Modeling of Sheet Metal Forming Based on Implicit Embedding of the Elasto-Plastic Self-Consistent Formulation in Shell Elements: Application to Cup Drawing of AA6022-T4 MILOVAN ZECEVIC 1 and MARKO KNEZEVIC 1,2 1.—Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA. 2.—e-mail: marko.knezevic@unh.edu This article is concerned with multilevel simulations in sheet metal forming using a physically based polycrystalline homogenization model that takes into account microstructure and the directionality of deformation mechanisms acting at single-crystal level. The polycrystalline-level model is based on the elasto-plastic self-consistent (EPSC) homogenization of single-crystal behavior providing a constitutive response at each material point, within a boundary value problem solved using shell elements at the macro-level. A recently de- rived consistent tangent stiffness is adapted here to facilitate the coupling between EPSC and the implicit shell elements. The underlining EPSC model integrates a hardening law based on dislocation density, which is calibrated to predict anisotropic hardening, linear and nonlinear unloading, and the Bau- schinger effect on the load reversal for AA6022-T4. To illustrate the potential of the coupled multilevel finite element elasto-plastic self-consistent (FE- EPSC) model, a simulation of cup drawing from an AA6022-T4 sheet is per- formed. Results and details of the approach are described in this article. INTRODUCTION In metal forming, metals are usually deformed to large plastic strains and develop nonuniform stress–strain fields. 1–5 It is well known that the glide of dislocations (crystallographic slip) accom- modates most plastic strains. Crystallographic slip induces anisotropy in the mechanical response by evolution of texture and dislocation structure. Additionally, intra- and inter-granular elastic deformation fields develop playing an important role in the overall deformation process and, in particular, during unloading and strain path changes. 6–8 For example, during application of strain in the reversed direction, the material exhibits nonlinear unloading first 2 and then a reduction in yield stress from that reached at the end of prestraining known as the Bauschinger effect (BE). 6 The hardening rate that follows with continuation of straining in the reverse direction is usually lower from that during prestraining. This stress offset between forward and reversed flow is referred to as the permanent softening. 9,10 These characteristics of material behavior are governed by the evolution of the underlying physical phe- nomena created by crystallographic slip within the material microstructure. The nonlinear unloading is facilitated by partial re-emission of dislocations impeded by grain bound- aries during forward loading. 11 The impeded dislo- cations are referred to as the dislocation pile-ups. The dislocation re-emission from the pile-ups is facilitated by the relaxation of micro backstresses acting in the vicinity of pile-ups. The higher the prestrain level, the higher the deviation from the linear elastic unloading behavior. Hence, to predict the nonlinear unloading, a constitutive law in use must accurately model prestraining. The BE has been extensively studied in both single-crystal 12 and polycrystalline metals. 13,14 The origin of BE is stablished to be backstress. The built-up backstress acts against the applied stress during forward loading. During loading in the reverse direction, the applied stresses combine with the backstresses, which results in a drop of the reverse yield stress. The change in the hardening rate after load reversal JOM DOI: 10.1007/s11837-017-2255-4 Ó 2017 The Minerals, Metals & Materials Society