Edmund Chu

Springback in plane strain stretch/draw sheet forming

Abstract Accurate prediction of springback is essential for the design of tools used in automotive sheet stamping operations. The plane strain stretch/draw operation presents a complex form of springback occurring in sheet metal forming since the sheet undergoes stretching, bending and unbending deformations. The two-dimensional draw bending is an example of such an operation in which the complex stress-strain states in the sheet cause the formation of side wall curls after the sheet is allowed to unload. Accurate prediction of the side wall curl requires using finite element shell models which can account for curvature and through-thickness stresses caused by bending and unbending of the sheet. Since such models are generally slow and expensive to use, an alternative and efficient method of predicting side wall curls will be desirable. This paper describes a novel and robust method for predicting springback in general and side wall curls in the two-dimensional draw bending operation as a special case, using moment-curvature relationships derived for sheets undergoing plane strain stretching, bending and unbending deformations. This model modifies a membrane finite element solution to calculate through-thickness strains and stresses and springback. Accuracy of this models predictions are verified by comparisons with finite element (ABAQUS) and experimental results.

Prediction of spring-back and side-wall curl in 2-D draw bending

Accurate prediction of spring-back is essential for the design of tools used in automotive sheet-stamping operations. The 2-D draw bending operation presents a complex form of spring-back occurring in sheet-metal forming since the sheet undergoes stretching, bending and unbending deformations. These three sets of deformation can create complex stress-strain states in the sheet which result in the formation of side-wall curls after the sheet is allowed to unload. Accurate prediction of the side-wall curl requires using finite-element shell models which can account for curvature and stress variation through the thickness caused by bending and unbending of sheet. Since such models are generally computationally intense, an alternative and efficient method of predicting side-wall curls is desirable. This paper describes a novel and robust method for predicting spring-back and side-wall curls in 2-D draw bending operations, using moment-curvature relationships derived for sheets undergoing plane-strain stretching, bending and unbending deformations. This model makes use of the membrane finite-element solution to calculate spring-back. The accuracy of the model is verified by comparison with finite element (ABAQUS) and experimental results.

An energy approach for predicting springback of metal sheets after double-curvature forming, Part I: axisymmetric stamping

Abstract In our previous study (Xue P, Yu TX, Shu E. International Journal of Materials Processing Technology 1999; 89-90:65-71.), based on the membrane theory of shells of revolution and an energy method a mechanics model and corresponding analytical procedure have been proposed to predict springback of circular and square metal sheets after a double-curvature forming operation. The strain hardening of the material is incorporated into the mechanics model. In the present paper, the method is extended to the cases, in which bending effect, as well as bending-and-unbending effect are taken into account. It is shown that the procedure developed is capable of quantitatively predicting the strain distribution and springback of metal sheets after axisymmetric stamping with a relatively minor effort of calculation and a good accuracy. The effect of stretching force applied at the edge of the plate on springback is also considered. Excellent agreement is found between the theoretical prediction of springback and experiment results.

Theoretical prediction of the springback of metal sheets after a double-curvature forming operation

Abstract By establishing a mechanics model and corresponding analytical procedure based on the membrane theory of shells of revolution and an energy method, a theoretical prediction of springback is formulated for thin metal sheets after they have undergone a double-curvature forming operation, e.g. stamping and stretching-bending. The strain-hardening of the material is incorporated into the mechanics model. The effect of stretching force applied at the edge of the plates on springback is also considered. Excellent agreement is found between the theoretical prediction of springback and experiment results. It is shown that the procedure developed is capable of quantitatively predicting the springback of circular and square plates after axisymmetric stamping with a relatively minor effort of calculation and a good accuracy.

