Analysis of the interactions between joint and component properties during clinching

Clinching is defined as joining by cold forming of two or more overlapping sheet metals using a punch and a die thereby creating a frictional and form-fit connection without additional connecting elements, additives or auxiliary materials [1]. The main task of clinching is the joining of sheets with thicknesses between 0.5 mm and 3.0 mm [2] and is used in automotive engineering [3], in space travel [4], in civil applications such as bridges [5], electrical household goods [6] and many more. Due to the small tool dimensions, however, clinching is considered a bulk forming process [7]. It is possible to join dissimilar materials in metal-to-metal joints [8] and also metal-to-non-metal joints [9]. The use of dissimilar materials is useful for the lightweight construction, in which suitable materials are used in terms of functionality, load capacity, production and costs, in order to save resources and reduce environmental pollution [8]. The properties of a clinched joint in strength testing are characterized by strength, stiffness and energy absorption [2]. The most commonly used tests are the head tension test, the shear test and the peel test [1]. Typical failure modes are unbuttoning, neck fracture or a combination of the two [4]. The joint properties depend on the main factors geometry, component properties and load type. The influence of the tool geometries on the clinching point has been investigated in many publications. The influence of variation of the mechanical properties of the joining partners and corresponding process parameters has been studied less. The influence of pre-stretching in preceding forming processes, which has an influence on the clinch joint [10], requires further studies. For example, 5 % pre-stretching can reduce the strength of the connection by 20 % and larger pre-stretches can lead to a failure of the clinched point in the joining process [11]. Material aging, especially with aluminum, also influences the material properties [10] and thus the joining process.

Pre-stretching or pre-strengthening can occur during the manufacturing process of the sheet metal or through preceding processes to clinching and can amount to 10 % to 15 % elongation in automotive engineering [12]. In general, work hardening during pre-stretching increases the strength of the material [13], thereby increasing the resistance to deformation [11] and reducing ductility [11] by adding ductile damage to the material [14]. Pre-stretching of the sheets before clinching leads to a reduction in joint strength or even to an insufficient joint due to cracking in the material during the joining process [11]. It is therefore necessary to select clinching tools and clinching parameters that can tolerate influences such as pre-stretching [11] before joining. The influence of pre-stretching can then be determined in material tests, such as the tensile test [15], or directly in the process, e.g. by clinching [11] the specimens. The pre-stretched specimens are often not available in the product development process [11], which means that the tool design must be carried out with the material in its delivery condition. However, pre-stretching can be applied in uniaxial tension [16] or biaxial tension [12]. Although the tensile tests do not reflect the real stresses and strains of a preceding forming process, it can be used to simulate an increase in strength and to introduce ductile damage [11]. However, pre-stretching can only be carried out up to the maximum homogeneous elongation at which no necking occurs [17] and thus depends on the elongation capacity of the selected material.

With finite element analysis (FEA), sensitivity analyses, technological optimization [8], creation of joining process windows [9] and parameter studies [18] are possible. Previous FEA investigations have mainly focused on the investigation of clinching parameters and basic mechanisms, such as tool geometries [19]. To reduce the calculation time, rotational symmetry [8] or the selection of one or more symmetry planes in 3D [20] can be used. The pure Coulomb friction model [21] or the Tresca friction model with modification by a shear limit [6] can be used, for which coefficients of friction between 0.0 [7] and 0.4 [22] are usually applied. Fine meshing is important due to the large local deformation [8]. Mesh sizes used in simulations with sufficient accuracy are reported between 0.05 mm [10] and 0.25 mm [8].

To determine the material data for the simulation, the multi-layer compression test, the uniaxial tensile test, the plane strain upsetting-test [8] and the bulge test [23] have been successfully applied in the literature. To interpret the material data in the simulation, a flow curve and a yield curve must be determind. The isotropic assumption must be used e.g. for 2D simulations [19], but can also be sufficient for 3D simulations in many cases [24]. The extrapolation of the yield curve can be done e.g. with the Swift model [25], the Voce model [26], the Hollomon model [10] or the Cowper-Symonds model [27]. The Swift and Voce model are the most commonly used in the more recent publications.

To ensure the accuracy of the FE-model, a mesh study, a parametric study of the contact conditions [28], a study of the friction coefficients [29] and a check and adaption of the material modeling for the simulation of a clinching process is necessary [23]. The geometry of the joint can be considered for evaluation and calibration [29] until an acceptable deviation from the real experiment is achieved [28]. In [30] the influence of strain hardening and the variation of sheet thickness on the joint characteristics \(t_{{\mathrm {n}}}\), f and \(t_{\mathrm {b}}\) are studied using a metamodel to investigate the robustness of the clinching process. In [31] the possibilities and limitations of FEM-based sensitivity analysis and optimization for the clinching process are discussed. For the optimization of the clinching tools, the sensitivities of the most important tool dimensions and a robustness analysis are determined. For exact simulations, it is recommended to consider the damage development [28]. Without the inclusion of damage, the simulation is less accurate and may not be able to determine the correct failure mode and overestimate the loading capacity [6]. According to [7], however, there are still relatively few FEA studies on the relationship between tool geometry and process-induced defects. Damage models that have been used for clinching simulations include Oyane [7], Cockroft-Latham [9], Rice and Tracey’s [7], Rousselier [7], Lemaitre [6] and Gurson-Tvergaard-Needleman damage model [2].

