Ceramic Materials and Components for Energy and Environmental Applications
Ceramic Transactions, Volume 210
A Collection of Papers Presented at the 9th International Symposium on Ceramic Materials for Energy and Environmental Applications and
the Fourth Laser Ceramics Symposium November 10-14, 2008, Shanghai, China
Edited by Dongliang Jiang
Yuping Zeng Mrityunjay Singh Juergen Heinrich
®WILEY A John Wiley & Sons, Inc., Publication
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Ceramic Materials and Components for Energy and Environmental Applications
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Ceramic Materials and Components for Energy and Environmental Applications
Ceramic Transactions, Volume 210
A Collection of Papers Presented at the 9th International Symposium on Ceramic Materials for Energy and Environmental Applications and
the Fourth Laser Ceramics Symposium November 10-14, 2008, Shanghai, China
Edited by Dongliang Jiang
Yuping Zeng Mrityunjay Singh Juergen Heinrich
®WILEY A John Wiley & Sons, Inc., Publication
Copyright © 2010 by The American Ceramic Society. All rights reserved.
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Contents
Preface xv
Acknowledgements xvii
I. Basic Science, Design, Modeling and Simulation
FRACTURE STATISTICS OF SMALL SPECIMENS 3 Robert Danzer and Peter Supancic
STRUCTURE AND PROPERTY OF Ti-AI-C/TiB2 COMPOSITE 13 CERAMICS
Xinmin Min, Gang Xu, and Bin-Chu Mei
THE EFFECT OF DOPED SINTERING AIDS FOR Nd(Mg0 5Ti0 5)03 17 MICROWAVE DIELECTRIC CERAMICS PROPERTIES
Kok-Wan Tay and Teng-Yi Huang
MICROWAVE DIELECTRIC PROPERTIES OF 25 (1-x)(Mg0.6Zn0.4)o.95Co005Ti03-xSrTi03 CERAMIC SYSTEM
Jun-Jie Wang, Chun-Huy Wang, Ting-Kuei Hsu, and Yi-Hua Liu
OXYNITRIDE GLASSES: EFFECTS OF COMPOSITION ON GLASS 31 FORMATION AND PROPERTIES WITH IMPLICATIONS FOR HIGH TEMPERATURE BEHAVIOUR OF SILICON NITRIDE CERAMICS
Stuart Hampshire and Michael J. Pomeroy
THE HYDROLYSIS OF ALUMINIUM NITRIDE: A PROBLEM OR AN 39 ADVANTAGE
Kristoffer Kmel and Tomaz Kosmac
PREPARATION AND COMPARISION OF TWO TYPICAL CVD FILMS 47 FROM CH4 AND C3H6 AS CARBON RESOURCES
W. B. Yang, L. T. Zhang, L. F. Cheng, Y. S. Liu, and W. H. Zhang
v
KINETIC INVESTIGATION ON THE DEPOSITION OF SiC FROM 55 METHYLTRICHLOROSILANE AND HYDROGEN
Cuiying Lu, Laifei Cheng, Chunnian Zhao, Litong Zhang, and Fang Ye
II. Nanomaterials and Nanotechnologies
SYNTHESIS OF HEMATITE-ZIRCON-SILICA NANO COMPOSITE AS 65 A NON TOXIC CERAMIC PIGMENT BY SOL-GEL METHOD
Maryam Hosseini Zori
FORMATION OF NANOCRYSTALLINE α-ALUMINAS IN 71 DIFFERENT MORPHOLOGY FROM GEL POWDER AND BOEHMITE POWDER: A COMPARATIVE STUDY
Xiaoxue Zhang, Yanling Ge, Simo-Pekka Hannula, Erkki Levänen, and Tapio Mäntylä
SYNTHESIS AND IN VITRO RELEASE OF GENTAMICIN FROM 79 CaMCM-41/PLLA COMPOSITE MICROSPHERES
Yufang Zhu and Stefan Kaskel
HIGHLY ORDERED CUBIC MESOPOROUS COBALT OXIDE BY AN 85 ACCURATELY CONTROLLED INCIPIENT WETNESS TECHNIQUE
Limin Guo, Xiangzhi Cui, and Jianlin Shi
PREPARATION OF Fe304 NANOPARTICLES BY TWO DIFFERENT 93 METHODS
Mingxin Geng, Futian Liu, and Zengbao Zhao
NANO-ZIRCONIA/MULLITE COMPOSITE CERAMICS PREPARED 99 BY IN-SITU CONTROLLED CRYSTALLIZATION FROM THE Si-AI-Zr-0 AMORPHOUS BULK
Liang Shuquan, Zhong Jie, Zhang Guowei, and Tan Xiaoping
PREPARATION AND CHARACTERIZATION OF Er:Gd203 109 POWDERS
Rong Zhang, Lian-Jie Qin, Bo Wang, Zhi-Qiang Feng, and Ru Ge
III. Ceramics in Energy Conversion Systems
CMC MATERIALS AND BIOMORPHIC SiSiC FOR ENERGY 117 APPLICATIONS
B. Heidenreich, J. Schmidt, Sandrine Denis, Nicole Lützenburger, J. Goring, P. Mechnich, and M. Schmücker
CRYSTALLIZATION, MICROSTRUCTURE AND PHYSICAL 125 PROPERTY OF NEW TYPES OF BOROSILICATE GLASS-CERAMICS
Shufeng Song, Zhaoyin Wen, Liu Yu , Qunxi Zhang, Jingchao Zhang, and Xiangwei Wu
vi · Ceramic Materials and Components for Energy and Environmental Applications
A STUDY OF Al203 AND YSZ CERAMIC SUPPORTS FOR 131 PALLADIUM MEMBRANE
M. Kitiwan and D. Atong
SYNTHESIS OF OLIVINE (LiFeP04) and Ni/OLIVINE (LiFeP04) 139 CATALYSTS FOR UPGRADING SYN-GAS PRODUCTION
D. Atong, C. Pechyen, D. Aht-Ong, and V. Sricharoenchaikul
FABRICATION AND CHARACTERIZATION OF CERMET 147 MEMBRANE FOR HYDROGEN SEPARATION
S. Vichaphund and D. Atong
POROUS CERAMICS FOR HOT GAS CLEANING; DEGRADATION 155 MECHANISMS OF SiC-BASED FILTERS CAUSED BY LONG TERM WATER VAPOUR EXPOSURE
Pirjo Laurila and Tapio Mantyla
