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UNIVERSITÄT Zentrum für Technomathematik BREMEN Fachbereich 3 – Mathematik und Informatik Übersicht über einige makroskopische Modelle für Phasenumwandlungen im Stahl Michael Böhm Serguei Dachkovski Martin Hunkel Thomas Lübben Michael Wolff Report 03-09 Berichte aus der Technomathematik Report 03-09 August 2003

UNIVERSITÄT Zentrum für Technomathematik · 8 fp e eÚsinip k uonqÜ w nrâ[ws"w Û â[wÎã>ºßäg u"áx»sduoÜ w u Ý 8 8 8 å nqkiâÖËw ã>³ß g u"áx¬svuoÜ

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Page 1: UNIVERSITÄT Zentrum für Technomathematik · 8 fp e eÚsinip k uonqÜ w nrâ[ws"w Û â[wÎã>ºßäg u"áx»sduoÜ w u Ý 8 8 8 å nqkiâÖËw ã>³ß g u"áx¬svuoÜ

UNIVERSITÄT Zentrum für Technomathematik BREMEN Fachbereich 3 – Mathematik und Informatik

Übersicht über einige

makroskopische Modelle für

Phasenumwandlungen im Stahl

Michael Böhm Serguei Dachkovski

Martin Hunkel Thomas Lübben Michael Wolff

Report 03-09

Berichte aus der Technomathematik

Report 03-09 August 2003

Page 2: UNIVERSITÄT Zentrum für Technomathematik · 8 fp e eÚsinip k uonqÜ w nrâ[ws"w Û â[wÎã>ºßäg u"áx»sduoÜ w u Ý 8 8 8 å nqkiâÖËw ã>³ß g u"áx¬svuoÜ
Page 3: UNIVERSITÄT Zentrum für Technomathematik · 8 fp e eÚsinip k uonqÜ w nrâ[ws"w Û â[wÎã>ºßäg u"áx»sduoÜ w u Ý 8 8 8 å nqkiâÖËw ã>³ß g u"áx¬svuoÜ

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Page 22: UNIVERSITÄT Zentrum für Technomathematik · 8 fp e eÚsinip k uonqÜ w nrâ[ws"w Û â[wÎã>ºßäg u"áx»sduoÜ w u Ý 8 8 8 å nqkiâÖËw ã>³ß g u"áx¬svuoÜ

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Berichte aus der Technomathematik ISSN 1435-7968

http://www.math.uni-bremen.de/zetem/berichte.html- Vertrieb durch den Autor –

Reports Stand: 25. August 2003

98-01. Peter Benner, Heike Faßbender:An Implicitly Restarted Symplectic Lanczos Method for the SymplecticEigenvalue Problem, Juli 1998.

98-02. Heike Faßbender:Sliding Window Schemes for Discrete Least-Squares Approximation byTrigonometric Polynomials, Juli 1998.

98-03. Peter Benner, Maribel Castillo, Enrique S. Quintana Ortí:Parallel Partial Stabilizing Algorithms for Large Linear Control Systems, Juli1998.

98-04. Peter Benner:Computational Methods for Linear-Quadratic Optimization, August 1998.

98-05. Peter Benner, Ralph Byers, Enrique S. Quintana Ortí, Gregorio QuintanaOrtí:

Solving Algebraic Riccati Equations on Parallel Computers Using Newton’sMethod with Exact Line Search, August 1998.

98-06. Lars Grüne, Fabian Wirth:On the rate of convergence of infinite horizon discounted optimal valuefunctions, November 1998.

98-07. Peter Benner, Volker Mehrmann, Hongguo Xu:A Note on the Numerical Solution of Complex Hamiltonian and Skew-Hamiltonian Eigenvalue Problems, November 1998.

98-08. Eberhard Bänsch, Burkhard Höhn:Numerical simulation of a silicon floating zone with a free capillary surface,Dezember 1998.

99-01. Heike Faßbender:The Parameterized SR Algorithm for Symplectic (Butterfly) Matrices, Februar1999.

99-02. Heike Faßbender:Error Analysis of the symplectic Lanczos Method for the symplectic EigenvalueProblem, März 1999.

99-03. Eberhard Bänsch, Alfred Schmidt:Simulation of dendritic crystal growth with thermal convection, März 1999.

99-04. Eberhard Bänsch:Finite element discretization of the Navier-Stokes equations with a freecapillary surface, März 1999.

99-05. Peter Benner:Mathematik in der Berufspraxis, Juli 1999.

99-06. Andrew D.B. Paice, Fabian R. Wirth:Robustness of nonlinear systems and their domains of attraction, August1999.

99-07. Peter Benner, Enrique S. Quintana Ortí, Gregorio Quintana Ortí:

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Balanced Truncation Model Reduction of Large-Scale Dense Systems onParallel Computers, September 1999.

99-08. Ronald Stöver:Collocation methods for solving linear differential-algebraic boundary valueproblems, September 1999.

99-09. Huseyin Akcay:Modelling with Orthonormal Basis Functions, September 1999.

