Thin-Walled Tube Made of AZ31 Magnesium Alloy Fabricated by New Compound Extrusion Including Direct Extrusion and Multi-pass Bending

A new severe plastic deformation for manufacturing thin-walled tube made of AZ31 magnesium alloy called TEB(Tube-Extrusion-Bending ) process, which combines direct extrusion with two step bending,has been developed to manufacture tube.The TEB process has been researched by using nite element modeling (FEM) method. The rules of extrusion temperatures and the extrusion forces varying with process parameters have been developed. A TEB process with installed containers and dies has been constructed to perform tests in order to validate the FEM model with different process conditions. And the microstructures evolution have been researched based on effective strains evolution. The results showed that rened and uniform microstructures can be achieved by TEB process. The research results showed that the TEB process would produce the serve plastic deformation and improve the recrystallization of the grains.The comparisons of FEM simulation and experimental results have been made to obtain the relative important principles of TEB process.


Introduction
Magnesium alloys are widely used in aerospace and automotive industry because of their considerable reserves in the earth's crust and the ocean, and their advantages are light weight, high speci c strength, good thermal and electrical conductivity, and good electromagnetic shielding effect [1][2] . Structural lightweight is an important means to achieve weight reduction and e ciency improvement of aerospace and other national defense equipment, energy conservation and emission reduction of transportation vehicles and improve maneuverability.Magnesium alloy is known as "21st century green engineering metal", the country should vigorously develop magnesium material industry, magnesium material is one of the few materials that can lead the world; In order to promote the mature development of magnesium metal e ciently, alloy design, deformation processing, especially the proportion of standard structure products in deformation processing should be promoted [3][4] .
Magnesium industry vigorously promotes the structure products of transformation to high value-added deep processing products,and focus on meeting the needs of large, porous, special-shaped and hollow magnesium alloy pro les and supporting parts, instrument panel beam skeleton assembly for transportation, such as automobiles, rail trains and high-speed trains. It mainly meets the requirements of thin-walled hollow magnesium alloy pro les with high strength, toughness, high temperature, corrosion resistance, fatigue resistance, high precision and high electromagnetic shielding performance for aerospace and national defense. The development of magnesium alloy mainly focuses on the extrusion pro les for aerospace and transportation. The hollow pro le of magnesium alloy can further reduce the weight of the structure, and has a good application prospect in automobile instrument panel, seat, bumper, radiator bracket, engine bracket and other structural parts. It is signi cant to produce a high strength magnesium alloy pro le to replace structural materials such as steel and aluminum.As a hollow pro le, high-performance magnesium alloy thin-wall tube(wall thickness 1-5mm) is widely used in national defense and transportation elds.With the wide application of magnesium alloy pro le, the performance demand of thin-walled magnesium alloy tube is increasing day by day. The new magnesium alloy tube forming will become one of the new research hot spots.
In recent years, serve plastic deformation (SPD) methods such as equal channel angular extrusion (ECAE) which processed bulk nano-structure materials have attracted the growing interest of specialists in materials science. One phenomenon observed in the case of AZ31 magnesium alloys are the DRX (Dynamic recrystallization) and DRV (Dynamic recovery), which could improve the work ability of the material at elevated [5][6][7] .But the ECAP process is only used in the laboratory scale processing and preparation for nanocrystalline material, there exits an unbridgeable gap between the experiments and industrial applications. The productivity of ECAP in industrial manufacturing is very low, ECAP usually involves a large number of steps and is not easily applied from the laboratory to an industry for it is not a continuous process, but the dimension of extruded rod is the same as the initial billet. Although it has been invented in the early 1980s, the process did not progress as much as one would desire and is still con ned to the laboratory scale experiments [8][9][10] .
Direct extrusion is one of the most basic deformation methods in the traditional extrusion process. It has the characteristics of simple die structure and convenient operation. However, there is uneven strain from the core to the surface, which makes the microstructures and properties of the surfaces and middle layers of the extruded product unstable. Magnesium alloy tubes are extruded along the extrusion direction,and banded structure and strong basal textures would be formed, and the textures are not conducive to secondary processing of tube, such as the internal high pressure forming, heat bending, etc.This kind microstructures would seriously reduce the quality of magnesium alloy tubes, severely reduce the mechanical properties of magnesium alloys.
Composite extrusion method for AZ31 magnesium alloy have been presented which combines the traditional direct extrusion and the serve plastic deformation ECAP (equal channel anger pressing), that is to say extrusion and multi-pass bendings (one or more than one) are combined.To obtain the deformation mechanisms of new composite extrusion for thin-walled tube fabricated by extrusionbending process has been researched which is shorten as "TEB" in this paper.
The TEB as a continuous extrusion processes may improve the industrialization preparation and processing of tubes. In order to secure a process with a sustainable high level of accuracy, tools must be adjusted and utilized precisely. In addition, process parameters must be checked carefully to ensure a high level of quality in production.
Commercial software DEFORM-3D can be used to assist analysis of TEB process. It is accepted that material properties are closely correlated to the microstructures. Process conditions include some extrusion parameters such as the extrusion speeds, the initial temperatures, and friction and heat transfer coe cients of the billets, container and die and have great effects on the microstructures [11][12] .
To illustrate the potential industrial application of the TEB process, TEB die used in the extrude has been designed, and TEB process has been simulated. The aim of the present study is to reveal the microstructures evolution and clarify the grain re nements mechanism in AZ31 magnesium alloy during TEB process. The present study employs DEFORM ™ -3D nite element software to simulate the loads, temperatures and strain evolution during TEB process. The microstructures of AZ31 magnesium alloy sampled from the extrudes tubes have been observed. Deformed microstructures evolution for AZ31 magnesium alloy have been studied in order to analyze the deformation mechanisms of TEB process.

