Extrusion Ratio in Cold Heading: Safe Limits and Die Design

The extrusion ratio is the single number that decides whether a shank reduction can be formed in one blow, needs two, or cannot be cold formed at all. It is also the number most often left off the drawing, which is why shank-reduction dies fail in ways that look like material defects but are really a geometry problem.

What the Extrusion Ratio Measures

The ratio compares the cross-section before forming with the cross-section after forming. If a wire of diameter D0 is reduced to a shank of diameter D1, then the extrusion ratio is the ratio of the two areas, not the two diameters:

R = A0 / A1 = (D0 / D1) squared

A 10 mm wire reduced to 8 mm looks like a 20% reduction in diameter, but it is a 36% reduction in area, and the die sees the area. Confusing diameter ratio for area ratio is the most common mistake we see in incoming enquiries.

Why a Limit Exists at All

Three things break when the ratio gets too large:

• Die pressure. The forming pressure rises roughly with the logarithm of the ratio. Past a point, the pressure exceeds what the die nib and casing can carry, and the failure is a cracked casing rather than a worn bore.
• Punch buckling. A long, slender punch pushing into a hard reduction behaves like a column. It buckles, then it snaps, usually at the transition.
• Material ductility. The wire has to flow. Beyond its capacity it tears internally, and the part passes dimensional inspection while carrying a hidden crack.

For a well-annealed low-carbon wire in a single blow, the practical ceiling sits around 1.4 to 1.5. Above that the process becomes unreliable even if the press has the tonnage.

Safe Ranges by Material

These are the working limits we use when quoting. They assume good quality wire, proper lubrication and a die with a generous approach angle.

Material	Single blow, max R	Notes
Low carbon steel (1008-1018)	1.4-1.5	Most forgiving, annealed condition
Medium carbon (1035-1045)	1.3-1.4	Spheroidise anneal improves the ceiling
Boron steel (10B21, 10B38)	1.3-1.4	Common for property class 8.8 and 10.9
Alloy steel (40Cr, 35CrMo)	1.25-1.35	Two blows usually cheaper than one hard blow
Stainless (304, 316)	1.2-1.3	Work hardens fast, keep the reduction conservative
Copper T2 / brass	1.5-1.6	Very ductile, but galling risk is high

Worked Example: M10 Flange Bolt

Take an M10 flange bolt with a reduced shank. Wire diameter 9.6 mm, shank diameter 7.2 mm.

Area ratio: (9.6 / 7.2) squared = 1.78. That is well past the single-blow ceiling for medium carbon steel, so a one-blow shank die will either crack its casing or tear the part internally.

Four ways to make it work, in the order we would evaluate them:

• Split the reduction across two stations. 9.6 to 8.3 in the first blow, 8.3 to 7.2 in the second. Each step stays under 1.4. This is the cheapest fix on a multi-station former.
• Reduce the starting wire. If the head can still be formed, a 9.0 mm wire brings the ratio down to 1.56, close enough to try.
• Change the material condition. Spheroidise annealing buys roughly 0.1 of ratio, and costs a process step.
• Use a split die. When the shank also has a feature that will not release from a solid die, the split dies solves the release problem and the reduction in one step.

When the Ratio Exceeds the Limit

If a customer insists on one blow, we will say no and explain why. The failure mode of an over-loaded shank die is not a worn die, it is a cracked casing and a damaged machine, and the cost lands on the customer. The honest alternatives are always one of these four: more stations, smaller wire, softer material, or a different die architecture.

Die Design Details That Move the Limit

The ratio is set by the part, but the achievable ratio is set by the die. Five details matter:

• Approach angle. A 15 to 20 degree half-angle keeps the work of deformation low. A blunt entry raises pressure sharply for the same reduction.
• Land length. Long enough to size the shank, short enough to avoid friction build-up. Typically 1.0 to 1.5 times the shank diameter.
• Relief behind the land. Prevents the shank from being dragged back through a tight bore on withdrawal.
• Entry radius. A radius instead of a chamfer removes the stress concentration where ring cracks start.
• Coating and lubricant. A TiAlN or similar coating plus the right lubricant can effectively buy 0.05 to 0.1 of ratio by reducing friction at the interface.

Together these are worth more than a grade change. A correctly profiled HSS die will out-perform a badly profiled carbide one on a marginal reduction, and cost less doing it. The die material selection guide covers how the grade interacts with these choices.

Send the Drawing

Send us the bolt drawing, the wire grade and the machine model. We will calculate the ratio at every step, tell you whether one blow is realistic, and if not, propose the station split. For the forming side rather than the reduction side, see cold heading dies and cold forging die.

To check a specific reduction before you send us anything, use the free extrusion ratio calculator — it returns the area ratio, true strain, minimum blow count and a suggested station split.