This paper presents synthetically the most recent models for description of the anisotropic plastic behavior. The first section gives an overview of the classical models. Further, the discussion is focused on the anisotropic formulations developed on the basis of the theories of linear transformations and tensor representations, respectively. Those models are applied to different types of materials: body centered, faced centered and hexagonal-close packed metals. A brief review of the experimental methods used for characterizing and modeling the anisotropic plastic behavior of metallic sheets and tubes under biaxial loading is presented together with the models and methods developed for predicting and establishing the limit strains. The capabilities of some commercial programs specially designed for the computation of forming limit curves (FLC) are also analyzed.

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Advances in anisotropy and formability

A new crystal plasticity scheme for explicit time integration codes to simulate deformation in 3D microstructures: Effects of strain path, strain rate and thermal softening on localized deformation in the aluminum alloy 5754 during simple shear

Numerical simulation is becoming one of the main methods to investigate various engineering problems with sophisticated conditions. A considerable amount of research is conducted on numerical analysis of sheet metal forming process to address different aspects of the problem. Among the numerical simulation methods for sheet metal forming process, finite difference method (FDM) and finite element method (FEM) have been the main methods. In this paper, the progresses in simulation techniques, advantage and disadvantage of numerical methods for simulating sheet metal forming process are discussed based on these numerical methods. Currently, FEM being the main simulation method for sheet metal forming, development in solution strategies and formulation, element selection are further brought into attention. Historical development of anisotropy and yield criteria, which are theoretical foundation for numerical simulation, and their application in simulation software are briefly classified. Formability of sheet metal is presented from the numerical simulation point of view. Numerical investigations on springback are reviewed in terms of simulation techniques and factors influencing springback. Simulation techniques for novel sheet metal forming techniques such as laser forming and incremental sheet forming (ISF) are presented.

Numerical simulation of sheet metal forming: a review

Compensation for process-dependent effects in the determination of localized necking limits

Forming severity concept for predicting sheet necking under complex loading histories

This paper presents an extended stress-based forming limit curve (XSFLC) that can be used to predict the onset of necking in sheet metal loaded under non-proportional load paths, as well as under three-dimensional stress states. The conventional strain-based eFLC is transformed into the stress-based FLC advanced by Stoughton (1999, Int. J. Mech. Sci., 42, pp. 1-27). This, in turn, is converted into the XSFLC, which is characterized by the two invariants, mean stress and equivalent stress. Assuming that the stress states at the onset of necking under plane stress loading are equivalent to those under three-dimensional loading, the XSFLC is used in conjunction with finite element computations to predict the onset of necking during tubular hydroforming. Hydroforming of straight and pre-bent tubes of EN-AW 5018 aluminum alloy and DP 600 steel are considered. Experiments carried out with these geometries and alloys are described and modeled using finite element computations. These computations, in conjunction with the XSFLC, allow quantitative predictions of necking pressures; and these predictions are found to agree to within 10% of the experimentally obtained necking pressures. The computations also provide a prediction of final failure location with remarkable accuracy. In some cases, the predictions using the XSFLC show some discrepancies when compared with the experimental results, and this paper addresses potential causes for these discrepancies. Potential improvements to the framework of the XSFLC are also discussed.

Prediction of Necking in Tubular Hydroforming Using an Extended Stress-Based Forming Limit Curve

Computational analysis of stress-based forming limit curves

An extension of the stress-based forming limit curve (FLC) advanced by Stoughton (2000, "A General Forming Limit Criterion for Sheet Metal Forming," Int. J. Mech. Sci., 42, pp. 1-27) is presented in this work. With the as-received strain-based FLCs and stress-strain curves for 1.6-mm-thick AA5754 and 1-mm-thick AA5182 aluminum alloy, stress-based FLCs are obtained. These curves are then transformed into extended stress-based forming limit curves (XSFLCs), which consist of the invariants, effective stress, and mean stress. By way of application, stretch flange forming of these aluminum alloy sheets is considered. The AA5754 stretch flange displays a circumferential crack during failure, whereas the AA5182 stretch flange fails through a radial crack at the edge of the cutout. It is shown that the necking predictions obtained using the strain- and stress-based FLCs in conjunction with shell element computations are inconsistent when compared with the experimental results. By comparing the results of the shell element computations with those in which the mesh comprises eight-noded solid elements, it is demonstrated that the plane stress approximation is not valid. The XSFLC is then used with results from the solid-element computations to predict the punch depths at the onset of necking. Furthermore, it is shown that the predictions of failure location and failure mode obtained using the XSFLC are in accord with the differences observed between the two alloys/gauges.

Application of an Extended Stress-Based Forming Limit Curve to Predict Necking in Stretch Flange Forming

Prediction of necking of high strength steel tubes during hydroforming—multi-axial loading

This paper reports a novel extension of the stress‐based flow limit curve approach. A conventional strain‐based FLC is converted into a stress‐based FLC using the method proposed by Stoughton. This stress‐based FLC is then transformed into the XSFLC by casting the stresses in terms of the invariants — effective stress and mean stress that are the variables that constitute the XSFLC. This curve is used in conjunction with LSDYNA finite element simulations that use eight‐noded solid elements to predict the onset of necking in tubular hydroforming. The particular case of straight tube hydroforming of ENAW 5018 aluminum alloy tubes is considered. The XSFLC is able to predict the internal pressure at the onset of the neck and the final failure location in the tube with remarkable accuracy.

C. Hari Manoj Simha

Papers

Prediction of Necking in Tubular Hydroforming Using an Extended Stress-Based Forming Limit Curve

Computational analysis of stress-based forming limit curves

Application of an Extended Stress-Based Forming Limit Curve to Predict Necking in Stretch Flange Forming

Prediction of necking of high strength steel tubes during hydroforming—multi-axial loading

Application of an Extended Stress‐Based Flow Limit Curve to Predict Necking in Tubular Hydroforming