Numerical and experimental identification of fatigue crack initiation sites in clinched joints

In this paper, a study based on experimental and numerical simulations is performed to analyze fatigue cracks in clinched joints. An experimental investigation is conducted to determine the failure modes of clinched joints under cyclic loading at different load amplitudes with single-lap shear tests. In addition, numerical FEM simulations of clinching process and subsequent shear loading are performed to support the experimental investigations by analyzing the state of stresses at the location of failure. An attempt is made to explain the location of crack initiation in the experiments using evaluation variables such as contact shear stress and maximum principal stress.


Introduction
In recent years, energy conservation has become more important than ever, especially in the mobility sector. Therefore, mechanical joining technologies have gained importance due to the lower energy requirements compared to welding or soldering. In this way, mechanical joining technologies such as self-piercing riveting (SPR) and clinching can be used to join different material combinations. Mori et al. [1] compared self-piercing riveting (SPR), clinching and spot-welding of aluminum sheets with respect to the static and fatigue properties. In [2] it was shown that welding of aluminum and steel sheet materials leads to the formation of brittle intermetallic phases, which significantly influence the joint properties. Compared to self-piercing riveting, clinching does not require any auxiliary parts [3]. In clinching, two sheets of materials are joined together by cold forming. However, using a laser assistant the process can be realized as a warm forming process [4]. In clinching process, a punch moves downwards and presses the materials into the die cavity. As a result, the quality-relevant geometric parameters such as interlock, bottom thickness and neck thickness are formed. Bielak et al. [3] presented a method to study the joinability of material combinations in the numerical simulation of clinching process based on the geometric properties of the joint. Furthermore, Ewenz et al. [5] investigated the influence of tool geometry on the mechanical and fatigue properties of the clinched joints. Lee et al. [6] investigated the mechanical properties of the clinched joints subjected to different loading conditions. These studies demonstrate the complexity and versatility of the clinching process and its impact on the structural reliability. However, in the work of Abe et al. [7] and Lin et al. [8], it was reported that the characterization of component reliability of clinched structures is primarily based on phenomenological testing and evaluation of individual joint designs. In fact, clinching can be considered a versatile process, as it can be individually adapted to the sheet thickness, the material and, in particular, the tool geometry. This versatility becomes a disadvantage when it comes to design of clinch and considering the complexity of influencing factors. Typical variations in sheet thickness [9], material [10] or tool geometry [11] lead to significant changes in the mechanical properties. In addition, the arrangement of the clinch points influences the mechanical properties [12]. Su et al. [10] and Zhang et al. [13] reported the complexity of failure behavior of clinched joints subjected to the fatigue loads. Consequently, it would not be possible to transfer the results with respect to the characteristics values as well as process 1 3 window to other joints. In this regard, Krause and Chernenkoff [14] investigated the fatigue behavior of spot-welded structures compared to mechanically joined structures. However, the results of their investigation cannot be used in case of other clinch geometries. Kim [15] investigated the fatigue behavior of clinched joints without considering the stresses and strains induced during the clinching process. The results of aforementioned investigations show that it is not possible to optimally design a clinch joint in advance. In addition, various series of experiments have to be carried out and evaluated. In fact, for the safe design of clinch joints, a detailed knowledge of the highly stressed areas is essential. Nevertheless, considering different load ranges (from low to very high cycle fatigue) this seems to be not sufficient due to different failure modes corresponding to the different load ranges. As well, the influence of form versus force closure is not necessarily represented in this way. To achieve this goal, experimental characterization of the fatigue behavior has to be combined with simulation-based analysis of the stress state in the highly stressed region. In this way, the complexity of the joint geometry and its various notch effects should be taken into account.
The motivation of this study is to analyze the location of fatigue crack initiation in clinched joints by considering the generated stress and strains during the joining process as well as the joint strength simulation. In fatigue analysis, the notch effect is determined by comparing the fatigue life of unnotched and notched specimens. For this purpose, experimental investigations are carried out on clinched joints of HCT590X steel sheets to analyze the failure modes under different cyclic loads. In this work, the FEM simulations of a single lap shear test is used to investigate the notch effect and analyze the fatigue strength of the joined structures. An FEM simulation of the joining process is performed to calculate the geometric properties and the plastic strains and stresses. To create the 3D model for the strength analysis of the joint, the results of the joining process are rotated 180° around the axis of symmetry, taking into account the plastic deformations and stresses. The shear tensile model is tested under specific quasi-static loads, and evaluated. Since there is no material modeling for fatigue damage of clinched joints, no crack calculation or prediction is possible. The FE simulation is mainly performed to support the experimental results. The aim is to evaluate the stress peaks as well as contact properties during different loads on the joints and to find a correlation with the experimental results in terms of cracking.

