3-D FE Forming Simulations Accounting for Texture Induced Anisotropy

Material processing induces preferential arrangements of the grains which in turn results in anisotropy in the macroscopic plastic properties. Improvement of the finite-element predictions of the geometry of the final part (e.g. shape, thickness reduction) necessitates accurate modeling of the plastic anisotropy (see [1]). In this paper, we present finite-element (FE) simulations of deep-drawing process in which we account for both the anisotropy in the plastic deformation of the constituent grains and the initial texture of the material. Specifically, an elastoplastic anisotropic constitutive model recently developed [2] is used to model the crystal level behavior. This crystal model is defined for any stress state and fulfills the symmetry requirements associate with crystal lattice. In the FE simulations, a polycrystalline aggregate is associated with each FE integration point. The FE code imposes the computed macroscopic velocity gradient on the polycrystal. The orientation and the hardening of the individual grains, which depend on the deformation history of the element, are updated, and the macroscopic stress for use in the solution of the continuum equilibrium equations is obtained from the stresses in each grain, which in turn were calculated by solving the full-set of coupled equations governing the elasto-plastic single crystal behavior (i.e. elastic response, the crystal yield condition expressed in terms of anisotropic invariants (see [3]), flow rule, consistency-condition) using a fully-implicit backward Euler method. Illustrative examples presented demonstrate the predictive capabilities of our model to describe the behavior of strongly textured materials for the highly non-linear applications.