1 Introduction

The quality of the magnesium element is about 2.4% of the total mass of the earth’s crust. In addition, magnesium is also distributed in seawater, salt lakes, and brine widely, such as Qinghai Salt Lake, where the reserves of magnesium chloride are as high as 8 billion tons, which exist in various forms, and magnesium alloys are inexhaustible metal materials [1,2,3]. Magnesium alloy, as a “green engineering material in the 21st century,”, has high specific strength and specific stiffness, good dimensional stability, thermal conductivity, and strong vibration resistance; can withstand large impact load; and has excellent casting, machining performance, and easy recycling. These characteristics make it occupy a place in the aerospace field and can be used as aircraft, missiles, spacecrafts, satellites, etc. With the development of science and technology, the development of aerospace field is more and more inseparable from the participation of magnesium alloy [4].

In recent years, magnesium alloys are used in transportation, communication, electronics, and aerospace industries extensively. However, these alloys are difficult to be deformed at room temperature due to its hexagonal lattice structure with limited numbers of separate slip systems [5]. Although more than 90% of the magnesium alloy products are made by casting currently, large-scale production of wrought magnesium alloy products may be the future development direction. As comparing with magnesium alloy productions by casting process, the plastic deformation process can produce a variety of plates, rods, tubes, profiles, and forging products, and their strength, ductility and mechanical properties are higher than those made by casting.

As one of the key forming process, extrusion process is realized by plastic deformation under the action of three direction compression stresses. Therefore, extrusion process is suitable for the formation of low ductile materials, and which makes extrusion method an important method to produce deformed magnesium alloy products. However, the thermomechanical response of magnesium alloys affected by extrusion conditions is very complex. The experimental results show that the flow stresses and strain rates are not easy to be measured. In this case, finite element (FE) simulation can play a unique role in understanding the thermal-mechanical interaction in extruded materials [6]. The finite element simulation of extrusion process for magnesium alloy are reported. For example, it is assumed that the Mg-Zn-Zr alloy is thermoplastic and the temperature limit is defined by the FE for precision reverse extrusion. A two-dimensional finite element method is used to determine the size and capability of a press for extruding a magnesium-aluminum-zinc alloy in a temperature range [7]. In addition, the behavior of the AZ31 alloy in the extrusion forming process is predicted by the real-rigid plastic material model, and the heat exchange between the workpiece and the extrusion die is included [2].The variation of the grain size of the cross-section of the extruded sheet is explained by the stress and strain distribution. Other work makes use of iron to construct the limit view of the extrusion of the billet from the AZ31 billet into the rod [8].

In recent years, some new manufacturing processes and technologies have been used to process new magnesium alloy materials, such as die casting and semi-solid forming technology [3]. Large nanostructured materials treated by (SPD) with severe plastic deformation, such as equal channel angular extrusion (ECAE), have also attracted more and more attention from experts in the field of material science. (ECAE) process was invented in the early 1980s, but its development is not as much as people expected, and it is still limited to laboratory scale experiments [9,10,11].

In this paper, the direct extrusion process and continuous shearing-bending process are combined to produce thin-wall magnesium tube, abbreviated as “TESB” (tube extrusion shear-bending) in this paper. In order to illustrate the potential application of TESB process in industry, a complex extrusion die has been designed. The microstructure analysis and hardness testings of the tube fabricated by TESB process have been carried out. In this study, DEFORMTM-3D finite element software is used to simulate the evolution of extrusion force, effective stress, and strain in TESB process.

2 Experimental and results

2.1 Experimental setup

Figure 1 illustrates the TESB process which combines direct extrusion with consecutive shearing process to fabricate fine grained AZ31 Mg alloy tube for the first time. In this process, the punch pushes the billets into the extrusion die. In the whole experiment, one time direction extrusion and two time shearings and one time bending deformation occurred. The extrusion tooling consists of die, container, and ram which are made of H13 hot-working tool steel. The die includes direction extrusion part with extrusion ratio 9. The used tooling and the press are shown in Fig. 2 a and b is the tube prepared by TESB process.

Fig. 1
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Schematic of TESB process

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Fig. 2
figure 2

TESB equipment (a) and extruded tube (b)

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2.2 Microstructural analysis

The tube manufactured by TESB process is shown in Fig. 2b. The longitudinal direction along extrusion direction is chosen as the examined position for microstructural analysis on the processed tube. The metallographic structure was observed by picric acid 5g, glacial acetic acid 5g, distilled water 10ml, and ethanol 100ml. The metallographic structure was observed on Leica DMI5000M metallographic microscope. In order to analyze the microstructure evolution of AZ31 magnesium alloy during extrusion deformation and study the grain refinement mechanism of AZ31 magnesium alloy during TESB deformation, the four typical deformation of extruded products are sampled and analyzed; as shown in Fig. 3, the Fig. 3b is the primary shear zone, the Fig. 3c is the primary shear zone, and the Fig. 3d is the formed tube. The forming of the tube finally experienced two shear actions and one bending action. In Fig. 3a, the original grains of the as-cast AZ31 magnesium alloy billet is coarse and the average grain size is 82 μm.