For the investigation of numerous influencing variables and parameters, the use of a design of experiments (DoE) is useful [22]. In case of numerous experiments or long experimental time, it is reasonable to reduce the number of experiments via a DoE. A suitable experimental design must be selected to conduct the experiments and evaluation methods for the results must be determind. For the study of the clinching process, Taguchi’s DoE has proven useful for different influencing factors and has been used for observing the effects of tool geometry on clinching point geometries. In [28], Taguchi’s method is named as effective for studying influences of individual factors on quality characteristics and for optimizing product and process designs. The reduction in experimental effort was achieved by using an orthogonal array to consider all parameter combinations [22]. An orthogonal array is the smallest possible matrix of parameter combinations in which all parameters are varied at the same time [32]. Thereby, the orthogonal array can still be used to reproduce the complete information about the factors [33]. Thus, the study of the complete parameter space is possible with a few experiments [32]. It is necessary to choose an orthogonal array according to the number of factors and factor levels. It is useful to use at least three factor levels, with the middle factor level being the central point of the parameter [33]. The experimental design only provides the basis for considering all effects and interactions [2]. For the evaluation of the effects and interactions, the calculation of the average effect [32] of each parameter, the main effects, a range analysis, the analysis of variance ANOVA [34] and the signal-response relationship of the parameters to the results [33] are possible.

The investigation of the clinching process for the selected materials and sheet thicknesses requires the determination of suitable clinching tool combinations to produce a joint with sufficient neck thickness \(t_{\mathrm {n}}\) and interlock f without failure caused by material damage. Only closed dies with a joint diameter of 8 mm and conical punches are used. The conical punch relieves the neck area of the die-side sheet, which is relevant for the strength of the joint. However, it decreases f. However, a sufficient f is still achievable with a suitable parameter set and tool. The resulting bottom thickness \(t_\mathrm {b}\) was used as the primary criterion for the tool selection. With a \(t_\mathrm {b}\) lower than 25 % of the thickness of the sheets, the strength decreases and the risk of damage increases. With \(t_\mathrm {b}\) greater than 60 % of the thickness, there is no mechanical closure due to an insufficient formation of f. The bottom thickness can only be reduced with a given tool until the die is completely filled. A further reduction can cause the sheets to lift off the die or lead to punch fracture. The bottom thickness \(t_\mathrm {b}\) depends on the displaced volume by the punch and thus on the punch diameter. Therefore, with a larger punch diameter, the minimum possible \(t_\mathrm {b}\) increases, but with a smaller diameter the formation of f is reduced. Different punch and die combinations are tested for the different sheet thicknesses and the final tool selection is based on cross-section analysis regarding \(t_{\mathrm {n}}\) and f.

A position-controlled pneumohydraulic drive from TOX with a maximum joining force of 100 kN is used to produce the clinched joints. A spring with a spring rate of 628 N/mm is used for the blank holder. With the 4.7 mm pre-load stroke, this results in a blank holder force of approx. 3 kN. The die BD8016 and the punches AC62100 and AC52100 are selected as preferred variants, because a bottom thickness of more than 25 % and an f greater than 0.1 mm are achieved. The die BD8016 has a diameter of 8.0 mm and a depth of 1.6 mm. The conical punch AC62100 has a diameter of 6.2 mm and AC52100 has a diameter of 5.2 mm. The interlock f, the neck thickness \(t_{\mathrm {n}}\) and the achievable bottom thickness \(t_\mathrm {b}\) of the preferred variants are listed in Table 1. The chosen variant does not necessarily lead to the highest joint strength. Since a high strength material is used, a smaller f, which is associated with a greater \(t_{\mathrm {n}}\), can technically achieve a higher strength. However, the preferred variant is used for further testing, because of its greater sensitivity to parameter changes that are to be investigated here.

Since the influence of pre-strains on clinched joint quality is to be investigated virtually and as well as experimentally, the tool variants are tested in combination with pre-stretched material (Chapter 2.3). The 1 mm sheets can be joined up to an uniaxial pre-strain of 7.5 %. At a pre-strain of 10 % of the 1 mm sheets, cracks appear at the neck. Joining of the 1.51 mm sheets is possible with a pre-strain of 10 % without defects.The 1.00 mm sheet has a greater elongation at fracture compared to the 1.51 mm sheet. This leads to greater safety against damage and fractures.

