Probabilistic description of the cyclic R-curve based on microstructural barriers

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. • Probabilistic model of cyclic R-curve for predicting non-propagating cracks. • Explains the difference between short through-plate and small 3D cracks. • Excellent match with the fatigue limit of different sizes and shapes of defects. • Provides a natural explanation for the asymptotic fatigue limit in the KT-diagram.