When we talk about bend radius it refers to the radius measured to the center line of the tube.
Every CNC pipe/tubing bending machine will have a different set of draw bend radius tooling based on previous jobs that they have done, but by far the most common will be in line with the first rule of thumb;
The standard draw bend radius is 2 x D
What that means is that if you have a tube OD (outside diameter) of 20 mm then the bend radius to choose, if you can, is 40 mm. It is possible to have a tighter bend radius, even as low as ½ x D, although anything below 2 x D will usually require costly tooling and probably mandrel bending.
At the other end of the scale, the maximum draw bend radius is not dictated by the performance of the tube but more by what tooling it is feasible to fit onto the bending machine. Depending on the tube diameter this could be a very large multiple but again moving away from the standard 2 x D invites tooling charges.
If you need larger radius bends then push or roll bending could be the solution and the minimum radius that is really feasible with that is;
The minimum roll bending radius is 7 x D
It is technically feasible to be tighter than 7 x D but it depends a lot on wall thickness and material properties, so for safety stick to this guideline.
There is no maximum limit to the radius from roll bending, except of course leaving the tube straight, which is the same as an infinite bend radius!
Obviously, it always makes sense to check with your tube manipulator what tooling they have for the tube diameter that you have chosen before you start designing your component.
Alternatively, wherever possible allow a wide tolerance in your bend radii. For example, if you have a simple 90-degree bend in a 20 mm tube does it really matter to your design whether the bend radii are 40 mm, 50 mm, or 60 mm? So why not label it as 50 mm +/- 10 mm?