# Mathematical Research of the Phase Transformation Kinetics of Alloyed Steel

### Abstract

Regulation of the process parameters allows obtaining the required properties of the metal. A computer simulation of technological processes with allowance for structural and phase transformations of the metal forms the basis for the proper choice of those parameters. The purpose of the paper is to study the main diffusion and diffusion-free transformation processes in alloyed steels during heating and cooling using the methods of mathematical modeling. A comparative analysis of the kinetic equations of phase transformations including the Kolmogorov–Avrami and Austin–Rickett equations that describe in different ways the dependence of the diffusion transformation rate on the time and the attained degree of transformation is carried out. It is shown that the Austin–Rickett equation is equivalent to the Kolmogorov–Avrami equation with a smooth decrease of the Avrami exponent during the transformation process. The advantages of the Kolmogorov–Avrami equation for modeling the kinetics of ferrite-pearlite and bainite transformations and the validity of this equation for modeling the kinetics of martensite transformations during tempering are shown. The parameters for describing the tempering process of steel 35 at different temperatures are determined. The proposed model is compared with equations based on the Hollomon–Jaffe parameter. The diagrams of martensitic transformation of alloyed steels and the disadvantages of the Koistinen–Marburger equation used to describe them are analyzed. The equations of the temperature dependence of the degree of transformation, similar to the Kolmogorov–Avrami and Austin–Rickett equations, are derived. The equations contain the minimum set of the parameters that can be found from published data. An iterative algorithm for determining parameters of the proposed model providing the minimum rms deviation of the constructed dependence from the initial experimental data is developed. The dependence of the accuracy of approximation on the temperature of the onset of transformation is presented. The complex character of the martensitic transformation development in alloyed steels is revealed. The advantage of using equations of the Austin–Rickett type when constructing models with a limited amount of experimental data is shown. The results obtained make it possible to extend the approaches used in the modeling of diffusion processes of austenite decomposition to the description of the processes of martensite formation and decomposition in alloyed steels.

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Correspondence to A. S. Kurkin.

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Translated by N. Semenova

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Kurkin, A.S. Mathematical Research of the Phase Transformation Kinetics of Alloyed Steel. Inorg Mater 56, 1471–1477 (2020). https://doi.org/10.1134/S0020168520150091

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### Keywords:

• Kolmogorov–Avrami equation
• Austin–Rickett equation
• martensitic transformation
• alloyed steel
• martensite decomposition during tempering