PSI - Issue 76

Mirco Daniel Chapetti et al. / Procedia Structural Integrity 76 (2026) 89–98

93

Ds th by using the Murakami-Endo (1994) model, as follows:

∆ $% =2.86 (6 $ 9√);7#)10<8 ) %'& : 1& 0 " ;

8.00>78.8881 6 $

(6)

where Ds th is in MPa, H V in Kgf/mm 2 , R is the load ratio, and √ area in µ m, being √ area the representative size of a defect and is defined by the square root of the area obtained by projecting the defect onto a plane perpendicular to the applied stress. The constant is 2.86 for a surface defect and is 3.12 for an internal defect (Murakami 2019). Figure 4 schematically illustrates the concept proposed by Murakami et al. In Figure 4(a), a double logarithmic Kitagawa-Takahashi diagram is presented, where the threshold is defined by expression (6). The upper and lower bounds correspond to the intrinsic fatigue limit, Ds eR , and the long-crack fatigue growth threshold in terms of stress range, Ds thR (derived from D K thR ), respectively. Five configurations are shown, each characterized by different defect sizes ( a i ) and applied stress ranges ( Ds i ). Figure 4(b) plots the corresponding Ds / Ds th versus fatigue life ( N ) data for these cases, with fatigue lives assumed for illustrative purposes.

Fig. 4. a) Schematic K–T diagram showing the threshold proposed by the Murakami–Endo (1994) model ( Ds th ), and different cases of initial crack length a i and applied stress range Ds i . b) Ds / Ds th vs. N curve according to the proposal by Murakami et al. (2020). While the approach by Murakami et al. effectively captures the underlying fatigue mechanisms, the model used to estimate the fatigue limit Ds th as a function of defect size (Eq. 6) has certain limitations that can be significant in specific cases. The schematic fatigue life distribution in Figure 4(b) assumes that fatigue life is determined solely by the relative value of Ds / Ds th , according to Eq. (5). Within this framework, two notable cases of potential overestimation can be observed. For a defect of size a 4 , where the behavior transitions beyond the short crack regime, the estimated crack growth threshold exceeds the threshold for long cracks (upper limit), leading to an overprediction of fatigue life. Conversely, for a defect of size a 5 and applied stress range Ds 5 , the model would predict a run-out (no failure) even though, based on the threshold for long cracks, fatigue failure would actually be expected. 6. The proposal: D K/ D K th vs. N An alternative driving force parameter is proposed here, defined by the ratio between the applied stress intensity