Drawing–upsetting–extrusion–clinching of high-strength steel and aluminum alloy

To realize good point connection between high-strength steel and aluminum alloy, a process of drawing–upsetting–extrusion–clinching was proposed. First, the sheets were drawn; then, the bottom of the protrusion part was extruded, forming the necessary initial interlock; and finally, the protrusion part was reverse press clinched, forming a certain height of the clinched head. Taking DP980 high-strength steel and Al5083 aluminum alloy as the connection objects and using the method of numerical simulation combined with experimental test, the mold was made, and the experiment was carried out on the basis of numerical simulation. The experimental results proved the feasibility of the process and the effectiveness of the numerical model. The simulation and experimental results show that the necessary interlock in the drawing–upsetting–extrusion stage is the premise of effective connection. The relative protrusion height should be around 55.6% after reverse-press-clinching. The best comprehensive mechanical properties measured by strength test were shear resistance of 2644 N, fatigue life of 24,535 times and peel resistance of 1522 N. Through failure analysis, the relationship between the interlock Tu and the neck thickness Tn of the joint with the best comprehensive mechanical properties was established as Tu = 0.35Tn. The design method of die and process parameters when the sheet thickness changes was researched by numerical simulation. The results show that the clearance between the punch and the die and the bottom thickness are directly proportional to the sheet thickness, and the drawing depth is directly proportional to the punch radius.


