BIZOMAT MAKEOS · Fabrication
Minimum and Maximum Bend Radius
What is the smallest bend radius this sheet takes without cracking, and the largest that still forms permanently?
Minimum inside bend radius from the material’s reduction of area in a tensile test, and the maximum radius that still produces permanent (plastic) deformation, by the handbook formulas.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Material thickness | mm | Sheet or plate thickness. |
| Reduction of area in a tensile test | % | Percentage reduction of area from a tensile test of the material (from the mill certificate or material data). |
| Elastic modulus | GPa | Elastic modulus. |
| Yield strength | MPa | Yield strength. |
| Planned inside bend radius | mm | Inside radius you intend to use. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Material thickness
- What it is
- The thickness of the sheet or plate being bent, measured with a micrometer or taken from the material certificate.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Both the minimum and the maximum radius scale in direct proportion to thickness.
- Get it right
- Use the actual thickness; sheet supplied at the top of its tolerance needs a larger minimum radius.
What this means: Reduction of area in a tensile test
- What it is
- How much the cross-section of a tensile test piece shrinks at the point of fracture, as a percentage of its original area. It measures ductility and appears on mill certificates and material data.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% to 99%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher reduction of area means a more ductile material and a smaller minimum radius.
- Get it right
- Do not confuse it with elongation, which is a different ductility measure also given on certificates.
What this means: Elastic modulus
- What it is
- The stiffness of the material in tension (Young’s modulus), from the material data sheet. With the yield strength it sets the largest radius that still gives a permanent bend.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The maximum radius for a permanent bend rises in direct proportion to the modulus.
- Get it right
- Enter gigapascals: 1 GPa = 1000 MPa.
What this means: Yield strength
- What it is
- The stress at which the material begins to deform permanently, from the mill certificate or material specification.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher yield strength lowers the maximum radius that will still set permanently.
- Get it right
- Use the yield strength for the actual temper or condition; work-hardened stock yields much higher than annealed.
What this means: Planned inside bend radius
- What it is
- The radius on the inside of the bend you plan to form, set by the punch nose or bending die. The tool checks it against both limits.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- This is the inside radius, not the radius to the neutral axis or the outside of the bend.
Method and formulas
- R_min = T (50 ÷ r − 1), with r the reduction of area in per cent.
- R_max = T E ÷ 2 YS (beyond this the outer fibres stay elastic).
- Example: 3 mm sheet with 40% reduction of area can be bent to 0.75 mm minimum radius.
Limitations
- Bends across the rolling direction tolerate tighter radii than bends along it.
- Edge condition (burrs, shearing) causes cracks at larger radii than predicted.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose a punch radius that will not crack the bend
- Check whether a large-radius bend will form at all
- Compare materials for formability
Who it is for
- Fabrication supervisors
- Manufacturing engineers
- Estimators
What you get
- Minimum bend radius
- Maximum bend radius for a permanent bend
- Check of the planned radius
Interpreting the result
- Allow extra radius for bends parallel to the grain and for sheared edges.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1346–1347. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Bend radius and what limits it
In Sheet Metal Parts by the Numbers
What it covers: Choose an inside bend radius: outer fibre strain, a minimum radius from the material's ductility, the radius air bending actually forms, the folder's tooling, and why tighter is not better.
Method explained here · BIZOMAT original book
Bending plate past yield
In Yield and Plastic Flow by the Numbers
What it covers: What happens through the thickness of a bend, the tightest radius a plate takes without cracking, how much it springs back, and why a punch change and a nesting change cracked a batch of brackets.
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