Manufacturing · Chapter 4 of 10 · Intermediate
Sheet-Metal Forming
Car bodies, cans, and chassis all start as flat sheet. Cut it, fold it, and draw it into cups, but watch for the springback and tearing that fight you the whole way.
Readiness check
This chapter applies forces and strains to thin sheet. Tick only what you can do closed-notes.
- Compute a perimeter and an area.
- Recall shear strength relative to tensile strength.
- Distinguish elastic from plastic deformation.
- Work in radians for angles.
- Recall yield and tensile strength.
The core idea
Sheet metal is cut by shearing and shaped by bending and drawing, with a constant nuisance: the elastic part of the deformation springs back when the tool releases.
Fshear = L·t·τBA = α(R + k·t)Fdraw = πdpt·UTS(D₀/dp − 0.7)Shearing forces a crack across the thickness to cut a blank. Bending folds the sheet along a line, but because part of the strain is elastic, the sheet springs back to a larger radius when released. Deep drawing pulls a flat blank into a cup, limited by tearing if the reduction is too severe and wrinkling if the blank is not held down. Each operation has a force and a limit you can compute.
The skills, taught in order
Sheet forming is a handful of operations with their own forces and limits. Five skills cover shearing, bending, springback, drawing, and formability.
4.1 Shearing
Blanking and punching cut the sheet by shearing it across the thickness. The force is F = L·t·τ, the cut perimeter times thickness times shear strength (τ ≈ 0.7·UTS). Punch-die clearance, a few percent of thickness, controls the cut-edge quality.
4.2 Bending
Bending folds the sheet along a straight line. The neutral axis lies near the inside, so the developed (flat-pattern) length of the bend is the bend allowance BA = α(R + k·t), with α the bend angle in radians and k ≈ 0.33 to 0.5. Too tight a radius cracks the outer fibres, setting a minimum bend radius.
4.3 Springback
Because part of the bending strain is elastic, the sheet unbends slightly when the tool releases: the angle opens and the radius grows. Stronger, thinner, or larger-radius bends spring back more. Engineers compensate by overbending, or by coining the bend to set it plastically.
4.4 Deep drawing
Deep drawing pulls a flat blank through a die with a punch to form a cup. The drawing ratio DR = D₀/dp must stay below the limiting drawing ratio (about 2), or the wall tears. The force is F = πdpt·UTS(D₀/dp − 0.7), and a blank-holder prevents the flange from wrinkling.
4.5 Formability
How far a sheet can stretch before it necks is captured by the forming-limit diagram, a map of safe strain combinations. Anisotropy from rolling causes earing (wavy cup rims) and changes drawability. Good formability needs ductility and the right texture.
| Defect | Cause | Remedy |
|---|---|---|
| Springback | elastic recovery on release | overbend or coin the bend |
| Tearing | drawing ratio too high | smaller reduction, redraw in stages |
| Wrinkling | too little blank-holder force | increase hold-down pressure |
| Earing | planar anisotropy | control the rolling texture |
Engineering connection: car panels, beverage cans, enclosures, and brackets are stamped, bent, and drawn from sheet, where springback and tearing decide whether the press tool works on the first try.
Worked example 1: blanking force
A 50 mm diameter disk is blanked from 2 mm steel sheet with tensile strength 400 MPa (shear strength about 0.7 of that). Find the blanking force.
- ProblemFind the blanking force for the disk in Figure 1.
- Given / findD = 50 mm, t = 2 mm, UTS = 400 MPa, τ ≈ 0.7·UTS. Find F.
- AssumptionsClean shear around the full perimeter, shear strength about 0.7 of tensile strength.
- ModelForce is the sheared area (perimeter times thickness) times the shear strength.
- Equationsτ = 0.7·UTS F = (πD)·t·τ
- Solveτ = 0.7 × 400 = 280 MPa. Perimeter = π × 50 = 157.1 mm. F = 157.1 × 2 × 280 = 87 970 N ≈ 88 kN.
- CheckForce scales with perimeter and thickness, so a thicker sheet or larger blank needs proportionally more. Grinding a shear angle onto the punch would spread the cut over time and cut the peak force, a standard press trick.
- ConclusionBlanking force comes straight from geometry and shear strength. It sizes the press tonnage, the first number a stamping engineer needs.
Worked example 2: deep drawing a cup
A cup is drawn from a 100 mm diameter blank, 1 mm thick (UTS = 350 MPa), with a 55 mm punch. Check the drawing ratio against the limit, and find the drawing force.
