The theoretical model of the effective strain establishment for the plate during the snake rolling

Abstract

Abstract The snake rolling for the heavy plate rolling has been verified that it can refine the grain and solve the problem of insufficient deformation in the center of the plate to some extent. The effective strain along the thickness is mainly obtained by the finite element method and the experiments which cost a long time and great material resources. A theoretical model of the effective strain is required to solve the problem. The metal flow model including the shear deformation is established according to the actual asymmetric distribution of stress and strain in the deformation zone. The parabolic roll gap inlet boundary equation is proposed according to the kinematic characteristics of plate rolling. The plastic deformation power, shear power and friction power models are established according to the first variational principle of the rigid plasticity and the principle of virtual velocity. The analytic model to calculate the effective strain of the snake rolling has been established by the principle of minimum energy and the theory of continuum mechanics. The model accuracy has also been verified by the finite element method and the experiments. The minimum and the maximum relative error is 1.33% and 13.44% which is acceptable for industrial applications. This research will provide an important guidance for the process and process parameters setup.