There will be significant stress variation across the notch throat plane due to the presence of notch. In addition to that, during creep exposure, stress redistribution will take place around the notch. The distribution of different stress components (von-Mises, maximum principal and hydrostatic stress) which are responsible for creep damage will vary depending on the notch root radius. You can see this paper: Materials Science & Engineering A 615(2014)348–360.
In notched bar you can expect a change in stress triaxiality while you move within it. In many cases creep damage is sensitive to this, since for many steels the creep ductility drops signifcantly with e increase of traxiality. Even using a damage model based on stress, the "rupture" stress will be function of von Mises (max at the surface) and principal one ( that will Be high within the specimen). You can look at Hyde papers on creep damage, Holdsworth on creep fatigue on CMV steel and Mike Spindler on creep ductility.
Thanks for Dr Daniele's excellent answer. Indeedly I use Wen-Tu MDF to describe the mutiaxial stress/strain state on creep deformation. Also, your paper named as "Advances on creep fatigue damage assessment in notched componets" is of great importance to my current research paper.
There will be significant stress variation across the notch throat plane due to the presence of notch. In addition to that, during creep exposure, stress redistribution will take place around the notch. The distribution of different stress components (von-Mises, maximum principal and hydrostatic stress) which are responsible for creep damage will vary depending on the notch root radius. You can see this paper: Materials Science & Engineering A 615(2014)348–360.