/RT). σsat − σ , σsat − σss 2025 εp = 0.00147ε̇ 0.09117 Xdrx = Journal of Materials Research equation of TC21 titanium alloy in the dual-phase region is Eq. (11): 8 Article Figure 7: Dynamic recrystallization grain size cloud diagram at different deformation temperatures. (a) 850 °C, 0.1 s­ −1; (b) 890 °C, 0.1 s­ −1; and (c) 930 °C, 0.1 ­s−1. ε − εc Xdrx = 1 − exp −0.994 ε0.5 1.687 , ε0.5 = 0.03594ε̇0.13 exp(20330.94/RT). (16) (17) The predicted volume fraction values under various deformation conditions were calculated by dynamic recrystallization model and then compared with the experimental values of dynamic recrystallization volume fraction, as shown in Fig. 6, and the comparison between experimental value and predicted value of dynamic recrystallization volume fraction at a deformation temperature of 930 °C and a strain rate of 0.01 ­s−1 was given. From Fig. 6, it can be seen that experimental values fit well with predicted values, with a correlation coefficient of R2 = 0.967, fully demonstrating that the model can effectively predict the dynamic recrystallization behavior of TC21 titanium alloy. © The Author(s), under exclusive licence to The Materials Research Society 2025 ddrx = a3 d0h3 εn3 ε̇m3 exp (Q3 /RT) + C3 , (18) where a3, h3, n3, m3, and C3 are material constants, Q3 (J/mol) is the recrystallization activation energy, R is the molar gas constant, and T is the deformation temperature. The parameters d0h3 and εn3 with initial grain size are regarded as constants. Fitted the corresponding data in Eq. (18), by fitting the slope of curve, m3 = 0.1288, similarly, Q3 = −49551.406 J/mol, and a3 = 10985.516, and the dynamic recrystallization grain size model is obtained as Eq. (19): ddrx = 10985.516ε̇−0.1288 exp (−49551.406/RT). (19) Hot compression simulation Import established kinetics models into DEFORM-3D finite element software for hot compression simulation of TC21 titanium alloy; the deformation amount is 70%. The effects of deformation temperature and strain rate on the dynamic recrystallization grain size and volume fraction were analyzed, respectively. www.mrs.org/jmr Grain size is an important characteristic parameter that characterizes dynamic recrystallization behavior. This paper uses Photoshop (PS) and Image Pro Plus (IPP) to calculate the average recrystallization grain size in the metallographic image. The original grain size is 38 μm and then the parameters are fitted based on dynamic recrystallization grain size model and is shown in Eq. (18): 2025 Grain size model Journal of Materials Research mol, the values of m2 and Q2 obtained are substituted into Eq. (15), the values of a2 under each condition are calculated, and the average value of a2 is taken as 0.03594. Substitute the obtained parameters into Eq. (15) for fitting and then calculate kd and βd based on slope and intercept obtained from the fitting curve, the values of them are 1.687 and 0.994, respectively. Therefore, the dynamic recrystallization kinetics model is provided as Eqs. (16) and (17): 9 Article As depicted in Fig. 7, as strain rate is 0.1 ­s , average grain size shows increasing trend with increasing deformation temperature, which is 9.1, 10.6, and 11.9 μm, respectively. This phenomenon occurs due to the increasing deformation temperature, leading to an increase in the internal hot energy of structure, thereby facilitating the growth of recrystallized grains. Moreover, when the deformation temperature is 890 °C, the grain size distribution of the sample is most uniform. As depicted in Fig. 8, grain size shows decreasing trend with increasing strain rate; the grain sizes are 9.3, 10.6, 8.8, and 8.2 μm, respectively. This occurs because higher deformation rates result in shorter deformation time, thus, the nucleated recrystallized grains do not have sufficient time to grow. Moreover, when the strain rate is 0.1 and 1 ­s−1, the grain size of the sample is relatively uniform. The influence of deformation parameters on volume fraction As depicted in Fig. 9, at a strain rate of 0.1 ­s−1, volume fraction increases with increasing deformation temperature. With increasing temperature, atomic activity is strengthened and a greater amount of energy is supplied for dynamic recrystallization. In order to offset the dislocation accumulation caused by compression, leading to more complete dynamic recrystallization, so, the volume fraction increases. © The Author(s), under exclusive licence to The Materials Research Society 2025 Figure 10 illustrates the impact of various strain rates on volume fraction at deformation temperature of 890 °C. As the strain rate rises, the volume fraction gradually decreased, this phenomenon arises due to the gradual increment of dislocation density with increasing compression. However, higher strain rates result in shorter time for the alloy to counter dislocation accumulation through dynamic recrystallization; therefore, dynamic recrystallization will not be carried out sufficiently, and the volume fraction will decrease. Based on the above analysis, a higher volume fraction of dynamic recrystallization does not necessarily indicate the attainment of a fine-grained microstructure. Because with the deformation temperature increases, the grain size also enlarges; however, a higher volume fraction suggests that dynamic recrystallization has proceeded more thoroughly, resulting in a relatively more uniform microstructure. Combining the simulation results of grain size, increasing the strain rate leads to slighter recrystallized grains; however, combined with microstructure analysis, when the strain rate is 10 ­s−1, most of the grains are elongated and flattened, which is not conducive to the macroscopic properties of the material; therefore, a higher strain rate does not necessarily mean that fine recrystallized grains can be obtained. In summary, combining microstructure morphology, according to the experimental and simulate result, when the hot compression deformation temperature is 890 °C and the strain rate is 0.1 and 1 ­s−1, a relatively uniform and fine equiaxed structure can be obtained. 