Crystal Plasticity Modeling of Al Alloy under Linear and Non-Linear Loading

Abstract

The crystal plasticity (CP) model is widely used in many applications to link microstructure and mechanical properties. There are varying CP constitutive laws with phenomenological or physical-based formulation to cover a large range of loading conditions. In order to predict the deformation behavior of an Al alloy during the sheet metal forming process with either linear or non-linear strain path, both phenomenological and physical-based CP constitutive laws have been chosen, and the prediction performance of both models is compared. For the linear loading condition, the uniaxial tensile tests are performed on the smooth-dog-bone (SDB) specimens along rolling and transverse directions (RD/TD). The non-linear strain path is achieved by the Marciniak testing followed by uniaxial tension. In the first stage, the Marciniak testing is performed under the stress states of RD-uniaxial, plane strain, and biaxial tension. After being loaded to a certain strain level, mini-SDB specimens are cut along RD and TD from the uniform deformation region and reloaded under RD-uniaxial tension. The digital image correlation (DIC) technique is employed to measure the strain during testing. The electron backscatter diffraction (EBSD) technique is used to characterize the initial microstructure as well as the microstructure evolution of the specimens after the first stage loading in the non-linear strain path. A phenomenological power law and a dislocation-density-based hardening law have been employed in this study. The parameters are calibrated based on the flow curve of the RD uniaxial tension. The model performance is validated by stress–strain response under all the rest loading conditions including the non-linear loading path.