Ideal Flow Design of Plane-Strain Bending Driven by Springback

Abstract

The present paper is concerned with the design of the plane-strain bending of wide sheets driven by the sheet’s geometric shape after unloading. The solution is based on the ideal flow theory. It determines the loading path (the dependence between the dimensionless bending moment and the dimensionless tensile force) that produces the desirable shape. The ideal flow theory is valid for the rigid perfectly plastic material model. A method proposed in the literature combines a rigid plastic solution at loading and an elastic solution for springback. The final design solution is practically analytical. A numerical method is only necessary to solve a system of transcendental equations. An illustrative example is provided. This example shows that, in some cases, it is sufficient to use the solution at loading to determine an accurate loading path that produces the desirable sheet’s shape after springback.