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Modeling and simulation of thermochemical heat treatment processes [Elektronische Ressource] : a phase field calculation of nitriding in steel / von Yakub Adesoga Tijani

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Modeling and Simulation of ThermochemicalHeat Treatment Processes: A Phase FieldCalculation of Nitriding in Steelvon Yakub Adesoga TijaniDissertationzur Erlangung des Grades eines Doktors der Ingenieurwissenschaften– Dr. Ing. –Vorgelegt im Fachbereich 3 (Mathematik & Informatik)der Universit¨ at Bremenim Juni 2008iiDatum des Promotionskolloquiums: 14.07.2008Gutachter:Prof. Dr. Michael Bohm¨ Prof. Dr.-Ing. Franz HoffmannZentrum fur¨ Technomathematik Institut fur¨ Werkstofftechnik (IWT)Universit¨ at Bremen, Deutschland. Bremen, Deutschland.AbstractIn order to provide greater improvements in material performance with respectto hardness, fatigue, wear resistance and corrosion resistance, among other me-chanical properties, nitrogen is commonly introduced on steel surface at elevatedtemperature. Such enhancement, referred to as nitriding, results in the diffusion ofnitrogen into the steel with development of continuous layers of iron-based nitridesand precipitation of alloying-element nitrides, depending on the nitriding kinetics.Up till now, the simulation of nitriding process is done only under restricted con-ditions by using classical models which describe the diffuse nitriding layers withsharp interfaces. However, the classical models lead to difficulties in the compu-tation of the free boundary problem, since the position of the interface has to becalculated explicitly.

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Published 01 January 2008
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Modeling and Simulation of Thermochemical
Heat Treatment Processes: A Phase Field
Calculation of Nitriding in Steel
von Yakub Adesoga Tijani
Dissertation
zur Erlangung des Grades eines Doktors der Ingenieurwissenschaften
– Dr. Ing. –
Vorgelegt im Fachbereich 3 (Mathematik & Informatik)
der Universit¨ at Bremen
im Juni 2008ii
Datum des Promotionskolloquiums: 14.07.2008
Gutachter:
Prof. Dr. Michael Bohm¨ Prof. Dr.-Ing. Franz Hoffmann
Zentrum fur¨ Technomathematik Institut fur¨ Werkstofftechnik (IWT)
Universit¨ at Bremen, Deutschland. Bremen, Deutschland.Abstract
In order to provide greater improvements in material performance with respect
to hardness, fatigue, wear resistance and corrosion resistance, among other me-
chanical properties, nitrogen is commonly introduced on steel surface at elevated
temperature. Such enhancement, referred to as nitriding, results in the diffusion of
nitrogen into the steel with development of continuous layers of iron-based nitrides
and precipitation of alloying-element nitrides, depending on the nitriding kinetics.
Up till now, the simulation of nitriding process is done only under restricted con-
ditions by using classical models which describe the diffuse nitriding layers with
sharp interfaces. However, the classical models lead to difficulties in the compu-
tation of the free boundary problem, since the position of the interface has to be
calculated explicitly.
This work provides a generalized approach for studying the evolution of the mi-
crostructure during nitriding process in steel. It presents the application of a phase
field model to describe the nitriding of steel in order to numerically deal with the
moving free boundary. The treated nitriding layers are described in terms of a
phase field parameter which represents a property of the system that is non-zero
in a distinct region of the steel surface and 0 otherwise. A partial differential
equation is formulated to govern the time evolution of the phase field parameter
and it is coupled to other equation that determines the relevant field of transport
phenomenon. This allows the whole domain to be treated simultaneously. In par-
ticular, the interface is not tracked but is given implicitly by the value of the phase
field parameter as a function of time and space.
