Magnesium alloys have been widely used in recent years due to their good dimensional stability, low density, good damping properties and low casting costs. However, close-packed hexagonal crystal structure of magnesium alloy results in low ductility at room temperature and difficulty in forming, which limits its industrial application. Therefore, it is necessary to systematically study mechanical behavior of AZ series magnesium alloys under superplastic deformation. Most previous studies used tensile tests to study superplasticity of magnesium alloys, paying less attention to problem of superplastic compression deformation. In actual production, there are fewer tensile forming conditions and more compression forming conditions. Therefore, it is particularly important to study superplastic forming under compression conditions (such as superplastic extrusion, superplastic upsetting, etc.), and current research on magnesium alloys is limited to a certain type of AZ magnesium alloy, and research on AZ series magnesium alloys is not systematic enough. Constitutive equation plays a crucial role in analyzing and predicting superplastic deformation behavior. Therefore, commonly used AZ31, AZ61, and AZ91 magnesium alloys are used as research objects. By conducting compression tests on magnesium alloy specimens after recrystallization and annealing, its microstructures were analyzed to study its superplasticity during unidirectional compression deformation, enrich theory of superplastic deformation, and lay foundation for expanding scope of engineering applications of material.

Materials used in study are industrial extruded AZ31, AZ61, and AZ91 magnesium alloys, whose chemical compositions are Mg-3%Al-1%Zn, Mg-6%Al-1%Zn, and Mg-9%Al-1%Zn respectively. First, sample was processed into a cylinder of φ8 mm * 12 mm, then a recrystallization annealing test was performed on it. Figure 1 shows microstructure of sample after isothermal annealing at 573 K for 30 min. Results show that grain sizes are 12.7, 12.5, and 12.0 μm respectively.

 

Figure 1 Microstructure of magnesium alloy after annealing at 573 K for 30 minutes
Compression test was conducted on a modified DNS200 electronic universal testing machine. Due to addition of a split high-temperature furnace, deformation temperature in compression test can be controlled between 423 and 673 K, strain rate can be controlled between 1*10-4 and 1* 10-2 s-1.

True compressive strain of specimen can be calculated by following formula:
ε=ln（h/H）
In formula: ε - true compression strain of sample; h - height of sample before compression deformation, mm; H - height of sample after compression deformation, mm.
Index to measure compression superplasticity of this material is circumferential elongation of outer edge of sample λ, and calculation formula is as follows:
λ=（d-D）/D*100%
Among them, d is diameter of sample before compression deformation, mm; D is diameter of sample after compression deformation, mm.
During process of compression deformation, drumming will occur on the side of specimen. In order to eliminate influence on calculation of circumferential elongation of outer edge, according to principle of invariance of volume and compression true strain calculation formula, it can be obtained:
Circumferential elongation of outer edge of sample = (-1) * 100%
Calculation formula of strain rate sensitivity index m is as follows:
 
Among them, σ represents stress, MPa;  represents strain.
Strain rate sensitivity index m is an important parameter of superplastic deformation, reflecting material's ability to resist necking. According to load-deformation curve obtained from unidirectional compression test, Cook-Larke extrapolation method is used to calculate and draw true stress-strain curve (σ-ε curve) of unidirectional superplastic compression deformation shown in Figure 2. High-temperature deformation of metal is a thermally activated process. Deformation mechanism can be inferred based on calculation formula of thermal activation energy. Influence of deformation temperature and strain rate on flow stress can be expressed by following formula.

 

Figure 2 True stress-true strain curves of magnesium alloy under compression deformation at different strain rates at 673 K
Q=
Among them, Q is thermal deformation activation energy, kJ/mol; σ is stress, MPa; m is strain rate sensitivity index; R is gas constant, its value is 8.314 J/K·mol; T is thermodynamic temperature, K; dlnσ /d(1/T) is estimated from slope of curve shown in Figure 3.

 

Figure 3 Relationship between lnσ and 1/T of magnesium alloy

Table 1 shows compression test results of AZ31, AZ61, and AZ91 magnesium alloys after recrystallization annealing and refinement treatment at a temperature of 673 K and a strain rate of 1*10-2 s-1.

