A quick napkin 'analysis' of bend radius vs rod diameter comes up with the bend radius being proportional to rod diameter to keep the bending stress the same. I was surprised it's linear, but that's what I came up with, coming at it by two different methods. So for a given rod material, the bending radius of a rod that's twice the diameter of another would be, well, twice that. If you have the minimum bend radius for a rod of known diameter and material, you could scale the minimum bend radius up or down by the rod diameter ratio.
Using properties of Nitronic 50 SS, with Fy=55 ksi or more, a bend radius of 37.5 in for 1/8" solid rod gives max bending stress of 50 ksi, which is below yield of course.
Just napkin doodling - you should ask the manufacturer for min. bend radius, as material properties will govern here. And my math may be off. :neutral: