*Article* **Research on the 2A11 Aluminum Alloy Sheet Cyclic Tension–Compression Test and Its Application in a Mixed Hardening Model**

**Guang Chen, Changcai Zhao \*, Haiwei Shi, Qingxing Zhu, Guoyi Shen, Zheng Liu, Chenyang Wang and Duan Chen**

> Key Laboratory of Advanced Forging and Stamping Technology and Science of Ministry of Education, Yanshan University, Qinhuangdao 066004, China

**\*** Correspondence: zhao1964@ysu.edu.cn; Tel.: +86-185-3351-1399

**Abstract:** The increasing application of aluminum alloy, in combination with the growth in the complexity of components, provides new challenges for the numerical modeling of sheet materials. The material elastic–plasticity constitutive model is the most important factor affecting the accuracy of finite element simulation. The mixed hardening constitutive model can more accurately represent the real hardening characteristics of the material plastic deformation process, and the accuracy of the material property-related parameters in the constitutive model directly affects the accuracy of finite element simulation. Based on the Hill48 anisotropic yield criterion, combined with the Voce isotropic hardening model and the Armstrong–Frederic nonlinear kinematic hardening model, a mixed hardening constitutive model that considers material anisotropy and the Bauschinger effect was established. Analysis of the tension–compression experiment on the sheet using finite element method. Using the finite element model, the optimum geometry of the tension–compression experiment sample was determined. The cyclic deformation stress–strain curve of the 2A11 aluminum alloy sheet was obtained by a cyclic tensile–compression test, and the material characteristic parameters in the mixed hardening model were accurately determined. The reliability and accuracy of the established constitutive model of anisotropic mixed hardening materials were verified by the finite element simulation and by testing the cyclic tensile–compression problem, the springback problem, and the sheet in bending, unloading, and reverse bending problems. The tensile–compression experiment is an effective method to directly and accurately obtain the characteristic parameters of constitutive model materials.

**Keywords:** 2A11 aluminum alloy plate; anisotropic; Bauschinger effect; mixed hardening; cyclic tension–compression experiment

#### **1. Introduction**

The use of stamping to form parts is common in various fields, such as metal material processing, the aerospace industry, the automobile industry, and scientific research [1,2]. The finite element numerical simulation technology is an effective means of shortening the stamping die design cycle, achieving process optimization, and improving the quality of stamping parts. In the stamping process with cyclic loading characteristics, the selection of an elastic–plastic constitutive model and related hardening behavior are of great significance in predicting the actual forming process [3]. A kinematic hardening model and a mixed hardening model can accurately represent the true hardening characteristics during plastic deformation. The accuracy of material characteristic parameters in the constitutive model directly affects the accuracy of the finite element simulation [4].

The elastic–plastic constitutive model of materials includes three components: yield criterion, the flow rule, and a hardening model. In simulating stamping and forming, the commonly used hardening models can be divided into isotropic hardening models,

**Citation:** Chen, G.; Zhao, C.; Shi, H.; Zhu, Q.; Shen, G.; Liu, Z.; Wang, C.; Chen, D. Research on the 2A11 Aluminum Alloy Sheet Cyclic Tension–Compression Test and Its Application in a Mixed Hardening Model. *Metals* **2023**, *13*, 229. https://doi.org/10.3390/ met13020229

Received: 19 November 2022 Revised: 16 December 2022 Accepted: 23 January 2023 Published: 26 January 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

kinematic hardening models, and mixed hardening models. In the isotropic hardening models, the subsequent yield surface B only changes in size and position relative to the initial yield surface A, as shown in Figure 1a. The typical isotropic hardening models are the Mises model and the Hill model, which are simple and easy to program. However, they can only describe the similar changes in the yield surface under a single strain path and they cannot describe some changes in material properties (such as the Bauschinger effect and the cross effect) when the strain path changes [5]. In the kinematic hardening models, the size of the subsequent yield surface remains unchanged only when the position changes, as shown in Figure 1b. The Ziegler model and the Armstrong–Frederic (A–F) model are widely used. Ziegler [6] proposed linear kinematic hardening based on the proportional relationship between the back stress increment and the strain increment. The Armstrong– Frederic nonlinear kinematic hardening model introduced a dynamic recovery item with decreasing memory for the deformation path, eliminated the defects of linear kinematic hardening, and better described the Bauschinger effect, which is the research foundation for the nonlinear kinematic hardening model [7]. The kinematic hardening model avoids the isotropic hardening model's drawback of being unable to describe the Bauschinger effect, but it cannot describe the expansion of the yield surface during deformation [8,9].

**Figure 1.** Schematic diagram of yield surface variation in the classic hardening theories: (**a**) isotropic hardening model; (**b**) kinematic hardening model; (**c**) combined hardening model; (**d**) kinematic hardening (center movement of yield surface and corresponding uniaxial stress–strain curve).

The above two hardening models only describe part of the hardening behavior of materials. In plastic deformation, the yield surface of most materials undergoes both size and position changes. Therefore, when describing the hardening behavior of actual metal materials, the above two hardening models are often combined and a mixed hardening model is used, as shown in Figure 1c. Han [10] and Li Qun et al. [11] established a mixed hardening model based on the Voce isotropic hardening model and the A–F kinematic hardening model, introduced the hardening model into an equivalent drawbead resistance model, proposed an equivalent drawbead model that considered the Bauschinger effect, and verified the accuracy of the model via experiments. With the development of ABAQUS software (version 6.14, Dassault Systemes Simulia Corp., Providence, RI, USA) for finite element analysis, some parameters related to the material properties required by the kinematic hardening model and the mixed hardening model can be directly input into the software without sophisticated secondary development.

ABAQUS (version 6.14, Dassault Systemes Simulia Corp., Providence, RI, USA) provides linear and nonlinear kinematic hardening models to simulate the cyclic loading of metals. The linear kinematic model has a constant hardening modulus, which is suitable for analyzing hardening behavior with an approximately constant hardening rate. The nonlinear kinematic hardening model defines the kinematic hardening part as an incremental combination of a pure motion term (the linear Ziegler hardening rule) and a relaxation term (the recall term), so that nonlinearity is introduced to the kinematic hardening part. At the same time, in ABAQUS/Explicit, the yield stress ratio *Rij* of the input plate can be used with the Hill48 yield surface [12]. ABAQUS (version 6.14, Dassault Systemes Simulia Corp., Providence, RI, USA) provides three methods—assigning parameter input, assigning semi-cyclic tension-compression experiment data, and assigning sheet cyclic tension-compression experiment data to define the kinematic hardening part. The kinematic hardening material characteristic parameters obtained from the cyclic stress–strain curve of the sheet can most accurately reflect the hardening behavior of the plate under cyclic loading. The cyclic sheet tension–compression test is required to obtain the cyclic sheet tensile–compression stress–strain curve.

The buckling tendency of a thin sheet under compression is very large, and it is difficult to obtain a large compression strain. In order to obtain the tensile and compressive properties of a thin sheet under large strain, scholars have proposed various methods to suppress the buckling of the thin plate in the compression process. Boger et al. [13] used a solid plate to clamp the two sides of the thin sheet sample and applied normal pressure via a hydraulic clamping system to constrain the buckling of the thin sheet during compression. However, the thickness of the thin plate changes during the tensile–compression process, and there will inevitably be a gap between the chuck of the tensile machine and the antibuckling fixture, resulting in excessive test error. Kuwabara et al. [14] designed a device with two pairs of comb teeth to reduce areas that are not clamped. However, the comb-tooth area is prone to bending, and the comb-tooth device is expensive. Yoshida [15] designed a special device to combine multiple samples for the tensile–compression test to overcome the defect of instability of a single sample. It measured the strain in the test process, but could not avoid the compression instability under strain. On the basis of a wedge-shaped unit designed by Cheng et al. [16], Cao et al. [17] designed an anti-buckling wedge fixture using transparent materials, which could be used to measure the whole optical strain in the deformation region of the sample by an optical strain-measurement method. Although this method can obtain tensile–compression strain under a large strain, the sample is prone to lateral instability. For the compression tests, Kurukuri [18] and Abedini et al. [19] prepared bonded sheet laminates to overcome any buckling during the tests. Due to the action of the glue between the plates, the test results had a large error, and the preparation of the sample was very complicated. In summary, in order to make the cyclic tensile–compression test of a thin sheet perform smoothly, the following three problems must be solved:


• selecting a high-precision optical strain-measuring instrument in order to accurately measure the deformation of the thin sheet sample gauge.

Based on the above research, this paper aimed to establish an A–F nonlinear kinematic hardening constitutive model according to the Hill48 anisotropic yield criterion. Based on the Hill48 anisotropic yield criterion, the Voce isotropic hardening model, and the A–F nonlinear kinematic hardening model, a constitutive model inclusive of anisotropy and mixed hardening was established. A set of sheet tension–compression buckling-restrained fixtures was designed, and the shape parameters that affect stress-measurement error and inhibit in-plane buckling were determined. The optimal shape of the sample used in the in-plane compression test was determined to accurately obtain the material propertiesrelated parameters of the kinematic hardening model and the mixed hardening model. ABAQUS (version 6.14, Dassault Systemes Simulia Corp., Providence, RI, USA) finite element software was used to analyze the applicability of the constitutive model for the cyclic tensile–compression problem of the sheets and the problem of the plate after bending, unloading, and reverse bending. The accuracy and reliability of the constitutive model were verified by experiments. This provides a reliable research method for studying the deformation behavior of sheet metal under complex loading conditions with cyclic loading characteristics.

#### **2. Description of the Constitutive Model**

*2.1. Establishment and Parameter Determination of the Nonlinear Kinematic Hardening Constitutive Model*

Most of the sheets used in stamping had anisotropy and a high material hardening rate, so the Mises yield criterion and the isotropic hardening model could not truly reflect the plastic behavior of the sheets during deformation. The Hill48 yield criterion considers the anisotropic characteristics of the material and considers that the contribution of stress in each direction of the sheet to the plastic yield is different, which information can be used for the plastic description of the sheet-forming process.

Assuming that the thickness anisotropy index *r* is constant during the plastic deformation process, if the sheet metal conforms to the flow rule of the total strain theory, then the *r* value can be obtained by measuring the strains in the width direction (*ε*w) and thickness direction (*ε*t) using a single tensile test. Specifically, the *r* value is expressed as follows:

$$
\sigma = \frac{\varepsilon\_w}{\varepsilon\_t} \tag{1}
$$

The expressions for the ratio of six anisotropic yield stresses [12]—*R*11, *R*22, *R*33, *R*12, *R*<sup>13</sup> and *R*23—can be derived by combining the Hill48 anisotropic yield conditions.

For the anisotropic behavior and the Bauschinger effect exhibited by the material during plastic deformation, the kinematic hardening model provides a simple explanation that the yield surface of the material only moves as a rigid body and does not rotate in the stress space during deformation, and the back stress represents the center of the plastic yield surface in the stress space.

The yield surface function of kinematic hardening materials is generally expressed as follows:

$$
\Phi = F(\sigma\_{i\bar{j}} - \mathfrak{a}\_{i\bar{j}}) - \sigma\_Y = 0 \tag{2}
$$

where *σ<sup>Y</sup>* is the initial yield stress and *αij* is the back stress.

The back stress represents the movement of the center of the yield surface in the stress space, which plays a crucial role in the kinematic hardening model and in yield surface evolution. Its value is related to the material hardening characteristics and deformation history. As shown in Figure 1d, the material is subjected to unidirectional elastic–plastic loading along the direction of *σ*2, and the stress increases from *σ*<sup>2</sup> = 0 to *σ*<sup>2</sup> = *σy*. During the loading process, when the deformation state of the material changes from elastic deformation to plastic deformation, the center of the yield surface begins to move. When the stress in the *σ*<sup>2</sup> direction is loaded to loading point 1, unloading and reverse loading are implemented to deform the material and the material stress reaches the loading point 2 to produce reverse plastic yield. It is clear from Figure 1d that the yield stress of the material under reverse loading is smaller than the initial yield stress *σy*.

The A–F nonlinear kinematic hardening model has been extensively utilized to study the cyclic plastic behavior of materials. This model contains a linear hardening term and a dynamic restoration term. The evolution equation can be expressed as follows:

$$d\alpha\_{ij} = \frac{2}{3} \mathbb{C} d\epsilon^p\_{ij} - \gamma \alpha\_{ij} d\mathbb{E}^p \tag{3}$$

where *C* and *γ* are material parameters; *αij* is the back stress component; *dε p ij* is the increment in the plastic strain; *dε<sup>p</sup>* is the equivalent plastic strain increment [11]; and *dε<sup>p</sup>* = *<sup>d</sup><sup>ε</sup> p ij p* .

When the material is subjected to uniaxial tensile loading, *dε<sup>p</sup>* = *dεp*. Therefore, it can be determined that

$$d\alpha\_1 = \frac{2}{3} \mathbb{C} d\varepsilon\_1^p - \gamma \alpha\_1 d\varepsilon\_1^p \tag{4}$$

*dε*

*ij*

The above equation can be simplified as follows:

$$\frac{d\alpha\_1}{\frac{2}{3}C - \gamma\alpha\_1} = d\varepsilon\_1^p \tag{5}$$

Integrating the above first-order differential equation, we obtain

$$\alpha\_1 = \frac{2}{3}\frac{\mathbb{C}}{\gamma} + \left(\alpha\_1^0 - \frac{2}{3}\frac{\mathbb{C}}{\gamma}\right)e^{-\gamma(\varepsilon\_1^p - \varepsilon\_{1,0}^p)}\tag{6}$$

where *α*<sup>0</sup> <sup>1</sup> is the initial value of the back stress and *ε p* 1,0 is the initial value of the plastic strain.

The initial conditions are *α*<sup>0</sup> <sup>1</sup> = *ε p* 1,0 = 0. Using these initial values, the back stress equation can be obtained as follows:

$$\alpha\_1 = \frac{2}{3} \frac{\mathbb{C}}{\gamma} \left( 1 - e^{-\gamma \varepsilon\_1^p} \right) \tag{7}$$

According to the above equation, the parameters *C* and *γ* can be determined by the nonlinear fitting of the experimentally acquired plastic strain data and the real stress obtained from the uniaxial tensile test of the sheet sample. The six anisotropic parameters (*R*11, *R*22, *R*33, *R*12, *R*13, and *R*23) and the kinematic hardening parameters (*C* and *γ*) were input into the ABAQUS (version 6.14, Dassault Systemes Simulia Corp., Providence, RI, USA) material model library to obtain the material characteristic parameters related to the follow-up hardening constitutive model, based on the Hill48 yield criterion.

#### *2.2. Establishment of the Mixed Hardening Constitutive Model*

According to the Hill48 anisotropic yield criterion, combined with the Voce isotropic hardening model and the A–F nonlinear kinematic hardening model, a constitutive model that considers anisotropy and mixed hardening was established. The isotropic hardening part adopted the Voce nonlinear isotropic hardening criterion, and the equation is as follows: \_ *p*

$$
\bar{\sigma} = \sigma\_0 + Q \left( 1 - e^{-b\epsilon\_1^p} \right) \tag{8}
$$

where *ε p* <sup>1</sup> is the plastic strain, *Q* and *b* are the parameters of the isotropic hardening materials, and *σ*<sup>0</sup> is the initial yield stress.

Under the uniaxial stress state, combined with the Equation (9), the material flow stress can be expressed as follows:

$$
\sigma = \sigma\_0 + Q \left( 1 - e^{-hc\_1^p} \right) + \frac{2}{3} \frac{\mathbb{C}}{\gamma} \left( 1 - e^{-\gamma c\_1^p} \right) \tag{9}
$$

In order to determine the nonlinear relationship between flow stress *σ* and plastic strain *ε p* <sup>1</sup>, it is necessary to determine the four material characteristic parameters *Q*, *b*, *C*, and *γ*. These material characteristic parameters can be obtained by the cyclic tensile–compression stress–strain curve obtained by the sheet cyclic tensile–compression test.

#### *2.3. Material and Experimental Procedure*

The 2A11 aluminum alloy plate with a thickness of 0.6 mm was selected as the research object. 2A11 aluminum alloy is a hard aluminum alloy that is widely used in the aerospace industry, the transportation industry, and other fields. The sheet sample was cut with a line cutting machine, according to the China National Standard "Tensile testing method for metal materials at room temperature" (GB/T 228-2002). The uniaxial tensile test of the original sheet was conducted on the InspektTable-100 material universal testing machine (Huibo, Germany). The standard size of the sheet sample used in the unidirectional tensile test was 50 mm. Three groups of unidirectional tensile samples were cut along the directions of 0◦, 45◦, and 90◦ with respect to the rolling direction. The strain rate during the tensile test was 0.0013/s. To obtain the anisotropy coefficient, the axial strain, and the transverse strain during the deformation process of the sample were recorded by an online strain-measurement system based on digital image correlation (DIC). The testing machine and the DIC online strain-measurement system are shown in Figure 2a, and the size of the uniaxial tensile sample is shown in Figure 2b.

**Figure 2.** Uniaxial tensile test diagram of 2A11 aluminum alloy sheet: (**a**) test drawing machine diagram; (**b**) uniaxial tensile sample.

The engineering stress–strain curve of the large sample was obtained by the uniaxial tensile test, and the real stress–strain data were obtained according to the conversion formula, as shown in Figure 3a. In the uniaxial tensile process of the sample in three directions, the strains in the width and thickness directions were measured to obtain the *r* value, and the results are shown in Figure 3b. According to Equation (9), the initial yield point in the real stress–strain curve of 2A11 aluminum alloy sheet was taken as the starting point of the back stress parameter fitting curve for obtaining the relevant parameters. The parameters of each material model are listed in Tables 1 and 2.

**Figure 3.** (**a**) True stress–strain curve of 2A11 aluminum alloy sheet; (**b**) anisotropy coefficient of 2A11 aluminum alloy sheet.


**Table 1.** Simulation of material parameters required.

**Table 2.** Ratio of anisotropic yield stress of materials.


#### **3. Cyclic Sheet Tension-Compression Test and Sample Shape Optimization**

*3.1. Shape Optimization of Cyclic Sheet Tension-Compression Sample*

The cyclic tensile–compression test of aluminum bars is relatively easy to perform and there are corresponding standards to follow [20,21]. However, an aluminum alloy sheet is prone to instability during compression, and the optimum sample shape to minimize the stress-measurement error and suppress the in-plane buckling of the sample has not yet been defined [22]. Therefore, this study used the finite element method (FEM) to identify the shape parameters that had an effect on the stress-measurement error and the shape parameters that had an effect on the suppression of in-plane buckling to determine the optimum shape of the sample for use in the cyclic tension-compression tests.

Figure 4 represents the shape parameters of the sheet tensile–compression sample evaluated in this study. The width and length of the parallel section are *W* and *L*, respectively; the radius of the fillet of the transition section between the parallel section and the clamping end is *R*; the width of the clamping end is *B* and the length of the clamping end was determined by the clamping head size of the test machine and was set at 30 mm.

