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The last few years have seen an enormous increase in the research, development and, especially, in the application of computer modeling of sheet metal forming operations. This increased industrial use is due to many factors, including: enhanced accuracy and robustness of forming codes, a growing sophistication in their use by engineers, common availability of CAD data for panels, and advances in hardware capability. This paper attempts to describe the current state-of-the art. We begin by offering a brief history of mathematical modeling of sheet forming, and then discuss some of the current formulations of finite element methods. We also speculate on some possible future accomplishments.

Many stretch flanges in sheet metal parts are formed from material which has been significantly strained in a previous forming operation. This paper uses the assumption of axisymmetry and an engineering approximation to develop a formula for the final flange length, given the shape of the intermediate configuration and the trim location. The maximum flange length is limited by splitting of the metal at the free edge, and the strain level at which splitting takes place depends strongly on the strain state and magnitude of the intermediate configuration. Using the above-mentioned formula with experimentally determined forming limits, a computer program is developed to calculate maximum flange lengths for balanced biaxial prestrain. Comparison is made to some limited experimental data.

An approximate plane strain analysis of the springback of sheet metal which has been bent under tension around a small radius is presented. The tensile load can be applied either before the bending takes place (called a “preload”) or after bending (“postload”). Some of the material and process parameters which govern springback are identified, and it is shown that postloads are always more effective than preloads in reducing spring-back. In principle, if all parameters are fixed, the springback would be constant from part to part and the required overbend could be determined. In practice, the material and process parameters have unavoidable variations. Using the springback model developed here, a Monte Carlo simulation is carried out to estimate the effects of these variations. It is found that the metal thickness has the greatest impact on springback variation.