Introduction
Automotive lightweight is one of the most effective measures to reduce energy consumption and emissions.Automobile bearing structure is generally characterized by thin wall.Tisza and Czinege [1] reported that the mixing of aluminum alloy and high-strength steel can give full play to their respective advantages and has become an inevitable choice for the lightweight of automobile body at present.
The connection and assembly of metal parts can adopt point connection mode, mainly including resistance spot welding and mechanical connection.However, Wallerstein et al. [2] reported that in spot welding of high-strength steel and aluminum alloy, it is difficult to form an effective joint due to the large difference in melting point and linear expansion coefficient and the formation of brittle and hard intermetallic compounds at the weld.Wan et al. [3] found that the aluminum-steel resistance spot welding joint interface is composed of two kinds of intermetallic compounds: One consists of a mixture of FeAl 3 and Al, and the other is composed of serrated FeAl 3 on the Al side and tongue-shaped Fe 2 Al 5 on the steel side.In addition, Taufiqurrahman et al. [4] reported that the austenite changes into other low-strength structures rather than high-strength martensite during the welding process, resulting in a significant reduction in the tensile strength of the highstrength steel at the welding part.As a plastic cold connection technology of light alloy sheet, traditional clinching has the advantages of simple equipment, low cost, little surface damage and stable connection quality.Peng et al. [5] reported that clinching has been widely used in automobile body assembly in aluminum alloy sheet parts and the connection between aluminum alloy and lowstrength steel parts.
Due to the low ductility and poor plasticity of highstrength steel, the interlock of high-strength steel and aluminum sheet after clinching is small.In addition, Abe et al. [6] reported that compared with the flat bottom die, the clinching die with annular groove will increase the tendency of cracks in the sheet and seriously affect the clinching quality.Furthermore, the joint has protrusion, which makes the clinching connection unable to be used on the outer surface or functional surface.In recent years, to solve these problems, many researchers optimized die parameters or improved forming process to increase the joint connection quality.Abe et al. [7] proposed a preformed clinching process.The lower sheet was preformed before clinching to reduce the thinning degree of the upper sheet at the joint neck which can avoid cracking and effectively improve the rivetability of low-ductility materials.Jiang et al. [8] found that the preforming of aluminum has a significant impact on the strength of riveted steelaluminum riveting without rivets.The work hardening caused by the preforming reduces the ductility of aluminum and produces certain ductile damage to the riveted aluminum workpiece.Babalo et al. [9] proposed electrohydraulic clinching, and the experiment showed that this method improved clinching efficiency and joint strength.Lee et al. [10] proved the practicability of pre-punched clinching method in the connection between lightweight plastic materials and high-strength and low-ductility materials.Wen et al. [11] proposed a pre-punched clinching method suitable for the connection of different sheets without protrusion joints.The upper sheet is punched into the pre-punched hole of the lower sheet to form an interlock structure.This technology is applied to the connection between Al6063 and AZ31 alloys, and the strength of the formed joint is greater than that of the traditional clinching.However, this process is complex and costly.To solve this problem, Ho ¨rhold et al. [12] proposed a shear clinching connection technology, which can complete the shear punching and stamping connection of the lower sheet after one stamping without pre-punching, simplifying the prepunched multi-stage clinching connection technology.However, for high-strength steel with high shear strength and poor plasticity, it is difficult to achieve shear punching of the lower sheet.On this basis, Ho ¨rhold et al. [13] studied the influence of the distance between the clinching point and the material boundary on the material flow.The material flow depends on the edge distance, as a lower edge distance causes a lower resistance against material flow outside the joining zone.Lambiase and Ko [14] used the two-step clinching method to connect aluminum sheet and carbon fiber reinforced polymer sheet and found that the shear strength and absorption energy of the joint increased by 32% and 30%, respectively, compared with that of the non-reformable joint.Li et al. [15] optimized the mold parameters of the clinching of steel and aluminum by Kriging model and proved that the optimization scheme is effective.
In order to improve the plasticity of materials, researchers use external heat sources to heat and soften the sheet to improve the ductility of materials.Osten et al. [16,17] applied laser heating to the clinching of highstrength steel, analyzed the thermal effect and heating process, and realized the rapid clinching of high-strength steel with the help of laser.They found that there was a loss of joint strength due to the introduction of laser heating during the laser-assisted clinching.Vorderbru ¨ggen et al. [18] found that the formability of metal materials and tension-shear strength of the joint could be improved by using a heat-assisted elastic die for clinching.Zhuang et al. [19] proposed hot clinching cold die quenching clinching process, verified the feasibility of the process through experiments, made the high-strength steel at the joint have full martensite structure, ensured the strength of the joint, and found that 700 °C is the best initial clinching temperature of high-strength steel sheet.Han et al. [20] verified the feasibility of thermal-assisted pre-punched clinching process for connecting magnesium alloy and ultra-highstrength steel by combining numerical simulation and experiment.It is found that the temperature of the upper sheet has a significant effect on the connection ability, and the connection can be realized when the upper sheet temperature is 250 °C.Wang et al. [21] placed two layers of ductile copper foil above the perforated stainless steel sheet and applied impulse laser to the upper foil.The two layers of foil were concave downward through the hole of the perforated sheet, impacting the rigid bottom support, and then expanded radially to produce a double interlock, so as to connect the three sheets together.Ge and Xia [22] studied the mechanical properties of the steel-aluminum clinched joint under impact load from both experimental and numerical aspects and found that the mechanical response of the joint under dynamic loading showed strengthening effect.Through quasi-static three-point bending test, Khalkhali and Miandoabchi [23] verified the effectiveness of ABAQUS simulation in studying the bending energy absorption of aluminum alloy 5052-SPFC 390 high-strength steel clinched beam.Yu et al. [24] gave the formula for calculating the tensile and shear strength according to the sectional geometry of clinched joints and the failure mode of tensile and shear tests, and proved the reliability of the formula through experiments.
In order to solve the problems of small interlock and large protrusion in the clinching process of high-strength steel and aluminum alloy sheet, this paper presents a drawing-upsetting-extrusion-clinching process.At first, the double-layer sheet was thinned and drawn, and then, the bottom was upsetted and extruded to form interlock.Finally, the protrusion after upsetting-extrusion was reverse press clinched to increase the interlock and neck thickness, reduce the relative protrusion height of the joint and improve the quality of the joint.Taking DP980 highstrength steel and Al5083 aluminum alloy as the connection objects, the influence of process parameters on deformation, clinching strength and failure form was studied by numerical simulation and experiment.

Experimental and numerical analysis methods
The drawing-upsetting-extrusion-clinching process is shown in Fig. 1.First, the sheets are drawn: The double sheets is stacked on the appropriate position of the die; according to the depth of the drawing requirements, the punch moves to the corresponding position and locks, and the blank holder presses the sheets; the upper punch draws the sheets downward until the lower sheet contacts with the lower punch; then, the die goes down until its upper surface is flush with the lower punch.The upper punch continues to descend and extrude the bottom of the protrusion part, forcing the material in this area to flow outward along the radial direction and forming the necessary initial interlock.Then, reverse-press-clinching is carried out: unloading the upper punch pressure, the lower punch and the die move upward synchronously to reverse press clinch the protrusion part, and the upper punch is pushed by the bottom of the protrusion part and moves synchronously, forming a certain height of the clinched head.Finally, the clinching process is completed after resetting.

