Study on magnetic pulse crimping process for joining large-diameter aluminum alloy tube/magnesium alloy shaft

A structure for joining 6061T6 aluminum alloy tube and AZ31B magnesium alloy shaft via the magnetic pulse crimping process was proposed. The forming process, mechanical properties, failure modes, and corrosion behaviors of the joint were studied. The results showed that the enormous Lorentz force drove the wall of aluminum alloy tube to move towards the groove of magnesium alloy shaft at high velocity, thus realized mechanical locking and formed joint. Through torsion tests, it was found that the mechanical properties of the joint with different process parameters varied. There were two failure modes for joint: torsional separation and torsional crack. Specifically, discharge time, groove angle, and discharge energy for torsional crack were, respectively, 1, 90°, and 28 kJ and 3, 90°, and 25 kJ. The maximum torque was up to 961.99 N·m under discharged twice, 90° groove angle, and 25-kJ discharge energy. Through neutral salt spray corrosion tests, it was found that the maximum torque only decreased by 28.03% after corrosion for 192 h. It indicated that the corrosion resistance of joint was good relatively.


Introduction
In recent years, with the increase of vehicle ownership, the danger of energy consumption and greenhouse effect is increasing [1][2][3]. Vehicle lightweight could not only conserve energy and reduce emission, but also improve handling and comfort, which is an important development trend of the vehicle manufacturing industry [4][5][6][7][8]. Using light metals such as aluminum alloy and magnesium alloy instead of steel is a direct and effective way to reduce the weight of vehicle [9][10][11][12]. Meanwhile, there are a large number of shaft and tube parts in vehicles, such as transmission shafts and seat frames. Under the background of lightweight manufacturing, the vehicle industry is facing a new challenge, that is, the joining of shaft and tube parts made of dissimilar materials.
The traditional joining processes of shaft and tube parts include fusion welding, bolting, riveting, and bonding [13][14][15][16]. Fusion welding is used widely in vehicle manufacturing, while it is difficult to form reliable joint due to the existence of inter-metallic compounds caused by the difference of chemical properties of dissimilar materials. Bolting and riveting can get excellent joint without heat input, but the additional fittings increase assembly costs and structural weight. The applicability of bonding is wide, and the stress distribution of the joint is uniform; there are also some defects such as great environmental impact on properties, low peeling strength, and easy aging of joint. There are some limitations of above-mentioned processes in the application of joining of shaft and tube parts made of dissimilar materials under the background of lightweight [17][18][19][20][21].
Magnetic pulse crimping (MPC) is a process to realize reliable joining of dissimilar materials by using Lorentz force in electromagnetic field. Weddelling et al. [22] explored the influence of various groove geometries on the strength of MPC joint. The strength of joint obtained via triangular groove was weaker than that obtained via 1 3 rectangular and circular groove with equivalent dimensions. The strength of the joint could be improved by increasing the discharge energy or reducing the width of groove. Hanse [23] established the finite element model of quasi-static tensile failure of the three-groove MPC joint in LS-DYNA ® . He explored the influence of friction on the tensile strength of the MPC joint. It was found that the friction between the inner tube and the outer tube would affect the tensile strength of the joint greatly. Finally, the correctness of simulation results were verified by experiments. Park et al. [24] studied two typical joints of MPC: those were joint with better tensile property and joint with better torsional property. They analyzed the force and deformation of the outer tube during the electromagnetic forming theoretically. Meanwhile, the influence of the various parameters of the groove on the strength of the joint combined with experiments were also investigated. Faes et al. [25] studied the MPC joint with double-groove structure. It was found that when the depth was smaller and the length was larger of the first groove, the diameter between the two grooves was less than the outer diameter of the inner tube. The joint could get the best tensile properties. Cui et al. [26] proposed a structure of 5A02 aluminum alloy and CFRP tube joined by MPC and magnetic pulse welding (MPW). They adopted a "sandwich" structure, which the CFRP tube was sandwiched between the 5A02 aluminum alloy outer tube and the 6061T5 liner tube. The outer tube was deformed by Lorentz force, and then passed through the three prefabricated holes on the CFRP tube. Finally, it hit the liner tube at high velocity to realize the joining. In general, MPC have been used in the connection of aluminum alloy/aluminum alloy or aluminum alloy/steel, while few investigations have been performed on joining large-diameter aluminum alloy/magnesium alloy shaft and tube parts using it so far, and the influence degree of corrosive environment on the mechanical properties of aluminum alloy/magnesium alloy MPC joint has also not yet been explored.
In this work, the purpose is to investigate the joining process, mechanical properties, failure modes, and corrosion resistance of MPC joint between large-diameter aluminum alloy tube/magnesium alloy shaft. Firstly, numerical simulations were performed with LS-DYNA ® , and the accuracy of the model was verified. Subsequently, torsion tests were conducted after MPC experiments, the morphologies of the joint were observed, and failure modes were analyzed. In addition, the macroscopic corrosion behaviors of the joint were observed, and the influence of corrosion to torsional failure modes were discussed. Finally, the corrosion resistance of the joint was measured quantitatively by the value of torque. This work could offer a reference for the application of lightweight metals in the vehicle manufacturing industry.

