Crystallographic homogenization finite element method and its application on simulation of evolution of plastic deformation induced texture

Abstract

A crystallographic homogenization method is proposed and implemented to predict the evolution of plastic deformation induced texture and plastic anisotropy (earring) in the stamping of polycrystalline sheet metals. The microscopic inhomogeneity of crystal aggregate has been taken into account with the microstructure made up of a representative aggregate of single crystal grains. Multi-scale analysis is performed by coupling the microscopic crystal plasticity with the macroscopic continuum response through the present homogenization procedure. The macroscopic stress is defined as the volume average of the corresponding microscopic crystal aggregations, which simultaneously satisfies the equation of motion in both micro- and macro-states. The proposed numerical implementation is based on a finite element discretization of the macro-continuum, which is locally coupled at each Gaussian point with a finite element discretization of the attached micro-structure. The solution strategy for the macro-continuum and the pointwise-attached micro-structure is implemented by the simultaneous employment of dynamic explicit FE formulation. The rate-dependent crystal plasticity model is used for the constitutive description of the constituent single crystal grains. It has been confirmed that Taylor’s constant strain homogenization assumption yields an undue concentration of the preferred crystal orientation compared with the present homogenization in the prediction of texture evolution, with the latter having relaxed the constraints on the crystal grains. Two kinds of numerical examples are presented to demonstrate the capability of the developed code: 1) The texture evolution of three representative deformation modes, and 2) Plastic anisotropy (earring) prediction in the hemispherical cup deep drawing process of aluminum alloy A5052 with initial texture. By comparison of simulation results with those obtained employing direct crystal plasticity calculation adopting Taylor assumption, conclusions are drawn that the proposed dynamic explicit crystallographic homogenization FEM is able to more accurately predict the plastic deformation induced texture evolution and plastic anisotropy in the deep drawing process.