Forming limit diagrams of AZ31 Mg sheet at elevated temperatures and high strain rates by electromagnetic hybrid forming

Abstract

Weight reduction is a primary concern in the automotive and electrical industries because of the intensive requirements of energy conservation and emission reduction. As the lightest structural metal, magnesium (Mg) alloys are widely used in the automotive and aerospace industries. However, the current industrial application of this material is mainly limited to pressure casting parts due to its poor formability at room temperature. Therefore, identifying the factors that affect the formability of Mg alloy is highly important. In this study, forming limits of Mg alloy sheet under electromagnetic forming (EMF) condition were analyzed at different temperatures based on the Johnson–Cook constitutive model and the failure model. The complete forming limit diagrams of AZ31 Mg alloy at different temperatures and high strain rates were established. The effects of voltage, capacitance, and temperature on the forming limit of AZ31 Mg alloy under EMF were systematically investigated. Results showed that increased discharge voltage and temperature can effectively improve the EMF limit of Mg alloy. The effect of increasing capacitance on the formability of Mg alloy was not obvious.

Keywords

AZ31 magnesium alloy electromagnetic forming warm forming high strain rates forming limit diagrams

1 Introduction

New materials and advanced technologies have been developed and used with the increasing competition in the global automotive industry. Automotive lightweighting has become a mainstream trend of modern design. The application of high-strength steel, aluminum (Al) alloy, magnesium (Mg) alloy, and a variety of composite materials in advanced manufacturing application fields, such as aviation, and spacecraft, is increasing quickly. Friedrich et al. predicted the wide use of magnesium illustrated by example components and projects [1]. As the lightest structural metal, Mg alloy has the advantages of high specific strength, stiffness, vibration damping, and thermal conductivity. Froes et al. reported that Mg alloy also has the advantages of electromagnetic shielding effect and easy recyclability [2]. Manufacturing thin-walled Mg parts by plastic forming is attracting increasing interests of the industrial and academic fields, and a great deal of effort has been exerted to improve the formability of Mg alloy.

The formability of metal sheet is generally defined as the ability of a metal to be formed into the required shape before necking or cracking. Localized necking or fracture occurs when metal sheet deformation reaches a specific limit. Forming limit diagram (FLD) is a very important indicator in metal sheet forming. It reflects the maximum plastic deformation of metal sheet. FLD is widely used in the industry because of its effectiveness in evaluating sheet-forming performance and sheet stamping problem. The FLD concept was first presented by Keeler [3] who came up with the right half of FLD.

Given the difficulty in predicting the necking and rupture of metal sheet, many researchers have attempted to use ductile fracture criterion to predict FLD. Mekonen et al. established a suitable constitutive model of AZ31 Mg alloy through an experimental mechanical characterization [4]. Their model incorporated a rate effect, a thermodynamically consistent based on the finite strain plasticity theory for Mg alloys forming. Kim et al. proposed two failure criteria to predict the fracture behavior of Mg alloy sheets deforming at different temperatures [5]. Wang et al. used Drucker–Prager plasticity to predict the fracture in a rectangular cup drawing for AZ31 alloy sheet [6]. The simulation predictions were in good agreement with the experimental results. The finite element numerical simulation can be used to replace the experimental method and the theoretical calculation to obtain FLD to a certain extent. However, calculation accuracy is the key problem. The accuracy of finite element simulation is influenced by various factors, such as display and implicit algorithm, unit type, mesh size, contact, and material model, of which the material constitutive and failure models are the most important. A reliable material model is the key to obtaining FLD by finite element method.

Chen et al. investigated the FLD, conical cup value (CCV), and bending performance of AZ31 Mg alloy at 100 °C–400 °C [7]. The CCV test results showed that the CCV value decreased initially along with the temperature, but increased when the temperature reached 400 °C. Zhang et al. investigated the warm deep drawing of AZ31 Mg alloy sheet [8]. The results showed that the Mg alloy rolling sheet has excellent plastic deformation ability between the drawing temperature of 120 and 170 °C.

