Hot compression deformation behavior and constitutive model of 2050 Al-Li alloy

Isothermal compression experiments of 2050 AL-Li alloy were carried out by Gleeble-3800 thermal-mechanical simulator. Hot compression deformation behavior of the alloy under the conditions of deformation temperature of 300~500 °C and strain rate of 0.01~10 s-1 was studied. The constitutive model of thermal deformation was established. Results indicate that there is an obvious rheological steady state in the isothermal compression process of 2050 aluminum alloy. The microstructure shows that the alloy has recrystallization. 2050 aluminum alloy is a positive strain rate sensitive material. At constant temperature, the steady state flow stress increases with the increase of strain rate. Arrhenius constitutive model can accurately predict the rheological behavior of 2050 aluminum alloy. The average absolute relative error (AARE) of the relative error between the experimental value and the predicted value is 8.59%.


Introduction
2XXX series aluminum alloys are widely used in transportation and aerospace industries because of their high strength and low density [1]. As one of the 3rd generation Al-Li alloys, 2050 aluminum alloy has excellent static and fatigue properties [2]. Through forging, rolling and other processes, 2050 aluminum alloy can be processed into components for aircraft wings, fuselage and other parts [3]. Due to the influence of microstructure, deformation temperature, strain rate and stress-strain state of deformation area in the hot working process of Al-Li alloy, improper process may lead to defects such as part cracking.
The constitutive model reflects the coupling relationship between strain stress, strain rate and temperature, so it is an important basis for the formulation and optimization of hot working process. At present, many studies have been carried out on the thermal deformation behavior of aluminum alloys [4,5]. For example, Ning Liu et al. [6] discussed the flow stress characteristics of 2055 aluminum alloy at 480 ℃ ~ 540 ℃, and established the constitutive model of the alloy. Zhenyang Chen et al. [7] established the thermal deformation constitutive model of 2219 aluminum alloy at 330 ℃ ~ 450 ℃. However, the research on the hot deformation behavior of 2050 aluminum alloy is limited. In addition, the establishment of constitutive model in previous studies is based on a narrow temperature range. In 2 this paper, 2050 aluminum alloy was compressed at high temperature, the high temperature thermal deformation behavior of 2050 aluminum alloy was studied, and the constitutive model of the alloy was established.

Experimental materials and methods
The experimental material was 2050 aluminum alloy rolled plate, and its main chemical composition was shown in Table 1. The alloy was processed into a size of Ф 8mm × 12 mm standard hot compression specimen. The thermal compression test was carried out on Gleeble-3800 thermal-mechanical simulator. Bal. According to the deformation temperature and strain rate of 2050 aluminum alloy in actual production, isothermal compression tests were carried out at different temperatures (300, 350, 400, 450 and 500 ℃) and different strain rates (0.01, 0.1, 1 and 10 s -1 ). The specific process route was shown in Fig. 1. After isothermal compression, the specimens were cut along the center of the compression axis to observe the microstructure of the section. After grinding, polishing and Keller reagent corrosion, the microstructure was characterized by optical microscope.  Fig. 2 shows the true stress true strain curve of 2050 Al-Li alloy after compression at different deformation temperatures and strain rates. As shown in the Fig. 2a, b, c and d with the increase of true strain, the true stress -strain curves at different deformation temperatures have the same trend. The true stress gradually increases to the peak, then decreases slowly, and finally tends to be stable. This can be attributed to the interaction between work hardening and dynamic softening. At a constant strain rate, the true stress decreases with the increase of temperature. This is because the increase of temperature leads to the increase of atomic kinetic energy and easier diffusion, which is conducive to softening behaviors such as dynamic recovery or dynamic recrystallization. At a constant temperature, the steady flow stress increases with the increase of strain rate, indicating that 2050 Al-Li alloy is a positive strain rate sensitive material.  Fig. 3 shows the microstructure of 2050 aluminum alloy before and after isothermal compression. It can be seen that the obvious fibrous structure is shown in Fig. 3a, which is a typical structure of aluminum alloy after rolling. There are two softening mechanisms in Al-Li alloys: dynamic recovery and dynamic recrystallization [8,9]. At the deformation temperature of 450 ℃ and the strain rate of 1 s -1 , equiaxed small particles of dynamic recrystallization appear along the grain boundary (as shown in the circle area of Fig. 3b), which proves that dynamic recrystallization occurs in the deformation process of 2050 aluminum alloy under this process condition. The area of dynamic recrystallization is concentrated near the centerline perpendicular to the compression direction, which may be related to the friction force on the specimen.

