2019, Hömberg, Dietmar, Krumbiegel, Klaus, Togobytska, Nataliya

An optimal control problem for the production of multiphase steel is investigated that takes into account phase transformations in the steel slab. The state equations are a semilinear heat equation coupled with an ordinary differential equation, that describes the evolution of the steel microstructure. The time-dependent heat transfer coefficient serves as a control function. Necessary and sufficient optimality conditions for the control problem are derived. For the numerical solution of the control problem, a reduced sequential quadratic programming method with a primal-dual active set strategy is developed. The numerical results are presented for the optimal control of a cooling line in the production of hot-rolled Mo–Mn dual phase steel. © 2019, The Author(s).

2015, Gorelova, S., Schaeben, H., Skrotzki, Werner, Oertel, Carl-Georg

Multi-pass rolling experiments with an AZ31 Twin Roll Cast (TRC) alloy were performed on an industrial scaled four-high rolling mill. Within the rolling with an intermediate annealing the evolution of texture was investigated. To quantify the extent of preferred crystallographic orientation experimental X-ray pole figures were measured after different process steps and analyzed using the free and open Matlab® toolbox MTEX for texture analysis. The development of the fiber texture was observed and analyzed in dependence on rolling conditions. In the initial state the specimen exhibits a texture composed of a weak basal texture and a cast texture with {0001}-planes oriented across the rolling direction. During the following rolling process a fiber texture was developed. The expected strength increment of the fiber texture was quantitatively confirmed in terms of volume portions of the orientation density function around the fiber and in terms of the canonical parameters of fitted pseudo Bingham distributions. On the results of this work a model for prediction of the texture evolution during the strip rolling of magnesium in the examined parameter range was developed.