PSI - Issue 76

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

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The cyclic threshold curve is proposed by Chapetti (2003) to be estimated using the following expression: ∆ $% =∆ !" +(∆ $%" −∆ !" ) .1− &'()&!) 1 ≥ (2) = 41 ∆ !" (∆ $%" −∆ !" ) where D K thR is the threshold for long crack propagation, constant for a given load ratio, a is the crack length, and k is a material constant. These equations are fully defined once Ds eR , D K thR , and d are known. Further details of this model can be found in references (Chapetti 2003) and (Chapetti et al. 2022). The fracture mechanics approach that employs the concept of the cyclic R -curve is used to compare this threshold curve ( D K th ) with the applied D K as a function of crack length. Figure 2 illustrates this concept.

Fig. 2. Schematic illustration of the fracture mechanics approach using the cyclic R -curve concept.

The difference between the applied D K and the threshold D K th represents the driving force effectively available to propagate a crack of length a . Comparing these curves in those configurations where the crack nucleation stage is eliminated allows the estimation of the fatigue life for a given nominal stress level, thus enabling the construction of Ds - N curves that include fatigue limits or endurance at a given life (e.g., 10 7 cycles). The crack propagation rate da/dN for those cases where D K is greater than D K th can be estimated using different expressions, among which we could introduce the following: ! ! + ) = (∆ , −∆ $% , ) (3) Where C and m are parameters that depend on the material, the environment, and the load ratio. More complex expressions that take into account the load ratio, fracture toughness to consider the final failure configuration, etc., can be used (Zerbst et al. 2016). 3. Estimation of Ds - N curve for metallic alloys containing defects Figure 3presents the estimated Ds vs. N curves for a 2.25Cr-1Mo steel (Lukás et al 1989), characterized by the following properties: Ds eR = 500 MPa, d = 0.02 mm, D K thR = 10 MPa × √m, H V = 170 kgf/mm 2 , C = 1.65 10 -8 mm/cycle and m = 3. The continuous curve corresponds to fatigue life predictions assuming an initial crack length equal to the microstructural size d (grain size). Long-dashed curves represent the Ds vs. N relationships for initial crack lengths of 0.1, 0.2, 0.35, and 0.5 mm, with a common final crack length of 2 mm. Calculations use expressions (2) and (3) and assume axial loading with semi-circular crack fronts (Schijve 2009). A short-dashed line illustrates a hypothetical Ds vs. N curve for defect-free material, where an additional stage of microcrack initiation and growth must be considered. According to the fatigue limit definition given in Figure 1 and expression (1), this curve reaches the same fatigue limit as the curve corresponding to an initial defect size equal to the microstructural size d .