The set of coupled evolution equations - the concentration field and the phase-field
model equations, is solved by using a finite element software. The approach is ap-
plied to compute nitriding of a low-carbon steel and evolution of compound layer
formation. The numerical calculations correlate with experimental measurements
at different times.iv
Acknowledgement
My sincere gratitude goes to Prof. Dr. Michael Bohm¨ and Prof. Dr.-Ing. Franz
Hoffmann for their inspirational supervision and incredible openness throughout
the duration of this doctoral thesis. They have provided an invaluable guidance,
good recommendations and abundant zeal that catalyzed the completion of this
work.
I would like to thank Dr.-Ing. Martin Hunkel for his support and priceless magna-
nimity. The tremendous incentives provided by Prof. Dr. Peter Maaß, the courte-
ous motivation of Prof. Dr. Angelika Bunse-Gerstner and the masterly advice of
Prof. Dr. Alfred Schmidt cannot go without being acknowledged. I thank you all.
My appreciation extends to the University of Bremen for providing the PhD schol-
arship that cushioned my financial liabilities throughout the dissertation. I am
equally thankful to all academic, administrative and technical staff of the ’Zentrum
f¨ur Technomathematik’ for their unrelenting support, in particular all members of
’AG Bohm’.¨ My fellow colleagues at the graduate school Scientific Computing in
Engineering (SCiE) have been fantastic: my ’Tandem’ S. Meier, for the successful
cooperation, D. Kubalinska, J. Montalvo, L. Pru¨nte,Z.Akbay,S.Vudathu,Y.
Wang and Dr. D. Lorenz for their productive discussions and good working rela-
tionship.
Furthermore, I am grateful to my wife - Abibat, and children - Abibat (Jnr) and
Abdulsalam, for their numerous sacrifices and utmost perseverance throughout
the duration of this programme. I will always love you all. I thank all the un-
mentioned people who supported me in one way or the other during my doctoral
thesis. Finally, I thank God for making it possible.
Yakub Adesoga Tijani
Zentrum für
TechnomathematikContents
1 Introduction 1
2 Thermochemical Heat Treatment Processes in Steel 5
2.1 Nitriding Process ......................... 5
2.1.1 Gas Nitriding ....................... 9
2.1.2 Pack12
2.1.3 Plasma Nitriding .....................13
2.1.4 Salt Bath or Liquid Nitriding ..............14
2.1.5 The Parameters influencing Nitriding Process in Steel . 16
2.2 Nitrocarburizing Process18
2.3 CarburizingProces........................20
2.4 Carbonitriding ..........................2
3 Modeling Nitriding of Steel: A Classical Approach 25
3.1 KineticsoftheSurfaceReaction.................25
3.2 AnalyticalSolutionforNitrogenDiffusion ...........27
3.3 Formation and Growth of Nitriding Layers28
3.4 Numerical Modeling of Nitriding31
4 Modeling Nitriding with Phase Field Method 35
4.1 ThePhaseFieldMethod.....................35
4.2 MethodofDerivationofaPhaseFieldModel .........38
4.3 Multiphase Field Model for Nitriding ..............39
4.3.1 ClasificationoftheModelParameters42
vvi CONTENTS
4.4 DiffusionModelbasedonPhaseFieldMethod.........4
4.4.1 Simplification for a Single Nitriding Layer .......46
4.4.2 ConsiderationofaTwo-LayerModel..........46
4.4.3 Adaptation to Three Nitriding Layers49
5 Phase Field Simulation of the Nitriding Process in Steel 51
5.1 Tools for the Numerical Calculation ...............53
6 Simulation Results of Nitriding with Phase Field Model 55
6.1 Developmentofthediffusionlayer................5
6.2 Formationofthecompoundlayer58
7 Influence of Parameters on the Nitriding Simulation 63
7.1 EffectofInterfacialEnergy....................63
7.2 Effect of Interfacial Mobility ...................6
7.3 Impact of Gibbs Energy on the Simulation Results.......68
8 Consequences of Varying Boundary Conditions and
