Constitutive Models for Tensile Deformation Behavior of Ti-22Al-25Nb Alloy Sheet at Elevated Temperatures

Abstract

Isothermal uniaxial tension tests for O phase-based Ti-22Al-25Nb alloys were conducted at 1203–1283 K with temperature interval of 20 K. The strain rates were 2.5×10^-4, 5.0×10^-4, 1×10^-3, 2×10^-3, 4×10^-3, 1×10^-2, and 5×10^-2 s^-1. The microstructures of specimens at different deformation temperatures were characterized. Through the experiment results, the material constants for the constitutive models are determined and the tensile deformation activation energies are 845 165 and 412 779 J/mol at α₂+B2/β+O three-phase region (1203–1243 K) and α₂+B2 two-phase region (1243–1283 K), respectively. Arrhenius-type constitutive models are constructed to characterize the tensile deformation behavior of Ti-22Al-25Nb alloy at different temperatures.

Keywords

Ti₂AlNb; constitutive model; microstructure; deformation behavior

Conventional Ti₃Al-based titanium alloys have excellent mechanical properties at room temperatures. With the Nb addition, their tension strength and ductility at room temperature can be further enhanced. Banerjee^[1] and Nandy^[2] et al found the new ordered orthorhombic phase, namely O phase (Ti₂AlNb). Song et al^[3] improved the plasticity of Ti₂AlNb alloys by high density electropulsing and investigated the enhancement mechanism. Yang et al^[4] investigated the creep deformation mechanism and environmental effects of Ti₂AlNb alloys and proposed different creep deformation mechanisms. Boehlert^[5–6] and Cowen^[7] et al discussed the fabrication process (forging, rolling) and mechanical behavior (creep behavior, tensile behavior) of Ti₂AlNb alloys. Zhang et al^[8] studied the tensile behavior and deformation mechanism of Ti-22Al-25Nb alloy with lamellar O phases. Sim et al^[9] investigated the influence of mechanical alloying on the mechanical properties and microstructure of Ti₂AlNb alloys prepared by powder metallurgy and mechanical alloying (MA) coupled with spark plasma sintering (SPS).

Typical Ti₂AlNb alloys with the composition of Ti-22Al-25Nb (at%) exhibit the advantages of low density, fine creep resistance, and high specific strength and toughness at ele-vated temperatures^[10–13], therefore attracting much attention as a lightweight structural material in aerospace and automotive industries^[14–16]. However, the deformation behavior of Ti-22Al-25Nb titanium alloys at elevated temperatures has rarely been investigated. Generally, the constitutive equation is critical for the formability evaluation of alloys^[17–22]. Richardson et al^[23] proposed a model for the prediction of strain-stress relation-ship at elevated temperatures^[18,24]. In addition, the microstruc-tural evolution and phase transformation of Ti₂AlNb alloys at different temperatures are different, which affects the mechanical properties. Therefore, it is necessary to study the microstructural evolution of the alloy during deformation.

In this research, the deformation behavior of Ti₂AlNb alloys was studied through tension tests at different strain rates and temperatures. Moreover, the constitutive models of Ti-22Al-25Nb alloys at elevated temperatures and different strain rates were established. Finally, the effect of temperature on deformation activation energy was discussed based on the microstructure evolution.

1 Experiment

The as-received material used in this research was a hot-rolled Ti-22Al-25Nb alloy sheet with thickness of 1.25 mm, which contained 10.90wt% Al, 42.0wt% Nb, 0.07wt% O, 0.008wt% C, 0.006wt% N, and balance Ti. The raw sheets were heat-treated under different conditions: (1) at 1203, 1223, and 1243 K for 4 h; (2) at 1263 K for 2 h; (3) at 1283 K for 0.5 h. The final pass of hot-rolling for all heat-treated alloy sheets was conducted at 1213 K. The sheets were cooled down to room temperature by water spraying after the heat treatments. The uniaxial tensile specimens with gauge length of 10 mm and width of 3 mm were machined from the quenched sheet along the rolling direction by the low-speed electrical discharge machine.

