Deep Drawing

From flat disc to seamless cup

Deep drawing converts a flat sheet-metal blank into a hollow, three-dimensional shape with no seams, welds or joints. The four essential tools are the punch (which has the shape of the inside of the finished part), the die (a ring with a rounded opening), the blank holder or binder (which clamps the flange against the die face) and the flat blank itself. The punch descends, pinches the centre of the blank, and pulls it down through the die radius. Metal that started in the flange is dragged radially inward, around the die radius, and up the cup wall.

The defining feature — and the reason it is called drawing rather than stretching — is that the blank is allowed to flow. The flange feeds material into the cup. Wall area grows mostly because metal is pulled in, not because the trapped sheet is thinned under tension. That distinction is the single most important idea in the process: a good deep draw moves a lot of metal a long way with very little thinning.

What the metal actually does

Picture an annular element in the flange, partway between the rim and the die opening. As the punch pulls metal inward, that element moves toward a smaller radius. Its circumference has to shrink, so it experiences circumferential (hoop) compression. At the same time the punch tension pulls it radially, so it sees radial tension. The compression is what wants to buckle the flange into folds; the tension is what draws it in. The blank holder exists purely to keep that compression from turning into wrinkles.

Once an element rounds the die radius and becomes part of the wall, the situation flips: the wall is in nearly pure axial tension, carrying the load that drags the whole remaining flange in. Because the wall is loaded but not being thickened, it is the weakest link. The flange, by contrast, thickens slightly as it is compressed inward — a finished cup is therefore thinnest at the bottom corner (just above the punch nose) and thickest at the rim, often 10–15% thicker than the original blank there.

Draw ratio and the limiting draw ratio

The amount of metal that must be gathered is captured by the draw ratio:

DR = D / d

where:
  D = blank diameter   (the flat disc you start with)
  d = punch / cup diameter (the cup you end with)

A DR of 1.0 means no drawing at all; the blank is already cup-sized. A DR of 2.0 means the blank is twice the cup diameter, so the flange area is four times the cup-bottom area and all of it must flow in. There is a hard ceiling: the limiting draw ratio (LDR) is the largest DR a material can survive in one stroke before the wall tears.

LDR ≈ 1.8 – 2.2 for a single draw

LDR rises with the plastic strain ratio (Lankford r-value):
  r ≈ 0.6  (aluminum)        → LDR ≈ 2.0
  r ≈ 1.4  (drawing steel)   → LDR ≈ 2.2
  r ≈ 1.8  (DDQ / IF steel)  → LDR ≈ 2.3

The r-value — the ratio of width strain to thickness strain in a tensile test — measures a sheet's resistance to thinning. A high r-value means the metal would rather draw in from the flange than thin in the wall, which is exactly what you want. This is why deep-drawing-quality (DDQ) and interstitial-free (IF) steels are texture-engineered during rolling and annealing to maximise r, and why the same blank diameter that draws cleanly in steel will tear in aluminum.

The drawing force and the blank-holder force

The peak punch force needed to draw a cup is approximated by the empirical relation:

F = π · d · t · UTS · (D/d − C)

where:
  d   = punch diameter (m)
  t   = blank thickness (m)
  UTS = ultimate tensile strength of the sheet (Pa)
  D/d = draw ratio
  C   = a constant ≈ 0.6 – 0.7 covering friction and bending losses

The blank-holder force is the other dial. It is usually set as a fraction of the drawing force — a common rule of thumb is one-third of the punch force — or specified directly as a holder pressure of roughly 0.7–3.0 MPa across the flange area. Set it too low and the flange wrinkles; set it too high and the flow is choked, the wall over-stresses, and the cup tears at the nose. The drawing operation is a balancing act between these two failure modes, and the safe span between them is the process window.

Worked example: force to draw a steel cup

Draw a 100 mm diameter cup from a 180 mm blank of 1 mm mild steel (UTS ≈ 350 MPa). First check the draw ratio, then estimate the punch force.

Draw ratio:
  DR = D / d = 180 / 100 = 1.8   →  below LDR (2.2 for DDQ steel) ✓

Drawing force (take C = 0.6):
  F = π · d · t · UTS · (D/d − C)
    = π · 0.100 · 0.001 · 350×10⁶ · (1.8 − 0.6)
    = π · 0.100 · 0.001 · 350×10⁶ · 1.2
    = π · 42,000
    ≈ 1.32 × 10⁵ N
    ≈ 132 kN  (about 13.5 tonnes-force)

Blank-holder force (≈ 1/3 of draw force):
  F_BH ≈ 44 kN

A 132 kN punch force means a press of at least ~15 tonnes capacity with comfortable margin. Notice how the force scales: it is linear in diameter, thickness and strength, but climbs steeply with draw ratio because (D/d − C) grows. Push DR from 1.8 toward 2.2 and the term (D/d − C) rises from 1.2 to 1.6 — about a third more punch force — while the wall, which must carry that load, is not getting any stronger. That is part of why the LDR ceiling exists: beyond it the wall simply cannot carry the load.

