| A more general model for predicting the sheet forming limits under linear and complex strain paths is proposed. The model utilizes the Theory of Plasticity and the Marciniak-Kuczinsky analysis. A modular and user-friendly software is developed, which allows the implementation and combination of different constitutive equations, changing the corresponding subroutine, while keeping intact the main part of the program. The phenomenological approach as well as the physical one, are utilized for modelling the anisotropic behaviour of sheet metals. In order to demonstrate the generality and validity of the new model, several phenomenological constitutive equations such as, Swift hardening power law and Voce saturation hardening law, the isotropic Von Mises yield criterion, the quadratic Hill yield criterion (Hill'48), the non-quadratic Hill yield criterion (Hill'79) and the Yld96 Barlat yield criterion are implemented. Finally, a physics - based constitutive model accounting for the texture and strain path induced anisotropy is considered. This advanced model is based on the Van Houtte' s anisotropic texture plastic potential expressed in a strain rate space coupled with the Teodosiu and Hu microstructural hardening model. A detailed strain and stress based forming limits analysis is performed to assess the potentiality and efficiency of the new developed model on the Forming Limit Diagrams and Forming Limit Stress Diagrams predictions. It is also of particular interest its aptitude in the selection of the best combination of constitutive equations for an accurate description of the material behaviour. This quality of the material model was shown to be vital for good predictions on plastic flow localization from the Marciniak-Kuczinsky theory and consequently for a correct analysis on the material formability. |