99-10. Heike Faßbender, D. Steven Mackey, Niloufer Mackey:Hamilton and Jacobi come full circle: Jacobi algorithms for structuredHamiltonian eigenproblems, Oktober 1999.

99-11. Peter Benner, Vincente Hernández, Antonio Pastor:On the Kleinman Iteration for Nonstabilizable System, Oktober 1999.

99-12. Peter Benner, Heike Faßbender:A Hybrid Method for the Numerical Solution of Discrete-Time Algebraic RiccatiEquations, November 1999.

99-13. Peter Benner, Enrique S. Quintana Ortí, Gregorio Quintana Ortí:Numerical Solution of Schur Stable Linear Matrix Equations onMulticomputers, November 1999.

99-14. Eberhard Bänsch, Karol Mikula:Adaptivity in 3D Image Processing, Dezember 1999.

00-01. Peter Benner, Volker Mehrmann, Hongguo Xu:Perturbation Analysis for the Eigenvalue Problem of a Formal Product ofMatrices, Januar 2000.

00-02. Ziping Huang:Finite Element Method for Mixed Problems with Penalty, Januar 2000.

00-03. Gianfrancesco Martinico:Recursive mesh refinement in 3D, Februar 2000.

00-04. Eberhard Bänsch, Christoph Egbers, Oliver Meincke, Nicoleta Scurtu:Taylor-Couette System with Asymmetric Boundary Conditions, Februar 2000.

00-05. Peter Benner:Symplectic Balancing of Hamiltonian Matrices, Februar 2000.

00-06. Fabio Camilli, Lars Grüne, Fabian Wirth:A regularization of Zubov’s equation for robust domains of attraction,, März2000.

00-07. Michael Wolff, Eberhard Bänsch, Michael Böhm, Dominic Davis:Modellierung der Abkühlung von Stahlbrammen, März 2000.

00-08. Stephan Dahlke, Peter Maaß, Gerd Teschke:Interpolating Scaling Functions with Duals, April 2000.

00-09. Jochen Behrens, Fabian Wirth:A globalization procedure for locally stabilizing controllers, Mai 2000.

00-10. Peter Maaß, Gerd Teschke, Werner Willmann, Günter Wollmann:Detection and Classification of Material Attributes -- A Practical Application ofWavelet Analysis, Mai 2000.

00-11. Stefan Boschert, Alfred Schmidt, Kunibert G. Siebert, Eberhard Bänsch,Klaus-Werner Benz, Gerhard Dziuk, Thomas Kaiser:

Simulation of Industrial Crystal Growth by the Vertical Bridgman Method, Mai2000.

00-12. Volker Lehmann, Gerd Teschke:Wavelet Based Methods for Improved Wind Profiler Signal Processing, Mai2000.

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00-13. Stephan Dahlke, Peter Maaß:A Note on Interpolating Scaling Functions, August 2000.

00-14. Ronny Ramlau, Rolf Clackdoyle, Frédéric Noo, Girish Bal:Accurate Attenuation Correction in SPECT Imaging using Optimization ofBilinear Functions and Assuming an Unknown Spatially-Varying AttenuationDistribution, September 2000.

00-15. Peter Kunkel, Ronald Stöver:Symmetric collocation methods for linear differential-algebraic boundary valueproblems, September 2000.

00-16. Fabian Wirth:The generalized spectral radius and extremal norms, Oktober 2000.

00-17. Frank Stenger, Ahmad Reza Naghsh-Nilchi, Jenny Niebsch, Ronny Ramlau:A unified approach to the approximate solution of PDE, November 2000.

00-18. Peter Benner, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí:Parallel algorithms for model reduction of discrete-time systems, Dezember2000.

00-19. Ronny Ramlau:A steepest descent algorithm for the global minimization of Tikhonov-Phillipsfunctional, Dezember 2000.

01-01. Torsten Köhler, Peter Maaß, Peter Wust, Martin Seebass:Efficient methods in hyperthermia treatment planning, Januar 2001.

01-02. Peter Benner, Ralph Byers, Rafael Mayo, Enrique S. Quintana-Ortí, VicenteHernández:

Parallel Algorithms for LQ Optimal Control of Discrete-Time Periodic LinearSystems, Februar 2001.

01-03. Peter Benner, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí:Efficient Numerical Algorithms for Balanced Stochastic Truncation, März 2001.

01-04. Peter Benner, Maribel Castillo, Enrique S. Quintana-Ortí:Partial Stabilization of Large-Scale Discrete-Time Linear Control Systems,März 2001.

01-05. Stephan Dahlke:Besov Regularity for Edge Singularities in Polyhedral Domains, Mai 2001.

01-06. Fabian Wirth:A linearization principle for robustness with respect to time-varyingperturbations, Mai 2001.

01-07. Stephan Dahlke, Wolfgang Dahmen, Karsten Urban:Adaptive Wavelet Methods for Saddle Point Problems - Optimal ConvergenceRates, Juli 2001.

01-08. Ronny Ramlau:Morozov’s Discrepancy Principle for Tikhonov regularization of nonlinearoperators, Juli 2001.

