Analytical description of the hot rolling process by the plastic flow method

Abstract

Titov V., Lavrinenkov A., Vlasiuk I. Analytical description of the hot rolling process by the plastic flow method

The stress-strain state of the metal in the deformation zone during hot rolling is investigated by analytical and numerical methods. The relevance of the work is due to the need to improve the accuracy of engineering calculations of rolling parameters for multilayer and thick billets, for which classical one-dimensional models do not reflect the real inhomogeneity of the plastic flow of metal along the thickness. The aim of the study is to develop an analytical method for estimating mean and normal stresses in the deformation zone based on the theory of plastic flow using a predetermined kinematically admissible velocity field. An analytical review of modern approaches to modeling the rolling process, in particular the force balance method and the upper bound method, is carried out in the paper. A plane model of metal flow with a nonlinear distribution of displacement velocity components in the zone of contact with the rolls is proposed. Based on the continuity equation, strain rates are obtained and the strain rate intensity is determined in the entire volume of the deformation zone. The position of the neutral section is established from the condition of the balance of external forces acting on the strip. For a perfectly plastic material, the stiffness coefficient, mean and normal stresses are determined by integrating the plastic flow equations taking into account the boundary conditions at the entrance to the deformation zone. To verify the reliability of analytical results, numerical simulation of the rolling process was performed using the finite element method in the Abaqus CAE environment. Distributions of mean stresses were obtained and compared with analytical dependencies in the symmetry plane of the strip. Quantitative coincidence of stresses at the entrance and exit from the deformation zone and qualitative correspondence of the nature of their distribution along the length of the zone were established. The obtained results can be used for engineering analysis of hot rolling processes of multilayer samples and samples in shells, and the prospects for further research are associated with taking into account the influence of contact friction on the kinematic field, temperature inhomogeneity, real laws of material hardening and extending the method to multilayer rolling problems.