A B S T R A C T Dominant factors affecting fatigue failure from non-metallic inclusions in the very-highcycle fatigue (VHCF) regime are reviewed, and the mechanism for the disappearance of the conventional fatigue limit is discussed. Specifically, this paper focuses on the following: (i) the crucial role of internal hydrogen trapped by non-metallic inclusions for the growth of the optically dark area (around the non-metallic inclusion at fracture origin), (ii) the behaviour of the crack growth from a non-metallic inclusion as a small crack and (iii) the statistical aspects of the VHCF strength, in consideration of the maximum inclusion size, using statistics of extremes. In addition, on the basis of the aforementioned findings, a new fatigue design method is proposed for the VHCF regime. The design method gives the allowable stress, σ allowable , for a determined design life, N fD , as the lower bound of scatter of fatigue strength, which depends on the amount of components produced.Keywords bearing steel; non-metallic inclusion; small crack; the ffiffiffiffiffiffiffiffi ffi area p parameter model; very-high-cycle fatigue.
N O M E N C L A T U R Effiffiffiffiffiffiffiffi ffi area p = square root of the area of crack or defect ffiffiffiffiffiffiffiffi ffi area p ODA = square root of the area of ODA ffiffiffiffiffiffiffiffi ffi area p max = maximum inclusion size ffiffiffiffiffiffiffiffi ffi area p max;j = maximum inclusion size in the j th inspected area or volume C H = hydrogen content F j = cumulative distribution function HV = Vickers hardness value j = integer number (=1, 2, 3…) n = number of inspections N = number of loading cycles N f = number of loading cycles to failure N fD = design life R = stress ratio S = area for prediction S 0 = standard inspection area T = return period V = volume for prediction V 0 = standard inspection volume y = reduced variate y j = j th reduced variate γ = growth ratio of ODA (¼ ffiffiffiffiffiffiffiffi ffi area p ODA = ffiffiffiffiffiffiffiffi ffi area p max ) σ allowable = allowable design stress