Experimental scheme
In order to analyze the influence of process parameters on the clinching deformation and quality conveniently, the process is divided into two stages: drawing-upsetting-extrusion and reverse-press-clinching.The joint strength is mainly determined by the thickness of aluminum sheet, and thus, the thickness of aluminum sheet was set larger than that of steel sheet to ensure a certain strength while realizing connection between steel and aluminum.The 0.8mm-thick DP980 high-strength steel as rolled and 1.0-mmthick Al5083 aluminum alloy as rolled are used as the connection objects, and their compositions are shown in Tables 1 and 2. Experiments were performed at room temperature.

Experiment of drawing-upsetting-extrusion stage
To facilitate mold making and simplify the experimental equipment, the experimental tooling in the drawingupsetting-extrusion stage is simplified to the form shown in Fig. 2, so as to be realized on the ordinary hydraulic press.
The aluminum sheet is stacked on the die with the steel sheet at the bottom.The pressure sensor is placed on the upper end of the punch, and the punch moves downward with the hydraulic press equipment and controls the stroke by adjusting the thickness of the backing block.The upper and lower sheets are pulled into the die, forming drawing protrusion.The punch force was recorded, and the samples were cut along the center of the punch.The parameters (interlock, neck thickness and bottom thickness) were measured.

Experiment of reverse-press-clinching stage
As shown in Fig. 3, the reverse-press-clinching experiment was also completed on the hydraulic press equipment.The sample after drawing-upsetting-extrusion experiment is placed on the punch, and the punch moves downward with the hydraulic press equipment.The stroke is controlled by

Analysis model of drawing-upsetting-extrusion process
The numerical model of high-strength steel-aluminum alloy drawing-upsetting-extrusion process was established by Abaqus.
Since the geometric model and load boundary conditions are symmetric to the central axis of the joint, a twodimensional axisymmetric model was adopted in the simulation, as shown in Fig. 5.In Fig. 5, X is the vertical distance between the upper surface of the upper sheet and the lower surface of the lower sheet after drawing-upsetting-extrusion, that is, the bottom (rivet head) thickness; T n is the minimum wall thickness of the circular surface depression of the upper sheet, referred to as neck thickness; R max is the radial distance from the maximum convex point to the axis of the annular surface of the upper sheet; R min is the radial distance between the maximum inner concave of the annular surface of the lower sheet metal and the axis; T u is the radial distance between the upper sheet and the lower sheet embedded in the neck, referred to as the interlock, and T u = R max À R min ; R p is the punch radius; r p is the punch filet radius; R d is the die radius; r d is the die filet radius; H is the die depth (corresponding to drawing depth); and T 1 and T 2 are the initial thickness of the upper and lower sheets, respectively.In order to facilitate the analysis of clinching deformation rule and quality, the following parameters are further defined: where B is the bottom thinning rate; C is the relative clearance between the punch and die; U is the relative interlock; N is the relative neck thickness; and K is the relative drawing depth.The molds were made of isotropic analytical rigid materials.The upper sheet is 1-mm-thick Al5083 aluminum alloy, and the lower sheet is 0.8-mm-thick DP980 high-strength steel.The material properties and model dimensions are shown in Tables 3 and 4, respectively.
The mesh division of the model was partitioned, and the upper and lower sheets were divided into three areas (see Fig. 6).Areas A and B are the main deformation areas with fine mesh division: Area B is the neck forming region of the joint with the largest deformation, and mesh size is 0.05 mm 9 0.1 mm axisymmetrical element; the deformation of area A is large, and the mesh size is 0.1 mm 9 0.1 mm axisymmetric element.Area C has small deformation and is not the main area for investigation; thus, the mesh size is large with a 0.1 mm 9 0.2 mm axisymmetric element.The die, punch and blank holder need not to be meshed because they are analytical rigid bodies.
In addition, the die was completely constrained.The whole process was completed by defining the displacement of the punch, and the solution time was set as 1 s.

