Constitutive equation and microstructure evolution of TiAl alloy during hot deformation

The hot deformation behavior of TiAl alloy is analyzed by combining the true stress–strain curve and microstructure analysis. The results show that the flow stress of TiAl alloy presents the characteristics of work hardening-dynamic softening, it increases with the increase of strain rate and decreases with the increase of temperature. Based on the true stress–strain curves, the flow stress of TiAl alloy under different deformation conditions is predicted by hyperbolic sinusoidal formula. In addition, the effects of deformation temperature and strain rate on the microstructure evolution of TiAl alloy are revealed. In the process of hot compression deformation, dynamic recrystallization and γ→α, β→α phase transformation occurs. During tensile deformation, TiAl alloy exhibits super-plasticity, which is mainly due to grain rotation and coordinated deformation of β phase.


Introduction
Since the 70s of last century, researchers have regarded increasing the working temperature and reducing the weight of parts as two important goals for the new high-temperature structural materials [1][2][3][4][5].Among the intermetallic compounds, TiAl alloys have great potential to be applied to aerospace structural parts due to their high-temperature strength and stiffness higher than that of Ni-based and Ti-based alloys [6][7][8][9][10].
At present, TiAl alloys have been initially applied to the aero engine GEnx.At the same time, they have attracted researchers to carry out relevant research on their microstructure evolution and mechanical properties.Zhang Yu et al studied the deformation behavior of Ti-43Al-9V-0.2Yalloy and concluded that the dynamic recrystallization (DRX) and grain boundary slip of the γ and β phases were the main deformation mechanisms [11].Chen Lin et al carried out α single-phase zone quenching-tempering heat treatment on TiAl alloy and found that the refinement effect was closely related to the substructure of the quenching microstructure, including grain size and residual β phase content [12].Zheng Guo-ming et al obtained nanostructure layer structure through a two-step heat treatment process and studied the influence of the LPSO phase on the mechanical properties of TiAl alloy during deformation [13].
However, the long-range ordered arrangement of intermetallic atoms and the coexistence of metal/covalent bonds not only bring excellent high-temperature performance, but also bring problems such as the limited number of movable slip systems.This results in low plasticity and toughness of intermetallic compounds [14][15][16].For TiAl alloys, it is necessary to conduct in-depth research on their component design, processing, and service failure to further promote the large-scale commercial application of TiAl alloys.

Materials and methods
The raw material used in this paper is forged TiAl alloy cake, and its chemical composition is Ti-43.0Al-7.5V-0.2Y(at.%).Cylindrical samples (j10 mm × 15 mm) are cut on the forging cake using the wire-cutting method.
Gleeble-3500 thermal simulation machine is used for hot compression experiments, the deformation temperatures are 1080 °C, 1120 °C, 1160 °C and 1200 °C, and the strain rates are 0.001 s −1 , 0.01 s −1 , 0.1 s −1 and 1 s −1 , respectively.Thermocouple wires are welded on the smooth cylindrical surface to test the sample temperature in real time.First, the temperature is raised to the target temperature at a rate of 5°C/s, then the temperature is kept for 5 min to homogenize the microstructure of the sample.After that, thermal compression with different deformation conditions is carried out, and blow nitrogen to cool samples immediately after the set strain is reached.The corresponding strain-strain data is read from the thermal simulation machine and processed using the Origin 8.0 software.
Cut the hot compression specimen along the center and observe the cross-sectional microstructure.The specimen to be analyzed is ground from 200 to 2000 mesh on sandpaper, followed by mechanical polishing using a SiO 2 suspension.The microstructure observation is conducted on FEI scanning electron microscopy using backscattering mode.The identification of phases in TiAl alloys is carried out using the D8 ADVANCE type x-ray diffractometer (Bruker, Germany).The scanning speed is about 3°/min, the scanning step size is 0.02°, and the scanning angle is 20°∼ 90°.XRD data is analyzed and processed using Jade 6.0 software.The tensile test is carried out on the universal testing machine to test the mechanical properties of TiAl alloy.The tensile deformation temperature is 750°C and the strain rate is 2×10 −4 s −1 .