Fig. 3
figure 3

The metallographic structure of the TESB extruded AZ31 magnesium alloy tube blank at different positions. a Common crush zone. b Primary shear zone. c Bending zone. d Shaped tube

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From the metallographic diagram of Fig. 3c, it can be seen that the proportion of fine and recrystallized round grains increase obviously, which is due to the high deformation temperature, and with the increase of deformation degree, the distortion energy stored in the grains increase sharply and cannot be released in a short period of time, which increases the number of nucleation of recrystallized grains and further occurs dynamic recrystallization. Although many grains are already significantly refined after the process, the grain structure is more homogeneous than as-received, with very fine grains of 4–6μm as well as few coarse grains of greater than 25μm, and average grain size is 12μm.

The grains are subjected to strong triaxial stress, the dislocation density inside the grains increases sharply, and the lattice distortion intensifies. Although the grains in the Fig. 3d are no longer affected by stress after passing through the shear zone, the recrystallizing can continue, such as Fig. 3d. The diagram shows that the average grain size is reduced to 13.4μm from a large number of wafer grains below 10μm.

To sum up, a series of continuous deep shear deformation was introduced when AZ31 magnesium alloy thin-wall tube was extruded by TESB process. Only once extrusion can make the grain refinement effect of as-cast tube billet obvious, and the tube with uniform grain size is obtained

2.3 Microhardness test

The hardness is the mechanical property index used to measure the soft and soft degree of the material and the elastic-plastic and deformation characteristics of the reaction material. The extrusion and deformation process of the TESB of the AZ31 magnesium alloy tube blank includes the process of common extrusion, shearing, bending and the like, and the work hardening and dynamic recrystallization caused by the new pipe forming process have an important influence on the hardness of the material. Figure 4 shows the hardness distribution of the longitudinal section of each process in the process of extrusion and forming of the TESB at different temperatures. The numerical error range is about 5HV. As can be seen from the figure, during the whole TESB extrusion forming process, the hardness of the tube blank is decreased after the first increase, and the maximum hardness is 72HV, 78HV, and 83HV, respectively. In that process of the early deformation, the deformation amount is gradually accumulated, the work hardening is serious, and the later-stage shaping stage, due to the friction action and the plastic deformation work, the temperature of the tube blank is high, the deformation energy storage is high, the dynamic recrystallization is fully carried out, the final grain generation is abnormal, and the crystal grain is reduced, and therefore the hardness is reduced. The higher the temperature, the lower the hardness value for each process location, which is due to the higher the temperature, the stronger the dislocation movement ability, and the lower dislocation entanglement, resulting in a decrease in hardness, and the final hardness of the formed pipe is 66 HV, 74 HV, and 79 HV, respectively.

Fig. 4
figure 4

Hardness distribution of longitudinal section of tube blank during TESB extrusion of AZ31 magnesium alloy

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3 FE model and results

3.1 FE model

DEFORMTM-3D finite element software is used for modeling purpose [10, 12, 13]. The present study adopts the following assumptions: (1) both the container and the die are rigid bodies, (2) the extrusion billet is a rigid-plastic material, and (3) the friction factors between the extrusion billet and the ram, container, and die are constant following the generalized Coulomb’s law [14, 15]. The material for simulation and experiment is commercial AZ31B (Mg-3%Al-1%Zn, wt) magnesium alloy, the composition of which is shown in Table 1.

Table 1 The main element mass fraction of AZ 31 magnesium alloy (c%)
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Many parameters are involved in the process of extrusion, mold structure, and experimental conditions parameters such as extrusion temperature, extrusion speed, lubrication, or not. Each parameter has the influence to the extrusion process as well as the extrusion product. TESB process has the characteristics of ordinary extrusion; its mold structure is more complex. Therefore, the finite element simulation experimental parameters as shown in Table 2 are set (It mainly includes the billet size, extrusion ratio, minimum size of grid, etc., among the minimum grid size is determined by the minimum size of the die. In this experiment, minimum grid size is 1/3 of billet mesh size.) and the influence law of extrusion parameters on TESB process is studied by simulating extrusion pressure, metal flow, and temperature distribution under different parameter conditions.