2025 −1 Journal of Materials Research The influence of deformation parameters on grain size www.mrs.org/jmr Figure 8: Dynamic recrystallization grain size nephogram under different strain rates. (a) 890 °C, 0.01 s­ −1; (b) 890 °C, 0.1 s­ −1; (c) 890 °C, 1 ­s−1; and (d) 890 °C, 10 ­s−1. 10 Article Figure 9: Dynamic recrystallization volume percentage cloud diagram at different deformation temperatures. (a) 850 °C, 0.1 s­ −1; (b) 890 °C, 0.1 s­ −1; and (c) 930 °C, 0.1 ­s−1. Through thermal compression tests, the dynamic recrystallization behavior of TC21 titanium alloy was investigated within the dual-phase region. The following conclusions were summarized: 1. 2. Based on experimental data, kinetic model was established, the correlation coefficient between experimental data and predicted values of dynamic recrystallization model reached 0.967. The results of the thermal compression simulations demonstrate a strong concordance with the established mode, and the average error in grain size is approximately 10.8%. © The Author(s), under exclusive licence to The Materials Research Society 2025 Materials and methods The experimental material is Φ300 mm TC21 titanium alloy bar produced by China Baotai Group, which is an eight-element two-phase titanium alloy independently developed by Northwest Nonferrous Metals Research Institute of China. The initial microstructure consists of equiaxed α phase and fine lamellar α phase distributed within the β transformation matrix. In this experiment, the thermal compression test of the alloy was carried out by Gleeble-3800 thermal simulator, and the size of the sample was Φ10 mm × 15 mm. The surface of both ends of the sample was clean, parallel, and smooth, without defects, such as cracks. In order to reduce the influence of friction on the thermal compression specimen and ensure uniform deformation of the specimen, graphite lubrication sheets were attached to both ends of the specimen in this experiment. The thermal compression experimental plan is www.mrs.org/jmr Conclusion When the deformation temperature is 890 °C and the strain is 0.1 and 1 ­s−1, more uniform and finer microstructure of TC21 titanium alloy can be obtained. 2025 The grain size of the metallographic structure was measured using IPP software, and the results under different deformation conditions are obtained. Comparing the simulated values of grain size with the actual measured values, the average error is obtained to be 10.8%, so, the established model has a certain level of reliability. 3. Journal of Materials Research Verification of grain size 11 Article Figure 10: Dynamic recrystallization volume percentage cloud diagram at different strain rates. (a) 890 °C, 0.01 s­ −1; (b) 890 °C, 0.1 s­ −1; (c) 890 °C, 1 ­s−1; and (d) 890 °C, 10 s­ −1. as follows: deformation temperature is 850, 890, 930 °C, strain rate is 0.01, 0.1, 1, 10 ­s−1, rate of heating is 15 °C/s, insulation time is 2 min, compression amount is 70%, and the cooling method after compression is water cooling. After test, specimen underwent corrosion using a solution consisting of HF, ­HNO3, and H ­ 2O in a volume ratio of 1:3:7. Subsequently, the microstructure was observed using an optical metallographic microscope (OLYMPUS SZ-51). Funding There is no funding source available. Data availability The data are not publicly available due to their containing information that could compromise the privacy of research participants. © The Author(s), under exclusive licence to The Materials Research Society 2025 Conflict of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Supplementary Information The online version contains supplementary material available at https://doi.org/10.1557/s43578-025-01519-5. 2025 Rui Deng contributed to writing—original draft, investigation, and the use of software; Song Xue contributed to resource, writing—review and editing, conceptualization, and supervision; Minglong Xu contributed to formal analysis and validation; Zenong Li contributed to investigation and visualization; Shaoxiang He contributed to the use of software and investigation; Ying Zhang contributed to investigation and formal analysis; Rongchao Li contributed to the use of software and validation; Qiankun Li contributed to visualization and investigation. Journal of Materials Research Author contributions www.mrs.org/jmr Declarations 12 Article Chinease) 2. D. Banerjee, J.C. Williams, Perspectives on titanium science and technology. Acta Mater. 61(3), 844–879 (2013) 3. C. Cui, B. Hu, L. 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