Material models for AZ31 magnesium alloy
A thermo-viscoplastic material models have been used for the billet, and thermo-rigid material for the TEB dies have been applied. The ow stress-strain data of the AZ31 magnesium alloy were determined through hot compression tests using Gleeble1500D machine. A set of ow stress-strain curves include the experimental data over a temperature range of 250-550℃ and a strain rate range of 0.01-10s − 1 have been used. The ow stress data have been implemented in the commercial FE code DEFORM ™ . The dislocation density is treated as an internal state variable and it is computed by numerical integration of the evolution equation [13][14][15] .Microstructures observations have been carried out by using PME OLYMPUS TOKYO-type optical microscope.

Simulation conditions
The description of the physical model includes the material properties of the billet, the forming temperatures,and the friction coe cients between the concave die and the workpiece,punch and die. AZ31 magnesium alloy have been used in the simulation and extrusion experiments. The extrusion tooling consisting of die, container and ram have been made of the H13 hot-work tool steel. The physical properties of AZ31 magnesium alloy are given in Table.1. Schematic of TEB process is shown in Fig.  1.Extrusion equipment and extrusion die and mandrel and extruded tube are shown in Fig. 2.The billets and the dies of experiments have identical geometrical parameters and materials with those in simulations. The AZ31 magnesium alloy should be preheated, the ram and the lubricated dies in the furnace have been heated for 2 hours before the actual TEB process. The TEB process is then employed to manufacture the AZ31 magnesium alloy tubes. Real extrusion experiments have been carried out by employing a 200 ton press with a resistance heated container and heaters which are shown in Fig. 2b.
The die material, die dimensions, billet dimensions and extrusion conditions are all the same as those used in numerical simulation as described in Table 2. The physical property of AZ31 magnesium alloy is given in Table 1. Simulation and experimental parameters are shown in Table 2.