Table 1 Compression test results
As can be seen from Table 1, under conditions of a temperature of 673 K and a strain rate of 1*10-2 s-1, AZ series magnesium alloy specimens did not crack, cylindrical elongation was ≥100%, and true compression strain was ≥1 , showing good compression superplasticity.
Figure 2 shows compressive true stress-true strain curves of AZ31, AZ61, and AZ91 magnesium alloys at different initial strain rates at a temperature of 673K. It can be seen from Figure 2 that compression true stress-true strain curve shapes of AZ31, AZ61 and AZ91 are basically same. In the early stage of compression, samples undergo work hardening. As strain increases, material undergoes dynamic recrystallization and dynamic recovery, slope of curve decreases and tends to level. As compression deformation continues to increase, dynamic recrystallization, dynamic recovery, work hardening tend to balance, flow stress in the later period tends to be constant.

Figure 3 shows linear relationship between lnσ and 1/T for AZ31/AZ61/AZ91 magnesium alloy at a constant strain rate. According to slope in Figure 3, corresponding superplastic deformation activation energy of magnesium alloy can be calculated. Superplastic deformation activation energies Q of AZ31/AZ61/AZ91 magnesium alloys are 105.8, 165.4, and 126.2 kJ/mol respectively.

Figure 4 shows relationship curve between flow stress and strain rate of AZ31/AZ61/AZ91 magnesium alloy when temperature is 673 K and strain is 0.2. After calculating slope of curve, strain rate sensitivity index m of AZ31/AZ61/AZ91 magnesium alloy is 0.25, 0.23, and 0.24 respectively. According to m value, it can be inferred that contribution of dislocation creep is small during process of compression superplastic deformation, and grain boundary slip mechanism plays a major role.

 

Figure 4 Relationship between flow stress and strain rate of magnesium alloy at 673 K (ε=0.2)

At a temperature of 673 K, stress index n of magnesium alloy is 4. Mechanism of superplastic deformation is mainly grain boundary slip. Constitutive equation is:

 

Among them, DL is lattice diffusion coefficient of magnesium alloy, which is 1.3*10-14 m2/s; b is Burgers vector, which is 3.21*10-10; G is elastic modulus of magnesium alloy, which is (1.92*104-8.6 T) MP; K is Bohr-Sedman constant, which is 1.38*10-23 J/K; T is temperature, K. By substituting above parameters into formula and comparing them with test results, constant A can be calculated and substituted into above formula as follows:
AZ31:
AZ61:
AZ91:
Based on test results, superplastic constitutive equation of AZ31/AZ61/AZ91 magnesium alloy was established above.

Figure 5 shows microstructure after isothermal superplastic compression at a temperature of 673 K and a strain rate of 1*10-2 s-1. Comparing Figure 1, it can be seen that grain size is significantly refined after isothermal superplastic compression, and it can be judged that dynamic recrystallization process has occurred in compressed structure.

 

Figure 5 Microstructure of magnesium alloy after isothermal superplastic compression at a temperature of 673 K and a strain rate of 1*10-2 s-1

During process of compression deformation, circumferential elongation of outer edge of sample is an important criterion for judging whether material has superplastic behavior. It is generally believed that when circumferential elongation of outer edge is ≥100%, material has achieved compression superplasticity. The greater circumferential elongation of outer edge of sample, the better superplastic deformation ability. In the early stage of superplastic compression deformation, material undergoes a dynamic recrystallization process. On the one hand, it can make solid α-Mg grains finer, and on the other hand, it can increase number of high-angle grain boundaries. Above changes are conducive to slip of grain boundaries and provide structural conditions for subsequent superplastic deformation. In addition, grain boundary diffusion coefficient of magnesium is relatively high. During superplastic deformation process, grain boundary dislocation pile is easily absorbed by α-Mg solid solution, which makes dynamic recrystallization process easier, equiaxed fine grains are also easier to rotate, grain boundaries are easier to slide, and providing possibility to achieve superplasticity.