Development of Crystallographic Homogenization Finite Element Method to Study Crystal Texture Effects on Sheet Formability

摘要

A "semi-implicit" elastic/crystalline viscoplastic finite element analysis(FEA)code based on a "crystallographic homogenization" theory for the multi-scale analysis are developed,by introducing SEM-EBSD measured crystal texture.The homogenization algorithm is introduced to calculate macro-continuum plastic deformations and material properties by considering a micro-structural in-homogeneity,which is characterized by the crystal texture and the initial and deformation induced hardening evolutions.Its micro-structure is defined as the unit cell,which satisfy the periodicity condition,where both compatibility and equilibrium are satisfied.The conventional rate-dependent type crystal plasticity constitutive equation is employed in a micro-structure modeling.In the homogenization procedure,the asymptotic series expansion is introduced to define the displacement,which can be decomposed into two parts: the homogenized deformation defined by using the macro-continuum displacement and the perturbed one,defined only in the micro-structure.This "two-scale" analysis code enables to carry out transition from a representative micro-structure to the macro-continuum.This consistency model satisfies both the compatibility and the equilibrium in the micro-structure.This homogenization FE code is applied to study texture evolution induced by the plastic deformation,assess the formability of sheet metal,which has a ferrite phase,and confirm the availability through comparison with EBSD-SEM observation results.