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Project Details
| Project ID |
C11
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| Application Area |
C
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| Project Title |
Modeling and optimization of phase transitions in steel
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| Description |
Steel is still the
basic construction material for industrial societies.
A distinct feature of steel is that one can change its physical
properties by thermal interference. The reason for this behavior lies in the
occurring solid--solid phase transitions. It is utilized in the heat treatment
of steel, which is a process of controlled heating and cooling to achieve a
desired distribution of metallurgical phases corresponding to locally
varying, heterogeneous physical properties.
The mathematical description of solid-solid phase transitions in steel started
with the pioneering works of Avrami and Kolmogorov in
the thirties of the last century. They investigated so-called nucleation- and
growth phase transitions like the transformation from austenite to pearlite.
Stimulated by the development of ever-faster computer hardware, numerous papers
were published on the numerical simulation of diffusion controlled phase
transitions in steel. The
first analytical investigation of phase transitions in steel, concerned
with the austenite - pearlite transformation, is due to Visintin.
In a series of papers, Hömberg has investigated the interplay between
temperature evolution and phase volume fractions in steel, with respect to
modeling and analysis as well as with respect to numerical simulations of heat treatments.
In a joint project with industrial partners and metallurgists
from the TU Bergakademie Freiberg related to laser and electron beam hardening,
temperature-dependent data functions
for a number of important steels have been identified.
During the
last 15 years, also the thermomechanical modeling of phase transitions in steel
became an active research topic of physical metallurgy.
It seems that there is no unified thermomechanical model at
hand so far that is well accepted and that allows to reproduce all
experiments. However, it is quite clear what the principle
effects are that a macroscopic model be able to reproduce.
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| Duration |
04/03-05/10
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| Status |
running
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| Members |
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| Heads |
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| Guests |
| Dr. Martijn Anthonissen | | Prof. Dr. Viorel Arnautu | | Prof. Dr. Krzysztof Chelminski | | Prof. Dr. Krzysztof Chelminski | | Prof. Dr. Juan Carlos de los Reyes | | Prof. Dr. Alexander Khludnev | | Prof. Dr. Alexander Khludnev | | Prof. Dr. Jijun Liu | | Prof. Dr. Francisco Ortegón Gallego | | Lucia Panizzi | | Verena Petzet | | Tyrone Rees | | Prof. Dr. Wolfgang Ring | | Prof. Dr. Elisabetta Rocca | | Prof. Dr. Jan Sokolowski | | Prof. Dr. Masahiro Yamamoto | | Prof. Dr. Masahiro Yamamoto |
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| Publications |
A mathematical model for case hardening of steel
Fasano, Antonio, and Hömberg, Dietmar, and Panizzi, Lucia, in: Math. Models Methods Appl. Sci. (2009) | On the evaluation of dilatometer experiments
Hömberg, Dietmar, and Togobytska, Nataliya, and Yamamoto, Masahiro, in: Appl. Anal. (2009) | The heat treatment of steel - a mathematical control problem
Hömberg, Dietmar and Kern, Daniela, in: Materialwiss. Werkstofftech. (2009) | Optimal control for the thermistor problem
D. Hömberg, C. Meyer, J. Rehberg, R. Ring, in: SIAM J. Control Optim. (2009) | Modeling, analysis and stability of milling processes including workpiece effects
Hömberg, Dietmar and Rott, Oliver, in: Proceedings ECMI 2008 (2009) | On a thermomechanical model of phase transitions in steel
