A Combined Upper Bound and Fnite Element Model for Prediction of Velocity and Temperature Fields During Hot Rolling Process

Controlling strain distribution during rolling of metals is a significant task in designing a proper rolling layout. There are several models and approaches for prediction of strain, strain rate and temperature distributions during and after rolling operations. For instance, plane strain rolling process has been considered by Takuda et al. They have used an upper bound method to calculate roll force and required energy for cold rolling of metals under plane strain conditions. In another work, an upper bound method employing a spherical velocity field has been proposed to analyze hot rolling of austenitic steel sheets. Marques and Martins have used a dual stream function coupled with an upper bound model to determine required energy in three-dimensional rolling operations. Chung et al. have predicted velocity field during steady-state hot deformation operations including hot strip rolling of metals, by combining of stream-line coordinates and a two-dimensional finite difference method. Chen et al. have calculated temperature and strain fields by a coupled finite element method (FEM) and FDM codes. Nepershin has modeled metal flow in plane-strain rolling process assuming fully sticking friction conditions. A combined finite element-boundary element approach has been used to analyze the cold plane strain rolling process . the FEM has been used to determine the velocity field within the metal being deformed while the boundary element method has been employed for the determination of work-roll deformation. Bar rolling operations have been investigated using a steady-state rigid–viscoplastic finite element approach by Kim et al. There are also other published researches concerning mathematical modelling of cold or hot rolling of metals, while numerical techniques particularly the finite element analysis have been utilized for determining the deformation behavior in rolling metal . Although several published researches on the modelling of rolling can be found in the literature; however, because of the complex geometry of the deformation zone and the nonlinear behavior of metal particularly during hot rolling, more accurate models with relatively shorter run-time duration is still necessary in order to analyze the process during on-line rolling practice. a new approach is developed to propose an admissible velocity field in hot strip rolling process. This approach is based on the principle of volume constancy and a combination of upper bound method and the finite element analysis. A velocity field is first proposed, utilizing the principle of volume constancy, and then the velocity field is modified using the upper bound theorem. At the same time a thermal-finite element analysis is coupled with the deformation model to predict flow stress of deforming material as a function of temperature as well as to determine temperature distribution within the metal. The main point of the proposed model is its relatively short run-time duration in comparison with that inregular fully finite element codes.