Hot processing map and high temperature deformation behaviour of TB17 Ti alloy

The thermal compression experiments of TB17 titanium alloy under different thermal deformation process parameters were carried out using a thermal simulation compressor. The high-temperature plastic flow behaviour of the alloy was studied. It was found that with the decrease of the deforming temperature and the increase of the strain rate, the flow stress increased, and the discontinuous yield phenomenon occurred in hot deformation. The larger the strain rate, the more obvious the discontinuous yield phenomenon. The thermal activation energy Q decreased with the increase of strain, and the average value of activation energy Q is 209.54 KJ / mol. The constitutive equation of high-temperature plastic flow of TB17 titanium alloy was established. The predicted values of this equation are in good agreement with the experimental values. The average error is 3.987 %, and the correlation coefficient is 0.9972, which has high accuracy. Based on the Prasad criterion, the hot processing map of TB17 titanium alloy was constructed. It was found that the flow instability zone was mainly concentrated in the high strain rate region. The flow instability zone was determined to be 795 °C ~ 895 °C, 0.046s-1 ~ 1s-1, and the stable deformation zone was mainly located in the region with high temperature and low strain rate. The optimum processing parameter range is 860 °C ~ 895 °C, 0.001 s-1 ~ 0.025 s-1.


Introduction
Since the first application of titanium alloy in the aerospace field during the 1950s, wide attention on Ti alloys has been gained, and rapid development occurred as the Ti alloys have unique properties [1,2].To meet aircraft safety requirements, long life, and high reliability, the aerospace industry also demands titanium alloys' performance.Developing Ti alloys with high strength, toughness, and improved properties has become an important research object of Ti alloys [3].Metastable β high-strength titanium alloy has gained prominence in the aerospace industry in recent years because of its exceptional qualities, including good heat treatment, hardenability, and welding performance [4].
The primary application of metastable titanium alloy in airplanes is to substitute high-strength structural steel components, resulting in a weight reduction of 30% to 40% [5].The AECC Beijing Institute of Aeronautical Materials has produced a novel metastable β-type alloy called TB17 titanium

Experimental
The experimental material was TB17 titanium alloy.The TB17 after solution treatment (890 °C heat preservation 30 min water cooling) was used as the raw material for the experiment.The phase transition temperature of TB17 titanium alloy was about 845 °C measured by metallographic method.The structure of the raw material is shown in the figure 1.The structure was equiaxed β grains, the grain boundary is relatively flat, some grain boundaries were not clear, and there were some smaller grains.

Figure 1. Primitive microstructure of TB17 titanium alloy
The raw materials were processed into Φ8×12mm cylindrical specimens as thermal simulation compression specimens, and the constant temperature and constant strain rate thermal deformation test was conducted by the thermal simulation testing machine Gleeble-3500.The experimental conditions are as follows: deformation temperature is 795 ℃, 820 °C, and 895 °C; the strain rates were 0.001s-1,0.01s-1,0.1s-1and 1.0s-1; the deformation amount during the test is 30 %, 50 %, 60 %, and 70 % (true strain is 0.36,0.69,0.92,and 1.2).To ensure that the internal temperature of the sample before deformation is uniform, the holding time was 3 minutes at this temperature, and the speed of raising the temperature was 10 ℃/s.The selection of deformation temperature was mainly considered: when the hot deformation temperature was low, the deformation resistance of the alloy was high, which is not conducive to the forming process.In the condition of the high deformation temperature the β grains were easy to grow, which influences the mechanical properties of the alloy.

