J. Cent. South Univ. (2020) 27: 3721-3732

DOI: https://doi.org/10.1007/s11771-020-4572-y

Mechanism of necking defect of 6082 aluminium alloy rolled by cross-wedge rolling method based on material thermal properties

WANG Dong-gang(王东钢)^{1, 2, 3}, SHU Xue-dao(束学道)^{1, 3}, WANG Rui(汪锐)^{1, 3}, XU Sheng(徐生)^{1, 2}

1. Faculty of Mechanical Engineering & Mechanics, Ningbo University, Ningbo 315211, China;

2. Institute of Mechanical and Electrical Engineering, Zhejiang Business Technology Institute,Ningbo 315012, China;

3. Zhejiang Provincial Key Laboratory of Part Rolling Technology, Ningbo 315012, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract: Necking defects have long troubled the application of cross-wedge rolling technology in aluminium alloy shaft parts. To accurately predict necking defects, new judgement conditions are established based on the thermal performance of 6082 aluminium alloy. The limit-sectional shrinkage without necking defects is achieved by combining theoretical calculation and finite-element model analysis, which couples heat transfer and deformation. In this paper, a 6082 aluminium alloy extruded rod with a 40 mm diameter rolled at a preheated temperature of 500 °C and a rolling angular velocity of 1 rad/s is taken as an example. The simulation and experimental results show that necking defects do not occur on the rolled pieces if the sectional shrinkage is below the limit-sectional shrinkage but will occur when the sectional shrinkage is above it. The results prove that the prediction model of necking defects in cross-wedge rolling of 6082 aluminum alloy is feasible, and this research provides a theoretical basis for the qualified aluminum alloy shafts produced by the cross-wedge rolling.

Key words: 6082 aluminium alloy; cross wedge rolling; limit-sectional shrinkage; necking mechanism; temperature field

Cite this article as: WANG Dong-gang, SHU Xue-dao, WANG Rui, XU Sheng. Mechanism of necking defect of 6082 aluminium alloy rolled by cross-wedge rolling method based on material thermal properties [J]. Journal of Central South University, 2020, 27(12): 3721-3732. DOI: https://doi.org/10.1007/s11771-020-4572-y.

1 Introduction

With the development of new technologies and new processes, lightweight materials have become a new trend in the automotive industry [1], and aluminium alloy has become the first choice for its high specific strength and high formability. The 6082 aluminium alloy in the Al-Mg-Si series of aluminium alloys has become the most commonly used aluminium alloy in the automotive industry due to its excellent overall performance, high specific strength and good processability. However, the forming performance of 6082 aluminium alloy is greatly affected by the temperature, the strain rate and the degree of deformation [2]. The deformation resistance of 6082 aluminium alloy decreases when the temperature rises, and the tensile resistance decreases too. Therefore, the high temperature performance must be studied in the forming process. The flow stress behaviour of 6082 aluminium alloy under the deformation temperature of 300-500 °C and the strain rate of 0.01-10 s^-1 is studied and the dynamic recovery is found to be the typical softening mechanism when a transition from strain hardening toward steady deformation [3].

Although 6082 aluminium alloy has many advantages, its application in the automotive industry is greatly restricted due to low material utilization. The cross-wedge rolling (CWR) process is often used to make billets to improve the material utilization by redistributing the material [4]. CWR is a forming process for reshaping a round stock into a rotationally symmetrical workpiece with variable diameter in axial direction with two oppositely moving wedge-shaped dies [5]. The mechanical structure of round CWR process is shown in Figure 1. The forming process of the billet is mainly determined by the wedge tools, and the guide plates are used to prevent the workpiece from swinging during deformation.

The divisions of the forming zones, the forming surfaces and the parameters of the dies are shown in flat CWR dies for convenience in Figure 2 [5]. The CWR dies are usually divided into three zones according to the forming stage and its characteristics [6]: (a) the knifing zone, (b) the stretching zone and (c) the sizing zone, as shown in Figure 2. In the knifing zone, wedges are cut into the blank; in the stretching zone, the material deformation begins to expand in the axial direction; and in the sizing zone, shaft bending and surface defects are corrected [7].

Figure 1 Mechanical structure of round cross wedge rolling process

Despite its advantages, many process defects occur because of the complicated deformation mechanism. Necking defects are among the most common problems of aluminium alloy due to the axial component force during the CWR process [8]. As shown in Figure 3(b), when a necking defect occurs, the product becomes thinner locally, and the mechanical performance of the productg drops sharply.

