The Electric-Thermal Uneven Characteristics Simulation of Wide Mg Alloy Strip and Electroplastic Rolling Experiment

Abstract

In order to solve the problem of wide magnesium strip uneven deformation in electroplastic rolling, an uneven field measurement device was designed. The device simulates the actual electro-thermal characteristics and provides as even and constant field conditions as possible for high-efficiency wide Mg strip rolling. Firstly, the effect of electrode position and distance on the electric field unevenness of magnesium strip is observed by setting the electric rolling condition, to provide the optimal electrical-thermal field quantity coupling conditions required by electric rolling. Secondly, in order to reveal the changing trend of the transient field in the actual rolling, the three-dimensional electric field of wide magnesium strip are simulated by the finite element method. The results show that the even temperature field and stable stress field required by the EPR of a wide Mg strip can be guaranteed to the greatest extent by setting electric field parameter Online. The case proves that the continuous EPR of Mg strip with a thickness of less than 0.13 mm without heat treatment can be realized by fine control of the EPR process.

1. Introduction

Mg alloys are promising structural materials due to their low density, high specific strength and specific stiffness. However, it is difficult to achieve large reduction rates rolling at room temperature, resulting from the densely packed hexagonal structure and the plane texture of the Mg-based alloy. The traditional “Hot rolling + heat treatment” method can weaken the texture, refine the grain [1] and realize continuous rolling. Plate convexity and flatness are major metrics to evaluate the quality of the product, which are not only related to the roll geometry parameters, but also closely related to the internal reduction rate and the rolling temperature, especially the strip transverse temperature [2]. Moreover, microstructural homogeneity is also a major factor affecting the homogeneous deformation of wide strip rolling [3]. However, the high thermal conductivity leads to problems of cooling, transverse temperature difference and uneven deformation during the deformation of the Mg foils, which aggravate the texture strength or anisotropy and easily induce edge cracking, surface cracking or fracture [2,4]. It is generally accepted that special deformation methods should be used to improve the rolling capacity of traditional Mg alloy materials and the deformation uniformity of Mg alloy thin strip, such as asymmetric rolling [5], width-limited rolling [6] and cross variable thickness rolling [7]. However, the industrial application of these methods is quite limited, due to their demanding requirements of facility and complex procedures.

Over the past few decades, the electroplastic rolling process has been shown to be an effective plasticization method to not only improve the plasticity of highly brittle Mg alloys by fast temperature rise, but also to obtain fine crystal structures by combining large plastic deformations with on-line electrical pulse processing [8]. The effect of pulse current on the deformation of metal materials mainly has two aspects: on the one hand, it has been proved that there is a pure electroplastic effect (non-thermal effect) which can directly reduce the flow stress of materials [9] and improve their plastic deformation ability [10]. On the one hand, the coupling of non-thermal and Joule thermal effects can promote nucleation and selectively induce recrystallization at specific temperatures and current density values. Kuang et al. [11] compared thermoelectric coupling rolling with warm rolling experiment results, and found that pulsed currents can induce dynamic recrystallization at lower temperatures, leading to better product surface quality. At constant values of the rolling temperature, the orientation texture and the twin structure can be improved by adjusting the peak current, and the rolling capacity of the Mg alloy can be further improved [12,13].

A number of studies showed that pulsed current can effectively improve the poor plasticity of the Mg alloy rolling at room temperature, and there are many technical methods to introduce a pulsed current into the rolling process, such as online heating rolling (O-LHR) and electroplastic rolling. The method of on-line heating rolling is to use a pulsed current to heat the strip before rolling, and rolling it after the target temperature is reached. The O-LHR has the advantages of a high heating rate, uniform transverse temperature and stable rolling temperature compared to traditional hot rolling. By adjusting the temperature and tension of the O-LHR, the surface quality of the strips is significantly improved, and the comprehensive mechanical properties of the rolled strips are excellent for meeting the experimental requirements [14,15,16]. Electroplastic rolling, in which a pulsed current is introduced during the rolling process, is characterized by high efficiency for automated production, and EPR is a promising rolling technology for industrial production. However, the experimental objects for electroplastic rolling were mainly narrow strips and filament, and the wide Mg alloy strip was rarely studied. Due to the influence of the conductivity properties of the electrical pulse, however, the electric field uniformity will be apparent during the electroplastic rolling of the wide Mg foil. The uneven electric field can greatly affect the electroplastic deformation law of wide Mg foils, and eventually lead to uneven properties and dimension deviation Mg foils.