Analysis of stress-strain curve
Figure 2 is the stress-strain curve of TB17 alloy under different hot deformation parameters.In the early stage of thermal deformation, the flow stress increased sharply with the increase of strain.At this time, the stress-strain curve was close to a straight line, the slope was large, and the stress reached a peak quickly.This is attributed to that work hardening occupied a major position.When the stress reached the peak stress, as the deformation continued, the strain gradually increased and the stress tended to be stable, which is a combination of work hardening and flow softening.
During the hot deformation process of TB17 alloy, discontinuous yielding occurred under almost all deformation conditions, that is, the stress suddenly decreased after reaching the highest point.Discontinuous yielding has occurred in many Ti alloys, such as TB9 [14], TC8 [15], Ti-5553 [16], Ti-7333 [17], Ti-42Al-9V-0.3Y[18].For this phenomenon, many scholars have put forward the mechanism theory through many experimental analyses, mainly including the pinning principle of the Cottrell atmosphere, the high temperature softening theory caused by dynamic recrystallization, and the dislocation proliferation theory.According to the pinning principle of the Cottrell atmosphere [19], before plastic deformation, many dislocations are pinned by the Cottrell atmosphere in metal materials, and a higher critical stress is required to make dislocations break away from pinning.When the applied stress reaches this critical stress, many dislocations begin to move, and the stress required for plastic deformation decreases, resulting in discontinuous yield.However, it is difficult to explain the influence of strain rate and deformation temperature on the discontinuous yield phenomenon [20].Ankem et al. [21] proved that the static theory of the pinning principle of the Cottrell atmosphere is not feasible through clever experiments.According to the high-temperature softening theory [22,23], in the process of plastic deformation, the discontinuous yield phenomenon appeared due to the occurrence of dynamic recrystallization, which reduces a large number of dislocation densities and makes the flow stress decrease sharply.However, this theory cannot explain the discontinuous yield phenomenon at a low strain rate and small strain ratio during high-temperature deformation [18].According to the dislocation multiplication theory [24,25], the dislocation density in metal materials is very low before the beginning of plastic deformation.After the beginning of plastic deformation, the dislocations increase and move in large quantities, which are accumulated because of grain boundary obstruction, and the flow stress rises.When the dislocation density increases to a certain extent, dynamic recovery suddenly occurs.The dislocations on the β grain boundary make the opposite sign dislocation annihilate through dislocation motion, and the dislocation density decreases, which leads to the decrease of flow stress and discontinuous yield phenomenon.
It can be found from Figure 2 that the greater the strain rate, the more obvious the yield phenomenon of TB17 Ti alloy during thermal deformation at the same temperature.When the strain rate is large and the deformation time is short, a large number of dislocations will be produced in the alloy.The effect of temperature on the discontinuous yield of TB17 alloy during high-temperature deformation is not obvious.Compared with the smooth flow stress curves at strain rates of 0.001s -1 ,0.01s -1 and 0.1s -1 , the flow stress curve at a strain rate of 1s -1 showed irregular wavy fluctuation.This phenomenon has been found in many other titanium alloys such as Ti6554 alloy [26] and TC11 alloy [27].The reason is that during the plastic deformation process, a large number of dislocations proliferate and move, and eventually pile up at the grain boundary.The higher the strain rate, the shorter the deformation time, the dynamic recovery and dynamic recrystallization cannot be fully carried out, and the fewer dislocations are consumed, increasing dislocation density.The movement of dislocations is hindered, which in turn leads to an increase in flow stress.Under certain favorable conditions, the grains rotate, the grain orientation changes and the grains continue to undergo deformation in a favorable direction, causing the flow stress to decrease.When the dislocation movement is hindered again in this favorable direction, the flow stress rises, and the grains continue to rotate under favorable conditions, continuing to repeat the process, causing the flow stress to fluctuate up and down [28].At the strain rate of 1s -1 , the wave fluctuation phenomenon of the flow stress curve at the deformation temperature of 895 °C is more obvious than that at 795 °C and 820 °C.  Figure 3 is the influence of strain rate on peak stress of TB17 alloy.As can be seen from Figure 3, the higher the deformation temperature, the lower the peak stress when the strain speed is constant.First, this is closely related to the activation energy.The higher the temperature, the greater the activation energy of the alloy, and the easier the dislocation moves, the lower the peak stress.Secondly, the higher the temperature, the stronger the atomic diffusion ability, and the stronger the softening effect of dynamic recovery and dynamic recrystallization, resulting in a decrease in peak stress.Finally, the higher the temperature, the more β phase.The α phase is a hexagonal close-packed, and the β phase is a body-center cubic structure.The slip system of the body-centered cubic structure is more than that of the close-packed hexagonal structure, and the macroscopic deformation resistance is low, so the peak stress is low.

