A novel concurrent multiscale method based on the coupling of Direct FE2 and CPFEM

Performing concurrent simulations of macroscopic behaviors and microscopic structures using the crystal plasticity finite element method (CPFEM) presents a substantial difficulty with existing numerical techniques. To address this issue, a novel multi-scale method is proposed that couples CPFEM with a multiscale FEM, specifically Direct FE². This facilitates the implementation of Direct CP-FE² in this work. The micro representative volume elements (RVEs) equipped with a crystal plasticity constitutive model and the macro mesh are integrated into a monolithic solution scheme within the Direct FE² framework. The proposed method integrates the multiscale simulation capability of Direct FE² with the crystal plasticity model of CPFEM. Alpha titanium (α-Ti), which exhibits two distinct plastic mechanisms of slip and twinning, is chosen as the subject of investigation for conducting numerical experiments. The accuracy and efficiency of the Direct CP-FE² model are evaluated through multiple plate tension and beam bending tests. The effective validation against the FEM model demonstrated the capability of Direct CP-FE² to forecast macroscopic deformation behaviors. Meanwhile, the Direct CP-FE² model can reveal the activation of slip/twinning systems and the evolution of crystal texture at a microscopic level. The influence of the grain orientation-dependent effect can be well considered into the macroscopic analysis with the help of Direct CP-FE². Based on the testing examples, we demonstrate that the yield state of the macrostructure is enhanced when the crystal orientation is closer to the (0001) direction. Consequently, there exist very little crystal rotation behavior, hindering the evolution of the crystal texture.