Analysis model of reverse-press-clinching stage
The upper and lower sheets after drawing-upsetting-extrusion were introduced into the reverse-press-clinching model shown in Fig. 7.The model was composed of guide sheet, punch, terrace die, blank holder, aluminum sheet and steel sheet.In addition, the guide sheet was completely constrained.The whole reverse-press-clinching process In Fig. 7, H p refers to the protrusion height of rivet head after reverse-press-clinching, and the relative protrusion height is defined as P = H p /(T 1 ?T 2 ).
3 Analysis of clinching experiment and simulation results

Analysis of drawing-upsetting-extrusion process
Figure 8 shows the relationship between forming force and bottom thinning rate in the drawing-upsetting-extrusion experiment with different parameters (R p and H).As can be seen from Fig. 8, the forming force increases with the increase in punch radius because the wall thickness reduction during thinning drawing increases with the decrease in relative clearance between the punch and die.
Under the same punch radius, the forming force decreases with the increase in drawing depth.This is because the sheet size is larger than that of the punch radius, the material at the flange region is hard to flow into the die, and the bottom sheet is thinned due to expansion and drawing during the descending process of the punch, leading to the  increased initial thinning of the bottom caused by bulging with the increase in drawing depth and thus the decreased forming force required for upsetting-extrusion to the same bottom thickness.It should be noted that when the punch radius increases to 3.3 mm, the forming force is so large that the data of some experimental points are difficult to obtain due to the strength limitation of the punch.Figure 9 shows the relationship of the relative interlock and the relative neck thickness to the bottom thinning rate of the protrusion in drawing-upsetting-extrusion stage under different parameters, in which the solid line is the experimental value and the dotted line is the simulation value.It can be seen that the relative interlock increases significantly and the relative neck thickness increases slightly with the increase in the bottom thinning rate.With the increase in relative drawing depth, the relative interlock increases and the relative neck thickness decreases.This is because during the punch upsetting the bottom of the protrusion, before the lower sheet contacted with the side wall of the die completely, the resistance of the horizontal flow of the bottom sheet is much smaller than that of the upward flow, most of the sheet will flow horizontally, and a small portion will flow upward; after the lower sheet contacted with the side wall of the die completely, the resistance of the horizontal flow of the bottom sheet is much larger than that of the upward flow, most of the sheet will flow upward, and a small portion will flow horizontally; thus, with the increase in the bottom thinning rate, the relative interlock significantly increases, and the relative neck thickness slightly increases.When the relative drawing depth increases, the neck thickness decreases due to the aggravation of thinning, and the resistance of upward flow in the upsetting-extrusion process of bottom sheet increases accordingly; therefore, the relative interlock increases.By comparing Fig. 9a, c, e and Fig. 9b, d, f, it can be found that the relative interlock increases and the relative neck thickness decreases with the increase in the punch radius.This is because with the increase in the punch radius, the relative clearance between the punch and die decreases, the thinning amount of the neck wall thickness increases, and the resistance to upward flow of the bottom sheet increases in the upsetting-extrusion process.
Comparing the experimental (solid line in Fig. 9) and simulation (dotted line in Fig. 9) values, it can be found that the experimental values of interlock are slightly larger than the simulation values, and the experimental values of neck thickness are slightly smaller than the simulation values.The experimental values are in good agreement with the simulation values, indicating that the model can accurately simulate the deformation of drawing-upsettingextrusion stage of steel and aluminum sheets.