Material preparation
Aluminum alloy tube and magnesium alloy shaft were used. The designation of aluminum alloy is 6061, and the heat treatment state is T6. The outer diameter, inner diameter, and length are 70 mm, 67 mm, and 100 mm, respectively. The designation of magnesium alloy is AZ31B, the outer diameter is 67 mm, and the length is 30 mm. The length of the overlapping zone of the two parts is 30 mm. The element compositions of the two materials are shown in Table 1.
In order to reduce the cost of this work, the structural assembly was simplified, and the length of aluminum alloy tube and magnesium alloy shaft was reduced, only retained the joining part. The length and depth of groove is 30 mm and 3.5 mm. The radius of top fillet R1 and bottom fillet R2 is 1 mm and 2 mm. The groove angle α is 90°, 120°, and 150° in different experiment groups, respectively. Figure 1 shows the simplified structural assembly and relevant dimensional parameters. The burrs of the specimen were polished by 1200-mesh fine sandpaper, and then oil stains were removed by ultrasonic cleaning equipment to cleaning for 5 min prior to assembly.

MPC experiments
The MPC system in this work mainly included control cabinet, capacitor cabinet, and cable, as shown in Fig. 2(a). The maximum discharge energy, voltage, self-frequency, and capacitance of the system is 48 kJ, 16 kV, 100 kHz, and 408 μF, respectively. The main structure of the MPC tool included coil, field shaper, and support block, as shown in Fig. 2(b). The capacitor cabinet emitted pulse current and led it into the coil through the cable, resulting in induced eddy current in the field shaper. Under the action of electromagnetic induction and skin effect, eddy current and Lorentz force were generated on the surface of the aluminum alloy tube close to the field shaper. The wall of aluminum alloy tube was embedded into the groove of the magnesium alloy shaft by Lorentz force, so that realized mechanical locking.   In this work, all experiments were under the control of single variable. The groove length L, groove depth D, groove number N, top fillet R1, and bottom fillet R2 of magnesium alloy shaft constant were kept. Meanwhile, the angle α of the groove, discharge energy, and discharge time in turn were changed. The discharge energy was 22 kJ, 25 kJ, and 28 kJ, and the discharge time were 1, 2, and 3 (processed once, twice, and thrice times at the same position repeatedly). The designed experiment groups are shown in Table 2.

Torsional performance test methods
Torsion tests were performed on SUNS TTM 303 electronic torsion testing machine at torsion speed of 10°/min, as shown in Fig. 4. The test standard was GB/T 10128-2007 Room Temperature Torsion Test Method for Metallic Materials. A square hole in the middle of the magnesium alloy shaft was made and a square steel was inserted to clamp the specimen effectively; the length of the matching zone was 30 mm. The other end of the square steel was clamped on the four-jaw chuck of the torsion testing machine. The end of the aluminum alloy tube was supported by steel plug to avoid the influence of deformation and slipping on the result.

Numerical models
In the process of MPC, the huge Lorentz force made the incredible deformation velocity of the specimen, and the process was completed in several microseconds. Therefore, it was difficult to analyze the entire process of MPC only by theoretical calculation; the assistance of numerical simulation technology was needed. The coupled electromagnetic and mechanical model was established in LS-DYNA ® . The model included 11,268 units and 11,268 nodes for the coil, 14,464 units and 17,226 nodes for the field shaper, 33,000 units and 44,880 nodes for the aluminum alloy tube, and 3462 units and 4536 nodes for the magnesium alloy shaft. Figure 6 shows the assembly structure and dimensional parameters.
The parameters such as yield stress, strength limit, and elongation of the materials would change at high strain rate [27]. Therefore, a constitutive model to describe the mechanical properties of the material within this strain rate range was necessary. Johnson-Cook model (J-C model) could describe the constitutive relation of materials at high strain rate accurately, which was widely used in the analysis of  where δ is the equivalent strain; n is the hardening coefficient, which indicates the degree of stress change when the material is hardened; ε is the reference strain rate; ̇ is the equal effect speed change rate; ̇0 is the reference strain rate; A is the inherent stress value of the material measured at the reference temperature; B, C, and m are the constants calculated by fitting the measured strain without strain rate; and T * is the dimensionless temperature. Since the MPC is completed in microsecond time, the temperature of specimen changes little; the temperature correction part (1 − T *m ) in J-C model is ignored. The J-C model parameters of aluminum alloy are shown in Table 3 and the material parameters of each part in the model are shown in Table 4.
The time-current curve was obtained by Rogowski coil, which was converted into EM model in LS-DYNA ® . Figure 7 shows the Rogowski coil used in this work and the time-current curves at discharge energy of 22 kJ, 25 kJ, and 28 kJ.

