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Article

Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical Effects

1
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cádiz, 11510 Puerto Real, Spain
2
Departamento de Matemática Aplicada I, Escuela Técnica Superior de Ingeniería Informática, Avda. Reina Mercedes, s/n, 41012 Sevilla, Spain
3
Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale, 72, 09124 Cagliari, Italy
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editors: Pablo Gregori and Vicente Martínez
Mathematics 2021, 9(11), 1203; https://doi.org/10.3390/math9111203
Received: 28 April 2021 / Revised: 18 May 2021 / Accepted: 21 May 2021 / Published: 26 May 2021
(This article belongs to the Special Issue Computational Methods in Nonlinear Analysis and Their Applications)
This paper summarizes a mathematical model for the industrial heating and cooling processes of a steel workpiece corresponding to the steering rack of an automobile. The general purpose of the heat treatment process is to create the necessary hardness on critical parts of the workpiece. Hardening consists of heating the workpiece up to a threshold temperature followed by a rapid cooling such as aquaquenching. The high hardness is due to the steel phase transformation accompanying the rapid cooling resulting in non-equilibrium phases, one of which is the hard microconstituent of steel, namely martensite. The mathematical model describes both processes, heating and cooling. During the first one, heat is produced by Joule’s effect from a very high alternating current passing through the rack. This situation is governed by a set of coupled PDEs/ODEs involving the electric potential, the magnetic vector potential, the temperature, the austenite transformation, the stresses and the displacement field. Once the workpiece has reached the desired temperature, the current is switched off an the cooling stage starts by aquaquenching. In this case, the governing equations involve the temperature, the austenite and martensite phase fractions, the stresses and the displacement field. This mathematical model has been solved by the FEM and 2D numerical simulations are discussed along the paper. View Full-Text
Keywords: steel hardening; thermomechanical problem; phase transitions; nonlinear coupled system of PDEs/ODEs; finite element method steel hardening; thermomechanical problem; phase transitions; nonlinear coupled system of PDEs/ODEs; finite element method
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MDPI and ACS Style

Díaz Moreno, J.M.; García Vázquez, C.; González Montesinos, M.T.; Ortegón Gallego, F.; Viglialoro, G. Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical Effects. Mathematics 2021, 9, 1203. https://doi.org/10.3390/math9111203

AMA Style

Díaz Moreno JM, García Vázquez C, González Montesinos MT, Ortegón Gallego F, Viglialoro G. Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical Effects. Mathematics. 2021; 9(11):1203. https://doi.org/10.3390/math9111203

Chicago/Turabian Style

Díaz Moreno, José Manuel, Concepción García Vázquez, María Teresa González Montesinos, Francisco Ortegón Gallego, and Giuseppe Viglialoro. 2021. "Industrial Steel Heat Treating: Numerical Simulation of Induction Heating and Aquaquenching Cooling with Mechanical Effects" Mathematics 9, no. 11: 1203. https://doi.org/10.3390/math9111203

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