In a previous study, an experimental device was designed to simulate synchrotron variations of the electric, thermal and stress fields of a wide Mg alloy strip [17]. The influence mechanism of different electrode materials, positions and pulses on the local field characteristics of an Mg strip is tested by an electric heating tensile (EHT) experiment, and the correlation law of electric pulse on Joule heating temperature field and stress field is preliminarily analyzed. In this paper, the original setup is optimized and the guide roll setup was added to more realistically simulate the contact conditions between the work roll and the guide roll. Experiment and finite element simulation were used to investigate the influence of electric pulse parameters and connection mode on the electric-thermal coupling field. Thus, the electric rolling process is optimized to improve the deformation uniformity of wide Mg foil electric rolling, and the best electric rolling condition of wide Mg foil is obtained.

2. Materials and Methods

A commercial Mg alloy AZ31 (3.1 wt% Al, 1.0 wt% Zn, Mg) was used in this study. To obtain a homogenized microstructure, the obtained sheets were annealed at 573 K for 1 h, and then cooled to room temperature in air. In order to simulate the electric field distribution law between the guide roll and the work rolls during EPR, a guide roll was added to the multi-point electric stretching device. The Mg alloy strip was in contact with the cylindrical electrode at a fixed wrapping angle, and x and y were set to be the length and width directions of the sample, as shown in Figure 1. Meanwhile, the FLIR T460 thermal imager with a resolution of 320 × 240 pixels was used to monitor the transient temperature change, as shown in Figure 2.

For good effectiveness, the high-temperature-resistant matte black paint was sprayed on the surface of the sample to reduce the online measurement error. The sample specification was 850 mm × 130 mm × 0.5 mm, the distance between two electrode guide rolls was 466 mm and the wrapping angle between the Mg alloy strip and electrode guide rolls was set as 24°. Electrode materials of guide rollers are copper inlaid steel and solid steel with a diameter of 40 mm, respectively. The copper-embedded steel was a copper bar with a diameter of 7 mm inlaid on the axis on the basis of a solid steel roll. The electrode guide rolls were connected in symmetric and asymmetric ways, and electric pulse widths of 70 μs and 40 μs were set. Eight control experiments were performed. To ensure a stable contact condition between the electrode and the Mg strip, a tension of 20 MPa was uniformly applied to the strip, and the surface roughness of the cylindrical electrode and Mg strip was controlled between 0.3 μm and 0.4 μm.

3. Modeling of Electro-Thermal Coupling

3.1. Electric-Thermal Relationship

In the EPR process, it is not only the use of the Joule heating effect that is important, but also how to fully exploit the non-Joule heating effect, which is to achieve the low-temperature or even room-temperature EPR key effect. However, the test conditions subject to the electric field are very difficult. At present, the electric field distribution can only be tested by the temperature field conditions induced by Joule heat. Therefore, the electro-thermal relation is the major method to test the electric field distribution, which can feed back the distribution characteristics of the current density, which is conducive to better control of the electric field distribution and the maximization of the actual electroplastic effect of the wide Mg strip. Suppose that the temperature rises of Mg strip caused by an electric pulse under ideal conditions is represented as

$$\frac{\mathrm{d}{T}_m}{\mathrm{d}t}=\frac{R_m}{c_m{\rho }_m}{\left(\frac{I_A}{S_m}\right)}^2=\frac{R_m{J}_e{}^2}{c_m{\rho }_m}$$

(1)

where T_m is the temperature, t is the time, ρ_m is the density, c_m is the specific heat capacity, R_m is the resistivity, S_m is the cross-sectional area of Mg strip, I_A is the root mean square current, J_e is the root mean square current density. According to Equation (1), Joule heat is linearly related to the square of current density, and the temperature rise of Mg strip can be calculated by the current. In this way, the characteristics of the electric field distribution can be obtained by regression based on the distribution law of the temperature field, and feedback control of the temperature and electric pulse parameters can be achieved. It is clear that an accurate measurement of the distribution of the current density field of a Mg foil under different conditions is significant for the realization of a high-precision electric rolling process for wide Mg foils.

