S-N curves in the very-high-cycle fatigue regime: Statistical modeling based on the hydrogen embrittlement consideration

The continuous increment of durability and reliability requirements for many machinery components is significantly enhancing the research activity in the Very-High-Cycle Fatigue (VHCF) characterization of metallic materials, in particular of high-strength steels for critical structural applications. According to the SQRT (area) model, the VHCF strength of high-strength steels can be estimated from the projected area of the ‘Optically Dark Area’ (ODA), which plays a key role in the VHCF response of high-strength steels: more than 95% of the total VHCF life is consumed in the ODA formation, with crack growing even though the Stress Intensity Factor (SIF) is below the threshold for crack growth. Following the hydrogen embrittlement theory proposed by Murakami, hydrogen is supposed to assist crack growth within the ODA. The present paper proposes a general SIF formulation for the analytical model of the hydrogen assisted crack growth within the ODA. Starting from the general SIF formulation, a general expression for the material fatigue limit is obtained in the paper. The statistical method for the estimation of the parameters involved in the proposed model is finally illustrated in the paper and numerically applied to an experimental dataset.