Fast Numerical Model for Predicting Residual Stresses in Hot Rolled Profiles Taking into Account Phase Transformations in Steel

The magnitude of residual stresses in hot-rolled profiles influences the quality of the final product. Cooling conditions after rolling are the main factor affecting the residual stresses. Beyond the thermal expansion, dilatation due to phase transformations is of particular importance. The prediction of residual stresses is usually associated with the three-dimensional coupled thermomechanical problem solved by the finite element method (FEM). In some cases, this is unacceptable due to the high costs of calculation. The paper proposes an alternative approach based on simplifying the description of the stress state in the profile. The model is based on the representation of the profile as a system of bars connected at the ends. Thus, only longitudinal stresses in the profile are taken into account. An elastic-plastic model of the material, which takes into account both the active load and the unloading when the temperature is equalized over the profile section is used. The thermal problem is solved for the cross-section of the profile using the FEM. To create a model of phase transformations, an approach based on a modified Leblond equation was used, which also significantly accelerates the calculation of the kinetics of phase transformations. All models were calibrated for 20MnCr5 steel based on appropriate mechanical and dilatometric tests on a range of steels. The last part of the work is devoted to the validation of the obtained model by comparing the calculation results with the measured residual stresses in the profiles. Simulation of the cooling process of the profiles under production conditions recapitulates the work.