When a sheet tensile–compression sample was subjected to in-plane compression, the deformation within the parallel section was not uniform due to the transition section constraining the deformation near the ends of the parallel section, resulting in inconsistent compressive stresses. Therefore, the sample shape had to be optimized to improve the accuracy of the stress measurement. In addition, in order to retard the onset of in-plane

buckling and to allow greater compression to be applied, shape parameters that helped to suppress in-plane buckling had to be defined to optimize the cyclic drawing of the sheet samples.

**Figure 4.** Geometrical parameters of the sample for in-plane compression test and schematic illustration of the difference between mean stress <sup>σ</sup>(G) <sup>x</sup> and local stress <sup>σ</sup>(L) <sup>x</sup> .

In the cyclic sheet tensile–compression test, the average stress <sup>σ</sup>(G) <sup>x</sup> can be found from the compression force F and the area of the central section of the sample derived from the constant volume criterion. However, the local stress <sup>σ</sup>(L) <sup>x</sup> at the center of the sample in the experiment could not be obtained in the sample and could be extracted in the postprocessing results of the FEM. The smaller the difference between the absolute value of the local stress <sup>σ</sup>(L) <sup>x</sup> and the mean stress <sup>σ</sup>(G) <sup>x</sup> in the central part of the sample, the higher the accuracy of the stress measurement. Therefore, the FEM was used to analytically determine the sample shape that minimizes the difference between the local stress <sup>σ</sup>(L) <sup>x</sup> and the mean stress <sup>σ</sup>(G) <sup>x</sup> .

The relative deviation of <sup>σ</sup>(L) <sup>x</sup> from <sup>σ</sup>(G) <sup>x</sup> is given by the following equation:

$$\pi\_{\rm ll} = \frac{\sigma\_{\rm x}^{(G)} - \left| \sigma\_{\rm x}^{(L)} \right|}{\left| \sigma\_{\rm x}^{(L)} \right|} \times 100\% \tag{10}$$

The smaller the τ<sup>m</sup> sample shape, the greater the accuracy of the stress measurement.

The deformation was not uniform in the parallel part of the sample, due to cyclic tension–compression. To clarify the sample shape parameters that inhibit surface buckling using the FEM, the width difference W-W1 = 0.05 mm between the two ends of the parallel section was set as the initial unevenness to perform the buckling analysis. Under compression, the parallel section of the sample will produce shear stress σ(L) xy . The ratio of shear stress σ(L) xy in the central part of the sample to local stress <sup>σ</sup>(L) <sup>x</sup> was used to determine the buckling of the sample. The determination formula of in-plane buckling is as follows:

$$\mathbf{r\_s} = \frac{\left| \sigma\_{xy}^{(L)} \right|}{\left| \sigma\_x^{(L)} \right|} \times 100\% \tag{11}$$

The smaller the *τ*s, the less the possibility of buckling during compression.

#### *3.2. FEM Model for Sample Shape Optimization*

To obtain the optimum sample shape for the cyclic sheet tensile–compression test, a finite element model for the cyclic sheet tensile–compression test was established, as shown in Figure 5a. The aspect ratio of the deformation zone to the width of the clamping end B and the corner radius R of the corner transition zone had a great influence on the accuracy of the stress measurement and the compression limit, so a variety of dimensional parameters were set for the FEM analysis, as shown in Figure 5b. The clamping plates on both sides of the sample deformation zone were always clamped with a clamping force of 940 N. The clamping plates on both sides of the clamping end were bound together with the clamping end of the sample. The friction coefficient between the cyclic tension– compression sample and the clamping plates was set to 0.084. The strain rate during the cyclic tension-compression test was 0.0013/s. In the finite element model for the cyclic sheet tensile–compression test, the cyclic sheet tensile–compression sample was set up as a deformed body and all the remaining components were defined as rigid bodies. The sample was set up with five integration points in the thickness direction by applying a four-node curved thin-shell or thick-shell reduction integral, an S4R cell with finite film strain, and an hourglass control. The element size of the sample was set to 0.5 mm to ensure that no distortion occurred in the process of compression, so as to obtain accurate stress calculation results.

**Figure 5.** (**a**) Finite element simulation model; (**b**) sample geometries investigated in this study.

#### *3.3. Sample Shape Optimization Simulation Results*

#### 3.3.1. Effect of Sample Deformation Zone Aspect Ratio *λ* and Clamping End Width B

During the compression of the cyclic sheet tensile–compression sample, *B*/*W* = 1.4, *R*/*W* = 1.2; *B*/*W* = 2.4, *R*/*W* = 1.2 were set to investigate the effect of the aspect ratio *λ* of the deformation zone of the sample and the width *B* of the clamping end. From the simulation results, as shown in Figure 6a,b, when the width *B* of the sample clamping end and the radius *R* of the fillet area were certain, the stress-measurement accuracy gradually increased with the increase in the sample deformation zone aspect ratio *λ*. The stress-measurement accuracy decreased due to the increase in the length of the sample deformation zone and the influence of the corner area on the measurement accuracy became smaller when the width of the clamping end *B* was too large. Buckling was more likely to occur when the sample deformation zone was too long, as shown in Figure 6c,d. The wider the sample clamping end, the more serious the deformation of the rounded area as the transition area, which exerted more influence on measurement accuracy. From the simulation results and the above analysis, it can be seen that the longer the deformation zone of the sample, the higher the accuracy of the stress measurement, but buckling was also more likely to occur; therefore, the best aspect ratio of the deformation zone of the sample was moderately chosen as *λ* = 2. The deformation of the fillet area of the sample directly affects the accuracy of the stress measurement, so it was necessary to investigate the influence of the shape and size of the fillet area on the accuracy of the stress measurement.

**Figure 6.** Effect of aspect ratio λ on the variation of τ<sup>m</sup> and τ<sup>s</sup> with true strain: (**a**) B/W = 1.4; (**b**) R/W = 1.2; (**c**) B/W = 2.4; (**d**) R/W = 1.2.

During the compression of the cyclic sheet tensile–compression sample, *B*/*W* = 1.4, *R*/*W* = 1.2; *B*/*W* = 2.4, *R*/*W* = 1.2 were set to investigate the effect of the aspect ratio *λ* of the deformation zone of the sample and the width *B* of the clamping end. From the simulation results, as shown in Figure 6a,b, when the width *B* of the sample clamping end and the radius *R* of the fillet area were certain, the stress-measurement accuracy gradually increased with the increase of the sample deformation zone aspect ratio *λ*.

#### 3.3.2. Effect of Fillet Radius R in the Fillet Area of the Sample

Applying *B*/*W* = 1.4, *λ* = 2, different sizes of fillet radius *R* were set to analyse the effect on stress-measurement accuracy and buckling. The simulation results are shown in Figure 7. An increase in the fillet radius improved the accuracy of stress prediction and it was less likely that buckling occurred. The reason for this was that the large fillet radius area weakened the restraint on both ends of the parallel section, so the parallel section deformed more uniformly and was less likely to buckle.

**Figure 7.** Effect of fillet radius R on (**a**) τ<sup>m</sup> and (**b**) τs.

#### 3.3.3. Influence of n-Values of the Sample

With sheets of different materials, n-values (the strain hardening exponent in Swift's equation) vary widely, and it is known from studies related to buckling formation that the larger the n-value of the sheet, the less likely it is to buckle [23]. The uniaixal tensile curve of 2A11 aluminum alloy sheet was fitted and its *n* value was obtained as 0.3468. The n-values of 0.2, 0.3468 and 0.5 were set, and the parallel section aspect ratio *λ* = 2 and *B*/*W* = 1.4 were used for FEM analysis. The results are shown in the Figure 8. With the increase in n-value, the stress-measurement accuracy was higher and the tensile samples were less likely to buckle during the compression process. In summary, the sheets with large n-values had a higher stress-measurement accuracy in sheet drawing and in the cyclic sheet tensile–compression test, due to stable deformation and the sample was less prone to buckling; the plates with large n-values had better forming performance in stamping and forming with cyclic loading characteristics.

**Figure 8.** (**a**) Effect of n-values on τm; (**b**) Effect of n-values on τs.

Based on the above analysis of the FEM results for the optimization of the cyclic sheet tensile–compression sample shape, it can be seen that the sample shape with a moderate aspect ratio of parallel sections and larger radius of fillet was selected for higher accuracy of stress measurement and less susceptibility to buckling. The final determination of the shape and size of the cyclic sheet tensile–compression sample is shown in Figure 9b.

#### *3.4. The Cyclic Sheet Tensile–Compression Test*

To obtain the cyclic tensile–compression stress–strain curves of the studied sheets, an anti-buckling fixture was designed, as shown in Figure 9a. The cyclic tensile–compression test of the studied sheets used the specimen geometry of Figure 9b. The anti-buckling fixture was made of transparent acrylic sheets on both sides as raw material, and optical strain-measurement equipment was used to accurately measure the strain change of the sample. The transparent acrylic sheet did not affect the DIC camera's shooting, as shown in Figure 9c. The sheet had a change in thickness during the tensile–compression process, so the disc spring placed between the bolt and the clamping plate ensured that the clamping plate was always clamping elastically during the clamping process.

The relative sliding between the tensile–compression sample and the clamping plate generated friction, and the direction of the friction force was opposite to the direction of the movement of the tester chuck, making the load measured by the tester large. Assuming that the friction force was uniformly distributed on the contact surface, the Coulomb friction formula was applied to calculate the magnitude of the friction force during the test, and the friction force was removed from the measured test data to eliminate the error caused by friction on the load measurement. In order to determine the friction coefficient between the sheet and the clamping plate, the friction coefficient between the 2A11 aluminum alloy sheet and the acrylic plate was tested using a friction and wear tester produced by the Center for Tribology (CETR) in the United States The friction coefficient, using transparent silicone oil as a lubricant, was 0.084. The anti-buckling fixture was used to perform cyclic tensile–compression tests on sheet metal on the InspektTable-100 material universal testing machine, and the strain changes during sample deformation were recorded by the DIC online strain-measurement system.

**Figure 9.** Cyclic tensile–compression test: (**a**) schematic diagram of cyclic tension and compression test; (**b**) schematic drawing of used tensile–compression specimen; (**c**) cyclic tension and compression test device.

The disc spring gasket was of type A (GB/T1972-2005), with dimensions of outer diameter ϕ10 mm, inner diameter ϕ5.2 mm, thickness 0.5 mm, initial height 0.75 mm, and compressible amount 0.25 mm. The disc springs buckled in two groups of the same specification, each group made up of three stacked disc springs, and the combined buckling disc spring group was compressed by 0.75 mm, as shown in Figure 10a, while the stiffness curve of the single group of disc springs was measured by the InspektTable-100 material universal testing machine (Huibo, Germany). In the cyclic sheet tensil–compression test, the pre-compression of the disc spring group was 0.3 mm, and the total clamping force

of the four groups of disc springs varied with the thickness of the sample, as shown in Figure 10b. The cyclic stress–strain curve for the selected specimen of Figure 9b, after eliminating the effect of fixture friction, is shown in Figure 10c. Similar data were obtained by many cyclic tensile–compression tests, and the test results were reliable.

**Figure 10.** (**a**) Stiffness curve of butterfly spring group/mm; (**b**) tension and compression process node; (**c**) cyclic tension and compression stress–strain curve for the selected specimen of Figure 9b.

*3.5. Determination of the Mixed Hardening Constitutive Model Parameter*

The flow stress and the equivalent plastic strain in the constitutive model were nonlinearly mapped, and there were many parameters. In order to obtain each parameter of the constitutive model accurately, the solution was based on the cyclic sheet tensile– compression stress–strain curve. The material flow stress in the uniaxial stress state in uniaxial tension for the mixed hardening constitutive model can be expressed as follows:

$$
\sigma = \sigma\_0 + Q \left( 1 - e^{-\beta \varepsilon\_1^p} \right) + \frac{2}{3} \frac{C}{\gamma} \left( 1 - e^{-\gamma \varepsilon\_1^p} \right) \tag{12}
$$

When the uniaxial tension reached *σ* = *σ<sup>c</sup>* and the plastic pre-strain was equal to *ε<sup>D</sup>* during reverse loading and unloading, the flow stress was calculated as follows:

$$\sigma = -\sigma\_0 - Q\left(1 - e^{-\hbar \varepsilon\_1^p}\right) - \frac{2}{3} \frac{C}{\gamma} \left(1 - e^{-\gamma \varepsilon\_1^p}\right) \left(1 - \left(2 - e^{-\gamma \varepsilon\_D}\right) e^{\gamma \left(\varepsilon\_D - \varepsilon\_1^p\right)}\right) \tag{13}$$

When it is reverse loading to *εG*, it is reverse loading again. At this time, the plastic strain is *εH*, and the flow stress is as follows:

$$\sigma = \sigma\_0 + Q\left(1 - e^{-h\varepsilon\_1^p}\right) + \frac{2}{3}\frac{\mathcal{C}}{\gamma}\left(1 - \left(2 - \left(2 - e^{-\gamma\varepsilon\_D}\right)e^{\gamma(\varepsilon\_H - \varepsilon\_D)}e^{\gamma(2\varepsilon\_D - \varepsilon\_H - \varepsilon\_1^p)}\right)\right) \tag{14}$$

Let *A* = *σ*<sup>0</sup> + *Q* + *<sup>C</sup> <sup>γ</sup>* , *B* = −*Q*, *C* = *b*, and *E* = *γ*, and through the summary Equations (12)–(14), it can be obtained that the general stress-strain equation in the process of the uniaxial cyclic tension-compression loading process is as follows:

$$
\sigma = A + B e^{-\mathbb{C}x\_1^p} \pm D e^{-\mathbb{E}x\_1^p} \tag{15}
$$

where, *A*, *B*, *C*, and *E* are material constants that can be obtained by fitting the cyclic tensile–compression stress–strain curve derived from the cyclic sheet tensile–compression test, and *D* is a constant related to the direction of the pre-strain, with a plus sign for the forward direction and a minus sign for the reverse direction.

According to the cyclic tensile–compression stress–strain curves derived from the cyclic tensile–compression tests, four material characteristic parameters—*Q*, *b*, *C*, and *γ*—in the mixed hardening model can be obtained by fitting. The goodness of fit R<sup>2</sup> was 0.99 and the fitting accuracy was high. *Q* and *b* are the parameters related to isotropic hardening; *C* and *γ* are the parameters related to kinematic hardening, as shown in Table 3.

**Table 3.** Parameters obtained in the combined hardening model.


#### **4. Reliability Analysis of the Constitutive Model**

*4.1. The Application of the Constitutive Model in the Cyclic Sheet Tensile–Compression Problem*

The material characteristic parameters of the A–F nonlinear kinematic hardening constitutive model, based on the Hill48 anisotropic yield criterion, and the material characteristic parameters of the mixed hardening constitutive model, based on the Hill48 anisotropic yield criterion, the Voce isotropic hardening model, and A–F nonlinear kinematic hardening model, were input into the cyclic sheet tensile–compression simulation model. The simulation results of the two constitutive models were compared with the experimental results, as shown in Figure 11.

In the initial tensile stage, the simulated results of the two constitutive models were in general agreement with the experimental results. When the sheet was subjected to tensile deformation unloading, and reverse compression, the simulated results deviated from the experimental results, with an average deviation of 7.4% for the simulated results of the kinematic hardening model and 2.1% for the simulated results of mixed hardening model. When the sheet was stretched again, the average deviation of the simulated results of mixed hardening model was 1.3%, while the average deviation of the simulated results of kinematic hardening model was 11.7%.

**Figure 11.** Fitting and calibration of constitutive elastic–plastic material model parameters and comparison of simulation and experimental results.

#### *4.2. The Application of the Constitutive Model in the Continuous Bending Problem*

The kinematic hardening model and the mixed hardening constitutive model were applied to the simulation of continuous bending, straightening, and reverse bending deformation. The FEM model was established for simulation analysis, as shown in Figure 12. The continuous bending model structural parameters were as follows: the transitions rounding of the upper and lower die were 7.34 mm and 8 mm, respectively; the radii of the semicircular rounding of the upper and lower die were 8.66 mm and 8 mm, respectively; the 2A11aluminum alloy sheet with a thickness of 0.6 mm was chosen as the object of study, and the sheet's length, width, and thickness were 100 mm, 10 mm, and 0.6 mm, respectively. After the upper and lower die closed the die, a gap of 0.06 mm was retained. A 4-node reduced integration S4R unit was used to divide the sheet, and five integration points were set in the sheet thickness direction. In order to ensure the smooth progress of the continuous bending test, no fracture occurred in the sample, Coulomb friction was used between the contact surface of the upper and lower die and the sheet, and the friction factor was set to 0.096. The front end of the sheet was bound to the pulling plate and the displacement constraint was used.

**Figure 12.** Finite element simulation model.

The material characteristic parameters of the A–F nonlinear kinematic hardening constitutive model, based on the Hill48 anisotropic yield criterion, and the material characteristic parameters of the mixed hardening constitutive model, based on the Hill48 anisotropic yield criterion, the Voce isotropic hardening model, and the A–F nonlinear kinematic hardening model, were input into the sheet continuous-bending model and compared with the sheet continuous-bending test for analysis.

The continuous-bending test die of the sheet is shown in Figure 13. Figure 13a,b show the upper and lower die of the continuous bending test die, respectively, and the size is the same as the size of the die in the simulation model. The upper and lower dies were fixed by bolts, and the upper chuck of the InspektTable-100 material universal testing machine clamped the clamping end of the upper die, and the lower chuck of the universal testing machine clamped the lower end of the continuous bending sample, as shown in Figure 13c. In the continuous-bending test, the specimen was easy to break because of the large bending deformation. In order to ensure the smooth progress of continuous-bending test without fracturing the sample, an oil-based molybdenum disulfide lubrication was applied between the continuous-bending sample and the mold, and the friction coefficient was 0.096. During the test, the upper chuck was fixed and the lower chuck was moved down at a constant speed of 50 mm/min. The state of the continuously bent sample after the die assembly and after experiencing continuous bending is shown in Figure 13d.

**Figure 13.** (**a**) Upper die; (**b**) Lower die; (**c**) Continuous bending test die; (**d**) Continuous bending Sample.

Figure 14 shows the results of the comparison between the lower chuck tension during the continuous-bending test and the pulling plate tension in the simulation results. The computational error of the mixed hardening model is smaller than that of the kinematic hardening model and is closer to the test value. The wall thickness distribution of the sample after continuous bending was measured with a micrometer and compared with the simulation results of the two constitutive models in the same state. The wall-thickness distribution of the samples in the simulation results of the kinematic hardening model and the mixed hardening model was consistent with the trend of the experimental results, and the simulation results of the mixed hardening model were closer to the experimental results, with little deviation. It was demonstrated that the material characteristic parameters of the mixed hardening constitutive model, based on the Hill48 anisotropic yield criterion, the Voce isotropic hardening model, and the A–F nonlinear kinematic hardening model, can be

used to study the continuous-bending deformation behavior of the sheet under a complex loading condition, and its calculation results are reliable.

