Statistical models for estimating the fatigue life, the stress–life relation, and the P-S–N curves of metallic materials in Very High Cycle Fatigue: A review

The research on the Very High Cycle Fatigue (VHCF) response of materials is fundamental to guarantee a safe design of structural components. Researchers develop models for the fatigue life in VHCF, aiming at assessing the stress–life relation and, accordingly, the probabilistic S–N (P-S–N) curves. In the paper, the models for the stress–life relation in VHCF are comprehensively reviewed. The models are classified according to the approach followed for defining the stress–life dependency, that is, power law, probabilistic, fracture mechanics, or Paris law-based approach. The number of failure modes that can be modeled, the statistical distribution for the fatigue life, and the characteristics of the estimated P-S–N curves are also reviewed by analyzing the fitting capability of experimental datasets for each model. This review is supposed to highlight the strengths and weaknesses of the currently available models and guide the future research.