PSI - Issue 57

Jan Papuga et al. / Procedia Structural Integrity 57 (2024) 79–86 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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• Crossland (1956) criterion (CROSS) representing the invariant-based criteria. Their respective formulations can be found in Table 3. All criteria assessed in this paper are evaluated with the shear stress amplitude and the amplitude of the second invariant of the stress tensor deviator calculated via the minimum circumscribed circle (or hyperball in the case of CROSS criterion).

Table 3. Fatigue criteria analyzed in this paper. QCP , =max , √ ∙ ( + ∙ )+ ∙ ( + ∙ ) LZ , =√∫ ∫ [ 2 (1+ 2 )+ 2 (1+ )] =0 2 =0

(2)

(3)

DV , =max , ( ∙ + ∙ ) CROSS , = ∙ (√ 2 ) + ∙ ,

(4)

(5)

3.2. Evaluation

All criteria summarized in Table 3 are in the format where the equivalent stress amplitude  a,eq is computed from the stress inputs related to different fatigue lives shown in Fig. 2 . The equivalent stress  a,eq amplitude is compared to the fatigue strength in fully reversed axial loading  FS at the same number of cycles, by a fatigue index FI computed as the ratio of both parameters: ( ) = , ( ) ( ) (6) FI should result in 1.00, ideally. The relative error induced in estimating the fatigue response perfectly, the fatigue index error  FI, is defined as: ∆ ( ) = , ( )− ( ) ( ) = − 1 [%] (7) The papers by Papuga et al. (2019 and 2021) are based on the expectation that most of current multiaxial fatigue strength criteria provide good estimates in cases of in-phase (IP) axial and torsion loading, and what makes their response different is the response to the induced phase shift between both load channels in the out-of-phase (OP) regime. The difference in experimental response for the OP scenario and for the IP scenario is shown in Fig. 2 right on the primary vertical axis (blue color), where the ratio between the fatigue strengths in the terms of applied axial stresses is shown. Data points and the regression curves in Fig. 2 show that the tension and torsion push-pull fatigue curves are quite close around the lifetime of 100,000 cycles The difference of the computational response will be provided in the next section, but in another metrics, in the ratio of fatigue indexes FI OP for the OP load regime to FI IP for IP load regime. Fig. 3 shows, how the four criteria evaluated here respond to the phase shift for fatigue strength ratios k of 1.11 and 1.35 like the range of the ratio observed in Fig. 2, right. 3.3. Results Results in the fatigue index errors obtained for both multiaxial configurations can be found in Fig. 4. This brings