Sheet Metal Forming
Bend allowance and K-factor, springback, minimum bend radius, blanking force and deep drawing.
The sheet metal processes
Sheet metal (0.3 to 6 mm thick) is cut and formed into brackets, enclosures, guards, panels and tanks. The steps are: cutting (laser, plasma, waterjet, punching, shearing: see Laser Cutting), forming (bending on a press brake, rolling, stretching, drawing, spinning), joining (welding, spot welding, riveting, clinching, bolting: see Welding Processes and Weld Design) and finishing (deburr, powder coat, plating). Press-brake bending and laser cutting dominate low-volume work; stamping and drawing dominate high volume.
Bending, K-factor and bend allowance
When sheet is bent, the inside surface is compressed and the outside is stretched. Somewhere between is the neutral axis, which keeps its original length; it lies at a distance K × t from the inside surface, where the K-factor is 0.33 to 0.5 (lower for tight bends and hard material). The length of the flat blank needed is the sum of the straight legs plus the bend allowance for each bend:
BA = (π ÷ 180) × θ × (R + K t) setback = tan(θ ÷ 2) × (R + t) bend deduction BD = 2 × setback − BA
Worked example: a guard bracket
Worked example: a U-channel guard of 3 mm steel
A U-shaped guard for the press has outside dimensions 50 mm, 100 mm and 50 mm, with two 90° bends of inside radius 3 mm in 3 mm steel (K = 0.40).
- Bend allowance BA = (π ÷ 2) × (3 + 0.40 × 3) = 6.60 mm.
- Outside setback = tan 45° × (3 + 3) = 6.0 mm; bend deduction = 2 × 6.0 − 6.60 = 5.40 mm.
- Flat blank length = (50 + 100 + 50) − 2 × 5.40 = 189.2 mm. Check: legs 50 − 6 = 44, web 100 − 12 = 88, flanges 44, plus two bends 2 × 6.60 = 13.19: total 189.2 mm.
- The press-brake force for a 1 m bend in a V-die of width 8 t = 24 mm and UTS 400 MPa: F ≈ 1.33 × UTS × L × t² ÷ W = 200 kN per meter (about 20 tonnes-force). The force rises with t² and falls with the die width.
- Use the Sheet-Metal Bend Allowance Calculator for other angles, radii and K-factors.
Springback
After the load is removed the bent metal relaxes slightly (the elastic part of the strain recovers), so the angle opens up. The ratio of the initial to the final radius is Ri ÷ Rf = 4 (Ri σy ÷ (E t))³ − 3 (Ri σy ÷ (E t)) + 1, which shows that springback grows with the yield strength and the bend radius and falls with the modulus and the thickness. A tight bend (R = t) springs back little; a gentle bend (R = 10 t) a lot:
| Material | Springback at R = t | at R = 5 t | at R = 10 t |
|---|---|---|---|
| Mild steel (σy 250, E 210) | 0.21° | 1.46° | 3.07° |
| Aluminum 5052-H32 (195, 70) | 0.50° | 3.43° | 7.18° |
| Stainless 304 half-hard (500, 193) | 0.47° | 3.19° | 6.68° |
Compensate by over-bending (bending to 90° − springback), by bottoming or coining (pressing the metal into the die to set it), or by stretching the sheet while bending. High-strength steels and stainless spring back more; always test a bend on a scrap piece.
Minimum bend radius and grain
| Material | Minimum inside radius (typical) |
|---|---|
| Mild steel (low carbon), annealed | 0.5 t |
| Stainless 304, annealed | 0.5 to 1 t |
| Aluminum 5052-H32 | 1 t |
| Aluminum 6061-T6 | 3 to 4 t (crack-prone) |
| Aluminum 6061-O | 0.5 t |
| Copper, soft | 0.5 t |
| Brass, half hard | 1 t |
| Titanium Ti-6Al-4V | 4 to 6 t (warm form) |
Rolled sheet has a grain direction; bends made across the grain tolerate a smaller radius than bends along it (cracks open along the grain). Bend lines are oriented at 90° to the rolling direction where possible. Cracks on the outside of a bend mean the radius is too small, the metal is too hard (a T6 temper) or the edges of the blank are rough: use a larger radius, an annealed temper, or deburr the edge.
Shearing and blanking force
Cutting sheet in a die or with shears is shear failure of the metal along the cutting edge: the force is F = L t τ, with L the length of the cut (the perimeter for a blank or a hole), t the thickness and τ the shear strength, about 0.8 times the tensile strength. The clearance between punch and die is 5 to 10 percent of the thickness per side; the cut edge shows a burnished band, a fracture zone and a burr.
