What is the tightest radius for a bend for any given thickness of sheet metal?

atleast thickness of the part.
t=2 then r=2

http://sheetmetal.me/air-bend-force-chart/

From: http://www.thefabricator.com/article/bending/bending-basics-the-fundamentals-of-heavy-bending

"A Simple Rule of Thumb

There’s a rule of thumb to determine a steel’s minimum bend radius, and this generally works for aluminum too: Divide 50 by the material’s tensile reduction percentage as specified by your supplier. This value will vary by grade.

If the steel has a tensile reduction value of 10 percent, divide 50 by that value: 50/10 = 5. Next, subtract 1 from that answer: 5 – 1 = 4. Now, multiply that answer by the plate thickness. If the material is 0.5 in. thick: 4 × 0.5 = 2. So in this case, the minimum inside bend radius is 2 times the material thickness.

Note that this is just a rule of thumb. Finding the true minimum bend radius for steel or aluminum plate requires a little research. This should include data from your material supplier, whether you are bending with or against the grain, as well as information specific to the application. Nonetheless, the answers are there, waiting for you to find them."

Bending Radius
There should have bending radius for sheet metal bending, bending radius should not be too large or too small, it should be chosen appropriately. If the bending radius is too small, it will cause cracking at the bend position; if the bending radius is too large, it is easy to rebound.

The optimum bending radius of different thickness of various materials (bend inner RADIUS) see table below:
Metal Annealing Condition Cold Hardening State
The corresponding position of bending direction and fiber direction
Vertical Parallel Vertical Parallel
08, 10 0.1t 0.4t 0.4t 0.8t
15, 20 0.1t 0.5t 0.5t 1.0t
25, 30 0.2t 0.6t 0.6t 1.2t
45, 50 0.5t 1.0t 1.0t 1.7t
65Mn 1.0t 2.0t 2.0t 3.0t
Aluminum 0.1t 0.35t 0.5t 1.0t
Brass 0.1t 0.35t 1.0t 2.0t
Soft Brass 0.1t 0.35t 0.35t 0.8t
Semi-rigid Brass 0.1t 0.35t 0.5t 1.2t
Phosphor bronze / / 1.0t 3.0t

The data in the table above is the preferred data for reference only. In fact, the rounded corners of press brake are usually 0.3, and a small number of the rounded corners of the press brake punch is 0.5.

For ordinary low carbon steel plate, anti-rust aluminum plate, yellow copper, purple copper, etc., the inner radius 0.2 is no problem, but for some high carbon steel, hard aluminum, super-hard aluminum, the use 0.2 radius will lead to bending fracture or the outer radius crack.

You can check full details in this post:
https://machinemfg.com/press-brake-ultimate-guide/