Predicting the shear strength of round clinched joint

Transcription

1 Indian Journal of Engineering & Materials Sciences Vol. 21, October 2014, pp Predicting the shear strength of round clinched joint F Xu a,b & S D Zhao a * a School of Mechanical Engineering, Xi an Jiaotong University, Xi an, , China b Department of Civil Engineering, Zhejiang University, Hangzhou, , China Received 31 October 2013; accepted 30 June 2014 The quality of clinching joints is evaluated by visual and strength tests. This paper describes the shear strength of the round clinched joints of three sheets materials including the Al6061, Al5052, and Q235. The strength of mechanical clinching is affected by sheet thickness, the geometry of the tool, the material performance and the direction of the applied shear (i.e., the press joint orientation). To obtain the shear strength and reduce cost of the tensile tests, two equations for predicting the maximum failure load can be derived by using these parameters. A total of 180 shearing tests are conducted to check the maximum failure load obtained by predictive equations, and the results are in agreement with our predictions. Keywords: Clinching, Mechanical interlock, Neck thickness, Failure load Clinching is a joint technique in which metal sheets are deformed locally without the use of any additional materials. Mori et al. 1 found that clinching joints and self-pierce riveting have superior fatigue strength. Clinching itself is not a recent invention, as the first patent for clinching was granted as early as 1897 in Germany, but it was not used widely on industrial scale until the 1980s. Clinching is applied in the automobile and construction industries, and it is used to connect not only for some ductile materials but also for some hard materials. Clinching technology has also been applied to join magnesium alloys. Neugebauer et al. 2 sought to improve the forming capability of magnesium alloys at higher temperatures. They discovered that if the parts are heated, connections can be formed without cracks by using state-of-the-art joining methods such as clinching. Gao et al. 3 studied how clinching technology was applied on dissimilar sheet metals or materials with different surfaces and thicknesses. The quality of the clinched joint is evaluated by performing visual and strength tests. The actual strength of the joint including the shear strength, the tensile strength and the fatigue strength 4, can only be obtained by using destructive testing. Pedreschi et al. 5 presented a predictive model to predict the shear strength of rectangular joints in cold-formed steel structures. Previous literature mainly focused on experimental research, theoretical *Corresponding author ( sdzhao@mail.xjtu.edu.cn) predictions on the shear strength of a rectangular joint, and factors that influence the shear strength. Lennon et al. 6 compared the differences between some mechanical connections and studied the influence of ultimate tensile strength on a rectangular joint. Pedreschi et al.7 presented an experimental study on cold-formed steel trusses by using mechanical clinching. They discovered that the number of clinched joints has a marked influence on the strength, deformation, and failure mode of the trusses. Davies et al. 8 discussed moment-rotation behavior of groups of rectangular joints. Their study described the behavior of pressed joints in coldformed steel subjected to pure bending. The influence of material thickness and spacing of the joints has also been studied. Davies et al. 9 studied the shear behavior of press joining in cold-formed steel structures, the effect of the ultimate tensile strength (UTS), steel thickness, and the incline angle of the joint on both strength and deformation characteristics of the press joint. Pedreschi et al. 10 applied a theoretical method for predicting the strength of joints and discovered that the strength of press joints used to connect materials of different thicknesses is influenced by the orientation of the sheets to the press joining tools. These studies present some predictive empirical formulas to obtain the shear strength of a rectangular joint. However, these empirical formulas are unsuitable for predicting the shear strength of round joints. Earlier studies presented an analytical method to predict the pull-out strength of the round