Analysis of reverse-press-clinching process
Based on simulation, the relationship of relative interlock and relative neck thickness to relative protrusion height after drawing-upsetting-extrusion and reverse-pressclinching under five process conditions was obtained, as shown in Fig. 10.It can be seen that with the increase in relative drawing depth, the relative interlock increases, and the relative neck thickness decreases.When the relative protrusion height is small, the relative interlock increases with its increase.When the relative protrusion height increases to 55.6%, the relative interlock tends to be constant.The relative neck thickness decreases monotonically with the increase in the relative protrusion height.Generally speaking, the interlock and neck thickness both affect the joint strength.The greater the interlock is, the more favorable it is to resist the peel load.The larger the neck thickness is, the more favorable it is to resist shear load.The influence of interlock may be more critical to the quality of clinched joints.Considering comprehensively, the value of relative protrusion height around 55.6% is more reasonable.
Under the conditions of different punch radii and relative drawing depths, the protrusion part after drawingupsetting-extrusion was reverse press clinched to a reasonable relative protrusion height of 55.6%, and the relationship of relative interlock and relative neck thickness to bottom thinning rate could be obtained, as shown in Fig. 11, in which the solid line is the experimental value and the dotted line is the simulated value.Similar to the drawing-upsetting-extrusion process, the experimental values of interlock are slightly larger than the simulated values, and the experimental values of neck thickness are slightly smaller than the simulated values.The experimental values are in good agreement with the simulated values, which further verifies the accuracy and reliability of the simulated results.It can be seen that the effect of bottom thinning rate on interlock after reverse-pressclinching inherits the characteristics of the drawingupsetting-extrusion process, but has almost no effect on neck thickness.That is, the greater the bottom thinning rate is, the greater the relative interlock after reverse-pressclinching is, and the better the clinching quality is.The relative neck thickness of reverse-press-clinching with different bottom thinning rates has little change under the same process parameters.According to Fig. 9, if there is no interlock between upper and lower sheet before reversepress-clinching, that is, if the interlock is 0 (corresponding relative interlock value is 1), the interlock cannot be realized after reverse-press-clinching (relative interlock is still 1).There is a critical value of the bottom thinning rate.Under the experimental conditions of this paper, when the bottom thinning rate is greater than 61%, the relative interlock after reverse-press-clinching under various process conditions will increase, with an increase of 15%-40%.After reverse-press-clinching, the relative neck thickness increased by 15%-25%.

Analysis of joint strength and failure form
According to the simulation and experiment, with the increase in bottom thinning rate, the interlock, the neck thickness, and the joint strength increase.Therefore, samples with the bottom thinning rate of 72.2% were prepared It can be seen from Fig. 12a, b that shear failure has two failure forms: interface collapse and neck fracture.In Fig. 13a, the shear strength of the joint increases firstly and then decreases with the increase in the relative drawing depth and reaches the maximum value near 0.266.The smaller the relative clearance between the punch and die is, the smaller the relative drawing depth corresponding to the maximum value is.When the relative drawing depth is small, the joint has larger relative neck thickness and smaller relative interlock, the shear bearing area of neck is larger, and the ultimate load of interface collapse failure is smaller than that of neck fracture failure; therefore, the failure form of the joint is interface collapse, and its shear strength is determined by relative interlock.With the increase in the relative drawing depth, the relative interlock increases, the relative neck thickness decreases, and the ultimate load required for interface collapse increases; thus, the shear strength increases.Because the shear bearing area of neck decreases continuously with the increase in the relative drawing depth, the ultimate load required for fracture failure decreases continuously; when the ultimate loads corresponding to the two failure forms are equal, the shear strength of the joint reaches the maximum, and the failure form changes from interface collapse to neck shear fracture.As the relative drawing depth continues to increase, the shear strength depends on the relative neck thickness and decreases with the increase in the relative drawing depth.
