PSI - Issue 68

Lucia Morales-Rivas et al. / Procedia Structural Integrity 68 (2025) 493–499 Lucia Morales-Rivas, Eberhard Kerscher / Structural Integrity Procedia 00 (2025) 000–000 5 between the threshold condition for the propagation of long cracks and the estimated 678,19:),;< modified by the previously described Neuber’s rule (illustrated in Fig. 2.a), σ 2=>?=@,;< . The ( ′′ values by Mueller et al. (2016) (Table 3) differ depending on the ) of the specimen geometry. It implies that the ( ′′ values do not correlate to characteristic length values intrinsic to the microstructures with a precision lower than the difference between ( ′′ corresponding to ) =2 and ( ′′ corresponding to ) =4 (0.5-1 μm from the results in Table 3). Moreover, it implies that σ 2=>?=@,;< values do not define Δσ ( . In the present work, σ 2=>?=@,;< values at the fatigue limit -not reported by Mueller et al. (2016)- have been recalculated by using the values of ( ′′ (Table 3) and the threshold condition for the propagation of long cracks, both reported by Mueller et al. (2016). It can be noticed that some of the σ 2=>?=@,;< values (Table 3) are below the corresponding YS (Table 1), which, nevertheless, might be explained by the cyclic stress-strain behaviour of the studied microstructures -not reported by Mueller et al. (2016)-.The observation that ( ′′ values for ) =2 are within the dimensions of the proposed effective grain size (bainitic blocks) could rather be explained by the typical dimensions of the plastic size corresponding to the long cracks in the near-threshold regime, as observed by the present authors in Morales-Rivas et al. (2022, 2023). In this sense, Irwin’s equation (eq. 5) can be applied for the determination of the plastic zone diameter at the tip of a long crack at the propagation/non-propagation threshold ( AB,), ), which is a function of the corresponding stress intensity factor ( ), ) and the yield strength ( YS ). The intersection of the straight line defining the propagation/non-propagation threshold for long cracks with σ CDEFDG , which is in the order of magnitude of YS , leads to characteristic length values similar to the theoretical plastic zone diameter at the propagation/non-propagation threshold condition (i.e, ( ′′ ~ AB,), ). The use of ( H , would, therefore, not totally capture the role of the microstructure within the short-crack regime. EF,#$ = G . - H -3 IJ . 2 (5) Table 3. Results from notch fatigue testing of advanced bainitic microstructures, corresponding to MECBAIN and inferred from data published by Mueller et al. (2016). The explanation on the parameters is given in the subsection 3.1. Note that the value marked with “*” is higher than its corresponding =>?,@AB<,CD . ′′ /µm , [16] /MPa < =2 < =4 < =2 < =4 0.6C-1.5Si-890°C-220°C (114h) 2.4 1.7 1522 1809 0.6C-1.5Si-890°C-250°C (16h) 2.3 1.8 1464 1655 1C-2.5Si-950°C-250°C (16h) 2.9 2 1439* 1733 3.2. Application of a modified Neuber´s equation for notched fatigue In the present work, a different approach has been taken, by using directly the Neuber-modified equation (eq. 4) that estimates the fatigue limit from notch fatigue. Since, as mentioned, two specimen geometries have been used for each microstructure, and assuming that ( ′ is a microstructure-specific parameter, a two-equation system (eqs. 6,7) can be solved for each microstructure, where ( and ∆ ( are the unknown variables, whereas Δσ ',!" and receive the values listed in Table 1. ⎩⎪⎨ ⎪⎧ ∆P ( ∆P 4,-3(,-78) =1+ .+ . 0 1 / 1 ( 2 ∆P ( ∆P 4,-3(,-7:) =1+ .+ Q 0 1 ; 1 (2 (6,7) Estimated ∆ ( and ( H values from eqs. 6,7 are listed in Table 4. Since ∆ ( and ( H are now known, it is possible to represent the evolution of 1/ 1 = ∆J "% ∆J ! as a function of for each bainitic microstructure (Fig. 4.a). For the sake of comparison, curves corresponding to eqs. 1,2 (particularized to ∆ ( values from eqs. 6,7 in Table 4) and their asymptotes (the straight lines defining the propagation/non-propagation threshold for long cracks, obtained from crack growth experiments), are also shown in Fig. 4.a. Such asymptotes define ( , the EHST parameter (eq. 2), as they intersect the horizontal axis ( 1/ 1 =1). The linear part of the curves corresponding to eqs. 6,7 (Fig. 497