Computational simulation of rolling process of polycrystalline plane strain model using second-order homogenization finite element method

The computational simulation of the rolling process of the polycrystalline metal plate is performed using the second-order homogenization finite element (FE) method. The dynamically updated boundary condition (BC), which can describe the relative slip displacement under counter-friction force, is introduced to reproduce the progress of nodal displacement and force BCs during the rolling process. To directly solve the displacement under the BC accompanying friction force, the components of the stiffness matrix constructed by the macroscopic FE structure are edited using the friction coefficient and the contact angle. The elasto-viscoplastic mechanical behavior of the microscopic polycrystalline structure is described by the conventional crystalline plasticity FE method, and the relative scale-depended micro- to macroscopic FE model is established using the second-order homogenization method. The computational simulations of the rolling process with different friction coefficients, rolling radii, compression ratios, and grain sizes were performed using the established FE model. The macroscopic computational results could represent the fundamental mechanical behaviors of the rolling process, e.g., reduction of the plate thickness, increase and decrease in the rolling force owing to changes in the contact area, tensile and compression stresses at the inlet and outlet areas of rolling, X-shaped local deformation band beneath the work roll, increase in the rolling load owing to the friction coefficient, work roll radius, and compression ratio. Furthermore, the microscopic computational results clarified that nonuniform deformation in the polycrystalline structure changes depending on the macroscopic position, and the nonuniformity increases with the compression ratio. The microstructure located at the upper area of the rolled material experiences a two-stage deformation characterized by the contact angle while such a two-stage deformation is not observed in the microstructure located inner area of the rolled material.