Minimum bend radius for wire: a practical table by material and temper

Which radius the drawing means

A wire drawing can show three different radii, and they are not interchangeable. The inside radius is the radius of the tool that touches the inside of the bend. The centreline radius is the inside radius plus half the wire diameter. The outside radius is the inside radius plus the full wire diameter. Most forming discussions use the inside radius, because that is what the tool sets.

The distinction matters because the strain on the outside of the bend depends on both the inside radius and the wire diameter. A 0.5 mm inside radius is generous on 0.2 mm wire and severe on 2 mm wire. That is why the table in this guide expresses the limit as a multiple of the wire diameter rather than as a fixed number of millimetres.

For a helical spring there is a second convention. Spring design uses the spring index, which is the mean coil diameter divided by the wire diameter. A spring index of 4 corresponds to an inside radius of 1.5 wire diameters, so the two conventions meet if you convert carefully.

The strain behind the number

When a wire is bent, the inside of the bend shortens and the outside stretches. The engineering strain on the outside fibre can be estimated as the wire radius divided by the sum of the inside radius and the wire radius. In symbols, strain equals r divided by R plus r, where r is half the wire diameter and R is the inside radius.

For an illustrative example, take 1.2 mm music wire bent to an inside radius of 0.9 mm. The wire radius is 0.6 mm, so the strain is 0.6 divided by 1.5, which is 0.40, or 40 per cent. At an inside radius of 1.8 mm the strain falls to 0.6 divided by 2.4, which is 25 per cent. The radius doubled, but the strain did not halve, because the wire radius stays in the denominator.

That strain is a forming strain, not a working stress. A part can be formed at a strain well above its elastic limit and still work, because forming is a one-time event. The practical limit is cracking, orange peel or a loss of section on the outside of the bend. Fatigue and spring rate are separate calculations.

Starting radii by material and temper

The table gives starting values for the inside bend radius as a multiple of the wire diameter. They assume a single bend at room temperature, a good surface, and a tool that supports the wire on both sides of the bend. They are not a substitute for a trial on the actual lot of wire.

Temper matters more than the alloy name

Two wires with the same alloy name can behave very differently. Annealed 316 bends like soft copper. Spring temper 316 is a different material in practice: higher yield strength, more springback and a much larger practical radius. The alloy sets the corrosion and electrical behaviour. The temper sets the forming behaviour.

This is why a drawing that says only 316 stainless is incomplete. The supplier has to guess whether the part is a spring or a trim piece. If the answer is a spring, the temper is half hard or spring temper and the radius call has to reflect it. If the answer is a cover or a trim, annealed material may be correct and the radius can be tighter.

The same logic applies to music wire and oil tempered wire. They are both high carbon spring steels, but the oil tempered grade is available in larger diameters and behaves differently at the same radius. State the standard and the temper, not just the trade name.

Radius, springback and the tool

The radius on the drawing is the radius after the tool is removed, not the radius of the tool. Every bend recovers elastically when the load is released, so the tool has to be made tighter than the finished part. The amount of recovery rises with the yield strength and the radius, and falls with the wire diameter and the elastic modulus.

A high tensile music wire at a radius of 1.5 diameters may need an overbend of a few degrees to finish at the required angle, and the tool radius may need to be slightly tighter than the drawing. That correction is normally found by trial on the machine, not calculated once and fixed forever, because wire lots and tool wear move it.

The practical consequence for the designer is that the radius call should be a nominal with a tolerance, not an absolute. If the radius is functionally important, say so and give the band. If it is not, let the supplier use a standard tool radius and put the tolerance on the features that locate the part.

When the design needs a radius below the guide

Sometimes the envelope forces a tight bend. A clip that has to sit inside a 2 mm gap cannot use a 3 mm inside radius. In that case, the options are technical rather than commercial, and they need to be decided before the drawing is released.

None of these options is free. A softer temper may need a post-form heat treatment. A split bend adds a bend to the sequence. A gusset adds a weld. The point is to choose the cost deliberately rather than discover it in the first article.

• Increase the radius and recover the space elsewhere, for example by moving the bend or reducing the leg length.
• Switch to a softer temper or an annealed condition, then stress relieve or age harden after forming if the part needs strength.
• Form at a high temperature for materials that tolerate warm working, with the process agreed by the supplier.
• Split the bend into two larger radii with a short straight between them, which lowers the strain at each bend.
• Use a larger radius and add a gusset, a welded rib or a second wire to recover stiffness without a tight bend.
• Accept a tighter radius with a defined inspection for cracking, and agree the sampling and the reject rule.

What to put on the drawing

State the wire standard, the grade and the temper. Give the wire diameter with its tolerance class. Dimension the inside radius at each bend, or give a minimum inside radius in a general note and call out the exceptions. If a bend is functionally critical, give it a tolerance and say what it controls.

Add a note on the bend direction if the part is asymmetric, and identify the datum leg. If the part is a spring, give the free length, the load at a stated deflection and the spring rate rather than a chain of linear dimensions. If the part is plated after forming, say whether the plating thickness is included in the finished diameter.

Finally, ask for a bend trial or a first article that reports the radius and the angle at each bend. A first article that reports only the overall length does not prove that the bends are inside the process window.

What to ask before you commit

Ask the supplier three questions. What radius will you use at each bend, and is it a standard tool? What overbend will you apply, and how will you confirm the finished angle? What is the reject risk at the tightest bend, and how will you inspect for cracking?

The answers tell you whether the quote is built on a standard setup or on a special one. They also give you a record to compare against the first article. A supplier who can answer those questions has already done the DFM review that the drawing needs.