Table 2 Experimental parameters used in numerical simulation
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In order to study the variation of real stress and strain with process parameters, the stress-strain curve is shown in Fig. 5. According to the curve regular in the figure, it can be found that at the same extrusion temperature, the stress of the material increases first and decreases with the increase of strain, subsequently. When the strain is the same, the stress of the material decreases with the increase of temperature.

Fig. 5
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Real stress-strain curve of AZ31 magnesium alloy

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3.2 FE results

3.2.1 Temperature field change

In order to study the temperature distribution of each part of the billet in the process of TESB deformation, the axial section of the billet is analyzed, as shown in the Fig. 6; when the initial extrusion temperature is 400 °C, the temperature distribution of the billet in the extrusion process is shown. During ordinary extrusion, the temperature in the undeformed area of the upper part of the billet does not change much. As shown in Fig. 6 (a, b), the temperature in the lower deformation zone of the billet increases obviously because at the beginning of plastic deformation, the heat of plastic deformation work transformation increases the temperature of the deformed area, and the billet passes through the ordinary extrusion zone, the diameter expansion shear zone, the bending zone, and the shrinkage shear zone in turn under the action of the extrusion rod, as shown in Fig. 6 (b). As shown by (c), (d), (e), the billet enters the stable deformation stage after the reduced diameter shear zone, and the extrusion load changes little at this stage. It is not difficult to see from the figure (e) that the shear deformation zone is the region with the highest temperature of the whole billet. The heat that causes the billet temperature to rise comes partly from its own plastic deformation work and partly from the friction between the billet and the die [16, 17]. Most of the plastic deformation work produced by the deformation of the billet increases the surrounding temperature in the form of heat, and very few of them remain in the interior of the billet in the form of crystal defects. On the whole, the temperature distribution in the deformation area of the billet is uniform, which is about 10 °C higher than the initial deformation temperature.

Fig. 6
figure 6

The distribution of temperature field in different stages during the extrusion process

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The shear deformation zone is always at high temperature in the whole extrusion process, which is also the key to determine the quality of the final extrusion pipe, which directly affects the microstructure and mechanical properties of the parts, and the large stress in the shear deformation zone, coupled with the sharp change of temperature, will also affect the dimensional accuracy of the die and then affect the size and shape of the extruded tube.

3.2.2 Effect of friction factor on equivalent effect stress

The change of friction factor will inevitably lead to the change of deformation load. Figure 7 shows the equivalent stress distribution in TESB extrusion process under different friction conditions. As shown in the figure, the shear deformation zone is the concentrated area of equivalent stress distribution. With the increase of friction factor, the blocking effect of die on billet flow increases, which leads to the increase of equivalent stress in shear deformation area. The overall analysis shows that the equivalent stress distribution of the billet is also changed due to the change of the contact conditions between the billet and the die [18]. Properly increasing the friction factor can make the equivalent stress distribution in the shear deformation region more uniform, which is similar to the back pressure applied to the deformed billet in the actual production process.

Fig. 7
figure 7

Equivalent stress distribution of TESB extrusion of AZ31 magnesium alloy tube billet with the same friction factor. a 0.1. b 0.2. c 0.4

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3.2.3 Effect of different temperatures on equivalent stress

Figure 8 shows the equivalent stress cloud diagram at extrusion speed of 10 mm/s and initial extrusion temperature of 370 °C, 400 °C, and 430 °C, respectively. It can be seen from the diagram that the equivalent force value in the shear deformation region is higher, and the maximum equivalent force value corresponding to the shear zone is different when the initial extrusion temperature is different. With the increase of deformation temperature, the maximum equivalent stress in the shear zone decreases, and the uniformity of the equivalent stress distribution increases with the increase of the deformation temperature. In the process of plastic deformation of magnesium alloy billet, reasonable selection of deformation temperature is beneficial to prolong the life of die and improve the surface quality of the product [19, 20].

Fig. 8
figure 8

Equivalent stress distribution of axial section of AZ31 magnesium alloy tube billet with different deformation temperatures. a 370°C. b 400°C. c 430°C

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4 Conclusion

The bending process is added to the forming of magnesium alloy tube, which has obvious effect on the grain refinement of magnesium alloy tube. The grain size of magnesium alloy tube after bending process is about 1/7 of which prepared by direct extrusion. The grain size fabricated by direct extrusion is about 80μm and after bending process the grain size is about 13.4μ m.

Through the combination of finite element model and experiment, the high temperature region in the experimental process is mainly distributed in the deformation zone, and different friction factors will affect the stress and strain in the billet, and it is usually easier to obtain the pipe under the smaller friction factor. The effect of different temperature on stress distribution is that the higher the temperature, the smaller the stress distribution in the billet, but at the same time, too high temperature will lead to the coarse grain size and decrease the mechanical properties of the finished product. Therefore, the appropriate experimental parameters are very important for bending molding process.