The Mode III elastic stress distribution near the root of (a) an intrusion-type notch and (b) a key-hole notch

An important element of a research programme aimed at developing a fracture mechanics methodology for blunt notches, is the representation of the elastic stress distribution in the immediate vicinity of a notch root. Earlier work for a general two-dimensional blunt notch model has shown that, for Mode III deformation, the stress at a distance x ≪ ρ (notch root radius of curvature) ahead of the notch root only depends on x, ρ and σp (peak stress), irrespective of the notch shape and the loading characteristics. This uniqueness has been confirmed in earlier work for an elliptically cylindrical notch, a special case being a circular cylindrical notch. This paper provides further underpinning for the uniqueness conclusion by analysis of the models of (a) an intrusion-type notch and (b) a key-hole notch.