- ProblemCheck the drawing ratio and find the drawing force for the cup in Figure 2.
- Given / findD₀ = 100 mm, dp = 55 mm, t = 1 mm, UTS = 350 MPa. Find DR and F.
- AssumptionsSingle draw, adequate blank-holder force, the standard drawing-force estimate applies.
- ModelDrawing ratio from the diameters (compare with the limit ~2), then the empirical drawing-force formula.
- EquationsDR = D₀/dp F = πdpt·UTS(D₀/dp − 0.7)
- SolveDR = 100/55 = 1.82, below the limiting ratio of about 2, so a single draw is feasible. F = π × 55 × 1 × 350 × (1.82 − 0.7) = π × 55 × 350 × 1.12 = 67.6 kN.
- CheckThe 1.82 ratio leaves a modest margin to the tearing limit; a deeper cup would need a redraw. The force is far below the blanking force of the previous example, as drawing strains rather than cuts the metal.
- ConclusionDrawing is limited by tearing (drawing ratio) and wrinkling (blank-holder force), not just by tonnage. Deep cups are made in several draws, each within the ratio limit.
Misconceptions and diagnostics
| Mistake | Symptom | Diagnostic question | Correction |
|---|---|---|---|
| Ignoring springback | Bend angle comes out too shallow | "Did I overbend to compensate?" | Overbend or coin; the elastic part recovers on release. |
| Drawing ratio too high | Cup wall tears | "Is DR below about 2?" | Redraw in stages, each within the limiting ratio. |
| No blank-holder | Flange wrinkles | "Is the flange held down?" | Apply enough blank-holder force to suppress wrinkles. |
| Flat pattern ignores bend allowance | Part comes out the wrong length | "Did I add the bend allowance?" | Develop the flat length with BA = α(R + k·t). |
Practice ladder
Punch a 20 mm square hole in 1.5 mm sheet of shear strength 250 MPa. Find the punching force.
Show answer
Perimeter = 4 × 20 = 80 mm. F = L·t·τ = 80 × 1.5 × 250 = 30 000 N = 30 kN. Perimeter, not area, drives shearing force.
Find the bend allowance for a 90° bend (α = π/2) with inside radius 6 mm in 3 mm sheet, taking k = 0.4.
Show answer
BA = (π/2)(6 + 0.4 × 3) = 1.571 × 7.2 = 11.3 mm. This is the developed length added at the bend when laying out the flat pattern.
A cup needs a 40 mm punch from a 95 mm blank. Is a single draw feasible, and if not, what is the fix?
Show answer
DR = 95/40 = 2.38, above the limiting ratio of about 2, so a single draw would tear. Draw in two stages: a first draw to an intermediate diameter (DR ≈ 1.8), then a redraw, keeping each within the limit.
Find a sheet-metal product (a can, a bracket, a car panel). Identify which operations made it, and where springback or tearing would have been a design concern.
What good work looks like
The operations identified (blank, bend, draw), a force or ratio estimated, and a springback or drawing-ratio concern named with how it was managed.
Working with AI, and proving it yourself
Use AI as an examiner, not a solver
Portfolio task
Plan the sheet-metal forming of one part: size the blanking force, develop a flat pattern with bend allowance, and check any draw against the limiting ratio.
Retrieval and spaced review
Closed notes. Answer out loud, then reveal.
1. Write the shearing force.
F = L·t·τ, perimeter times thickness times shear strength (τ ≈ 0.7·UTS).
2. What is springback, and how is it handled?
Elastic recovery that opens a bend on release; compensate by overbending or coining.
3. Give the bend allowance.
BA = α(R + k·t), the developed length of the bend.
4. What limits deep drawing?
Tearing if the drawing ratio exceeds about 2, and wrinkling without enough blank-holder force.
5. What does the forming-limit diagram show?
The combinations of strains a sheet can take before necking.
Textbook mapping
| Item | Mapping |
|---|---|
| Primary source | Kalpakjian and Schmid, Manufacturing Engineering and Technology, Chapter 16 (Sheet-Metal Forming) |
| Cross-reference | Groover, Ch. 20 · DeGarmo, sheet-metal chapters |
| Core topics | 4.1 Shearing · 4.2 Bending · 4.3 Springback · 4.4 Deep drawing · 4.5 Formability |
| Engineering connection | Car panels, cans, enclosures, and brackets. |
| Read next | Chapter 5: Theory of Metal Cutting. |