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Numerical simulations of cup drawing for aluminium sheets based on asymmetric non-quadratic yield function and non-associated flow rule

In this article, finite element simulations of cylindrical cup drawing process for Al2008-T4 sheet sample are performed with constitutive formulations based on an asymmetric orthotropic yield function and non-associated flow rule. In order to describe the strenght differential effect observed for the considered material asymmetric non-quadratic yield function is proposed. The proposed yield function is derived by extending the original orthotropic Karafillis-Boyce equivalent stress term with a linear combination of the normal stress components. For the derived yield function, the yield loci shapes and the capability in predicting the yield stress directionality and the strenght differential effect are investigated. Constitutive formulation based on the proposed yield function and non-associated flow rule is implemented into the finite element program ADINA 8.1. The results of the cylindrical cup drawing for the considered material, predicted cup profiles and thickness strain distributions, are compared with experimental data. The influence of the yield surface shape and the strenght differential effect on the predictions of the cup drawing process is assessed.

cup drawing; orthotropic material; asymmetric yield function; non-associated formulation

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