01-09. Michael Wolff:Einführung des Drucks für die instationären Stokes-Gleichungen mittels derMethode von Kaplan, Juli 2001.

01-10. Stephan Dahlke, Peter Maaß, Gerd Teschke:Reconstruction of Reflectivity Desities by Wavelet Transforms, August 2001.

01-11. Stephan Dahlke:Besov Regularity for the Neumann Problem, August 2001.

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01-12. Bernard Haasdonk, Mario Ohlberger, Martin Rumpf, Alfred Schmidt, Kunibert G. Siebert:h-p-Multiresolution Visualization of Adaptive Finite Element Simulations,Oktober 2001.

01-13. Stephan Dahlke, Gabriele Steidl, Gerd Teschke:Coorbit Spaces and Banach Frames on Homogeneous Spaces withApplications to Analyzing Functions on Spheres, August 2001.

02-01. Michael Wolff, Michael Böhm:Zur Modellierung der Thermoelasto-Plastizität mit Phasenumwandlungen beiStählen sowie der Umwandlungsplastizität, Februar 2002.

02-02. Stephan Dahlke, Peter Maaß:An Outline of Adaptive Wavelet Galerkin Methods for Tikhonov Regularizationof Inverse Parabolic Problems, April 2002.

02-03. Alfred Schmidt: A Multi-Mesh Finite Element Method for Phase Field Simulations, April 2002.02-04. Sergey N. Dachkovski, Michael Böhm: A Note on Finite Thermoplasticity with Phase Changes, July 2002.02-05. Michael Wolff, Michael Böhm:

Phasenumwandlungen und Umwandlungsplastizität bei Stählen im Konzeptder Thermoelasto-Plastizität, July 2002.

02-06. Gerd Teschke:Construction of Generalized Uncertainty Principles and Wavelets inAnisotropic Sobolev Spaces, August 2002.

02-07. Ronny Ramlau:TIGRA - an iterative algorithm for regularizing nonlinear ill-posed problems,August 2002.

02-08. Michael Lukaschewitsch, Peter Maaß, Michael Pidcock:Tikhonov regularization for Electrical Impedance Tomography on unboundeddomains, October 2002.

02-09. Volker Dicken, Peter Maaß, Ingo Menz, Jenny Niebsch, Ronny Ramlau:Inverse Unwuchtidentifikation an Flugtriebwerken mit Quetschöldämpfern,October 2002.

02-10. Torsten Köhler, Peter Maaß, Jan Kalden:Time-series forecasting for total volume data an charge back data, November2002

02-11. Angelika Bunse-Gerstner:A Short Introduction to Iterative Methods for Large Linear Systems, November2002.

02-12. Peter Kunkel, Volker Mehrmann, Ronald Stöver:Symmetric Collocation for Unstructured Nonlinear Differential-AlgebraicEquations of Arbitrary Index, November 2002.

02-13. Michael Wolff:Ringvorlesung:Distortion Engineering 2Kontinuumsmechanische Modellierung des Materialverhaltens von Stahl unterBerücksichtigung von Phasenumwandlungen, Dezember 2002.

03-01. Michael Wolff, Michael Böhm, Serguei Dachkovski:Volumenanteile versus Massenanteile – der Dilatometerversuch aus der Sichtder Kontinuumsmechanik, Januar 2003.

03-02 Daniel Kessler, Ricardo H. Nochetto, Alfred Schmidt:A posteriori error control for the Allen-Cahn Problem: circumventing Gronwall'sinequality, March 2003.

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03-03 Michael Böhm, Jörg Kropp, Adrian Muntean:On a Prediction Model for Concrete Carbonation based on Moving Interfaces -Interface concentrated Reactions, April 2003.

03-04 Michael Böhm, Jörg Kropp, Adrian Muntean:A Two-Reaction-Zones Moving-Interface Model for Predicting Ca(OH)_2-Carbonation in Concrete, April 2003.

03-05 Vladimir L. Kharitonov, Diederich Hinrichsen:Exponential estimates for time delay systems, May 2003.

03-06 Michael Wolff, Michael Böhm, Serguei Dachkovski, Günther Löwisch:Zur makroskopischen Modellierung von spannungsabhängigemUmwandlungsverhalten und Umwandlungsplastizität bei Stählen und ihrerexperimentellen Untersuchung in einfachen Versuchen, Juli 2003.

03-07 Serguei Dachkovski, Michael Böhm, Alfred Schmidt, Michael Wolff:Comparison of several kinetic equations for pearlite transformation in 100Cr6steel, August 2003.

03-08 Volker Dicken, Peter Maass, Ingo Menz, Jenny Niebsch, Ronny Ramlau:Nonlinear Inverse Unbalance Reconstruction in Rotor dynamics, Juli 2003.

03-09 Michael Böhm, Serguei Dachkovski, Martin Hunkel, Thomas Lübben, Michael Wolff: Übersicht über einige makroskopische Modelle fürPhasenumwandlungen im Stahl, August 2003.