A comparative study between elasto-plastic self-consistent crystal plasticity and anisotropic yield function with distortional hardening formulations for sheet metal forming

Abstract

A comparative study between micro- and macro-mechanical constitutive models is carried out while predicting deformation behavior of an aluminum alloy (AA) 6022-T4 during several loading scenarios of increasing complexity including monotonic tension, large strain cyclic deformation, and drawing of a cylindrical cup. The micro-model is a recently developed implicit formulation of the elasto-plastic self-consistent (EPSC) crystal plasticity, which is coupled with the implicit finite element method (FEM) through a user material subroutine in Abaqus. In the coupled formulation, every finite element integration point embeds the implicit EPSC constitutive law that accounts for the directionality of deformation mechanisms and microstructural evolution. The crystallography based EPSC model integrates a dislocation-based hardening law and accounts for inter-granular and slip system level back-stresses, which make it capable of capturing non-linear unloading and the Bauschinger effect. The macro-model is a recently developed anisotropic yield function incorporating distortional hardening using the homogeneous anisotropic hardening (HAH) approach. The model is also implemented as a user material subroutine in Abaqus. Parameters pertaining to the micro and macro models are identified using experimental data from a set of monotonic and cyclic tests performed for AA6022-T4. Additional experimental data for the alloy in terms of flow stress curves, R-value, and anisotropic yield surface evolution are used to verify the models. Finally, the cup drawing simulations are carried out in the FEM using the two constitutive formulations and geometrical changes including the earing profile and sheet thinning/thickening are compared against each other and with experiments to further verify the predictive characteristics of the models. The two formulations and results are discussed in terms of accuracy and computational efficiency.