Numerical simulation is the main method used to simulate the metal sheet forming process and analyze the formability. Palaniswamy et al. reported the forming process of an Mg alloy cup and square plate at a certain temperature by nonlinear finite element simulation [9]. The simulation and experimental results both showed that the limit drawing ratio increased with the rise in temperature. Chandrasekaran et al. investigated the effect of temperature on the forward extrusion of Mg alloys [10]. The numerical simulation results and experimental data indicated that AZ31 Mg alloy could be formed at the elevated temperature of 300 °C. Ren et al. reported the numerical simulation of AZ31 Mg alloy drawing and the results showed that the formability of Mg alloy sheet could be improved conspicuously at elevated temperatures [11]. El-Morsy et al. reported the influence of heat conduction on workpieces in AZ31 Mg alloy sheet deep drawing by simulation [12]. Chang et al. also simulated and analyzed the deep drawing process of Mg alloy sheet [13]. Xu et al. investigated the formability of AZ31 Mg alloy sheets in high strain rate conditions and showed that energy efficiency increases from 0.2% (no Al driver sheet) to 1.8% (with a 2 mm Al driver piece) [14]. Berge et al. reported that high punch velocity deformation at 1700 mm/s decreased the formability of AZ31 Mg alloy, which may be attributed to the high amounts of mechanical twinning and constraint of dynamic recrystallization affected by temperature and punch velocity [15]. Overall, the formability of Mg alloy sheet can be improved by warm forming and other forming compound processes. However, the present warm forming technology of Mg alloy sheet is still in laboratory research stage. Lubrication, materials, environmental pollution, forming rate limit, mold strength, and harsh forming technology conditions (e.g., a small adjustable parameter range) are the key problems that must be solved in industrial applications.

The Electromagnetic forming (EMF) technology is a kind of green and high strain rate forming method by the magnetic field between coil and workpiece [16,17]. Daehn et al.’ work indicated the EMF process can not only improve the formability of the metal sheet but also reduce the springback [18]. Li et al. used a 3D numerical simulation method to study on the homogeneity of deformation under electromagnetic expansion of metal tube [19]. Muthukumaran et al. worked on the magnetic pulses for joining of dissimilar materials by experimental and numerical simulation [20]. Chen et al. studied the magnetic force to optimize the process parameters of EMF by ANSYS numerical simulation software [21]. Li et al. used a 3D model to analyze and discuss the EMF process with a drive piece by the combine of ANSYS and ABAQUS software [22]. Li et al. discussed strain state of deformed workpieces under different voltages on EMF [23]. Gies et al. presented an approach for temperature measurement inside the working coil during the electromagnetic forming process [24]. And Cao et al. proposed a method to reduce the Joule heating by the new discharge circuit [25]. Luo et al. claimed that the energy efficiency of work coils would increase with the enlargement of the skin depth in EMF process [26]. You et al. worked on the temperature effect on electromagnetic forming process and indicated that the temperature increasing was significant especially during working cycles [27]. Kim et al. studied the electromagnetic forming process with sequential electromagnetic-structural coupling simulation [28].

Electromagnetic forming is widely used in different materials. Iriondo et al. studied the springback of DP600 and TRIP700 high strength steel (HSS) workpieces by EM shape calibration [29]. Jiang et al. discussed the non-twinning deformation mechanism of pure copper under EMF [30]. Xu et al. investigated the effects of process parameters on AZ31 Mg alloy sheets at room temperature by electromagnetic bulging experiments [31]. Ulacia et al. discussed the potential of Mg sheets to be formed by incremental forming, deep drawing, hydroforming, and EMF methods at warm temperature [32].

In view of the above concerns, the warm and electromagnetic hybrid forming method for Mg alloy sheets was presented, investigated the formability improvement, and established the right half of FLD through an experiment [33]. A constitutive and fracture model for AZ31 Mg alloy in the tensile state was designed [34]. In this work, the ANSYS and ABAQUS software were used to extend the research to an analysis of the deformation and failure process of AZ31 Mg alloy sheets on warm and electromagnetic hybrid conditions. Subsequently, the complete FLD of AZ31 Mg sheets under warm and high strain rate were predicted. Finally, the effects of process parameters (i.e., voltage, capacity, and temperature) on the forming limit of AZ31 Mg alloy under electromagnetic forming (EMF) were discussed.

2 Materials and methods

2.1 Experiment materials

The materials used in the experiments are commercial 1.0 mm thick Mg-based alloy AZ31 sheets obtained by tandem rolling. The sheets were annealed for 1 h at 300 °C. The chemical compositions of the AZ31 alloy sheets are listed in Table 1, while the property parameters are listed in Table 2.

