Sheet metal bending and springback

A drawing says 40 mm, 60 mm and a 90° bend. Add them up, cut a 100 mm blank, bend it, and the part is too long and the angle is not 90°. Both errors are normal, both are predictable, and this topic is about where they come from.

The flat pattern — why addition does not work

Bend the sheet and the outside of the bend is stretched, the inside is compressed, and somewhere between them a line neither stretches nor shortens. That line is the neutral axis, and the flat blank has to be developed along it.

The K-factor is where that neutral axis sits, as a fraction of the thickness measured from the inside surface:

Inside radius ÷ thickness	Typical K-factor
0.5	0.33
1.0	0.38
2.0	0.42
3.0 and above	0.44 – 0.46

The sharper the bend, the further the neutral axis moves towards the inside surface, and the more developed length the bend consumes. A tight bend eats more blank than a generous one.

Springback — the part that relaxes

Only part of the strain in a bend is permanent. When the punch lifts, the elastic component recovers and the angle opens. Nothing has gone wrong.

The size of the recovery scales roughly with yield strength ÷ elastic modulus. Every steel grade has close to the same modulus, so:

Material	Typical yield	Relative springback
Mild steel (DC01)	200 MPa	Baseline
HSLA 420	420 MPa	About double
Dual phase 780	780 MPa	Three to four times
6061-T6 aluminium	275 MPa, and a third the modulus	Substantially more again

Overbending is the production answer: form past the nominal angle so the recovery lands on the drawing. The amount is settled on the first parts, not calculated exactly.

Three ways to make the bend, and what each buys

Method	How the angle is set	Tonnage	Angle consistency
Air bending	Punch depth over a die opening	Lowest	Sensitive to material variation
Bottoming	Sheet pressed onto the die faces	3 – 5× air	Good
Coining	Sheet forced to take the punch radius	5 – 10× air	Best, and repeatable batch to batch

Air bending is flexible — one set of tools, any angle — and that flexibility is exactly why it follows every wobble in incoming material thickness and strength. Coining removes the variation by overpowering it, at a tonnage most parts do not justify.

Two things that crack the outside of a bend

Too small a radius. Strength is normally bought with ductility, and the outer fibre of a tight bend is the most strained material in the part. A mild steel may take an inside radius of one thickness or less; an advanced high strength grade routinely needs three to four.

Bending along the rolling direction. Rolling stretches grains and inclusions into lines. A bend running parallel to those lines opens the outer fibre along them.

Prove the pattern on a part

The calculated allowance is a starting point. The real K-factor depends on the tooling, the bending method and the material batch, and the same nominal grade from two suppliers will not develop identically.

So the first-off exists to correct the flat pattern, not to confirm it — which is the same argument as agreeing the inspection method before production in measurement and gauging.

What to take away

• The blank is developed along the neutral axis; adding flange lengths always over-counts.
• The K-factor locates that axis, around 0.33 – 0.45, moving inwards as the bend tightens.
• Springback is elastic recovery. It is normal, and it is designed around, not removed.
• Springback scales with yield ÷ modulus — a stronger steel springs back further.
• Overbend so the part relaxes onto the drawing angle.
• Air bending is flexible and variable; coining is consistent and expensive.
• Stronger material needs a larger minimum inside radius, not a smaller one.
• Bend across the rolling direction, or open the radius if you cannot.
• The flat pattern is proved on the first part. Calculation gets you close.