Materials and methods
For the experimental investigation, steels of HCT590x (t = 1.5 mm) with zinc coating was used. HCT590x is a cold working steel and has a two-phase structure consisting of a ferritic matrix, in which a martensitic phase is homogeneously embedded. This steel is widely used in the automotive industry. The chemical composition of HCT590x is given in Table 1.
Jeol JIB-4610F scanning electron microscope (SEM) with an electron backscattered diffraction (EBSD) System from Oxford was used to determine the microstructure and in particular, the texture of the base material since this can influence the forming behavior. Cross-sections of six specimens were used to determine the geometric features, bottom thickness, interlock and neck thickness. Therefore, three specimens, each longitudinal ( =) and perpendicular (⊥) to the thin sheets' rolling direction, were measured. The validation results for the simulation were determined using a NICON MeF4 light microscope. For the dual-phase steel HCT590X, the mechanical properties are listed in Table 2 according to experimental material investigations.
The mechanical properties of dual-phase steel HCT590X are listed in Table 2.
A total of 12 single-lap shear specimens with the dimension of 105 mm × 45 mm and an overlapping length of 16 mm were used for the strength analysis (see Fig. 1). To determine the F-N curve of the material, fatigue tests with load cycles of 10 5 to 2*10 7 were conducted. The experiments were carried out on the resonance pulsation test system Testronic by Russenberger Prüfmaschinen AG at a frequency of 70 Hz and under force ratio of R = 0.1. The end of the experiment was defined when a frequency change of 5 Hz occurs. To determine the failure modes, penetrant testing (PT) according to ISO 23277 and SEM investigations were carried out.
In addition to the experimental investigations of crack initiation, an FE analysis was performed. Due to lack of damage model, it was not possible to predict the location and growth of the cracks in the numerical simulation. In  addition, in the numerical simulation a quasi-static load was applied to the shear tensile specimen. Therefore, the dynamic effects were not considered. The aim of the numerical analysis is to obtain a better understanding of the relevant conditions with respect to the crack locations corresponding to the different load levels.
The commercial simulation software LS-DYNA® (smp_d_R11.1.0) was used to model the joining process and to investigate the strength of the joint under quasistatic shear tensile loading condition. Due to the slow process of clinching and only low local heat dissipation, dynamic and thermal effects were neglected. In addition, no failure or damage model was used in the numerical simulation because the model is primarily used to predict the specific geometric features, local degrees of material deformation and stresses after joining process. The elastic-plastic tabulated material model of Johnson-Cook (MAT224 in LS-DYNA) was used for all numerical simulation analysis. The material model is able to simulate the dynamic response of the material by defining only the effective stress as a function of the effective plastic strain at different strain rates and temperatures [16]. To determine the flow curve of the material, the layer compression test was conducted and the flow curve was extrapolated using the Hockett-Sherby approach for large plastic strains. The flow curve used is shown in Fig. 2.
For the simulation of the joining process, the 2D rotationally symmetric FE-model presented in [3] was used. For the simulation of joint strength, the result of joining process simulation was used. The computation was performed using an implicit solver and an element formulation of ELFORM 15 (pentahedron element) was defined in to the model. Figure 3 shows the results of joining process simulation in terms of force-displacement curve and the micrograph of the joint.
The contour comparison with the experimental micrograph, the process force curve and the comparison of the specific geometric characteristics of the clinch joint are used to validate the model.
A comparison with respect to specific characteristic values can be seen in Table 3.
Due to the non-axisymmetric loading of the shear tensile tests, the model must be extended to a 3D model. For this purpose, the function *INITIAL_LAG_MAPPING_ implemented in the LS-Dyna was used. The mapping procedure and the FE model have already been published in [17]. The model was used to predict the load bearing capacity of the joints under shear load. A similar method was developed in [18] for the process of self-pierce riveting. The study focuses on the experimental and simulative development of a material model for damage and failure prediction for maximum loading under head and shear tension. Starting from the formed 2D clinched joint at the end of the joining process, a 3D model is generated by a rotation procedure. Before rotating and performing the mapping process, the geometry of the joint is trimmed beyond the area with high plastic deformations. In addition, the stress and strain data from the 2D model are mapped into the 3D clinch point. Figure 4 shows the process of mapping and inserting the 180° rotated clinch joint into the 3D shear test model. The 3D shear test model is adjusted in sheet height by a script, taking into account the formed clinch joint sheets in height.
The model is used to analyze the crack initiation in the clinch joints under shear loading based on experimental investigations. The model is calculated in implicit and uses standard solid elements of ELFORM 1. Due to the symmetry condition, only half of the geometry is considered in the shear test model. The force is measured via a section plane defined in the top sheet. The load is applied via a displacement of the top sheet. INTFOR is used to evaluate the contact-specific quantities such as normal interfacial pressure as well as the shear stress. The model attempts to explain the location of crack initiation in the simulation based on an evaluation variable such as contact shear stress and maximum principal stress. For more accurate analysis or numerical predictions, a material model that includes fatigue damage is essential.

