PSI - Issue 57

678 Giovanni M. Teixeira et al. / Procedia Structural Integrity 57 (2024) 670–691 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 is the effective stress range that includes crack closure effect: Δ = (23) Where is the maximum normal stress in the hysteresis cycle (see Figure 8) and is the crack closure stress. is viscoplastic strain range. The method for calculating the crack closure stress is thoroughly discussed in [14]. The crack opening stress is calculated as a function of the maximum stress : = ( 0 + 1 + 2 2 + 3 3 ) (24a) = ( 0 + 1 ) (24b) Where: = (25) 0 = 0.535 ( ( 2 0 ())()) (26) 1 =0.344 0 (27) 3 =2 0 + 1 −1 (28) 2 =1− 0 − 1 − 3 (29) Then is computed iteratively as outlined in [15]. The first step involves the calculation of the crack opening strain for constant amplitude loading according to: = = − ( − 2 ′ () 1 ′ ) (30) is known from Equations 24a or 24b. and are known from the hysteresis cycle (Figure 8). These cycles are determined by the rainflow counting method, which is applied to the normal strain (elastic-plastic) histories. These normal strain histories are normal projections on candidate planes (as part of the adopted critical plane approach). In case the opening crack strain is found to be smaller than the minimum strain the crack closure stress is equal to the minimum stress: ≤ (31) 9