Numerical study of instability patterns of film-substrate systems

216 Pages·2017·19.75 MB·English

by  Fan Xu

Numerical study of instability patterns of film-substrate
systems
Fan Xu
To cite this version:
Fan Xu. Numerical study of instability patterns of film-substrate systems. Other. Université de
Lorraine, 2014. English. ￿NNT: 2014LORR0309￿. ￿tel-01751474￿
HAL Id: tel-01751474
https://hal.univ-lorraine.fr/tel-01751474
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LIENS

Code de la Propriété Intellectuelle. articles L 122. 4
Code de la Propriété Intellectuelle. articles L 335.2- L 335.10
http://www.cfcopies.com/V2/leg/leg_droi.php
http://www.culture.gouv.fr/culture/infos-pratiques/droits/protection.htm
Universit(cid:19)e de Lorraine E(cid:19)cole doctorale EMMA
UFR MIM
(cid:19)
Etude num(cid:19)erique des modes
d’instabilit(cid:19)es des syst(cid:18)emes (cid:12)lm-substrat
Numerical study of instability patterns of film-substrate
systems
(cid:18)
THESE
pr(cid:19)esent(cid:19)ee et soutenue publiquement le 02 d(cid:19)ecembre 2014
pour l’obtention du
Doctorat de l’Universit(cid:19)e de Lorraine
Spécialité : Mécanique des Matériaux
par
Fan XU
Composition du jury
Rapporteurs : Pr. Basile Audoly Universit(cid:19)e Pierre et Marie Curie (Paris 6), France
Pr. Yibin Fu Keele University, UK
Examinateurs : Pr. Martine Ben Amar E(cid:19)cole Normale Sup(cid:19)erieure, France
Pr. Hachmi Ben Dhia E(cid:19)cole Centrale Paris, France
Directeur : Pr. Michel Potier-Ferry Universit(cid:19)e de Lorraine, France
Co-directeur : Dr. Salim Belouettar CRP Henri Tudor, Luxembourg
Laboratoire d’E(cid:19)tude des Microstructures et de M(cid:19)ecanique des Mat(cid:19)eriaux | UMR CNRS 7239
Centre de Recherche Public Henri Tudor
Mis en page avec la classe thloria.
Acknowledgments
After all the confusion or epiphany, depression or inspiration, sadness or happiness,
finally it comes to the stage when we are modest and grateful, as the last thing that I
learned from my doctoral studies.
I would like to begin by expressing my most sincere gratitude to my Ph.D. advisor,
Professor Michel Potier-Ferry, an inspiring and extraordinary person to work with during
the entire span of this thesis. In addition to introducing me to the subject of instability
and guiding me to grow in computational mechanics, his patient guidance and relentless
pursuit of excellence have helped shape me into not only a good researcher with rigorous
attitude but also a responsible and considerate person than I otherwise would have been.
Plainly put, he has been a great mentor. It has been an honor and a privilege working
with him over the last three years.
Sincere appreciation is extended to my co-advisor, Dr. Salim Belouettar, for his kind
supports and helps as well as deep trusts for giving me full autonomy in research activity.
I would like to express my gratitude to the other thesis committee members, Professor
Basile Audoly, Professor Yibin Fu, Professor Martine Ben Amar and Professor Hachmi
Ben Dhia, for taking the time to read this thesis and for offering helpful comments and
suggestions. Professor Basile Audoly and Professor Yibin Fu deserve a special thank for
their inspiring and encouraging reports on this thesis.
Many thanks go in particular to Professor Yanping Cao at Tsinghua University for
his expert advice and valuable scientific discussions, which enlightened me and eliminated
my confusions on some technical points.
I would also like to record my gratitude to my colleagues and my friends, Dr. Yu Cong
and Dr. Yao Koutsawa, for our scientific (and not-so-scientific) discussions. It has been
a pleasure working with them.
Special thanks go to Professor Hamid Zahrouni for allowing me to use his powerful
workstation to perform heavy simulations.
My thanks also go to my friends, Kodjo Attipou, Cai Chen, Yajun Zhao, Junliang
Dong, Qi Wang, Dr. Wei Ye, Dr. Jingfei Liu, Dr. Kui Wang, Alex Gansen, Qian Shao,
Sandra Hoffmann, Dr. Duc Tue Nguyen, etc. for sharing my joy and sadness, and offering
helpsandsupportswheneverneeded. ItreasureeveryminutethatIhavespentwiththem.
Lastly, I would like to give my most special thanks to my parents and my fiancée for
their unconditional love, 24/7 support, share of happiness and for always believing in me.