It can be seen from Fig. 12c, d that fatigue failure also shows two failure forms: interface collapse and neck fracture.In Fig. 13b, when the punch radius is 3.1 mm, the relative interlock of the joint is very small due to the large relative clearance between the punch and die.The fatigue failure form is interface collapse due to the insufficient relative interlock, and the fatigue life is determined by the relative interlock.With the increase in the relative drawing depth, the relative interlock increases, and the fatigue life increases.
When the punch radius increases to 3.2 mm, the fatigue failure of the joint shows interface collapse and neck shear fracture of aluminum alloy due to the decrease in the relative clearance between the punch and die and the increase in the relative interlock of the joint.When the relative drawing depth is small, the relative interlock is smaller, and the neck of aluminum alloy is relatively thicker; in this case, the failure form is the interface collapse.With the increase in the relative drawing depth, the relative interlock of the joint increases, and the relative neck thickness decreases; consequently, the ability of resisting interface collapse failure increases, but the ability of resisting neck fracture failure decreases.Therefore, under the interface collapse failure form, the fatigue life increases with the increase in the relative drawing depth.When the relative drawing depth increases to a certain value, the ability of the joint to resist the two failure forms tends to balance, and the failure form also transitions from interface collapse to neck aluminum alloy fracture.At this time, the fatigue life is determined by the relative interlock and the relative neck thickness, and reaches the maximum value.With the relative drawing depth increasing continuously, the fatigue life is determined by the relative neck thickness and decreases with the increase in the relative drawing depth.
There are three failure forms in the peel test of the joint: interface pull-off, interface pull-off combined with fracture of partial aluminum alloy neck and neck fracture as shown in Fig. 12e, f and g.In Fig. 13c, the relationship between When the punch radius is 3.1 mm, due to the large relative clearance between the punch and the die, the relative interlock of the joint is small, and the failure form is always a single interface pull-off due to the insufficient relative interlock.The peel strength depends on the relative interlock and increases with the increase in the relative drawing depth.When the punch radius increases to 3.2 mm, the relative interlock of the joint increases due to the decrease in the relative clearance between the punch and die.With the increase in the relative drawing depth, the relative interlock further increases, and the relative neck thickness decreases; therefore, the ability of the joint to resist interface pull-off increases, while the ability to resist neck fracture decreases.When the former is lower than the latter, the joint shows a single interface pull-off, and the peel strength depends on the relative interlock and increases with the increase in the relative drawing depth.When the relative drawing depth increases to a certain value, the two approaches the balance, and the failure form of the joint transitions to interface pull-off combined with fracture of partial aluminum alloy neck.The peel strength of the joint is determined by the relative interlock and the relative neck thickness, and reaches the maximum value at this time.With the relative drawing depth increasing continuously, the relative interlock of the joint continues to increase, and the relative neck thickness further decreases.Its ability to resist interface pull-off is higher than that of resisting neck fracture.The failure form transitions to a single neck aluminum alloy fracture.The peel strength depends on the relative neck thickness and decreases with the increase in the relative drawing depth.
The above analysis shows that the shear strength, peel strength and fatigue life of the joint depend on the relative interlock and relative neck thickness and are closely related to the process parameters.It can be seen from Fig. 13 that the sample obtained under the condition of relative clearance of 0.722 (die radius of 4.5 mm), relative drawing depth of 0.266 and bottom thinning rate of 72.2% has the best comprehensive mechanical properties.
It should be noted that due to the limitation of sheet thickness and its bearing capacity, compared with riveting with rivets, the experimental results may not meet the requirements of connection strength and fatigue performance, which needs attention and improvement in process application.

