Sheet metal stretch forming is a plastic deformation process involving controlled stretching and bending around dies to produce accurately contoured parts. New forming technologies based on compliant reconfigurable tooling are available for this process, but there is a need for a formalism that can accurately predict the three-dimensional shape of the required tooling, a priori. In this thesis, a finite element modeling and simulation system has been developed for numerical simulations of sheet metal stretch forming over compliant “discrete-die” reconfigurable tools. The simulation system takes into account the deformation of the compliant polymeric layer. A robust tooling design algorithm has been developed that is based on an inverse springback approach that uses the elastic-plastic stress state prior to unloading to elastically deform the sheet in a direction opposite to springback. The resulting algorithm is thus referred to as the “spring forward” method. The optimized tooling design algorithm, developed as part of this thesis, is based on improving the convergence behavior of the spring forward method using an interpolation scheme. The interpolation scheme uses prior iterations to predict spatially varying spring forward factor values that account for the local part shape error history. Using these values, a springback compensated tool shape is predicted by the spring forward method. The modified spring-forward method is a self-correcting tool shape prediction algorithm that estimates the spring forward factor values by fitting a quadratic relationship between the tool shape and the part shape errors. The optimized tooling design algorithm is extended to compliant dies by developing a method that corrects the die shape for polymer through the thickness compression. The compliant die shape is predicted by adding the polymer deformation to the initial die shape, such that, at the fully loaded state, the effective die shape is equal to the initial die shape. The algorithm was applied to large-scale airframe skin parts commonly found in aerospace structures. Two shapes were investigated, a 90-inch radius cylindrical die and a 90-inch radius spherical die. In both cases the predicted tool shape produced the desired part shape within the acceptable tolerance of ±0.030 inches.
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