Without their encouragement I would never have made it this far.
Financial support for this research was provided by AFR Ph.D. Grants from Fonds
National de la Recherche of Luxembourg (Grant No. FNR/C10/MS/784868).
i
ii
To my parents
To my fiancée
iii
iv
Table of contents
List of Figures ix
General introduction 1
Introduction générale 5
Chapter 1 Bibliographic review 9
1.1 Surface morphological instabilities of film/substrate systems . . . . . . . . 9
1.1.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1.2 Challenges and discussion . . . . . . . . . . . . . . . . . . . . . . . 16
1.2 Asymptotic Numerical Method for nonlinear resolution . . . . . . . . . . . 18
1.2.1 Perturbation technique . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.2.2 Path parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.2.3 Continuation approach . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.2.4 Bifurcation indicator . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.3 Multi-scale modeling for instability pattern formation . . . . . . . . . . . . 23
1.4 Arlequin method for model coupling . . . . . . . . . . . . . . . . . . . . . 25
1.4.1 Energy distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.4.2 Coupling choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.5 Chapter conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Chapter 2 Multiple bifurcations in wrinkling analysis of film/substrate sys-
tems 31
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2 Mechanical model and dimensional analysis . . . . . . . . . . . . . . . . . 34
2.3 1D reduced model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.3.2 Finite element formulation . . . . . . . . . . . . . . . . . . . . . . . 39
v
Table of contents
2.4 Resolution technique and bifurcation analysis . . . . . . . . . . . . . . . . 43
2.4.1 Path-following technique . . . . . . . . . . . . . . . . . . . . . . . . 43
2.4.2 Detection of bifurcation points . . . . . . . . . . . . . . . . . . . . . 46
2.5 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.5.1 Film/substrate with simply supported boundary conditions . . . . . 50
2.5.2 Film/substrate with clamped boundary conditions . . . . . . . . . . 51
2.5.3 Functionally Graded Material (FGM) substrate with simply sup-
ported boundary conditions . . . . . . . . . . . . . . . . . . . . . . 55
2.5.4 FGM substrate with clamped boundary conditions . . . . . . . . . 58
2.5.5 FGM substrate with stiffening Young’s modulus . . . . . . . . . . . 58
2.5.6 Anisotropic substrate . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.5.7 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.6 Chapter conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Chapter 3 Pattern formation modeling of 3D film/substrate systems 69
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2 3D mechanical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2.1 Nonlinear shell formulation for the film . . . . . . . . . . . . . . . . 74
3.2.2 Linear elasticity for the substrate . . . . . . . . . . . . . . . . . . . 76
3.2.3 Connection between the film and the substrate . . . . . . . . . . . . 77
3.3 Resolution technique and bifurcation analysis . . . . . . . . . . . . . . . . 78
3.3.1 Path-following technique . . . . . . . . . . . . . . . . . . . . . . . . 78
3.3.2 Detection of bifurcation points . . . . . . . . . . . . . . . . . . . . . 80
3.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.4.1 Sinusoidal patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.4.2 Checkerboard patterns . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.4.3 Herringbone patterns . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.5 Chapter conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Chapter 4 Bridging techniques for pattern formation modeling 97
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.2 Macroscopic modeling of instability pattern formation . . . . . . . . . . . . 100
4.2.1 Description of the microscopic model . . . . . . . . . . . . . . . . . 100
4.2.2 Reduction procedure by Fourier series . . . . . . . . . . . . . . . . . 101
4.2.3 A simple macroscopic model with two real envelopes . . . . . . . . 102
vi