**Figure 14.** Comparison between FEM results and experimental results.

#### *4.3. Application of Constitutive Model in the Springback Problem*

A three-point bending FEM model was created, as shown in Figure 15, to test the correctness of the two constitutive models used to simulate the springback issue. The three-point bending test model's indenter diameter was 20 mm, the support point diameter was 30 mm, the distance between the two support points was 100 mm, and the threepoint bending sample's length, width, and thickness were 120 mm, 20 mm, and 0.6 mm, respectively. The sheet material was divided into five integration points in the direction of the sheet thickness using a 4-node reduced integration S4R cell. Coulomb friction was used between the contact surfaces, and the friction factor was set to 0.1. Two support points were fixed, and the indenter was constrained by displacement. The material characteristic parameters of the A–F nonlinear kinematic hardening constitutive model, based on the Hill48 anisotropic yield criterion, and the material characteristic parameters of the mixed hardening constitutive model, based on the Hill48 anisotropic yield criterion, the Voce isotropic hardening model, and the A–F nonlinear kinematic hardening model, were input into the sheet three-point bending model and compared with the three-point bending test for analysis.

In sheet metal forming, the prediction of springback is important to show the desired final geometrical quality of the parts. Figure 15 presents the final result after springback was obtained from the kinematic hardening model, the mixed hardening model, and the experimental results. The results of the mixed hardening model matched the experimental data with superior accuracy than the results of the kinematic model, according on comparisons of the final shapes after the anticipated springback.. This proved that the mixed hardening model implemented in ABAQUS (version 6.14, Dassault Systemes Simulia Corp., Providence, RI, USA) can be applied for an accurate prediction of springback in complex industrial sheet metal forming operations.


**Figure 15.** Comparison of the FEM results and the experimental results.

#### **5. Conclusions**

(1) The FEM analysis of the in-plane compression sample quantitatively specified the shape parameters that minimize the measurement error of compressive stress and help to suppress in-plane buckling. A transparent anti-buckling fixture was designed to accurately measure the strain variation of the cyclic tensile–compression sample using optical strain-measurement equipment.

(2) An anisotropic mixed hardening constitutive model based on the Hill48 anisotropic yield criterion, the Voce isotropic hardening model, and the A–F nonlinear kinematic hardening model was established. The cyclic deformation stress–strain curves of 2A11 aluminum alloy sheet were obtained by cyclic sheet tensile–compression tests, and the material characteristic parameters in the mixed hardening model were accurately determined. The obtained material characteristic parameters were directly input into the Abaqus simulation software, eliminating the need for tedious secondary development.

(3) The reliability and accuracy of the established constitutive model for anisotropic mixed hardening materials were verified through finite element simulations and tests of the aluminum alloy sheet cyclic tension-compression problem, the springback problem, and the sheet in bending, unloading, and reverse bending problems. It provided a reliable research tool for predicting the deformation behavior of the sheet under complex loading conditions with cyclic loading characteristics.

**Author Contributions:** Conceptualization, G.C.; methodology, G.C., Q.Z. and C.W.; software, G.C. and H.S.; validation, C.Z., Q.Z. and D.C.; formal analysis, C.Z.; investigation, C.Z., H.S., Z.L., C.W. and D.C.; resources, G.S.; data curation, G.S.; writing—original draft preparation, H.S.; writing review and editing, G.C.; visualization, Z.L.; supervision, G.C.; project administration, G.C.; funding acquisition, G.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All data were obtained by the author through experiment.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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**Junlong Tang 1,\*, Shenbo Liu 1, Dongxue Zhao 1, Lijun Tang 1, Wanghui Zou <sup>1</sup> and Bin Zheng <sup>2</sup>**


**Abstract:** Surface defects, which often occur during the production of aluminum profiles, can directly affect the quality of aluminum profiles, and should be monitored in real time. This paper proposes an effective, lightweight detection method for aluminum profiles to realize real-time surface defect detection with ensured detection accuracy. Based on the YOLOv5s framework, a lightweight network model is designed by adding the attention mechanism and depth-separable convolution for the detection of aluminum. The lightweight network model improves the limitations of the YOLOv5s framework regarding to its detection accuracy and detection speed. The backbone network GCANet is built based on the Ghost module, in which the Attention mechanism module is embedded in the AC3Ghost module. A compression of the backbone network is achieved, and more channel information is focused on. The model size is further reduced by compressing the Neck network using a deep separable convolution. The experimental results show that, compared to YOLOv5s, the proposed method improves the mAP by 1.76%, reduces the model size by 52.08%, and increases the detection speed by a factor of two. Furthermore, the detection speed can reach 17.4 FPS on Nvidia Jeston Nano's edge test, which achieves real-time detection. It also provides the possibility of embedding devices for real-time industrial inspection.

**Keywords:** real-time detection; lightweight network structure; YOLOv5s; attention mechanism; edge computing

#### **1. Introduction**

Due to their excellent thermal conductivity and moisture resistance, aluminum profiles have become an important primary material for buildings, vehicles, ships, houses, and other fields. With the rapid development of related industries, the demand for highquality aluminum profiles is also increasing. Surface defects on aluminum profiles directly affect the quality of products. Therefore, it is significant to detect those defects during their production.

It is difficult to use traditional manual visual inspection to ensure the accuracy of inspection results and inspection efficiency because manual processes can produce a series of problems, such as inefficiency and human physiological fatigue [1]. Some scholars have applied machine learning methods for industrial defect recognition to solve those problems. Yu et al. [2] utilized SVM (support vector machine) to classify wood surface defects. The recognition accuracy of the back propagation neural network model proposed by the authors was 92.7% and 92.0% in the training and test sets, respectively. Hu et al. [3] proposed an algorithm based on ellipse fitting with distance thresholding to detect crater defects on steel shell surface. Elliptical fitting of the extracted inner circle curve was performed, and thus there was high accuracy and detection efficiency for crater defects. You et al. [4] identified crack defects of 0.15 mm using the C-scanning method. This

**Citation:** Tang, J.; Liu, S.; Zhao, D.; Tang, L.; Zou, W.; Zheng, B. An Algorithm for Real-Time Aluminum Profile Surface Defects Detection Based on Lightweight Network Structure. *Metals* **2023**, *13*, 507. https://doi.org/10.3390/ met13030507

Academic Editor: John D. Clayton

Received: 9 February 2023 Revised: 24 February 2023 Accepted: 27 February 2023 Published: 2 March 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

approach can only identify crack defects and has its limitations. K et al. [5] realized the detection of internal defects in carbon-fiber-reinforced plastics and glass-fiber-reinforced plastics using recurrence methods and C-scans. Chen et al. [6] presented smooth filtering to detect steel plate surface defects. Wang et al. [7] use SUSAN operator to detect the edges of the foil image and obtain the threshold aluminum foil image to determine the effective area of the foil in the image. The localization and identification of defects on the surface of aluminum foil were achieved. Although the abovementioned works have achieved some good results in surface defect detection, there are still some limitations, such as poor robustness and weak adaptability.

With the convolutional neural networks (CNNs) proposed, deep learning, which overcomes the limitations of machine learning methods, has been widely used for surface defect detection [8]. Deep-learning-based target detection algorithms are mainly divided into two categories. One is a two-stage classification, and the representative algorithms include R-CNN (regions with CNN features) [9], Fast R-CNN(fast region-based CNN) [10], and Faster R-CNN [11]. These algorithms are applied to the creation and the classification of candidate boxes. The other is single-stage classification, and the representative algorithms include SSD (Single Shot MultiBox Detector) [12], YOLO (You Only Look Once) [13–16], CenterNet [17], and Retinanet [18]. These algorithms generate class probability values and coordinates of the position of the target object during the creation of a candidate frame. The final detection result can be obtained directly after detecting the target. Fu et al. [19] proposed an end-to-end model based on SqueezeNet to achieve steel strip detection under inhomogeneous illumination with a detection speed of more than 100 fps. However, a dataset with insignificant difference in defect target size was used. Li et al. [20] have improved the network structure of YOLO and achieved an accurate detection of steel strips with 95.86% mAP for defects. Yang et al. [21] have realized the detection of surface defects in automotive pipe joints based on wavelet decomposition and convolutional neural networks. Amin et al. [22] fulfilled the detection of surface defects in steel based on U-NET [23]. Defects can be detected quickly, but the detection accuracy is only 0.731. Zhang et al. [24] proposed the MRSDI-CNN algorithm, which combined SSD with YOLOv3 for the recognition of surface defects on steel rails. The detection speed was improved to a certain extent, but the real-time detection is not realized on embedded devices. Chen et al. [25] have fulfilled the recognition of steel rail surface defects based on Faster R-CNN with 97.8% mAP of blemishes. However, it is not real-time to detection of surface defects. Y et al. [26] implemented the defect depth detection of 3D woven composites using Fully Convolutional Neural Network and recurrence methods. Zhou et al. [27] implemented microtubule defect detection on wafer surface by embedding DA attention module in YOLOv5. The algorithm model has good detection capability on small target defects; however, it is large in size and cannot achieve real-time detection. A CNN-based detection algorithm can be accurate regarding aluminum surface defects, but the detection speed cannot meet industrial inspection needs.

With the development of lightweight network technology, many scholars have realized the real-time detection of surface defects of aluminum profiles by adding a lightweight network to the detection algorithm. Ma et al. [28] implemented the detection of surface defects on aluminum strips by embedding a Ghost module with union attention mechanism in YOLOv4 network. The method achieved an mAP value of 94.68%, a model volume reduction of 80.41%, a threefold increase in detection speed, and better performance than the YOLOv4 model. However, the model size of the algorithm is 48.5 MB and the detection speed is 20.749 f/s, so there is still room for improvement. Wang et al. [29] proposed an improved MS-YOLOv5 model based on the YOLOv5 algorithm. A multi-stream network was present as the first detection head of the algorithm, and the Neck layer was optimized. The model recognition ability and model localization extraction at different sizes were improved. However, the mAP of the model is 87.4%, which cannot meet the needs of industrial inspection. Yang et al. [30] achieved accurate identification of dirty spots by embedding FPN structures in Faster R-CNN to improve the model's ability to extract feature

information about defects. There were strong limitations for the algorithm. It was used to only identify defects within a single category under specific conditions, and is not suitable for surface defect detection of aluminum profiles in industrial manufacturing processes. Li et al. [31] implemented the detection of 10 kinds of aluminum profile surface defects based on migration learning, and the classification accuracy reached 98.47%. However, the speed of detection was not mentioned. Wu et al. [32] proposed a defect detection model based on YOLO X, which replaced the original CSP-DarkNet with CSP-ResNeXt and integrated an attention mechanism. The algorithm achieved 90.69% mAP with a detection speed of 33.6 FPS. Although the above work has achieved some good results in the detection of aluminum surface defects, the detection speed and detection accuracy still need to be further improved.

Deep-learning-based defect detection algorithms can achieve high accuracy rates for specific datasets. As the size of defects on the surface of aluminum profiles varies greatly, those methods fail to achieve good results, and real-time detection is difficult to implement in embedded devices. Therefore, this study designs a novel lightweight network based on the YOLOv5s algorithm to realize a real-time defect detection of aluminum profile surfaces on an embedded system with promising detection accuracy. Depth-separable convolution and Ghostconv are used to compress the lightweight network model, and an attention mechanism is embedded in the backbone network to increase the attention of the network to channel information. As a result, the detection accuracy of the algorithm is improved. The proposed algorithm of the novel lightweight network can reach an accurate real-time detection on embedded devices in this study. Specific innovation points are as follows:


#### **2. Image Preprocessing and Datasets**

Insufficient training samples during the training process can lead to low detection accuracy, overfitting, and low robustness. The number of images is increased by appropriate enhancement of the original images to effectively solve the problem of insufficient training samples [33]. Four typical types of defects on the surface of an aluminum profile are scuffing, soiling, folds, and pinholes, as shown in Figure 1. For the dataset, the pixel size of each image is 640 × 480. A pinhole is caused by the formation of tiny pores during the solidification of aluminum, with an average pixel size of 20 × 20. According to the definition in the literature [34], a pinhole with less than 1.23% of annotated pixels is a small object. Dirt is introduced by the contamination of equipment lubricants. Scratches are caused by relative friction between aluminum and equipment during processing and production. Folds are caused by unbalanced forces during aluminum processing and production. Lin et al. [35] have improved the robustness of defect detection using Gaussian filtering for noise reduction regarding the target. Simonyan et al. [36] processed the images by random flip, rotate, and crop to effectively expand the dataset. This easily leads to missed detection and false detection for low-resolution small targets, the presence of few available features, and high positioning accuracy requirements and aggregation. To enhance the semantic information of small targets, this paper adopts noise reduction by utilizing Gaussian low-pass filtering during copy-pasting in specific regions. The pinholes generated by copy-pasting and Gaussian blur techniques have more effective feature information. Following this, the images are expanded by random flip, rotation, and cutout. The cutout is able to further enhance the localization capability of the model by requiring the model to identify objects from a local view and adding information about other samples to the cut region. Color space transformation generally eliminates lighting, luminance and color differences. These image preprocessing operations increase the number of training datasets to make them as diverse as possible, which in turn improves the generalization ability and robustness of the model. The results of the expanded images are shown in Figure 2. After image enhancement and expansion, the dataset reached 4400 images. Among the dataset, 3600 images are randomly selected for the training set, 400 images for the testing set, and the remaining 400 images for the validation set.

**Figure 1.** The four defects of aluminum profiles: (**a**) pinhole; (**b**) dirt; (**c**) fold; (**d**) scratch.

**Figure 2.** *Cont*.

**Figure 2.** Images were obtained using the expansion technique.

#### **3. Description of Methodology**

#### *3.1. Network Architecture*

In this study, a lightweight model network structure based on the four basic structural frameworks of YOLOv5s is proposed, and consists of Input, GCANet backbone, Neck, and Prediction. Through the lightweight modules with embedded attention mechanisms, real-time accurate detection of surface defects on aluminum profiles is achieved.

Figure 3 shows the lightweight model network structure based on YOLOv5s. In the Input layer, the input image is resized to 640 × 640 × 3, and is input to the GCANet backbone. The attention mechanism is embedded in the C3Ghost module to improve ability of the model to focus on channel information and spatial information. Three scale feature maps, (80 × 80) (40 × 40) (20 × 20), are extracted at different levels. Following this, based on the DwConv module, the images are inputted to Neck for further compression of the model. Finally, detection is performed in Prediction.

#### *3.2. GCANet Backbone Structure*

The GCANet backbone architecture consists of the CBL module, Ghost module, and AC3Ghost module. The CBL module consists of Conv, BatchNorm, and Leaky relu. The ghost module is from GhostNet, proposed by Huawei in 2020. Compared to traditional convolution, Ghost convolution is divided into two steps, which can effectively reduce the amount of computation and number of parameters. Firstly, the standard convolution is used to compute and obtain *m* feature maps with fewer channel features, then *s* feature maps are generated using cheap linear operations. Secondly, the two feature maps are concatenated to obtain the new output of *m* · *s* feature maps. The structure of the Ghost module is shown in Figure 4. In standard convolution, the number of convolution kernels is assumed to be *n*, the size of the input feature map is *h* · *w* · *c*, the output feature map is *n* · *h* · *w* , and the convolution kernel is *k* · *k*. The model floating-point computations for standard convolution and Ghost convolution are *q*<sup>1</sup> and *q*2, respectively.

$$q\_1 = n \cdot h' \cdot w' \cdot c \cdot k \cdot k \tag{1}$$

$$q\_2 = \frac{n}{s} \cdot h' \cdot w' \cdot c \cdot k \cdot k + (s-1) \cdot \frac{n}{s} \cdot h' \cdot w' \cdot d \cdot d \tag{2}$$

hh

where *c* denotes the number of channels of the input image, *k*·*k* denotes the size of the convolution kernel of the standard convolution operation, *h* and *w* are the height and width of the original feature map by Ghost convolution, *h* and *w* denotes the height and width of the original feature map generated by Ghost convolution, *d*·*d* is the size of the convolution kernel of the linear operation, and *s*<<*c*. hh hh

hh

**Figure 3.** The lightweight model network structure based on YOLOv5s.

**Figure 4.** Ghost module structure.

The comparison of the computation of the standard convolution operation and the Ghost module is shown in (3). A comparison of the parametric quantities of the two convolutions is shown in (4). From Equations (3) and (4), it can be seen that when *k* and *d* are equal in size, the number of parameters and the computational effort for feature extraction of Ghost convolution is about 1/*s* for that of the standard convolution.

$$\begin{array}{rcl} r\_s &=& \frac{\frac{n \cdot h' \cdot w' \cdot c \cdot k \cdot k}{\frac{n}{s} \cdot h' \cdot w' \cdot c \cdot k \cdot k + (s-1) \cdot \frac{n}{s} \cdot h' \cdot w' \cdot d \cdot d}}{\frac{c \cdot k \cdot k}{\frac{1}{s} \cdot c \cdot k \cdot k + \frac{s-1}{s} \cdot d \cdot d} \approx \frac{s \cdot c}{s + c - 1} \approx s} \end{array} \tag{3}$$

$$r\_{\varepsilon} = \frac{n \cdot c \cdot k \cdot k}{\frac{\underline{n}}{s} \cdot c \cdot k \cdot k + (s - 1) \cdot \frac{\underline{n}}{s} \cdot d \cdot d} \approx \frac{s \cdot c}{s + c - 1} \approx s \tag{4}$$

#### *3.3. AC3Ghost Structure*

Adding attention mechanisms to neural networks can effectively improve the performance of network feature extraction. Hu et al. [37] proposed an SE attention mechanism to establish spatial correlation in feature maps. Hou et al. [38] proposed the CA attention mechanism to integrate spatial coordinate information into feature maps effectively. Woo [39] proposed the CBAM attention mechanism to pay attention to channel and spatial information. To effectively utilize the channel and spatial information, this paper proposes an AC3Ghost module consisting of the CBAM attention mechanism and C3Ghost module, and the CBAM attention mechanism is embedded in C3Ghost. The structure of the AC3Ghost module is shown in Figure 5. When the data processed by the Ghost are input to AC3Ghost, the AC3Ghost module is divided into two branches to process in parallel, one for hierarchical feature fusion by multiple Ghost Bottleneck stacks and three 1 × 1 convolution modules, and the other for reducing the number of channels by only one 1 × 1 convolution module. Following this, feature maps of the two branches are fused as output feature maps by concat, and the CBAM attention mechanism focuses on the channel and spatial information. Finally, it passes through a 1 × 1 convolution module.