Results
The results of the EBSD investigations of the HCT590X base material are shown in Fig. 5. The crystal orientation map shows a homogeneous grain size distribution of the globular grains. In pole figure {111} an area with a high multiple of uniform density (MUD) is identifiable that indicates a slight z-orientated texture. For validation of the influence of the texture, geometric features (interlock, bottom thickness and neck thickness) were measured in the direction of rolling and perpendicular to the direction of rolling. The results are shown in Table 3. Next, the results of the shear fatigue tests of the clinch joints are given. Figure 6 shows the F-N curve of the fatigue testing. Lifetimes are plotted double logarithmically against the maximum force, and different failure modes are highlighted. Three different failure modes could be observed for the fatigue test and can be assigned to the load level. The colored areas mark the respective failure modes. Failure modes one and two occur simultaneously between 3500 and 3600 N in the three observed specimens, whereas mode 3 is clearly separated and is  the dominating mode at low force amplitudes. However, an outlier at approx. 15,000,000 load cycles, which could be assigned to mode 2, was not considered in the further analysis, as it only occurred once in this range. Figure 7 shows exemplary PT results and SEM images of the crack initiation regions of the different failure modes. The acting forces and regions of the possible crack initiation site are marked. Failure mode 1 is a neck fracture where the crack propagates only in the neck region and the cup of the punch side sheet is still in the die side sheet. Due to the thin neck thickness, the crack initiation site was not clearly detected, but it could be determined that the initiation site was between 40° and 80° to the center of the clinch joint in the direction of the force. This mode occurs at force amplitudes with a maximum force between 3500 and 3700 N (red area in Fig. 6). Failure mode 2, which appeared between 3300 and 3600 N maximum force (blue area in Fig. 6), shows a fracture where the crack initiation takes place on the die side sheet in the clinch joint. Moreover, fretting wear between the sheets could be observed, as shown at the crack surface for failure mode two in Fig. 7. Failure mode 3 shows a similar cracking behavior as the first mode, a crack initiation site at the neck region between 30° and 70°. However, crack propagation was not limited to the neck region, as the crack propagates into the base material out of the joint.
In order to obtain the most precise results of the simulation, representative force amplitudes were taken. The mean values of the different force regions can create results lying in an overlap region and are therefore not clearly assigned to the modes. In Fig. 6 the forces that are used for the simulation are marked with bold-coloured bars for the different load cases.  Figure 8 shows the results of the numerical simulation for all loading conditions. In addition, the SEM images of the fracture surface are presented. The red arrows mark the direction of crack growth. The directions are assumed based on the experimental data. The black arrows (failure mode 1) and the white circles (failure mode 2 and 3) indicate the crack initiation sites. The red circle shows the location of the residual fracture surface. Failure mode 1 shows a top view of neck fracture, failure mode 2 a fracture surface of a die side sheet and failure mode 3 a perspective top view of a fractured joint.
It can be seen that in the neck region of the clinch joint the maximum principal stress has the highest value. Furthermore, it can be observed that the maxima of the maximum principal stresses are located at the points where experimentally the crack initiation sites are assumed to occur. In addition, the distribution of the maximum principal stress on the surface of top sheet is presented. It can be seen that there is no difference between the second and the third failure modes. However, considering the results of the simulation for the first failure mode, it can be observed that the maximum stress is more concentrated at the region of crack initiation. Furthermore, the analysis of the local contact pressure as well as the shear force is shown in Fig. 8. It can be seen that for the load cases Fmax1 = 3700 N and Fmax2 = 3400 N the shear stress between the sheet surfaces reaches its limit value. Besides, it can be observed that for failure mode 1 (Fmax1 = 3700 N) and Fmax2 = 3400 N, the shear stress is exceeded in the lower and neck regions, respectively.
In addition, the plot of relative surface displacement versus shear load force at different positions is presented in Fig. 9. The contact points are representative of the different areas of the clinched joint. For each area, the relative contact displacement was determined by applying an increasing static load to the specimen. The local displacement was evaluated for the three failure modes, which are marked in the diagram in Fig. 9.

