M–K Analysis of Forming Limit Diagram Under Stretch Bending

Abstract

Since the forming limit diagram (FLD) was introduced by Keeler, etc., five decades ago, it has been intensively studied by researchers and engineers. Most work has focused on the inplane deformation which is considered as the dominant mode of the majority forming processes. However the effect of outofplane deformation becomes important in the accurate prediction of formability when thick sheet metals and/or smaller forming radii are encountered. Recent research on the stretchbending induced FLD (BFLD) has been inconclusive. Some studies indicated that the bending effect will enhance a sheet metal's formability while others suggested otherwise. In this paper, we present an indepth study of the throughthickness bending effect on the forming limits. The Marciniak–Kuczynski (M–K) analysis is extended to include bending, and models based on both flow theory and deformation theory of plasticity are proposed. The study is limited to the righthandside of FLD where the bending is along the major stretch direction. The radial return method is adopted as the framework to integrate constitutive equations. The results show that the bending process decreases the sheet metal formability with the flowtheory based model, while the opposite is true if the deformation theory based analysis is adopted. A detailed examination of the deformation histories from those two models reveals that the loading–unloadingreverse loading process during stretchbending holds the key to the understanding of the conflicting results. The insight gained from the proposed FLD prediction model in this paper provides a new understanding of how the bending process affects the FLD, which can be used to predict and explain the localized necking phenomenon under the stretchbending condition.