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Cooperation with: LASERVORM Volumen und Oberflächenbearbeitung (Mittweida), probeam HÖRMANN GmbH (Neukirchen), J. Sokoowski (Université de Nancy I, France), H.J. Spies (TU Bergakademie Freiberg), S. Volkwein (KarlFranzensUniversität Graz, Austria)
Supported by: Stiftung Industrieforschung, Köln
Description:
In most structural components in mechanical engineering, there are surface parts which are particularly stressed. The aim of surface hardening is to increase the hardness of the corresponding boundary layers by rapid heating and subsequent quenching. This heat treatment leads to a change in the microstructure, which produces the desired hardening effect.
Depending on the respective heat source one can distinguish between different surface hardening procedures, the most important ones being induction hardening and radiation treatments like laser and electronbeam hardening.


To complete our industrial project on simulation and control of laser and electronbeam hardening a Mathematica tool has been developed and used to identify the transformation parameters of our phase transition model for a number of relevant steels. These parameters have been added to the data base of WIASSHarP. Numerical simulations for all these steels, with varying laser intensity and different workpiece geometries, have been carried out. The results, which are in good agreement with experiments (cf. Figures 1, 2), are documented in [1].
Another important control problem related to surface hardening is the optimal design of inductor coils for induction surface hardening. In [4] the speed method has been applied to investigate the sensitivity of solutions to the state equations with respect to perturbations of the inductor. In the case of inductors constructed from space curves it has been shown in [2] that one can relate the resulting shape gradient to a perturbation of the generating curve.
Figure 3 shows the complex interdependence of the relevant physical quantities for phase transitions in steel. The interplay between temperature and volume fraction z is well understood (cf., e.g., [1]). The metallurgical phases z_{i} have material parameters with different thermal characteristics, hence their effectice values have to be computed by a mixture ansatz. The different densities of the metallurgical phases result in a different thermal expansion. This thermal and transformation strain is the major contribution to the evolution of internal stresses during heat treatments. Experiments with phase transformations under applied loading show an additional irreversible deformation even when the equivalent stress corresponding to the load is far below the normal yield stress. This effect is called transformationinduced plasticity. The irreversible deformation leads to a mechanical dissipation that acts as a source term in the energy balance.
Neglecting the influence of internal stresses on the transformation kinetics, a consistent mathematical model which takes care of all these effects has been developed and analyzed in [2], [3].
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