Effect of sheet thickness on die parameters
In the clinching process of high-strength steel and aluminum alloy sheet, most researchers only verified the feasibility of the clinching process for the specific sheet thickness combination and did not explore the influence of the change of die size on the clinching process under different sheet thicknesses.Therefore, when it is applied to industrial production, the clinching die of high-strength steel and aluminum alloy plate with different sheet thickness combinations must be redesigned, which consumes a lot of manpower and material resources.On the premise that the accuracy of the simulation model is confirmed, this section simulates and studies the variation law of die parameters under different sheet thicknesses, so as to provide reference for engineering application.

Simulation analysis method
According to the analysis of mechanical properties in Sect.4, the shear strength is determined by the neck thickness, and the maximum shear force of the joint increases with the increase in the neck thickness.The fatigue strength and peel strength increase with the increase in the neck thickness; when the neck thickness is constant, the fatigue strength and peel strength increase with the increase in interlock value, and the failure form is the interface pull-off failure.Beyond the bearing range of neck thickness, even if the interlock value increases, the fatigue strength and peel strength will not increase, and the interface failure form is neck thickness fracture failure.Therefore, when the maximum force that the neck thickness can bear is equal to the maximum force that the interlock can bear, the comprehensive mechanical properties are better.Let F n and F u be the maximum force that the neck can bear and the maximum force that the interlock can bear, respectively.
where h is the angle between the interlock curve and the axis; and r b and r s are the yield strength and tensile strength of the aluminum alloy sheet, respectively (see Fig. 5).Let F n = F u , then, Among the effective joints obtained by clinching, h is about 25°, and T u is very small relative to R min , while T n is very small relative to R p and R min & R p ? T n .The tensile strength of 5083 aluminum alloy sheet after clinching is about twice the yield strength, and thus, Eq. ( 8) can be simplified as That is, when the interlock value of the joint is about 0.35 times the neck thickness, the comprehensive mechanical properties are the best.In Sect.4, the interlock value and neck thickness of the joint with the best mechanical properties are 0.183 and 0.554 mm, respectively, and the interlock value is about 0.35 times the neck thickness.
To reduce the cost and improve the universality of the die, the increment of the die radius is set as 0.5 mm, so that the same die can be used when the sheet thickness changes slightly.According to the mechanical test in Sect.4, when the comprehensive mechanical properties of the joint are the best, C, K, B, and P are about 0.722, 0.266, 72.2%, and 55.6%, respectively.For a certain sheet thickness t 0 , given R d , there are The simulation analysis process can be divided into the following steps: (1) Given t 0 and initial R d , calculate p , H, X and P according to the corresponding formula, and then simulate and record the interlock value and neck thickness.(2) Change R p or H in increment of 0.1 mm until the best combination of interlock value and neck thickness under this die radius is found.(3) Change the die radius and repeat Steps (1) and (2).
Finally, compare the optimal combination of interlock value and neck thickness to obtain the optimal die parameters under the given sheet thickness.(4) Change t 0 and repeat Steps (1) to (3).

Analysis of optimization results
According to the simulation method in Sect.5.1, the optimal die parameters under different sheet thickness combinations were obtained by simulation, and the corresponding C, K and B were calculated, as shown in Fig. 14.It is worth mentioning that the thickness of aluminum alloy sheet is greater than or equal to the thickness of highstrength steel sheet in all sheet thickness combinations.
As can be seen from Fig. 14, when t 0 is not more than 1.8 mm, R d is 4.5 mm; when t 0 is less than 2.2 mm, R d is 5.0 mm; when t 0 is equal to 2.2 mm, R d is 5.5 mm.C, K, B and P fluctuate at about 0.75, 0.25, 72% and 55%, respectively.C, X and H p are proportional to t 0 , and K is proportional to R p .Therefore, as long as t 0 is determined, R d can be selected, and then according to Eqs. ( 10)-( 12), R p , H, X and H p can be calculated.

Conclusions
1.In the process of drawing-upsetting-extrusion and reverse-press-clinching, the relative interlock increases and the relative neck thickness decreases with the decrease in the relative clearance between the punch and die (the increase in the punch radius).The relative interlock increases and the relative neck thickness decreases with the increase in the relative drawing depth.With the increase in the bottom thinning rate of the protrusion, the relative interlock increases, the clinching quality is better, but the forming force required is larger, and mold strength requirements are higher.The interlock in the drawing-upsetting-extrusion stage is the premise of effective clinching.The relative clearance between the punch and die should be less than 0.778.After reverse-press-clinching, the relative protrusion height is reasonable at 55.6%.2. Under the conditions of experimental sheet thickness, when the die radius is 4.5 mm, the relative clearance between the punch and die is 0.722, the relative drawing depth is 0.266, the bottom thinning rate of upsetting-extrusion is 72.2%, and the relative protrusion height is 55.6%, and the shear resistance, peel resistance and fatigue life of the joint are the best, which are 2644 N, 1522 N and 24,535 times, respectively.3. The clearance between the punch and die and bottom thickness are proportional to the sheet thickness, and the drawing depth is proportional to the punch radius.Therefore, as long as the sheet thickness is determined, the die radius can be selected, and then, the punch radius, the drawing depth, the bottom thickness, and the protrusion height can be calculated. Declarations

Fig. 4
Fig. 4 Test samples for mechanical properties.a Shear test sample; b fatigue test sample; c peel test sample

Fig. 9
Fig. 9 Relationship of relative interlock (a, c, e) and relative neck thickness (b, d, f) to bottom thinning rate in drawing-upsetting-extrusion stage

Fig. 10
Fig. 10 Relationship of relative interlock (a) and relative neck thickness (b) to relative protrusion height after reverse-press-clinching

Fig. 14
Fig. 14 Optimal die parameters under different sheet thickness combinations

Table 1
Chemical composition of DP980 high-strength steel (mass%)

Table 3
Properties of Al5083 aluminum alloy and DP980 high-strength steel