A Special Extrusion-shear Manufacturing Method for Magnesium Alloy Rods Based on Finite Element Numerical Simulation and Experimental Verication

To research the inuences of process parameters on a special extrusion-shear manufacture method for magnesium alloy rods, deform-3d software with nite element simulations has been used to analyze the material ows of deformed magnesium alloys AZ31B during the extrusion-shear (ES) process, as well as the grain sizes and distribution of extrusion loads, stresses and strains, and blank temperatures. Temperature elds, stress elds, strain elds and temperature elds varying with different blank preheating temperatures, extrusion speed and extrusion ratios were simulated. Inuences ofdifferent extrusion conditions and different die structures on microstructures of rods prepared by ES process has been researched. Extrusion forces decrease with the increasing extrusion temperatures, decreasing extrusion ratios, increasing die channel angles and decreasing friction coecients. The ow velocities of metal in the ES die increase with development of ES process. Increasing the channel angles and reducing the friction factors would increase the outow velocities of metal, but it has little effect on the uniformity of metal ow. The increase in friction and extrusion speed would increase the temperatures of the ES die. The ES process can prepare ner and more uniform microstructures than those prepared by direct extrusion under the same conditions. with different extrusion ratios, billet preheating temperatures, extrusion speeds, and friction coecients between the blank and die. The simulations involve extruding forces, strain elds, velocity elds and temperature elds during the ES process. Extrusion experiments and microstructure observations were performed under the same simulation conditions.


Introduction
Magnesium alloys are regarded as green engineering materials in the 21st century. In recent years, it has developed rapidly in many elds (such as the auto industry, aerospace industry and electronic industry).
Moreover, its development prospects would become increasingly better [1]. Magnesium alloy enjoys a great reputation as the lightest metal in all the structural metallic materials, because its density is only 1.74 g/cm³, which is 2/3 of that for aluminum. Magnesium alloys are 78.9% lighter than steel [2][3][4]. The features of magnesium and magnesium alloys include lower density, good damping properties along with damping effects, higher speci c modulus along with a good quality of thermal conduction and electromagnetic shielding, and excellent machining quality. Rolling, forging and extrusion are the three main deformation methods of magnesium alloys. Cracks easily form in magnesium alloys during rolling.
Thus, the reductions of each rolling pass are restricted, which results in a small deformation quantity and a nonideal warping effect. A magnesium alloy is subjected to triaxial compression stress during extrusion. The strong compressive stress that comes from three triaxial compression stresses provides a large amount of deformation, which is under hydrostatic pressure for the extrusion process of magnesium alloy and strongly improves its deformation capacity [5][6][7][8]. Compared with rolling and forging, the size of the extrusion product can be controlled in a quite accurate range. At the same time, its surface quality of products is good. Therefore, extrusion has been a signi cant way to produce magnesium alloy products. Although the traditional extrusion process tends to be mature, the effects of grain re nements for magnesium alloys are not obvious.
To obtain a better grain re nement effect, a large extrusion ratio of extrusion has sometimes been used.
Extrusion with a larger extrusion ratio can produce a larger stress-strain during the procedure of direct extrusion, which would reduce the service lives of the die. Extrusion can cause a second or multiple deformations to improve the effects of grain re nements. However, in this way, the designs and manufacturing of dies would be increased, and the production e ciency would be poor. At the same time, industrial production costs are rising.
Moreover, some parameters of the experiments such as ow stresses and strain rates are hard to measure by testing. Therefore, nite element modeling plays a vital role in verifying whether the new forming modes and technology parameters are reasonable [9][10][11][12].
To illustrate the potential industrial application of the ES process, ES dies have been designed, and ES processes with different process parameters have been simulated. The aim of the present study is to reveal the microstructure evolution and clarify the grain re nement mechanism in AZ31 magnesium alloy during the ES process. DEFORM TM -3D nite element software was employed to simulate distributions of extrusion loads, stresses and strains, and blank temperatures varying with different blank preheating temperatures, extrusion speeds and extrusion ratios during the ES process. Microstructures of AZ31 magnesium alloy sampled from the extruded tubes were observed. Deformed microstructures of evolution for AZ31 magnesium alloy with different manufacturing condtions were studied to analyze the deformation mechanisms of the ES process.

