Numerical investigation and experimental validation of a plasticity model for sheet steel forming

This paper investigates a recently developed elasto-plastic constitutive model. For this purpose, the model was implemented in a commercial finite element code and was used to simulate the cross-die deep drawing test. Deep drawing experiments and numerical simulations were conducted for five interstitial-free steels and seven dual-phase (DP) steels, each of them having a different thickness and strength. The main interest of the adopted model is a very efficient parameter identification procedure, due to the physical background of the model and the physical significance of some of its parameters and state variables. Indeed, the dislocation density, grain size and martensite volume fraction explicitly enter the model's formulation, although the overall approach is macroscopic. For the DP steels, only the chemical composition and the average grain sizes were measured for the martensite and ferrite grains, as well as the martensite volume fraction. The mild steels required three additional tensile tests along three directions, in order to describe the plastic anisotropy. Information concerning the transient mechanical behavior after strain-path changes (reverse and orthogonal) was not collected for each material, but for only one material of each family of steels (IF, DP), based on previous works available in the literature. This minimalistic experimental base was used to feed the numerical simulations for the twelve materials that were confronted to deep drawing experiments in terms of thickness distributions. The results suggested that the accuracy of the numerical simulations is very satisfactory in spite of the scarce experimental input data. Additional investigations indicated that the modeling of the transient behavior due to strain-path changes may have a significant impact on the simulation results, and that the adopted approach provides a simple and efficient alternative in this regard.

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