What are stress concentrators?

Flaws typically exist in materials. Maybe on the surface, maybe on the interior. These flaws have a real impact on the fracture or yield strength of the materials. Why? Early fracture mechanics scientists recognized that in the vicinity of the crack tip there was a stress magnification. They also found that the magnitude of this stress magnification was proportional to the half crack length divided by the crack tip curvature of radius.

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Is there a Kt value where flaw/defect tip becomes so sharp the fracture toughness of a material is no longer a factor in fatigue crack initiation?