metals
Article
Mathematical Modelling of Isothermal Decomposition of
Austenite in Steel
Božo Smoljan
1
, Dario Iljki´ c
2,
* , Sunˇ cana Smokvina Hanza
2
and Krunoslav Hajdek
1
Citation: Smoljan, B.; Iljki´ c, D.;
Smokvina Hanza, S.; Hajdek, K.
Mathematical Modelling of
Isothermal Decomposition of
Austenite in Steel. Metals 2021, 11,
1292. https://doi.org/10.3390/
met11081292
Academic Editors: Jose Diaz and
Henrik Saxen
Received: 15 June 2021
Accepted: 13 August 2021
Published: 16 August 2021
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1
Department of Packaging, Recycling and Environmental Protection, University North, University Center
Koprivnica, Trg Dr. Žarka Dolinara 1, 48000 Koprivnica, Croatia; bozo.smoljan@unin.hr (B.S.);
krunoslav.hajdek@unin.hr (K.H.)
2
Department of Materials Science and Engineering, Faculty of Engineering, University of Rijeka,
Vukovarska 58, 51000 Rijeka, Croatia; suncana@riteh.hr
* Correspondence: darioi@riteh.hr; Tel.: +385-51-651-474
Abstract: The main goal of this paper is mathematical modelling and computer simulation of
isothermal decomposition of austenite in steel. Mathematical modelling and computer simulation of
isothermal decomposition of austenite nowadays is becoming an indispensable tool for the prediction
of isothermal heat treatment results of steel. Besides that, the prediction of isothermal decomposition
of austenite can be applied for understanding, optimization and control of microstructure composition
and mechanical properties of steel. Isothermal decomposition of austenite is physically one of the
most complex engineering processes. In this paper, methods for setting the kinetic expressions for
prediction of isothermal decomposition of austenite into ferrite, pearlite or bainite were proposed.
After that, based on the chemical composition of hypoeutectoid steels, the quantification of the
parameters involved in kinetic expressions was performed. The established kinetic equations were
applied in the prediction of microstructure composition of hypoeutectoid steels.
Keywords: mathematical modelling; computer simulation; austenite decomposition kinetics;
microstructure transformations
1. Introduction
The research of the mathematical simulation of microstructure distribution in steel
is one of the highest-priority research areas in the simulation of phenomena of the heat
treatment of steel. By using the additivity rule and kinetic equations of isothermal de-
composition of austenite, it is possible to calculate kinetics of austenite decomposition at
continuous cooling of steel. The prediction of isothermal decomposition of austenite can
be applied for understanding, optimization and control of microstructure composition and
mechanical properties of steel [1–4].
The most common method of computer prediction of isothermal decomposition of
austenite results is based on the chemical composition of steel by using time-temperature-
transformation (TTT) diagrams [5].
Studies of the kinetics of isothermal decomposition of austenite have been intensified
in the course of some pioneering studies on the isothermal decomposition of austenite [6–8].
The prediction of microstructure composition is usually based on semi-empirical meth-
ods derived from kinetic equations of microstructure transformation [9]. To describe the
transformation kinetics by mathematical methods, a semi-empirical approach is employed
using the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation together with additivity
rule [10,11].
The phase transformations can be categorized into two categories: reconstructive
phase transformations and displacive phase transformations. Decompositions of austenite
into ferrite and pearlite in steels are typical examples of reconstructive phase transforma-
tions, while martensite, bainite, and Widmanstatten ferrite phase transformations can be
recognized as displacive phase transformations [12].
Metals 2021, 11, 1292. https://doi.org/10.3390/met11081292 https://www.mdpi.com/journal/metals