Worked example: blanking a 100 × 50 mm plate and punching a hole
- Perimeter 300 mm in 3 mm steel (UTS 400 MPa, τ = 320 MPa): F = 300 × 3 × 320 = 288 kN (29 tonnes-force). A press of about 35 tonnes (with a 20 percent margin) is needed. A shear angle on the punch (an inclined edge) cuts the peak force by 30 to 50 percent (144 kN with an angle that halves it) at the cost of a longer stroke.
- Punching a 10 mm hole in the same plate in 304 stainless (UTS 600 MPa): F = π × 10 × 3 × 0.8 × 600 = 45 kN.
- Clearance 7 percent of 3 mm = 0.21 mm per side. Laser or waterjet cutting needs no tooling and is preferred for low volumes (the cutting guide covers its settings).
Deep drawing
In deep drawing a punch pushes a flat blank through a die into a cup. The blank diameter follows from the equal-surface-area rule, D = √(d² + 4 d h) for a cup of diameter d and height h; the limiting draw ratio D ÷ d is about 2.0 for a good steel (1.8 to 2.2 for deep-drawing grades) in a single draw, so deeper cups are drawn in stages with annealing between. A blank holder presses the flange to prevent wrinkles, and lubricant reduces friction and tearing.
Worked example: a cup of 60 mm diameter and 40 mm height
- Blank diameter D = √(60² + 4 × 60 × 40) = 114.9 mm; draw ratio 1.91: within the limit of about 2.0, so one draw is possible (but marginal: choose a deep-drawing grade).
- Drawing force (approximate) F = π d t σu (D ÷ d − 0.7) = π × 60 × 1.5 × 400 × (1.91 − 0.7) = 137 kN for 1.5 mm sheet.
- Sheet thickness at the cup corner thins by 10 to 20 percent; the rim thickens. Wrinkling (too little blank-holder force) and tearing (too much, or too high a draw ratio) are the two failures.
Design rules
- Bend radius at least equal to the thickness (or the supplier’s minimum), the same radius on every bend so one tool does all.
- Hole position: at least 2 to 3 t from a bend line and 1.5 t from the edge; features near a bend stretch and distort. Use relief cuts at corners where two bends meet.
- Minimum flange about 4 t plus the radius, otherwise the die cannot grip it.
- Tolerances: ±0.1 to 0.2 mm on cut features; ±0.3 to 0.5 mm and ±1° on bends; plan for adjustment or slotted holes on assemblies.
- Standard sheet sizes and gauges (see the gauge table), standard thicknesses and one material to keep costs down.
- Nesting: design the blanks so that they pack well on the sheet; the cost is dominated by the material and the machine time.
Related
- Previous: Casting, Forging and Powder Metallurgy. Next: Injection Molding and Plastics Processing.
- Sheet-Metal Bend Allowance Calculator and Steel and Plate Weight Calculator.
- Laser Cutting.
- Materials and Processes: the whole guide.
FAQ
What K-factor should I use?
Start with 0.33 to 0.40 for air bending of steel and 0.4 to 0.45 for aluminum; confirm by bending a test piece and measuring. Your press-brake supplier may publish a table.
Why is my bend angle not 90°?
Springback. Over-bend by the amount measured on a test piece, or use bottoming. The spring-back angle varies with the material batch.
Why do holes go oval near a bend?
They are within the deformation zone of the bend. Keep holes at least 2 to 3 times the thickness away, or punch them after bending.
Is laser cutting better than punching?
For low volumes, yes: no tooling, any shape. For thousands of identical parts with many holes, a turret punch or progressive die is faster and cheaper per piece.
References
- Kalpakjian, S., Schmid, S. R., Manufacturing Engineering and Technology, Pearson (sheet-metal forming); Groover, M. P., Fundamentals of Modern Manufacturing, Wiley.
- Machinery’s Handbook, Industrial Press (bending allowances, blanking forces, sheet gauges); Marciniak, Z., Duncan, J. L., Hu, S. J., Mechanics of Sheet Metal Forming.
- ASM Handbook, Volume 14B: Metalworking: Sheet Forming; DIN 6935 (bending of cold-rolled steel), ISO 2768 (general tolerances).
Last reviewed: October 2026. K-factors, radii and springback are typical; test on the real material and press brake.