Effect of anisotropic yield function evolution on formability of sheet metal

Abstract

For the evaluation of anisotropic yield functions and hardening models, formability has been often investigated in the forming of sheet metals. The formability has been investigated in many ways, but a common conclusion is that it is significantly influenced by sheet anisotropy, especially the directional differences in yield stress and r-value along the material direction. Therefore, numerous works have been presented in terms of the accurate modeling of anisotropic behavior of sheet metals and its implementation into the finite element simulations. The previous efforts include the effects of quadratic or non-quadratic yield functions, their associated or non-associated flow rules and isotropic or non-isotropic hardening laws on formability. However, most of these works assumed that the anisotropic yield functions maintain their initial shapes, while they evolve by isotropic expansion or kinematic translation. Then, they could not consider the anisotropic evolution under monotonic loading with different deformation modes. In the present work, various anisotropic constitutive models were comparatively evaluated for the performance in predicting the earing profile in the cup drawing and the forming limit diagram. The constitutive models include the Hill48 quadratic yield function with associated and non-associated flow rules, and the non-quadratic Yld2000-2d function with associated flow rule. For both yield functions, the evolution of anisotropy was employed by considering the anisotropic coefficients as a function of equivalent plastic strain. The influence of the anisotropy evolution was comparatively evaluated by the computational simulations.