Many scholars have studied the necking mechanism. TSUKAMOTO and HAYAMA established the judgment conditions of limit- sectional shrinkage (LSS), in which the effect of parameters such as the forming angle α, the spreading angle β and sectional shrinkage δ is more comprehensively analyzed on the necking defects [9-11]. JIA et al [12, 13] performed an in-depth study of the necking mechanism of heavy section shrinkage in the CWR process and proposed the relationship between the spreading angle β and the LSS. PATER et al [14] proposed a necking mechanism according to the first strength theory, which confirmed that necking would occur during the CWR process if the tensile stress (caused by the axial component) is greater than the yield stress of the material, and he recommended the new equations related to the forming angle, the spreading angle, the sectional shrinkage and other processing parameters to determine the limit condition for the CWR process. JIA et al [15] presented the distribution coefficient of area reduction to analyse the laws of necking in twice-stage.

Figure 2 Typical CWR die and its division

Figure 3 Normal workpiece (a) and necking workpiece (b)

The judgement conditions above have explained the relationship among the die parameters, the sectional shrinkage and the necking mechanism clearly and have been applied in the analysis of many necking defects in the CWR process successfully. However, to improve plasticity, to reduce deformation resistance and to reduce process defects, the billet is often preheated in the CWR process [16]. And the forming performance of the heat-sensitive materials changes greatly with temperature, so the necking mechanism is much more complicated [17]. The 6082 aluminium alloy is a heat-sensitive material, so its tensile strength drops sharply at high temperatures, and its flow stress also changes greatly with the temperature and the strain rate. Therefore, the influence of the deformation temperature and the deformation rate on the properties of the material must be considered to predict necking defects accurately. In early studies, technical restrictions made it impossible to reasonably predict the distribution of the internal temperature field, which restricted further study of the necking mechanism. The development of computer technology has greatly facilitated the prediction of the distribution of the internal temperature field [18].

In this paper, the 6082 aluminium alloy rod extruded with the preheated temperature of 500 °C and the rolling speed of 1 rad/s is taken. The distribution law of the temperature field in the deformation zone is obtained by theoretical calculation and numerical simulation, and the functional relationships among the limit radius r_lim, the geometric parameter G and the material parameter M is obtained to determine the LSS. This theory thus has great significance for accurate prediction of the LSS and improvement in the quality of aluminium alloy products of CWR.

2 Thermal mechanical performance of 6082 aluminium alloy

In the CWR process, the material’s thermal performance is the most important factor for the forming quality. Because the 6082 aluminium alloy is a heat-sensitive material, its flow stress and strength limit will change significantly at high temperatures.

2.1 Calculation of strength limit σ_b of dangerous section

The strength limit of the 6082 aluminium alloy drops sharply as the temperature increases above 200 °C, and the relationship between the strength limit and the temperature of the 6082 aluminium alloy is approximately logarithmic and can be expressed by Formula (1) according to the experimental data [19].

                      (1)

where T is the temperature of the material in ℃, and σ_b is the strength limit of 6082 aluminium alloy at temperature T. The strength limit σ_b is calculated according to Formula (1).

2.2 Calculation of flow stress σ_f in deformation zone

Rolling stock with sectional shrinkage of 57.8% (d₂=26 mm) was selected to calculate the LSS. To calculate the flow stress σ_f, the Z-parameter [20] must first be obtained, as shown in Formula (1). The average strain rate in the forming process is obtained from Formulas (2) and (3) [21], and Z is calculated with instead of the strain ratefor simplification.

                        (2)

                               (3)

                               (4)

T in Formula (2) is the absolute temperature of the deformation area of 6082 aluminium alloy, d₀ is the diameter of the billet (40 mm), △d is the maximum reduction and R is the radius of the top surface of the dies. Finally, Z is substituted into Formula (4) to obtain the flow stress σ_f.

               (5)

All parameters are shown in Table 1.

Table 1 Simulation scheme with different sectional shrinkages

2.3 Relationship curves of σ_b and σ_f with temperature

According to the Formulas (1), (2), (3), (4) and (5), the changes of σ_b and σ_f with temperature are shown in Figure 4; σ_b and σ_f can be obtained if the temperature distribution is known.

Figure 4 Relationship between flow stress σ_b and strength limit σ_f of 6082 aluminium allowy and temperature

3 Establishment of finite-element model

The billet drawing and the artifact drawing are shown in Figures 5(a) and (b), respectively. Because different sectional shrinkage must be used during the simulation and the experiment, the diameters in the sizing zone are expressed by the variable d.