Deep drawing versus related sheet processes

	Deep drawing	Stretch forming	Ironing	Spinning	Hydroforming
Metal flow	Flange flows inward	Edges locked, metal stretches	Wall squeezed thinner & longer	Metal flows over a mandrel	Fluid pressure pushes sheet into die
Dominant stress	Radial tension + hoop compression	Biaxial tension	Compression between die & punch	Local bending + tension	Tension under hydrostatic pressure
Wall thickness	Roughly preserved (rim thickens)	Thins everywhere	Deliberately thinned	Roughly preserved	Mostly preserved
Key material number	r-value (anisotropy)	n-value (hardening)	Ductility	Ductility, r-value	r and n value
Limiting defect	Wrinkling / tearing	Necking / splitting	Wall fracture	Wrinkling, buckling	Bursting, wrinkling
Typical part	Cans, sinks, cups, casings	Car door & roof panels	Beverage-can wall	Rocket domes, cones, cookware	Exhaust & chassis tubes

Tooling geometry that makes or breaks a draw

• Die radius. The rounded entry of the die. Too sharp and metal is over-bent and tears; too generous and the unsupported flange between holder and die can wrinkle. A common starting point is a die radius of 6–10× the sheet thickness.
• Punch nose radius. Too small a corner concentrates strain at the cup bottom — the classic tearing site. Punch radii are usually 4–10× the sheet thickness.
• Clearance. The gap between punch and die is set slightly larger than the sheet thickness, typically 1.07–1.15 t, to allow the rim's natural thickening to pass without ironing (unless ironing is intended).
• Draw beads. Ridges in the binder surface that the sheet must bend over. They add a controllable restraining force, used on irregular automotive panels to balance flow around the perimeter.
• Lubrication. Drawing oils, dry-film soaps or polymer films cut friction at both the die radius and the holder face. Friction directly raises the punch force and shrinks the process window, so lubrication is not optional — it is a process parameter.

Failure modes and trade-offs

• Wrinkling. The flange buckles into radial folds under hoop compression. Cause: blank-holder force too low, or holder pressure unevenly distributed. Fix: raise holder force or add draw beads — but only up to the point where tearing begins.
• Tearing (fracture). A ring crack just above the punch nose where the wall carries peak tension. Cause: draw ratio above LDR, holder force too high, sharp punch radius, or poor lubrication. Fix: reduce DR (use redrawing), ease the punch radius, lubricate, or pick a higher-r material.
• Earing. A scalloped, wavy rim caused by planar anisotropy (Δr) — the r-value varying with direction in the sheet. Ears waste material and must be trimmed. Fix: control rolling texture; minimise Δr in the sheet spec.
• Springback & non-uniform wall. Elastic recovery and uneven flow leave dimensional error and a wall thinner at the bottom than the rim. Managed with overdraw, calibration strokes and tooling tuning.
• Galling & scoring. Metal pickup on the tool surface drags scratches down the wall. Fix: harder/coated tooling (e.g. nitrided or TiN-coated dies) and better lubrication.

When one stroke is not enough: redrawing and ironing

If the target cup is deeper than the LDR permits, it cannot be made in a single draw. Instead the part is formed in stages. A first draw produces a shallow, wide cup well inside the LDR; successive redraws push that cup through progressively smaller dies, each adding depth and reducing diameter. Because the metal work-hardens with each operation, redraw ratios are smaller — about 1.2 to 1.6 — and an intermediate anneal may be needed to restore ductility for very deep parts.

For thin-walled cylinders the wall itself is then deliberately thinned by ironing: forcing the cup through one or more ring dies whose gap is smaller than the wall, squeezing it longer and thinner at constant volume. The aluminum beverage can is the showcase: a coil of 0.25 mm aluminum is blanked, drawn into a shallow cup, redrawn, then ironed through three carbide rings in a single high-speed bodymaker that produces a can with a wall as thin as 0.10 mm — at hundreds of cans per minute. The thick base resists internal pressure; the gossamer wall saves metal. That entire shape is one continuous, seamless piece of drawn metal.