minger, since you say that there is no set screw, are you then saying that there is a D-shaped hole in the mating part? And with an interference fit?
If that is the case, it would seem to me that the stress distribution around the shaft is going to be quite complicated, but that the corner of the D is going to be a hot spot, a potential crack starter because it is a stress raiser.
When you say that the stress distribution should be linear across half the face of the D, you are imposing an assumed displacement field on the system, are you not? This may, or may not, be what really exists. It is one way to approach the analysis, but I don't think it can be supported as being reality. (That would assume that the other side unloads linearly until contact breaks, the interference having been overcome. There is torque associated with that side also.)