Numerical simulation of the surface hardening of steel

We discuss a model that is capable of describing the solid‐solid phase transitions in steel. It consists of a system of ordinary differential equations for the volume fractions of the occuring phases coupled with a nonlinear energy balance equation to take care of the latent heats of the phase changes. This model is applied to simulate surface heat treatments, which play an important role in the manufacturing of steel. Two different technologies are considered: laser and induction hardening. In the latter case the model has to be extended by Maxwell’s equations. Finally, we present numerical simulations of laser and induction hardening applied to the steel 42CrMo4.

[1]  Dietmar Hömberg,et al.  Optimal Control of Laser Hardening , 1997 .

[2]  Dietmar Hömberg,et al.  Irreversible phase transitions in steel , 1997 .

[3]  J. Fuhrmann.  On Numerical Solution Methods for Nonlinear Parabolic Problems , 1997 .

[4]  D. Hoemberg.  A numerical simulation of the Jominy end-quench test , 1996 .

[5]  A. Fasano,et al.  An analysis of phase transition models , 1996, European Journal of Applied Mathematics.

[6]  D. Hömberg.  A mathematical model for the phase transitions in eutectoid carbon steel , 1995 .

[7]  A. Samarskii.  Mathematical modeling in the technology of laser treatments of materials , 1994 .

[8]  J. Rappaz,et al.  Numerical Modeling of Induction-Heating for 2-Dimensional Geometries , 1993 .

[9]  Ilja Schmelzer,et al.  3D anisotropic grid generation with intersection-based geometry interface , 1993 .

[10]  José Francisco Rodrigues,et al.  A NONLINEAR PARABOLIC SYSTEM ARISING IN THERMOMECHANICS AND IN THERMOMAGNETISM , 1992 .

[11]  R. Hoppe,et al.  Multi‐grid solution of two coupled Stefan equations arising in induction heating of large steel slabs , 1990 .

[12]  A. Visintin,et al.  A mathematical model of the austenite-pearlite transformation in plain carbon steel based on the Scheil's additivity rule , 1987 .

[13]  A. Visintin.  Mathematical Models of Solid-Solid Phase Transitions in Steel , 1987 .

[14]  Jean-Baptiste Leblond,et al.  A new kinetic model for anisothermal metallurgical transformations in steels including effect of austenite grain size , 1984 .

[15]  Energie und Betriebswirtschaftsstelle des Vereins Deutsche Eisenhüttenleute.  Anhaltszahlen für die Wärmewirtschaft in Eisenhüttenwerken , 1957 .

[16]  Verein Deutscher Eisenhüttenleute,et al.  Atlas zur Wärmebehandlung der Stähle , 1954 .