Results and discussion
3.1.Microstructure of the as-forged TiAl alloy Figure 1 shows the microstructure of the as-forged TiAl alloy.In the backscattering mode, the γ, β, and α phases in the TiAl alloy show different colors due to the difference in atomic numbers of Ti and Al atoms.As can be seen from figure 1, the TiAl alloy is mainly composed of equiaxed γ phase (dark color) and β phase (bright color), and the α phase content is very small.The average grain size of the equiaxed γ phase is about 29 μm.At the same time, a small amount of bright white particles can be observed, they are YAl 2 compounds composed of Al and Y.The fine YAl 2 particles are distributed at the grain boundary, thus inhibiting grain growth and refining the grains.Besides, they can pin the dislocations during deformation, playing a strengthening role [17].
Figure 2 shows the XRD patterns of different parts of the forging TiAl alloy cake.It can be seen that whether at the side, 1/4, or the central region, TiAl alloy is composed of γ phase, β phase, and a small amount of α phase.Among them, the (001) diffraction peak representing the γ phase has the highest intensity, which means that the γ phase has the highest content, and this is consistent with the results of SEM.

Hot deformation behavior of TiAl alloy
Figure 3 shows the true stress-strain curves of TiAl alloy compressed at different conditions.In the early stages of deformation, the flow stress increases rapidly, showing a clear trend of work hardening.After the strain reaches a certain level, the work hardening and softening effects reach equilibrium, and the stress plateau appears, which represents the steady-state flow stage.At constant deformation temperature, the flow stress increases with the increase of strain rate, this change trend is closely related to the dislocation density and dislocation rate [18].At the same strain rate, the flow stress gradually decreases with the increase in temperature, and this temperature-softening effect is attributed to softening factors such as dislocation annihilation, dynamic recovery (DRV), and DRX [19].strain rate on the flow stress, but the Z-A model is not good at predicting the flow stress at temperatures over 0.6 T Melt and at low strain rates [21].Artificial neural network models are capable of processing complex nonlinear data through a large number of nonlinear processing units, but artificial neural network models are unable to explain the intrinsic relationship between flow stress and deformation conditions, and lack effective monitoring of flow stress prediction under unknown deformation conditions [22].Sellars and Tegart found that the flow stress σ and other factors satisfy the Arrhenius-type equation, which can be expressed in the form of hyperbolic sine [23].A modified Arrhenius relationship containing deformation activation energy Q and temperature T is proposed to describe thermally activated deformation behavior.
Under low stress conditions: Under high stress conditions: Under general stress conditions: where n, n 1 are stress exponents; A, A1, A2, α, β are material constants, where α = β/n 1 ; R is gas constant (8.3145J•mol −1 • K −1 ); Q is thermal deformation activation energy (kJ•mol −1 ); T is the absolute temperature (K).Zener and Hollomon [24] demonstrated that the relationship between strain rate e  and temperature T can be expressed by a parameter Z.The thermal deformation conditions of the material are comprehensively described as follows: Solving the hyperbolic sinusoidal formula above, the flow stress can be derived: The Arrhenius model, which combines the Zener-Holloman parameter, can effectively take into account the effect of strain on the flow stresses and accurately predict the flow stresses under different deformation conditions.At the same time, it is necessary to recognize that, as a phenomenological model, the accuracy of the Arrhenius model will be degraded when the deformation conditions vary greatly.For TiAl alloys, which have a narrow thermal processing window, the Arrhenius model can be used to describe their deformation behavior.
Draw the scatter plots of ln ln , e s - ln , e s - ln sinh ln ( ) as e - at different conditions, then perform linear fitting on them , and the average values of the obtained slopes are n1, β and n, respectively.The scatter plot of T 1 Rnln sinh ( ) / as is plotted, and the average slope obtained after linear fitting is the activation energy Q.The lnA value is the intercept of Z ln lnsinh( ) as fitting line on the y-axis.As an example, the stress data at strain of 0.4 are linearly fitted and mathematically analyzed, and the calculated results are shown in figure 4.
Table 1 shows the n, Q, lnA, and α values calculated under different strains.In order to predict the stress under different strain, it is necessary to construct the relationship between the above four parameters and strain.The result shows that a fifth-degree polynomial fit can accurately describe the relationship between these four parameters and strain [25].The expression is X=B 0 +B 1 ε+B 2 ε 2 +B 3 ε 3 +B 4 ε 4 +B 5 ε 5 .The B 0 ∼B 5 corresponding to n, Q, lnA, and α are solved respectively, as shown in table 2.
According to equation 5, the flow stress of TiAl alloy under different deformation temperatures, strain rates, and strains can be predicted.In order to evaluate the accuracy of the constitutive model, the deformation conditions of 1160 °C, 0.001 ∼ 1s −1 are selected, and the data within 0.1 ∼ 0.6 strain are calculated and compared with the experimental values, as shown in figure 5.
The predicted values are lower than the experimental values at the low-stress zone.At the high-stress zone, the difference between the predicted value and the experimental value is very small, and the average relative error is only 1.54%.Considering that the TiAl alloys usually deformed at high strain rate and high stress during actual processing, thus the model can accurately predict the flow stress of TiAl alloy.

