Problem of Identification of Phase Transformation Models Used in Simulations of Steels Processing

Abstract

Accuracy of phase transformation models depends on the correctness of coefficients evaluation, adequate to the investigated material. Dilatometric tests combined with the inverse analysis are used to perform identification. Since the problem is nonlinear, analytical approach is not possible and the inverse solution is transferred into the optimization task. It leads to difficulties typical for optimization of multivariable function such as local minima and lack of proof of the uniqueness. The problem of the effectiveness and uniqueness of the inverse algorithms used for identification of phase transformation models for steels was investigated for two models. The first was a modified JMAK (Johnson-Mehl-Avrami-Kolmogorov) equation. The second was an upgrade of the Leblond equation, in which second-order derivative of the volume fraction with respect to time was introduced. In classical identification, the result for one transformation depends on the coefficients for the remaining transformations and optimization has to be performed several times until the compatibility between transformations is reached. To avoid encountered problems, complex optimization simultaneously for all coefficients in the models was performed. This approach was based on nature-inspired optimization techniques. Models with identified coefficients for various steels were validated in simulations of industrial processes of laminar cooling and continuous annealing of strips.

Phase transformation model for adjusting the cooling conditions in Stelmor process to obtain the targeted structure of thermomechanically rolled wire rod used for fastener production

“…The second reason for using CCT diagrams is connected with the fact that an algorithm which allows the identification of the phase transformation model on the basis of constant cooling rate experiments, could be used. This algorithm is described in [14,15] and an example of its practical application can be found in [16].…”

“…An inverse algorithm developed by the Authors of [14] was applied in the identification procedure. The adaptation of this algorithm to the dilatometric tests is described in [15]. The results of the CCT tests were used in the objective function:…”

Application of the Phase Transformation Model for the Design of the Cooling Conditions in Stelmor Process to Obtain a Favorable Multiphase Microstructure of Wire Rod for Cold Heading Applications

“…Adaptation of this algorithm to the dilatometric tests is described in ref. [30]. The results of the CCT tests were used in the objective function Coefficients in the model were determined by searching for the minimum of the objective function (10) with respect to the confidents a.…”

“…Since for the slow cooling the difference between the two points was negligible, the results for the point A only are shown. [30] Different situation has to be considered for the accelerated cooling, which is needed when bainitic microstructure in the wire rod is expected. The temperature difference between the surface and the center of the rod reaches 20 °C for the diameter of 10.5 mm, over 30 °C for the diameter of 16 mm, and over 70 °C for the diameter of 24 mm.…”

Physical and Numerical Simulations of Closed Die Hot Forging and Heat Treatment of Forged Parts

“…In the analysis, the phase transformations start and finish temperatures, as well as volume fractions of structural constituents, determined in the dilatometric experiments, were used. Basic principles of application of this method to phase transformation models are described in [22]. In a majority of earlier applications of this method, results of the constant cooling rate (CCT) tests only were satisfactory to obtain reliable results.…”