**Figure 5.** AC3Ghost module Structure.

#### *3.4. DwConv Module*

Depthwise separable convolution (DwConv) was proposed in MobileNet [40] in 2017. DwConv reduces the number of parameters needed during the convolution calculation and improves the efficiency of convolution by splitting the standard convolution in the spatial dimension and channel dimension. As shown in Figure 6, the DwConv module

structure is divided into two main processes of Depthwise Convolution and Pointwise Convolution. One convolution kernel of Depthwise Convolution is responsible for one channel. One channel is convolved by only one convolution kernel. The process producing the Pointwise Convolution is very similar to regular convolution. It has a convolution kernel size of 1 × 1, and is weighted in the direction of the map depth from the previous step to generate a new feature map. The computational complexity of a regular convolution *CConv* is shown in Equation (5), and the computational complexity of a depth-separable convolution *CseparableConv* is shown in Equation (6). The ratio of the computational cost of deep separable convolution to that of standard convolution is shown in Equation (7). Experiments show [32] that the computation is 8–9 times less than the standard convolution when the convolution kernel size of DwConv is set to 3 × 3.

$$\mathbb{C}\_{\text{Conv}} = D\_{\text{out}} \cdot D\_{\text{out}} \cdot D\_{k1} \cdot D\_{k2} \cdot \mathbb{C}\_{\text{out}} \cdot \mathbb{C}\_{\text{in}} \tag{5}$$

$$\mathbb{C}\_{\text{separable}}{}^{\text{c}}\_{\text{conv}} = D\_{\text{out}} \cdot 1 \cdot D\_{\text{out}} \cdot 2 \cdot D\_{\text{k1}} \cdot D\_{\text{k2}} \cdot \mathbb{C}\_{\text{in}} + D\_{\text{out}} \cdot 1 \cdot D\_{\text{out}} \cdot 2 \cdot \mathbb{C}\_{\text{out}} \cdot \mathbb{C}\_{\text{in}} \tag{6}$$

$$\frac{\mathbb{C}\_{\text{Separible Conv}}}{\mathbb{C}\_{\text{Conv}}} = \frac{D\_{\text{out 1}} \cdot D\_{\text{out 2}} \cdot D\_{\text{k1}} \cdot D\_{\text{k2}} \cdot \mathbb{C}\_{\text{in}} + D\_{\text{out 1}} \cdot D\_{\text{outt}} \cdot \mathbb{C}\_{\text{out}} \cdot \mathbb{C}\_{\text{in}}}{D\_{\text{out1}} \cdot D\_{\text{out 2}} \cdot D\_{\text{k1}} \cdot D\_{\text{k2}} \cdot \mathbb{C}\_{\text{out}} \cdot \mathbb{C}\_{\text{in}}} \tag{7}$$

where *D*in1, *D*in2 are the input dimensions, *D*out 1, *D*out 2 are the output dimensions, *Dk*1, *Dk*<sup>2</sup> are the convolution kernel size, *C*in is the number of input channels, and *C*out is the number of output channels.

**Figure 6.** DwConv module Structure.

#### **4. Experiments and Discussion**

#### *4.1. Experimental Environment*

All experiments were performed on a CPU with NVIDIA GeForce RTX 3090 24 GB GPU and Intel i7–12700. The computing software environment was set to python 3.8, CUDA Version 11.6, and the compiler was PyTorch 1.11. In the network training, this study took a batch size of 64, a learning rate of 0.001, an epoch of 500, and an SGD momentum is 0.937.

#### *4.2. Evaluation of Model Performance*

Average precision (AP) indicates the accuracy of categories. The mAP is the average of AP, representing the averaged accuracy of all categories. mAP@0.5 indicates the mAP with an IOU greater than 0.5, while mAP@0.5:0.95 indicates the mAP with an IOU at [0.5,0.95]. The IOU is shown in Equation (8). Precision measures the exactness of classification, as shown in Equation (9). AP and mAP are shown in Equations (10) and (11), respectively. In Equations (8)–(11), *boxgt* is the ground truth of the defect; *boxp* is the predicted area of the defect; TP and FP are, respectively, the numbers of true-positive cases and false-positive cases; and *n* is the number of detection classes. TN and FN are, respectively, the numbers

of true-negative cases and false-negative cases, and FPS is used to evaluate the detection speed of the model. In this paper, mAP@0.5, mAP@0.5:0.95, FPS, and model size are chosen to evaluate the experimental method.

$$IOLI\left(\left.box{\_{\mathcal{S}^{t\prime}}}\right.box{\_{p}}\right) = \frac{\left|\left.box{\_{\mathcal{S}^{t}}} \cap \left.box{\_{p}}\right|}{\left|\left.box{\_{\mathcal{S}^{t}}} \cup \left.box{\_{p}}\right|}\right|}\right.$$

$$\text{Precision} = \frac{TP}{(TP + FP)}\tag{9}$$

$$AP = \frac{\sum\_{i=1}^{n} P\_i}{n} \tag{10}$$

$$mAP = \frac{\sum\_{i=1}^{k} AP\_i}{k} \tag{11}$$

#### *4.3. Test Result of Defect Detection*

This paper adopts a fivefold cross-validation method to test the algorithm's accuracy. The dataset is divided into five groups, four of them are used as training data, and the remaining one as the test data. Experiments were conducted, with the results shown in Table 1. The experiments with the best mAP in Table 1 will also be used for the subsequent comparison experiments. The experiments show that the Precision, Recall and AP@.5 of the fold reach 99.45, 100, and 99.37, respectively, which has a better performance, because the folds are distinctive, fixed in shape, and easy to locate. Similarly, the accuracy and detection rate of this paper's method for both types of scratches and dirt are very high, and there are few cases of missed detection. These two defects have distinctive features and slight shape variations, and are less subject to interference from the background and other defects. However, for Pinhole, which has fewer pixel points, the algorithm captures and displays less texture information. In this paper, copy-pasting and Gaussian blur techniques are used to generate more feature information to meet the model training requirements. The results showed that the AP of the pinhole reached 82.45%. The various defect detection visual results of image detection are shown in Figure 7. All four defects can be detected accurately with a confidence score above 0.8.

**Table 1.** Test results for four types of defect detection.


#### *4.4. Comparison of the Effect of Different Defect Detection Algorithms*

The proposed method in this paper is compared with the following single-stage algorithms: SSD, YOLOv3-tiny, YOLOv4-tiny, YOLOv5-Mobilenetv3, YOLOv5-Shufflenetv2, and YOLOv5. The visualization results of the detection results of different algorithms are shown in Figure 8. The features of mAP@0.5, mAP@0.5:0.95, Model Size, and Detection Speed are compared, as shown in Table 2. Compared with the other six algorithms, the proposed algorithm has the best performance in mAP@0.5 and mAP@0.5:0.95 with 94.85 and 73.36. YOLOv5-Mobilenetv3 and YOLOv5-Shufflenetv2 have good detection speed, but the mAP@0.5 is below 90% and cannot achieve the accurate detection of surface defects in aluminum profiles. From the analysis of the results, it can be seen that the proposed method possesses great advantages in the accuracy and real-time detection of surface defects in aluminum profiles, and the detection speed reaches 136 FPS.


**Figure 7.** Visual inspection results for four types of defects.



#### *4.5. Ablation Study*

To understand well the contribution of the improved module to the defect detection effect, a large number of ablation experiments were performed to further verify the YOLOv5s. The results of the ablation study are exhibited in Table 3, where the baseline is the YOLOv5s after data enhancement is performed.

**Table 3.** Effects of various design modules on surface image.


**Figure 8.** Visual comparison of the results of the five algorithms on the dataset.

As shown in Table 3, image preprocessing has a good effect on the model's accuracy. Image preprocessing can increase the number and diversity of images and enrich the characteristics of defects. The mAP@0.5 has been increased by 2.77%. Adding a GCANet Backbone Network Structure on top of the proposed lightweight model can significantly reduce the model's size and improve the model's detection capability, and mAP is increased by 0.81%, because ghostconv in GCANet network can reduce a lot of redundant information by linear transformation. Continually adding the AC3Ghost structure after the GCANet Backbone, the detection accuracy of the model is improved further, and the model mAP is increased by 1.06%, but the model size is also slightly increased by 0.3 MB. The DwConv module improves the standard convolution by splitting the correlation between spatial and channel dimensions, reducing the number of parameters needed for the convolution calculation and improving the efficiency of the convolution. For DwConv Module, the model size is reduced by 0.4 MB, and the mAP was slightly dropped from 94.96% to 94.84%, only decreased by 0.12%. At the end, the overall mAP of the model was increased by 0.94%. These results verify that the proposed network model is effective for detecting surface defects in aluminum strips, and that the detection accuracy can be ensured while the model's size is significantly reduced.

#### *4.6. Edge Testing*

To verify the detection of the improved algorithm on the embedded platform, an edge surface defect-detection system was built, as shown in Figure 9 and Table 4. The system consists of an LED light source, a CCD image sensor, a 7-inch touch screen, an Nvidia Jeston Nano, an encoder, a conveyor belt, and two power supplies. The testing sample arrives at the center of the CCD image sensor via a conveyor belt. The CCD image sensor detects the sample and displays the results on the Touch screen. The experimental results show that the edge surface defect-detection system can achieve real-time detection of surface defects on aluminum profiles with a detection speed of 17.4 FPS with good robustness. In summary, the proposed method takes into account both accuracy and real-time operation, and can achieve good detection results in the detection of defects in the industrial production of aluminum profiles.

**Figure 9.** Edge surface defect detection system.

**Table 4.** Serial number and name of component in detection system.


#### **5. Conclusions**

Surface defects on aluminum profiles directly affect their quality. Advanced inspection processes and methods can ensure the accuracy of detection results with high-efficiency detection process. In this paper, a lightweight network model was proposed by adding an attention mechanism and depth-separable convolution for the detection of surface defects in an aluminum strip. By combining the ghost module and the attention mechanism, a new backbone was built. The model size was reduced by 6.2 MB and the mAP was increased by 4.64%. In the neck network of the lightweight model, the regular convolution was replaced by the deeply separable convolution. The model size was further compressed to 7.8 MB. Compared with other object detections and lightweight model experiments, the proposed algorithm has better real-time performance and accuracy than other single-stage detection algorithms. The detection accuracy mAP@0.5 is 94.85, mAP@0.5:0.95 is 73.36, and the detection speed is 136.98 FPS. Furthermore, in edge testing, the proposed algorithm in the present work can achieve real-time detection. Experiments show that it can detect the surface defects of aluminum profiles in real time with guaranteed high accuracy. In addition, the algorithm has high scalability and can be extended to other fields such as PCB surface defects. In the future, this research work will be focused on continuing to improve pinhole detection accuracy in complex contexts. At the same time, we will continue to carry out research efforts on the types of aluminum profile surface defects to achieve the identification of more defect types.

**Author Contributions:** Conceptualization, J.T. and S.L.; methodology, J.T.; software, J.T.; validation, J.T., S.L. and D.Z.; formal analysis, J.T.; investigation, J.T.; resources, W.Z.; data curation, J.T.; writing—original draft preparation, B.Z.; writing—review and editing, D.Z.; visualization, J.T.; supervision, L.T.; project administration, J.T.; funding acquisition, J.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Open Research Fund of Hunan Provincial Key Laboratory of Flexible Electronic Materials Genome Engineering under grant (No. 202015).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** The authors would like to acknowledge the anonymous reviewers and editors whose thoughtful comments helped to improve this manuscript.

**Conflicts of Interest:** The authors declare they have no conflict of interest.

#### **References**


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**Jiansheng Xia 1,2,\*, Rongtao Liu 2, Jun Zhao 1, Yingping Guan <sup>1</sup> and Shasha Dou <sup>2</sup>**


**Abstract:** Friction during contact between metals can be very complex in pulse current-assisted forming. Based on stamping process characteristics, a reciprocating friction tester was designed to study the friction characteristics between AA7075 aluminum alloy and P20 steel under different current densities. Origin software was used to process the experimental data, and a current friction coefficient model was established for the pulse current densities. The results show that the friction coefficient of the aluminum alloy sheet decreased with the increase in the pulse current density (2–10 A/mm2). After that, the friction mechanism was determined by observing microscopic morphology and SEM: some oxide cracked on the friction surface when the current was large. Finally, finite element simulations with Abaqus software and a cylindrical case validated the constant and current friction coefficient models. The thickness distribution patterns of the fixed friction coefficient and the current coefficient model were compared with an actual cylindrical drawing part. The results indicate that the new current friction model had a better fit than the fixed one. The simulation results are consistent with the actual verification results. The maximum thinning was at the corner of the stamping die, which improved the simulation accuracy by 7.31%. This indicates the effectiveness of the pulse current friction model.

**Keywords:** AA7075 aluminum alloy; friction; pulse current; friction coefficient; numerical simulation

#### **1. Introduction**

With the development of the automotive industry, lightweight materials have gradually replaced traditional steel and have become one of the hot spots in the development direction of the automotive industry [1–3]. Among them, aluminum alloy has become the first choice to replace traditional steel because of its low density, high strength, and good processing formability. It has received attention for its use in lightweight automobiles [4]. Among the different types, 7075 aluminum alloy has the best intensity and is commonly used in aircraft manufacturing [5]. Although the traditional hot forming technology can avoid the problems of easy cracking, it has a small drawing limit ratio and there is considerable rebound of the aluminum alloy at room temperature [6]. Moreover, the heating time is long, and the heating efficiency is low, which reduces the quality of the sheet metal forming parts. It is therefore urgent to find a new forming technology to replace the traditional forming technology [7]. Electro-assisted forming (EAF) [8–10] improves metal forming performance by applying pulse current-assisted metal forming. Many studies have shown [11] that deformation resistance and spring back can be reduced under a pulse current, improving the metal-forming accuracy and quality. Hence, pulse current-assisted metal-forming technology has gradually become a research focus in recent years. Lv Z et al. [12] studied the electro-plastic effect of drawing high-strength steel; their results showed that introducing a pulse current can effectively improve the forming performance of high-strength steel and increase its deep drawing depth. The friction between

**Citation:** Xia, J.; Liu, R.; Zhao, J.; Guan, Y.; Dou, S. Study on Friction Characteristics of AA7075 Aluminum Alloy under Pulse Current-Assisted Hot Stamping. *Metals* **2023**, *13*, 972. https://doi.org/10.3390/ met13050972

Academic Editor: Evgeny A. Kolubaev

Received: 10 April 2023 Revised: 10 May 2023 Accepted: 14 May 2023 Published: 17 May 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

sheet metal and stamping mold impacts the forming quality and simulation accuracy in current-assisted hot stamping technology. Therefore, studying the friction characteristics under different currents is essential to better apply current-assisted forming technology to the sheet metal-forming process.

In recent years, some researchers have established friction models from a macroscopic perspective to study the influence of process parameters on sheet forming. Nie Xin [13] and Tan Guang et al. [14] of Hunan University measured DP480 high-strength steel considering the influence of temperature on the friction coefficient and established a variable friction model, which showed that it could better describe the actual stamping situation. Wang Peng et al. of the Hunan University of Technology [15] considered the influence of different interface loads on the friction coefficient between aluminum alloy sheets and mold steel under boundary lubrication conditions through the pin friction testing machine. They established a variable friction model under different loads and through experimental verification and finite element simulation. They found that the error of the variable friction model was small and verified the effectiveness of the friction mode. Subsequently, Dou S et al. [16] established a mixed friction model considering the influence of the sliding velocity and boundary load on the friction coefficient under boundary lubrication conditions, and combined experimental verification with finite element simulation to verify the effectiveness of the hybrid friction model. X J Li et al. [17] used the anti-problem optimization method to explore the influence of friction behavior on forming quality. They tested hot stamping on 7075 aluminum alloy sheets with different lubricants and analyzed the effects of the force–displacement curve, surface morphology, and thickness distribution. The results showed that compared to the experimental results, the determined friction coefficient could accurately predict the force–displacement curve and thickness distribution of the formed parts under different lubrication conditions. Liu Yong [18], Xu Yupeng [19], and Li Jiahao [20] of the Wuhan University of Science and Technology conducted a detailed study on the high-efficiency stamping process of high-strength aluminum alloy, mainly including the high-temperature rheological behavior of sheets and the high-temperature friction and lubrication behavior of aluminum alloy and mold steel, and applied it to the simulation of aluminum alloy sheet hot stamping. They analyzed the rupture mechanism of aluminum alloy hot stamping forming and provided a basis and reference for the actual stamping.

In addition, other researchers have begun to explain friction behavior from a microscopic perspective, and friction models have been established based on this. C. Wang et al. [21] established a micromechanical friction model considering the influence of the temperature, contact pressure, volumetric strain, and relative sliding velocity on friction during the forming process, and verified the model by comparing the actual contact area and experimental results. The results showed that the model could be used for formability analysis and the prediction of optimal stamping parameters, providing theoretical guidance for actual stamping. However, C. Wang only established a cold stamping process friction model based on temperature-dependent micromechanics. Jenny Venem [22] established a multi-scale friction model considering local contact pressure, temperature, and strain. They then applied it to hot stamping. The results showed that the model could predict the friction of the actual stamping process well. Deng Liang et al. [23] proposed a finite element model of the friction process at the microscopic scale based on the high-temperature one-way friction experimental process. They analyzed the actual contact conditions under the microscopic mechanism. The results showed that undulating the contact surface caused the friction factor calculated using the finite element model of the friction process to change within the range of the set friction factor. J. Han [24] considered the changes in the tangential stiffness and friction coefficient caused by the difference in the stress distribution and established a modified stick–slip friction model. The experimental verification and finite element simulation showed that the model could describe the friction behavior of the contact parameters at different stages in the stick–slip process. Its simulation results agreed with the experimental data, which showed significant improvement in the prediction accuracy

of the mechanical system's performance. The authors of [25] investigated the friction and occlusion properties of 7075 aluminum alloy sheets at different temperatures and found that the formation of a compaction layer on the wear surface affected the friction behavior. They established a friction evolution model, which showed that at 25 ◦C and 150 ◦C, the dominant friction mechanism was furrow friction, while at temperatures above 300 ◦C, the dominant friction mechanism was sticking. Similarly, the authors of [26], in conjunction with the hot forming of 7075 aluminum alloys, established a friction mechanism at high temperatures, loads, and sliding speeds, which were used to explain the friction mechanism and showed that the wear rate gradually decreased as the load and sliding speed increased.

With the general study of variable friction models, some researchers have begun to study friction models related to current factors. ZH. C [27] used the pin–disc friction testing machine and Matlab software to establish a mixed friction model based on friction, sliding velocity, and average load. They verified the effectiveness of the friction model by comparing it with the predicted value of the friction model through experimental verification. Afterwards, the team led by ZH. C [28] conducted experiments to study the relationship between frictional force and multiple current factors, established a LuGre static model for frictional force on a bowstring, introduced dynamic parameters to develop a LuGre dynamic model, and identified the model parameters using the genetic algorithm combined with simulation. The results demonstrated the superiority of the dynamic model, which can provide a reference for predicting frictional force and studying frictional wear performance. On this basis, Ping Yu [29] of Liaoning Technical University considered the law of change of fluctuating contact force and current with friction, combined this with the Stribeck friction model, established a modified hybrid friction model of contact force current, and verified the effectiveness of the friction model through experimental measurement and model prediction. However, the application of the above models has mainly been in the field of high-speed bullet trains. Jx Bao et al. [30] established a multiscale friction model considering the effect of the current density and size from a microscopic perspective through a current-assisted compression test. The results showed that the model could predict the friction coefficient well.

Many researchers have studied the friction characteristics in the hot forming process, but the friction characteristics under a pulse current are unclear, and there is relatively little research on related content. In this study, we used AA7075–T6 aluminum alloy as the research object. We studied the influence of a pulse current on the friction coefficient of materials under dry friction conditions and established a current friction model. Finally, through simulation and experimental verification, we verified the effectiveness of the new friction model by comparing it with the predicted values of the fixed friction coefficient.