The procedure for building and calibrating the simulation is detailed in this chapter. A reference model is built and subsequently calibrated by adapting the material model and friction conditions using experimental data. For this purpose, the material model is calibrated first, which has a great influence on the beginning of the simulation and strongly affects the resulting neck thickness \(t_{\mathrm {n}}\) due to different yielding conditions. The numerical study of the clinching process are performed with SimuFact.Forming in 2D regarding influencing parameters like sheet thickness variation, pre-strain, sheet arrangement and punch stroke length. The effects of the different parameters are studied using the geometric quality criteria of the clinching point, but it is also useful to consider material damage. The Cockroft-Latham damage model [35] is used for this purpose. In Cockroft-Latham damage, a damage value is calculated from the ratio of the maximum tensile stress and the equivalent stress and summed over the plastic strain [36]. When a critical damage value is reached, the damage is indicated. Therefore, the Cockroft-Latham model is well suited to reproduce damage due to predominantly tensile stresses. The model can be used to compare different parameter sets regarding damage evolution. The dimensions of tools and sheets and their arrangement in the FE-model are shown in Fig. 1. In the model, the sheet thickness t and the corresponding punch diameter D are dependent on the sheet thickness.

The spring of the blank holder is modeled with a spring rate of 628 N/mm and a preload force of 3 kN. To achieve the required bottom thickness in the simulation, the penetration depth of the punch has to be adjusted. A mesh refinement box is defined for both sheets in the area of large deformations. The coarse meshing in the remaining areas saves computing time and is sufficient for accurate results as tested with a meshing study.

The dual-phase steel HCT590x in 1.00 mm and 1.51 mm sheet thicknesses is characterized in uniaxial tensile tests. For the tensile tests, the specimen geometry DIN 50125 - H 12.5 x 50 is used. The tensile tests are performed on a universal testing machine (Inspekt 250, Hegewald & Peschke) in combination with a GOM ARAMIS system using Digital Image Correlation (DIC). The results from tensile tests shown that the stress-strain curves of the 1.00 mm and 1.51 mm thick sheets differ greatly in the range up to 8 % strain and are almost the same thereafter. The 1.00 mm sheets have lower strength up to 8 % strain, which leads to the material yielding sooner.

Due to the large strains during clinching, a suitable extrapolation method is crucial for reliable results. For this purpose, different ranges can be chosen which are within the uniform strain. Swift, Voce and Hockett-Sherby are considered as possible yield curve models. Furthermore, the yield curves can also be adapted over the range of parameter determination. The Hockett-Sherby yield curve model with a fitting range between 10 – 15 % elongation provides the best results for the 1.51 mm sheet thickness. For the 1 mm sheet thickness, the best fitting of the yield curve is achieved with the Voce yield curve model and the fitting range between 10 - 15 %. The method of least squares was used for the fitting of the yield curves and the determination of the parameters for the models.

For model calibration, a mesh analysis is carried out first. Then the material model must be calibrated. This influences the start of the clinching process and controls the neck thickness through the material strength. Friction influences the force-displacement curve and the creation of interlock [37] and is calibrated last.

First, the workpieces are meshed as in Fig. 1. For this purpose, an initial mesh size is defined with a mesh refinement box for larger deformations. Local mesh sizes from 0.20 mm to 0.012 mm are tested in the relevant area for the clinch point formation. In general, the different meshing only has a slight influence on the geometric cross-section parameters. However, a greater accuracy due to finer meshing leads to an increased accuracy of the calculated plastic strain. The difference in finer meshing is most visible in the neck region of the upper sheet at the upper surface. Based on the investigation, a mesh size of 0.10 mm is used for the simulations. The mesh size in the refinement box for the upper sheet is 0.025 mm and for the lower sheet 0.05 mm.

For the study on friction, different friction coefficients are assumed for the two contact areas: tool-workpiece and workpiece-workpiece. The neck thickness \(t_{\mathrm {n}}\), the interlock f and the punch force are evaluated. Based on this analysis, a value of 0.02 is assumed for the friction between workpiece and tool and 0.2 for the friction between workpiece and tool for the 1.00 mm sheets. For the 1.51 mm sheets, a coefficient of friction of 0.1 is assumed for the friction between the workpiece and the tool, and 0.3 for the friction between the workpiece and the tool. The different friction coefficients are likely caused by different surface conditions of the sheets. The 1.00 mm sheets have a lower surface roughness than the 1.51 mm sheets. The comparison of the cross-sections from the experiment and the simulation for the calibrated models is shown in Fig. 2. When comparing the cross-sections, the characteristic course of the parting line between the two sheets can be reproduced well for both sheet thicknesses. The simulation results generally show very good agreement with the experimental results.

The geometric quality characteristics can also be reproduced with sufficient accuracy. These are compared in Table 2.

The deviations of the simulations from the real experiment are sufficiently small. In the neck area, the deviation is less than 10 %, which corresponds to a good accuracy when taking into account the many simplifications made. For the interlock f, especially for the 1.51 mm sheets, the deviation is larger, but still acceptable. The deviation of the bottom thickness \(t_\mathrm {b}\) is partly due to the deviation of the neck thickness \(t_{\mathrm {n}}\). The error of the deviated \(t_{\mathrm {n}}\) affects the f more than the \(t_{\mathrm {n}}\) itself. With a larger \(t_{\mathrm {n}}\), the f would also become smaller and more accurate. Possible causes for the deviations are the extrapolated material model, the assumed constant Coulomb friction conditions and the simplified 2D model.