The specimens printed on grids used for measuring forming limit used in experiment were shown in Fig. 1. The Mg alloy sheets were processed into square plates (150 mm × 150 mm) shown as Fig. 1(a) and strips with different widths (20 mm × 150 mm, 30 mm × 150 mm, 40 mm × 150 mm, 50 mm × 150 mm, and 60 mm × 150 mm) shown as Fig. 1(b). The square plates were used to obtain biaxial tensile deformation, whereas the strips were used to obtain information on different stretching and compressive deformation.

2.2 Experimental equipment and tools

A self-developed WG-IV EMF machine (Fig. 2) was used to perform the experiments. The technical parameters of the machine are given in Table 3.

A uniform pressure coil was designed to bulge the square plate workpiece (Fig. 3(a)). The mutual inductance of the strip workpiece was limited by the small coupling area between the workpiece and the coil. The electromagnetic force was not large enough to make the strip workpiece undergo instability or rupture deformation. Thus, the flat spiral coil with copper driver was designed to bulge the strips with different widths (Fig. 3(b)).

The tools for electromagnetic bulging of the square plate workpiece with the uniform pressure coil at different temperatures are shown in Fig. 4(a). The tools for electromagnetic bulging of the strip workpiece with the flat spiral coil at different temperatures are shown in Fig. 4(b). The specimen was placed in the equipment at the beginning of the test. The quantity of heat was provided by the heating rods in the die. The temperature of the specimen was monitored by a real time temperature measuring device (Apuhua TM-902C).

2.3 Material model and analysis method

2.3.1 Constitutive model

An appropriate material model can reasonably predict the EMF and failure process of AZ31 Mg alloy under different temperatures and high strain rates. The failure model can also be used to predict the forming limit of Mg alloy sheet. The Johnson–Cook constitutive and Johnson–Cook failure models from the earlier work of the present authors [34] are used in the analysis to obtain the forming limit.

According to the Johnson–Cook model [35], flow stress is expressed as follows: $\begin{eqnarray}\displaystyle {\sigma}=(A+B{\varepsilon}^{n})(1+C\ln \dot{{\varepsilon}}^{\ast })(1-T^{\ast m}). & & \displaystyle\end{eqnarray}$ (1)

The first factor of the right side describes the quasi-static material behaviors. Consequently, the parameters A, B, and n are determined by the quasi-static tensile tests. Where σ is the flow stress, A is the yield stress at reference temperature and reference strain rate, B and n are the strain hardening coefficient and exponent, respectively. ϵ is the equivalent plastic strain, $\dot{{\varepsilon}}^{\ast }=\dot{{\varepsilon}}/\dot{{\varepsilon}}_{0}$ is the dimensionless strain rate with $\dot{{\varepsilon}}$ being the strain rate and $\dot{{\varepsilon}}_{0}$ is the reference strain rate, the $\dot{{\varepsilon}}_{0}$ is the quasi-static strain rate, $\dot{{\varepsilon}}_{0}=1\times 10^{-3}$ , m is the material constant, and T ^∗ = (T − T _r)∕(T _m − T _r) is the homologous temperature with T being the current temperature, T _m is the melting temperature, and T _r is the reference temperature. In this work, T _r is 20 °C.

The value of A is calculated from the yield stress of the quasi-static tension test. The material constant B and n are determined by using the least squares fitting method. Using the peak stress data and the corresponding plastic strain at different strain rates, C is obtained at each strain rate, then taking the average value of C. m is the temperature sensitivity coefficient which can be converted into the following form: $\begin{eqnarray}\displaystyle m\ln T^{\ast }=\ln \left[1-\frac{{\sigma}}{(A+B{\varepsilon}^{n})(1+C\ln \dot{{\varepsilon}}^{\ast })}\right]. & & \displaystyle\end{eqnarray}$ (2)

Taking different temperatures and strain rates into the (2) formula can obtain average value of m.

The Johnson–Cook fracture model [39] is defined as follows: $\begin{eqnarray}\displaystyle {\varepsilon}_{f}=[D_{1}+D_{2}\exp (D_{3}{\sigma}^{\ast })][1+\dot{{\varepsilon}}^{\ast }]^{D_{4}}[1+D_{5}T^{\ast }]. & & \displaystyle\end{eqnarray}$ (3)

Where D ₁, D ₂, D ₃, D ₄, and D ₅ are fracture model constants. The constants D ₁, D ₂, and D ₃ are determined from the quasi-static tests on smooth and notched axisymmetric specimens, assuming that fracture initiation takes place in the center of the notch. The effects of strain rate and temperature on fracture strain are represented by the material constants D ₄ and D ₅, respectively.

