Development of Dynamic Explicit Crystallographic Homogenization Finite Element Analysis Code to Assess Sheet Metal Formability

摘要

The Crystallographic texture evolution induced by plastic deformation in the sheet metal forming process has a great influence on its formability.In the present study,a dynamic explicit finite element(FE)analysis code is newly developed by introducing a Crystallographic homogenization method to estimate the polycrystalline sheet metal formability,such as the extreme thinning and "earing." This code can predict the plastic deformation induced texture evolution at the micro scale and the plastic anisotropy at the macro scale,simultaneously.This multi-scale analysis can couple the microscopic crystal plasticity inhomogeneous deformation with the macroscopic continuum deformation.In this homogenization process,the stress at the macro scale is defined by the volume average of those of the corresponding microscopic crystal aggregations in satisfying the equation of motion and compatibility condition in the micro scale "unit cell," where the periodicity of deformation is satisfied.This homogenization algorithm is implemented in the conventional dynamic explicit finite element code by employing the updated Lagrangian formulation and the rate type elastic/viscoplastic constitutive equation.At first,it has been confirmed through a texture evolution analyses in cases of typical deformation modes that Taylor's "constant strain homogenization algorithm" yields extreme concentration toward the preferred crystal orientations compared with our homogenization one.Second,we study the plastic anisotropy effects on "earing" in the hemispherical cup deep drawing process of pure ferrite phase sheet metal.By the comparison of analytical results with those of Taylor's assumption,conclusions are drawn that the present newly developed dynamic explicit Crystallographic homogenization FEM shows more reasonable prediction of plastic deformation induced texture evolution and plastic anisotropy at the macro scale.