I think there are 2 things to consider here.
1. failure criteria. for this, you'll have to tell us about the material, what loading this will be affected by, heat treating, what you're concerned with (cracking...etc). this is separate from anything FEA related.
2. the stresses that you are using. it appears that you may be using the max stress that you see on the plot. remember that FEA is not perfect. your element size has an effect on the stress and so do sharp corners. so I would ensure that before you choose a stress to evaluate your failure criteria, you consider whether you have a displacement converged solution and then second, ensure that you aren't just reading the max stress at a singularity/stress concentration.
Firstly, you have completely changed the geometry and that changes the stresses flowing from the load(s) to the constraint(s). Second, P1, P2, & P3 need to be considered together (Google "Mohr's Circle" on Bing). If you have a stress (not necessarily a stress concentration) that exceeds your maximum YS then you have plastic deformation (and a non-linear problem). If your stress is greater than the UTS then you have failure (most likely) and, again, a non-linear problem.