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Modelling of particle growth and application to the carbide evolution in special steels for high temperature service

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192 Pages
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E URO PEAN COMMISSION SCIENCE RESEARCH DEVELOPMENT technical steel research Properties and in-service performance Modelling of particle growth and application to the carbide evolution in special steels for high temperature service hi Report STEEL RESEARCH EUR 18633 EN EUROPEAN COMMISSION Edith CRESSON, Member of the Commission responsible for research, innovation, education, training and youth DG XII/C.2 — RTD actions: Industrial and materials technologies — Materials and steel Contact: Mr H. J.-L. Martin Address: European Commission, rue de la Loi 200 (MO 75 1/10), B-1049 Brussels — Tel. (32-2) 29-53453; fax (32-2) 29-65987 European Commission technical steel research Properties and in-service performance Modelling of particle growth and application to the carbide evolution in special steels for high temperature service P. E. Di Nunzio CSM Via di Castel Romano, 100/102 1-00129 Rome H. P. Hougardi, Y. Lan MPI Max-Planck-Straße 1 D-40237 Düsseldorf Contract No 7210-MA/117/424 1 February 1990 to 30 November 1995 Final report Directorate-General Science, Research and Development EUR 18633 EN 1999 LEGAL NOTICE Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use which might be made of the following information. A great deal of additional information on the European Union is available on the Internet. It can be accessed through the Europa server (http://europa.eu.int).

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E URO PEAN
COMMISSION
SCIENCE
RESEARCH
DEVELOPMENT
technical steel research
Properties and in-service performance
Modelling of particle
growth and application
to the carbide evolution
in special steels for
high temperature
service
hi
Report
STEEL RESEARCH EUR 18633 EN EUROPEAN COMMISSION
Edith CRESSON, Member of the Commission
responsible for research, innovation, education, training and youth
DG XII/C.2 — RTD actions: Industrial and materials technologies —
Materials and steel
Contact: Mr H. J.-L. Martin
Address: European Commission, rue de la Loi 200 (MO 75 1/10),
B-1049 Brussels — Tel. (32-2) 29-53453; fax (32-2) 29-65987 European Commission
technical steel research
Properties and in-service performance
Modelling of particle growth and application
to the carbide evolution in special steels
for high temperature service
P. E. Di Nunzio
CSM
Via di Castel Romano, 100/102
1-00129 Rome
H. P. Hougardi, Y. Lan
MPI
Max-Planck-Straße 1
D-40237 Düsseldorf
Contract No 7210-MA/117/424
1 February 1990 to 30 November 1995
Final report
Directorate-General
Science, Research and Development
EUR 18633 EN 1999 LEGAL NOTICE
Neither the European Commission nor any person acting on behalf of the Commission
is responsible for the use which might be made of the following information.
A great deal of additional information on the European Union is available on the Internet.
It can be accessed through the Europa server (http://europa.eu.int).
Cataloguing data can be found at the end of this publication.
Luxembourg: Office for Official Publications of the European Communities, 1999
ISBN 92-828-5044-7
© European Communities, 1999
Reproduction is authorised provided the source is acknowledged.
Printed in Luxembourg
PRINTED ON WHITE CHLORINE-FREE PAPER CSM Contribution
ECSC Agreement No. 7210-MA/424 INDEX
1. OBJECTIVES OF THE RESEARCH PROJECT 15
2. INTRODUCTION: HISTORICAL OVERVIEW ON THE COARSENING OF SECOND
PHASES 16
3. COARSENING OF CARBIDES: EXPERIMENTAL EVIDENCES9
3.1 The M3C - type carbides
3.1.1 Materials and kinetic results from MPI
3.1.2 Analysis of experimental results on Ck45 steel and discussion
3.2 The M3C + M7C3 system 24
3.2.1 Materials and kinetic results from MPI
3.2.2 Analysis of experimental results on Cr-steel and discussion
3.3 Some comments on the occurrence of lognormal size distributions 27
4. THERMODYNAMIC APPROACH TO THE FORMATION OF COMPLEX CARBIDES 29
4.1 The formation of M3C in ferrite
4.1.1 Collection of thermodynamic data for M3C - type carbides
4.1.2 Application of the model
4.1.3 ΊΈΜ/STEM investigation ofCk45 steel
4.2 The formation of M7C3 carbide in ferrite 41
4.2.1 Collection of thermodynamic data for MyC3- type carbides
4.2.2 Application of the model of MjC3 formation
5. GENERAL FEATURES OF THE OSTWALD RIPENING MODELS7
5.1 Topology of the system
5.2 The driving force for Ostwald ripening 48
5.3 The growth equation 50
5.4 The continuityn
5.4.1 The solution of the continuity equation
5.5 Critical analysis of the basic topological assumptions of coarsening models 53
6. GREENWOOD-LIKE APPROACH TO THE OSTWALD RIPENING OF M3C
COMPLEX CARBIDES5
6.1 Outline of the general model Gl
6.1.1BDH approach to complex cementite-containing systems.