2 XU & ZHAO: SHEAR STRENGTH OF ROUND CLINCHED JOINT 511 clinched joints and investigated numerical and experimental work regarding the mechanical strength of a single clinched connection. The mechanical characteristics of the material are an important parameter of shear strength. Few studies have discussed the anisotropy of the materials. Saberi et al. 14 investigated the anisotropy of materials and found that it enforced the shear strength. However, in the present study, anisotropy is neglected. This paper seeks to obtain the relation between the angle of the applied shear and the maximum failure load. Although the round clinched joint is axisymmetric, the clinching process is a new connection method obtained by plastic deformation. Therefore, different angles of applied shears have an influence on the failure load exist. In discussing the shear strength of the rectangular joint, the press join orientation is commonly studied, whereas for the shear strength of the round joint, the angle of the applied shear is discussed and can be considered important. The experimental procedure consists of the clinching experiments and the shear strength tests. The relation between the direction of the applied shear and the failure load is developed. A comparison has been made between experimental results with theoretical predictive results, and found that the failure load increases with increase in the angle of the applied shear. Clinching was conducted in a laboratory environment by using our own tools. No additional materials were used. Therefore, the strength of the clinched joint was entirely determined by the clinch geometry, and, consequently, by the geometry of the die and punch. The valid joint is a joint without punctures or tensile failure of joined sheets at the location of a joint. No gap may exist between joined elements. Figure 1 shows the valid and the failure joints. The clinched joint has an S shape. A sufficient S shape is needed to keep the sheets together while the joint is subjected to shear force. This shape is created when pressing the material into the bottom of the die. Parameters, such as neck thickness, mechanical interlock, and combination thickness of the bottom, are shown in Fig. 1a. The mechanical interlock and the neck thickness are obtained by performing SEM analysis, whereas the combination of the bottom is obtained by the percentage scale. Figure 1b shows the normal failure joint. Commonly, the failure mode is divided into the normal mode and the abnormal mode. The failure mode obtained by the shear test and the tensile test is called the normal failure mode; other failure modes are called abnormal failure modes. Shear strength tests To obtain the influence of press joint orientation on shear strength, two type of joints, horizontal and Experimental Procedures Clinching experiments A typical clinching process involves the use of two pieces of sheet metal placed on the upper surface of a female die. The punch, driven by hydraulic or pneumatic units, drives into the sheet metal. As the punch moves downward, the upper layer is spread onto the lower layer through an annular gap at the bottom of the die, and the two layers are locked together. In this paper, three materials were used to explore the clinching process. The Al6061, Al5052, and Q235 sheets with thicknesses of 2 mm, 1.9 mm, and 1.5 mm, respectively, were produced by rolling. The specimens, which are 80 mm in length and 25 mm in width, with an overlapping length of 40 mm, were used as the substrate. The specimens were cut at three different directions by rolling at 0, 45, and 90, and will be regarded as the different materials to be studied. Although these materials exhibit anisotropy, anisotropy is neglected in this study. Fig. 1 Valid joint and the failure joint

3 512 INDIAN J ENG. MATER. SCI., OCTOBER 2014 perpendicular lap joints, were implemented. A series of shearing tests was performed on each connection type to evaluate the joint quality. Shearing tests could obtain the shear strength indirectly, and they could obtain the maximum shear strength of the clinched joint directly. The connected specimens, including the perpendicular lap joint and the horizontal lap joint, were clamped into the grips of the Instron testing machine (see Fig. 2) 15. In the connection specimen tests, all displacements were assumed to take place at the connection, and the elastic deformation of the materials was neglected. The tensile test was the same for two groups. The horizontal lap joints were fixed as shown in Fig.2a, and the perpendicular lap joints were fixed as shown in Fig. 2b. In other words, Fig. 2a shows the shearing test at 180 (press joint orientation 0 ), whereas Fig. 2b shows the shearing test at 90. The force was regulated by the tensile testing machine to produce a displacement rate specified by the machine operator, the velocity was 2 mm/s 15. The test was carried out until the joint failed. Varis 16 evaluated the quality of a joint made with a fixed die by measuring the material thickness in the middle of the base of the joint. The present study mainly explores shear behavior under different angles of the applied shear. The final mechanical strength depends on the geometric configuration of the clinched joint. Different geometrical parameters are defined, the most importance of which is the thickness in the middle of the base of the joint or the so-called X parameter. This parameter is often compared with values provided by the producer of the applied clinching method. Figure 3 shows the six groups of specimens tested at 90 and 180. A similar trend is observed for all samples. Maximum peak load occurs when the load is applied perpendicular to the axis of the punch, i.e., at 180. Although the round clinched joint is axisymmetric, the clinching joint process is a new connection method obtained by plastic deformation. Therefore, some differences under the different angles of the applied shear affect the maximum failure load. The clinched joint at 90 endures combination deformation, including extrusion, torsional, and tensile deformations. The clinched strength is smaller than that at 180 ; however, the phenomenon occurs because the contact areas between the sheets are sliding relatively, as shown in Fig. 3. Figure 3 shows that the start point will determine whether relative sliding occurs; the trends of the curves are the same at 90 and 180 before this point. After this point, the load still increases as the displacement increases; the increment is smaller than that at 180. However, the relative sliding leads to a decrease in the increment, and deformation still exists in the clinched joint. Any resistance to the displacement is supplied by lateral deformation against the slits. A small plastic deformation of the clinched parent metal is observed, and consequently, a lower peak load is achieved in comparison with the press joints at 180 and 90. When the load reaches the stop point, the relative sliding stops, and the two sheets are locked by the mechanical interlock. The failure is caused by local bending, tearing, and pulling out; thus, the deformation at 90 belongs to the combination deformation. At 180, failure occurs because of shear force on the punch side sheet as they bear against the edges of the die side sheet. However, the load drops rapidly after reaching the peak load. At 90, a different type Fig. 2 Tensile machine

