In this paper, push-pull fatigue tests of notched specimens under R = -1, 0 and 0.5 are carried out on annealed 0.1 % carbon steel and quenched-tempered 0.5 % carbon steel with HB ≃ 600. The fatigue limit of a long crack, σw2, is obtained from that of a notched specimen with a sharp and deep notch whose radius is smaller than the branch point ρ0. Using the present and past σw2 data, the effect of the positive mean stress on the δKw of the long crack is evaluated using 3.2 HB (≃σB) and σS/ (3.2HB), where δKw is the stress intensity factor range for predicting the fatigue limit of a metal with an arbitrary crack, σS is the lower yield stress or 0.2% proof stress, σB is the ultimate tensile strength and HB is the Brinell hardness. Although the σw2 decreases with the mean stress, σw2 is cut off by the threshold stress σwe of the plastic deformation at the crack tip. For the quantitative prediction of the fatigue limit of a cracked steel with an arbitrary crack length under a positive mean stress, the σw2 and σwe values are approximated by simple formulae.
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