PSI - Issue 38

Boris Spak et al. / Procedia Structural Integrity 38 (2022) 572–580 Author name / Structural Integrity Procedia 00 (2021) 000 – 000

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Fig. 2 a) Distribution of residual stresses as result of the process simulation for clinched joint with bottom thickness of 1.4 mm. b) Clinched joint after mapping from 2D to 3D with an element edge length of 0.13 mm. c) Location of stress concentration indicated by the first principal stress for clinched joint with bottom thickness of 1.4 mm. d) Location of crack initiation from micrograph after cyclic loading.

results of the loading simulation with elastic-plastic material behavior and a micrograph showing the crack initiation location after cyclic loading in the transition area from neck to the surrounding material, supports the hypothesis that the first principal stress is a suitable criterion for fatigue life estimation, see fig. 2d). Similar results have been reported by Kim et al. (2014). Within the region of the critical location hexahedral elements with an average edge length of 0.13 mm are used. A convergence study revealed that a reduction of element edge length up to 0.07 mm yields a change in stress of less than 0.3%. Main objective of research in the study at hand is the identification of the location of crack initiation and a fatigue life assessment for clinched joints with different geometric properties, solely using an elastic-plastic loading simulation in combination with the clinched joint geometry obtained as a result of the process simulation. It is evident, that the clinched joint properties such as neck thickness, bottom thickness, undercut and the radius in the transitional area from the neck region to the surrounding sheet material will affect local stress state in the critical region. To further investigate the validity of the local strain approach from a FEA with elastic-plastic material behavior, two clinched joint configurations simulated with the same tooling but with different bottom thicknesses, 1.0 mm and 1.4 mm, are loaded in shear mode in a virtual test setup as shown in fig. 2c). The stress ratio is kept constant with = 0.1 , the peak force F max is varied. Each variant is loaded with at least three cycles to check if the spatial arrangement of the sheets with respect to each other after the first cycle will impact the stress state. The element with the highest value of the first principal stress is assumed to indicate the location of crack initiation. S max is the peak nominal stress equivalent to the peak force F max related to the cross section area of the upper sheet, where the force is applied. It is worth mentioning, that with the elastic-plastic material behavior used in the loading simulation described by eq. (2), a converging result could be reached only for relatively small force amplitudes, not covering the experimentally investigated force range. Reason for this can be found in the change of mechanical material properties as a result of the forming operation. Fig. 1d) shows the measured Vickers hardness distribution in the clinched joint variant 1.4. Especially in the neck of the joint a significant change in hardness is noticeable. Thus, the physical clinched joint is likely to endure higher forces due to cold working compared to a component with mechanical properties of the aluminum alloy in the as-received state without pre-strain. Consequently, a fatigue life estimation based on cyclic mechanical properties without pre-strain will probably show a divergent number of cycles to failure in comparison to a material with strain history and altered cyclic material properties.