Verification of models
To verify the accuracy of the finite element model, the deformation velocity of aluminum alloy tube was measured by Photonic Doppler Velocimeter (PDV). In this system, a laser was aligned normal to aluminum alloy tube, which reflected off the surface with a shifted frequency. The frequency shift was proportional to the velocity of aluminum alloy tube  [29]. Figure 8 shows the schematic of PDV test. PDV tests were performed at discharge energies of 22 kJ and 25 kJ, respectively; the displacement-velocity curves are shown in Fig. 9(a). With the increase of discharge energy, the velocity of aluminum alloy tube increased in the deformation process. When the deformation of aluminum alloy tube was 3.5 mm, the maximum velocity at discharge energy of 25 kJ was 271.53 m/s, which was 8.4% higher than 250.50 m/s at 22 kJ. The velocity of the aluminum alloy tube at discharge energy of 25 kJ measured by PDV test was compared with the simulation data, as shown in Fig. 9(b). Although the curves did not overlap completely, the deviation was minimal, the maximum velocity of the simulation was higher than that measured by the PDV test slightly, and the error was just 3.48%. Thus, the finite element model established in LS-DYNA ® was accurate for MPC relatively. Figure 10 shows the comparison of macro-morphology of joint between experiment and simulation. Good consistency could be obtained in the comparison of macro-morphology viewed from the end presented in Fig. 10(a). Figure 10(b) shows the comparison of the distance from the bottom of the groove to the two measuring points. It could be seen that the distance of the two points in the experiment and simulation was similar. Specifically, the error of point 1 was just 9.72%. The distance of point 2 in experiment was 1.672 mm, which was 19.34% higher than 1.401 mm in simulation. Generally, both errors were within 20%. The consistency of macro-morphology verified the reliability of the finite element model further.

Joining process analysis
The joining process was explored from the current density, magnetic induction intensity, Lorentz force, and deformation of aluminum alloy tube. Figure 11 shows the current density distribution of the aluminum alloy tube at the moment before deformation (t = 16 μs) at discharge energy of 25 kJ. There was the current I 2 on the aluminum alloy tube opposite to the current I 1 of the field shaper, which resulted in Lorentz force to deform the aluminum  alloy tube. The current density near the center of field shaper was stronger than that at both sides, and the current density decreased from outside to inside along the wall of tube due to the skin effect. The gap between the two field shapers also caused the current density of the aluminum alloy tube in this zone to be slightly weak. Figure 12 shows the variation law of current density of the outer surface of aluminum alloy tube at six important moments at discharge energy of 25 kJ. The variation law could be divided into three stages. In the first stage, the current density increased with the time, kept the law that the zone near the field shaper was the strongest, and decreased to both sides. In the second stage, although the pulse current was still increasing, the increasing speed of current density reduced due to the aluminum alloy tube was far away from the field shaper by inward contraction. In the third stage, as the current in the coil decreased, the induced current density also decreased until the end of the simulation. The distribution and variation law of magnetic induction intensity at discharge energy of 25 kJ were similar to that of current density extremely, as shown in Figs. 13 and 14.     Fig. 15(b). The maximum Lorentz force appeared on the surface of the aluminum alloy tube located in the position without grooves. This was caused by its inconspicuous deformation led to closer distance from the field shaper. When t > 25.3 μs, with the further increase of distance and the decrease of pulse current, Lorentz force also decreased until the end of simulation.
In order to observe the deformation of the aluminum alloy tube conveniently, two sections were selected as shown in Fig. 16(a). Section 1 was the radial section and section 2 was the axial section, wherein the radial section was located in the middle of the field shaper. Figure 16(b) shows the deformation of the aluminum alloy tube at six important moments for section 1 and section 2 at discharge energy of 25 kJ. At the beginning (t = 16 μs), the deformation of the aluminum alloy tube on the section 1 was more uniform. While, the deformation near the field shaper zone was more and decreased to both sides on the section 2. From the beginning of deformation until the inner wall of aluminum alloy tube touched the groove (t = 16~32.1 μs), the deformation law was similar to that before. The maximum deformation occurred in the red part, and the central part first collided with the surface of the magnesium alloy shaft. As the deformation continued (t > 32.1 μs), the collision zone between aluminum alloy tube and groove increased, from single collision point to circular collision surface. It could be found in section 1 that the aluminum alloy continued to deform until both ends were filled with groove. Aluminum alloy tube rebounded due to the reactive force generated after high-velocity collision with the bottom of the groove (35 μs). Because the displacement of the first collision zone was the largest and the acceleration was the most sufficient, the collision velocity was also the highest. Therefore, the position where the rebound first occurred was the position where the collision first occurred too, the rebound degree was also the largest, and the rebound zone increased with the simulation. Throughout the simulation (t = 0~35 μs), the function of collecting magnet for field shaper could enhance the electric field and magnetic field significantly. Therefore, the large deformation always appeared near the zone of field shaper, both in radial and in axial direction.
When the system energy was released, the oscillating decay current was generated in the circuit. The generated magnetic field could be expressed by Eq. (2) through Maxwell equations.
where H is the magnetic field intensity and J is the totalcurrent density. The magnetic induction intensity B can be expressed by Eq. (3).
where μ is the permeability. According to the research of Psyk et al. [30], Lorentz force can be expressed by Eq. (4).
As shown in Fig. 7, it had been measured by Rogowski coil that the peak current increased with the discharge energy. The increase of peak current resulted in the increase of maximum current density, maximum magnetic induction strength, and maximum Lorentz force. In addition, the deformation velocity of aluminum alloy tube would increase due to the increase of Lorentz force. Maximum current density, maximum magnetic induction intensity, maximum Lorentz force, and time to reach the maximum deformation (3.5 mm) at three different discharge energies (22 kJ, 25 kJ, and 28 kJ) are shown in Table 5. The simulation results were consistent with related theories.

