Work hardening models and the numerical simulation of the deep drawing process

The sheet metal forming process is used in almost all kinds of industrial domains. It is controlled by an enormous amount of technological parameters, reason why the numerical simulation became a fundamental tool for the process analysis. To obtain accurate solutions, the mechanical models implemented in the simulation codes should use reliable descriptions of the plastic behaviour of the deformed materials. The most widely used constitutive model is the classical Hill '48 yield criterion, to characterize the anisotropy, with a power law that describe the hardening behaviour. However, during a stamping operation, the stress condition is not always uniaxial and the strain paths are not monotonic even in single stage processes. Under complex strain-path changes a simple power law does not provide an accurate simulation of the material behaviour. Thus, more sophisticated models, involving non-linear kinematic hardening and internal state variables, are expected to allow an improvement in the simulation of the deep drawing forming process. The present paper presents a short review of a few advanced constitutive models. The five selected models were previously implemented in the finite element code DB3IMP. Two are classical pure isotropic hardening models described by a power law (Swift) or a Voce type saturation equation. Those two models were also combined with a non-linear (Lemaitre and Chaboche) kinematic hardening rule. The final one is the Teodosiu microstructural hardening model. Comparative analyses of numerical results, obtained with these constitutive models, are presented. The simulations consist on the stamping of a curved rail developed in the project 3DS.