The Mode III Elastic Stress Distribution Near the Root of a Deep Sharp Notch With a Parabolic Root Profile

In developing a fracture initiation methodology for blunt notches, the basic starting point is the elastic stress distribution immediately ahead of a notch root. Earlier work for Mode III deformation of a two-dimensional blunt notch has shown that the shear stress immediately ahead of the notch root (i.e. at a distance small compared with the notch root radius of curvature) is dependent on the peak stress and notch root radius, but is independent of the notch shape and the loading characteristics. However there are many situations, i.e. with sharp notches, where we are interested in the stress at a distance that is not necessarily small compared with the notch root radius. Thus this paper shows that with a notch that has a parabolic root profile, when this distance and the notch root radius are both small compared with the notch depth, then the stress at this distance is again dependent on the peak stress and notch root radius, but is independent of the notch shape away from the root and the loading characteristics.