Question: I encountered a bend problem, which confused me a great deal. I was using a die of 0.984 inch together with a punch of 0.03 inch. I dealt with 6061-T6 aluminum of 0.125 inch thickness. Since I experienced some cracks, I turned to 1100-O aluminum possessing defined extension force of 13.000 PSI. In accordance with 20 % principle the inner radii achieved was expected to be some 0.033 inch. Still, the experimental bending gave inner bending of about 0.170 inch. Having done some calculation I discovered that the value mentioned is workable in case of materials with 68.000-PSI extension force. How could these differences be explained? This is the predicament I happened to face. I find it right to have the answer prior to cutting materials. Precise calculations will help to deal with more than one bending under different angles. The mismatch you came across is due to sharp bending with the narrow-tipped punch that you use. The narrow-tipped punch could also contribute to cracks on the T-6 aluminum.

I guess you know that in air bending the inner appears proportionate in relative with die breadth dependent on the sheet types or extension force. This is the case for all types of air formation, in contempt of the die type used by you, whether they are V-shaped, sharp or channel dies. The 20 % principle assumes this.

 20 % is some kind of title. Real percentage changes according to types of materials and their extension force. Every value herein implies simplicity in usage while fabricating metal sheets:

  • 304 stainless steels: 20-22% die aperture
  • 60.000 psi cold-roll steels: 16 %
  • 5052 H32 aluminum: 12-14 %
  • Hot-roll steels: 14-16 %

To interpret the 20% principle we take 60-KSI cold-roll steels as base materials, and they provide basis for other estimations, as well as the easiest and mainline method to find inner radii for air bending, particularly useful in workshops if the main data are unavailable.

Estimation of an accurate value

As you delivered in the question, the percentage for 20% principle is dependent upon the extension force of materials instead of types of materials. Nevertheless, it is possible to gain high precision in estimation through math. The main 20% principle works quite properly. It is simple to find the precise percentages so long as you are aware of the extension force of your materials. In case of encountering materials the extension force of which you do not know, look it up in appropriate webs.

To gain defined percentages for particular materials, the extension force has to be divided by 60.000 psi, later the results ought to be multiplied by 16 % (the 20% principle). Next, the results have to be multiplied by die aperture.  

The Principle of 20% Practiced to Various Types of Material

Sheet extension in psi/60.000 equals the coefficient of extension difference

Coefficient of extension differences × 0,16 equals percentage of die breadth

Percentage of die breadth × die breadth equals the inner bending radii of air formation.

As I guess you applied this method of estimation of inner bending radii to 68.000-psi as well as 13.000-psi mild aluminum.

20% Principle Practice for 68-ksi Materials:

68,000/60,000 = 1.13

1.13 × 0.16 = 0.181 (or 18.1% of die breadth)

0.181 × 0.984 = 0.178-inch inner bending radii

20% Principle Practice for 13-ksi Aluminum:

13,000/60,000 = 0.216

0.216 × 0.16 = 0.034 (or 3.4% of die breadth)

0.034 × 0.984 = 0.033-inch bending radii

Acute Bending in Mild Materials

As soon as you gain the sheet extension information, it becomes easy to make predictions about the exact inner bending radii. Making use of an extension force factor can lead to highly precise bending allowance, setback, bending deduction. Yet, your measure was 0.170 inch radii, which is nearly 0.137 inch as much as your correct calculation. How does this mismatching occur? 

It is related to the concepts of acute bending. Acute bending implies the least inner bending radii possible to gain prior to the punching nose action of forming creases towards the bending length. To realize acute bending tonnages must be no more as compared to the punch tonnages. The latter provides the necessary force for punching tips for penetration into materials and fold formation towards the bending length. The formation tonnages are as follows:

Sheet coefficient equals extension force in psi/60.000

Formation tonnages for each ft. equals {[575 × (sheet thickness squared)]/

Die breadth} × material coefficient

Sheet coefficient equals 13.000/60.000=0.21

Formation tonnages for each ft. equal [(575 × 0.015625)/0.984] × 0.21 = 1.917 tons for each ft.

For the calculation of the punch tonnages some land space is needed in the midst of 0.03-inch punch and work-piece more than 12 inch or 1 foot. So for the calculation of the punching tonnages, once more the material coefficient for the 0.30mild aluminum is incorporated.

 Land space equals punch radii multiplied by 12.

Punching tonnages equal land space multiplied by sheet thickness × 25 × sheet coefficient.

Land space equals 0.03×12=0.36

Punching tonnages within land space equal 0.36 × 0.125 × 25 × 0.30 = 0.337

Thus, each ft. formation requires 1.917 tons and just 0.337 tons within the land space (1 foot width with 0.03 inch deepness) for punches to puncture the materials. For the formation of such material 568 % of tons is demanded compared to punches to pierce the sheet starting the formation of creases towards the bending length. Now, which can be the least acute radii for this case? It can be as follows:

Land space equals 0.172 × 12 = 2.064

Punching tonnages equal 2.064 × 0.125 × 25 × 0.3 = 1.935

Judging from the math calculations the least punching radii not to make bending creased for 13.000-psi materials appear 0.172 inch. Thus, as you see it is near your radii measurements. Perhaps you anticipated 0.033-inch inner radii, yet, if you do not include the radii into your parts, the least accessible float radii must be about 0.172 inch.

There are principles guiding us to the precise bend, though there might always be an exception. If the material extension force is great, the floating inner radii will be large as well. Yet, in your case you deal with lower extension-force materials and the least acute radii seems rather great.

To achieve and maintain the radii, required for your task, make sure the punching nose radii is close to your desired radii as far as possible.     

Accurate Estimation- More Improved Work Pieces

You are surely right about making precise calculations prior to experimental bend, regardless of handling with more than one bending under different angles. Certainly, in case of changing bending angles, radii will change as well. Back spring (bending angles vs. bent angles) makes its effects. Besides, while bending sheets in dies, radii formation is far from being ideal. Virtually, at this point you get parabolas, which are the result of deep-radii bending, where the radii are ten times as thick as the sheet.

Note that these relate to air formation. For bottom and coin formation inner radii develop in accordance with other estimations or procedures. While bottom forming the inner radii weaken after pressures get released, just as back spring weakens as the loading releases. 

Various angles, impact of parabolas, radius in bottom and coin formation- all these can be calculated under various facts and this is going to be a matter of our tackling for further.