## Definitions

Bend allowance, \(L_b\), is the length of the neutral axis and is used to determine the blank length of a bent part.- The
positionof the neutral axis depends on the radius and thickness of the bend

where:

- \(\alpha\) is bend angle in radians
- \(R\) is the bend radius
- \(T\) is the thickness of the sheet
- \(k\) the K-Factor, a constant

\(k\) is a factor proportioning the neutral axis in the thickness direction, with zero at the inner surface. Therefore, a smaller \(k\) value places the neutral surface closer to the inside of the bend radius.

Thus, when the neutral axis is at the center of the sheet's thickness (midplane), \(k = 0.5\). For sharp bends with a small \(R/T\) ratio, the neutral axis shifts towards the center of the bend and the factor \(k\) decreases. This causes the blank length to be smaller than the case of when it is at the midplane.

The engineering strain in a sheet during bending is:

## Rules of Thumb

\(k\) vales range from 0.33 for \(R<2T\) to 0.5 for \(R > 2T\).

## Minimum Bend Radius for Various Materials at Room Temperature

Values in this table are based on the minimum bend radius, which is that radius which does not produce a crack in the outer fibers when bent. This is dependent on material properties and in particular the reduction of area.

where \(r\) = reduction of area.

Material | Soft | Hard |
---|---|---|

Aluminum alloys | 0 | 6T |

Beryllium copper | 0 | 4T |

Brass, low-leaded | 0 | 2T |

Magnesium | 5T | 13T |

Austenitic stainless steel | 0.5T | 6T |

Low-carbon, low-alloy, HSLA | 0.5T | 4T |

Titanium | 0.7T | 3T |

Titanium alloys | 2.6T | 4T |

## References

- Manufacturing Engineering and Technology, Kalpakjian, 3rd Ed.