A novel approach for anisotropic hardening modeling. Part I: Theory and its application to finite element analysis of deep drawing
Résumé
Advanced macroscopic models give a good description of initial plastic behavior of most metallic materials like initial anisotropy. However, the modeling of anisotropic hardening, in particular for non-proportional loading paths, still is a difficult task for these models. The complex distortion of the yield locus is related to the activation and cross-hardening of different slip systems, depending on crystallographic orientations. These physical mechanisms are taken into account in polycrystalline models. The novel approach consists in: (i) drastically reducing the number of crystallographic orientations, (ii) applying a specific parameter calibration procedure to obtain a good agreement with all stress–strain and transverse strains curves of an extended experimental database including pseudo-experimental tests. In the present study, the methodology has been applied to a strongly anisotropic aluminum alloy (Part I) and to an initially isotropic fcc material (Part II, submitted to Int. J. Plasticity). Very good modeling is achieved with 8 and 14 crystallographic orientations, respectively, in particular for the Lankford ratios along different loading directions. The additional hardening for non-proportional loadings, such as simple shear followed by tension, can be modeled. The effects of texture evolution are also qualitatively investigated. It must be emphasized that the objective of the methodology is not to obtain results at the microscopic scale or material science level. The polycrystalline models are used in the same way as macroscopic models are, provided the computation times are similar. In order to validate the methodology and to evaluate its performance, finite element calculations of a deep drawing test have been performed. The CPU time of the polycrystalline model is only twice larger than the one with an advanced anisotropic macroscopic model. The calculated cup heights with six ears are in good agreement with the experimental measurements.