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Plane strain bending (e.g. bending about a straight line) is a major sheet forming operation and it is practiced as brake bending (air bending, U-die, V-die and wiping-die bending). Precise prediction of springback is the key to the design of the bending dies and to the control of the process and press brake to obtain close tolerances in bent parts. In this paper, reliable mathematical models for press brake bending are presented. These models can predict springback, bendability, strain and stress distributions, and the maximum loads on the punch and die. The elasto-plastic bending model incorporates the true (nonlinear) strain distribution across the sheet thickness, Swift's strain hardening law, Hill's 1979 nonquadratic yield criterion for normal anisotropic materials, and plane strain deformation mode.

Shrink flanging is a major sheet forming operation to produce convex flanges in structural sheet metal components. Flanges are used for appearance, rigidity, hidden joints, and strengthening of the edge of sheet parts such as automobile front fender and complex panels formed by stretch/draw forming. Wrinkling around the flange edge is the major defect in shrink flanging operation. There has been a lack of reliable mathematical modeling to predict the strains and wrinkles in shrink flanging operations. A trial-and-error approach has been usually practiced in tooling and process designs. In this paper, a wrinkling criterion in shrink flange is proposed based on a simplification from a general criterion for a doubly curved anisotropic shell. The mathematical model for strain analysis in shrink flanging is established based on Wang and Wenner's strain model for stretch flange. Shrink flanging experiments were conducted to validate the theories.

In sheet metal forming, drawbeads are often used to control uneven material flow which may cause defects such as wrinkles, fractures, surface distortion and springback. Appropriate setting and adjusting the drawbead force is one of the most important parameters in sheet forming process control. However, drawbead design and drawbead force adjustment still rely on trial-and-error procedures. This paper summarizes the guidelines in drawbead design, evaluates a number of mathematical models in estimating drawbead forces, and investigates the effects of sheet thickness, material properties, drawbead geometry and penetration on the drawbead force.