Material Property
Materials for simulations and experiments are commercial AZ31B magnesium alloy wt), and the speci c components are shown in Table.1. The billets were annealed at 400℃ for 15 hours before extrusion started and cooled to room temperature in the furnace to obtain homogeneous microstructures of AZ31 magnesium alloy. The die structures include extrusion die, container, and extrusion rod, and they are made of H13 hot-work die steel. Table 1 Mass fraction of main elements in AZ31 magnesium alloy% [13]

Die structures
The design idea of the ES die is based on the combination of extrusion and shear, and the ES process would increase the compressive stresses and shear stresses of magnesium alloy billets. Consequently, the ductility of magnesium alloy improved. According to the principle of more pressure and better plasticity, the back pressure is increased in the procedure of metal forming, and thus ductility is enhanced. ES process involves a huge number of parameters. The parameters of die structures, such as extrusion ratios. For the experimental condition parameters, there are extrusion temperatures, extrusion speed, lubrication and so on. As a consequence, the nite element simulations and experimental parameters are shown in Table 2. Through the simulation of extruding forces, metal ows and temperature distributions under different parameter conditions, the in uences of extrusion parameters on the ES process were investigated. top die and bottom die were built with the 3D modeling software UG in this research. The geometric models of the workpiece and dies are shown in Fig. 1. The workpieces and models are symmetrical, and we choose half of the models to conduct simulations.

Varieties of extrusion forces with extrusion strokes
During the ES process, the extrusion force is the key element to determine whether the blank can be successfully extruded. The extrusion force is affected by process parameters such as the extrusion temperature, extrusion speed and friction conditions. It can also be in uenced by the composition and states of the materials, as well as the die structures. To successfully obtain good-quality of magnesium alloys and extrusion, the parameters of the extrusion process die structures should be optimized. Thus, the change in extrusion loads was analyzed by using FEM software to simulate the ES process in different situations. During the ES process of AZ31 magnesium alloy with a preheated billet temperature of 370℃, the changing situations of extruding forces and equivalent stresses are shown in Fig. 3. From tendencies of extruding forces changing with time, variations of extruding forces, The extrusion forces vary regularly with the changing of extrusion steps.In this process, the main process of magnesium alloy includes upsetting,sizing, primary shearing, secondary shearing and shaping.During the whole process, equivalent stresses increase.It can be seen from Fig. 2b shows that the extrusion forces increase rapidly, and the equivalent stress is as high as 112 MPa in the partial zone.

The variation in loads during the ES process with different preheating temperatures
To study the variation rules of extrusion forces with different extrusion ratios, curves of extrusion load and extrusion time are shown in Fig. 3. Throughout the whole ESprocess, the variation laws of the extruding force curves are nearly consistent.Increasing temperatures hardly in uence the extruding force during the initial stage of upsetting. We can see from the gure that the upsetting force is basically coincident at different temperatures.
It can be observed in the curves that upsetting forces are basically the same under different temperatures. The extrusion forces of direct extrusion at different temperatures also coincide with each other, but as the extrusion forces increase with the development of the ES process. Fig. 3 shows that the extrusion forces increase with decreasing preheated billet temperatures. During the primary shearing and secondary shearing stages, the increase magnitudes of extrusion forces with different temperatures are basically the same.

The load varieties of the ES process with different extrusion ratios
To study the changing rule of extruding forces varying with different extrusion ratios, the ES process with a preheated billet temperature of 400℃ was simulated, and extrusion

Effects of different channel angles on extrusion forces
The ES die contains an ordinary direct extrusion zone and an equal channel angular zone. As a main parameter of equal channel extrusion, the channel angles of the die have certain effects on the extrusion forces. The changing curves of extruding forces with different channel angles and extrusion ratios of 12 and billet preheating temperature of 420℃ are shown in Fig. 5.
Because the channel angle is located in the equal-channel extrusion zone, the extrusion force is not affected by the upsetting stage, which is before the equal-channel extrusion zone and the ordinary extrusion zone. Extrusion platforms of the extrusion force curves corresponding to different channel angles coincide. In the equal channel extrusion zone, the slopes of rising for extrusion forces are different due to the in uences of the angles. When the channel angle is smaller, the slope of the extrusion force increase is larger, and the nal stable extrusion force is larger [14][15][16][17][18][19][20].

