The Mechanics of Sheet Metal Plastic Deformation
When flat sheet metal is bent over a press brake die, the material undergoes both tensile and compressive stresses. The outer fibers of the bend stretch in tension, while the inner surface compresses. Somewhere between the outer stretched skin and inner compressed skin lies the Neutral Axis—a theoretical plane that neither stretches nor compresses.
The K-Factor: Locating the Neutral Axis
The K-factor represents the position of the neutral axis as a fraction of total material thickness (T):
In unstressed sheet, the neutral axis sits at the 50% midpoint ((K = 0.50)). However, during air bending, compression displaces the neutral axis inward, causing (K) to range from 0.33 to 0.45 depending on material hardness and ductility.
Bend Allowance (BA) vs. Bend Deduction (BD)
Two methods exist to calculate the flat pattern blank:
- Bend Allowance (BA): The actual curved arc length along the neutral axis around the bend radius:
BA = (pi / 180) × Angle × (Radius + K × T). Flat Length = Flat Flange 1 + Flat Flange 2 + BA. - Bend Deduction (BD): The amount by which total outside flange lengths must be reduced to account for elongation:
BD = (2 × OSSB) - BA. Flat Length = Outside Flange 1 + Outside Flange 2 - BD.