Deep drawing turns a flat sheet of metal into a hollow cup, can, sink, or fuel tank by pushing it through a die with a punch. Unlike stamping (which mostly cuts and bends), deep drawing actually stretches and flows the material. The metal in the flange is squeezed circumferentially as it's pulled radially inward, then bent over the die radius into the cup wall. Get the geometry or lubrication wrong and you get one of three classic failures: tearing at the punch corner, wrinkling in the flange, or earing (wavy rim) from anisotropic grain structure.

Three parameters dominate the process:

• Drawing ratio (DR): blank diameter ÷ punch diameter. Above ~2.0 for a single pass, the wall stress exceeds the tensile strength and the cup tears off at the bottom corner. Aluminum cans achieve DR ≈ 1.7 in the first draw, then use ironing passes to thin the wall.
• Blank holder force: a ring presses the flange against the die to prevent wrinkles. Too little force → wrinkles. Too much → tearing because the metal can't flow inward fast enough. The sweet spot is usually 0.5–1.5% of the blank's yield strength times its area.
• Die radius: the rounded edge the metal bends over. A radius of 6–10× sheet thickness is typical. Too sharp and the metal thins catastrophically; too generous and wrinkles form because the flange isn't constrained.

Rule of thumb — maximum single-pass drawing ratio: DR_max ≈ 2.0 for low-carbon steel, 1.8 for aluminum, 2.2 for deep-drawing steel (DDQ grade). For deeper cups, use multiple draws with annealing between stages to reset the work hardening.

Example — a stainless steel cookware pot. You want a 200 mm diameter pot, 100 mm tall, from 1.2 mm 304 stainless. Required blank diameter (by surface-area conservation, ignoring wall thinning):

D_blank = √(d² + 4·d·h) = √(200² + 4·200·100) = √120,000 ≈ 346 mm

Drawing ratio = 346 / 200 = 1.73. That's within single-pass territory for 304 (DR_max ≈ 1.9), so one draw will do it — but you'll need aggressive lubrication (drawing compound or chlorinated oil) because stainless galls badly against tool steel dies.

Material choice matters enormously. The key property is the Lankford coefficient (r-value): the ratio of width strain to thickness strain in a tensile test. High r-value means the metal would rather get narrower than thinner — exactly what you want for deep drawing. DDQ steel hits r ≈ 1.8; ordinary cold-rolled steel only ≈ 1.0; pure aluminum struggles at ≈ 0.6, which is why beverage cans use specific 3004/5182 alloys engineered for formability.