PSI - Issue 38

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

576

5

Hereafter, the damage parameter Wöhler-Curve ( ) b N P +  = ' ' ' 2 2 2 

( ) b c f + 2

E N

    

(6)

SWT

f

f

f

f

is established to compare with the damage parameter P SWT from hysteresis counting and obtain the number of cycles to failure. The linear damage accumulation hypothesis  = = n i f i N D 1 , 1 (7) is applied, with the assumption that crack will initiate if damage sum D = 1. To retrieve the cyclic material parameters, specimens with a thickness of 2 mm are prepared according to the German guideline SEP 1240 (2006) and tested under constant strain amplitudes ranging from 0.15% to 0.8% engineering strain. To study the impact of deformation on the cyclic material properties during the forming operation, three different batches of specimen are prepared: one batch without pre-strain, one batch with a uniaxial pre-strain of 4% engineering strain and another one with 6% uniaxial pre-strain. Although it is worth mentioning that the level of pre strain is significantly lower than strains present in the actual forming process. For each batch a strain Wöhler-Curve was fitted with at least twelve valid results. A summary of the obtained cyclic material parameters is given in Table 2. For comparison, estimated cyclic properties of the studied aluminum alloy are presented according to the “Uniform Material Law” (UML) developed by Bäumel and Seeger (1990) as well as “FKM method” derived by Wächter (2016) for the FKM Guideline nonlinear (FKM nonlinear, 2019).

Table 2. Cyclic material properties of EN AW-6060 T66.

Material parameter

0% pre-strain

4% pre-strain

6% pre-strain

FKM method

UML 413.2 -0.095 0.35 -0.69 398.3

σ f ' in MPa

455.2

571.2

554.3

544.4

b

-0.097641 0.24124 -0.69605

-0.12743 0.21330 -0.63666

-0.12441 0.24859 -0.66569

-0.1060 1.32077

ε f '

c

-0.83 525.4

K’ in MPa

428.5

687.2

621.6

n’

0.0895

0.1699

0.1583

0.1280

0.11

3.2. Loading simulation To replicate the testing condition of the lap shear specimen according to DVS/EFB 3480-1 (2007) under cyclic loading and to identify the critical location, the geometry of the clinched joint as a result of the 2D process simulation is mapped to a 3D model using the inbuilt features of LS-Dyna®. The 3D clinched joint is tied to the surrounding sheet material using the appropriate tied contact options. The contact definition between the upper and lower sheet is set to a penalty formulation with an automatic detection of surfaces. The friction coefficient is the same as in the process simulation. In a first approach, the residual stresses and the strain history as shown in fig. 2 a), are omitted from the 3D model. From the low amount of research available on the residual stresses in clinched joints, for example by Gibmaier et al. (2002) and Sjöström et al. (2005) under consideration of cyclic loading, no clear impact of residual stresses on fatigue life can be concluded. To reduce computation time, a half model with appropriate symmetry boundary conditions is developed, see fig. 2 b). A displacement boundary condition is applied at the lower sheet to keep the lap shear specimen in position, at the upper sheet the specimen is cyclically loaded with constant force amplitudes ranging from 675 N to 1125 N with a stress ration R = 0.1 as depicted in fig. 2 c). A comparison of the