A phenomenological approach to the prediction of material behaviours during co-sintering [Elektronische Ressource] / vorgelegt von Marc Delporte

Informations

• Publié par: julius-maximilians-universitat_wurzburg
• Publié le: 01 janvier 2009
• Nombre de lectures: 53
• Langue: English
• Poids de l'ouvrage: 7 Mo

Extrait

A phenomenological approach
to the prediction of
material behaviours
during co-sintering
Dissertation zur Erlangung
des naturwissenschaflichen Doktorgrades
der Julius-Maximilians-Universitat¨ Wurzb¨ urg
vorgelegt von
Marc Delporte
Wurzb¨ urg 2009Eingereicht am: . . . . . . . . . . . . . . . . . . . . . . . .
bei der Fakultat¨ fur¨ Chemie und Pharmazie
1. Gutachter: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Gutachter: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
der Dissertation
1. Prufer:¨ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Prufer:¨ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. Prufer:¨ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
das o¨entlichen Promotionskolloquiums
Tag des o¨entlichen Promotionskolloquiums: . . . . . . . . . . . . . . . . . . . . . .
Doktorurkunde ausgehandigt¨ am: . . . . . . . . . . . . . . . . . .Contents
Contents i
Foreword and acknowledgment v
Summary / Zusammenfassung vii
1. Introduction 1
2. Material model description 7
2.1. Sintering kinetics with the Master Sintering Diagram (MSD) . . . . . . . . . . . 7
2.1.1. Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2. How to construct and interpret the MSD? . . . . . . . . . . . . . . . . . 9
2.2. Characterization of creep during sintering . . . . . . . . . . . . . . . . . . . . . 12
2.2.1. Viscous moduli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2. Principle of the cyclic unloading method . . . . . . . . . . . . . . . . . 13
3. Experimental techniques 15
3.1. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.1. Partially stabilized zirconia . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.2. Bi-layer alumina/zirconia . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1.3. glass-ceramic/alumina . . . . . . . . . . . . . . . . . . . . . . 17
3.2. Optical dilatometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.1. Instrument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.2. Image analysis: principle, precision, repeatability and deviation . . . . . 18
3.2.3. Data treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.4. Specific setups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.4.1. Free sintering of tapes . . . . . . . . . . . . . . . . . . . . . . 20
3.2.4.2. Loading setup . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.4.3. Bending setup . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.5. Experimental procedures and data treatment . . . . . . . . . . . . . . . . 23
3.2.5.1. Free sintering of tapes . . . . . . . . . . . . . . . . . . . . . . 23
3.2.5.2. Cyclic unloading dilatometry . . . . . . . . . . . . . . . . . . 23
3.2.5.3. Warpage of asymmetric composites . . . . . . . . . . . . . . . 25
iCONTENTS
3.2.5.4. Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3. Additional characterization methods . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.1. X-ray diraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.2. Microstructure investigation . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.3. Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4. Material model construction for one specific material: zirconia pressed com-
pacts 31
4.1. Sintering characterization and input data . . . . . . . . . . . . . . . . . . . . . . 31
4.1.1. Free sintering kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.2. Sintering kinetics with load . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2. Construction of the MSD with the input data . . . . . . . . . . . . . . . . . . . . 38
4.3. Viscous behaviour during sintering . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3.1. Experimental determination of the viscous moduli . . . . . . . . . . . . 43
4.3.2. Influence of the load on the viscous moduli . . . . . . . . . . . . . . . . 44
4.3.3. of the heating rate on the viscous moduli . . . . . . . . . . . . 44
4.3.4. Influence of the holding time on the viscous moduli . . . . . . . . . . . . 46
4.4. Microstructure investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4.1. Measurement of the particle size in the green-body . . . . . . . . . . . . 48
4.4.2. Influence of the thermal treatment on the microstructure of free sintered
samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4.3. Microstructure evolution during loaded sintering . . . . . . . . . . . . . 49
5. Model validation 53
5.1. V procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1.1. Procedure for the validation of the sintering kinetics with the MSD . . . 53
5.1.2. for the v of the viscous moduli . . . . . . . . . . . . 53
5.2. Prediction of the sintering kinetics with the MSD . . . . . . . . . . . . . . . . . 54
5.3. of the warpage of a bi-layer with the experimentally determined viscous
moduli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.3.1. Free sintering mismatch between alumina and zirconia stacks . . . . . . 58
5.3.2. Characterization of the viscous moduli of alumina and zirconia stacks . . 58
5.3.3. Prediction of the curvature rate of a bi-layer . . . . . . . . . . . . . . . . 64
6. Co-sintering of a glass-ceramic and alumina bi-layer 67
6.1. Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.2. Sintering kinetics and crystallization of the glass-ceramic tape . . . . . . . . . . 67
6.3. Viscosity measurement of the glass-ceramic tape . . . . . . . . . . . . . . . . . 72
6.4. Co-sintering of a bi-layer/alumina . . . . . . . . . . . . . . . . . . 73
6.4.1. Sintering mismatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
iiCONTENTS
6.4.2. Qualitative description of co-sintering . . . . . . . . . . . . . . . . . . . 73
6.5. Conclusions on the co-sintering case of a glass-ceramic and alumina bi-layer . . 77
7. Discussion 79
7.1. Free sintering kinetics and apparent activation energy . . . . . . . . . . . . . . . 79
7.2. Constrained sintering in zirconia . . . . . . . . . . . . . . . . . . . . . . . . . . 82
7.3. Experimental determination of the viscous moduli . . . . . . . . . . . . . . . . . 84
7.3.1. Uniaxial viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
7.3.2. Viscous Poisson ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8. Conclusions and outlook 89
8.1. Conclusions on the material model . . . . . . . . . . . . . . . . . . . . . . . . . 89
8.2. Parameters aecting co-sintering . . . . . . . . . . . . . . . . . . . . . . . . . . 91
8.3. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
A. True strain 95
A.1. Strains and strain rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
A.2. Linear true and engineering strains . . . . . . . . . . . . . . . . . . . . . . . . . 95
A.3. Volumetric strains and densities . . . . . . . . . . . . . . . . . . . . . . . . . . 96
B. Phase diagram ZrO - Y O 1012 2 3
Bibliography 103
List of Figures 109
List of Tables 113
List of symbols and abbreviations 115
iiiForeword and acknowledgment
This work was being performed between April 2006 and April 2009 in part time at the Fraunhofer
Institute for Silicate Research in Wurzb¨ urg and at the department for Advanced Research Materials
at Robert Bosch GmbH in Stuttgart. The work was presented in October 2009 at the University of
Wurzb¨ urg in the Department for Chemistry and Pharmaceutical.
My first thanks go to Prof. Dr. Sextl who accepted to direct my work in his Chair and for his
justified comments in the final corrections.
I would like to thank Dr. Lindner, head of the department for Advanced Research Materials at
Robert Bosch GmbH and Mr Lindemann, Dr. Selten, Dr. Hiller, group leaders for the financial
support of this work.
In 2008, I had the opportunity to take part at the international conference Sintering 2008. The
scientific community debated the ”major challenges and opportunities in the field of sintering”.
One of these was the co-sintering and constrained sintering. For having initiated this project
combining industrial interests and up-to-date scientific challenges, I would like to thank Dr. Eisele
(Robert Bosch) and Dr. Raether (Fraunhofer). Furthermore I am very grateful to Dr. Raether for
his scientific support and guidance in this work. I appreciated his availability at all times, his
experienced look and valuable hints in the dicult matter of sintering. I would like also to thank
Dr. Eisele for his critical look on the scientific approach though keeping in focus the industrial
interests.
Kind aknowledgements are addressed to Philipp Spies and Andre´ Moc for accepting to review the
first version of this work.
Many thanks go precisely to Hans Schomig¨ (Fraunhofer) who oered his assistance in the lab
and his thoroughness. Thank you Hans, without your help my work would have been much more
arduous! I als