IV. Solid Oxide Fuel Cells (SOFCs): Materials and Technologies
DEVELOPMENT OF NANO-STRUCTURED YSZ ELECTROLYTE 165 LAYERS FOR SOFC APPLICATIONS VIA SOL-GEL ROUTE
Feng Han, Tim Van Gestel, Robert Mücke, and Hans-Peter Buchkremer
DEVELOPMENT OF SINGLE-CHAMBER SOLID OXIDE FUEL 173 CELLS: PERFORMANCE OPTIMIZATION AND MICRO-STACK DESIGNS
Bo Wei, Zhe Lü, Xiqiang Huang, Mingliang Liu, Dechang Jia, and Wenhui Su
DEVELOPMENT OF BUNDLE/STACK FABRICATION 179 TECHONOLOGY FOR MICRO SOFCS
Toshio Suzuki, Toshiaki Yamaguchi, Yoshinobu Fujishiro, Masanobu Awano, and Yoshihiro Funahashi
AN OVERVIEW OF SCANDIA STABILIZED ZIRCONIA 185 ELECTROLYTE DEVELOPMENT FOR SOFC APPLICATION
K. Ukai, M. Yokoyama, J. Shimano, Y. Mizutani, and O. Yamamoto
FABRICATION OF Ni-GDC ANODE SUBSTRATE BY TAPE 191 CASTING PROCESS
Fu Chang Jing, Chan Siew Hwa, Liu Qing Lin, and Ge Xiao Ming
V. Ceramics in Environmental Applications
INFLUENCE OF LATTICE STRAIN ON THE Ce0 5Zr0 5 0 2 AND Al203 199 DOPED Ce0.5Zr0.5O2 CATALYTIC POWDERS
Chia-Che Chuang, Hsing-I Hsiang, and Fu-Su Yen
Ceramic Materials and Components for Energy and Environmental Applications · vii
MICROSTRUCTURE AND PROPERTIES OF CORDIERITE- 207 BONDED POROUS SiC CERAMICS PREPARED BY IN SITU REACTION BONDING
Shifeng Liu, Yu-Ping Zeng, and Dongliang Jiang
FABRICATION OF LIGHTWEIGHT CLAY BRICKS FROM 213 RECYCLED GLASS WASTES
Vorrada Loryuenyong, Thanapan Panyachai, Kanyarat Kaewsimork, and Chatnarong Siritai
THE PERFORMANCE OF GEOPOLYMER BASED ON RECYCLED 221 CONCRETE SLUDGE
Z.X. Yang, N.R. Ha, M.S. Jang, K.H. Hwang, B.S. Jun, and J.K.Lee
STRUCTURE AND MICROWAVE DIELECTRIC PROPERTIES OF 225 THE 2.02L¡2O-1Nb?O5-1T¡O2 CERAMICS
Qun Zeng, Wei Li, and Jing-kun Guo
PHOTOLUMINESCENCE PROPERTIES AND X-RAY 231 PHOTOELECTRON SPECTROSCOPY OF ZnO MICROTUBES SYNTHESIZED BY AN AQUEOUS SOLUTION METHOD
Liwei Lin, Masayoshi Fuji, Hideo Watanabe, and Minoru Takahashi
THE DYNAMICS OF WATER MOLECULES ON YV04 PHOTO- 237 CATALYST SURFACE
Mitsutake Oshikiri, Akiyuki Matsushita, Jinhua Ye, and Mauro Boero
PREPARATION OF SILICON CARBIDE HOLLOW SPHERES BY A 243 TEMPLATE METHOD
Lei Zhang, Jiu-jun Yang, Xue-ping Wang, and Feng-chun Wei
NONDESTRUCTIVE TESTING OF DEFECT IN A C/SÍC 249 COMPOSITE
Hui Mei, Xiaodong Deng, and Laifei Cheng
VI. Advanced Structural Ceramics
FABRICATION OF BARIUM ALUMINOSILICATE-SILICON 259 NITRIDE-CARBON NANOTUBE COMPOSITES BY PRESSURELESS SINTERING
Bo Wang, Jian-Feng Yang, Ji-Qiang Gao, and Koiichi Niihara
NONLINEAR FINITE ELEMENT ANALYSIS OF CONVECTIVE 265 HEAT TRANSFER STEADY THERMAL STRESSES IN A Zr02/FGMATi-6AI-4V COMPOSITE EFBF PLATE WITH TEMPERATURE-DEPENDENT MATERIAL PROPERTIES
Yangjian Xu, Daihui Tu, and Chunping Xiao
viii · Ceramic Materials and Components for Energy and Environmental Applications
EFFECT OF MULLITE GRAINS ORIENTATION ON TOUGHNESS 273 OF MULLITE/ZIRCONIA COMPOSITES
Y. K. Tür, A. E. Sünbül, H. Yilmaz, and C. Duran
CONTROLLED CRYSTALLISATION OF GRAIN BOUNDARY-TYPE 279 Y-SIALON GLASS TYPICAL OF THOSE FOUND IN SILICON NITRIDE CERAMICS
Michael J. Pomeroy and Stuart Hampshire
HIGH TEMPERATURE COMPRESSION CREEP BEHAVIOR OF 285 AMORPHOUS Si-B-C-N CERAMICS IN CONTROLLED ATMOSPHERE
Ravi Kumar, C. Eswarapragada, A. Zimmermann, and F. Aldinger
FABRICATION AND PROPERTIES OF SÍ3N4/BN COMPOSITE 291 CERAMICS BY PRESSURELESS SINTERING WITH Yb203-Al203-Y203 AS SINTERING ADDITIVES
Yongfeng Li, Ping Liu, Guanjun Qiao, Jianfeng Yang, Haiyun Jin, Xiangdong Wang, and Guojun Zhang
EFFECT OF B4C ADDITIONS ON THE PRESSURELESS SINTERING 297 OF ZrB2-SiC ULTRA-HIGH TEMPERATURE CERAMICS
Hui Zhang, Yongjie Yan, Zhengren Huang, Xuejian Liu, and Dongliang Jiang
TRANSLUCENT AND TOUGHENED Dy-a-SiAION CERAMICS WITH 303 LiF AS SINTERING ADDITIVE
Qian Liu, Junming Xue, and Wei He
PROPERTIES OF SILICON CARBIDE CERAMIC FROM 309 GELCASTING AND PRESSURELESS SINTERING
Jingxian Zhang, Dongliang Jiang, Qingling Lin, Zhongming Chen, and Zhengren Huang
MICROWAVE DIELECTRIC PROPERTIES OF Nb203- 315 Zn0.95Mg0.05TiO3+0.25TiO2 CERAMICS WITH Bi203 ADDITION
Ying-Chieh Lee, Hui-Hsiang Huang, Wen-Hsi Lee, Yen-Lin Huang, and Shin-Feng Chien
FABRICATION OF YTTRIA-STABILIZED ZIRCONIA CERAMICS 321 WITH RETICULATED PORE MICROSTRUCTURE BY FREEZE-DRYING
Yuan Zhang, Kaihui Zuo, and Yu-Ping Zeng
THE NOTCHED BALL TEST—A NEW STRENGTH TEST FOR 327 CERAMIC SPHERES
Peter Supancic, Robert Danzer, Zhonghua Wang, Stefan Witschnig, and Oskar Schöppl