The dies are important guarantee for product forming. As shown in Figure 6, the forming angle takes the value 30° to avoid internal hole defects, and the spreading angle takes a larger value between 4° to 9° to reduce the length of the dies [9], where R_b is the radius of the base circle of the dies and R is the top radius of the dies.

Figure 5 Billet drawing (a) and artifact drawing (b)

Figure 6 Design parameters of dies

To reduce the amount of calculation without affecting the accuracy of the simulation results in this project, the pre-processing of FEM is set as follows:

1) The process temperature has a great influence on the deformation process, so the FEM coupling deformation and heat transfer are established.

2) The billet is assumed to be isotropic, and Mises yield criterion is selected as the yield criterion.

3) Due to the large plastic deformation and even rheology of the deformed body during the CWR process, the elastic deformation can be ignored, so the deformed body adopts a rigid plastic FEM.

4) Little deformation occurs on the dies and the guides, so they are set as rigid bodies.

5) Shear friction is selected as the type of friction between the dies and the rolled piece.

All parameters related to the finite-element simulation are shown in Table 2.

The geometric model of the finite-element model (FEM) in the CWR process is shown in Figure 7.

4 Analysis of numerical simulation results

The simulation scheme is shown in Table 3.

Table 2 Parameter setting of CWR simulation parameter

Figure 7 FEM of CWR

Table 3 Simulation scheme with different sectional shrinkage

The sectional shrinkage of rolled pieces are selected between 50% and 70% by taking the integer value of final forming diameters between 24 and 28 mm.

4.1 Analysis of mechanism of necking defect

The heat exchange during hot CWR is a complicated physical process that includes heat conduction between the deformed body and the dies, the convective heat exchange between the deformed body and the air mixed with the heat radiation and the effect of deformation work. Because the 6082 aluminium alloy is a heat-sensitive material, the accuracy of numerical calculation of macro- mechanical indicators such as the strain and the stress can be greatly improved by considering the influence of temperature on the entire deformation [25].

Figure 8 shows a cross-sectional view of the rolling process, and the upper half of the deformation zone of the rolled piece is studied. Point K is the tangent point of the top fillet of the die and the sizing zone. A perpendicular line is drawn from K to the axle of the rolled piece, and the intersect point is drawn as A. The intersection point between the AK and the surface of the rolled product is B. The highest contact point of the die and the surface of the rolled piece is point C, so △ABC is defined as the deformation zone during the CWR process.

Figure 8 Schematic of temperature distribution in deformation zone

As shown in Figure 8, four points are taken on lines BC and AB in the same distance, respectively, and P₁ is selected as the common point. The average temperature on the line BC is the effective temperature T₁, which is selected as the temperature to calculate the flow stress σ_f, and the average temperature on line AB is the effective temperature T₂, which is selected as the temperature to calculate the strength limit σ_b. The temperature at point P_i is presented as T_pi. The effective temperature is shown as Formula (5).

                       (6a)

                      (6b)

It is assumed that a necking defect occurs if the effective stress on the cross-section AB of the rolled product exceeds the material’s strength limit σ_b. The limit radius r_lim without necking defects can be expressed as Formula (7).

               (7)

                              (8)

            (9)

             (10)

where S_axial is the projected area of the deformed area in the axial direction, r₀ is the radius of the billet, C is the distance between the centre of the die and the billet, R is the top radius of the dies and is the flow stress, with strain rateand temperature T₁ in the deformation zone. is the strength limit with the sectional temperature of T₂.

In the end, the LSS δ_lim can be expressed as Formula (11).

         (11)

Therefore, the limit condition for the CWR process relates not only to the geometric parameter G, but also to the material’s thermal performance parameter M. The larger the value of M, the smaller the limit section shrinkage. This can allow a more accurate judgment of the necking defect condition.

To calculate the LSS accurately, points tracked are taken in three positions in the stretching zone, including the initial stage, the middle stage and the end stage respectively. The temperature distribution lines are drawn in the deformation zone in Figures 9(a), (b) and (c), and four floating points on the lines AB and BC are selected for tracking in the deformation zone.

The changes in the temperatures of the tracked points are shown in Figure 10. It can be seen from the figure that the temperature begins to decline linearly, and obviously fluctuates from the adjacent stretching zone until entering the sizing zone, and begin to decreases steadily.

As shown in Table 4, the temperatures of different points with the maximum difference at the time of 1.74 s, 2.40 s and 3.28 s are obtained from the simulation data, respectively.

