Prediction of springback in sheet metal forming
Abstract: The prediction of springback is probably the area in sheet metal forming simulation, where the least success has been achieved in terms solution accuracy. The springback is caused by the release of the stresses in the workpiece after the forming stage. An accurate prediction of the stresses puts, in turn, high demands on the Finite Element modeling of the problem. There are many things that affect the quality of the numerical model. One of the most evident is perhaps the modeling of the material behavior. Among the various ingredients that make up a reliable phenomenological material model for sheet metals, the yield surface and the hardening law are some of the most important ones for an accurate springback prediction. The yield surface should be able to capture the in-plane anisotropic behavior, whilst the hardening law should be able to consider some, or all, of the phenomena that occurs during bending and unbending of metal sheets, such as the Bauschinger effect, the transient behavior, and permanent softening. Five different hardening models and three different phenomenological yield criteria have been studied and evaluated in the present investigation. The unknown material parameters used in the description of the hardening behavior are determined by either inverse modeling of three-point bending tests, or from uniaxial tension/compression tests. Furthermore, the material behavior during “elastic” relaxation of stresses is investigated in detail. It is shown that the unloading/loading path in fact describes a nonlinear hysteresis loop. It is also observed that the secant stiffness is decreasing with increasing plastic pre-strain. Since the springback deformation mainly is an elastic recovery process, the elastic stiffness has a large influence on the final amount of springback. Within the current work a methodology has been developed, in which the true hysteresis unloading/loading behavior can be considered. The various material models were applied to the springback simulation of a simple “U-bend” problem. It was observed that, when the most advanced material constituents were used in combination, excellent agreement with experiments was obtained. It was also noted that inappropriate combinations of the different constitutive ingredients could result in highly erroneous springback predictions. Finally, the springback behavior of a more industrial-like component was investigated. Besides the material modeling, several other effects were found to have a strong influence on the springback predictions. Especially, the strong effect of the distribution of the blankholder pressure on the resulting springback was brought to light. The difficulties in predicting this pressure distribution in a correct way were also realized.
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