Ceramic Materials and Components for Energy and Environmental Applications · ix
LIQUID PHASE SINTERED α-SILICON CARBIDE WITH AIN-Re203 337 AS SINTERING ADDITIVE
Yuhong Chen, Laner Wu, Yong Jiang, Youjun Lu, and Zhenkun Huang
PREPARATION OF Si3N4 CERAMICS FROM LOW-COST Si3N4 345 POWDER WITH HIGHER ß PHASE AND OXYGEN CONTENT
Yong Jiang, Laner Wu, Fei Han, and Zhenkun Huang
MICROSTRUCTURE OF LIQUID PHASE SINTERED SILICON 349 CARBIDE CERAMICS WITH HIGH FRACTURE TOUGHNESS
Yong Jiang, Laner Wu, Yuhong Chen, and Zhenkun Huang
VII. Advanced Ceramic Coatings
DEVELOPMENT OF ELECTROSPINNING TITANIA WEB FROM 357 SUSPENSION
W. D. Teng and Nassya M. Said
HIGH-SPEED ENGINEERING CERAMIC COATING BY LASER 363 CHEMICAL VAPOR DEPOSITION
Takashi Goto, Teiichi Kimura, and Rong Tu
A REVIEW OF NANOCRYSTALLINE DIAMOND/ß-SiC COMPOSITE 371 FILMS
Vadali. V. S. S. Srikanth, Thorsten Staedler, and Xin Jiang
EFFECT OF TEMPERATURE FIELD ON DEPOSITION OF BORON 379 CARBIDE COATING FORM BCI3-CH4-H2 SYSTEM
Yongsheng Liu, Litong Zhang, Laifei Cheng, Wenbin Yang, Weihua Zhang, and Yongdong Xu
EFFECT OF DEPOSITION RATE ON MICROSTRUCTURE AND 387 THERMAL CONDUCTIVITY OF YSZ FILMS PREPARED BY MOCVD
Rong Tu and Takashi Goto
VIII. Novel Processing of Ceramics
PREPARATION OF Na-ß"-AI203 GREEN BODIES THROUGH 397 NONAQUEOUS GEL-CASTING PROCESS
Xiaogang Xu, Zhaoyin Wen, Ning Li, Xiangwei Wu, Jiu Lin, and Zhonghua Gu
ROD-LIKE ß-SIALON POWDER PREPARED BY A NEW 403 N2-ASSISTED CARBOTHERMAL REDUCTION OF CARBON AND ALUMINUM NANOCASTED MESOPOROUS SILICA
Tongping Xiu, Qian Liu, Minghui Wang, and Qiang Yan
x · Ceramic Materials and Components for Energy and Environmental Applications
CERIA-STABILIZED ZIRCONIA/ALUMINA NANOCOMPOSITE 407 SUITABLE FOR ELECTROPHORETIC DEPOSITION IN THE FABRICATION OF DENTAL RESTORATIONS
Takashi Nakakmura, Hisataka Nishida, Tohru Sekino, Xuehua Tang, and Hirofumi Yatani
PREPARATION OF POROUS ALUMINA BY GEL-CASTING 413 PROCESS USING COMMERCIAL STARCHES AS A GELLING AGENT
Vorrada Loryuenyong, Ajcharaporn Aontee, Daruni Kaeoklom, and Adisorn Sridej
THE EFFECT OF POLYVINYL ALCOHOL ON THE 417 MICROSTRUCTURE OF THE POROUS Ti02 SHEETS FABRICATED BY FREEZE TAPE-CASTING
Linlin Ren, Yu-Ping Zeng, and Dongliang Jiang
PRECERAMIC PAPER DERIVED FIBRILLAR CERAMICS 421
Cynthia M. Gomes, Bjoern Gutbrod, Nahum Travitzky, Tobias Fey, and Peter Greil
IX. Composites
IN-SITU SYNTHESYS AND PROPERTIES OF TiB2/Ti3SiC2 431 COMPOSITES
Wei Gu, Jian Yang, and Tai Qiu EFFECT OF La203 ADDITIVE ON MICROSTRUCTURE AND 437 PROPERTIES OF Si3N4-AIN COMPOSITE CERAMICS
Peng Xu, Jian Yang, and Tai Qiu
VAPOR SILICON INFILTRATION FOR FIBER REINFORCED 443 SILICON CARBIDE MATRIX COMPOSITES
Qing Zhou, Shaoming Dong, Haijun Zhou, and Dongliang Jiang
TAILING PROPERTIES OF C/SiC COMPOSITES VIA 449 MODIFICATION OF MATRIX COMPOSITION
Shaoming Dong, Zhen Wang, Yusheng Ding, Xiangyu Zhang, Ping He, and Le Gao
STATUS AND CRITICAL ISSUES OF SiC/SiC COMPOSITES FOR 455 FUSION APPLICATIONS
Zhou Xingui, Yu Haijiao, Cao Yingbin, Liu Rongjun, Wang Honglei, Zhao Shuang, and Luo Zheng
PREPARATION AND CHARACTERIZATION OF C/SiC-ZrB2 467 COMPOSITES VIA PRECURSOR INFILTRATION AND PYROLYSIS PROCESS
Jun Wang, Haifeng Hu, Yudi Zhang, Qikun Wang, and Xinbo He
Ceramic Materials and Components for Energy and Environmental Applications · xi
FABRICATION OF Cf/SiC-BN COMPOSITES USING 473 POLYCARBOSILANE(PCS)- BORON-SiC FOR MATRIX DERIVATION
Zhen Wang, Shaoming Dong, Le Gao, Haijun Zhou, Jinshan Yang, and Dongliang Jiang
SINTERABILITY, THERMAL CONDUCTIVITY AND MICROWAVE 479 ATTENUATION PERFORMANCE OF AIN-SiC SYSTEM WITH DIFFERENT SiC CONTENTS
Wenhui Lu, Xiaoyun Li, Weihua Cheng, and Tai Qiu
EFFECT OF ALKALINE EARTH OXIDES ON DIELECTRIC 485 PROPERTIES OF POLYCRYSTALLINE BaTi205 PREPARED BY ARC MELTING
Xinyan Yue, Rong Tu, Takashi Goto, and Hongqiang Ru
JOINING AND INTEGRATION OF ADVANCED CARBON-CARBON 493 AND CARBON-SILICON CARBIDE COMPOSITES TO METALLIC SYSTEMS
M. Singh and R. Asthana
JOINING OF ZIRCONIUM DIBORIDE-BASED CERAMIC 505 COMPOSITES TO METALLIC SYSTEMS FOR HIGH-TEMPERATURE APPLICATIONS
M. Singh and R. Asthana
X. Bioceramics
PREPARATION AND CHARACTERISATION OF PLGA-COATED 517 POROUS BIOACTIVE GLASS-CERAMIC SCAFFOLDS FOR SUBCHONDRAL BONE TISSUE ENGINEERING
Timothy Mark O'Shea and Xigeng Miao
CERAMIC MATERIALS FOR BONE TISSUE REPLACEMENT AND 525 REGENERATION
W. Swieszkowski, Z. Jaegermann, D.W. Hutmacher, and K. J. Kurzydlowski