Effect of the deformation conditions on the microstructure of TiAl alloy
To study the effect of temperature on the microstructure of TiAl alloy, the samples compressed at different temperatures are observed.The results are shown in figure 6.The original γ phase and β phase in TiAl alloy are broken when deformed at 1080 °C (figure 6(a)).In addition, a small amount of gray α phase can be observed.
Previous results show that the main phases in TiAl alloy are α+ B2 + γ phases between 1000 °C and 1109 °C, and the main phases are α (α 2 ) + β + γ phases between 1109 °C and 1226 °C [26].When deformed at 1080 °C, it is in the α + B2 + γ three-phase region, this explains the existence of the α phase.When deformed at 1120 °C, the microstructure is mainly composed of equiaxed γ, β, and a small amount of α phase (figure 6(b)).The equiaxed α phase is wrapped outside the γ phase, and the content of the γ phase decreases.This is because the γ → α phase transition occurs as the temperature increases.At the same time, the grain size is lower than the original microstructure due to the DRX.As the temperature further increases to 1160 °C, the microstructure is composed of 'fishbone' -like β phase and gray phase (figure 6(c)).The gray phase is γ/α lamellar colony.Due to the nanoscale spacing between the lamellae, it shows a single gray phase under the scanning electron microscope.The 'fishbone' -like β phase is distributed along the boundary of the lamellar colony, and the content of the β phase is significantly lower than that of the original microstructure.This indicates that there are two sources of α phase, namely γ→α and β→α phase transition.During high-temperature deformation, the DRX of the α phase occurs.During the subsequent cooling process, γ laths precipitate from α grains to form nano-scale γ/α lamellar colonies.Thus, the appearance of the nano-γ/α lamellar colony is product of the DRX α phase.At 1200 °C, the size of γ/α lamellar colony increases compared with 1160 °C (figure 6(d)).In addition, a small amount of γ laths can be observed inside the β phase, which indicates that the β→γ phase transition occurs.Studies have shown that heat treatment and quenching can induce β→γ phase transition process, and there is a certain orientation  relationship between the newly generated γ lath and the original β phase [27].In a word, with the increase of deformation temperature, the degree of DRX is strengthened, and the microstructure of TiAl alloy changes obviously due to the occurrence of phase transformation.
Figure 7 shows the microstructures of TiAl alloys deformed at 1120 °C with different strain rates.It can be seen that the microstructures of TiAl alloys are sensitive to strain rate.When deformed at 1 s −1 , the TiAl alloy is mainly composed of γ phase, β phase, and a small amount of α phase.The γ phase slightly presents a curved shape (figure 7(a)).As the deformation completes in a few seconds, no obvious DRX phenomenon is observed.At the same time, local stress concentration occurs in some areas due to the high strain rate, resulting in the initiation of cracks.When the strain rate is 0.1 s −1 (figure 7(b)), the β phase is significantly flattened and extended, and the extension direction is perpendicular to the compression direction.The broken decomposition of the β phase appears.In previous studies, the fragmentation and decomposition of the β phase is one of the prerequisites for the beginning of DRX [28].
When the strain rate reaches 0.01 s −1 , the β phase presents a block distribution, and the grain size of the γ phase and the β phase is obviously refined compared with the initial microstructure (figure 7(c)).With further reducing the strain rate, the deformation time of TiAl alloy is prolonged, which fully guarantees the DRX.When the strain rate is 0.001 s -1 , the microstructure of TiAl alloy is mainly composed of equiaxed γ phase and lamellar colony (figure 7(d)), and the grain size is larger than that of 0.01 s -1 , indicating that the recrystallization is fully completed and the secondary growth of grains occurs.
It is found that with the decrease of strain rate, the average grain size of TiAl alloy at strain rates of 1 s −1 , 0.1 s −1 , 0.01 s −1 , and 0.001 s −1 strain rates is 28 μm,15 μm, 17 μm, and 21 μm, respectively.With the decrease in strain rate, the average grain size of TiAl alloy decreases first and then increases.This is closely related to the DRX of γ phase and β phase.
During the deformation process, DRX occurs, which makes the material soften and shows a decrease in flow stress.Because the stacking fault energy of the β phase is higher than that of the γ phase, DRX of the γ phase is prior to that of the β phase [29].For the β phase, DRV and DRX mainly occur during deformation.The discontinuous DRX of the γ phase occurs during deformation, which is different from the continuous DRX of the α phase [30].When the deformation temperature is low and the strain rate is high, the DRX of TiAl alloy is not obvious, which is mainly manifested by the twisting and bending of each phase.With the increase of deformation temperature and the decrease of strain rate, the equiaxed phase of TiAl alloy tends to be broken and decomposed, and the degree of DRX gradually increases.Especially when the temperature is high, the grain size further increases with the γ → α and β → α phase transition.