#### **2. Materials and Methods**

#### *2.1. Experimental Materials*

The sheet used for this friction test was an AA7075–T6 aluminum alloy sheet with a thickness of 0.5 mm, manufactured by Alcoa and marketed by Suzhou Xiehe Metal Co., Ltd. (Suzhou, China). The chemical composition is shown in Table 1. First, the aluminum alloy sheet was cut into 900 mm × 30 mm × 0.5 mm using the wire-cutting technique, as shown in Figure 1a. In addition, this test used P20 die steel as the friction sub, whose chemical composition is shown in Table 2. The die steel was heat-treated to a hardness of 50 HRC, and the structure dimensions are shown in Figure 1b. The samples were then placed in an ethanol solution, which was used to remove the oil from the surface of the samples. Finally, the samples were ultrasonically cleaned for 15 min and then sealed for storage.

**Table 1.** Chemical composition of AA7075 aluminum alloy (mass fraction, %).


**Figure 1.** Structural dimensions of aluminum alloy strip and P20 steel pin. (**a**) 7075 Aluminum alloy strip. (**b**) P20 steel pin diagram.



The microscopic structure of the sample surface of the aluminum strip is shown in Figure 2a. This alloy predominantly comprises Al, Mg, and Zn, along with minor Fe and Si constituents. Due to the limited solubility of most alloying elements in Al, the microstructure of the alloy is characterized by a complex distribution of different particle phases over the α-Al solid solution matrix. The primary particle phases present in the 7075 alloys are η-MgZn2, S-Al2CuMg, T-Al2Zn3Mg2, and T-Al2Zn3Mg2. The nonequilibrium MgZn2 phase is the primary strength-reinforcing phase. The complex phase particles are predominantly oriented along the tensile direction of the sample [31]. The EDS of this surface indicates that the main components of the original sample are Al, Mg, and Zn (Figure 2b).

**Figure 2.** (**a**) A microscopic structure of the 7075 sample surface; (**b**) EDS surface analysis.

#### *2.2. Test Principle*

The pulse current friction tester, as shown in Figure 3a, mainly consisted of a friction test platform, control platform, pulse power loading platform, and data acquisition platform. The device can perform friction tests under the action of different currents, and its test schematic is shown in Figure 3b. In order to direct the current supplied by the external power supply to the friction test, the tester needs to be modified. The conductive clamps made by the group were installed on both sides of the aluminum alloy sheet, and the current was passed to the conductive clamps, P20 mold steel, and the sheet in turn to complete the closed circuit, as shown in Figure 3b.

**Figure 3.** Testing machine. (**a**) Pulse current friction testing machine. (**b**) Schematic diagram of the friction testing machine. (**c**) Detailed parts of the friction test rig.

In addition, to ensure the safety of the test, an alumina ceramic insulation ring was installed on the drum, a nylon insulation pin was installed on the P20 mold steel, and an insulation spacer made of polyether ether ketone material was installed between the fixture and the plate material, thus insulating the conductive parts from the tester, as shown in Figure 3c.

The friction coefficient test platform included friction measurement components and vertical and horizontal actuators. The platform ensured insulation between the friction tester and the sheet material through the alumina ceramic ring, the epoxy resin sheet, and the nylon compression head. Using the fixtures to fix the two ends of the sheet, we connected to the two actuators and mounted the P20 die steel at the top surface of the sheet. The control platform comprised a stepping motor controller, driver, and motor power supply, which controlled the movement speed and direction of the two actuators and ensured the synchronous operation of vertical and horizontal directions. Two conductive clamps connected the pulse power platform to the sheet material. The pulse current was loaded through the conductive clamp, the roller, the material pressure head, and the sample material. It could quickly reach the temperature required for the friction test by adjusting

the power supply parameters. The data acquisition system measured the force in the horizontal and vertical directions through the sensor installed in the two directions of the sheet and realized the automatic data acquisition with the help of LABVIEW programming. The formula of the friction coefficient was obtained using Coulomb's law of friction during data acquisition:

$$
\mu = \frac{F}{2P} \tag{1}
$$

where, *F* is the difference between the horizontal and vertical sensor values, and *P* is the normal vertical load.

#### *2.3. Test Arrangement and Test Procedure*

The friction mechanism of aluminum alloys during pulsed current-assisted forming is complex, often accompanied by the coupled effects of electric and thermal fields and many influencing factors, such as the current density, temperature, normal load, sliding speed, etc. In this paper, we focus on the effect of a pulsed current on the friction characteristics of the contact interface between an aluminum alloy sheet and a P20 die steel. The specific test parameters are shown in Table 3.

**Table 3.** Specific test parameters for the friction test of 7075 aluminum alloys.


In this study, the steps in conducting the pulsed current friction test were as follows. First, the position of the plating fixture was adjusted so that the aluminum alloy sheet could be fixed to the test machine. After fixing the plates, conductive grips were installed at each end of the machine to ensure that the pulse power supply was energized. The plates were then preheated for 10 min using the pulsed power supply. After the preheating was complete, the current parameters were adjusted, and the plates were continuously energized. The temperature of the plates was monitored in real time using an infrared thermographer. Finally, the remaining test parameters were set using the computer program, and the friction test began. After the friction test reached the predetermined effective stroke, the friction test was completed. All friction tests were repeated three times to ensure the accuracy of the data.

#### *2.4. Material Characterization Methods*

The frictional wear mechanism of the 7075 aluminum alloy was analyzed by posttesting the specimens under the action of a pulsed current. Firstly, we utilized the VK-X100 laser scanning microscope to analyze its three-dimensional morphology after conducting the friction test on the aluminum alloy sheet. Secondly, the wear surfaces of the plates were then analyzed using the JXA-840A scanning electron microscope (SEM) and the energy dispersive spectrum (EDS), and then the chemical composition was analyzed. Finally, the shape of the aluminum alloy ports perpendicular to the sliding direction of the aluminum alloy was also analyzed using SEM.

#### **3. Results**

#### *3.1. Friction Coefficient at Different Current Densities*

The aluminum alloy sheet produced a Joule heating effect when the pulse current was loaded, and the temperature of the sheet metal increased, which is significant in explaining the friction characteristics of metal sheet forming. The Optris infrared thermometer was used to measure the temperature in real time and the curve of the sheet metal temperature with the time under different current densities was obtained using Origin software, as shown in Figure 4. As seen in the Figure, the temperature curves under different current densities had a standard feature. The heating rate of the aluminum alloy sheet metal was fast until 20 s and tended to be stable with the continuous increase in time. The main reason is that the Joule thermal temperature under the pulse current increased with the influence of the air convection and thermal radiation coefficient on the sheet at the beginning of the test [32–34].

**Figure 4.** Curve of sheet metal temperature with time under different current densities.

The current intensity values of the frictional tests were 30 A, 60 A, 90 A, 120 A, and 150 A, and the corresponding current densities were 2 A/mm2, 4 A/mm2, 6 A/mm2, 8 A/mm2, and 10 A/mm2, respectively. Under dry friction conditions, the friction coefficient curved with time at different current densities with a load of 8N and a speed of 4 mm/s (Figure 5a). In the graph, the coefficients of friction at different current densities have common characteristics: the coefficients of friction increased rapidly at first, then gradually decreased, and then finally plateaued. Moreover, the friction coefficient gradually decreased with the increase in the current density.

**Figure 5.** (**a**) Friction coefficient curves with time at different current densities. (**b**) Average coefficient of friction in the stabilization phase.

The effects of the current on the coefficients of friction are mainly manifested in the following aspects:


The average coefficients of friction with different current densities are shown in Figure 5b. The friction coefficients vary with different current densities as follows: (*μ*2=0.573) > (*μ*4=0.341) > (*μ*6=0.299) > (*μ*8=0.253) > (*μ*10=0.249). The maximum friction coefficient was 0.573 when the current density was 2 A/mm2, and the minimum friction coefficient occurred at 10 A/mm2. Although the tests were carried out in the dry friction state, the average friction coefficients were lower than about 0.5, which was close to the friction coefficient in the boundary lubrication state. This phenomenon is normal, and the authors of [30] mention that proper current density can increase lubrication and thus reduce mechanical wear.

#### *3.2. The Effect of Current Density on Surface Friction Mechanism*

After the friction test, a VK-X100 laser microscope was used to observe the surface morphology of the AA7075 aluminum alloy at different currents, as shown in Figure 6. When the current density was 2 A/mm2, few scratches and peeling occurred on the aluminum alloy sheet surface (Figure 6a). A possible reason is the instantaneous heating effect of the pulse current, softening the metal. Under the dual impacts of Joule heat and frictional heat, the viscosity of the material increased, resulting in a higher friction coefficient value, and the primary friction mechanisms were viscous wear and furrow wear. When the current density increased to 4 A/mm2, the peeling traces on the sheet material disappeared, but it had more dents and deep scratches (Figure 6b). A possible reason is that the current density increased the continuous action of Joule heat, the metal surface oxide film reduced the friction coefficient, and the friction mechanism was furrow wear. When the current increased to 6 A/mm2, the number of dents decreased gradually, and the width became shallow (Figure 6c). A possible reason is the shrinkage effect of the current: the temperature of the pulse current at the conductive spot increased, resulting in the softening of the micro-convex body, thus reducing the friction coefficient, and the primary friction mechanism was furrow wear. As shown in Figure 6d, when the current reached 8 A/mm2, there were still multiple dents on the board, but the width and depth of the marks were reduced. The surface was relatively smooth, and the critical friction mechanism was furrow wear. When the current continued to rise to 10 A/mm2, there were only a few dents on the board, the friction marks became shallow, and the friction mechanism was furrow wear, as shown in Figure 6e.

**Figure 6.** Surface morphology of 7075 aluminum alloy sheet at different current densities. (**a**)2A·mm<sup>−</sup>2; (**b**)4A·mm<sup>−</sup>2; (**c**)6A·mm<sup>−</sup>2; (**d**)8A·mm<sup>−</sup>2; (**e**) 10 A·mm<sup>−</sup>2.

To further investigate the friction and wear mechanism under a pulsed current, the microscopic morphology of the surface of the aluminum alloy sheet was observed via a scanning electron microscopy (SEM) with a pulsed current density of 6 A·mm−<sup>2</sup> as an example, and the results are shown in Figure 7. As shown in Figure 7a, wear marks parallel to the sliding direction were observed on the friction specimen, while the wear surface was relatively smooth with only shallow grooves present. In addition, some oxidation cracks were observed in the morphology beneath the wear surface, as shown in Figure 7b. The chemical composition of the wear surface of the sheet was further analyzed using EDS, and the results in Figure 8 show that it was mainly Al and O, with the mass fraction of O reaching 37.3% (i.e., 80% of the overall composition of the aluminum oxide). The generation of a continuous oxide film on the friction surface effectively avoided direct metal-to-metal contact between the friction pairs and reduced the occurrence of adhesive wear. This is mainly because when the pulsed current was passed into the metal during the process, the current easily produced an oxide layer on the aluminum alloy surface, and the current improved the oxidation properties of the sliding surface through surface polarity. The Joule heating effect of the pulsed current on the metal and the heat from the friction process also made the aluminum alloy surface more susceptible to oxidation, while the friction coefficient gradually decreased as a result.

**Figure 7.** SEM diagram of the frictional profile of an aluminum alloy sheet at a current density of 6 A·mm−<sup>2</sup> at different magnifications; (**a**) Surface profile perpendicular to the wear track (**b**) Oxide cracks under surface morphology.

**Figure 8.** EDS results of the surface of a sheet at a current density of 6 A/mm2.

To investigate the frictional wear mechanism under pulsed current, the cross-sectional specimens of the aluminum alloy were observed using scanning electron microscopy (SEM) after the friction test, as depicted in Figure 9. A high-temperature softening effect occurs in aluminum alloy under the influence of the current, as seen from the microscopic state of the surface morphology of the cross-section after friction. The white layer that appears in the middle of the cross-sectional after friction, as shown in Figure 9a, is due to the frictional heat generated during the friction process and the Joule heat after the introduction of the current. This results in adhesive deformation on the upper surface of the aluminum alloy, leading to an increase in the frictional area and surface roughness of the sheet. The morphology of the intermediate white layer was further observed in Figure 9b, which revealed the presence of a mechanically mixed layer (MML) formed by the combination of the oxide generated during the wear process and the substrate under the action of the pressure of the two contact surfaces. The composition of the MML layer was analyzed using EDS, and the results in Table 4 showed that at the wear of 6 A·mm<sup>−</sup>2, the O content was 18.1%, the Al content was 67.8%, and the Fe content was 10.9%. The presence of Fe indicated the occurrence of material transfer on the wear surface of the plate, where the mold material was attached to the surface of the aluminum alloy sheet [37].

**Figure 9.** SEM surface morphology of frictional wear cross-sections of aluminum alloys at different magnifications at a current density of 6 A/mm2; (**a**) Section shape of the aluminum alloy sheet after wear; (**b**) Mechanically mixed layer underwear morphology.

**Table 4.** EDS results of worn cross-section of the 7075 alloy at 6 A/mm2 (wt.%).


#### *3.3. Establishment of Friction Coefficient Model Based on the Current Density*

As can be seen in Figure 5b, when the current density was less than 6 A·mm−2, the average friction coefficient decreased with the increase in the current density. However, the trend of the friction coefficient decreasing with the increasing current density became stable when the current density was more than 6 A·mm−2. One reason is that before the current density increased to 6 A·mm−2, the Joule heat and frictional heat generated by instantaneous heating during the pulse current reduced the friction coefficient. The other reason is the low sliding speed: the micro-convex body between the surface of the plate and the surface of the P20 steel had enough time to produce plastic deformation, which increased the contact area and ultimately led to an increase in the friction coefficient of the plate. So, the friction coefficient decreased with the increasing current density and stabilized when the current density was above 6 A·mm<sup>−</sup>2. According to the above analysis and the law of curve change, the pattern of the evolution of the friction coefficient with the current density conforms to an inverse function. Therefore, the new friction coefficient expression is as follows:

$$
\mu = \frac{a}{l+b} + c \tag{2}
$$

where, *μ* is the coefficient of friction; *J* is the current density; and *a*, *b*, and *c* are constants. Then, the friction data were imported into the Origin software to fit the inverse function curve shown in Figure 10. The error between the fitted curve and the experimental data was small, and the fitting degree was 0.993, so the function accurately reflects the current friction coefficient with the current density. Using the Origin software fit, *a* = 0.50, *b* = −0.68, and *c* = 0.19 were obtained. Thus, the new friction model expression is as follows:

$$
\mu = \frac{0.50}{f - 0.68} + 0.19 \tag{3}
$$

Five groups of different current densities (1 A/mm2, 3 A/mm2, 5 A/mm2, 7 A/mm2, and 9 A/mm2) were selected to verify the correctness of the new current friction model. Five sets of actual experimental measurements under different current densities and the predicted values of the new friction model are shown in Table 5. As can be seen, the total errors were less than 9%, the lowest error was 3.89%, and the maximum error was 8.13%. This indicates that the fitted current friction model can better reflect the law of the friction coefficient with different current densities in the metal forming, verifying the effectiveness of the current friction model.

**Figure 10.** Friction fitting curves at different current densities.

**Table 5.** Friction coefficient measurement values and friction model prediction values.


#### **4. Simulation and Experimental Validation**

To improve the accuracy of the software simulation and verify the accuracy of the new friction model at different current densities, we adopted the sequential coupling model for simulation, used the same AA7075 aluminum alloy as the research object for the thermoelectric coupling simulation, and then imported the simulation temperature field results into the thermal stamping as a predefined field. Then, we intuitively and effectively analyzed the temperature, strain, and stress fields under the different process parameters to verify the effectiveness of the new current friction model.

#### *4.1. Finite Element Analysis of Thermoelectric Coupling*

In the thermoelectric coupling simulation, the copper electrode and the AA7075 aluminum alloy sheet models improved the computational efficiency, as shown in Figure 10. The aluminum alloy sheet had a diameter of 165 mm and a thickness of 0.5 mm; to facilitate current loading, the ends on both sides had a length of 60 mm and a width of 30 mm. The size of the grid mesh was 1 mm, the unit size was 4 mm, and the grid number was 29,696. The size of the copper electrode was 120 mm × 120 mm × 60 mm, the unit size was 2.5 mm, and the grid number was 4396. Due to the thermoelectric coupling analysis involving the current field, temperature field, potential field, etc., the mesh type of the model was set as an 8-node linear hexahedral thermoelectric coupling element (DC3D8E).

In thermoelectric coupling, the pulse current will bring the Joule heating effect. Hence, copper electrodes and aluminum alloys use temperature-related parameters, citing the simulation-related data of [38], as shown in Tables 6 and 7.


**Table 6.** Thermal performance parameters of the copper electrode at different temperatures.

**Table 7.** Thermal performance parameters of aluminum alloys at different temperatures data from [38].


In the thermoelectric coupling simulation, the heat transfer coefficient between the sheet and the surrounding environment is cited in the literature [39], as shown in Table 8. In the temperature boundary, the entire model was set to a room temperature of 298.15 K through a predefined field. The current was loaded on the sheet metal through the node set of the copper electrode. A zero-potential boundary was set on the other side of the sheet. The contact between the aluminum alloy metal sheet and the copper electrode was set to normal hard contact and a penalty function: when the distance between the aluminum alloy sheet and the copper electrode is less than 0.1 mm, the contact thermal conductivity is 10 mW/m2·K.

**Table 8.** Conduction heat transfer coefficient of aluminum alloy surface and air.


#### *4.2. Finite Element Analysis of Thermal Stamping Forming*

SolidWorks software was used to model the punch, die, and blank holder, and then the data were imported into ABAQUS after assembly, as shown in Figure 11a. The essential dimensions of the mold are shown in Table 9. The meshing type was the thermoelectric structure coupling unit (Q3D8R), the unit size was 2 mm, and the total number of grids was 11,132. The size of the sheet material was consistent with the thermoelectric coupling simulation, and the grid type was the thermoelectric structure coupling unit (Q3D8R). The analysis step units used thermoelectric structure coupled units, and the meshing assembly model is shown in Figure 12b.

**Figure 11.** Thermoelectric-coupled finite-element simulation model. (**a**) Thermoelectric coupling finite element simulation model. (**b**) Hot stamping finite element simulation model.

**Figure 12.** Finite element meshing diagram. (**a**) Thermoelectric coupling finite element meshing. (**b**) Current-assisted hot stamping finite element meshing.


**Table 9.** Specific parameters of stamping die (unit length: mm).

The mold material was P20 stainless steel, with a density of 7.81 g/cm3, Young's modulus of 205 GPa, and Poisson's ratio of 0.275, and its thermal performance parameters are shown in Table 10. The sheet metal material was also an AA7075 aluminum alloy, and its material parameters were consistent with the parameters in the thermoelectric coupling simulation. The stress–strain curve data are cited [39]. In the temperature boundary, the temperature field results of the thermoelectric coupling simulation were imported as the initial conditions into the predefined fields of the thermoelectric-structure coupling. The current was loaded on the sheet metal through the node. The current direction is shown in Figure 11a. Zero-potential loading occurred on the other side of the sheet. The die was set as a fixed constraint, the vertical displacement of the punch was set to 35 mm, and the pressing force was set to 2.5 kN. When the distance between the sheet and the mold was less than or equal to 0.1 mm, the contact thermal conductivity was 10 W/m2·K. When the space was more than 0.1 mm, the value was 0.