CHEMICAL INTERACTION BETWEEN HYDROXYAPATITE AND 531 ORGANIC MOLECULES IN BIOMATERIALS
K. Tsuchiya, T. Yoshioka, T. Ikoma, and J. Tanaka
POROUS Al203 PREPARED VIA FREEZE CASTING AND ITS 537 BIOCOMPATIBILITY
Jing Li, Kaihui Zuo, Wenjuan Liu, Yu-Ping Zeng, Fu-Qiang Zhang, and Dongliang Jiang
xii · Ceramic Materials and Components for Energy and Environmental Applications
XI. Laser Ceramics
PREPARATION OF TRANSPARENT CERAMIC Nd:YAG WITH MgO 547 AS ADDITIVE
Yongchao Li, Tiecheng Lu, Nian Wei, Ruixiao Fang, Benyuan Ma, and Wei Zhang
SYNTHESIS OF La, Yb CODOPED Y203 POWDER AND LASER 553 CERAMICS
Yihua Huang , Dongliang Jiang , Jingxian Zhang , and Qingling Lin
MICROCRYSTALLIZATION IN OXYFLUORIDE Nd3+ DOPED GLASS 561 DUE TO LASER IRRADIATION
S. González-Pérez, P. Haro-González, and I. R. Martin
OPTICAL GAIN BY UPCONVERSION IN Tm-Yb OXYFLUORIDE 567 GLASS CERAMIC
P. Haro-González, F. Lahoz, I. R. Martin, S. González-Pérez, and N. E. Capuj
FEMTOSECOND LASER MODIFICATION ON STRONTIUM 573 BARIUM NIOBATE GLASSES DOPED WITH Er3+ IONS
P. Haro-González, I. R. Martín, S. González-Pérez, L. L. Martin, F. Lahoz, D. Puerto, and J. Soli's
INFLUENCE OF POWDER TYPE ON THE DENSIFICARON OF 579 TRANSPARENT MgAI204 SPINEL
Adrian Goldstein, Ayala Goldenberg, and Meir Hefetz
SINTERING EVOLUTION OF NOVEL Nd:YAG POWDERS WITH 585 TEOS AS ADDITIVE
Ruixiao Fang, Tiecheng Lu, Nian Wei, Yongchao Li, Wei Zhang, and Benyuan Ma
THE EFFECT OF La203 ON THE PROPERTIES OF Nd3+-DOPED 591 YTTRIUM LANTHANUM OXIDE TRANSPARENT CERAMICS
Hongxu Zhou, Qiuhong Yang, and Jun Xu
Lu203:Eu3+ ULTRADISPERSED POWDERS AND TRANSLUCENT 597 CERAMICS
R.P. Yavetskiy, E. A. Vovk, M. B. Kosmyna, Z. P. Sergienko, A. V. Tolmachev, V. M. Puzikov, B. P. Nazarenko, and A. N. Shekhovtsov
FABRICATION AND SPECTROSCOPIC PROPERTIES OF Nd:Lu203 605 TRANSPARENT CERAMICS FOR LASER MEDIA
Ding Zhou, Yan Cheng, Yu Ying Ren, Ying Shi, and Jian Jun Xie
FABRICATION AND LASER PERFORMANCE OF (Ybo.osYo.gs-xLa^Os 611 CERAMICS
Qiuhong Yang, Chuanguo Dou, Hongxu Zhou.Qiang Hao, Wenxue Li, and Heping Zeng
Ceramic Materials and Components for Energy and Environmental Applications · xiii
A STUDY ON THE ZnO-AI203-Si02 SYSTEM NdF3-DOPED 617 TRANSPARENT FLUORIDE-OXIDE GLASS-CERAMICS
Jing Shao, Guohui Feng , Hongbo Zhang , Guangyuan Ma , and Chunhui Su
SYNTHESIS OF NANO-SIZED Lu203 POWDER FOR 623 TRANSPARENT CERAMICS FABRICATION USING CARBONATE DERIVED PRECURSORS
Xiaodong Li, Xudong Sun, Ji-Guang Li, Zhimeng Xiu, Di Huo, and Yan Liu
PREPARATION AND INVESTIGATION OF TRANSPARENT YAG 629 CERAMICS DOPED WITH d1 IONS
V. B. Kravchenko, Yu. L. Kopylov, S. N. Bagayev, V. V .Shemet, A. A. Komarov, and L. Yu. Zaharov
PREPARATION AND CHARACTERIZATION OF NEODYMIUM- 635 DOPED LZS TRANSPARENT GLASS-CERAMICS
Hongbo Zhang, Yimin Wang, Guang Cui, Jing Shao, Huashan Zhang, and Chunhui Su
PREPARATION AND CHARACTERIZATION OF ZnO-AI203-Si02 639 TRANSPARENT GLASS-CERAMICS
Jing Shao, Guohui Feng, Hongbo Zhang, Guangyuan Ma, and Chunhui Su
LUMINESCENCE OF Yb3+, Ho3+: Lu203 NANOCRYSTALLINE 645 POWDERS AND SINTERED CERAMIC
Liqiong An, Jian Zhang, Guohong Zhou, and Shiwei Wang
MIRRORLESS CONTINUOUS WAVE LASER EMISSION FROM 649 Nd:YAG CERAMIC FEMTOSECOND-WRITTEN WAVEGUIDES
A. Benayas, D. Jaque, A. Rodenas, E. Cantelar, L. Roso, and G. A. Torchia
Author Index 655
xiv · Ceramic Materials and Components for Energy and Environmental Applications
Preface
The global population growth and tremendous economic development has led to increasing demand for energy from all over the world as well as increasing con-cern for environment and global warming. The energy efficient and eco-friendly systems and technologies are critically needed for the further global growth and sustainable development. Advanced ceramics are enabling materials for a number of demanding energy efficient and eco-friendly applications in aerospace, power generation, ground transportation, nuclear, and chemical industries. These materi-als have unique properties such as high strength, high stiffness, long fatigue life, low density, and adaptability to the intended functions. Significant achievements have been made worldwide in the design, development, manufacturing, and appli-cation of these materials in recent years and considerable innovative research and technology development is still continuing to address technical and economic challenges.