Mechanical property of TiAl alloy
Figure 8 shows the stress-strain curve of TiAl alloy during tensile deformation at 750°C and a strain rate of 2× 10 −4 s −1 .The stress increases rapidly in a very short time and then begins to decrease slowly.During the tensile deformation process, the yield strength reaches 450 MPa and the plastic elongation reaches 49.4%, showing a certain degree of superplastic deformation.
Figure 9(a) is the morphology of the tensile fracture of TiAl alloy.The morphology shows an intergranular fracture mode as a whole, but a large number of micro-dimples can be seen at the same time, which explains the good plasticity of TiAl alloy during tensile deformation.surface of TiAl alloy.There are small steps on the surface of equiaxed grains.During the tensile deformation, new planes are continuously formed on the steps, which consumes energy and delays the initiation of cracking.At the same time, fine oxide particles are observed on the surface, but their size is small, which has a limited effect on the plasticity of TiAl alloy.Figure 9(c) is the cross-sectional microstructure of the tensile fracture of TiAl alloy.The cracks mainly propagate along the γ/β phase interface, and a large number of holes appear near the fracture.This is consistent with the result in figure 9(a).Figure 9(d) shows the microstructure at a distance of 3mm from the fracture of TiAl alloy.A large number of micro holes appear in the microstructure, and the holes are mainly concentrated in the γ phase or the γ/β phase interface.In addition, the extension direction of the γ phase and the β phase is consistent with the tensile direction, which indicates that the rotation of the grains occurs during the tensile deformation process to alleviate the stress concentration.With the further increase of deformation, micro-voids appeared at the β/γ interface.Subsequently, the holes further expand and merge into microcracks, until the fracture of the material is caused.
In TiAl alloys, the γ phase has a tetragonal L1 0 structure, and its dislocation slip preferentially occurs on the {111} plane.The main movable dislocations are b = 1/2 < 110], b = 1/2 < 11-2] and b = < 011] [31].The α phase is an ordered hexagonal D0 19 structure.The deformation of α phase mainly depends on two types of super dislocations, namely <a> type dislocation (b = 1/3<11-20>) and <2c+a> type dislocation (b = 1/3<-1-126>) [32], and the deformation ability is poor.The β phase has a body-centered cubic structure.Dislocations can move on the {110} close-packed plane, as well as on the {112} and {123} close-packed planes, and the movable slip system is sufficient.Among the three phases of TiAl alloy, the β phase has the strongest deformation ability and can coordinate the main plastic deformation [33].When deformed at 750 °C, the microstructure consists of γ and β phases.Therefore, the main deformation mechanism in the tensile deformation process is the rotation of the grains and the coordinated deformation of the β phase, thereby improving the plasticity of the material.