Figure 9 Tracked points in stretching zone at different times:

T₁ and T₂ can be obtained according to Formula (6a), (6b) and Table 4, so σ_b and σ_f can be obtained according to Figure 4. All geometric parameters are substituted into Formula (9) to obtain G. The LSS δ_lim can be obtained according to Formula (11). The calculated results are shown in Table 5.

Figure 10 Changes in temperature of tracked points in stretching zone in different stages:

Table 4 Temperatures of points at maximum temperature difference in different positions

It is shown in Table 5 that the geometric parameter G of the rolled piece is a fixed value when the die parameters and the section shrinkage are determined, at various stages of the stretching section of CWR. However, the material parameter M differs completely in various stages because the effective temperatures on lines AB and BC of the rolled piece changes. According to Formula 9, the thermal properties of the 6082 aluminium alloy material, including its strength limit and flow stress, differ significantly, which affect the limit sectional shrinkage of the rolled part at various stages. The theoretical calculations above show that the most likely necking position is the initial stage of the stretching section at 1.74 s, as shown in Figure 9(a). It can be concluded that a necking defect will occur on the rolled piece when the LSS is greater than 60.56%.

Table 5 Calculated results

4.2 Prediction of shrinkage defects

4.2.1 Damage analysis of tracked points

The necking defects of rolling products relate to the generation and propagation of internal micro- cracks. The damage model developed by Cockcroft- Latham is mainly used in the Deform software, which is shown in Formula (12) [26].

                            (12)

where D is the critical value for the macro-crack of the material, which indicates the degree of damage; σ₁ is the first principal stress; is the effective stress; is the effective plastic strain; and is the effective strain in the current state.

To compare the degree of damage to different rolled pieces at different positions in the Deform 3D software, two longitudinal feature points and two radial feature points were taken in the longitudinal section of every rolled piece with different sectional shrinkage. Figure 11 shows the location of these tracked points. The cross section A-A is the symmetry plane of the rolled piece, and the B-B plane is the cross section of the forming end position, and the distance from the B-B plane to section plane A-A is 38 mm. P₁, P₅, P₉ and P₁₃ are the points of the axis of the deformed body on the A-A surface; P₂, P₆, P₁₀ and P₁₄ are the points of the axis of the deformed body on the B-B plane; P₃, P₇, P₁₁ and P₁₅ are the points 1 mm below the forming surface on the A-A plane; and P₄, P₈, P₁₂ and P₁₆ are the points 1 mm below the forming surface on the B-B plane.

Figure 11 Damage factor with different shrinkage:

Figure 12 shows a comparison of the damage factor at the same location of the rolled pieces with different sectional shrinkage. Because the damage factor is the result of an accumulation of damage, it gradually increases as the process proceeds. The damage degree of a point is closely related to the sectional shrinkage of the rolled piece. At the same position, the higher the sectional shrinkage is, the greater the damage factor and the greater the possibility of damage at that point.

4.2.2 Analysis of internal fields

Figure 13 shows the differences in the damage factor, displacement field and temperature field in the rolled pieces with different sectional shrinkage.

Figure 12 Position of tracked points with different sectional shrinkage:

Figure 13 Comparison of damage factor (a), temperature field (b), internal displacement field (c) and FEM of rolled piece with different sectional shrinkage (d)

As is shown in Figure 13(a), the largest internal damage factor is less than 0.9 when the diameter is less than 26 mm. As the sectional shrinkage increases, the damage factor gradually increases. When the sectional shrinkage reaches 60.94%, which exceeds the calculated LSS of 60.56%, most of the stretching zone of the rolled part reaches 0.9 and even reaches 1.1 in some sections. When the sectional shrinkage reaches 66.94%, most of the damage factor of the stretching zone of the rolled part reaches 1.2, which indicates that the rolled product has been seriously damaged. As is shown in Figure 13(b), the temperature field distribution shows that the low-temperature metal on the surface and the high-temperature metal inside gradually form “convection” as the sectional shrinkage increases. When d=25 mm, the temperature distribution of the surface metal is discontinuous, which indicates that the inner and outer metals have combined. Thereby, surface defects are formed.

The displacement field describes the metal movement process. Figure 13(c) shows that when the sectional shrinkage is small, the metal flows in layers. As the cross-sectional shrinkage rate increases, the axial continuity of the metal displacement on the surface of the metal gradually breaks. When d=26 mm, the metal displacement field just happens to be damaged along the axial direction, which indicates that the metal of the rolled product has been separated on the surface, and when d=23 mm, the metal displacement field is obviously damaged along the axial direction and begins to become perpendicular to the axis. The discontinuity of the displacement in the axle indicates that the material has been separated, so the rolled part has experienced a severe surface spiral mark.

