PSI - Issue 75

Tomáš Karas et al. / Procedia Structural Integrity 75 (2025) 150–157 T. Karas et al. / Structural Integrity Procedia 00 (2025) 000–000

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Fig. 4. (a) FEA model boundary conditions and loads; (b) Submodel mesh.

2.5. Elastic-Plastic FEA Modeling

This study continues the work presented in Nesla´dek et al. (2024), and the FEA set-up follows the same numerical simulation procedure. The Abaqus FEM solver was used to first simulate global models (Fig. 4. (a)) of the fretting fatigue set-up, considering combination of two pad geometry, two R ratios, and lifetimes corresponding to four load levels derived from measured S-N curves. This resulted in 16 simulated cases. Subsequently, more refined submodel simulations were performed, with a mesh size as fine as 10 µ m , shown in Fig. 4. (b). The global model employs two axes of symmetry, allowing it to be simplified to a quarter-model. This simplification is important for the load application (see Fig. 4. (a)). Given that the sample is loaded with normal pressure (sine wave with σ a and σ m ) in the axial direction, selecting only a quarter of the top face does not cause any problems. However, the normal contact force P, applied using a bolt load, was halved to account for symmetry. Consequently, all results are presented for only half of the sample’s contact face. Finally, the contact was defined as hard contact in the normal direction and as a penalty contact with a coe ffi cient of friction (COF) of 0.5 in the tangential direction. Results of this simulation (global model) were then used to simulate only a contact part in the submodel to obtain a more precise solution. In this study, two multiaxial fatigue criteria were used to predict the onset of fretting fatigue cracks: the Dang Van criterion and the Papuga QCP criterion. The Dang Van criterion was selected to represent the category of invariant-based methods and also to serve as a reference since it is widely cited in the literature and implemented in the commercial fatigue solvers such as FE-Safe 2019. The Papuga QCP criterion published in Bo¨hme and Papuga (2024), a critical plane category criterion, was chosen based on its performance in Nesla´dek et al. (2024). An in-house fatigue post-processing solver by Nesla´dek and Sˇ paniel (2017) was used to evaluate both criteria. The final output of this postprocessing is a fatigue index (FI), which is saved in a new step in the Abaqus result file (.odb). FI indicates the ratio between the equivalent stress amplitude calculated by the chosen criterion and the fatigue strength. The value of FI = 1.0 indicating that the condition of initiation of fatigue crack has been met. If the test case ended by failure is evaluated and the relevant loads are induced in the FE analysis and in the subsequent fatigue analysis, the value of FI < 1.0 indicates a non-conservative prediction. It means that the used multiaxial fatigue criterion estimated the equivalent stress lower than it was proven experimentally. To also involve the e ff ect of the stress gradient in multiaxial fatigue analysis, a Theory of Critical Distances (TCD) approach was used. This required the use of Abaqus macros written in Python to extract sub-surface FI values in the sample cross-section at the critical nodes along the edge of the contact. Finally, both the Point Method (PM) and the Line Method (LM) of TCD (Susmel (2009)) were used to derive the final FI results. 2.6. Multiaxial Fatigue Criteria