3.2. Modeling of Joule Heat Temperature Field

In order to accurately model the electroplastic rolling, Joule heat is identified as the internal heat source, and the boundary conditions take into account the effects of radiation and air cooling. The three-dimensional transient heat balance equation, including the internal heat source, could be expressed as

$${\rho }_m{c}_m\frac{\mathrm{d}{T}_m}{\mathrm{d}t}=k_m\left(\frac{{\partial }^2{T}_m}{\partial x}+\frac{{\partial }^2{T}_m}{\partial y}+\frac{{\partial }^2{T}_m}{\partial z}\right)+Q_{me}$$

(2)

where k_m is the thermal conductivity and Q_me = R_mJ_e² is the Joule heat source intensity. The Mg strip in the anode and cathode electrodes was meshed, and a finite element model is established based on Equation (2). In order to accurately calculate the temperature in the rolling deformation zone, a current density field model was required. In the iterative procedure, it is necessary to take into account the deviations of the Joule heat distribution and transient fluctuations due to the variation of the electric field parameters, and to correct them by the measured values in order to satisfy the stable convergence condition, and thus more accurately reflect the true electric field distribution conditions.

3.3. Modeling of Electric Field

In order to better express the characteristics of electric field distribution, Equations (1) and (2) are used to calculate and fit the measured results for the convenience of application in the electroplastic rolling model. First, the following assumptions are made based on the actual situation: (1) the effects of skin effects and thickness on the electric field distribution are not considered; (2) the contact resistance between the sample and the electrode is constant; and (3) the total current is assumed to be constant during the current loading process.

Based on the characteristics of the measured results, the surface fitting formula was set as follows

$$J_e/J_{ave}=f(x,y)=p_0+p_1{y}^2{x}^4+p_{2}y{x}^3+p_3{x}^4$$

(3)

where J_ave is the average effective current density of all nodes and x and y are the rolling direction and transverse direction coordinate of electric rolled Mg strip, respectively. p₀~p₃ are polynomial fitting coefficients.

3.4. Finite Element Model

The accuracy of the prediction of the electric heating field will be somewhat affected by measurement errors due to the accuracy limits of the device installation and temperature acquisition. Based on the above considerations, the finite element simulation of the electric-thermal stretching test was carried out by using the ABAQUS software, and the electric-thermal coupling analysis of the electric field was performed for the copper-embedded steel roll and the solid steel roll electrodes, respectively. The hexahedron was chosen for meshing, and the minimum mesh size of the contact area was 0.5 mm, which was sufficient to satisfy the convergence of the results. We assume that the contact conductivity was 0.8 kS/mm² and the constant loading current density is 14.5 A/mm². Except the contact surface between the guide roll electrode and the Mg strip, the rest of the surfaces are air convection heat transfer, and the convective heat transfer coefficient is constant at 10 W/(m²·K). The initial temperature and sink temperature is 15 °C and loading tensile stress is 20 MPa, while other material coefficients are shown in

Table 1. Material coefficient.

	Density ρ/(kg·m−3)	Electrical Resistivity R/(nΩ·m)	Specific Heat Capacity c/(J·kg−1·°C−1)	Thermal Conductivity k/(W·m−1·°C−1)
AZ31	1770	Temperature-dependent [18]	Temperature-dependent [18]	Temperature-dependent [18]
Copper	8960	1.72 × 10−8	385	400
9Cr2Mo	7850	2.48 × 10−7	475	44.5

.

4. Result

4.1. Measured Electric Field

In order to better observe the action law of electrode connection mode on electric field distribution, J_e/J_ave when current is loaded for one second was calculated according to Equation (1). Previous measured results [17] show that electrode connection mode and electrode material will significantly affect the current density distribution, and thus affect the temperature and stress distribution. The electric field surface was fitted with reference to 18,200 J_e/J_ave measured data, and the effect of outliers on the surface fit in the eight groups of comparison experiments was eliminated, in order to improve the stability of the electric field model. Figure 3 shows the J_e/J_ave surface fitting results of solid steel guide roll electrodes (symmetric and asymmetric connection, electric pulse width 40 μs). It can be seen that symmetrical and asymmetrical connections will have a current density peak near the electrode, which is consistent with the measured results [17]. This rule can be used to improve the uniform distribution of the electric and temperature field in the deformation zone during the EPR of wide Mg strips, which lays the theoretical foundation for the realization of stable EPR and uniform deformation of wide Mg strips.

