The three main regions of the R‐curve and the experimental procedures adopted to characterize them.

The three main regions of the R‐curve and the experimental procedures adopted to characterize them.

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Fractures nucleated from defects and subjected to cyclic loading can experience propagation for a range of stress intensity factor ΔK well below the so‐called long crack threshold. This phenomenon is attributed to the development of crack closure mechanisms which may differ from those observed in laboratory tests conducted in accordance with curren...

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... The study of crack closure has been active for several decades from theoretical, experimental, and simulation perspectives [7][8][9][10][11]. Gradually, we could see these efforts paying off by providing prospective physical explanations for several phenomena common in the field of fatigue: mean stress sensitivity [11,12], physically short crack behavior [13], environmental effects [7,14] and notch fatigue [6,15,16], to name a few. However, widespread adaptation has yet to be realized, and phenomenological models are still commonly used. ...
... for positive stress ratios, and it should be corrected with a factor (1 − ) for negative stress ratios [12]. The terms th, and , ∈ [1, 2, … , ] denote the additional resistance development and saturation rate, respectively. ...
... However, reflections against the cyclic R-curves measured in [17] indicated that the baseline closure should be even lower (see Section 5.4). The data shows support for the modification of the intrinsic threshold with a factor of 1 − for negative stress ratios, as proposed by Patriarca et al. [12]. Given this input, the predicted KT-diagram could closely reproduce the observed El-Haddad type curve. ...
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A model for the probabilistic cyclic R-curve has been derived. The model is based on the commonly used hypothesis of consecutive microstructural barrier fronts defining the erratic behavior of microstructurally short cracks and the transition to physically short cracks with declining importance of the microstructural features. The model can describe the linkage between the traditional cyclic R-curve analyses and the El-Haddad type Kitagawa-Takahashi diagrams with the asymptotic fatigue limit at small defect sizes. The model fit against the experimental non-propagating crack lengths perfectly matches the observed and predicted fatigue limit for several defect types and sizes. The presented framework can be used to analyze any geometry, loading history, or defect configuration, including defect interaction problems.
... The procedure adopted to fit the ℎ, values, the solid red line in Fig. 6(a), is the same followed by Beretta et al. [51] and by Barricelli et al. [52]. The crack growth properties of the present Ti6Al4V alloy are coherent with values from Polimi database on the same material, the same printing direction and with heat treatments at temperature that guarantee a similar microstructure [52,53], as well as with literature data [54,55]. ...