**Table 10.** Thermal properties of P20 steel.


#### *4.3. Results Analysis and Example Verification*

The sheet temperature field distribution at a current density of 10 A·mm−<sup>2</sup> for 100 s is shown in Figure 13. In Figure 13, the highest temperature is about 450 K, and the lowest temperature in the middle of the sheet is 319 K. The high temperature is in the middle area, in which the distribution is relatively uniform, the temperature at both ends is low, and the change is not constant. The process considers the convection heat transfer coefficient of aluminum alloy sheet and air, the temperature rise of the joule thermal effect, and the contact between copper electrode and the left and right ends, which is why the temperature of aluminum alloy material was relatively high near the middle. The temperature change of the contact electrodes was small because the resistivity of the copper electrode was less than that of the aluminum alloy sheet.

**Figure 13.** Temperature field distribution of sheet material after thermoelectric coupling simulation.

The electro-assisted thermal stamping simulation was carried out in two groups: one used a fixed friction value, *μ* = 0.1, and the other used the new current friction model. The new friction model was written in the Fortran language with a subroutine of "fri-coef" to submit jobs to the Job module. Figure 14a,b show the equivalent plastic strain after thermal stamping simulation under the different friction models. As can be seen in the graphs, the equivalent peak plastic strain at the fixed friction values was greater than the current friction coefficient model, and the maximum equivalent plastic strain was concentrated at the rounded corners of the punch. Because the sheet metal was subjected to the stretching effect at the bottom of the punch fillet during the deep drawing process, the sheet metal had high fluidity.

**Figure 14.** *Cont*.

**Figure 14.** The equivalent plastic strain after thermal stamping simulation under different friction models. (**a**) The fixed friction value of *μ* = 0.1. (**b**) The new current friction model.

The sheet material was a cylindrical part with a radius of 165 mm and a thickness of 0.5 mm. The stamping speed was 20 mm/s, and the pressure edge force was consistent with the simulation, set to 2.5 kN. Figure 15a shows the actual electrical-assistance stamping platform, Figure 15b shows the stamped part, and Figure 15c shows the locations of the measurement points. The 3D model extracted the node coordinates through the path to observe the thickness rule, using the shell unit to study the thickness distribution and thinning rate. Origin software obtained the thickness distribution patterns (Figure 15d). Compared to the traditional fixed friction coefficient, the new current friction model was closer to the thickness rule of the actual stamping parts. The maximum thinning rate of the fixed friction coefficient was 12.5%, the current friction coefficient model was 15.3%, and the actual value was 14.3%. Compared to the actual value, the simulation error of the software decreased from 12.59% to 6.99%, and the simulation accuracy improved by 7.31%. The maximum thinning was also concentrated at the circular corner of the punch, consistent with the simulation results of the maximum equivalent plastic strain and within the allowable range of thinning. From the thickness distribution curves of the part, the current friction model was closer to the actual value. Therefore, the current friction model reflects the friction characteristics of sheet forming and provides a practical reference for current-assisted stamping simulation technology.

**Figure 15.** *Cont*.

**Figure 15.** (**a**) Current-assisted stamping platform. (**b**) Actual stamped part. (**c**) Thickness measurement point. (**d**) The thickness distribution of different friction models.

#### **5. Conclusions**


**Author Contributions:** Conceptualization, J.X. and J.Z.; Methodology, J.X. and Y.G.; Software, S.D. and R.L.; Validation: J.X., J.Z. and Y.G.; Data collection, R.L. and J.X.; Data analysis, R.L. and S.D.; Writing—original draft preparation, R.L. and J.X.; Writing—review and editing, J.X. and J.Z.; Supervision, J.Z. and Y.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by China's National Natural Science Foundation [51505408].

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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## *Article* **Modified Voce-Type Constitutive Model on Solid Solution State 7050 Aluminum Alloy during Warm Compression Process**

**Haihao Teng 1,2, Yufeng Xia 1,2,\*, Chenghai Pan 1,2 and Yan Li 1,2**


**\*** Correspondence: yufengxia@cqu.edu.cn

**Abstract:** The 7050 alloy is a kind of Al-Zn-Mg-Cu alloy that is widely used for aircraft structures. Although the deformation behavior of the solid solution state 7050 aluminum alloy is critical for engineering and manufacturing design, it has received little attention. In this study, the room and warm compression behavior of the solid solution-state 7050 alloy was researched, and a modified model with variable parameters was built for the flow stress and load prediction. The isothermal compression tests of the solid solution-state 7050 alloy were performed under the conditions of a deformation temperature of 333–523 K, a strain rate of 10−3–10−<sup>1</sup> s−1, and a total reduction of 50%. The strain-stress curves at different temperatures were corrected by considering interface friction. The flow stress model of aluminum was established using the modified Voce model. For evaluating the modified Voce model's prediction accuracy, the flow stresses calculated by the model were compared with the experimental values. Consequently, for assessing its prediction abilities in finite element applications, the whole compression process was simulated in the finite element analysis platform. The results sufficiently illustrated that the modified Voce-type model can precisely predict the complex flow behaviors during warm compression. This study will guide the prediction of the warm compression load and the optimization of the heat treatment process of the alloy.

**Keywords:** solid solution state; 7050 aluminum alloy; warm compression; constitutive model

#### **1. Introduction**

The high-strength, age-hardened 7050 alloy is a kind of Al-Zn-Mg-Cu alloy that is widely used for aircraft structures. After the forging of the 7050 alloy, it will be heated to a solid solution temperature and kept for some time [1]. Then the alloy will be quenched and finally artificially aged for improved performance [2,3]. The treatment will induce large residual stresses on the structures, resulting in severe distortion and even failure in the subsequent machining stage [4,5].

In previous studies, the warm compression between solid solution and aging treatment has been proven to have a good residual stress reduction effect on large aluminum alloy forgings [6,7]. The load of the warm compression process is large due to the high strength of the solid solution-state 7050 alloy [8]. To predict the load precisely, the deformation behavior and applicative constitutive model of solid solution-state 7050 aluminum at medium temperature are essential, but they are little studied. Some constitutive models, such as Swift, Ludwik, and Voce, have been used to predict flow stresses and loads in cold or warm forming designs [9–11]. At low temperatures, there is also softening due to mechanical work converting. However, the indicated constitutive models ignore softening phenomena in the deformation and are insufficient to predict flow stresses and loads during warm compression for the alloy.

Therefore, the goal of this research is to build a model of 7050 aluminum alloy in its solid solution state for flow stress and load prediction during warm compression. Room

**Citation:** Teng, H.; Xia, Y.; Pan, C.; Li, Y. Modified Voce-Type Constitutive Model on Solid Solution State 7050 Aluminum Alloy during Warm Compression Process. *Metals* **2023**, *13*, 989. https://doi.org/10.3390/ met13050989

Academic Editor: Elisabetta Gariboldi

Received: 22 March 2023 Revised: 1 May 2023 Accepted: 9 May 2023 Published: 19 May 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

temperature and isothermal warm compress tests from 333 to 523 K were performed. The flow properties of the aluminum in its solid solution state were studied. By considering the friction compensation, the modified Voce-type model with parameters variable by the effects of strain, temperature, and strain rate was established for flow stress prediction. For evaluating the modified model's prediction accuracy, the flow stresses calculated by the model were compared with the experimental values. The model's prediction abilities in finite element applications have also been assessed.

#### **2. Materials and Methods**

The 7050 aluminum alloy for the research was from Deyang Wanhang Die Forging Co., Ltd. (Deyang, China). The chemical compositions of the aluminum alloy are listed in Table 1.


**Table 1.** Chemical composition of 7050 alloy (wt, %).

The solid solution treatment and compressing processes are shown in Figure 1. The wrought 7050 alloy was heated and solution treated at 750 K for 4 h with 333 K water quenching. The quenched alloys were prepared into some cylinders of Φ8 × 12 mm for subsequent compressive tests. The warm upsetting tests were conducted on a Gleeble−3180 unit at different temperatures of 333, 423, 473, and 523 K for strain rates of 10−3, 10−2, and 10−<sup>1</sup> s<sup>−</sup>1. The total reduction is 50%, with stress-strain data recorded automatically. Before upsetting, tantalum with graphite lubricant was applied to the surfaces of both specimens and dies to minimize the friction effect. The specimens were heated at 10 K/s to deformation temperatures and then held for some time to eliminate the temperature gradient and microstructure inhomogeneity. The room-temperature compression tests of forged and solid solution states were carried out on a WDW-100 universal tester (Beijing Sinofound Co., Ltd, Beijing, China). The strain-stress curves are recorded by the tester automatically.

**Figure 1.** Schematic diagram of the experimental process for the 7050 alloy.

The samples before and after heat treatment were also wire-electrode cut and metallographically observed for comparison. The samples were ground and polished to eliminate any trace of cutting. Then they were etched with Graff-Sargent solutions. Optical micrographs of the samples in different states were characterized by an OLYMPUS GX-41 type microscope(Olympus Corporation, Tokyo, Japan). The microstructure was further examined using a TESCAN VEGA3 LMH scanning electron microscope (TESCAN CHINA Ltd., Shanghai, China).

#### **3. Results and Discussion**

#### *3.1. Flow Behavior*

The stress-strain curves of the 7050 alloy at room temperature in three states (forged state, solid solution state, and annealed state after forging) were obtained and depicted in Figure 2. From the comparison, it can be concluded that the solid solution-stated alloy has greater strength, plasticity, and fracture toughness. Firstly, as shown in Figure 3a–c, the grains in the wrought state were fibrous. After quenching, the grain is equiaxial (shown in Figure 3d–f), indicating that the treatment enhances recrystallization grain generation [12–14]. The volume fraction of recrystallized grains of 7050 alloy before and after solid solution treatment is measured by the software Image-Pro-Plus 6.0 (Media Cybernetics Inc., Rockville, MD, USA). The values are 18.9% and 52.6%, respectively. The volume fraction of recrystallized grains of 7050 alloy measured in other experiments is shown in Figure 4 [15–17]. The treatment can enhance the recrystallization of the 7050 aluminum. The recrystallization reduces intragranular dislocation density and intragranular-grain boundary strength differences, which will decrease work-hardening and increase plasticity. Secondly, the supersaturated solid solution generated in the treatment will finally transfer to the strengthening phase (the white region of the SEM image in Figure 5b), which will pin dislocation and improve the alloy strength [18]. Thirdly, the coarse second-phase particles of the alloy (the black part in Figure 5a) lessened during the treatment [19]. The coarse particles (above 2 nm) of 7050 alloy decreased by about 70% after solid solution treatment [20]. The refined particles hinder void generation and crack propagation to enhance the fracture toughness of the 7050 alloy.

**Figure 2.** Stress-strain curve for room temperature compression of 7050 alloys in different states.

**Figure 3.** Optical micrographs of 7050-aluminum alloy before and after solid solution treatment (**a**–**c**) Before solid solution treatment; (**d**–**f**) After solid solution treatment.

**Figure 4.** The volume fraction of recrystallized grains before and after solid solution treatment [15–17].

The true stress-strain curves of aluminum in the solid solution state at elevated temperatures from 333 K to 523 K at different strain rates are shown in Figure 6a–c. All curves could be divided into three distinct stages. In the first stage, the flow stress increases linearly with strain, and only elastic deformation predominates. In the second stage, plastic deformation happens and flow stress slowly increases. In the third stage, the flow stress will approach saturation and weave. Furthermore, it is seen that flow stress is negatively correlated with deformation temperature. The microstructure evolution (precipitation or recrystallization), deform-mechanism conversion (shear mechanism to Orowan mechanism), and reduction of dislocation movement resistance occurring at warmer temperatures can all alter the flow characteristics and decrease flow stress [21–23]. At lower temperatures, only the strain-hardening tendency exhibits itself in the curve. When the deformation temperature is approximately 423 K, the work hardening occurs first, and then the 7050 alloy begins to soften at a higher plastic strain. The tendency for flow softening becomes

more obvious at warmer deformation temperatures. Moreover, the flow stress of solid solution-state 7050 alloys has a positive correlation with strain rate. At high strain rates, dislocation density and dislocation slip velocity increase, resulting in a magnification of dislocation interaction and deformation resistance [24,25]. Additionally, at the same compression temperature, the amplification of flow stress with increasing strain rate is roughly the same. It is due to the balance of work hardening and deformation thermal softening at medium temperatures [26]. The strain rate effect of solid solution 7050 aluminum alloy is not obvious during the medium-temperature compression process, and the stress-strain curve is not sensitive to the strain rate [27].

**Figure 5.** SEM images of the 7050 alloy (**a**) without heat treatment; (**b**) after quenching.

**Figure 6.** The flow stress of solid solution-state 7050 alloy in different conditions: (**a**) 0.001 s−1; (**b**) 0.01 s−<sup>1</sup> (**c**) 0.1 s<sup>−</sup>1.

In compression tests, the friction will change the stress state, leading to heterogeneous deformation and non-negligible errors in the obtained flow stress, although the necessary lubricant was applied [28]. Friction correction is necessary for the accurate calculation of flow stress. The correction method is expressed in Equation (1) [29,30]:

$$\sigma = \frac{\overline{\sigma}}{1 + \left(\frac{2}{3\sqrt{3}}\right) \text{m}\left(\frac{\mathbb{R}\_0}{\mathbb{R}\_0}\right) \exp\left(\frac{3\varepsilon}{2}\right)}\tag{1}$$

where σ is the corrected stress, ɐഥ is the measured stress without correction, and ε is the strain, respectively. For this specimen, R0 and h0 respectively, represent the initial radius and height of the compressed sample (unit: mm). The R0-value is 4 and the h0-value is 12 for this compression. Additionally, m is the friction factor for warm upsetting, and the value is 0.2. Compared with the flow stress with and without correction, the measured values are significantly higher than the actual ones. The deviation increases with strain due to the incremental contact area. Also, the work-hardening effects are reduced after correction.

#### *3.2. Construction and Comparison of Constitutive Models*

The flow stress in the room and at medium temperature can be analyzed using Hollomon [31], Swift [32], Ludwigson [33], and Voce hardening models [34]. All constitutive models are shown in Equations (2)–(4) below:

$$\text{Hollomon } \sigma = \mathbf{k}\_{\text{H}} \varepsilon^{\text{nH}} \tag{2}$$

$$\text{Swift } \sigma = \mathbf{k}\_{\mathbb{S}} (\varepsilon 0 + \varepsilon)^{\text{nSwift}} \tag{3}$$

$$\text{Ludwigson } \sigma = \mathbf{k}\_1 \varepsilon^{\mathbf{n}} + \mathbf{e}^{\mathbf{k}\_2} \mathbf{e}^{\mathbf{n} \cdot \varepsilon} \tag{4}$$

$$\text{Vocce } \sigma = \sigma\_0 \left( 1 - \text{Ae}^{-\text{k}\varepsilon} \right) - \text{k}\varepsilon \tag{5}$$

where σ is the true stress in the compression, ε is the true strain, n is the strain hardening index, σ0, ε0, k and A are material constants.

Besides, some classical viscoplastic models, such as the Arrhenius-type model [35–37] and the Johnson–Cook model [38], were applied for comparison. The two models are shown in the equation as follows:

$$\text{Arrenius-type model } \dot{\varepsilon} = A \left[ \sinh(\alpha \sigma) \right]^n \exp\left(-\frac{\mathcal{Q}}{\mathcal{R} \mathcal{T}}\right) \tag{6}$$

where α, and n are material constants. Q is the activation energy of plastic deformation (J/mol); R is the gas constant; and T is the temperature.

$$\text{Johnson-Cook model } \sigma = (\text{A} + \text{B}\sigma^{\text{n}}) \left( 1 + \text{Cln} \frac{\dot{\varepsilon}}{\varepsilon\_{\text{ref}}} \right) \left( 1 - \text{T}\_{\text{H}}^{\text{D}} \right) \tag{7}$$

where A, B, and C are material constants. . εref is the reference strain rate; TH is the relative temperature.

In the above equations, all the parameters are obtained by the reference or fitted by the Levenberg-Marquardt approach. The predictions of the flow stress at 423 K and 0.1 s−<sup>1</sup> by the four models are shown and compared in Figure 7. The fitting degrees of the four models are different, and the order of priority is as follows: Voce > Swift > Ludwigson > Hollmon > Johnson-Cook > Arrhenius. The Arrhenius-type model uses a hyperbolic sine function to predict the flow stress of the material, and it cannot accurately predict the hardening behavior of the alloy at medium temperature. The unsaturated models (Johnson-Cook, Swift, Ludwigson, and Hollmon) utilize a certain exponent to predict the flow stress with strain hardening. The flow stress calculated by the models was greatly less than the measurement before the peak point. Due to the identical hardening exponent in the models, flow stress in the middle and late stages of compression will be exaggerated. [39]. However, for the saturation models (Voce model), it can better fit the different hardening rates at different states with variable exponents, and it can also better predict the saturated flow stress at stable states. For solid solution-state 7050 alloy during warm compression, the flow stress has a saturated value after the hardening stage, and the voice-type model is best for prediction.

**Figure 7.** Fitting results of the flow stress at 423 K in 0.01 s<sup>−</sup>1.

3.2.1. Voce-Type with Softening Coefficient

The original Voce model ignores the softening in high strain and the effects of temperature and strain rate on flow stress. To improve accuracy, a Voce-type with a hardening and softening coefficient is employed to describe the deformation behaviors with saturated flow stress at room and medium temperatures as follows [40,41]:

$$\begin{cases} \sigma = \mathbf{k} \dot{\varepsilon}^{\mathbf{m}\_0 + \mathbf{m}\_1 \mathbf{T}}\\ \mathbf{k} = (1 - \mathbf{k}\_{\mathrm{Soft}}) \mathbf{k}\_{\mathrm{Har}} \end{cases} \tag{8}$$

$$\begin{cases} \mathbf{k}\_{\rm{Flar}} = \mathbf{K} (\boldsymbol{\varepsilon} + \boldsymbol{\varepsilon} \mathbf{0})^{\mathbf{n}} \exp(\frac{\beta}{\mathbf{T}})\\ \mathbf{K}\_{\rm{Sof}} = 1 - \exp(-(\mathbf{r}\_0 + \mathbf{r}\_1 \mathbf{T}) \boldsymbol{\varepsilon}) \end{cases} \tag{9}$$

where σ is the flow stress (unit: MPa), T is the absolute temperature (unit: K), kHar is the strain strengthening index, and KSof stands for the softening index. Besides, β, m0, m1, r0, and r1 are dimensionless material constants.