The isothermal uniaxial tension tests were conducted by Instron 5500R electronic universal testing machine at 1203–1283 K with temperature interval of 20 K to investigate the influences of temperature and strain rate on the deformation behavior of Ti-22Al-25Ni alloys. The initial strain rates were 2.5×10^-4, 5.0×10^-4, 1×10^-3, 2×10^-3, 4×10^-3, 1×10^-2, and 5×10^-2 s^-1. Thermal couples were installed in the heating furnace to measure the specimen temperature. Before isothermal uniaxial tension tests, the specimens were heated to the designed temperature and held for 300 s to eliminate the thermal gradient. Then, the specimens were stretched until fracture. True stress-true strain curves were recorded automatically by the Instron Bluehill software during the isothermal uniaxial tension tests.

To observe the microstructure of specimens at different deformation temperatures, the specimens were rapidly quenched in water after deformation. The deformed specimens were sectioned parallel to the tension axis. A Quanta 200 FEG scanning electron microscope (SEM) was used to observe the microstructure of the as-received and deformed specimens for investigation of the deformation mechanism and the influence of microstructure on the deformation activation energy.

2 Results and Discussion

2.1 Initial microstructure

Fig.1 shows SEM microstructure of the as-received Ti-22Al-25Nb alloy. It is found that the dark, gray, and bright regions represent the α₂, O, and B2/β phases, respectively. The matrix microstructure consists of fine B2/β and lamellar O grains, and the equiaxed α₂ grains wrapped by rim-O grains are uniformly distributed in the matrix.

Fig.1  SEM microstructure of as-received Ti-22Al-25Nb alloy

2.2 Flow behavior

Fig.2 shows the true stress-true strain curves of Ti-22Al-25Nb alloys during isothermal uniaxial tension tests. The four-section analytical method is used to discuss the deformation behavior^[25]. In the first section, the true stress rises rapidly until the true strain reaches 0.05. This process is independent of strain rate and deformation temperature. The fast increase in stress can be attributed to the dramatically multiplied dislocations as well as the formation and multiplication of subgrain boundaries^[26]. Moreover, with decreasing the temperature and increasing the strain rate, the peak stress becomes less distinct and the flow stress is increased significantly. In the second section, the softening phenomenon of the specimen occurs, where the true stress drops due to the initiation of homogeneous plastic deformation. The true stress drops slightly and the softening occurs more obviously at higher temperatures and lower strain rates due to the dynamic balance between the work hardening and dynamic softening^[27]. Then, in the third section, the true stress drops sharply because of the localized necking. In the last section, the specimens fracture.

Fig.2  True stress-strain curves of Ti-22Al-25Nb alloys during isothermal uniaxial tension tests under different conditions: (a) at strain rate of 1×10^-3 s^-1 with different temperatures; (b) at 1243 K with different strain rates

2.3 Constitutive equation

Constitutive equations are designed to depict the deformation behavior of alloy specimens at different temperatures. Parameter Z is used to express the relationship between the strain rate $\dot{\epsilon }$ and temperature T^[23,28], as follows:

$$Z=\dot{\epsilon }\mathrm{e}\mathrm{x}\mathrm{p}(Q/RT)$$

(1)

where Z is the Zener-Hollomon parameter, $\dot{\epsilon }$ is the strain rate (s^-1), Q is the hot deformation activation energy (J·mol^-1), R is the mole gas constant (8.3145 J·mol^-1·K^-1), and T is the absolute forming temperature (K).

The Arrhenius equation can accurately depict the relationship between the parameter Z and peak stress σ_P:

$$Z=F({\sigma }_{\mathrm{p}})=A_{\mathrm{1}}{\sigma }_{\mathrm{p}}^{n_{\mathrm{1}}}$$ ασp<0.8

(2)

$$Z=F({\sigma }_{\mathrm{p}})=A_{\mathrm{2}}\mathrm{e}\mathrm{x}\mathrm{p}(\beta {\sigma }_{\mathrm{p}})$$ ασp>1.2

(3)

$$Z=F({\sigma }_{\mathrm{p}})=A[\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}(\alpha {\sigma }_{\mathrm{p}}{)]}^n$$ for all σp

(4)

where A₁, A₂, A₃, n₁, n, α, and β are material constants.

