| Abstract Scope |
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 (FE) of the geometry of the final part (e.g. shape, thickness reduction) necessitates accurate modeling of the plastic anisotropy [1]). We present FE simulations of deep-drawing process for both single-crystals and polycrystalline materials. We use a crystal model [2] is defined for any stress and fulfills the symmetry requirements associated with the crystal lattice. Specifically, the crystal model is expressed in terms of generalized stress invariants, developed in the framework of the theory of representation of tensor functions. The predictive capabilities are demonstrated for deep-drawing of Al single crystal sheets. It is shown that depending on the crystal orientation, either four, six, or eight ears develop. Next, we present 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 polycrystalline material. 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, flow rule, consistency-condition) using a fully-implicit backward Euler method. Illustrative examples are presented for deep drawing of aluminum 6000 series.
[1] O. Cazacu, B.Revil-Baudard Plasticity of Metallic Materials: Modeling and Applications to Forming, Elsevier, 2020.
[2] O. Cazacu, et al., A yield criterion for cubic single crystals, Int J Solids Struct. 151 (2018) 9-19. |