Minimum Bend Radius



General Concepts

The intent is to develop a quantitative description of the minimum bend radius that can be produced in forming sheet metal parts.

A useful concept for specifying the minimum radius to which a sheet metal workpiecce can be bent is

the minimum bend radius is the radius at which the tension surface of the bent material factures.

strainbending = strainfracture

Another idea is important, the specification of the fracture strain. The most widely used mechanical property test is the tensile test. So, the fracture strain for the work material is the fracture strain obtained in a tensile test.

Minimum Bend Radius Process Model

strainbending = straintensile test fracture

In a tensile test is is easy to measure the specimen cross section area at fracture.
The fracture strain used is the true strain efracture = ln ( Afracture / Ao
This strain is negative indicating a decrease in cross section area.
The magnitude of the strain is the useful quantity and so, the positive strain
efracture = ln ( Ao / Afracture is used.

The strain in bending a sheet of thickness t to radius R is needed.

The strain of interest is the maximum strain and is at the outer surface of the bend.
The engineering strain is è and
è = ( Lfinal - Lo ) / Lo
è = ( Lfinal / Lo ) - 1

Lfinal is a final length, i.e., bent length of surface
Lo is the original length

On bending to angle a the neutral plane length remains constant

Lo is the neutral plane length
Lo = ( R + t / 2 ) a
Outer surface length is
Lfinal = ( R + t ) a

è = { [ ( R + t ) a ] / [ ( R + t / 2 ) a ] } - 1
è = 1 / [ ( 2 R / t ) + 1 ]
To put this engineering strain in terms of true strain
in general, true strain e = ln ( l / lo )
engineering strain è = ( l - lo ) / lo
or l / lo = 1 + è
so e = ln ( 1 + è )
The true strain in bending is
ebending = ln ( è + 1 )
ebending = { 1 / [ ( 2 R / t ) + 1 ] } + 1
The bending strain = fracture strain condition is then

ln { 1 / [ ( 2 R / t ) + 1 ] } + 1 = ln ( Ao / Afracture )

The quantity usually used to describe ductility is the percent reduction of area
% reduction in area = [ ( Ao - Afracture ) / Ao ] 100%
the corresponing fractional reduction in area is f
f = ( Ao - Afracture ) / Ao
To put the bending strain = fracture strain condition in terms of f, Ao / Afracture is expressed in terms of f
( Ao - Afracture ) / Ao = 1 - ( Afracture / Ao )
Afracture / Ao = 1 - [ ( Ao - Afracture ) / Ao ]
Ao / Afracture = 1 / { 1 - [ ( Ao - Afracturer ) / Ao ] }
Ao / Afracture = 1 / ( 1 - f )
{ 1 / [ ( 2 R / t ) + 1 ] } + 1 = 1 / ( 1 - f )

The ratio of bend radius to work thickness is usually used in describing sheet forming and

2 R / t = { 1 / [ 1 / ( 1 - f ) ] - 1 } - 1

gives the minimum bend radius in terms of material ductility f.


© 2002 by Barney E. Klamecki. All rights reserved