5 Experimental verification

The experimental scheme is shown in Table 6.

Table 6 Experimental scheme

It is shown in Table 5 that the LSS is 60.56%. To verify the accuracy of the calculation results, rolled pieces with different sectional shrinkage were rolled in the experiment. As shown in Figure 14, little change happened in the minimum cross- sectional diameter when d≤26 mm. However, obvious necking defect occurs when the sectional shrinkage reaches 60.94%, and serious necking defects occur when the sectional shrinkage reaches 66.94%.

Figure 15 shows the parameters related to the necking defects. The assessment of the necking degree mainly includes parameters such as the final diameter, the necking diameter, the necking width and Dd. As the sectional shrinkage increases, the decrease in the necking diameter and the increase in the necking width gradually accelerate. As shown in Figure 16, the necking degree shows obvious acceleration when the sectional shrinkage exceeds the calculated LSS of 60.56%, which fully proves the accuracy of the calculated results.

Figure 14 Final deforming diameter and size of necking diameter

Figure 15 Diagram of necking product

6 Conclusions

The geometric parameter G and the material parameter M are considered in the new judgement condition of the necking defect of the CWR process based on the thermal performance of 6082 aluminium alloy. It can thus be used more widely with higher accuracy.

As the sectional shrinkage increases, surface quality defects will occur for the “convection” of the surface and internal metal in the WCR process of the 6082 aluminium alloy, which makes the surface temperature distribution uneven. The internal and external damage coefficient increases with the increasing of the sectional shrinkage, which indicates that the damage is more likely to occur.

Figure 16 Analysis of necking degree with different sectional shrinkage

The simulation and experimental results show that necking defects will occur when the sectional shrinkage exceeds 60.56%, that is, the calculated LSS, and necking defects will accelerate with the increases of the sectional shrinkage.

Nomenclature

σ_b

The strength limit

σ_f

The flow stress

The strain rate

The average strain rate

△d

Cross wedge rolling reduction of diameter of billet

R

The radius of base circle of dies

v₁

Linear speed of top surface of dies of rolling

d₀

Diameter of the billet

Z

Z parameter of material

M

Material related parameter

G

Geometry related parameter

T_Pi

The temperature at point P_i

f

Coefficient of friction between dies and billet

α

The forming angle

β

The spreading angle

S_axial

The projected area of the deformed area in the axial direction

C

The distance between the centre of the die and the billet

δ_lim

The limit section shrinkage

Contributors

WANG Dong-gang makes the experimental plans, performs data processing, performs finite element simulations, and writes the paper. SHU Xue-dao determines the direction of the paper and the purpose of the experiment. WANG Rui assists to complete the experiment and helps to revise the paper. XU Sheng assists to complete the experiment and checks the literature.

Conflict of interest

WANG Dong-gang, SHU Xue-dao, WANG Rui and XU Sheng declare that they have no conflict of interest.

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(Edited by HE Yun-bin)

中文导读

基于材料热性能的楔横轧轧制6082铝合金轴的颈缩机理

摘要：铝合金轴类零件在楔横轧工艺中的颈缩缺陷长期困扰着该技术在实际生产中的应用。为准确预测颈缩缺陷发生时的极限断面收缩率，建立了新的基于6082铝合金热性能的颈缩缺陷判断模型，即通过理论计算与热-机耦合的有限元模型相结合的方式，实现极限断面收缩率的预测。本文以直径为40 mm的6082铝合金挤压棒为例，模具展宽角和成形角不变，在预热温度为500 °C及轧辊角速度为1 rad/s的条件下，对不同断面收缩率下的楔横轧的仿真与试验结果进行了分析。仿真和实验结果表明，断面收缩率低于极限断面收缩率时，铝合金轴件上没有出现缩颈缺陷；断面收缩率高于极限断面收缩率时，出现了铝合金轴缩颈缺陷。该结果证明了6082铝合金楔横轧颈缩缺陷的预测模型是可行的,该研究为楔横轧轧制合格的铝合金轴件提供了理论依据。

关键词：6082铝合金；楔横轧；极限断面收缩率；缩颈机理；温度场

Foundation item: Project(51975301) supported by the National Natural Science Foundation of China; Project(LZ17E050001) supported by the National Natural Science Foundation of Zhejiang Province of China

Received date: 2020-05-13; Accepted date: 2020-10-01

Corresponding author: SHU Xue-dao, PhD, Professor; E-mail: shuxuedao@nbu.edu.cn; ORCID: https://orcid.org/0000-0001-9928-7344