PSI - Issue 46

L. Frank et al. / Procedia Structural Integrity 46 (2023) 3–9 L. Frank and S. Weihe / Structural Integrity Procedia 00 (2019) 000–000

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of the submodel. The time-dependent local stress and strain tensors were determined at highly loaded points in the blade root where fatigue damage is assumed to occur.

Fig. 5. FE models; global model (left), part of the submodel (right) with evaluation path (black arrow)

In the blade root, complex multiaxial and non-proportional fatigue stresses occur due to the loading situation from centrifugal force with superimposed oscillating bending stress. This complex multiaxial fatigue loading can be assessed using advanced fatigue damage parameters (FDP) in combination with the critical plane approach. This approach assumes that fatigue cracks initiate on a plane where a maximum value of a specific FDP occurs (Gupta et. al. (2011)). The FDPs are divided in stress, strain and energy based approaches and in Socie and Marquis (2000) as well as in Fesich (2013) numerous FDPs are listed. However, only the shear strain critical plane-based model suggested by Fatemi and Socie (1988) is chosen within this publication. This FDP is expressed by: �� � �� �������� � ���� � ����� � � ����� � � ��� where ∆γ /2 is the maximum shear strain amplitude and σ n,max is the maximum normal stress acting on a specific plane, k is a material parameter and set to 1 for the investigated material and R e is the yield strength. The right hand side f(N f ) of Eq. (1) can be approached according to Langer (1962) by: ��� � � � � � � � ��� �� ��� ��� where A , B and C represents individual coefficients for the FDP FS and which are calibrated by uniaxial strain controlled fatigue tests with smooth specimens, see Fig 4. The final step in the assessment concept is the comparison of the numerically determined FDP with the FDP-curve derived from the material behavior. 3.2. Results and Discussion Fig. 6 shows the distribution of the calculated FDP FS over the evaluation path in Fig. 5 as well as the derived predicted cycles for five different bending amplitudes. With higher amplitudes, higher FDPs are obtained over the entire course. Up to an amplitude of 0.8 mm, the highest damage value is obtained at the EoC. For an amplitude of 1.2 mm, the notch area is similarly highly loaded. For an amplitude of 1.5 mm, the highest damage value is obtained in the notch area. Here, the predicted failure occurs from an amplitude of 0.6 mm, and the predicted failure for amplitudes between 0.6 and 0.8 is only in the EoC area. Both results are consistent with the observations from the experiments shown in Fig. 2. The prediction of the cycles also fits very well with the experiment. For amplitude 1.2 mm approx. 10 5 cycles were obtained in the experiment. The predicted cycles at the EoC and at the notch are also 10 5 cycles.