4.2. Electro-Thermal Field Uniformity Analysis

In order to better evaluate the uniformity distribution characteristics of the electric field, the J_e/J_ave of the sample after one second was calculated according to Equation (1). Figure 3 shows the measured values of the electric field, with a peak J_e/J_ave less than 1.4 for the cylindrical electrode electrical pulse tensile test. The J_e/J_ave peak is lower and the electric field is more uniform after applying the packet Angle. In order to eliminate the effects of measurement scale and dimensionality, the coefficient of variation was used to reflect the uniformity of different electrode materials, electrode connection modes and current densities. The smaller the coefficient of variation, the smaller the dispersion of the data. The formula for the coefficient of variation is as follows

$$c_v=\sqrt{\frac{{\displaystyle \sum _{i=1}^n{\left(\Delta T_i-\Delta \overline{T}\right)}^2}}{n}}/\Delta \overline{T}$$

(4)

where $\Delta T_i$ is the temperature rise at the temperature measurement point when the electric pulse is loaded for one second, $n$ is the number of temperature points and $\Delta \overline{T}$ is the average temperature rise of all measurement points.

As presented in Figure 4, the coefficient of variation of the temperature rise is between 0.05 to 0.105 for the copper-embedded steel used as the electrode, which is smaller than the coefficient of variation of the temperature rise 0.1 to 0.11 for the solid steel as electrodes. The results confirmed that the copper-embedded steel used as electrodes could improve the uniformity of the electric field of the wide Mg strip. The above experimental results can provide methods and ideas for homogenizing the treatment of the EPR process, which can help to realize the fine tuning of the Joule thermal temperature field induced by the instantaneous electric field on the line. Moreover, the plasticization effect of purely electroplastic effects can be fully exploited to achieve significant changes in the deformation laws and mechanical properties for difficult-to-deform wide strips.

4.3. Simulation Result

Figure 5 shows the J_e/J_ave distribution on the surface of the Mg strip for the solid steel used for the electrodes, which is generally consistent with the experimental results in Figure 3. The peak current density appears at the electrode connection, where the transverse distribution range of the asymmetric connection J_e/J_ave is 0.215 and the transverse distribution range of the symmetric connection J_e/J_ave is 0.098. It is seen from Figure 5 that the symmetrical electrode connection can significantly increase the uniformity of the electric field, and it is easier to achieve the uniform distribution of temperature. The interaction between the electric fields at the cathode and anode electrodes was not observed, with a distance of 466 mm between the cathode and anode electrodes. Figure 6 shows that the variation coefficient of the J_e/J_ave can be reduced with the copper-embedded steel by using the guild rolls, which improves the uniformity of the electric field distribution. In particular, when a symmetrical electrode connection is adopted, the uniformity of electric-thermal coupling field in a wide Mg strip can be greatly improved. Figure 7 shows that the excellent conductivity of the copper leads to an accumulation of current in the copper core, which significantly improves the axial guiding electrical effect. The axial direction current distribution of the guide roll was uniform, leading to the transverse distribution of the electric field in the wide Mg alloy strip more uniform, which is beneficial for improving the uniformity of the transverse temperature distribution and microstructure.

The results of electric tensile experiment and finite element simulation both confirm that the copper-embedded roll can significantly improve electric field homogeneity. However, the calculated coefficient of variation for the experimental values has a larger gap than the simulated values, which proves that the actual uniform electric field effect is more pronounced for the copper-embedded guide rolls, as shown in Figure 4 and Figure 6. Contact resistance was unavoidable during the assembly of the copper-embedded rollers and the installation of the device. A small change in the resistance affects the characteristics of the electric field. The contact resistance between the copper core and the steel roll reduces the radial current conduction capability, and equivalently enhances the axial current conduction capability, resulting in a more homogeneous roll electric field. The experimental results show that the transverse distributions of the electric field and temperature are strongly affected by the electrode connection pattern. Therefore, the feasibility of the symmetric electrode connection method was first verified, and the effect of the electric field on the transient rolling temperature and microstructure was analyzed and optimized.

5. Example Verification of Mg Strip Electric Rolling

Based on the above conclusions, it is demonstrated that the symmetric connection and copper-embedded steel roller can significantly improve the electric field uniformity of Mg strip, and indirectly modify the temperature distribution and microstructure of Mg alloy in the EPR. In order to verify the EPR effect of Mg alloy strip under the condition of symmetrical electrode connection, the anode of the power supply was connected on both sides of the work roll. The Mg alloy billet was cut into sheets with dimensions of 500 mm × 40 mm × 1.0 mm. The sheets were rolled to 0.6 mm thickness though three passes without any off-line intermediate heat treatment in the process of the EPR. Figure 8 shows that the rolled Mg strip produces a large number of twins and shear bands. Then, a single pass electroplastic rolling with an 18% reduction rate was performed. The effective current density was 28.5 A/mm², and the rolling speed was 25 mm/s.

