PSI - Issue 38

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

575

4

To limit the friction force to a maximum, the coefficient of viscous friction is set to 133 MPa. A displacement boundary condition is applied to the punch. The force-displacement curve of the numerical simulation is compared to the one obtained from the test rig as depicted in fig 1 b). To validate the results of the process simulation, the cross sections of the physical clinched joints for variant 1.0 and variant 1.4 are compared to the ones obtained from simulation. Fig. 1 c) shows the comparison of simulation (red line) and micrograph for variant 1.4, proving an overall good agreement between simulation result and physical clinched joint.

3. Fatigue life estimation 3.1. Local Strain Approach

In contrast to other existing concepts to estimate fatigue life, e. g. the nominal stress concept or the structural stress concept, the LSA is a material-based concept. Thus it is attributed to be applicable to different geometries under constant and variable amplitudes, if the cyclic material properties are known. It is based on the assumption that the number of cycles up to crack initiation of a notched specimen and a smooth laboratory specimen are identical if exposed to identical cyclic strain history. To perform a fatigue life estimation with the LSA, it is firstly necessary to identify the critical location on the surface of the investigated component. This can be achieved either from a finite element analysis (FEA) or from examination of cracks in a physical clinched joint. Within the scope of this research, an elastic-plastic material behavior with isotropic cyclic hardening is used directly, that is described by cyclically stabilized elastic-plastic material behavior according to the Ramberg-Osgood equation

1/ ' n

'   = +     E K   

(2)

proposed by Ramberg et al. (1943). In case of a stress ratio of R = 0.1, isotropic and kinematic hardening will result in a similar stress state. Thus it is assumed that the memory effects and Masing’s law (1926)

1/ ' n



2 ' E K     +    2   

 =

(3)

are taken into account properly. In case of a general loading sequence with variable amplitudes a hysteresis counting method, e. g. according to Clormann and Seeger (1986), needs to be applied to count closed hysteresis loops and determine the residuum. Each closed hysteresis can be regarded as a possible damage that a component is exposed to. Within this paper, the attempt is made to use the damage parameter ( ) E P a m a SWT   = +    (4) to calculate the damage contribution of closed hysteresis loops and the residuum. From strain controlled cyclic loading tests with constant amplitudes and a stress ration of R = -1, the parameters of the strain Wöhler-Curve are derived ( ) ( ) c f f b f f a N N E ' 2 2 '  +  =    (5)