Flow velocities of billets in different zones of ES die
While blanks are extruded, blanks would be deformed with the pushing of punches and the constraints of dies. Metal ows through the ES die with different speeds and ways. During the ES process, the deformation behavior of the blank is related to the metal ow velocities and methods. To preferably study the new-type ES process, simulations and analyses of velocity elds have been conducted. The diameter of the blank is smaller than that of the cylinder, the ingot is upset rst in the extrusion cylinder during the initial extrusion of the ES process, and the metal ows to ll the whole extrusion cylinder with pushing of the extrusion punches and the constraint of the die. Because the billet only underwent upsetting deformation and the amount of deformation was small, the velocities of metal ows changed little during the upsetting stage, and the velocities were roughly the same as those of extrusion punches.
When the blank undergoes deformation in the ordinary direct extrusion zone, the blank is compressed, and the diameter decreases in the radial direction. At the same time, the cross-sectional area of the blank decreases in ordinary direct extrusion. When metal is deformed, elastic deformation is often neglected, and more attention is given to plastic strains because the small elastic deformation occurs.
On the basis of volume constancy in plastic strains, when cross-sectional areas of blank decrease, the amount of metal in cross-sectional area increases per unit time. It means the ow velocities of metal increase.It can be known from the Fig. 7 shows that the ow velocities of metal in the middle of the blank increases gradually from the upsetting zone to the ordinary direct extrusion zone. It increases from the initial 10 mm/s to a maximum of 55 mm/s.
In the equal channel angular zone, the reasons for decreasing ow velocities are frictional actions and inhibition of channel angularity on metal ows. From Fig. 8, the ow velocities of the metal decrease obviously compared with those before the primary shearing zone. There are obvious velocity gradients in the metal ow in the corner zones.
The ow velocities of metals which are in the second angular zone are shown in Fig. 9. The ow velocities of metal would change as it passed through the two shearing zones. Obvious gradients of velocities exist in the second shearing zone, which are the same as those in the rst angular zone.
Different from the gradients of velocities in the rst angular zone, the gradients of velocities in the second angular zone are incremental. The second angle has an inhibition on metal ows,which means that the second angular zone may exert back pressure on the metal in the rst angular zone, so the ow velocity would decrease. However, the blank will not be borne back pressure after the blank passes the second angular zone, and the ow velocities of the metal increases.
In the stable extrusion stage, the distribution of metal ow velocities is shown in the Fig. 10. During the stable extrusion stage, the extruding force remains within a small range of uctuations. From the gure, we know that in a stable extrusion, the metal velocities are consistent. 3.7 Variation in the temperature eld during the ES process Temperature would change due to the friction actions between the blank and die during the ES process, and heat transfer effects in air space are also a reason. 90% deformation energy billet during the plastic deformation process might be lost with heating. To research the variation in the temperature gradient during the ES process, deform software to simulate the ES process was used. The thermal conductivity between the die and blank was set to 11 N/℃s.mm². Different friction factors (0.08,0.3,0.7), different extrusion ratios (12,18,22), different extrusion velocities (2mm/s, 10mm/s, 20mm/s) and different initial temperatures (350℃,380℃,400℃) are adopted to analyze the in uences of temperature elds during ES process with different technological conditions [21][22].
During the ES process, one of the sources of heat that increases the temperature is the friction action between the die and blank. ES process was simulated with extrusion ratio 12. And those simulations are conducted with the three different friction coe cients, which are low friction(m=0.08), lubrication (m=0.3) and without lubrication (m=0.7).
Temperature variations with different friction coe cients are shown in Figure 8. From the gure, when the friction coe cient is smaller, the friction is small, and the temperature rise is smaller. Thus, friction would not only in uence extruding forces, but also affect the temperature distribution of the extrusion die. The temperature of the die increases with increasing friction coe cients [23][24][25].

