I'm not a Mech. Eng., but I'm close enough to know a little about shaft design. The transition in radii where the shaft broke is just too abrupt; as others have said.
http://www.aulro.com/afvb/attachment...1100578159.jpg
https://www.aulro.com/afvb/images/im...016/07/303.jpg
Kt - stress concentration factor.
I did run the numbers, but as it was a rough calculation based on eyeballing the picture above I won't post them. If you're getting a new shaft made, consider putting a larger radius in that transition. It may well have been misalignment, heat treating or the material; but that shaft design would've exacerbated the problem.