Constitutive model
The flow stress of 2050 aluminum alloy depends on deformation temperature and strain rate. In this paper, Arrhenius constitutive model [10] is used to describe the relationship between the three parameters: At low stress levels (ασ＜0.8) [11] : sinh (4) Therefore, under all stress states, Eq.1 can be expressed as: sinh (5) Where, f(σ) is a function related to the stress level, is the strain rate (s -1 ), is the flow stress (MPA), T is the absolute temperature (k), Q is the thermal deformation activation energy (kJ · mol -1 ), and R is the gas constant; Parameter A, n, α, β are constants, where A is the structural influence factor, n is the stress index, and α=β/n. The relationship between flow stress and thermal deformation conditions can be expressed by Zener Holloman parameter equation (parameter Z) [12]: exp sinh (6) After substituting Eq. 2 and Eq. 3 into Eq. 1, take logarithms on both sides at the same time: / (7) / (8) The true stress and true strain data obtained from the experiment when the true strain is 0.3 are substituted into Eq. 4 and Eq. 5. The relationship curves of and under different deformation temperatures are drawn by Origin software, as shown in Fig. 3. It can be seen that both and have a linear relationship. The slope of different straight lines is obtained by linear fitting of the curve with the least square method. β calculate under higher stress conditions, that is, the average value of the slopes of the two straight lines when the deformation temperature is 300 ℃ and 350 ℃. n 1 is the average value of the slopes of three straight lines when the peak stress is low, that is, the deformation temperature is 400 ℃, 450 ℃ and 500 ℃. Therefore, n 1 = 7.249; α=β/ n 1 =0.011.

Fig. 4 Relationship curve between
and . For all stress states, assuming that the activation energy Q is independent of temperature, find the natural logarithm on both sides of Eq. 5: ℎ (9) The peak stress and the calculated α substitute into Eq. 9 By performing linear regression on the fitting curve in Fig. 4, calculate the average value of different straight-line slopes, and get Q=286.370 kJ·mol -1 , n = 6.362.  (11) Select a strain value every 0.05 within the strain range of 0.05 ~ 0.6 for calculation. The calculation steps are the same as above. The material constants of the constitutive model of 2050 aluminum alloy under different strain values can be obtained by substituting the experimental data. The relationship between strain and material constant is established by cubic polynomial fitting. Eq. 12 is a functional relationship.
Where , , and 0,1,2,3,4,5,6 are all parameters. Solve the above fitting curve and calculate the parameter values in the formula. Table 2 shows the material constants of 2050 aluminum alloy under different strain conditions.   The fitting coefficient and experimental data are substituted into Eq. 5 to obtain the constitutive model of 2050 aluminum alloy. As shown in Fig. 7a, b, c and d, the true stress curve and the predicted value of the constitutive model are shown when the strain rate is 0.01, 0.1, 1 and 10 s -1 respectively. It can be seen that the predicted value of the model is close to the true stress curve. Where: E is the experimental value of flow stress, P is the predicted value of the model, and N is the number of data groups. Fig. 8 shows the relationship between experimental values and model predicted values. Their correlation coefficient R reaches 0.986 and the average absolute relative error AARE is only 8.59%. It is further verified that the model can accurately predict the true stress of 2050 aluminum alloy under thermal deformation.

Conclusion
The true stress-strain behavior of 2050 aluminum alloy at 300~500 ℃ and strain rate of 0.01~10 s -1 was (1) The flow stress enters the steady-state flow stage after the strain strengthening stage, which is related to the recovery and recrystallization softening behavior in the alloy. 2050 aluminum alloy is a positive strain rate sensitive material, and the increase of strain rate leads to the increase of flow stress.
(2) The Arrhenius constitutive model of 2050 aluminum alloy is established. The simulation results obtained by using the established constitutive equation are in good agreement with the experimental results. The correlation coefficient R reached 0.986 and the average absolute relative error AARE is 8.59%.