Uncertainty and Stochasticity in Modelling of Microstructure Evolution During Hot Rolling of Steels Uncertainty and Stochasticity in Modelling of Microstructure Evolution During Hot Rolling of Steels

Advanced numerical models, which predict heterogeneity of microstructural features, are needed to design modern steels with heterogeneous microstructures. Models based on stochastic internal variables meet this requirement. Our stochastic model accounts for the random character of the recrystallization and transfers this randomness into equations describing the evolution of the dislocation populations and the grain size during the hot deformation of steels. The idea of the internal variable model, with the dislocation density and the grain size being stochastic variables, is described in the paper. The material parameters, which influence accuracy and reliability of the model, were identified. They compose shear modulus, lattice friction stress and the mean free pass for dislocations. Numerical test showing influence of these parameters on the identification of the model coefficients were performed and a hint how these parameters should be selected is given. Compression loads and histograms of the grain size measured in the experimental compression tests were used to identify the coefficients in the model. The model was applied to simulations of the industrial process of the hot strip rolling. It was shown that the model can be used to both predictions of the microstructural heterogeneity caused by the stochastic character of microstructure evolution and to the evaluation of the uncertainty of phase composition in the final product. The latter is due to the uncertainty of the boundary conditions.