Establishment of strain compensation constitutive model
High temperature deformation of metals is a process of thermal activation.Sellars et al [29].An Arrhenius constitutive model equation including T and Q was proposed: Where ε̇ is the strain rate (s -1 ); Q is the deformation activation energy (J/mol), which is related to the material; σ is the flow stress (MPa); n is the stress index; T is the absolute temperature (k); R is the gas constant (8.314J/mol•k); g(σ) represents the function of stress σ (MPa); A is a constant related to the material.Arrhenius equation has different forms at different stress levels.At low-stress levels, ασ<0.8, as shown in Equation ( 2); At high-stress levels, ασ>1.2, as shown in Equation (3); Equation ( 4) applies to all stress levels and can well describe the strain characteristics under different deformation parameters [30].
A, α and β are material constants independent of deformation temperature, where α = β/n1, and n is the work hardening exponent.
Zener et al. [31] proposed a Z-parameter model to quantitatively describe the influence of deformation temperature and strain rate on flow stress by studying the flow stress of steel during tension, as shown in Equation (5).Different materials have different constitutive relations representing their dynamic characteristics, and the introduction of Z parameters can optimize the Arrhenius equation.
According to the Arrhenius equation, the flow stress under different deformation conditions can be obtained by determining the values of parameters α, n, Q, and A.
Taking the strain value 0.6 as the reference, the parameters are solved, and the logarithms are taken on both sides of the Equation ( 2 ) It can be seen from Equation.(6) and Equation.( 7) that n1 and β are obtained by the average of the slopes of the lnε-lnσ' and lnε-σ curves, respectively.
By this method, n1 = 0.0474, β = 4.0556, α = 0.0118.By taking the logarithm on two sides of Equation.( 8) and taking the derivation, we can get: Among them: Substitute Equation (10) into Equation ( 9) can be obtained:  =  (11) Bringing the corresponding data into Equation (10), the value of m can be obtained by calculation, and the Q = 205.48KJ/molcan be obtained.
According to the above test data, the constitutive model of TB17 titanium alloy at a strain of 0.6 can be obtained by substituting it into Equation (4): = 7.6 × 10 7 [ℎ0.0118] 2.9727 (13) Because the Arrhenius equation of TB17 alloy only considers the influence of ε、σ、T on the flow stress but does not consider the influence of strain on it.The related constants and activation energy of the material have a strong correlation with the strain, so the stress compensation is carried out based on the constitutive model.A more accurate constitutive model can be obtained.In this paper, the strain range is set in the range of 0.05-1.2, the material parameter values are calculated every 0.05, and the polynomial fitting is carried out by MATLAB software.It is found that the accuracy of 5-degree polynomial fitting is better.At this time, the model form is: 5  (16) In Equation (15), Y (ε) is the functional relationship between α, n, Q, lnA and strain (ε).k0-k5 are polynomial coefficients.
The fitted curves by calculating the constants are shown in figure 4, and the values of k0-k5 are shown in Table 1.  Figure 5 is a comparison of the experimental results and the predictive value of the flow stress model.It is clear that the flow stress curve determined by the above method can achieve very good fitting accuracy.Figure 6 shows the error comparison between the calculated value and the experimental result of the flow stress of TB17 alloy.The points falling in the two straight lines are data points with an error of less than 10 % between the calculated value and the experimental value.The data points are within 10 % of the deviation line, and the average error is 3.987 %.The related coefficient R between the two is 0.9972 and approaches 1.Therefore, the constitutive model can accurately reflect the plastic flow behavior of TB17 alloy during high-temperature deformation.

