Evaluation of Non-Uniform Deformation Behavior of Polycrystalline Materials Using Second-Order Homogenization Method

The effect of crystalline grain size on the macroscopic non-uniform deformation of polycrystalline materials was evaluated by FEM simulation based on the rate-form second-order homogenization method. The conventional crystalline plasticity theory was applied to represent the scale-independent deformation behavior of microscopic crystalline structure. Numerical simulations of macroscopically uniform bending and uniaxial tension of curved gage section specimen were performed to give the non-uniform deformation on the macroscopic region. Polycrystalline microstructures with different grain sizes were given to all Gauss integration points on macrostructure. In the bending simulation, the effect of microstructure size on the relationship between macroscopic strain gradient and its work conjugate higher-order stress was evaluated. Larger energy was required for the bending of larger microstructure model, and a similar characteristic was confirmed in the simulation of full scale model. Furthermore, higher deformation localization in the macrostructure was observed when a larger tensile deformation was given to the curved gage section specimen with smaller crystal grain. This size effect on the non-uniform deformation of the polycrystalline materials was caused by non-uniform deformation in microstructure, which was strongly characterized by the macroscopic strain gradient and the size of the microstructure.