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Evolution of Plastic Anisotropy During Deformation of Metal Sheets

机译：Evolution of Plastic Anisotropy During Deformation of Metal Sheets

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摘要

Plastic anisotropy evolution during metal forming processes of sheet elements and a corresponding FEM procedure are presented. It is assumed that the representative sheet element is composed of one kind of f.c.c. crystals. Grains are elastic-ideally plastic, but material of the macroscopic element is elastic-plastic with isotropic hardening. The element remains plastically orthotropic during a plastic flow. The orthotropy and its evolution are caused by a formation and development of deformation textures. The sheet element is considered simultaneously at the macroscopic level - as uniform continuum, and at the mezoscopic level - as a polycrystalline aggregate. At the macroscopic level, the stress and the strain rate are connected by the Prandtl-Reuss equations based on the Barlat and Lian formulation. According to this formulation the anisotropic yield function is described by four material parameters Y_1, Y_2, Y_p, k taken from four experimental tests: uniaxial tension in two orthogonal directions, equibiaxial tension and pure shear in the sheet plane along the above directions. In the presented paper, the parameters Y_1, Y_2, Y_p, k are determined on the beginning of the deformation process only. Later we pass at the mezoscopic level, and the above parameters are specified by a current crystallographic texture as functions of time: Y_1(t), Y_2(t), Y_p(t), k(t). Then, one can watch an evolution of plastic orthotropy during the whole deformation process. General strategy of computations is the same as in the standard FEM analysis. However, due to considerations at the mezoscopic level, the finite element analysis must be executed at each step of the process within three main loops: over the elements, over the integration points and over the grains filling out the volume of polycrystalline element.

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