Hot processing map analysis of TB17 titanium alloy
The primary purpose of a hot processing map is to study the behaviour of heat deformation in materials and offer guidance for the design of hot processing technologies.The machining drawing based on the dynamic materials mode is the most widely used.In the dynamic material model, the energy (P) input to the system during deformation is mainly composed of two parts: (G) and (J) [32]: In the formula, the dissipation G is the energy consumed during the plastic deformation of the alloy, and the dissipation covariate J is the energy required for the microstructure evolution during the plastic deformation of the alloy.The magnitude of these two parts of energy is determined by the strain rate sensitivity coefficient m during alloy deformation, which can be calculated from stress and strain: σ=K ε̇m (19) In the formula, where K is the rheological stress at a strain of 1 s -1 .When m=1, the alloy is in the ideal linear dissipative state.
To quantitatively analyze dissipated energy, power dissipation efficiency was introduced η, which is called the power dissipation factor.It is a dimensionless parameter that reflects the change mechanism of the microstructure and is determined by the ratio of the dissipation covariate (J) and the material in the ideal linear dissipation state (J max), that is: Combined with the deformation temperature (T), strain rate (ε̇ ), and power dissipation efficiency η, the power dissipation diagram of the alloy during hot deformation can be obtained.The higher the value of the power dissipation efficiency η, the more energy is consumed by the organizational evolution of the alloy during thermal deformation, and the more stable the thermal deformation of the alloy.Therefore, during the hot deformation process of titanium alloy, when the power dissipation efficiency η is greater than 35 %, it is considered to be a stable deformation zone.However, titanium alloys also have several other deformation mechanisms during the hot working process, such as DRV, DRX, lamellar structure spheroidization, and so on.Different deformation mechanisms have different rate dissipation efficiency η, so smaller power dissipation efficiency η cannot simply deemed unstable zones.Therefore, many researchers have proposed different instability criteria, but Prasad's [33] instability criterion is the most widely used.According to the principle of maximum entropy generation rate, Prasad [33] proposed a rheological instability criterion for the unstable flow of materials: In the formula, ξ is the stability function.It is a function of deformation temperature and strain rate.When the parameter ξ is less than 0, the deformation of the alloy will be unstable.Superposition the power dissipation diagram and flow instability diagram to get the thermal processing diagram.Figure 7 shows the processing map of TB17 alloy at various strains (ε = 0.1,0.3,0.5,0.7,0.9,1.2).As shown in the figure 7, the strain has a remarkable impact on the hot processing map of the alloy.
From figure 7, it is observed that the unstable region of the alloy is mainly in the high strain rate region, and the contour lines of the power dissipation factor in the unstable region are also dense.As shown in figure 7 (a), when the strain is 0.1, the unstable region of TB17 alloy is above the processing map at the temperature of 795 °C ~ 890 °C and the strain rate of 0.03s -1 ~ 1s -1 .As the deformation temperature rises, the strain rate range corresponding to the instability zone increases first and then decreases.When the strain is 0.3, the instability zone becomes wider and shorter, and others are similar to those when the strain is 0.1, as shown in figure 7(b), which shows that the instability phenomenon is easy to occur at a high strain rate.When the strain is 0.5, the corresponding strain rate range of the unstable region does not change obviously with temperature, and when the strain is 0.3, the unstable region does not change much, and it is still above the processing diagram, as shown in figure 7(c).When the strain is greater than 0.5, the area of the instability zone gradually decreases.When the strain is 0.7 and 0.9, the strain rate range of the instability zone decreases with the increase in temperature, which is different from the change rule of strain 0.1 ~ 0.5.When the strain reaches 1.2, the range of instability zone is 795 °C ~ 875 °C, 0.18s -1 ~ 1s -1 .It can be seen from figure 7 that when the strain increases, the power dissipation factor of the instability zone also decreases gradually, and its maximum value decreases from 42 % under the strain of 0.1 to 38 % under the strain of 1.2.When the strain increases from 0.3 to 0.9, the instability zone shrinks to the high strain rate region at high temperature and expands to the low strain rate region at low temperature, and the area of the instability zone gradually decreases.
In the actual machining deformation, to ensure that the alloy is located in the safe machining area during the whole machining process, the instability regions of the six strains in figure 7 will be superimposed to obtain the instability map that represents the whole deformation process as much as possible.Figure 8  .Superposition of instability zones of TB17 alloy under six strains Figure 9 is the phase diagram of TB17 alloy hot pressed at different deformation temperatures at a strain rate of 1s -1 and a strain of 1.2.At a high strain rate (1s -1 ), local plastic flow occurred in the center.After deformation at a high strain rate (1s -1 ) and 750 ° C ~ 950 ° C, the microstructure of TB9 alloy also showed the same flow instability [34].The plastic deformation of β grains in different regions was different, the ratio of length to diameter was quite different, and the plastic deformation distribution was uneven.In the unstable region at a high strain rate, the local plastic flow occurred in the plastic deformation process of TB17 alloy.In this unstable region, the power dissipation factor was small, that is, the dissipation power used for plastic deformation accounts for a large proportion, resulting in a large amount of heat generated.At a higher strain rate, the alloy had a large temperature rise in the local area due to the lack of heat dissipation, resulting in local softening and flow stress reduction in the local area due to temperature rise, and concentrated deformation in the local area, thus forming local plastic flow.(a)795℃, 1s -1 (b)820℃, 1s -1 (c)895℃, 1s -1 From figure 9(a-b), it can be concluded that when the deforming temperature is 795℃ and 820℃, the local plastic flow phenomenon is more serious, the grain boundary is unclear, the degree of grain unevenness is high, and the grain aspect ratio is higher, which corresponds to the darker gray degree of the rheological instability zones (a) and (b); As shown in figure 9 (c) When the rolling temperature was 895 °C, the localized plasticity flow phenomenon was less serious, which corresponds to the gray of the flow instability zone (c) to some extent.
Comparing figure 9 (a) -(c), it is difficult to observe dynamic recrystallization below the phase transition temperature, but a small amount of recrystallized grains with smaller grains were found near the grain boundary at 895 °C above the phase transition point.The reason for this is that the dynamic recrystallization rate slows down at low temperatures, and the strain rate increases at high temperatures, so the recrystallization grains of the core do not have time to grow fully during plastic deformation.At the same strain rate, with temperature increasing, the degree of local plastic flow and the inhomogeneity of plastic deformation are alleviated.The softening mechanism dominated by dynamic recovery below the phase transition temperature makes it difficult to change the local plastic flow phenomenon.The dynamic recrystallization that fails to occur fully above the phase transition temperature also difficult to eliminate the local plastic flow phenomenon, which can only slow down the flow instability to a certain extent.
Generally speaking, the local plastic flow phenomenon in the metal material during the hot deformation process will reduce the performance of the material and have a negative impact on the subsequent processing process.Therefore, when determining the deformation processing parameters of TB17, the processing parameters in the instability region should be avoided as far as possible to avoid the flow instability phenomenon in the alloy structure.

