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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3.3. Damage rule model To compute the total damage ( ) based on the experimental data, Miner's damage rule (Eq. 1) serves as the foundation for all damage models considered in this study. Miner's rule establishes that the damage produced by each block ( ) is permanent and cumulative. According to Eq. 1, failure occurs when the cumulative damage reaches a critical value ( ), typically set at 1. This assumption can be interpreted as a summation of damage percentages until the material reaches 100% damage. Additionally, three more models, represented by Eqs. 2, 3, and 4, are examined in this research. The model presented in Eq. 2 is referred to as LSM-Miner. It is essentially an adaptation of Miner's damage rule for two blocks, where each block's damage ( 1 or 2 ) is multiplied by a constant ( or ). This linear combination is designed to yield a unity value. The constants are determined using the Least Squares Method (LSM), which involves computing the block damages associated with H-L or L-H loading using the data presented in Table 1 and Table 2. The constants are then adjusted to best fit this dataset with Eq. 2. The model described in Eq. 3 introduces a function developed using an ANN, named ANN-damage, resembling the one depicted in Fig. 3, but with two inputs: the damage from block 1 ( 1 ) and the fretting ratio of this block ( 1 / ). The output represents the remaining life cycles ( 2 ) to failure (experimental observation). This function was devised to establish an ANN-based model capable of capturing variations in the total life based on the initial fretting loading block, as observed in the research conducted by Pinto et al. (2023). Data presented in Table 1 and 2 have used in the training process. The final damage model, see Eq. 4, is the one presented in Pinto et al. (2023), whose formulation closely resembles Miner's damage rule, differing only by the exponent appearingin the first term of the left-hand side of Eq. 4. Such an additional parameter have been incorporated to capture the effect of the loading sequence (L-H or H-L). = ∑ = ∑ (1) 1 + 2 = (2) ( 1 , 1 )= 2 (3) = ( 1 1 ) +( 2 2 ) , = ( ) (2.5 1 1 −1) (4) 4. Results and discussions The main findings are divided into the following four subsections, each one into a distinct approach for computing fretting fatigue life under varying shear loading amplitudes. As the results solely based on Miner's model have already been presented in Pinto et al. (2023), we will refrain from showcasing them again. Results here presented considered the experimental values of Table 1 for the calibration of the damage models introduced in the previous section. Total life estimates for the FF tests with variable amplitude tangential load were carried out based on the life estimates provided by the SHEAR ANN model (Subsection 3.2) in association with the calibrated damage models. Finally, we provide a comparative analysis of the errors associated with the outcomes of the approaches presented in subsection 3.3. This modelling consists of applying Eq. 2 considering the SHEAR model estimates for the High and Low load configurations. For the High loading, the estimated life is 101,920 cycles, and for the Low one is 327,200 cycles. These estimates fall within the 1.5 band-width limit, when compared to the experimentalones, which is considered a satisfactory outcome in the context of fatigue analysis. Hence, in order to calibrate the and parameters in the Eq. 4.1. SHEAR model + LSM-Miner rule approach results