Conclusions
1.The forged TiAl alloy is mainly composed of γ phase, β phase, and a small amount of α phase.During the hot compression process, the flow stress shows the characteristics of work hardening-dynamic softening, and the flow stress is negatively correlated with the deformation temperature and positively correlated with the strain rate.
2. The true stress-strain curve is mathematically processed to obtain the hot working deformation parameters (n, Q, lnA, and α) of TiAl alloy, and the flow stresses under different strains are predicted by the hyperbolic sinusoidal formula.At the high-stress zone, the difference between the predicted stress and the experimental value is only 1.54%, indicating that the constitutive equation can well describe the hot deformation behavior of TiAl alloy.
3. The effects of deformation temperature and strain rate on the microstructure evolution of TiAl alloy are analyzed.With the increase of deformation temperature, recrystallization and γ → α, β→ α phase transformation occurs.With the decrease of strain rate, the degree of DRX of TiAl alloy increases, and the overall grain size decreases first and then increases.

4.
During the tensile deformation process, the grain rotation and the coordinated deformation of the β phase together improve the plasticity of TiAl alloy, so that an elongation of about 49.4% can be obtained at 750 °C.

3. 3 .
Deformation constitutive equationAt present, empirical formulas are generally used to calculate and describe the correlation between strain rate, deformation temperature, and flow stress when materials are deformed at high temperatures.The commonly used deformation constitutive equations include the J-C (Johnson-Cook) model, the Z-A(Zerilli-Armstrong) model, the artificial neural network model, and the Arrhenius model.The J-C model treats thermal softening, strain rate hardening, and strain hardening as three separate phenomena.Since the model does not take into account the coupled effects of temperature, strain rate, and strain on the flow stress, the predicted flow stresses are sometimes not able to track the experimental data[20].The Z-A model has different expressions depending on the crystal structure of the material, and the Z-A model can analyze the effect of coupling temperature and

Figure 2 .
Figure 2. XRD patterns of forging TiAl alloy cake at different parts.

Figure 5 .
Figure 5.The predicted and experimental stresses.

Figure 9 (
b) is a local amplification image of the fracture

Figure 9 .
Figure 9. Microstructure of Tensile fracture of TiAl alloy (a) fracture morphology, (b) enlarged view of (a), (c) cross-section morphology at fracture, (d) Microstructure of deformation zone.(The red arrows in c and d represent the direction of tensile deformation).

Table 1 .
The values of n, Q, lnA, and α at different strains.

Table 2 .
The values of B 0 ∼B 5 coefficient for n, Q, lnA, and α.