PSI - Issue 57

Giorgio A. B. Oliveira et al. / Procedia Structural Integrity 57 (2024) 228–235 Giorgio A. B. Oliveira et al./ Structural Integrity Procedia 00 (2023) 000 – 000

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2, the LSM is employed in three modes. The first mode solely considers the H-L data presented in Table 1. The second mode considers only the L-H data. Finally, the third mode takes into account all data listed in Table 1, encompassing both H-L and L-H configurations. The corresponding parameters are presented in Table 3. Figure 4a illustrates the fretting fatigue life versus block 1 damage (d 1 ) diagram for both load configuration (H-L and L-H). This plot represents the experimental values for the H-L (orange circles) and L-H (green diamonds) load configurations. The Mode 1 estimates for the H-L configuration are represented by the orange dashed line, while the Mode 2 estimates for the L-H configuration are depicted by the green dashed line. The Mode 3 estimates, which take into account both load configurations, are shown as solid lines in both green and orange. From such a figure, it is evident that there is no significant advantage in utilizing separate models for each case, as the Model 3 estimates adequately capture the behavior in both configurations. This observation is further supported by the coefficients presented in Table 3, which demonstrates close values for the different models. The average error of all data are reported in Table 4, for each model. Table 3. Values of coefficients α and  for each approach considered (Mode 1, 2 and 3). Mode 1 Mode 2 Mode 3 1.170 0.993 1.091 0.882 0.789 0.812 4.2. SHEAR model + ANN-damage rule approach results As mentioned in subsection 3.3, this approach involves the utilization of an ANN trained using -data from Tables 1 and 2. In this setting, the ANN works as a representation of the equation presented in Eq. 3. The results are depicted in Fig 4b. Notably, the ANN curves demonstrate a higher level of consistency with the experimentalvalues, despite not considering the values at the extreme ends (d 1 = 0.0 or 1.0) during the training process. This observation is further supported by the values presented in Table 4, where this approach utilizing two neural networks proves to be the most effective, yielding the lowest error values.

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Experimental data (H-L) Experimental data (L-H)

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200000 Fretting Fatigue life - N f ( cycles ) 400000

200000 Fretting Fatigue life - N f ( cycles ) 400000

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Fig. 4. FF life vs. damage of first block (d 1 ) showingthe experimental data and (A) analytical models based on LSM and (B) ANN damage model. Note that the models investigated in this work performed worse for very low and very high values of fatigue damage ( 1 ) in the first loading block (Fig. 4). However, even in those cases, estimates are with the error band of 3, which can be regarded satisfactory in the view of the complexity and dispersion found in fretting fatigue problems. 4.3. SHEAR model + Pinto-damage rule approach results This approach employs Eq. 4 in order to estimate the FF life under varying shear loading amplitudes. Thus, the results from the SHEAR model are utilized to determine the N 1 and N 2 values in Eq. 4 for the High and Low load