Temperature evolution
During the TEB process, temperature eld is affected by many parameters which include initial billet temperatures, TEB speeds, extrusion ratios, and friction coe cients between the billet/die.Even the extrusion of simple rods is a complex process involving highly inhomogeneous deformation and high strain rates. The heat generated by the plastic deformation and friction would increase the temperatures of the tubes signi cantly, and in turn affect the microstructures and mechanical properties.Because TEB process is a non-linear process involving high inhomogeneous deformation and high strain rates, it is di cult to predict the temperatures of billet accurately [18][19] .
TEB process is divided into multistage according to material ow. Firstly, the tube billet is compressed, and initial tube billet is compressed into the die entrance. Secondly, the extruded tube is formed. Thirdly, the formed tubes are bent consecutively. There is no literature reported to predict the ow patterns of TEB process. Slip-line elds or upper bound approaches have been utilized to predict the ow patterns. But a constant value for the ow stress is assumed by the upper bound approach. The problem can be solved by numerical simulation with the development of three-dimensional FEM. In this study, the material ow during the extrusion process is demonstrated clearly by simulation [20][21] . Comparison of the temperature distributions at these two positions demonstrates the thermal characteristics within the billet, and the heat transfer from the deformation zone in front of the die towards the outsides of the tube billet. Fig.3a shows that the temperatures of the tube billets at the beginning of the process are various and below the initial billet temperature 400℃ if heat is produced in the extrusion zone and temperature gradients are formed. Obviously, this is due to heat loss to the TEB die. The heat ow along the radial direction and the axial direction in the tube billet. It is apparent that heat has already been conducted toward the periphery and the rear end of the billet.Temperatures for about a half of the billet below the initial billet temperature in Fig.3b, the reason is the result of time available for continuous heat loss to the TEB die and through the die the ambient surround.
The temperature evolution in the billet (initial temperature 400 ℃) as the TEB process proceeds steady state is shown in Fig. 3. It is clear that temperatures of rod surface decrease continuously with development of TEB process. The factors to decrease temperature during the TEB process are heat transfer from die and punch, frictions between the rod material and die, and plastic deformation during the TEB process [22] .
It is noticed that the difference increases of maximum temperature predicted by the nite element simulations are not signi cant. It is uniquely founded that the decrease of the maximum temperature is not change signi cantly. The reason for the temperature reduction is mainly due to temperature gradient between the die and tube billets. Since the temperature rise depends on the heat generation within the deformation zone. Heat generation depends on the internal power of deformation and frictional power.
Variations of different parameters affect the power constituents which affects the heat generation within the deformation zone. Higher surface temperatures may cause surface cracks and tears for higher surface temperatures would decrease the tensile strength of the AZ31 magnesium alloy.

Load-stroke curve of TEB process
TEB process is a hot working process, the AZ31 magnesium alloy may be heated over recrystallization temperature. TEB process could be done on hydraulic presses that range from 100 to 11,000 metric tons. As a result of FE analysis, Fig. 4 shows load-stroke for TEB process which have been obtained from the nite element simulations with initial temperature of 400 ℃.
The values for maximum extrusion forces are obtained from the nite element simulation by highresolution history plots. The extrusion load curve can be divided into three stages: the extrusion upsetting stage and the direction extrusion stage and continuous shears stage. At the initial stage, the load increases slowly during upsetting stage. When contacting with die channels, the tube is subjected to serve plastic deformation. The load increased rapidly to the rst maximum load and the value is about 1 ton,the force of this stage is not steady .But the load increases rapidly due to the work hardening which result from the continuous accumulation of dislocations and the values of extrusion forces are almost equivalent. The Increments of forces become slowly after 2.5 s,and TEB process is in the steadystage,and the values of extrusion forces are varying periodically. The load-stroke curves could exhibit the characteristic of strain softening with a peak stress to a steady state regime, which is a typical phenomenon caused by the dynamic recovery or recrystallization.

