Earing prediction with a stress invariant-based anisotropic yield function under non-associated flow rule

Abstract

In this work, a recently proposed anisotropic Drucker function is implemented with non-associated flow rule (non-AFR) to predict the earing profile during cup drawing. The finite element formulation under non-AFR is developed for the precise simulation of the deep drawing process with a strong anisotropic aluminum alloy of AA2090-T3. The comparison between the simulation and experimental results reveals that the earing profile numerically predicted by the anisotropic Drucker function under non-AFR is in good agreement with the measured profile from experiments. It's also reveal that the improvement of accuracy of prediction for r-values does not always mean the synchronously improvement in prediction the earing profile for strong anisotropic phenomena of deep drawing for AA2090-T3. The computation efficiency of the anisotropic Drucker function is also investigated and compared with the Yld2004-18p function, which shows that 40% reduction of computational cost can be reached. The influence of different shapes of yield and potential on earing prediction is also investigated by combining the anisotropic Drucker function and Yld2004-18p function under non-AFR, which demonstrates that a proper shape of plastic potential is very important to predict the small ear around 0o for AA2090-T3. It also proves that both the yield and plastic potential functions strongly influence the height and earing profile in the simulation of cup deep drawing. It's also should be mentioned that the r-value does not keep constant in the simulation in the uniaxial tension of a single cubic element, but varies with the increase of plastic deformation in directional uniaxial tension, which may raise the difficulty for accurately prediction in metal forming.