6.2 Rigorous approach to the Gibbs-Thomson equation for M3C complex carbides 57
6.3 The growth equation of the Gl model 61
6.4 Computation results of the Gl model
6.5 The model G2 for M3C carbides6
7. ASJMOW-LIKE APPROACH TO THE OSTWALD RIPENING OF M3C COMPLEX
CARBIDES 72
7.1 Outline of the general model Al
7.2 Modification of the Asimow's approach: the A2 model 75
7.3 The mass balance for the Asimow's approach
7.4 The rate controlling element in the Asimow's approach7
7.5 Computation results for the A2 model 80 8. THE COMPETITION BETWEEN M3C AND M7C3 CARBIDES 85
8.1 The A3 model 8
8.2 The mass balance in the A3 model6
8.3 The rate controlling element in the A3 model
8.4 Comments on the surface energies
8.5 Computation results of the A3 model for Cr-steel8
8.6 The evolution of grain growth inhibition during Ostwald ripening 94
9. TECHNICAL APPLICATIONS AND RECOMMENDATIONS 95
10. CONCLUSIONS 9
REFERENCES8
APPENDDC 1 : Numerical Constants 101
APPENDDC 2: Transformation of 3D distributions into 2D2 LIST OF TABLES
Tab. 3.1 Chemical composition of Ck45 steel used for investigating the coarsening process
of M3C carbides (wt%).
Tab. 3.2 Coarsening kinetics data for Ck45 steel annealed at 700°C.
Tab. 3.3 Chemical composition of Cr-steel used for investigating the coarsening process of
M3C and M7C3 carbides (wt%).
Tab. 3.4 Experimental data on coarsening kinetics of M3C in Cr-steel annealed at 700 °C.
Tab. 3.5l data on coarsening kinetics of M7C3 in Cr-steel annealed at 700 °C.
Tab. 3.6 Evolution of volume fractions for M3C and M7C3 in the Cr-steel at 700 °C. The
values have been computed from data in tables 3.4 and 3.5 and they must be
considered as rough approximations.
Tab. 4.1 Calculation results of the thermodynamic model predicting the formation of
complex cementite M3C in Ck45 steeL
Tab. 4.2 Alloy content of cementite particles measured by TEM/STEM-EDS in a Ck45
steel sample annealed for 10 minutes at 700 °C.
Tab. 4.3 Calculation results of the thermodynamic model predicting the formation of
complex M7C3 carbides in the Cr-steel.
Tab. 4.4 Calculation results of the thermodynamic model predicting the formation of
complex cementite M3C in Cr-steeL
Tab. 6.1 Effects of capillarity on equilibrium concentrations (wt%), compositional
parameters, cementite volume fraction and partition coefficients for Ck45 steel at
700 °C as a function of the critical radius of the particle population rc.
Tab. 6.2 Computed values of the upper and lower limits (τ^ and η respectively) for local
equilibrium at the interface for Cr and Mn in Ck45 steel at 700 °C as a function of
the critical radius of the particle population rc.
Tab. A2.1 Statistical properties of the starting 3D and computed 2D distributions used to
illustrate the transformation algorithm. LIST OF FIGURES
Fig. 3.1 Experimental data on coarsening kinetics of Ck45 steel at 700°C: log(<r>) vs. log(t)
plot.
Fig. 3.2 Evolution of the average particle size in Ck45 steel at 700°C.
Fig. 3.3 Evolution of the variation coefficient (ratio between the standard deviation and the
average radius of the 2D PSD) for cementite particles in Ck45 steel annealed at
700°C.
Fig. 3.4 Double logarithmic plot showing the evolution of the number of particles per unit
volume in Ck45 steel annealed at 700°C.
Fig. 3.5 Double logarithmic plot (average 3D particle radius vs. time) of the coarsening
kinetics of M3C and M7C3 particles in Cr­steel annealed at 700°C.
Fig. 4.1 Computed equilibrium carbon concentration for the Ck45 steel (quaternary system
Fe­C­Cr­Mn) compared with the Fe­C system according to Chipman [39].
Fig. 4.2 Computed equilibrium concentrations in solid solution for Cr and Mn in the Ck45
steel.
Fig. 4.3 Computed equiiïbrium mole fractions of Cr and Mn in cementite (χ and ν
respectively) for the Ck45 steeL Symbols represent an experimental TEM/STEM­
EDS determination in the sample annealed for 1000 hours at 700 °C.
Fig. 4.4 Computed equilibrium partition coefficients of Cr and Mn between cementite and
ferritie for the Ck45 steel.
Fig. 4.5 TEM image from a carbon extraction replica of the Ck45 steel annealed for 10
minutes at 700 °C.
Fig. 4.6 TEM image from a carbon extraction replica of the Ck45 steel annealed for 1000
hours at 700 °C.
Fig. 4.7 Comparison between computed solubilities of carbon for M3C and M7C3 in the Cr­
steel.
Fig. 4.8 Comparison between computed solubilities of chromium for M3C and M7C3 in the
Cr­steeL
Fig. 6.1 Schematic plot representing the substitutional/interstitial ranges for the particle
growth control as a function of the actual value of the critical radius of e
population.