Torsion test analysis
It could be found that the essence of MPC joining in this work was to lock the magnesium alloy groove by the deformation of the aluminum alloy tube mechanically. The torque of the joint mainly depended on two forces. The one was the friction force on the circumferential contact surface between aluminum alloy tube and magnesium alloy shaft. The other one was the normal force between tube and groove wall of shaft. Table 6 shows the maximum torque and failure modes of the joint at different experiment groups. When the angle α was same, with the increase of discharge energy or discharge time, the torque increased first and then decreased. This was because the low discharge energy (lesser discharge time) could not cause effective deformation, the friction force and normal force were not enough to resist torsion. High discharge energy (more discharge time) increased the deformation of the aluminum alloy tube, effective joining area and stressed zone between two alloys. However, excessive discharge energy (discharge time) would cause too much wall thickness reduction of the aluminum alloy tube at the top fillet R1 and then the strength reduced. Generally, as the angle α increased, the maximum torque of the joint decreased; this was because the effect of the normal force decreased with the increase of angle α. Figure 17 shows the typical failure modes of MPC joint. The failure mode in Fig. 17(a) is torsional separation, which involves the part of the aluminum alloy tube embedded in the magnesium alloy groove twisted out after plastic deformation in the torsion process. The failure mode in Fig. 17 16 Deformation of aluminum alloy tube: a sections for deformation observation of aluminum alloy tube and b deformation of aluminum alloy tube at different moments is torsional crack, which involves the aluminum alloy tube torn at the joint during torsion. Figure 18 shows the torsion process of the joint. The plastic deformation of the aluminum alloy tube occurred first at the top fillet. When the discharge time was few (the discharge energy was low), the thickness reduction rate of aluminum alloy at the top fillet was low; the plasticity and toughness of it was still good. Aluminum alloy tube in deformation zone would be pushed outward by the groove until it was completely separated from the groove. The normal force and part of friction force would be lost, resulting in decrease of torque and failure of torsional separation. When the discharged time was 3 (the discharge energy was 28 kJ), the thickness reduction rate of aluminum alloy at the top fillet was much; the toughness of it decreased greatly. Tearing occurred at just less torsion deformation, which led to failure prematurely. This explained why torsional crack occurred in Group 4 and Group 5. Figure 19 shows the macro-morphology of the joint at different discharge times when the discharge energy was 25 kJ and the angle α was 90°. The areas of the maximum deformation zone and the completely fitted zone increased with the discharge time, and the proportion of the completely fitted zone also increased. Figure 20 shows the angle-torque curves of the joint at different discharge times. It could be observed that the increase rate of torque increased with the discharge time. However, the maximum torque under discharged thrice was lower than that under discharged once and twice. The difference of the angle-torque curves could be analyzed. At the beginning of torsion, there was slight elastic deformation on the aluminum alloy tube. With the rotation angle increased, the friction force and the normal force hindered torsion together, resulting in the increase of torque. Combined with the macro-morphology of the joint shown in Fig. 19, the areas of the maximum deformation zone and the completely fitted zone increased with the discharge time. The expansion of the mechanical joining zone resulted in the increase of friction force and normal force. This explained why the increase rate of torque increased with the discharge time. However, joint