Discussion
The experimental fatigue tests were carried out, results were presented and the FE analysis was performed in context of a static load test. The EBSD results show a slight texture of the arrows main direction of the crack growth, black arrows (failure mode 1) and white circles (failure mode 2 and 3) area of crack initiation and red circle area of plastic deformation) and results of the shear load simulation for all three load cases base material. That may lead to a miscalculation in the FEA due to the rotationally symmetric 3D creation of the clinch joint based on the 2D model. Nevertheless, considering the results of the geometric joint characteristics (interlock, bottom thickness and neck thickness), no significant influence of the texture on the joining process or the geometric characteristics can be seen. Therefore, it can be concluded that the FEM simulation model is valid and can be used for the initial analysis. Hence, further consideration of the texture of the initial sheets is neglected. Three different failure modes could be observed for different force amplitudes (Fig. 6). This indicates that different mechanisms become effective at different amplitudes. These are due to the geometric shape of the clinch point, which most likely leads to different local notch effects. This assumption seems reasonable due to the asymmetry of the specimen and the loading condition. It should be mentioned that the asymmetry condition refers to the fact that the load center of the clinch joint is slightly shifted towards the die sheet. As a result, a moment acts on the clinch joint during the test. When calculating the deformation, it must be taken into account that the strain takes place on the punch side and the bending on the die side. The different types of deformation result in different plastic strains in the clinch joint. As a result, the effect of strain hardening is also different depending on the geometric position. The magnitude of local stresses and strains and their distribution are of similar importance, since different areas in the clinch joint can be loaded to failure to different degrees. Nevertheless, considering the results of simulation for failure mode 1 and mode 3, it can be concluded that the global stress maximum seems to dominate the crack initiation (Fig. 8). The analysis of the stress maxima provides information about the subsequent crack locations. However, considering the failure mode 2, it can be concluded the highest global stress value cannot explain the change in crack initiation location. Therefore, the analysis was performed with respect to the contact pressure, interfacial shear stress and relative motion. The results of simulation have shown an overlap of the contact pressure and a local stress peak between the punch-side and die-side sheets for the first and second load cases. The first load case shows overlap at the bottom of the joint and the second load case shows overlap at the neck. Looking at the motion, it can be seen that a much higher relative motion occurs in the neck region than in the bottom region. The correlation of a local stress peak and contact pressure together with relative motion between the sheets can lead to frictional wear. Zhang et al. [13] observed two types of frictional wear: frictional wear at the neck and frictional wear around the recess. Coppieters et al. [19] also showed that several failure modes exhibited frictional wear, suggesting that fatigue cracks are initiated in the friction-affected region.
The results show that it is not only the geometric features and material thickness that are responsible for the fatigue life, but also the friction and surface properties affect the fatigue behavior. In addition, it is still not possible to determine which side of the joining materials is responsible for fatal failure in the mode 1 and mode 2 (Fig. 6). Nevertheless, the analysis of the results indicates the complexity of fatigue life prediction for clinch joints. The calculated maximum stresses may be able to provide an initial indication of the subsequent crack locations. In summary, an accurate determination of the critical failure region for a given load case must take into account the entire loading situation and cannot only refer to the deformation-induced stress-strain situation, but must also include the material contact situation, which is even more challenging given the versatility of clinched joints. However, the presented results serve as a basis for future investigations to clarify the necessary conditions for a reliable fatigue assessment of clinched joints. Moreover, the results of analysis demonstrate the limitations of a simplified static FE simulation, which is not able to accurately predict the location of the crack.

Conclusion
In this work, fatigue tests were carried out to investigate the high cycle fatigue regimes on clinch joint. Numerical simulations for different load conditions were performed to analyze the critical locations of failure. Three different failure modes were observed in the experiments and were compared to the results of the simulation.  It was shown that for failure mode 1 and failure mode 3, the crack initiation occurs in a region of the highest global maximum principal stress values. However, high contact pressures and relative movements between the materials of the joined parts were observed in failure mode 2. This correlates with the observation of fretting wear at the fracture surfaces in failure mode 2 in the experiments. In conclusion, further research is needed to improve the model to fully understand and predict the crack initiation under cyclic loading conditions for clinch joints. In the area of SPR, a first approach was developed in past work by Otroshi [20]. In summary, damage modeling, strain rate effects, cyclic hardening, and the effects of different tool geometries should be considered in future work.

Conflicts of interest None.
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