Generalization of Hill's 1979 anisotropic yield criteria

Limitations of Hills 1979 yield criteria have been identified and a generalization of Case (4) of Hills theory has been developed. The new theory allows for the inclusion of shear stress components as well as planar anisotropy of the sheet metals. The conditions for convexity of the yield function have been established mathematically. The constitutive equation developed by the author can be incorporated readily into a finite-element code for producibility assessment and tool/die development of sheet-metal forming processes. It provides an accurate description of anisotropic material behavior of automotive body sheets and thus improves the predictive capability of finite-element simulation.

An elastoplastic analysis of flange wrinkling in deep drawing process

The onset of flange wrinkling of a deep drawing cup is analyzed as an elastoplastic bifurcation problem. The flange is modeled as an elastoplastic annular plate subject to axisymmetric radial tension along its inner edge. As observed in the laboratory as well as practical industrial applications, aluminum alloy sheets usually wrinkle in the plastic range. Therefore, the critical condition governing the onset of elastoplastic wrinkling is formulated within the context of the general bifurcation theory. A closed-form solution for the critical drawing stress is developed based on an assumed nonlinear plastic stress field and the deformation theory of plasticity. The theory properly accounts for the plastic anisotropy of the aluminum sheets and the critical drawing stress at the onset of wrinkling is also compared against the one employing the flow theory of plasticity. The predicted critical bifurcation stress and the wave numbers are compared to those obtained by Seniors one-dimensional theory. It is demonstrated that there is a strong dependency of the critical bifurcated stress at the onset of wrinkling on the shear stress induced on the flange. The effects of flange width, drawing ratios, material properties, strain hardening on the onset of wrinkling are investigated. The differences between the present theoretical approach and Seniors theory are emphasized.

An energy approach for predicting springback of metal sheets after double-curvature forming, Part II: Unequal double-curvature forming

Abstract Based on the membrane theory of shells of revolution and an energy method, theoretical predictions of springback of metal sheets after an equal double-curvature forming operation has been given in the part I of this paper (Xue et al., An energy approach for predicting springback of metal sheets after double-curvature forming, Part I: axisymmetric stamping. International Journal of Mechanical Sciences 2001;43(8):1893–1914). In Part II, the prediction of springback of metal sheets after unequal double-curvature forming is illustrated. It is shown that the proposed mechanics model and analytical procedure can be conveniently applied to predicting the springback, as well as the strain and stress distributions of metal sheets after unequal double-curvature forming, which is valuable for design of tools with complicated shapes in manufacturing industries.

Computer simulation of sheet metal forming based on damage mechanics approach

Abstract This paper presents an investigation of computer simulation to analyze the effects of plastic damage on the formability of VDIF steel under both proportional and non-proportional loading conditions. The simulation is carried out using LS-DYNA incorporated with a newly developed damage mechanics model and its damage criterion. Three forming processes, uniaxial tension, plane-strain deformation and biaxial stretching, are examined and deformation profiles are calculated and plotted. Finally, the forming limit strains are predicted for both proportional and non-proportional loading conditions, which are found to be in agreement with the test results.

Special Issue: Forming and Joining of Lightweight and Multimaterial Systems

With this special issue of the Journal of Manufacturing Science and Engineering (JMSE) our objective is to collect papers which enhance the understanding of material deformation processes; expand the lightweight material forming and multi-material joining processes and modeling capability; and promote R&D activities on forming and joining new materials and/or new forming and joining technologies at length scales varying from microto macro-scale.

Background and Tryout Report for BM2: Underbody Cross Member

An automotive underbody cross member was selected for one of the NUMISHEET’05 industrial benchmark to assess springback prediction capability of engineers around the world using various software. Binder and addendum were generated according to production intent process. Iterative design and draw simulation were performed on the part and addendum geometry to remove wrinkles and splits. Castings were poured and machined. Six different types of materials ranging from A15182‐O to DP965 were used in the production of the benchmark panels and three of these materials were included in the official benchmark data release. Draw panels were trimmed on a trimming fixture using laser and scanned with a whitelight optical device. Springback shapes at selected cross sections were recovered on the scanned data and original CAD data. In addition, major/minor and thickness strains were also measured at these sections.