Both sides of Equations (8) and (9) are taken as the natural logarithm and changed to Equation (10);

$$\ln \sigma = \text{lnk} + \text{ln} (\varepsilon + \varepsilon\_0) + \frac{\beta}{\text{T}} - (\mathbf{r}\_0 + \mathbf{r}\_1)\varepsilon + (\mathbf{m}\_0 + \mathbf{m}\_1 \mathbf{T}) \text{ln } \dot{\varepsilon} \tag{10}$$

All the material constants in the Voce model can be determined from the corrected strain-stress curves. At a given temperature and strain, hardening and softening coefficients are fixed. Therefore, Equation (8) can be simplified as follows:

$$
\ln \sigma = (\mathbf{m}\_0 + \mathbf{m}\_1 \mathbf{T}) \ln \ \dot{\varepsilon} + \mathbf{k}\_2 \tag{11}
$$

Therefore, m0 + m1T is the slope of lnσ-ln*ε*´ plot shown in Figure 8a. Then, the slopes in different conditions are shown in Figure 8b. The m0-value can be determined from the slope of plots, and the m1-value is obtained from the plots' intercept in Figure 8b.

**Figure 8.** Parameters fitting under different conditions: (**a**) lnσ-ln*ε*´ (**b**) m0+m1T-T (**c**) lnσ-strain (**d**) r0 + r1T-T.

At a given temperature, r0+r1T is a constant and is set to k3. lnk + nln (ε + ε0) + (m0 + m1T) lnε is also a constant at a certain temperature and the strain rate and should be set to K4. Equation (11) is changed to Equation (12);

$$
\ln \sigma = \text{nlm}(\varepsilon + \varepsilon\_0) - \text{k}\mathfrak{z}\varepsilon + \text{k}\_4 \tag{12}
$$

Figure 8c shows the relation between lnσ and ε, and Equation (12) is employed to characterize the relationship. The fitting result reveals the value of the material constants in different conditions. Besides, k3-T plots are shown in Figure 8d. The slopes and intercepts of the plots were calculated to determine the r0-value and r1-value in the model. Similarly, the constants K and β can be obtained from the k4-T plots. All the material constants in the voce-type model are obtained, and the constitutive model is shown as follows:

$$\sigma = 533.0765 \left( \left( \varepsilon - 0.02593 \right)^{0.2842} \right) \times \text{EXP} \left( \frac{142.13587}{\text{T}} \right) \times \text{EXP} \left( - \left( 0.43411 + 0.000162213 \text{T} \right) \varepsilon \right) \varepsilon^{0.0083 + 0.000183178 \text{T}} \tag{13}$$

#### 3.2.2. Modified Voce-Type Model with Variable Parameters

The material parameters in the conventional voce-type model are invariable. However, they are influenced by temperature and other conditions in the warm deformation due to microstructure evolution, which decreases simulation accuracy. The modification to the constitutive model is that the wave of material parameters can be corrected. The modified constitutive model with variable material parameters includes two parts: the Voce constant prediction and parameter wave correction. The prediction of the Voce constant (FVoce) is based on the traditional model in Equations (8) and (9). Then, a corrected function Kc is set as a compensation for the parameter wave in warm deformation. Therefore, Equation (8) can be rewritten as follows:

$$\begin{cases} \sigma = \mathbf{K\_c} \mathbf{F\_{Voc}}\\ \mathbf{F\_{Voc}} = \left(\varepsilon + \varepsilon\_0\right)^{\mathbf{n}} \exp(\frac{\beta}{\mathbf{T}}) \exp(-(\mathbf{r}\_0 + \mathbf{r}\_1 \mathbf{T})\varepsilon) \text{ } \varepsilon^{(\mathbf{m}\_0, \mathbf{m}\_1 \mathbf{T})}\\ \mathbf{K\_c} = \mathbf{k\_T} \mathbf{K\_c} \mathbf{K\_{c}} \end{cases} \tag{14}$$

where σ is the flow stress (unit: MPa), T is the absolute temperature, and m0, m1, r0, r1, ε<sup>0</sup> are dimensionless material constants. kT, K<sup>ε</sup> and K<sup>ε</sup> are the compensation coefficients that can be used to describe the effects of temperature, strain, and strain rate on flow stress respectively.

In the isothermal compression process, the deformation heat raises the alloy's temperature and affects the deformation behavior [42,43]. Therefore, the coupling effect of strain and deformation temperature on material parameter evolution must be considered. Meanwhile, the flow stress of 7050 alloy at warm temperatures is not sensitive to the strain rate due to the balance between work hardening and deformation thermal softening. The interaction between strain rate and deformation temperature and material parameter evolution could be neglected, and the compensation coefficients Kc can be described as follows:

$$\mathbf{K}\_{\mathbf{c}} = \mathbf{k}\_{\mathbf{T},\mathbf{c}} \mathbf{K}\_{\mathbf{c}} \tag{15}$$

where kT,<sup>ε</sup> means interaction effect of strain and deformation temperature with compensation coefficients.

The aim is to fit the function between deformation conditions and compensation coefficients. The compensation coefficients in different conditions are calculated and shown in Figure 9. It could be seen that the compensation coefficients and strain rate are positively correlated. The parameters *n* and –(r0+r1T) in the FVoce part are constant, but they are positively correlated with the strain rate by calculation. When the strain rate is increased, the value of the FVoce part increases more slowly than the truth, resulting in a larger error at a higher strain rate. Moreover, as shown in Figure 9, the strain rate increases by 10 times, k increases by a certain multiple, which means the value of K . <sup>ε</sup> and logarithm of strain rate show an approximately linear relationship, and the K . <sup>ε</sup>-value can be predicted by a logarithmic function. Meanwhile, a polynomial approach as follows was applied for describing the interaction among kT,ε, strain, and temperature [44]:

$$\mathbf{k}\_{\mathbf{T},\varepsilon} = \left(\mathbf{A}\_0 + \mathbf{A}\_1 \mathbf{T} + \mathbf{A}\_2 \mathbf{T}^2 + \dots + \mathbf{A}\_n \mathbf{T}^n\right) \left(\mathbf{B}\_0 + \mathbf{B}\_1 \varepsilon + \mathbf{B}\_2 \varepsilon^2 + \dots + \mathbf{B}\_n \varepsilon^n\right) \tag{16}$$

where *n* is the polynomial order. Fitting the functions in different orders used the correlation coefficient (R) [45] (shown in Equation (13)) to evaluate the fitting precision, and the results are shown in Table 2.

$$\mathcal{R} = \frac{\sum\_{i=1}^{N} (\mathbf{p\_{Ei}} - \overline{\mathbf{p\_{E}}})}{\sqrt{\sum\_{i=1}^{N} (\mathbf{p\_{Ei}} - \overline{\mathbf{p\_{E}}})^2 \sum\_{i=1}^{N} (\sum\_{i=1}^{N} (\mathbf{p\_{Pi}} - \overline{\mathbf{p\_{P}}})^2}} \tag{17}$$

where pEi stands for the true value of Kc, pPi is the calculation by a polynomial function, pE and pP stand for the mean-value of the true value and calculated value, respectively.

**Figure 9.** The value of Kc in different conditions (**a**) Kc in different strains and temperatures (**b**) Kc in different strains and strain rates.

**Table 2.** The correlation coefficient in different orders.


The correlation coefficients in the second to fifth orders are all above 0.95. To avoid the error of overfitting, a second-order polynomial function may be best for describing the interaction during the medium temperature range. The second-order polynomial function is shown in Figure 10b. Ultimately, the modified Voce-type constitutive model for 7050 alloy in medium-temperature compression is mathematically described below.

$$\begin{aligned} \sigma &= \mathbf{K}\_{\mathbf{C}} \mathbf{F}\_{\text{Vore}} \text{ MPa} \\ \mathbf{F}\_{\text{Vore}} &= \left(\varepsilon - 0.02593\right)^{0.211942} \exp\left(\frac{142.15857}{\Gamma}\right) \exp\left(-(0.43411 + 0.000162213)\varepsilon\right) \varepsilon^{(0.00683 + 0.0000183178 \Gamma)} \\ \mathbf{K}\_{\mathbf{C}} &= \left(0.0275 \hbar \upsilon + 1.0629\right) \left(-0.01252 \varepsilon^{2} + 0.01189 \varepsilon - 0.02068\right) \left(0.4515 \mathbf{T}^{2} - 321.3442 \mathbf{T} + 23582.594\right) \end{aligned} \tag{18}$$

**Figure 10.** The relationship between (**a**) strain, strain rate, and Kc; (**b**) strain, temperature, and Kc.

#### *3.3. Constitutive Model Evaluation and Application*

A good constitutive model cannot only fit the modeling data used but also accurately calculate all the flow stresses during the actual compressive process. Therefore, the data used for the model establishment and the load of thermal compression were calculated and compared. The comparison between the predicted stresses by the conventional and corrected Voce models and the experimental values is shown in Figure 11a,b. The comparison indicates that the predicted stresses by the conventional Voce model have remarkable deviations from the measurements. However, the calculations by the modified model are well matched to the measured ones.

**Figure 11.** Comparisons between experimental and predicted stress by conventional and corrected Voce models: (**a**) 473 K at different strain rates; (**b**) 0.1 s−<sup>1</sup> at different temperatures; (**c**) conventional model; (**d**) modified Voce model.

To compare the accuracy of the two models further, two statistical indexes, the correlation coefficient (R) and the average absolute relative error (AARE), were used as the evaluation criteria in this research [33]. The two indexes are expressed as follows:

$$\begin{cases} R = \frac{\sum\_{i=1}^{N} (\sigma\_{\text{Ei}} - \overline{\sigma\_{\text{E}}})}{\sqrt{\sum\_{i=1}^{N} (\sigma\_{\text{Ei}} - \overline{\sigma\_{\text{E}}})^2 \sum\_{i=1}^{N} (\sum\_{i=1}^{N} (\sigma\_{\text{Pi}} - \overline{\sigma\_{\text{P}}})^2}}\\ \quad \text{AARE} = \frac{1}{N} \sum\_{i=1}^{N} \left| \frac{\sigma\_{\text{Ei}} - \sigma\_{\text{P}i}}{\sigma\_{\text{E}}} \right| \times 100\% \end{cases} \tag{19}$$

where σEi stands for the measurement, σPi is the calculation by the constitutive model, and σ<sup>E</sup> and σ<sup>P</sup> stand for the mean value of the flow stress obtained by experiment and calculation, respectively.

Figure 11c,d show the comparison results for the two models. The R-value of the conventional Voce model and the AARE-value of the conventional Voce model are 0.9902 and 10.10%, respectively, while they are 0.9988 and 3.26%, respectively, for the modified model. Hence, the modified Voce model has better fitting ability than the convention for experimental data in a wide range.

The characterization of the flow behaviors of the 7050 aluminum alloy in its solid solution state contributes significantly to its warm forge process design. The final purpose of the modified Voce-type constitutive model is for better practical load prediction. In order to verify the prediction abilities of the practical loads of the modified model, the whole warm compression process was calculated and compared. The accuracy of flow stress correction and prediction for non-data points can also be evaluated by the FE simulation. The calculation was done on the Deform-2D 11.0 platform (Scientific Forming Technologies Corporation, Raleigh, North Carolina, USA). Here, we enrich the stress-strain data of the alloy utilizing the modified model. Then we simulated two compression processes at 333 K at different strain rates. The simulation model is shown in Figure 12. Only a representative plane was used for cylindrical compression. The size of the specimens is Φ8 mm × 12 mm. The aluminum specimen was assumed to be rigid viscoplastic and meshed with about 32,000 tetrahedral elements. The grid size was calculated by the simulation software from the curvature of the initial geometry. The deformation solver uses a conjugate gradient solver. It uses an iterative method to gradually approximate the optimal value. The parts were re-meshed between every 5 computational steps to avoid simulation errors since the mesh geometry changes significantly during compression. The heat transfer between the specimen and the air was neglected, and interface friction was characterized using the shear friction law with a friction factor of 0.2. Speed of top anvil and the strain rate of specimen can be converted as Equation (14) [46]:

$$\mathbf{V\_{T}} = \frac{\mathbf{H\_{B}} - \mathbf{H\_{A}}}{\varepsilon\_{\mathrm{T}} / \ \dot{\varepsilon}} \tag{20}$$

where HB is the height of the specimen before compression, and in this simulation, HB is 12. HA is the height after compression, namely 6 mm. ε<sup>T</sup> is the true strain after compression, and it is approximately 0.69. *ε*´ is the strain rate of the specimen.

**Figure 12.** Finite element model for isothermal comparisons.

The simulation results are shown in Figure 13a,b. Due to friction and heterogeneous deformation, the periphery of the specimen became typical drum-type. At the end of this compression, the inner region indicates a true strain of 0.69, and the true strain rates are about 0.1 s−<sup>1</sup> and 0.01 s−1, respectively, manifesting the simulated physical quantities having good agreement with the compression conditions. The upsetting loads, along with the top die stroke, were calculated and compared. The load trend is basically consistent with the experimental result. According to Equation (13), the AARE of the two is 5.71% and 4.61%, respectively. Consequently, it shows the positive accuracy of the friction correction, and the modified Voce model can be effectively applied in the FEM for stress calculation and load prediction during warm forming of the solid solution-state 7050 aluminum alloy.

#### **4. Conclusions**

In this study, the room and warm compression behaviors of the solid solution-state 7050 alloy were researched. Furthermore, a modified Voce-type constitutive model with variable parameters was built to enhance the prediction precision of the warm compression behavior of solid solution-state 7050 alloy. Meanwhile, the prediction accuracy of the modified Voce is evaluated in two ways. The following conclusions could be obtained:


**Author Contributions:** Investigation, methodology, data curation, and writing—original draft, H.T. and Y.X.; resources, conceptualization, formal analysis, and writing—review and editing, C.P. and Y.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research was funded the National Natural Science Foundation of China (No. 51775068) and the Chongqing Natural Science Foundation general project [No. cstc2021jcyj-msxmX1085].

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are not publicly available due to ongoing research in this field.

**Conflicts of Interest:** The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.

#### **References**


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## *Article* **A New Method for Preparing Titanium Aluminium Alloy Powder**

**Jialong Kang 1,2, Yaoran Cui 1,2, Dapeng Zhong 1,2, Guibao Qiu 1,2,\* and Xuewei Lv 1,2**


**\*** Correspondence: qiuguibao@cqu.edu.cn

**Abstract:** Due to TiAl alloys' excellent properties, TiAl alloys have received widespread attention from researchers. However, the high energy consumption and lengthy process of traditional preparation methods have always limited the large-scale application of TiAl alloys. This article develops a new method for preparing TiAl-based alloy powder via the magnesium thermal reduction of TiO2 in AlCl3-KCl molten salt. In this study, the proportion of AlCl3&KCl molten salts was determined. We conducted phase analysis on the final product by studying the changes in temperature and time. It was found that the TiAl3 alloy powder could be obtained by being kept at 750 ◦C for 2 h, with an oxygen content of 3.91 wt%. The reaction process for the entire experiment was determined through thermodynamic calculations and experimental analysis, and the principles of the reduction process are discussed.

**Keywords:** TiAl alloy; magnesium reduction; AlCl3-KCl; TiO2

#### **1. Introduction**

Metal compounds offer both the plasticity of metals, and the high-temperature strength of ceramics in specific compositions, due to the metal compound ordered arrangement of their atoms, and the coexistence of inter-atomic metal bonds and covalent bonds. TiAl-based intermetallic compounds were highly valued in the aerospace industry and other fields, due to their excellent mechanical properties and low density, in the 1950s [1,2]. Nowadays, the TiAl-based alloy is still recognized as a high-end material in the world [3,4]. Due to its high specific strength, high temperature resistance [5,6], corrosion resistance, oxidation resistance [7,8], and excellent biocompatibility, the TiAl-based alloy is widely used in the field of high-end materials in modern life [9,10]. For example, large aeroplanes, submarines, aerospace technology, and artificial bones [11–13]. This high-end material should also be popularized in ordinary daily life but, due to its high cost, it has not been applied, and can only be applied in high- and middle-value fields. The reason for this dilemma is the long cycle and high cost of preparing the metal Ti. Since the discovery of metallic titanium, only the Kroll method has produced sponge titanium on a large scale [14–17]. Therefore, most methods for preparing TiAl-based alloys are element approaches [18–21], prepared by adding proportional amounts of the elements Ti and Al in a high-temperature melting furnace. Adding Ti separately also causes production costs for TiAl-based alloys.

Many researchers have adopted different methods to find an efficient method for producing TiAl-based alloys. The most traditional way is to prepare TiAl-based alloys via casting [22–25] and cast alloys with different compositions using a vacuum induction melting furnace, centrifuge, hot press, and other equipment. Among them, J Lapin [26] et al. prepared the Ti-42.6Al-8.7Nb-0.3Ta-2.0C and Ti-41.0Al-8.7Nb-0.3Ta-3.6C (in at.%) TiAl alloys via the casting method, and studied the effect of adding 2.0C and 3.6C on the properties of the TiAl alloys. They also studied the solid-state phase transformation grain refinement of the

**Citation:** Kang, J.; Cui, Y.; Zhong, D.; Qiu, G.; Lv, X. A New Method for Preparing Titanium Aluminium Alloy Powder. *Metals* **2023**, *13*, 1436. https://doi.org/10.3390/ met13081436

Academic Editor: Wislei Riuper Osório

Received: 5 July 2023 Revised: 2 August 2023 Accepted: 7 August 2023 Published: 10 August 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

as-cast peritectic TiAl-based alloys. Powder metallurgy is also the preparation method for most TiAl-based alloys; it can overcome the defects generated through traditional manufacturing methods, and obtain uniform and fine microstructures, significantly improving the mechanical properties of the alloys. Heike Gabrisch et al. [27] added 0.5–1.0 at.% C into Ti-45Al-5Nb alloy via powder metallurgy, and used a transmission electron microscope and high-energy XRD to study the influence of solid-solution carbon and carbide precipitation on the hardness of the TiAl alloy. In addition to the above two methods, emerging additive manufacturing technologies [28–30] can also prepare designed alloys, by stacking powders layer by layer. The powder preparation methods mentioned above all require titanium powder as a raw material, which is expensive, and increases production costs. Therefore, there is a need for a method that can directly prepare alloys from TiO2, to improve the existing technology, reduce the process flow, and increase the popularity of TiAl-based alloys [31,32].

Researchers have now prepared TiAl-based alloys using other methods. Zhao et al. [33,34] proposed a two-step thermal reduction method for preparing TiAl-based alloys. In this method, firstly, Na2TiF6 is reduced by TiAl-based alloy powder, which is the first reduction stage. After vacuum distillation, the second-stage reduction of Al is carried out, to obtain TiAl-based alloys. The TiAl-based alloy powder collected in the purification process can also be used for the first-stage reduction. This method successfully realizes the overall round-robin preparation of TiAl-based alloys through the Al thermal reduction of Na2TiF6. Dou, Song, and Zhang [35,36] successfully prepared 20 kg TiAl-based alloy ingots with an oxygen content of approximately 1.09 wt% through multi-stage profound reduction. This method successfully achieved the one-step preparation of TiAl-based alloys through adding KClO3 as a heating agent, and self-propagating aluminium heat.