4 XU & ZHAO: SHEAR STRENGTH OF ROUND CLINCHED JOINT 513 of failure occurs, in which the mechanical interlock is reversed and stretched, and the upper sheet is twisted off under the sheet. Fig. 3 Influence of press join orientation on the shear strength Results and Discussion To decrease experimental costs, finite element (FE) analysis is used to describe the clinching process. It can obtain some parameters, such as neck thickness, mechanical interlock, combination thickness, stress distribution on the sheets, and so on. He et al. 17 reviewed recent developments in FE analysis of clinched joints. Fig. 4 3D simulation model and SEM analysis of the cross section

5 514 INDIAN J ENG. MATER. SCI., OCTOBER 2014 Several numerical techniques can be used to simulate such problems (dynamic or static implicit and explicit methods), and different industrial software can be used to describe the clinch forming process. Based on the elastic-plastic FE theory, Yang et al. 18 developed an ANSYS FE model for simulating the clinching process. The influence of the combination of die parameters and sheets' thickness on the interlock and neck thickness was investigated. Mori et al. 19 conducted FE simulations for the clinching process by using high-strength steel and aluminum alloy sheets. The geometrical tools are optimized to improve the joints resistance to tensile loading. An FE procedure that uses automatic re-meshing techniques was developed by Hamel et al. 20 In the present study, the clinching process is an example of an application that uses the ABAQUS FE code. FE model Conventional stress-strain curves were obtained by performing the shear test on regular test beams. The data for the FE model require true stress and plastic strain. In our study, we discovered that the Al6061, Al5052, and Q235 sheets have good weldability and excellent corrosion resistance. During the clinched process, the non-linear geometry (large displacement) is adopted during FE analyses. The FE analysis was conducted by using ABAQUS software 21, which built a 3D model. This 3D model used C3D8R elements and linear bricks that contain eight nodes. The tools were considered infinitely rigid. Friction was modeled by using the Coulomb friction model, with u = 0.2 for the friction coefficient between the sheets and the tools and u = 0.4 for the friction coefficient between the sheets 22. During the clinching process, the punch was moving 5.6 mm downwards, while the blank holder and die were fixed. Different algorithms were available in ABAQUS. The influence of these different algorithms was investigated, but no significant difference was observed. Contact was modeled by using the penalty friction formulation. Figure 4 shows the 3D simulation model and the SEM analysis of the cross-section. In Fig. 4, the right panel shows an encapsulated cross-section that is properly polished to reveal the interface between the assembled sheets. The left panel shows the contour of the joint measured by using an optical microscope. The mechanical behavior of these connections is solely dictated by the final geometry. This FE model of the clinching process was developed to obtain the neck thickness, the mechanical interlock, and the bottom thickness. Predicted shear strength This paper discusses the failure load at two press joint orientations. On the basis of the structural character, the rivet joint is first analyzed, as shown in Fig. 5a. The force distribution on the two laterals rivets is the same, and the direction of applied force is in the opposite direction. When the external load is applied on the rivet, dislocation occurs in the shear plane between the upper part and the underside of the rivet. Thus, shearing deformation occurs. When the external force exceeds a certain value, the rivet is ruptured along with the shearing plane. Although the clinching process is not similar to the rivet process, the structures of the two connections are analogical, as shown in Fig. 5b. The earlier studies presented a Fig. 5 Connection obtained by the pin and the clinched joint

