The mathematical modelling of thermo-mechanical processing of steel during multi-pass shape rolling

In this study, multi-pass shape rolling of bars, sections and rails is considered from theoretical point of view, first of all. For such a process, the material is subjected to the thermo-mechanical processing. The theoretical basis of such a process consists of mathematical modelling of metal flow, temperature and microstructural evolution, as well as the prediction of the final properties of sections. It allows the computer simulation of controlled rolling of products with very complicated cross-section shapes. The coupled thermo-mechanical-microstructural model, which is the main subject of the paper, can be split into several independent parts: thermo-mechanical processing, austenite microstructure evolution during thermo-mechanical steel treatment, pearlite transformation model and microstructural-mechanical properties. The mechanical part of the model uses a generalised plane-strain (GPS) approach, which allows savings in both the computing time and computer memory. The temperature distribution in the controlled volume at any stage is achieved by means of a non-steady-state solution of the general diffusion equation satisfying the coupled Neuman and Hankel boundary conditions. The microstructural evolution model predicts static recrystallisation to restore the austenite microstructure after deformation and dynamic recrystallisation; while the deformation temperatures and strain exceed the critical values at the same time as the metal is subjected to the deformation. In the processes considered, the static recrystallisation and austenite grain growth are the main processes, which determine the final austenite grain size. The majority of the paper is dedicated to theoretical considerations; some results of the modelling are also presented.