PSI - Issue 68

T. Korschinsky et al. / Procedia Structural Integrity 68 (2025) 1196–1202 Korschinsky et al. / Structural Integrity Procedia 00 (2025) 000–000

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are polished and rounded to minimize surface influences and guarantee an R a -value below 0.2 µm and an R z -value below 0.7 µm as recommended in (SEP1240, 2006). The validation of the calculations for the fatigue life assessment is carried out by force-controlled testing on notched specimens with a notch factor of ! =2.1 . The results of the experiment are the strain-life curve by Basquin (Basquin, 1910), Coffin (Coffin, 1954), Manson (Manson, 1965) and Morrow (Morrow, 1965) and the cyclic stress-strain curve according to Ramberg and Osgood (Ramberg, et al., 1943). 2.2. Chaboche combined hardening model The Chaboche model describes the material behavior using the kinematic and isotropic parameters. The kinematic hardening is described by quantifying the reduction in dislocation density at load reversal or unloading. For that the back stress tensor " is defined as follows (Chaboche, 1986). " = # ! $ ! ∙ (1 − %&$ ! ∙( "# ) ) (1) " is the kinematic hardening at the beginning in the dimension of a stress. " is a dimensionless rate and describes the change in kinematic hardening with increasing plastic strain ε pl . In the Chaboche model, multiple backstress tensors can be implemented, which increases the possibilities to describe the cyclic material behavior. The isotropic hardening is described by the isotropic variable , that describes the increase in dislocation density (Chaboche, 1986). = ∙ (1 − %&*∙( "# ) ) (2) is the saturation value in the dimension of a stress, is the dimensionless saturation rate and +, is the cumulative plastic strain. The parameters , , " and " are calibrated on the strain-controlled test data using the formulas described. With the help of the determined hysteresis loops, a fatigue life estimation is carried out according to the local concept using the damage parameter according to Smith, Watson and Topper (Smith, et al., 1970) and the associated P SWT -Wöhler curve. 2.3. Damage-dependent Modified Material Model (DD3M) The Damage-dependent Modified Material Model (DD3M) is designed to use the kinematic backstress-tensors calibrated directly on the hysteresis loops acquired in the experiments. This is realized for 100 hysteresis loops taken from the test data at equal intervals between the start and the technical crack initiation to calibrate the backstress tensors in 1 % increments of damage. The result is a set or table of kinematic parameters where each test with a specific strain amplitude has its own parameter set. The cyclic transient stress-strain behavior is thus stored in a database as a function of strain and damage. While the kinematic parameters already known from the Chaboche model are used to define the backstress-tensors, the isotropic parameters become obsolete, as the isotropic softening behavior is implicitly included in the damage dependent definition. To implement the load into the simulation, the Damage-dependent Modified Material Model initially uses the strain maxima and minima as input variables. The simulation of the first hysteresis loop is carried out using the parameters at 0 % of damage from the table of the closest strain amplitude. After the simulation of the first hysteresis loop the current total damage is determined using the P SWT -Wöhler curve. The calculated damage is then the new input variable in addition to the strain minima and maxima to find the best fitting parameter set from the table. With that parameter set, the second hysteresis loop is simulated, and the once again new current damage is calculated. In all further iterations, the parameter set of the current damage is taken from the table and the hysteresis simulation is carried out until a damage corresponding to the theoretical damage sum of !- =1 is reached. The procedure of the Damage dependent Modified Material Model is shown schematically in Figure 2.