Study on non-associated plasticity with various forward Euler stress integration algorithms and its prediction of earing in cylindrical cup drawing

Abstract

Three anisotropic yield criteria, such as Hill's 48 [3], Yld2000-2d [6] as well as Drucker [32] under non-associated flow rule (simplified as non-AFR) are applied to predict earing profile after cylindrical cup drawing of aluminum alloy sheet AA2090-T3. Three forward Euler stress integration algorithms, i.e. tangent cutting plane explicit method (TCPE), semi explicit method (SEMIE) and simple explicit method (SIMPE) are implemented into user subroutines of ABAQUS/Explicit to simulation the deformation process. The predicted anisotropy coefficients including stress directionalities and r-values by single element tensile simulation are made comparisons with observed experimental results. The computation stability of different stress integration algorithms are also compared using specified time increments. The prediction of earing profile by anisotropic Hill's 48 and Yld2000-2d as well as Drucker yield functions with non-associated plasticity are compared with results of experiment to evaluate their accuracy. The computation times are also compared to evaluate the computing efficiency of these yield functions with different stress integration algorithms in numerical simulation of cup deep drawing. The comparison demonstrates that non-associated plastic constitutive model for Yld2000-2d using TCPE and SEMIE stress integration algorithms is the most accurate to simulate 6 earing profiles, while non-associated plastic constitutive model for Drucker using 3D solid elements is the most efficient. All the numerical simulation results indicate that no matter 2D shell or 3D solid elements are used in the simulation models, the TCPE stress integration algorithm is advised in consideration of computational efficiency and accuracy.