9th International Conference on Ceramic Materials and Components for Energy and Environmental Applications (9th CMCEE) in Shanghai, China was continua-tion of series of international conferences held all over the world over the last three decades. The major goal of CMCEE was to bring together academicians, re-searchers, and end users in various disciplines from all over the world to share knowledge and exchange views leading to industrial applications of these technolo-gies. The current volume contains selected peer reviewed papers from more than 300 presentations from all over the world. The papers in this volume also highlight and emphasize the importance of synergy between advanced materials and compo-nent designs. This volume also contains selected papers from 4th International Laser Ceramics symposium which was held during the same time period. We would like to thank organizers and sponsors of this symposium.
We would like to acknowledge the financial support from Chinese Academy of Sciences, Shanghai Municipal Corporation, and Shanghai Institute of Ceramics. Our special thanks to Abhishek Singh from Case Western Reserve University, Cleveland, Ohio for the editing of the manuscripts. We would also like to thank Mr. Greg Geiger, Technical Content Manager of The American Ceramic Society for all
XV
the help in the production of this volume. We would like to thank all the contribu-tors and reviewers from all over the world.
Dongliang Jiang Yuping Zeng Shanghai Institute of Ceramics, Shanghai, China
Mrityunjay Singh Ohio Aerospace Institute, Cleveland, USA
Juergen Heinrich Clausthal University of Technology, Germany
xvi · Ceramic Materials and Components for Energy and Environmental Applications
Ac kn ow led g ernen t s
9th International Conference on Ceramic Materials and Compo- nents for Energy and Environmental Applications (9th CMCEE)
Hosted by: Shanghai Institute of Ceramics, Chinese Academy of Sciences
Endorsed by: The Chinese Ceramic Society The American Ceramic Society The European Ceramic Society The Ceramic Society of Japan The Korean Ceramic Society The Australian Ceramic Society
Conference Committee: Conference Chair (Asia): Prof. Dongliang Jiang Shanghai Institute of Ceramics, Chinese Academy of Sciences Chna
Co-Chair (America): Dr. Mrityunjay Singh Ohio Aerospace Institute NASA Glenn Research Center USA
Co-Chair (Europe): Prof. Jurgen Heinrich Clausthal University of Technology Germany
xvii
International Advisory Committee F. Aldinger (Germany) Longtu Li (China) José Ferreira (Portugal) J. Martinez-Fernandez (Spain) C.X. Ding (China) S. I. Milieko (Russia) Ludwig Gauckler (Switzerland) Dong-Soo Park (Korea) Jingkun Guo (China) Mrityunjay Singh (USA) Jürgen Heinrich (Germany) Louis Winnubst (The Netherlands) Zhanping Jin (China) Paolo Zannini (Italy) Walter Krenkel (Germany)
M.H. Lewis (U.K.) Jean Baumard (France) L.M. Manocha (India) Yibing Cheng (Australia) G.L. Messing (USA) Ruiping Gao (China) Dale E. Niesz (USA) Peter Greil (Germany) Yoshio Sakka (Japan) Stuart Hampshire (Ireland) Derek Thompson (U.K) Dongliang Jiang (China) Koichi Niihara (Japan) K. Komeya (Japan) Hasan Mandal (Turkey)
G.N. Babini (Italy) H.T. Lin (USA) I-Wei Chen (USA) S. Mathur (Germany) M.K. Ferber (USA) R. Naslain (France) Takashi Goto (Japan) Pavol Sajgalik (Slovakia) Victor Gusarov (Russia) N. Sobczak (Poland) S.I. Hirano (Japan) M. Yoshimura (Japan) A. Kohyama (Japan) L.T. Zhang (China)
4th International Laser Ceramics symposium (4th LCS)
Local Organizing Committee
Chair: Prof. Lidong Chen Shanghai Institute of Ceramics Chinese Academy of Sciences
Secretariat: Prof. Yu-Ping Zeng Shanghai Institute of Ceramics Chinese Academy of Sciences
Secretariat assistant: Mr. Hui Tong Shanghai Institute of Ceramics Chinese Academy of Sciences
Hosted by Shanghai Institute of Ceramics, Chinese Academy of Sciences
Endorsed by The Chinese Ceramic Society The American Ceramic Society The European Ceramic Society The Ceramic Society of Japan The Korean Ceramic Society The Australian Ceramic Society
xviii · Ceramic Materials and Components for Energy and Environmental Applications
Conference Chairman: S. W. Wang, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China
Co-chairs and Program Committee A. A. Kaminskii, Institute of Crystallography, Russia K. Ueda, Institute for Laser Science, University of Electro-Communications, Japan Q. H. Lou, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of
Sciences, China A. Ikesue, World-Lab. Co. Ltd., Japan W. Strek, Dept of Excited State Spectroscopy, Poland Academy of Sciences,
Poland V. Lupei, Institute of Atomic Physics, Romania Bruno Le Garree, CEA CESTA, France
International Advisory Committee T. Taira, Laser Research Center for Molecular Science, Institute for Molecular
Science, Japan T. Yanagitani, Konoshima Chem Co Ltd, Takuma, Japan J. Kawanaka, Osaka University, Japan R. L. Gentilman, Raytheon Company, USA T. F. Soules, Lawrence Livermore National Laboratory, USA M. Dubinskiy, US Army Research Laboratory, USA G. J. Quarles, II-VI Corp./VLOC, USA S. B. MIROV, University of Alabama at Birmingham, Birmingham, USA G. C. Wei, Osram Sylvania Inc., USA D. L. Jiang, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China Z. Y. Xu, Institute of Physics, Chinese Academy of Sciences, China D. Z. Shen, Research Institute of Synthetic Crystals, Beijing, China D. Y. Tang, School of Electrical & Electronic Engineering, Nanyang
Technological University, Singapore S. N. Bagayev, Institute of Laser Physics, Novosibirsk, Russia V. B. Kravchenko, Fryazino, FIRE RAS, Russia T. T. Basiev, Laser Materials and Technology Research Center, Moscow, Russia G. Boulon, LPCML, CNRS, Lyon, France M. Mortier, Ecole Nationale Supérieure de Chimie de Paris, France J. F. Baumard, SPCTS, Limoges, France Y. Rabinovitch, CILAS, ESTER Technopole, France H. J. Kong (Korea), Laser Science Research Lab, Korea Advanced Institute of
