A semi-implicit elastic/crystalline viscoplastic finite element（FE） method based on a ＂crystallographic homogenization＂ approach is formulated for a multi-scale analysis. In the formulation, the asymptotic series expansion is introduced to define the displacement in the micro-continuum. This homogenization FE analysis is aimed at predicting the plastic deformation induced texture evolution of polycrystalline materials, the constituent microstructure of which is represented by an assembly of single crystal grains. The rate dependent crystal plasticity model is adopted for the description of microstructures. Their displacements are decomposed into two parts： the homogenized deformation defined in the macrocontinuum and the perturbed one in the micro-continuum. This multi-scale formulation makes it possible to carry out an alternative transition from a representative micro-structure to the macro-continuum. This homogenization procedure satisfies both the compatibility and the equilibrium in the micro-structure. This developed code is applied to predict the texture evolution, and its performance is demonstrated by the numerical examples of texture evolution of FCC polycrystalline metals.
The aim of this paper is to review the state-of-the-art SFPs and their applications,and to provide a guide for researchers and engineers working in this field.Various SFPs are classified according to the combination ways of stamping and forging operations.The process principle of each combination is reviewed,with its applications discussed.The state-of-the-art of SFPs suggests that future work in this field should focus on the development of high-strength die materials,better lubrication control methods,forming machines with intelligent control capacity and special functions,and some new SFPs for high strength or ultra-high strength materials.