Hömberg, Dietmar, and Chelminski, Krzysztof, and Kern, Daniela, in: Adv. Math. Sci. Appl. (2008) | Optimal control of the thermistor problem
Meyer, Christian and Hömberg, Dietmar and Rehberg, Joachim and Ring, Wolfgang, in: Optimal Control of Coupled Systems of PDE, Workshop, March 2-8, 2008 (2008) | Analysis of a thermomechanical phase transition model
Chelminski, Krzysztof and Hömberg, Dietmar and Kern, Daniela, in: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007 (2008) | Optimal control of a thermomechanical model of phase transitions in steel
Hömberg, Dietmar and Kern, Daniela and Weiss, Wolf, in: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007 (2008) | Mathematik für Werkzeugmaschinen und Fabrikautomatisierung
Denkena, Berend and Hömberg, Dietmar and Uhlmann, Eckhart, in: Produktionsfaktor Mathematik. Wie Mathematik Technik und Wirtschaft bewegt, acatech diskutiert (2008) | Phase transformation modeling and parameter identification from dilatometric investigations
Suwanpinij, Piyada, and Togobytska, Nataliya, and Keul, Christoph, and Weiss, Wolf, and Prahl, Ulrich, and Hömberg, Dietmar, and Bleck, Wolfgang, in: Steel Res. Int. (2008) | The heat treatment of steel - A mathematical control problem
Hömberg, Dietmar, and Kern, Daniela, in: Proceedings of the 2nd International Conference on Distortion Engineering - IDE 2008, 17 - 19 September 2008 (2008) | Extended thermodynamics with consistent order
Weiss, Wolf, in: Waves and Stability in Continuous Media. Proceedings of the 13th Conference on WASCOM 2005, Catania, Italy, 19-25 June 2005 (2006) | Die Wärmebehandlung von Stahl - ein Optimierungsproblem
Hömberg Dietmar and Kern, Daniela and Weiss, Wolf, in: Distortion Engineering - Verzugsbeherrschung in der Fertigung III (2006) | Simulationsbasierte Regelung der Laserhärtung von Stahl
Alder, Holger and Hömberg, Dietmar and Weiss, Wolf, in: HTM Z. Werkst. Wärmebeh. Fertigung (2006) | A thermoelastic contact problem with a phase transition
Hömberg, Dietmar and Khludnev, Alexander, in: IMA J. Appl. Math. (2006) | PID-control of laser surface hardening of steel
Hömberg, Dietmar and Weiss, Wolf, in: IEEE Trans. Control Systems Technol. (2006) | Real-time control of surface remelting
Anthonissen, Martijn and Hömberg, Dietmar and Weiss, Wolf, in: Progress in Industrial Mathematics at ECMI 2004 (2005) | Entropy and Energy. A Universal Competition
Müller, Ingo and Weiss, Wolf (2005) | A mathematical model for induction hardening including mechanical effects
Hömberg, Dietmar, in: Nonlinear Anal. Real World Appl. (2004) | A thermoelastic contact problem with a phase transition
Hömberg, Dietmar and Khludnev, Alexander, in: Weierstraß-Institut für Angewandte Analysis und Stochastik (2004) | Optimal control strategies for the surface hardening of steel
Hömberg, Dietmar and Volkwein, Stefan and Weiss, Wolf, in: Proceedings of the 2nd International Conference on Thermal Process Modelling and Computer Simulation, Nancy, France, March 31 -- April 2, 2003 (2004) | Control of laser surface hardening by a reduced-order approach using proper orthogonal decomposition
Hömberg, Dietmar and Volkwein, Stefan, in: Math. Comput. Modelling (2003) | Optimal shape design of inductor coils for surface hardening
Hömberg, Dietmar and Sokolowski, Jan, in: SIAM J. Control Optim. (2003) | Extended thermodynamics --- consistent in order of magnitude
Müller, Ingo and Reitebuch, Daniel and Weiss, Wolf, in: Contin. Mech. Thermodyn. (2003) | Modeling, simulation and control of laser heat treatments
Fuhrmann, Jürgen and Hömberg, Dietmar and Sokolowski, Jan, in: Optimal Control of Complex Structure (Oberwolfach 2000) (2002) | Numerical simulation of surface heat treatments
Fuhrmann, Jürgen and Hömberg, Dietmar, in: Journal of Numerical Methods for Heat and Fluid Flow (1999) |
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| Preprints |
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| Website |
http://www.wias-berlin.de/projects/matheon-c11/
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