Science and Technology Witold Lojkowski, Institute of High Pressure Physics, Polish Academy of
Sciences, Poland R. Chaim, Department of Materials Engineering, Israel Institute of Technology,
Israel A. Krell, Fraunhofer Institute for Ceramic Technologies and Systems (IKTS),
Germany
Ceramic Materials and Components for Energy and Environmental Applications · xix
Local Organizing Committee H. J. Luo, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China J. Q. Zhu, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of
Sciences, China J. T. Zhao, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China Y. B. Pan, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China D. Y. Jiang, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China J. Zhang, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China G. H. Zhou, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China
xx · Ceramic Materials and Components for Energy and Environmental Applications
I. Basic Science, Design, Modeling and Simulation
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FRACTURE STATISTICS OF SMALL SPECIMENS
Robert Danzer, Peter Supancic
Institut tur Struktur- und Funktionskeramik, Montanuniversität Leoben, Peter-Tunner Strasse 5, A-8700 Leoben, Austria
and Materials Center Leoben, Roseggerstrasse 12, A-8700 Leoben, Austria. E-mail: [email protected]
ABSTRACT Strength data of brittle materials show significant scatter. Therefore designing with brittle materials has to be made with probabilistic methods. So far this is done using Weibull statistics, which is based on the weakest link hypothesis. It (implicitly) implies a particular type of defect distribution, which can be observed in many (but not in all) ceramic materials. It is shown that for very small specimens the Weibull assumptions claim unrealistic high densities of flaws. Then the flaws will interact, they are not longer statistically independent and the weakest link hypothesis is not valid. Consequently the Weibull distribution predicts too high a strength for very small specimens.
INTRODUCTION Fracture of ceramics usually initiates from flaws which are randomly distributed in the material. The strength of the specimen then depends on the length of the major flaw, which varies from specimen to specimen. The strength of brittle materials has to be described by statistical means [1 -3]. It follows from experiments that the failure probability increases with load amplitude and with size of the specimens [1-5]. The first observation is trivial. The second observation follows from the fact that it is more likely to find a major flaw in a large than in a small specimen. Therefore the mean strength of a set of large specimens is smaller than that of small specimens. This size effect of strength is the most prominent and relevant consequence of the statistical behaviour of the strength of brittle materials. Weibull developed his statistical theory of brittle fracture on the basis of the weakest link hypothesis, i.e. the specimen fails if its weakest element fails [6, 7]. In its simplest form and for an uniaxial homogenous and tensile stress state, σ, and for specimens of the volume, V, the so called Weibull distribution of the probability of failure, F, is given by:
F(a,V) = l-exp
The Weibull modulus, m, describes the scatter of strength data: the distribution is the wider the smaller m is. σ0 is the characteristic strength and V0 is the corresponding reference volume. Of course the probability of surviving (the reliability, R) is: R = 1 - F . Freudenthal [8] showed for sparsely distributed flaws, that the probability of failure only depends on the number of destructive flaws, NcS, occurring in a specimen of size and shape, S :
Fs(°) = l-exP{-Nc) ·
NcS is the mean number of destructive (critical) flaws in a large set of specimens (i.e. the value of expectation). Jayatilaka et al. [9] showed, that, for brittle and homogeneous materials, the distribution of the strength data is caused by the distribution of sizes (and orientations) of the flaws.
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3
mailto:[email protected]
Fracture Statistics of Small Specimens
A Weibull distribution of strength will be observed for flaw populations with a monotonically decreasing density of flaw sizes. Danzer et al. [10 - 12] extended these ideas to flaw populations with any size distribution and to specimens with an inhomogeneous flaw population. On the basis of these ideas a direct correlation between the flaw size distribution and the scatter (statistics) of strength data can be defined. The Weibull distribution is the state of the art statistics in the mechanical design process of ceramic components [1 - 3]. Strength testing and data evaluation are standardised. A sample of at least 30 specimens has to be tested. The range of "measured" failure probabilities increases with the sample size [3, 13] and is - for a sample of 30 specimens - very limited (it is between 1/60 and 59/60). To determine the design stress, the measured data have to be extrapolated with respect to the volume and to the "tolerated" failure probability. This often results in a very large extrapolation span [3]. In this paper the Weibull theory is applied to very small specimens. The analysis follows the ideas presented in [13]. The relationships between flaw population, size of the fracture initiating flaw and strength are discussed. It is shown that a limit for the applicability of the classical fracture statistics (i.e. Weibull statistics based on the weakest link hypothesis) exists for very small specimens (components).