6 XU & ZHAO: SHEAR STRENGTH OF ROUND CLINCHED JOINT 515 predictive equation of the shear strength of the rectangular joint. Although the shape of the clinched joint is not the same to the round joint and the rectangular joint, the deformed law is analogical. Whatever the clinched joints, the maximum failure load equals to that the shear area multiplies the maximum shear stress. On the basis of the balance condition 23, the shearing force is equal to the external load F. When the shearing deformation occurs in the clinched joint, the stress distribution on the shear plane is complex. It assumes that the shearing force distribution on the Q shearing plane is even. That is, τ =, where A A j 2 π d Q = is the shearing area, τ = [ τ ], 4 A whereq is the maximum failure load, τ is the shearing stress, and [ τ ] is the permissible shearing stress. For the plastic materials, [ τ ] = (0.5 ~ 0.7)[ σ ], as shown in Cai et al. 23 Figures 5c and 5d show the applied shearing force at 0 and 90 press joint orientation, respectively. The shear plane is located in the neck thickness. Although the round clinched joint is axisymmetric, the deformation process of the clinched joint is rather complex. The clinched joint depends on the mechanical interlock to ensure shear strength and is hardened during the clinching process. Therefore, the maximum failure load is related to the ultimate tensile strength. In this paper, two theoretical equations are deduced. Previous studies mainly discussed the shear strength of the rectangular clinched joint, and the shear strength was influenced by the direction of the applied shear and ultimate tensile strength (UTS) of the metal materials and cross-sectional area. The following equations refers to Cai et al. 20 Based on the performance of the round clinched joints, the following equations are presented. j j When the angle of the applied shear was 180 (press joint orientation was 0 ), the maximum failure load could be defined as: Q = τ A (1) max j A = 2π T R + πt (2) 2 j n d n Q = UTS πt R + πt (3) 2 max (2 n p n ) where Tn is the neck thickness, Rp is the radius of the punch, and Q is the maximum peak load. The neck thickness ( T n ) of the clinched joint determined the shear strength. UTS is the ultimate tensile strength. When the direction of the applied shear was not equal to 180, the maximum failure load could be defined as M n τ = (4) W W p p 3 π D 4 = (1 a ) (5) 16 d a = (6) D d = R d 2 (7) D = ( R + T ) 2 (8) d n 4 4 UTS π [( Rp + Tn ) Rp ] Qmax = (9) 1 ( Rp + Tn ) l cos( α) 2 where α is the press joint orientation, Q is the maximum failure load, and l is the moment arm of force. Table 1 shows the material properties of the Al6061, Al5052, and Q235 sheets that were measured in the tensile test. The predictive equation also indicates an approximately linear reduction in shear strength for intermediate angles of the applied shear between 180 and 90. Table 2 shows comparison between the Table 1 Material properties of the Al6061, Al5052 and Q Speciments Speciments Thickness 1.45mm 1.45mm 1.45mm 2.00mm 2.00mm 2.00mm 1.86mm 1.86mm 1.86mm YS (MPa) UTS (MPa)

7 516 INDIAN J ENG. MATER. SCI., OCTOBER 2014 Table 2 Comparative study of predictive and experimental results T n R p UTS P(180 ) E(180 ) (E-P)/P% P(90 ) E(90 ) (E-P)/P% 235-0~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

8 XU & ZHAO: SHEAR STRENGTH OF ROUND CLINCHED JOINT 517 Fig. 6 Relation between the failure load and angle of applied shear predictive and the experimental results on the maximum failure load. Eq. (3) can obtain the predictive results under an applied shear angle of 180. The errors between the predictive and the experimental results are shown in Table 2. Eq. (9) can obtain the predictive results under an applied shear angle of 90. The errors between the predictive and the experimental results are shown in Table 2. In Table 2, the neck thickness T n is obtained by using FE analysis, R p is the radius of the punch, and failure is initiated by the distortion of the projecting steel of the punch side material, so UTS is the ultimate tensile strength of the upper sheets. In fact, Lee et al. 24 presented an equation to obtain the neck thickness, which is determined by the geometry of the tool. In this paper, FE analysis should be performed to obtain the neck thickness. Table 2 shows a comparative study of the predictive and the experimental results. Eqs (3) and (9) can predict the maximum failure load, and the predictive results are close to the experimental results. Equation (9) can deliver the relation of press joint angle and the maximum failure load. When the angle of applied shear increases, the maximum failure load will increase. Comparing Fig. 6 with Eq. (9), it can

