Abstract The plastic blunting process is considered to operate during crack growth in the vicinity of the threshold stress intensity range as well as above. A model for determining the threshold stress intensity range for fatigue crack propagation at R ≥0 is proposed using linear elastic fracture mechanics concepts and Neuber's considerations to approximate local stress and strain near the crack tip. It is shown here that, for deep cracks, the threshold stress intensity range for a given material is a constant, depending only on material properties. Experimental results taken from the literature are in reasonable accord with predictions by the model.