FRACTURE STATISTICS AND DEFECT SIZE DISTRIBUTION The function NcS (σ) is obtained by integrating the local density, nc (σ, r), of destructive flaws
nc(a,r)= J g (a , r )da α,.(σ)
over the volume of the specimen: NcS = ¡ncdV [3, 8 - 10]. For simplicity, but without loss of generality [8], it is assumed that size and orientation of a flaw are described by a single variable (the flaw size, a). The frequency distribution of the density of flaw sizes, g(a,r), may depend on the position vector, r . A local fracture criterion (e.g. the Griffith criterion, [1, 2]) correlates stress amplitude and flaw length: the critical flaw size is the smallest flaw length, which - under the action of the stress - causes failure (the size of the smallest destructive flaw). Since ac depends on the magnitude of the applied stress, so do the values of nc and also Nc¿ (σ). For a homogeneous material loaded under uniaxial homogeneous tension the volume integral is trivial. For a flaw population with relative frequencies decreasing with a negative power the flaw size, a ,
8(a)=g0-(a/a0)"
a Weibull distribution (eq. 1) occurs [9]. This function has only two independent parameters: the exponent ( - r ) and the coefficient (g0 ·α0''). Using these assumptions and after some algebra the density of destructive flaws in terms of a critical flaw size is: n(ac) = (ac · g(ac)) / (r - 1 ) . The critical flaw size can be defined using the Griffith/Irwin criterion [1 - 3]:
c π \Υ·σ)
KIc is the critical stress intensity factor (the fracture toughness) and Y is a dimensionless geometric factor. Inserting in the above expression analytical equations for the Weibull parameters results: The Weibull modulus is only related to the path of the flaw size distribution:
m = 2 - ( r - l ) .
4 ■ Ceramic Materials and Components for Energy and Environmental Applications
Fracture Statistics of Small Specimens
The second parameter in the Weibull statistics is: V0-a0m = ( ( r - l ) / gQ -a0MKIC/ Υ^π·α0 V \
In the following a material behaving in the way as described above (eq. 1, eq. 4, etc.) is called "Weibull material". A Weibull type strength distribution also may arise for inhomogeneous stress and non uniaxial stress states (then the volume has to be replaced by an effective volume, [1 - 3]). If failure is caused by surface flaws, the volume has to be replaced by the surface [1,3, 12]. Danzer et al. have discussed the influence of other types of flaw populations (e.g. of bimodal distri-butions) on strength [11, 12]. In these cases the Weibull modulus might depend on the applied load amplitude and on the size of the specimen. Then the determination of a design stress in the usual way may become problematic. A stress and size dependent modulus occurs for materials with an R-curve behaviour [11] and may also be caused by internal stress fields [11]. It should be noted that on the basis of a small sample size, e.g. only 30 specimens, it is not possible to differentiate between a Weibull, a Gaussian, or any other similar distribution functions, as shown by Lu et al. [14] using statistical measures or by Danzer et al. [12] using Monte Carlo simulations. This is caused by the inherent scatter of the data and the difference between sample and true population. The ultimate test for the existence of a Weibull distribution is to test a material on different levels of (effective) volumes.
THE CORRELATION BETWEEN STRENGTH AND FLAW POPULATION In the following, the relationship between fracture statistics and defect size distribution is discussed for the simple case of tensile tests (uniaxial and homogeneous stress state) on a homogeneous brittle material. The tests are performed on specimens of equal size. It is assumed that the volume of the specimens is: V = V0. The number of tested specimens (the sample size) is X . In each test the load is increased up to the moment of failure. The strength is the stress at the moment of failure. In each sample the strength values of the individual specimens are different, i.e. the strength is distributed. If data determined in that way are evaluated the specimens are ranked according to their strength, / being the ranking parameter. To estimate the failure probability for an individual specimen an estimation function is used [1,3, 13]:
Fi=(i-\/2)/X , i = l,2,? X
Inserting eq. 7 into eq. 2 and making a few rearrangements, we get: NcS(σ,) = h 2X/(2X - 2i +1). In this way the mean number of critical flaws per specimen (volume VQ; stress ai) can be read from the ranking number and the sample size. For the weakest specimen (i = 1) of a sample the estimator for the probability of failing is: FY = F(al) = l/2X . That specimen contains on average NcS(al) = \ñ2[x/(2X-l)] destructive flaws. For the strongest specimen of the sample (i = X) it holdsthat: Fx = F(ax) = (2X -\)/2X and NcS(ax) = h2X. A special situation occurs if the strength is equal to the characteristic strength (i.e. for V =V0 and σ = σ0). Then the probability of failure is F(a0) = \-\/e and NcS(a0) = \ and the density of critical flaws is: nc (σ0, V0) = NcS (σ0) / V0 = 1 / V0 · If the calculations made for σ = σ0 and V = V0 are generalized for any stress value
Fracture Statistics of Small Specimens
The use of this equation opens a simple possibility to determine the frequency distribution of flaw sizes in a wide range of parameters by testing specimens of different volume. In the following these ideas are applied to describe bending test results of a commercial silicon nitride ceramic.
FRACTURE AND FLAW STATISTICS OF A TYPICAL COMMERCIAL SILICON NITRIDE MATERIAL
A typical commercial gas pressure sintered silicon nitride ceramic is used as model material. Its hardness (HV5) is 15.5 ± 0.3 MPa, the fracture toughness (SEVNB, [15, 16]) is 5.0 ± 0.2 MPaVm, the Young's Modulus is 297 ± 2 GPa and the Poisson ratio is 0.27. More details can be found in [19]. A sample of 30 bending specimens was machined out from large discs (diameter 250 mm, thickness 5 mm). The specimen preparation and the tests were done according to EN 843-1 and evaluated according to EN 843-5 [17, 18]. The characteristic strength of this sample is σ0 = 871 MPa and the Weibull modulus is m= 14.1. The effective volume [1] of the bending specimens is Vejf =V(ra+2)/ 4(m + l)2 =8.5·10"9 m3. This value is used as scaling parameter V0 = V. The Weibull distribution is shown in Fig. l.a. The measured data are nicely distributed around the straight line, which describes the Weibull distribution.
Fig. 1: a) Strength data of a silicon nitride ceramic tested in four point bending (4PB) in a Weibull plot and b) the relative frequency distribution of flaw sizes. The data points were determined by fracture experiments.
By fractographic inspection fracture [20, 21 ] origins within the volume (inclusions) were found in 3 specimens. In the other 27 specimens no clear evidence for the type of fracture origin was found. It is assumed that all flaws are small surface flaws, i.e. their geometric factor is Y = 1.12.