However, the two-step aluminothermic reduction of Na2TiF6, and the high-temperature self-propagation method, require experiments at high temperatures, resulting in energy consumption. However, due to the limited reduction effect of metal aluminium on TiO2 at low temperatures, it is impossible to prepare TiAl-based alloys by reducing TiO2 at low temperatures. Moreover, TiAl-based alloy ingots exhibit significant room temperature brittleness, with a derivation rate of less than 1%, and fracture during stretching, resulting in a poor machinability, and difficulties in their application. Due to the significant difference in melting points between Ti and Al, casting high-quality alloy ingots is difficult and costly. This article proposes a new method of preparing TiAl-based alloy powder by reducing TiO2 in AlCl3&KCl molten salt through a magnesiothermic reduction. This method can only be carried out at low temperatures, with a simple production method, and a low level of environmental pollution. This work provides new ideas for the future large-scale application of TiAl-based alloy powder, and to solve the problem of the long preparation process of existing TiAl-based alloys.

#### **2. Materials and Method**

#### *2.1. Materials*

Anhydrous AlCl3, KCl, HCl, TiO2, and binder were obtained from Aladdin Reagent Co., Ltd. (Shanghai, China). The particle size of anhydrous AlCl3, KCl, and TiO2 is below 74 μm. The binder used in this paper is ethyl cellulose, a polymer compound with the chemical formula (C12H22O5)n. Ethyl cellulose is a white powder at room temperature. The primary function of this binder is to aggregate the raw materials, and increase the contact area of raw materials. Under high-temperature conditions, ethyl cellulose will be decomposed into organic compounds that do not impact the experiment. As a reducing agent, Mg powder is obtained from Sinopharm Chemical Reagent Co., Ltd. (Ningbo, China). The Mg powder particle size is below 200 μm.

#### *2.2. Introduction to AlCl3 and Selection of AlCl3-KCl Molten Salt Ratio*

AlCl3 is a white crystalline powder with a solid hydrochloric acid odour, and a light yellow industrial product, and is easily soluble in water, alcohol, chloroform, etc. Its melting point is 194 ◦C, but it is prone to sublimation and deliquescence at 178 ◦C. Moreover, due to the exothermic hydration reaction, it may explode when encountering water. Therefore, the AlCl3 must be sealed and stored in a dry environment.

#### (1) Physical properties of AlCl3

AlCl3 was first prepared by Biltz. W [37] in 1923, via the reaction of 99.5% pure Al powder with dry HCl gas. Subsequently, Baker Analytics and Grothe studied the basic properties of AlCl3, etc. [37]. The density and viscosity of AlCl3 are key physical properties during the thermal reduction process. Based on previous research data, the density of AlCl3 varies with the temperature, as shown in Figure 1. It can be seen that the density of AlCl3 shows a steady downward trend with the temperature rising within 460–560 ◦C. The following formula is the density formula, fitted according to the data (estimated standard error: 0.15%).

$$\rho = 2.19 - 5.40 \times 10^{-4} \text{T} - 1.14 \times 10^{-5} \text{T}^2 + 3.04 \times 10^{-8} \text{T}^3 \tag{1}$$

<sup>ρ</sup> indicates the density of AlCl3 (g·cm<sup>−</sup>3); T indicates the temperature (◦C).

**Figure 1.** AlCl3 density changes with temperature, data from [37].

Figure 2 shows the viscosity data of AlCl3. According to these data, the viscosity formula of AlCl3 is fitted, and the estimated standard error is 1.05%.

$$\eta = 1.71 \cdot \exp(4943.8 / \text{RT}) \tag{2}$$

η indicates the viscosity of AlCl3 (Pa·s), and R indicates a constant of 8.314 (kJ/mol); T indicates the temperature (◦C).

**Figure 2.** AlCl3 viscosity changes with temperature, data from [37].

From the graph showing the viscosity and density changes with temperature, it can be seen that the density and viscosity of AlCl3 show an overall decreasing trend with an increasing temperature. The decrease in density and viscosity is conducive to the complete contact of reactants during the reduction reaction process, increasing the reaction efficiency, which is a favourable factor in magnesium thermal reduction.

(2) Basic Physical Properties of AlCl3-KCl Mixed Molten Salt

Due to the low melting point and easy sublimation of AlCl3, to prevent the loss of raw materials due to the large amount of sublimation and volatilization of AlCl3, a mixed molten salt AlCl3-KCl is configured, which can effectively suppress the volatilization of AlCl3. As shown in Figure 3, when the AlCl3 content accounts for 80 wt% and above, the binary phase diagram of AlCl3-KCl shows that a large amount of AlCl3 gas is generated. As the KCl increases, the blue part in the figure shows the liquid phase zone of the AlCl3-KCl eutectic salt without gas generation. Therefore, this part can be selected as the area used in the raw material ratio in this experiment, where the mass ratio of AlCl3/(AlCl3-KCl) is 0.65.

The density of the AlCl3-KCl is based on Carter and Morrey's [37] work to obtain the following AlCl3-KCl density data, as shown in Table 1. The temperature dependence of AlCl3-KCl under different KCl contents was plotted using Table 1, as shown in Figure 4. It can be seen that as the KCl content increases, the overall density of the AlCl3-KCl shows an upward trend. As the temperature increases, the density of the AlCl3-KCl decreases. When the molar ratio of KCl exceeds 50%, the overall density of the AlCl3-KCl does not change significantly with temperature. The incremented density is due to the melting point of KCl being higher. After the KCl content increases, the overall melting point of the AlCl3-KCl increases. An increasing KCl content can inhibit AlCl3 volatilization. This result is consistent with the calculation results in Figure 4.

**Table 1.** The density of the AlCl3-KCl varies with the KCl content.


**Figure 3.** Binary phase diagram of AlCl3-KCl.

**Figure 4.** Density variation in AlCl3-KCl with the temperature, under different KCl contents.

#### *2.3. Methods*

The raw materials are mixed with the binder in a mortar. After that, the mixed raw materials are pressed into a round green mass. For the reduction, we place the green mass into the molybdenum crucible and the tube furnace (KF1100 Nanjing Boyuntong (Nanjing, China), as shown in Figure 5). After reaching the specified temperature, this furnace can be loaded into the reaction furnace tube. The heating rate is 15 ◦C/min, and the insulation is maintained after reaching the specified temperature. According to the analysis of the physical properties and phase diagram of AlCl3&KCl in the previous section, to suppress the volatilization of AlCl3, the molten salt is weighed based on the mass ratio of AlCl3/(AlCl3+KCl) of 0.65. Therefore, this experiment's molten salt mass ratio of AlCl3: KCl is 1.8. Considering that AlCl3 has the characteristic of volatilizing at low temperatures, it is necessary to increase the content of AlCl3 appropriately during the raw material configuration process. The amount of TiO2 used in each experiment is 5 g, the proportion of molten salt is four times the total mass of the TiO2 added, and the amount of magnesium added is the molar mass of the AlCl3 completely reacted.

**Figure 5.** Experimental device.

The experimental process is shown in Figure 6. The experiment was conducted in a tubular box mixing furnace. The raw materials were mixed evenly, loaded into a molybdenum crucible, and placed in a reactor. Inert gas was first introduced into the reactor to exhaust the air, with a flow rate of 300 mL/min. After the high-temperature furnace rose to the set temperature, the reactor was loaded into the furnace, without increasing the temperature of the furnace (to reduce the evaporation of the molten salt). This experiment explored the influence of time on the reaction products' phase and oxygen content. The overall reaction time starts from the installation of the reaction furnace tube into the furnace, and a specific insulation time is set. After the reaction, argon gas is continuously introduced and cooled in the furnace, to ensure that the sample does not come into contact with oxygen. The final reactant is extracted for subsequent acid leaching and flotation, to obtain the final alloy product for analysis. Among the experiments, 5 wt% dilute HCl is used for acid leaching. The acid-leaching process is carried out in a water bath at 80 ◦C for 2 h. The acid-leaching process is mainly used to remove Mg and MgO. The specific reactions are shown in the formulae below. The reaction byproduct Al2O3 is removed via ball milling. The mass ratio of the ball-milling process as ball:material:H2O during ball milling is 1.6:1:3. The ball mill rotates at a speed of 350 r/min for 15 min each time. Each experiment requires ball milling at least three times.

$$\text{Mg} + 2\text{HCl} = \text{MgCl}\_2 + \text{H}\_2 \tag{3}$$

$$\text{MgO} + 2\text{HCl} = \text{MgCl}\_2 + \text{H}\_2\text{O} \tag{4}$$

**Figure 6.** Experimental flowchart.

#### *2.4. Analysis*

X-ray powder diffraction (XRD, Cu Kα radiation, PANalytical X'Pert Powder, Malvern PANalytical B.V., Almelo, The Netherlands), with a scanning range of 10–90◦ and a scanning step of 5 deg./min, was carried out, to confirm the phase composition of sample powder three times. Scanning electron microscopy (SEM, TESCAN VEGA 3 LMH system, TESCAN, Brno, Czech Republic) was also performed, to evaluate the microanalysis and surface morphology of the reaction product. Energy-dispersive spectroscopy (EDS) microanalysis was conducted. The accelerating voltage used for the EDS analysis was 10 kV. The thermodynamic software FactSage8.0 calculated the feasibility of the reaction. The oxygen content of the product was analyzed using the JXA82 electron probe from JEOL Corporation, and the particle size analyzer from NanoBrook Omni of Brookhaven Instruments, Holtsville, NY, USA.

#### **3. Results and Discussion**

#### *3.1. Phase Analysis of Reactants at Different Temperatures*

The XRD phase diagrams and SEM of the products at different reaction temperatures are shown in Figures 7 and 8. Comparing the XRD analyses of the products at reaction temperatures of 750~950 ◦C, it can be found that the reaction products are TiAl-based alloy powders. Compared with traditional magnesiothermic reduction, TiO2 is not directly reduced; other substances participate in the reaction. The Gibbs free energy diagram of the reaction between Mg and AlCl3, TiO2, was drawn using the thermodynamic software FactSage8.0, as shown in Figure 9. At temperatures ranging from 400 ◦C to 950 ◦C, the Gibbs free energy of the reaction between Mg and AlCl3, TiO2 can be observed. At the same magnesium content, Mg preferentially reacts with AlCl3, and the entire process uses aluminium as a reducing agent in reducing the TiO2. Moreover, magnesium-reducing AlCl3 releases a large amount of heat, to drive the aluminothermic reduction of TiO2. Therefore, the entire reaction process is as follows:

$$\text{3Mg} + 2\text{AlCl}\_3 \rightarrow 2\text{Al} + \text{3MgCl}\_2 \tag{5}$$

$$\text{Al} + \text{TiO}\_2 \rightarrow \text{Ti} + \text{Al}\_2\text{O}\_3 \tag{6}$$

$$6\text{Ti} + 6\text{Al} \to 4\text{Ti} + 2\text{TiAl}\_3 \tag{7}$$

$$\text{4Ti} + \text{2TiAl}\_3 \rightarrow \text{Ti}\_3\text{Al} + \text{TiAl} + \text{2TiAl}\_2 \tag{8}$$

$$\text{Ti}\_3\text{Al} + 2\text{TiAl}\_2 + \text{TiAl} \rightarrow 6\text{TiAl} \tag{9}$$

**Figure 7.** XRD patterns of products at different temperatures.

**Figure 8.** SEM and surface scanning of magnesium thermal reduction products, assisted by the AlCl3&KCl molten salt medium.

**Figure 9.** Gibbs free energy of the reaction between AlCl3 and TiO2, with Mg.

According to literature reports [38], the alloy reaction between Al and Ti at low temperatures is mainly liquid–solid. In this experiment, the main product phase is the TiAl3 alloy after 2 h of reaction at 750 ◦C. As the reaction temperature increases, from 800 ◦C to 950 ◦C, the peak of TiAl3 gradually decreases, while the peak of TiAl2 gradually increases. The peak of TiAl2 gradually increases because external Al reacts before Ti to generate TiAl3 during the reaction process, and then gradually forms TiAl2, as shown in Equation (8). The increase in temperature is more conducive to the formation of the TiAl alloy. From the energy spectrum detected via SEM surface scanning, it can be seen that the obtained TiAl alloy has a uniform distribution of components, with an oxygen content of 4.23 wt%. The reason for such a high oxygen content is that the reduction effect of Al is limited, and TiO2 cannot be reduced to a lower oxygen content state. However, due to the presence of Mg, some O is absorbed, to some extent. As the reaction temperature increases, it is found that the oxygen content in the reaction product is low, at 750 ◦C.

#### *3.2. Effect of Reduction Temperature*

In the previous section, the study of different reaction temperatures in the magnesiothermic reduction of TiO2 in the AlCl3&KCl molten salt system found that the oxygen content of the TiAl3-based alloys generated at 750 ◦C was relatively low and stable. Therefore, 750 ◦C was chosen as the optimal reaction temperature. This section takes the reaction time as a single variable, and experimentally studies the effect of different reaction times on the preparation of TiAl-based alloys at 750 ◦C. We set the reaction time at 750 ◦C for 1, 2, and 4 h, respectively, to study the effect of the reaction time on the reduction effect during the reaction process. Figures 10 and 11 show that XRD and SEM characterized the reaction products. After reacting at 750 ◦C for 1 h, the main phases of the reaction products are TiAl3 and metallic Al. The TiAl3 alloy is caused by the short reaction time between Al and Ti, and some of the reduced Al has not yet formed an alloy with Ti. Therefore, a large amount of metal Al has not reacted in the product after one hour of reaction. With the extension of the reaction time, when the reaction temperature is 2 h, the main product of the reaction is TiAl3. After further prolonging the reaction time to 4 h, the main reaction products are the TiAl alloy, and a small amount of Al2O3. The occurrence of Al2O3 is because, with the extension of the reaction time, some Al forms Al2O3 powder through solid-state diffusion with the alloy, after reducing the TiO2. This Al2O3 cannot be removed from the surface of the alloy through acid leaching and flotation. The attached Al2O3 can be seen in the SEM image in Figure 12; a small amount of matte and rough surface substance is attached to the metal surface, which is the Al2O3 generated through the extended reaction time.

As mentioned above, a stable TiAl3 alloy powder can be obtained by reacting TiO2 with AlCl3&KCl molten magnesium salt for 2 h at 750 ◦C.

**Figure 10.** Effect of different reduction times on the reduction products.

**Figure 11.** SEM and EDS of products with different reduction times.

**Figure 12.** Scanning electron microscopy (SEM) images and energy-dispersive spectroscopy (EDS) of the products at 950 ◦C.

As the reaction time increases, the oxygen content in the reaction product gradually increases. At the same time, this is also because the solid-phase-to-solid-phase diffusion reaction between the Al2O3 and TiAl-based alloys occurs at high temperatures, which finally causes part of the Al2O3 to enter the TiAl alloy phase, as shown in Figure 12. The TiAl alloy powder is a coarse powder bonded to the surface of the TiAl alloy, with a high oxygen content and no Ti element, which can be determined as Al2O3 powder. Based on the above analysis, the optimal reaction temperature for the thermal reduction of AlCl3&KCl mixed molten salt magnesium is 750 ◦C, and the main product generated by the reaction at 750 ◦C is TiAl3. The oxygen content of the product was analyzed using the JXA82 electric probe. The effect of the reaction time on the oxygen content of the product is shown in Figure 13, with the lowest oxygen content of 3.91 wt% after two hours of reaction.

#### *3.3. Analysis of the AlCl3&KCl-Molten-Salt-Assisted Magnesium Thermal Reduction Process*

The above experiments indicate that the AlCl3&KCl molten salt system serves as a medium for the magnesium thermal reduction of TiO2, to prepare TiAl3 alloy powder. The schematic diagram of the entire reaction process is shown in Figure 14. At the beginning of the reaction, Mg is ionized in the molten salt to form Mg2+, which reacts with Cl<sup>−</sup> in the molten salt to form MgCl2, while Al3+ is reduced to metallic aluminium. At this time, the metallic aluminium is not covered by a surface oxide film, and the generated liquid metal Al reacts with TiO2 to generate TiAl-based alloys. The melting temperature of Al is relatively low. At 750 ◦C, a liquid–solid reaction occurs between the Al liquid and the reduced Ti solid, generating TiAl3 on the surface of the titanium. Afterwards, the internal metal Ti reacts with TiAl3 to generate TiAl2. With the prolongation of the holding time, various TiAl-based alloys react, to generate TiAl alloy powder. The entire TiAl alloy formation process is shown in Equations (5)–(9). This experiment can prepare TiAl3 alloy powder stably at 750 ◦C for 2 h, demonstrating a new method for preparing TiAl alloy at low temperatures. Moreover, the TiAl3 alloy powder has a low density, high modulus, and strong oxidation resistance, making it an excellent high-temperature structural and layer material.

**Figure 13.** The effect of different reaction times on the oxygen content of products.

**Figure 14.** Schematic diagram of the AlCl3&KCl-molten-salt-assisted magnesium thermal reduction process.

#### *3.4. Product Analysis and Comparison*

The elements of the TiAl3 alloy powder product prepared in this experiment are shown in Table 2, and the particle size is shown in Figure 15. The Ti content is approximately 28.41 wt%, and the Al content is approximately 67.68 wt%. The TiAl3 alloy prepared in this experiment has a larger particle size. The final products D10, D50, and D90 were 135 μm, 453 μm, and 912 μm, respectively. From the discovery of metallic titanium to the current preparation of titanium alloys, in addition to traditional high-temperature melting and mechanical alloying, many low-cost methods have also been used for preparing TiAl-based alloys. The TiAl-based alloy shows an excellent performance. Developing lowcost and straightforward equipment for new processes, to meet increasing performance requirements, is a hot research topic. These new processes all have the advantages of continuity and low cost. Among emerging technologies, high-temperature self-propagation is the most representative method, but the process controllability of this method is too poor, and there are certain risks. The multi-level deep reduction method is also a relatively novel method that has recently emerged. Still, it also has the problem of a high reaction temperature, which leads to a high energy consumption. Table 3 compares new methods for preparing TiAl-based alloys in recent years, and this experiment. These preparation processes for preparing metallic titanium alloys are currently at the laboratory stage, and there is still a long way to go from the laboratory to industrial production.

**Table 2.** Composition of the TiAl3 alloy (wt%).


**Figure 15.** Particle size distribution of the TiAl3 alloy powder.



#### **4. Conclusions**

This article proposes a new process for preparing TiAl3 alloy powder, mainly discussing how AlCl3&KCl molten salt can prepare TiAl3 alloy powder via the magnesium thermal reduction of TiO2. At the same time, the influence of different experimental factors on the reduction effect is studied, mainly the influence of the reduction temperature and time on the product phase and oxygen content. Based on the experimental research, the following main conclusions have been drawn:


**Author Contributions:** Software, Y.C.; writing—original draft, J.K.; writing—review and editing, D.Z.; project administration, G.Q. and X.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, grant number [52074052].

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors are incredibly grateful for a grant from the National Natural Science Foundation of China (Grant No.52074052).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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