Nonlocal multiscale modeling of deformation behavior of polycrystalline copper by second-order homogenization method

Engineering materials usually exhibit heterogeneity such as that observed in the polycrystalline structure of metals, and this heterogeneity affects the nonuniform deformation of a material. In this study, the micro- to macroscopic nonuniform deformation of polycrystalline copper specimen with a curved gage section is evaluated by a finite element method (FEM) simulation based on the second-order homogenization method (2nd-HM). The effects of the microstructure size and macroscopic stress gradient on the nonuniform deformation of the material are then investigated by comparing the simulation and experimental results. A two-dimensional plane strain polycrystalline microstructure was periodically applied to all the integration points in the macrostructure; the anisotropic deformation of the crystal grains is represented by the conventional crystalline plasticity constitutive equation. The computational results indicate that the interaction between nonuniform deformation on the micro and macroscopic scales induces a slight size effect in the material. However, the FEM simulation based on the 2nd-HM could not predict the decrease in the macroscopic strain concentration in the specimens with large crystalline grains, which was observed in the experimental studies, because of random strain localization resulting from the microscopic heterogeneity. Graphical abstract