The above constants were obtained: A =172 MPa, B = 360.73 MPa, n = 0.45592, C = 0.092, m = 0.95, D ₁ = −0.35, D ₂ = 0.6025, D ₃ = −0.4537, D ₄ = 0.206, and D ₅ = 7.2. Hence, the Johnson–Cook constitutive and the Johnson–Cook failure models [38] are given by $\begin{eqnarray}\displaystyle {\sigma}=(172+360.73{\varepsilon}^{0.45592})(1+0.092\ln \dot{{\varepsilon}}^{\ast })(1-T^{\ast 0.95}) & & \displaystyle\end{eqnarray}$ (4) and $\begin{eqnarray}\displaystyle {\varepsilon}_{f}=[-0.35+0.6025\exp (-0.4537{\sigma}^{\ast })][1+\dot{{\varepsilon}}^{\ast }]^{0.206}[1+7.2T^{\ast }]. & & \displaystyle\end{eqnarray}$ (5)

2.3.2 Contact and friction

The choice of contact, friction type, and size of the friction coefficient are important to the results. In the dynamic display analysis of ABAQUS, the common analysis types include Surface-to-Surface contact, General contact, and Self-contact. In this study, Surface-to-Surface contact was used for the simulation process; a large blank-holder force was used to avoid sheet sliding. In ABAQUS, the friction coefficient of the Coulomb friction model is a constant. The friction coefficient between the metal sheet and the blank-holder was set to 0.3.

2.3.3 Analysis methods

The analysis flow chart is shown in Fig. 5, which takes the parameter temperature as an example to explain the analysis process. First, the temperature is set to a certain value while the other parameters remain the same (except for energy). Afterward, the deformation process of the workpiece is analyzed. If no instability or rupture is found in the deformation field of the workpiece, the energy (voltage or capacitance) will gradually increase. The deformation process is analyzed until instability or rupture occurs in the workpiece. The limit strain at the specific temperature is then calculated and the FLD is obtained. Finally, the temperature is set to another value. The above analysis process is repeated until the FLDs at different temperatures are obtained. Similar analysis process is followed for the other parameters.

The uniform pressure coil and square plate workpieces (150 mm × 150 mm) were used to measure and predict the right half of FLD for Mg alloy sheet. The flat spiral coil with copper driver and the strip workpieces with different widths (20 mm × 150 mm, 30 mm × 150 mm, 40 mm × 150 mm, 50 mm × 150 mm, and 60 mm × 150 mm) were used to predict the left half of FLD for the Mg alloy sheet.

Figure 6(a) and 6(b) shown the analysis model for electromagnetic forming with uniform pressure coil and flat spiral coil by numerical simulation respectively. The analysis model included the electric model, magnetic model, and mechanical model. ANSYS/Emag was used to implement the electric and magnetic model, whereas ABAQUS/Explicit was used to simulate the mechanical model of sheet forming in this work. The electromagnetic forces were firstly calculated in ANSYS/Emag, then imported to ABAQUS/Explicit to complete mechanical analysis for sheet forming. When the discharge current flows through the coil, a magnetic field near the tool coil and an eddy current in the sheet are generated. The workpiece is deformed by the lorentz force produced by inductive magnetic field. Then, the forming limits of AZ31 alloy sheets can be obtained from the deformed workpieces. And the calculation process is shown in Fig. 7.

The number of coil turns is 12; the coil separation is 2 mm; the cross-sectional area of the coil wire is 5 mm × 6 mm; and the separation distance between the coil and the workpiece is 0.5 mm. The mechanical model is set up in ABAQUS/explicit, where the node order is the same as that in the magnetic field to ensure that the load applied in the mechanical model is accurate. The solid97 element in the magnetic field is replaced by the C3D8R element. To expedite the calculation speed, the die elements are set to a rigid body. The C3D4 element meshes the die and holder, which is a discrete rigid element. During the forming process, the holder and the die are considered to be fixed, while the contact conditions between the die and the workpiece are considered the same as those between the workpiece and the holder.

Figure 8 illustrates the mechanical analysis models for the strip workpiece and the flat spiral coil bulging system. The number of flat spiral coil turns is 12; the cross-sectional area of coil wire is 2 mm × 6 mm; the coil separation is 1.5 mm; the workpiece thickness is 1 mm; and the separation distance between the coil and the workpiece is 1.5 mm. The driver is a copper pill (Cu-T3) with 0.5 mm thickness and 50 mm diameter. The separation distance between the coil and the driver is 1 mm. Similarly, the holder and the die are considered to be fixed, and contact conditions between the die and the workpiece are considered the same as those between the workpiece and the holder.

