For the prediction of the crack growth initiation from a blunt notch or a precrack in a prestrained material under plane strain tension and small-scale yielding conditions, a microscopic fracture criterion is proposed in terms of the crack tip opening displacement(COD) needed for the attainment of fracture strain at a microstructural distance. Smooth blunting of a crack tip with an initial root radius is assumed, and strain distributions on the crack-line axis are calculated at each deformation stage until the distributions against an original distance normalized to the COD are insensitive to an initial root radius. This case of no initial-root-radius effect is taken as for a sharp crack tip, on which the criterion is applied to determine the characteristic length of material from a critical COD for a fatigue-precracked specimen. The predicted COD at the fracture initiation from a crack with an initial root radius or a prestraining shows reasonable agreement with experimental values.