6 · Ceramic Materials and Components for Energy and Environmental Applications
Fracture Statistics of Small Specimens
In the following, the strength data are used to determine the frequency distribution function of the defects. Using eq. 5 the size of the critical flaw for the characteristic strength is ac0 = 26· 10"6 m. This value is used in the following for the arbitrary scaling parameter: a0 = ac 0 . For the exponent r we get using eq. 6: r= 8.05. With these data the factor in eq. 4 is: g0 = 3.21013m~4, and therefore all parameters in eq. 4 are determined. The relative frequency distribution of flaw sizes is shown in Fig. l.b. The transformation of strength into flaw size data was done using eq. 8. Again the data are nicely distributed around the straight line. This is characteristic for a Weibull material. An extremely strong dependency of the relative frequency on the critical flaw size can clearly be recognized: although the size of the critical flaws in the samples only varies by a factor of around 2.2 the corresponding relative frequency of the flaw sizes varies by a factor of around 500. That means that flaws with a radius of 21 μηι are about 500 times more frequent than flaws with a radius of 46 μπι.
SIZE EFFECT ON STRENGTH; APPLICATION TO VERY SMALL SPECIMENS As discussed in the introduction a size effect on strength exists [1 -3] , which - for a Weibull material - is described by:
Vvalm =V2-a2m
The probability of failure in a sample of specimens of volume V2 is equal to that in another sample containing specimens of volume V], if the stresses applied to the specimens are related according to eq. 9. Using the Griffith criterion we get [13]:
ac,xlaca={VxIV2)2lm
For the specimens with volume Vx the corresponding relative frequency of flaw sizes at σ = σ0 is g(ax) = gQ-{axlaQyr and the density of destructive flaws is ηα(σΟΪ,νϊ)= 1/Vlt The analogue holds for specimens of volume V2. In Fig. 2 the diameter (2ac) of the critical flaws (for the characteristic strength of the specimens) is plotted versus the (effective) volume in a double logarithmic scale (eq. 10) using the example of the silicon nitride material described above. The slope of the line is: l/(m/2) = l/(r — 1) = 1/7.05 . The dashed line describes a typical scaling parameter for the volume of the specimen. For simplicity the edge length of a cube with volume V is taken as the characteristic length: / = V1/3. For materials with a modulus m > 6, there exists a point of intersection between both lines, which is - in the selected example - at a volume of about V~ 4.210"17 m3 (this corresponds to the diameter of the critical flaw of about 2a c « 3.4 μπι). Obviously the assumption made in eq. 4 (the relative frequency of flaws follows an inverse power law) can only approximate the behaviour of materials for large flaws. It fails for very small flaws: the relative frequency goes to infinity if the flaw size goes to zero: a —* 0, g(a) —> oo [13]. At the intersection point in Fig 2, the density of dangerous flaws gets so high that the volume of the specimens is completely filled with flaws and, left of that point; the "volume of dangerous flaws" even exceeds volume of the specimens. For obvious reasons this is not possible in real materials. Another inconsistency is caused by the fact, that the derivation of the fracture statistics (eq. 1 and eq. 2) assumes non-interacting flaws [8]. This will only be true in the case of a low flaw density. If fracture statistics are applied to very small specimens made of a Weibull material the density of dangerous flaws gets high and the interaction between flaws cannot be neglected any longer [22]. For that case it can be assumed that interacting flaws link up. This would cause an upper limit for
Ceramic Materials and Components for Energy and Environmental Applications · 7
Fracture Statistics of Small Specimens
Table 1: Strength test on specimens of different size. Data set
Specimen dimension /mm
Charact. strength / MPa
2ar 0 /μηι Weibull modulus / -effective volume /
1012m3
x, /μπι
V2 ßr .O '-
4PB
45x3.95x2.98
871
52 14.1 [11-17]
8500
2041 39
A (B3B-test) 0 43;
t = 2.484
1053
36 12.4 [9-15]
280
654 18
B (B3B-test) 0 20;
t= 1.983
1123
31 15.9 [12-19]
65
402 13
C (B3B-test) 0 10.8,
t= 1.054
1226
26 21.7 [16-26]
4.3
163 6.3
D (B3B-test) 0 4.7;
t = 0.445
1275
24 17.7 [13-22]
0.6
84 3.5
4PB: four point bending test; B3B: ball on three balls test; 0 : diameter; t: thickness; 2ac0: diameter of the critical flaw corresponding to the characteristic strength, / : reference length (defined to be the third root of the effective volume). Numbers in square brackets are limits of the 90 % confidence interval.
the strength, if the distance between the flaws gets too close, say 2 - 3 times their diameter. Further strength tests (data sets A- D) were made in biaxial bending on specimens of different size. Specimens were cut from the same plates as used for the bending specimens. Tests and results are described in [19]. Key results are summarised in Table 1. The data show a significant size effect, i.e. the characteristic strength is much larger for small than for large specimens (Fig. 3). The straight line shows the size effect as predicted by eq. 9 based on the bending test data. Although the data sets A and B are in the 90 % confidence interval of the extrapolation, the sets C and D show a significantly lower strength than predicted. The behaviour of small specimens is discussed in more detail in [13]. A possible reason for this drop of strength is the fact that machining of very small specimens (as is the case of set D) is very demanding and some machining damage cannot be excluded in this case. Additional damage would cause a reduction of strength as observed in Fig. 3. Further possible reasons for the (apparent) deviation of the strength of small specimens from the Weibull behaviour are experimental measure-ment uncertainties, which become large for small specimens and which are not included in the scatter bars shown in Fig. 3. The plotted scatter bars refer to the uncertainties due to the sampling procedure (the sample is different from the underlying population, [12]). Another reason would be the interaction between flaws, as described above. The last line in Table 1 shows the ratio of the size parameter (corresponding with the effective volume; it is the length of the edge of a cube with the effective volume) divided by the diameter of the critical Griffith flaw for the characteristic strength. This ratio is larger than 10 for the sets 4PB, A and B. Here an interaction seems not to be likely. But for set D the ratio is as small as about 3. Here some overlapping of local stress field and linking of micro defects may become possible. But at present it is not clear if this really happens or not. Bazant formulated a statistical theory of fracture for quasibrittle materials [5, 23, 24]. He assumed that there exist several hierarchical orders which each can be described by parallel and serial linking of so-called representative volume elements (RVEs). For large specimens (and low probability of failures) the fracture statistics is equal to the Weibull statistics , i.e. if the specimens size is larger than 500 to 1000 times of the size of one RVE. In the actual case this is similar to the diameter of the critical flaw. For smaller specimens the volume effect disappears and the fracture
8 · Ceramic Materials and Components for Energy and Environmental Applications
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