WIAS Preprint No. 375, (1997)

Numerical simulation of the surface hardening of steel


  • Fuhrmann, Jürgen
    ORCID: 0000-0003-4432-2434
  • Hömberg, Dietmar
    ORCID: 0000-0001-9460-5729

2010 Mathematics Subject Classification

  • 35K20 65C20 65N30


  • finite volume method, heat treatment, induction hardening, laser hardening, phase transitions




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 surface hardening applied to the steel 42 CrMo 4.

Appeared in

  • Internat. J. Numr. Methods Heat Fluid Flow, 9 (1999), pp. 705-724.

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