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Anisotropic hardening during metal forming process with application to springback



w2       w3
Fig. 1a: Typical sheet metal forming       Fig. 1b: FEM model of sheet metal forming

Work hardening of materials plays an important role in metal forming processes, e.g. for springback in sheet metal components after forming (Fig. 1). Springback is a serious problem in the manufacturing of sheet metal components. In numerical simulations of deformation processes, especially in the area of sheet metal forming, purely phenomenological models are insufficient to account for the effect of strain path changes on the forming process. As a consequence, new material models have to be developed which for example, consider the anisotropy development during the forming process as well as the initial anisotropy of the material. Parallel to the typical anisotropic material model "kinematic hardening" which results in the materials shift of the center of the elastic region in the direction of the plastic flow. Furthermore a new type of anisotropic model which accounts for arbitrary directional hardening, taking the microstructure of the material into consideration, is developed. To determine the material parameters and to validate the model, suitable testing methods have to be developed for a variety of deformation circumstances.


Material model

Fig.2: Directional hardening during orthogonal strain path change


As it is well known, severe non-proportional loading path changes, ubiquitous in complicated multiple-stage forming processes, can induce strongly anisotropic material behavior. Among the material models accounting for the influence of loading path changes, the model of Teodosiu and Hu (1995, 1998) has been used by a number of authors (e.g., Li et al., 2003) to model the induced anisotropic hardening behavior and its effect on the springback processes. However, the model of Teodosiu & Hu needs unloading to activate the cross hardening effect. Thus, a recently modified Teodosiu model has been proposed and implemented into the FEM programm using the interface of user material subroutine UMAT and VUMAT in ABAQUS. Verifications show that this modified Teodosiu model can capture the directional hardening effects during continuous arbitrary loading path changes (Fig. 2).


Application to ring-splitting


Fig.3: Springback (ring opening) during ring-splitting test

In order to validate the modified Teodosiu model, a realistic stamping process, cup drawing, and ring-splitting test has been carried out (Fig. 3). The test has been simulated using ABAQUS with the modified model. The simulation with parameters for the material DP600 shows a relative good agreement with the experimental results. Further systematic investigation on the influence of the numerical and material parameters on springback pehomena are carried in work currently under progress.




MSc. Jian Wang