There's a few factors at play here:
1. Your model likely has perfectly sharp corners on that rectangular bar stock. In reality there is no such thing. there is some radius/transitioning geometry on there that could be finer than your eye can see, but it's there, therefore in the vicinity of this, your model is likely wrong.
2. Nothing is ever fully fixed. Everything is flexible, however, how much flexibility or lack thereof, determines on whether or not we can leave out a larger portion of the model and replace it with a fixed boundary condition. In reality, whatever you are connecting to would have more give relieving some of the stresses. Right now, at your fixture, the part wants to spread out in two directions due to poisson's ratio of the material, however it is restrained from doing so at the boundary, giving a stress increase.
3. In all likelihood at 20X the average stress, you are probably exceeding they yield strength of the material. In a linear analysis, whether or not you exceed the yield, the stress keep increasing on the same line. In reality, material behavior passed the yield is non-linear, you will get larger deformations than predicted in linear, but with lower associated stresses. In general, what happens for things like metals, is that after yield, the material stiffness decreases, and the load redistributes to the areas that haven't yielded yet.
All in all, there are probably more factors at play here than this, but I don't have a lot of time at the moment.