Modelling of Stress State, Centre Consolidation and Roll Force in Billet Rolling

Roll pressure models have been derived from theoretical studies, FEM simulations and experimental investigations. A model developed from slip line field theory has been shown to fit well to the experimental results. The Finite Element simulations overestimated the pressure function. This is a common problem in hot rolling experiments, since the problem of measuring the correct rolling temperature makes the estimation of the yield strength very difficult. The difference between the FE calculations and the experimental measurements is a measure for the error in the experimental temperature measurements rather than for the accuracy of the Finite Element Method. Traditional modelling has not been an appropriate tool to evaluate the material flow in the centre of the billet. In spite of the fact that the entire stress state can be modelled by slip line field theory, the slip lines which determine the stress state in the centre coincide for actual geometries only in one single point. Thus the strain increments are known only in that single point. Since a material element passes that point instantaneously, it is not possible to find any finite strains in the centre by integrating any incremental function. By FEM, strain modelling is simple and the possibility to consolidate a porous bloom or ingot core can be determined. FE modelling requires an entirely new approach to the modelling problem. It is not reasonable to use FEM to evaluate only the temperature distribution for the use in roll force models from the previous century. Instead, a fully thermomechanically coupled FE model is suggested. However, the calculation time is still far too long to be used for on‐line control purposes. For this application hybrid modelling can be a solution, where off‐line FE models are combined with empirical modelling, and simplified models can be used for the process control.