A simple model to predict the very high cycle fatigue resistance of steels

This work deals with the very high cycle fatigue behavior of high strength steels where fracture origins are mostly at non-metallic inclusions. From the analysis of several features involved in the crack initiation and propagation processes, and since the fatigue resistance usually observed for metals is mainly due to a microstructural threshold for pure fatigue crack propagation, the following expression is proposed to estimate the internal fatigue resistance for a given fatigue life for fractures produced by cracks initiated from an internal inclusion: σeInt=444ΔKthnRiwhere σeInt is given in MPa, the inclusion radio Ri is in μm, n is a dimensionless factor and the pure fatigue crack propagation threshold ΔKth is equal to the lower value given by the following expressions:ΔKth=4.10-3(HV+120)a1/3ΔKth-1=-0.0038σu+15.5where the pure fatigue crack propagation thresholds ΔKth (function of crack length) and ΔKth−1 (a constant value for a given tensile strength or hardness) are in MPa m1/2, the crack length a in μm, the Vicker harness HV in kgf/mm2 and the ultimate tensile strength σu in MPa. Such estimation becomes very important in the assessment of the fatigue resistance of components subjected to very high cycle fatigue, as this might become a very expensive and time consuming task.