PSI - Issue 39

Georg Schnalzger et al. / Procedia Structural Integrity 39 (2022) 313–326 Author name / Structural Integrity Procedia 00 (2019) 000–000

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stress elements with at least 10 elements along the crack faces. The plane stress thickness equals the wall thickness of the FCG sample. Periodic boundary conditions are prescribed through linear constraints enforcing a constant difference between the displacement vectors of the affine points on opposing edges of the rectangle (Fischer et al. (2000)). These boundary conditions allow loading the model with an arbitrary homogenous stress state. To simulate the axial force and torque applied in the tests the model is loaded with a force in axial and lateral direction, respectively.

Fig. 5. Modelling approach of the FEA. The 2D plane stress model geometry is taken from the FCG specimen. The model length, height and thickness equal the perimeter of the cylinder calculated from D m , the gage length and cylinder wall-thickness, respectively.

The penalty contact definition available in Abaqus is applied to include crack face interaction with a friction coefficient of 0.5. The FEA considers a cyclic Chaboche material model with combined isotropic and kinematic hardening (Dassault Systèmes (2019)). Table 2 summarizes the material parameter calibrated for undeformed R260 from multiaxial material tests at MCL. Parameters for the deformed material were not calibrated within the current work. The kinematic hardening behavior is described by four backstresses using the parameters C i and D i . R 0 represents the initial yield stress. Q and B are the parameters to quantify the isotropic hardening.

Table 2. Material parameters calibrated from multiaxial material tests at MCL for undeformed R260 required for the Chaboche material model.

Elastic

Isotropic hardening

Kinematic hardening

Young´s modulus [GPa]

210

R 0 [MPa] Q [MPa]

180 200

C 1 [MPa]

270,000

Poisson´s ratio [-]

0.3

D 1 [-]

3,000

B [-]

12

C 2 [MPa]

150,000

D 2 [-]

1,500

C 3 [MPa]

50,000

D 3 [-]

250

C 4 [MPa]

8,000

D 4 [-]

0

Ten cycles pre-fatigue and ten cycles FCG test are simulated with loads taken from the experiments. In the end, the analysis provides the evolution of stress and strain fields taking plasticity into account. Furthermore, the relevant contact parameters for the crack face contact are available. From the stress and strain output the cyclic crack driving forces, J-integral and equivalent stress intensity factors are computed based on configurational forces using the post processing routine from Daves et al. (2019). Additionally, the mode-mixity ratio parameter P mix is calculated from Eq.(3):