Strains evolution of TEB process
The distributions of strain in Fig. 5 show that the strain distribution is relatively steady throughout the whole extrusion cycle from the direct extrusion to the multi-step bending deformation. In order to gain the deformation characteristics of tube billets for TEB process, the predicted effective strains provide quantitative insight into the deformation behaviors of tube billet during TEB process. Figures in Fig. 5 show the effective strains contours of tube billets, which provided the important information regarding the effective strains distribution. The strain distributions for deformation ways of billets are signi cantly different. The Fig. 5a shows the strain distributions for direct extrusion when extrusion times are 1.67s,and strain distribution is characterized by symmetry along the extrusion axis.
Distributions of the strain are lamellar with distinct deformation gradients after the rst bend of TEB process in the Fig. 5b. The deformation of this zone is close to the simple shear deformation in the extrusion time 1 s. The maximum strain increase from 2 to 3. From the strain evolution during the TEB process it can be found that the strains increase with the TEB process progressing, the reason is that the dynamic recrystallizations take place. Figure 5c and Fig. 5d indicate the strain distributions when extrusion times are 2.68s and 3.03s respectively.It can be found that the minimum and maximum strains increase by comparing with the values caused by direct extrusion in the Fig. 5a and Fig. 5b, and the effective strains increase obviously. It indicates that the largest strains exist in the corner region, where the simple shearing occurs.The TEB process would increase the cumulative strains enormously by comparing with the direct extrusion. The serve plastic deformation can be obtained by two bending. The distribution patterns are very similar in spite of the fact that the actual values are somewhat different.
The principle of TEB process is to introduce compressive and accumulated shear strains into the samples. The characters of TEB process are that the sample is subjected to two bending. Accumulative strain is introduced by reduction in the cross sectional area. ECAE produces signi cant deformation strains without reducing the cross sectional area. The accumulative strains of TEB process include accumulative strain of direct extrusion and two continuous bending [23]. The TEB dies are completely lled in the case of perfectly plastic material. The multiple bending of the TEB process produce a systematic increase of deformation, leading to a successive decrease in grain size by means of forming a grid of rst low-angle and then high-angle boundaries. Maximum strains in the whole workpiece are seen in the plastic deformation zone. Fig.6 shows the microstructures in three parts within formed tube prepared by TEB process.. The use of TEB process, the average grain size can be changed from 100μm to 10μm; the microstructures were not only clearly re ned but also relatively uniform. This is because the TEB process includes additional two bending. So that the deformation degree of central part of rods increased, the part recrystallization occurred. Therefore, the microstructures became smaller and more homogeneous.

Microstructures observation
The relationship between the average recrystallization grain size (d) and the Zener-Hollomon parameter (Z) during dynamic recrystallization is given by equation (4).
-lnd = A + Bln Z (4) Where έ is strain rate, Q is the activation energy for the deformation, T is the temperature and R is the gas constant, A and B are constant.
Dynamic recrystallization (DRX) is one of the interesting mechanisms of microstructure evolution [24] . Grain re nement could be attributed to continuous dynamic recrystallization which involves a progressive increase in grain boundary disorientation and changes of low angle boundaries into high angle boundaries. The Zener-Hollomon parameter (Z) of rst direct extrusion is equal to Z 1 , v 1 is the extrusion speed. λ is the extrusion ratio, R 1 is the billet radius.
And the Z parameters of rst and second shearing are Z 2 Z 3 respectively.
Where inner corner angle (Φ), outer corner angle (ψ). V 1 is the speed of extruded rods. R 2 is radius of extruded rod.
Based on the present TEB process with extrusion temperature 400℃, from the Eq. (4) to Eq. (6) it can be found that the accumulative strain increase with the extrusion advancing, so the grains will be re ned consequently. It is clear that there are four phases recrystallization during TEB process. It can be found that the average sizes of grains for DRX were coarsened with the preheating temperature rise and Z parameter decreases with the temperatures.

Conclusions
Three-dimensional nite element DEFORM software has been utilized to research the plastic deformation behaviors of AZ31 magnesium alloy tube during TEB process.The high temperature region in the experimental process is mainly in the deformation zone.The load-stroke curves could exhibit the characteristic of strain softening with a peak stress to a steady state regime, which is a typical phenomenon caused by the dynamic recovery or recrystallization. TEB-extruded AZ31 magnesium alloy sample could product ne-grained microstructures for TEB process would cause serve plastic deformation and improve the dynamic recrystallization during TEB process. Zener-Hollomon parameters during TEB process showed that the grains of AZ31 magnesium alloy would be re ned gradually. The large strain rates can be introduced into the extrusion and continuous mulit-bending deformation,which would promote the occurrence of dynamic recrystallization of AZ31 magnesium alloy, at the same time reduce or eliminate the defects in the interior of the microstructures.

Declarations Acknowledgement
This work was supported by the National science foundation of china (52071042,51771038), and chongqing talent plan (CQYC202003047),and chongqing natural science foundation project of cstc2018jcyjAX0249 and cstc2018jcyjAX0653 ).

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-Availability of data and materials The raw/processed data required to reproduce these ndings cannot be shared at this time as the data also forms part of an ongoing study. Figure 1 Schematic of TEB process  Curve of load-stroke during TEB process