3 Results and discussion

The capacitor group discharge process is a RLC circuit in EMF analysis. The current is produced by the RLC circuit, and circuit model was established with CIRCU124 unit of ANSYS in this work, as shown in Fig. 9.

At room temperature, when the capacitance is 1100 μF and the other parameters remain constant, the voltage increases gradually to simulate the failure process of the Mg alloy square plate workpiece. The bulging height of the workpiece increases gradually with the increase in voltage. When the voltage is up to 8000 V, the workpiece ruptures. At this point, the ultimate strain of sheet fracture site is obtained by finite element. The grid near the fracture site is considered to be the instability site (Fig. 10). The deformation of the fracture site had exceeded the forming limit. So only the instability site or girds can be used for obtaining data. The experimental strain data were obtained by measuring the deformed grids printed on the surface of workpiece. And the numerical simulation strain data of the grids were produced by ABAQUS post-processing as shown in Fig. 11, where the red areas were the large stress sites. As the thickness of Mg alloy AZ31 sheets is only 1.0 mm, the number of grid layers in the thickness direction is set as one by C3D8R element, which is simplified for improving the calculation efficiency.

Figure 11 shows the right half of FLD for Mg alloy by electromagnetic bulging at room temperature based on experiments and simulation. The element size of 2.5 mm was used in the simulation, the picture was cut and enlarged to show the deformed part. The diameter of die was 50 mm shown in Fig. 4. The forming limit of the finite element calculation is relatively consistent; the simulation value and experiment FLD are consistent, and the simulation can effectively predict the forming limit.

Similarly, the FLDs for electromagnetic bulging Mg alloy sheet under different voltages, capacitances, or temperatures were obtained with the accurate numerical simulation established by the above work through changing process parameters.

Figure 12 presents the FLDs for electromagnetic bulging Mg alloy sheet under different voltages at room temperature by numerical simulation. The Mg alloy FLD on stretching and compressive deformation is shown in Fig. 12(a). The forming limit of Mg alloy undergoes an obvious improvement with the increase in voltage. Figure 12(b) shows that the voltage increases from 8000 V to 9000 V and the Mg alloy forming limit also increases when the other conditions remain constant.

When discharge voltage increases, the discharge current and the magnetic force acting on the workpiece increase as well. This effect increases the forming limit. For example, when the voltage is 8000 V and the capacitance is 1100 μF, the maximum strain rate of metal sheet center node is 4954 s⁻¹. When the voltage is 9000 V and the capacitance is 1100 μF, the maximum strain rate of metal sheet center node increases to 9151 s⁻¹. The strain rate on the sheet significantly increases, which indicates that increasing the deformation rate within a certain range can help improve the formability of Mg alloy.

Figure 13 shows the FLDs for electromagnetic bulging Mg alloy sheet under different capacitances at room temperature by numerical simulation. Small improvement occured in the forming limit of Mg alloy sheet with the increase in capacitance. The figure also indicates that increasing the capacitance has little effect on the forming limit.

Increasing the capacitance can also increase the discharge energy (E = CU ²∕2). The period of discharge current is prolonged with the increase in capacitance; however, the increase in its amplitude is not obvious compared with the increase in voltage. Moreover, the increase in maximum magnetic force on the workpiece and the effect of capacitance on the workpiece deformation rate are not obvious. Therefore, increasing the voltage is more effective than increasing the capacitance to improve the sheet forming limit.

Figure 14 illustrates the FLDs for electromagnetic bulging Mg alloy sheet at different temperatures by numerical simulation.

The forming limit of Mg alloy sheet increases significantly with the rise in temperature. This finding is attributed to the fact that temperature improves the plasticity of Mg alloy and reduces deformation resistance, thereby increasing the forming limit. Yu et al.’ experimental results show that: under 200 °C, the higher the forming temperature is, the better of the formability for Mg alloy sheets is [36]. Mg alloy AZ31B has excellent thermal deep drawing formability. Ji et al. also claimed that the formability of AZ31Mg alloy could be improved with the increase of temperature [37]. The above research results are consistent with this work.

Figure 15 shows the complex effects of voltage, capacitance, and temperature on the equivalent limit strain by numerical simulation.

Increase in the discharge voltage and the temperature can effectively improve the Mg alloy forming limit under EMF, whereas increasing the capacitance has little effect on the forming limit.

