The material parameter rho* - 4c/sigma3(-1) is put forward, which represents the crack tip radius independent of crack length under the action of the fatigue limit stress. According to the fatigue notch factor of the crack propagation, K(f) = K(t)2/3+n = (4d/rho*)1/3, the fatigue limits of sharp notch, long crack and short crack are calculated, which are very close to the measurements. The calculated results make it clear that for surface crack the transition point from long crack to short crack is a*=(DELTAK(th)3/12.8c)2, the range of physical short crack (a(s)) is P*14, less-than-or-equal-to a(s) less-than-or-equal-to a*, the threshold of the fatigue crack initiation is DELTAK(th)(i) = 0.66 DELTAsigma-1 (pirho*/4)1/2, the material parameter that indicates the fatigue crack sensitivity is rho*/a*, which represents the blunting condition of crack tip under the action of the fatigue limit stress.