By substituting Eq.(1) into Eq.(2–4), Eq.(5–7) can be obtained, respectively, as follows:

$$\dot{\epsilon }=A_{\mathrm{1}}{\sigma }_{\mathrm{p}}^{n_{\mathrm{1}}}\mathrm{e}\mathrm{x}\mathrm{p}(-Q/RT)$$

(5)

$$\dot{\epsilon }=A_{\mathrm{2}}\mathrm{e}\mathrm{x}\mathrm{p}(\beta {\sigma }_{\mathrm{p}})\mathrm{e}\mathrm{x}\mathrm{p}(-Q/RT)$$

(6)

$$\dot{\epsilon }=A[\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}(\alpha {\sigma }_{\mathrm{p}}{)]}^n\mathrm{e}\mathrm{x}\mathrm{p}(-Q/RT)$$

(7)

In order to calculate the value of n₁ and β, Eq.(5–6) are transformed into Eq.(8–9), respectively, as follows:

$$\mathrm{l}\mathrm{n}{\sigma }_{\mathrm{p}}=\frac{\mathrm{1}}{n_{\mathrm{1}}}\mathrm{l}\mathrm{n}\dot{\epsilon }-\frac{\mathrm{1}}{n_{\mathrm{1}}}\mathrm{l}\mathrm{n}{A}_{\mathrm{1}}+Q/RT$$

(8)

$${\sigma }_{\mathrm{p}}=\frac{\mathrm{1}}{\beta }\mathrm{l}\mathrm{n}\dot{\epsilon }-\frac{\mathrm{1}}{\beta }\mathrm{l}\mathrm{n}{A}_{\mathrm{2}}+Q/\beta RT$$

(9)

The relationship between lnσ_p and $\mathrm{l}\mathrm{n}\dot{\epsilon }$ can be obtained, as shown in Fig.3a. Through the linear regression method, the value of 1/n₁ can be calculated from the slope of lnσ_p-$\mathrm{l}\mathrm{n}\dot{\epsilon }$ line. Thus, n₁=3.785. Similarly, the value of 1/β can be calculated from the slope of σ_P-$\mathrm{l}\mathrm{n}\dot{\epsilon }$ line, as shown in Fig.3b. Thus, β=0.035 091 and α=β/n₁=0.009 271 1.

Fig.3  Relationships of lnσ_p-ln$\dot{\epsilon }$ (a), σ_P-ln$\dot{\epsilon }$ (b), ln[sinh(ασ_P)]-ln$\dot{\epsilon }$ (c), ln[sinh(ασ_P)]-T ^-1 (d), and lnZ-ln[sinh(ασ_P)] (e)

In order to get the value of n, the logarithm form of Eq.(7) is used, as follows:

ln$$\dot{\epsilon }$$=lnA+nln[sinh(ασp)]$$-$$Q/RT

(10)

The relationship between $\mathrm{l}\mathrm{n}\dot{\epsilon }$ and ln[sinh(ασ_p)] can be obtained, as shown in Fig.3c. The fitting line slope in Fig.3c represents the calculated value of n. As a result, the stress exponent of n is about 2.820 95.

Based on Eq.(10), Q can be obtained, as follows:

$$Q=nR\left\{\frac{\partial \mathrm{l}\mathrm{n}[\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}(\alpha {\sigma }_{\mathrm{p}})]}{\partial (\mathrm{1}/T)}\right\}\dot{\epsilon }$$

(11)

The value of $\partial$ln[sinh(ασ_p)]/$\partial$(1000/T) can be evaluated by the fitting line slope, as shown in Fig.3d, which is 36.036 at 1203–1243 K and 17.600 at 1243–1283 K. A great difference occurs due to the temperature range. Then, according to Eq.(11), the accurate value of Q at different temperatures can be obtained. It is calculated that Q=845 165 J/mol at 1203–1243 K, while Q =412 779 J/mol at 1243–1283 K.

In order to get the accurate value of Z, the logarithm form of Eq.(4) is used, as follows:

lnZ=lnA+nln[sinh(ασp)]

(12)

Combining Eq. (7), Eq. (13) can be obtained, as follows:

$$\dot{\epsilon }=Z\mathrm{e}\mathrm{x}\mathrm{p}(-Q/RT)$$

(13)

Therefore, the value of Z at different strain rates and different temperatures is determined.

By calculating, n and A are 2.570 and 8.377×10³² at 1203–1243 K, and 3.112 and 5.834×10¹⁴ at 1243–1283 K, respectively (Fig.3e).

