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Theoretical and experimental studies have shown that when a compressive stress is applied normal to the sheet surface its formability can be significantly improved. In forming processes such as hydroforming, the normal stress imposed at the surface of the sheet or tube can be very significant in specific locations and it is therefore necessary to account for this stress state when assessing the forming severity of industrial parts. It is also well known that the forming limit curve (FLC) can vary significantly in strain space as a result of non-linear strain paths. In this work, a numerical code based on the Marciniak and Kuczynski (MK) analysis (1967) was developed to predict the FLC of sheet metals by simultaneously accounting for the effects of strain path non-linearity and the normal stress. The FLC predicted with this code can be used to assess the forming severity of parts that are deformed under complex loading conditions in industrial metal forming processes. The predictive FLC model was validated using experimental data in which linear and bi-linear strain paths were applied to different steel and aluminum sheets or tubes under plane stress and three-dimensional stress conditions. This research work has two specific purposes: first, to investigate the influence of the magnitude of the prestrain in bi-linear loading on the sensitivity of the FLC to the normal stress, and second, to study the effect of the normal stress on the path dependence of the FLC. This work showed that, with increasing magnitudes of prestrain the influence of the normal stress on the formability of sheet metal will decrease, regardless of the loading path. Moreover, it was observed that even a significant normal stress will practically not affect the path dependence of the FLC.

The forming limit curve (FLC), a plot of the limiting principal surface strains that can be sustained by sheet metals prior to the onset of localized necking, is useful for characterizing the formability of sheet metal and assessing the forming severity of a drawing or stamping process. Both experimental and theoretical work reported in the literature has shown that the FLC is significantly strain-path dependent. In this paper, a modified Marciniak and Kuczynski (MK) approach was used to compute the FLC in conjunction with two different work-hardening models: an isotropic hardening model and a mixed isotropic–nonlinear kinematic hardening model, which is capable of describing the Bauschinger effect. Predictions of the FLC using the MK analysis have been shown to be dependent on the shape of the initial yield locus and on its evolution during work hardening; therefore the hardening model has an influence on the predicted FLC. In this investigation, published experimental FLCs of AISI-1012 low carbon steel and 2008-T4 aluminum alloy sheets that were subjected to various nonlinear loading paths were compared to predictions using both hardening models. The predicted FLCs were found to correlate quite well with experimental data and the effects of strain path changes and of the hardening model on predicted FLCs are discussed.

A semi-implicit integration scheme was used to implement the Yoshida–Uemori two-surface model into the finite element method. Hill’s quadratic yield function was employed to account for the orthotropic behaviour of the metal sheet. The model was used to predict the cyclic simple shear response of DP-600. In order to evaluate the capability of the model for sheet metal forming, the model was used to simulate both the forming stage of a channel draw process in the presence of drawbeads and the subsequent springback stage. The results show that the model predicts the springback profile very well, especially at deeper drawbead penetrations.

The objective of this work is to predict the springback of Numisheet’05 Benchmark#3 with different material models using the commercial finite element code ABAQUS. This Benchmark consisted of drawing straight channel sections using different sheet materials and four different drawbead penetrations. Numerical simulations were performed using Hill's 1948 anisotropic yield function and two types of hardening models: isotropic hardening (IH) and combined isotropic-nonlinear kinematic hardening (NKH). A user-defined material subroutine was developed based on Hill's quadratic yield function and mixed isotropic-nonlinear kinematic hardening models for both ABAQUS-Explicit (VUMAT) and ABAQUS-Standard (UMAT). The work hardening behavior of the AA6022-T43 aluminum alloy was described with the Voce model and that of the DP600, HSLA and AKDQ steels with Hollomon's power law. Kinematic hardening was modeled using the Armstrong–Frederick nonlinear kinematic hardening model with the purpose of accounting for cyclic deformation phenomena such as the Bauschinger effect and yield stress saturation which are important for springback prediction. The effect of drawbead penetration or restraining force on the springback has also been studied. Experimental cyclic shear tests were carried out in order to determine the cyclic stress–strain behavior. Comparisons between simulation results and experimental data showed that the IH model generally overestimated the predicted amount of springback due to higher stresses derived by this model. On the other hand, the NKH model was able to predict the springback significantly more accurately than the IH model.