Is there a formula to figure out how much stresses would come into play when bending a solid 5/8" non ferrous bar, specifically n04400? I want to know if it would crack?
From basic principles, you can figure out the strain for a particular radius. If you're plastically bending it, stress will be somewhere around the yield point, depending on how the stress-strain curve is shaped. Whether that results in a crack is a different issue.
ASME does have some limitations on the amount of forming that can be done cold, that I supposed relate indirectly to this problem.
AISC-ASD gives minimum bending radius for carbon steel.
Also, note that for a given material, it could be cold-worked, annealed, etc., so there may not be a single answer.
The outer fibers on the 5/8 bar will be pulled the furthest = they will break (tear through) first.
You'll find that the square 5/8 x 5/8 pieces will fail more often than the 5/8 round shapes - even though both are nominally the same distance from the center of the bend. More fibres on the sq piece to fail.