Conclusions
(1) The flow stress significantly increases with the strain rate increment and the decrease of deformation temperature.Compared with the deformation temperature, the influence of flow stress on strain rate is more obvious.Discontinuous yielding occurs in the alloy during high-temperature deformation.
The larger the strain rate, the more obvious the discontinuous yield phenomenon. (2) The important material parameters under different strains have been determined.The strain will affect the material constants.The hot deformation activation energy Q progressively decreases with the increase of strain, and its average value is 209.54KJ / mol.Based on the Arrhenius equation, a constitutive model of strain-compensated TB17 titanium alloy hot deformation is established, and the predicted value of the constitutive equation is in good agreement with the experiment data.The correlation coefficient is 0.9972, and the mean relative deviation is 3.987 %, which can accurately predict the change rule of flow stress.
(3) The rheological instability zones determined by the hot working diagram are 795℃~895℃ and 0.046s -1 ~1s -1 , and the power dissipation factor in these rheological instability zones is mostly below 40%.The region of rheological instability is mainly concentrated in the region of high strain rate.When selecting processing parameters, processing at a high strain rate (1s -1 ) should be avoided.

Figure 2 .
Peak stress change trend diagram of TB17 alloy at various deformation temperatures.

Figure 3 .
Figure 3. Influence of strain rate on peak stress of TB17 alloy