Temperature variation with different extrusion speeds
The temperature variations are shown in Fig. 9, and the different extrusion speeds are 5 mm/s, 10 mm/s and 20 mm/s. From the curves, it can be concluded that the temperatures of the blanks would increase with increasing extrusion speeds. Heat produced between the blank and mold can not transmit with increasing extrusion speed. Vigorous deformation would produce more heat, and prompt die temperatures and blank rise [26][27].  Figure 11 shows that the average grain size obtained by the ES process with the billet preheating temperature. From billet preheating temperatures of 370℃ to 420℃, the average grain size obtained by ordinary direct extrusion increases continuously with increasing extrusion temperature, and the increasing trend is basically linear. For ES-extruded rods, the average grain size changes little when the temperature increases from 370℃ to 400℃, but increases signi cantly when the temperature increases from 400℃ to 420℃. At the same time, Figure 11 shows that the average grain sizes of ES-extruded rods with three different billet preheating temperatures are much re ner than those of ordinary direct extruded rods. It is obvious that the ES process can prepare for ner and more uniform microstructures than those prepared by direct extrusion under the same conditions.

Conclusion
Deform-3D FEM software was adopted to simulate direct extrusion and ES processes with different extrusion ratios, billet preheating temperatures, extrusion speeds, and friction coe cients between the blank and die. The simulations involve extruding forces, strain elds, velocity elds and temperature elds during the ES process. Extrusion experiments and microstructure observations were performed under the same simulation conditions.
(1)The extrusion pressure changes with the structures of the ES die. There are two platforms in curves of load-time. Extrusion forces decrease with increasing extrusion temperatures, decreasing extrusion ratios, increasing die channel angles and decreasing friction coe cients.
(2) The metal ow velocity distribution in different zones of the ES die was observed through simulation, and metal ows were restricted by the die structures of the ES process.The ow velocities of metal in the ES die increase with the development of the ES process.However, the ow velocities of the metal at the rst turning corner decreased because the second corner exerts back pressure on the metal. Increasing the channel angles and reducing the friction factors would increase the out ow velocities of metal,but it has little effect on the uniformity of metal ow.
(3)The temperature eld changes with different friction conditions and different extrusion speeds were analyzed. The increase in friction and extrusion speed would increase the temperatures of the ES die. If the preheated billet temperature is higher, the temperatures of the ES die would be higher, but the amplitude of the temperature rise would decrease.
(4) The ES process can prepare ner and more uniform microstructures than those prepared by direct extrusion under the same conditions. Declarations Acknowledgment This work was supported by The Chongqing talent plan (CQYC202003047),and the Chongqing Natural Science Foundation Project of cstc2018jcyjAX0249 and cstc2018jcyjAX0653 ).

DECLARATIONS -Ethical Approval
No animals have been used in any experiments.

-Consent to Participate
There were no humans who were used in any experiments.

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The Author con rms: that the work described has not been published before (except in the form of an abstract or as part of a published lecture, review, or thesis); that it is not under consideration for publication elsewhere; that its publication has been approved by all coauthors, if any; that its publication has been approved (tacitly or explicitly) by the responsible authorities at the institution where the work is carried out.
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After submission of the agreement signed by the corresponding author, changes of authorship or in the order of the authors listed will not be accepted by Springer. Hongjun Hu is the corresponding author of this paper who wrote the paper.
Ou Zhang done the experiments in this paper.
Huiling Zhang done the simulation in this paper.
Hui Zhao done the testings in this paper.
Dingfei Zhang researahed the microstructure analysises in this paper Zhongwen Ou researahed the microstructure analysises in this paper -Funding This work was supported by the Chongqing talent plan (CQYC202003047),and the Chongqing Natural Science Foundation Project of cstc2018jcyjAX0249 and cstc2018jcyjAX0653 ).
I con rm that I have mentioned all organizations that funded my research in the Acknowledgments section of my submission, including grant numbers where appropriate.

-Competing Interests
The authors declare no competing non nancial/ nancial interests.
-Availability of data and materials The raw/processed data required to reproduce these ndings cannot be shared at this time as the data also form part of an ongoing study.