Salt spray corrosion behavior analysis
In order to obtain high-strength joint on the premise of reducing cost, the specimens for corrosion test were obtained with the discharge energy of 25 kJ, angle α of 90°, and discharged once. Figure 21 shows the macro-morphology changes of the joint after neutral salt spray corrosion in different cycles. Aluminum alloy and magnesium alloy gradually lose their metallic luster during corrosion. The off-white flocculent corrosion products of magnesium alloy first appeared at the end of joint, increased with time. Then, they flowed down the outer wall of aluminum alloy tube and remained on it partially, mixed with corrosion products of aluminum alloy. In addition, some yellowish-brown layered corrosion products appeared at the interface between the two alloys due to galvanic corrosion [31]. The end of the joint was horizontal plane and with grooves. Compared with the outer surface, the end was more conducive to the retention of salt solution for promoting corrosion. Therefore, corrosion at the end of aluminum alloy was more serious than that at the outer surface.
Specifically, there were a number of corrosion pits at the end, while no obvious corrosion pits were found at the outer surface. Figure 22 (a) and (b) show the failure modes of corroded joint, all of which were torsional crack, while the torn parts The mechanism of failure mode A was the same as that of uncorroded joint. Failure mode B appeared at the end of the aluminum alloy tube. As mentioned previously, corrosion at the end of aluminum alloy was more serious than that at the outer surface. This phenomenon was more obvious with the increase of corrosion cycle. In addition, the crevice between two alloys at the end of the joint evolved into sealing zone, resulting in high concentration of chloride salt in it. The chloride salt reduced pH value after hydrolysis and accelerated corrosion at the inner surface of the aluminum alloy [32]. Therefore, with the high cycle corrosion, the strength of the aluminum alloy at the end decreased much more seriously than that in other zones, which led to the failure occurred at here firstly. Figure 22(c) shows the torque of the joint after salt spray corrosion. At the initial stage of corrosion (24 h), the torque of the joint decreased to a certain extent (10.42%) due to the damage caused by corrosion. At the middle stage of corrosion (96~144 h), the torque decreased slightly (12.69~14.43%). It was because Al 2 O 3 films formed on the surface of aluminum alloy, which hindered the contact between aluminum alloy and salt solution, the corrosion was slowed down temporarily [33]. At last (192 h), a large amount of Cl − was electrolyzed from salt solution. The Cl − penetrated the Al 2 O 3 film and destroyed the aluminum alloy matrix, transforming insoluble oxides into soluble chloride [34,35]. The corrosion area and depth of aluminum alloy were further increased, so that increased the corrosion rate and torque decreasing rate (28.03%).

Conclusions
In this paper, a MPC process was proposed for joining largediameter aluminum alloy shaft tube and magnesium alloy shaft by forming. The forming process, mechanical properties, failure modes, and corrosion behavior of the joint were studied by numerical simulation and experiment. The main conclusions were as follows: (1) The coupled electromagnetic and mechanical model was established. Deformation velocity of aluminum alloy tube and macro-morphology of joint showed that the finite element model was accurate. It demonstrated  that the model could effectively analyze the forming process of MPC joint. (2) MPC could be used to realize the joining between largediameter aluminum alloy tube and magnesium alloy shaft. There were two failure modes of joint, torsional separation and torsional crack. Failure of torsional crack only occurred at discharge time, groove angle, and discharge energy was, respectively, 3, 90°, and 25 kJ and 1, 90°, and 28 kJ. Failure of torsional separation occurred at other parameters.
(3) Discharge energy, discharge time, and groove angle α could all affect the torque of the joint. Under the control of single variable, the torque first increased then decreased with the increase of discharge energy and discharge time, while the increase of groove angle α decreased the torque. In the 11 experiment groups, the maximum torque of joint was up to the highest value of 961.99 N·m at discharge time, groove angle, and discharge energy that was, respectively, 2, 90°, and 25 kJ. aluminum alloy tube torn at the side after low cycle corrosion and torn at the end after high cycle corrosion. The corrosion resistance of joint was good relatively. The corrosion resistance of joint was good relatively. Data availability The raw/processed data and material required to reproduce these findings cannot be shared at this time due to technical or time limitations.