Thickness of the Interface 69
8.1 Changing Flux of Nitrogen ....................69
8.2 Constant Flux of71
8.3 EffectofInterfaceThicknesontheSimulation.........74
9 Comparison of Phase Field Calculations of Nitriding Process
with Experiments 77
9.1 Concentration-DepthProfile...................7
9.2 ThicknessoftheCompoundLayer................82
10 Discussion, Summary and Outlook 85
10.1Discusion.............................85
10.1.1 Formation of Nitriding Layers ..............85
10.1.2ParameterizationsofthePhaseFieldModel......87
10.1.3ModelVs.Experiment..................90
10.1.4 Further Possibilities with the Present Model ......91CONTENTS vii
10.2 Summary .............................94
10.3Outlook..............................96
A Derivation of Phase Field Model for Nitriding of Steel 99
A.1Evolutionofphasefieldparameter................9
A.2Diffusionofnitrogenusingphasefieldmodel..........101
Bibliography 103viii CONTENTSList of Figures
1.1 Relative cost and mechanical strength of different metals. . . . 2
1.2 A typical industrial production chain............... 3
2.1 Atypicalschematicoftemperatureprofileinsteel. ...... 6
2.2 Causesofdistortionduringheattreatment............ 7
2.3 Schematics of nitriding layers. .................. 8
2.4 Kineticsofnitrogendiffusioninstel...............10
2.5 Optical micrographs of the evolution of the ε/γ -nitride layer. 11
◦2.6 Microstructure of a gas nitrided layer at 580 C.........12
2.7 SEMcros-sectionsofplasmanitridedAISIM214
2.8 Microstructureofaliquidnitridedstructuralstel........15
2.9 Lehrer diagram for nitriding number and temperature. ....17
2.10 A complete Fe-N phase diagram .................18
2.1Profileofanitrocarburizedstel. ................19
2.12SEMmicrographsofaplasmanitrocarburizedsurface. ....20
2.13AtypicalschematicofFe-Cphasediagram. ..........21
2.14 TEM cross-section views of plasma carburized AISI 304 steel. 22
2.15Profileofacarbonitridedstel. .................23
3.1 Schematicnitrogenprofileofanitridedstel...........28
3.2 Mass balance over a nitriding layer ...............29
3.3 Nitrogen flux at γ /αinterface.30
3.4 flux at ε/γ interface...................31
ixx LIST OF FIGURES
4.1 Schematicdiagramofdiffuseinterfaces..............35
4.2 Schematicdiagramofsharpinterfaces.36
4.3 Schematicprofileofanitrogendiffusion,M=1..........47
4.4 Schematic profile of a nitrogen diffusion and reaction, M=2. . 48
4.5 Schematic profile of a and M=3. . 49
5.1 The Gibbs energy as a function of nitrogen concentration. . . 52
5.2 Initialphaseandconcentrationprofiles..............54
6.1 Concentration profile in the beginning of nitriding process in
◦C45 steel at 540 C.........................56
6.2 Phase profile in the beginning of nitriding process in C45 steel
◦at 540 C. .............................56
6.3 Development of the concentration gradient with increasing ni-
triding time.............................57
6.4 Phase profile before γ -Fe N formation. ............58
4
6.5 Nitrogen concentration at the beginning of compound layer
formation.59
6.6 Phase profile at 4 minutes and 12 minutes in the compound
◦layer of C45 steel nitrided at 540 C................59
6.7 Nitrogen concentration in the compound layer of C45 steel
◦nitrided at 540 Catdifferenttimes.60
6.8 Phaseprofileofcompoundlayer..................61
7.1 Growthofconcentrationgradientwithinterfaceenergy.....64
7.2 Concentrationprofileathighinterfaceenergy..........64
7.3 Concentrationprofileatlowinterfaceenergy...........65
7.4 Concentration profile at high interface mobility. No influence
of μisobserved...........................6
7.5 Concentration profile at low interface mobility. No influence
of μisobserved.67
7.6 Increase of compound layer thickness with interface mobility. . 67
7.7 ImpactofanincreasingGibbsenergyonsimulation.......68