Figure 9 shows that the Mg alloy strip passes through the guide rolls into the deformation region in 6.2 s, and was subjected to Joule heat in the transition region to reach the target roll temperature. The transverse temperature distribution at the inlet measured by the thermal imager was relatively uniform. It can be seen that the temperature rise of the symmetric electric field after electrode attachment was more uniform under Joule heating, and there was no edge crack due to edge temperature drop. The optical micrographs show that the deformed twin and the shear band completely disappear before the mill inlet, and large area nucleation and recrystallization occurring at the edge and middle and fine recrystallized grains form in the shear band. Additionally, the grain sizes in the middle of the strip and at the edges of the Mg alloy are essentially the same. Therefore, the optimized electric field can significantly improve the uniformity of the rolling temperature and the uniformity of the microstructure properties at the inlet of the rolling mill, thereby improving the surface quality and mechanical properties of the rolled Mg alloy.

A large number of studies on electrical pulse-assisted forming show that the pure electroplastic effect mainly manifests in two aspects: promoting recrystallization; and reducing flow stress. On the one hand, the presence of pure electroplastic effects could reduce the activation energy and accelerate the nucleation and recrystallization of the Mg alloy under the combined action of pure electroplastic and Joule thermal effects [19,20]. On the other hand, the purely electroplastic effect that could reduce the flow stress and even greatly enhance the plastic deformability of the material without changing the temperature [17,21]. It can be seen that the electric field of electroplastic rolling not only directly affects the flow stress and the microstructure evolution of the strip, but also indirectly regulates the rolling deformation by changing the temperature distribution. Symmetric electrode connections are characterized by low load and uniform electric field, with peak current densities on both sides of the strip. Strong currents can improve the rolling ductility of the material to a certain extent, thus reducing the occurrence of edge cracks [22]. The non-thermal effects and a uniform transverse temperature profile may be responsible for the improved surface quality of the electroplastic rolling strips. The improvement of the symmetrical electrode connections and the copper rollers can not only improve the uniformity of the electric field, but also adjust the transverse temperature distribution and microstructure homogeneity of the electrically rolled Mg inlet by using the purely electroplastic and thermal effect.

6. Conclusions

(1)

A cylindrical electrode (work roll or guide roll) with copper-embedded steel was designed, and the electric field distribution characteristics of wide Mg strip EPR were simulated by the multi-point device. The influence of the electrode connection mode and electrode material on the electric field uniformity of an Mg strip was analyzed. The results showed that the variation coefficient of the temperature rise is 0.05 to 0.105 for the copper-embedded steel being used as a work roll, which is smaller than the variation coefficient of the temperature rise for the steel roller being used as a work roll. The copper-embedded steel being used as the work roll helps to improve the electric field uniformity of the wide Mg alloy strip. Moreover, as the J_e/J_ave distribution is fitted, the P₂ coefficient can be used to describe the uniformity of the electric field. This model is convenient for the online evaluation of transient electric field distribution characteristics of the Mg alloy strip.

(2)

In order to accurately analyze the electric field distribution characteristics of the Mg strip EPR process and reduce the errors in the electric field due to experimental bias in the electric field measurements, finite element simulations were performed to model the electric thermal field under the same operating conditions. The electric field is returned by combining the experimental and simulation results. On the one hand, the characteristics of the electric field distribution can be obtained accurately, which facilitates the analysis of the transient evolution law for localized electric fields. On the other hand, the electric field characteristics of the electrode (work roll and guide roll) can be analyzed, so that the influence of electrode material and structure on the electric field characteristics can be described quantitatively. The results demonstrate that the uniformity of an electric field can be improved by the copper-embedded steel electrode and the symmetrical connection mode of the electrode, which facilitate carrying out the obtain stable constant electric field and temperature field. Obviously, it is highly beneficial to improve the electroplastic effect of the wide Mg EPR.

(3)

A multi-pass EPR was performed on a wide Mg strip, and it was demonstrated that a uniform electric field distribution can improve the quality of the wide Mg strip. The thickness of the Mg strip was reduced from 1.0 mm to 0.5 mm by four passes without annealing by a reasonable electrostatic rolling process. It is shown that regulating electric field parameters can better complete the EPR process of the wide Mg strip, and reduce the occurrence of edge cracks.