9 518 INDIAN J ENG. MATER. SCI., OCTOBER 2014 reveal an approximately linear increase in the shear strength for intermediate angles of the applied shear between 180 and 90. Similar to the above analysis, the different press join orientations affect the shear strength. The influence of the angle of the applied shear on the shear capacity of the press joint is shown in Fig. 6. Figure.6 describes the predictive value (P) and the experimental value (E) of the shear strength. Figure 6a shows the shear strength of the Q235 sheet at 180 and 90. Figure 6b shows the shear strength of the Al5052 sheet at 180 and 90. The shear strength of the Al6061 sheet at 180 and 90 is shown in Fig. 6c. The shear strength of the Q235 and Al5052 sheets, the Q235 and Al6061 sheets, and the Al6061 and Al5052 sheets at 180 and 90 are shown in Figs 6d, 6e, and 6f, respectively. The joint is strongest at 180 and weakest at 90. An approximately linear relationship is observed between the angle of the applied shear and the peak load for all combinations of the clinched joints, including the Al 6061, Al5052, and Q235 sheets. Conclusions A total of 180 shear tests were carried out on samples that consist of two sheets of the same material, different materials, and different thicknesses. The following conclusions can be drawn: (i) During clinching processes, the Al6061, Al5052, and Q235 sheets were used to obtain different clinched joints, which can be used to test the relation between shear direction and failure load. As the angle increases, the maximum failure load increases. (ii) Predictive equations about the different angles of applied shears were deduced, and a total of 180 shear tests were tested. The two equations could obtain the failure load and are in good agreement with the experimental results. (iii) The shear strength of the clinched joint can be predicted using the equations developed. These equations take into account the connected material properties, the neck thickness of the clinched joint, the radius of the punch and the angle of applied force. The predictive capability of the prediction has been proved, the error between the predictive results and experimental results can be accepted in engineering practice. Acknowledgements This material is based upon work supported by the State Key Program of National Natural Science Foundation of China (Grant No ) and Major National Science and Technology Project of China (Grant No. 2011ZX HZ). References 1 Mori K, Abe Y & Kato T, J Mater Process Technol, 212 (2012) Neugebauer Reimund, Mauermann Reinhard, Dietrich Stephan & Kraus Christian, Prod Eng Res Devel, 1 (2007) Gao Shiming & Budde Lothar, Int J Mach Tool Manuf, 34 (1994) Carboni M, Beretta S & Monno M, Eng Fract Mech, 73 ((2006) Pedreschi Remo & Sinha Braj, J Mater Civil Eng, 18 (2006) Lennon R, Pedreschi R, Sinha B P, Constr Build Mater, 13 (1999) Pedreschi R F & Sinha B P, Constr Build Mater, 22 (2008) Davies R, Pedreschi R, Sinha B P, Thin Wall Struct, 27 (1997) Davies R, Pedreschi R, Sinha B P, Thin Wall Struct, 25 (1996) Pedreschi R F, Sinha B P & Davies R, J Struct Eng, (1997) Coppieters S, Lava P, Baes S, Sol H, VanHoutte P & Debruyne D, Thin Wall Struct, 52 (2012) Coppieters Sam, Lava Pascal, Hecke Renaat Van, Cooreman Steven, Sol Hugo, Houtte Paul Van, Debruyne Dimitri, Int J Mater Form, Coppieters Sam, Cooreman Steven, Lava Pascal, Sol Hugo, Houtte Paul Van, Debruyne Dimitri, Int J Mater Form, (2011) Saberi S, Enzinger N, Vallant R, Cerjak H, Hinterdorfer J & Rauch R, Int J Mater Form, (2008) Xu Fan, Zhao S D, Cai Jin, Han X L, J Eng Manuf Part B., DOI: / Varis Juha, J Mater Process Technol, 174 (2006) He Xiaocong, Int J Adv Manuf Technol, 48 (2010) Yang X, Tong Z, Dai X & Zhang F, Automob Tech, (10) (2006) Mori K, Abe Y & Kato T, Finite element simulation of plastic joining processes of steel and aluminum alloy sheets, AIP Conf Proc, 908 (2007) Hamel V, Roelandt J M, Gacel J N & Schmit F, Comput Struct, 77 (2000) ABAQUS/Explicit User s Manual Version 6.5, 2005, ABAQUS Inc, Providence, Rhode Island, USA. 22 Xu F, Zhao S D & Han X L, Fatigue Fract Eng Mater Struct, 37 (2014) Chong Huai & Cai Xing-Min, Material mechanics, (Xi an jiaotong University press), Lee Chan-Joo, Kim Jae-Young, Lee Sang-Kon, Ko Dae-Cheol & Kim Byung-Min, Mater Des, 31 (2010)