Inverse Problem in the Stochastic Approach to Modeling of Phase Transformations in Steels during Cooling after Hot Forming

Abstract The motivation for this research was the need for a reliable prediction of the distribution of microstructural parameters in steels during thermomechanical processing. The stochastic model describing the evolution of dislocation populations and grain size, which considers the random phenomena occurring during the hot forming of metallic alloys, was extended by including phase transformations during cooling. Accounting for a stochastic character of the nucleation of the new phase is the main feature of the model. Steel was selected as an example of the metallic alloy and equations describing the nucleation probability were proposed for ferrite, pearlite and bainite. The accuracy and reliability of the model depends on the correctness of the determination of the coefficients corresponding to the specific material. In the present paper these coefficients were identified using the inverse analysis for the experimental data. Experiments composed constant cooling rate tests for cooling rates in the range 0.1-20 °C/s. The inverse approach to a nonlinear model is ill-conditioned and must be transferred into an optimization problem, which requires formulating the appropriate objective function. Since the model is stochastic, it was a crucial, yet demanding task. The objective function based on a metric of the distance between measured and calculated histograms was proposed to achieve this goal. The original stochastic approach to identifying the phase transformation model for steels was tested, and an appropriate optimization strategy was proposed.