Moreover, the Mg alloy resistivity and the skin depth of the magnetic field increase with the increase in temperature. Mg alloy is easily oxidized when the temperature is too high. This effect can easily cause leakage of the magnetic field energy, thereby wasting energy. Increasing temperature also has considerably higher demand for mold material and coils. Thus, the temperature for the Mg alloy sheet EMF should not be too high. The appropriate combined deformation temperature is about 200 °C. At the appropriate temperature, on the one hand, the formability of Mg alloy sheet can be improved, on the other hand the coil and die life can be extended, the power consumption is low. Cost is in good control and efficiency can also be improved. At the same time, it contributes to energy conservation and environmental protection.

Overall, the formability of Mg alloy sheet can be improved by warm forming. Lee et al. is for that the changes of strain rate and temperature are the key factors for AZ31 Mg alloy forming process [38]. And Takuda et al. support that the formability of Mg alloy sheets can be improved at the elevated temperatures between 150 and 300 °C [39]. Therefore, the temperature range is of great significance for Mg alloys warm forming process. EMF can also improve the Mg alloy formability because of its high deformation rate. The formability of warm and electromagnetic hybrid forming is better than that of warm forming or EMF. At lower temperature, a better formability can also be obtained by changing other condition parameters. Warm and electromagnetic hybrid forming process can more effectively improve the Mg alloy forming limit.

In fact, during the forming process the strain rate and temperature both will vary. Deformation condition is not a single one and some conditions even will affect each other. Therefore, our discussion of the forming limit and effect factors at different temperature and strain rate is to control the process parameters (such as temperature, strain rate controlled by discharge energy, and other parameters) of actual industrial forming process, so that ideal formability can be obtained. So far, there are also some technical problems needed to be solved for controlling deformation temperature and strain rate during actual industrial forming process. According to the study of Li et al., FLDs of AZ31B Mg alloy sheet at different temperatures were established by hemispherical punch experiments with the help of grid analysis system [40]. Kim et al. obtained the FLDs of steel sheets by the punch stretch test with high speed [41]. Nguyen et al.’ work predicted the forming of AZ31 Mg alloy sheets by the multistep inverse method [42].

Thus, hot forming, high rate forming, and numerical simulation have been widely used to obtain the forming limit of metal materials. Developing a new forming process to improve the formability of Mg alloy is helpful for practical production. Warm and EM Hybrid forming is a good attempt for Mg alloy forming. Using numerical simulation through reasonable models to predict forming limit can effectively improve the efficiency and reduce the cost. This work attempted to provide some theoretical basis and orientation to solve these problems.

4 Conclusions

Formability of Mg alloy is greatly affected by the temperature and strain rate. The effects of voltage, capacitance, and temperature on the forming limit of AZ31 Mg alloy under electromagnetic forming were investigated. Two coils were designed to perform the Warm and EM Hybrid forming experiments. And the complete FLDs of AZ31 Mg sheet under different temperature and high rate conditions were established by ABAQUS and ANSYS simulation. The significant results can be summarized as follows:

The formability of warm and electromagnetic hybrid forming is better than that of warm forming or EMF. Warm and electromagnetic hybrid forming can more effectively improve the forming limit by improving the plasticity of Mg alloy and reducing deformation resistance.

Electromagnetic forming is able to provide very high strain rate. The strain rate on the sheet significantly increases, which indicates that increasing the deformation rate within a certain range can help improve the formability of Mg alloy.

The magnetic force acting on the workpiece, deformation rate, and forming limit increases with the increase of discharge voltage.

The discharge capacitance has little effect on the deformation rate. Hence, the effect of capacitance on the formability of Mg alloy is not obvious.

Deformation temperature has a significant effect on the forming limit of Mg alloy. Forming limit increases with the increase in deformation temperature within a certain range. However, the forming temperature should not be too high; otherwise, it will aggravate Mg alloy oxide, energy consumption, and reduce die service life. At lower temperature, a better formability can also be obtained by changing other condition parameters. The appropriate combined deformation temperature is about 200 °C for Mg alloy forming.

The forming limit predicted by the finite element calculation is relatively consistent and the simulation value is consistent with experiment result. This proves that the simulation parameters obtained by experiments are accurate and this method can be used for future work.

Footnotes

Acknowledgements

This work was finally supported by the National Natural Science Foundation of China (No.51475345, No. 51705169), the Open Fund Project of State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology (No. P2015-01), the China Postdoctoral Science Foundation (No. 2017M610472).

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