According to the above discussion, the constitutive models of Ti-22Al-25Ti alloy are as follows:

$$\begin{array}{l}\dot{\epsilon }=\mathrm{8.377}\times {\mathrm{10}}^{\mathrm{32}}[\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}(\mathrm{0.009}\mathrm{271}\mathrm{1}{\sigma }_{\mathrm{p}}{)]}^{\mathrm{2.570}}\\ \times \mathrm{e}\mathrm{x}\mathrm{p}(-\mathrm{845}\mathrm{165}/RT)\end{array}$$ T=1203–1243 K

(14)

$$\begin{array}{l}\dot{\epsilon }=\mathrm{5.834}\times {\mathrm{10}}^{\mathrm{14}}[\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}(\mathrm{0.009}\mathrm{271}\mathrm{1}{\sigma }_{\mathrm{p}}{)]}^{\mathrm{3.112}}\\ \times \mathrm{e}\mathrm{x}\mathrm{p}(-\mathrm{412}\mathrm{779}/RT)T=\mathrm{1243}‒\mathrm{1283}K\end{array}$$

(15)

2.4 Microstructure evolution

Fig.4 shows SEM microstructures of the tensile specimens before and after tension at different temperatures with strain rate of 1×10^‒3 s^-1. It can be seen from Fig.4a₁ that the alloy microstructure comprises α₂, B2, and lamellar O phases at 1203 K. The equiaxed α₂ grains are elongated during the hot deformation, indicating that the α₂ grains suffer a large plastic deformation at elevated temperature. The volume fraction of O phase is decreased with increasing the forming temperature. Fig.4a₂ and 4b₂ show that the microstructure of O phase is changed from the slatted shape to equiaxed shape with increasing the temperature. During the hot deformation, the softening is generally related to the globularization. The material with the globule microstructure would have the ideal workability and stable flow^[29].

Fig.4  SEM microstructures of Ti-22Al-25Ti alloys before (a₁–e₁) and after (a₂–e₂) tension at different temperatures with strain rate of 1×10^‒3 s^-1: (a₁, a₂) 1203 K; (b₁, b₂) 1223 K; (c₁, c₂) 1243 K; (d₁, d₂) 1263 K; (e₁, e₂) 1283 K

The temperature of phase transition α₂+B2/β+O→α₂+B2 in Ti-22Al-25Nb alloy is about 1243 K. Combined with Fig.3e, the low deformation temperature (1203–1243 K) of Ti-22Al-25Nb alloy results in the α₂+B2/β+O three-phase region, and the high deformation temperature (1243–1283 K) leads to the α₂+B2 two-phase region. For the three-phase and two-phase regions, their deformation activation energies are very differ-ent from the calculated ones of 845 165 and 412 779 J/mol, respectively. During the hot deformation, the higher apparent activation energy in the α₂+B2/β+O three-phase region at lower deformation temperature is related to the globulari-zation of lamellar O microstructure^[30]. In addition, with increasing the forming temperature, the apparent activation energy in the α₂+B2 two-phase region at higher deformation temperature is much lower than that in the three-phase region. As a result, the Ti-22Al-25Ti alloys are easier to deform at higher temperatures.

3 Conclusions

1) The peak stress is increased with increasing the strain rate and decreasing the temperature for Ti-22Al-25Ti alloys. The peak stress occurs at the strain of about 0.05, which is independent of strain rate and deformation temperature.

2) In the α₂+B2/β+O three-phase region (1203–1243 K) and α₂+B2 two-phase region (1243–1283 K) of Ti-22Al-25Nb alloys, their tensile deformation activation energies are differ-ent from the calculated ones of 845 165 and 412 779 J/mol, respectively.

3) The constitutive equations for the tensile deformation of Ti-22Al-25Nb alloys are established: at 1203–1243 K, $\dot{\epsilon }=\mathrm{8.377}\times {\mathrm{10}}^{\mathrm{32}}[\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}(\mathrm{0.009}\mathrm{271}\mathrm{1}{\sigma }_{\mathrm{p}}{)]}^{\mathrm{2.570}}\mathrm{e}\mathrm{x}\mathrm{p}(-\mathrm{845}\mathrm{165}/RT)$; at 1243–1283 K, $\dot{\epsilon }=\mathrm{5.834}\times {\mathrm{10}}^{\mathrm{14}}[\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}(\mathrm{0.009}\mathrm{271}\mathrm{1}{\sigma }_{\mathrm{p}}{)]}^{\mathrm{3.112}}$

×$\mathrm{e}\mathrm{x}\mathrm{p}(-\mathrm{412}\mathrm{779}/RT)$.