《材料失效分析 Materials Failure Analysis》课程教学资源（参考书籍）Fracture of Brittle Solids——Fracture of Brittle Solids（Second Edition）

Cambridge Solid State Science Series Brian Lawn Fracture of Brittle Solids- Second Edition

This is an advanced text for higher degre terials science students and researchers concerned with the strength of highly brittle covalent-ionic solids, principally ceramics. It is a reconstructed and greatly expanded edition of a book first published in 1975 The book presents a unified continuum, microstructural and atomistic treatment of modern-day fracture mechanics from a materials per pective. Particular attention is directed to the basic elements of bonding and microstructure that govern the intrinsic toughness of ceramics. These elements hold the key to the future of ceramics as high-technology materials-to make brittle solids strong, we must first understand what makes them weak. The underlying theme of the book is the fundamental Griffith energy-balance concept of crack propagation. The early chapters develop fracture mechanics from the traditional continuum perspective, with attention to linear and nonlinear crack-tip fields non-equilibrium crack states. It then describes the atomic structure of sharp cracks, the topical subject of crack-microstructure interactions in ceramics, with special focus on the concepts of crack-tip shielding and crack-resistance curves, and finally deals with indentation fracture, flaws, and structural reliability. Brittle fracture crosses the boundaries between materials science, structural engineering, and physics and chemistry. This book develops a cohesive account by emphasising basic principles rather than detailed factual information. Due regard is given to model brittle materials such icate glass and polycrystalline alumina, as essential groundwork for ltimate extension of the subject matter to more complex engineering This book will be used by advanced undergraduates, beginning aduate students and research workers in materials science. mechanical engineering, physics and earth science depa Its interested in brittle fracture of ceramic material

This is an advanced text for higher degree materials science students and researchers concerned with the strength of highly brittle covalent-ionic solids, principally ceramics. It is a reconstructed and greatly expanded edition of a book first published in 1975. The book presents a unified continuum, microstructural and atomistic treatment of modern-day fracture mechanics from a materials per- spective. Particular attention is directed to the basic elements of bonding and microstructure that govern the intrinsic toughness of ceramics. These elements hold the key to the future of ceramics as high-technology materials - to make brittle solids strong, we must first understand what makes them weak. The underlying theme of the book is the fundamental Griffith energy-balance concept of crack propagation. The early chapters develop fracture mechanics from the traditional continuum perspective, with attention to linear and nonlinear crack-tip fields, equilibrium and non-equilibrium crack states. It then describes the atomic structure of sharp cracks, the topical subject of crack-micro structure interactions in ceramics, with special focus on the concepts of crack-tip shielding and crack-resistance curves, and finally deals with indentation fracture, flaws, and structural reliability. Brittle fracture crosses the boundaries between materials science, structural engineering, and physics and chemistry. This book develops a cohesive account by emphasising basic principles rather than detailed factual information. Due regard is given to model brittle materials such as silicate glass and polycrystalline alumina, as essential groundwork for ultimate extension of the subject matter to more complex engineering materials. This book will be used by advanced undergraduates, beginning graduate students and research workers in materials science, mechanical engineering, physics and earth science departments interested in the brittle fracture of ceramic materials

Fracture of brittle solids Cambridge Solid State Science Series EDITORS Professor E. A. Davis Department of Physics, University of Leicester Professor I.m. Ward FR: Department of Physics, University of Leeds

Fracture of brittle solids Cambridge Solid State Science Series EDITORS: Professor E. A. Davis Department of Physics, University of Leicester Professor I. M. Ward FRS Department of Physics, University of Leeds

Titles in print in this series Polymer Surfaces An Introduction to Composite Materials D. Hull Thermoluminescence of solids s w.s. McKeever Modern Techniques of Surface Science D. P. woodruff and T. A. delchar New Directions in Solid State Chemistry Ce The Electrical Resistivity of Metals and Alloys P.L. rossiter The Vibrational Spectroscopy of Polymers D. I. Bower and w. f Maddan Glasses and the vitreous State Hydrogenated Amorphous Silicon Microstructural Design of Fiber Composites T-I. chou A. M. Donald and a.H. windle Fracture of Brittle Solids- Second Edition n Introduction to Metal Matrix Composites

Titles in print in this series Polymer Surfaces B. W. Cherry An Introduction to Composite Materials D. Hull Thermoluminescence of Solids S. W. S. McKeever Modern Techniques of Surface Science D. P. Woodruff and T. A. Delchar New Directions in Solid State Chemistry C. N. R. Rao and J. Gopalakrishnan The Electrical Resistivity of Metals and Alloys P. L. Rossiter The Vibrational Spectroscopy of Polymers D. I. Bower and W. F. Maddams Fatigue of Materials S. Suresh Glasses and the Vitreous State /. Zarzycki Hydrogenated Amorphous Silicon R. A. Street Microstructural Design of Fiber Composites T.-W. Chou Liquid Crystalline Polymers A. M. Donald and A. H. Windle Fracture of Brittle Solids - Second Edition B. R. Lawn An Introduction to Metal Matrix Composites T. W. Clyne and P. J. Withers

BRIAN LAWN NIST Fellow fracture of brittle solids SECOND EDITION KRSX CAMBRIDGE CS UNIVERSITY PRESS

BRIAN LAWN NIST Fellow Fracture of brittle solids SECOND EDITION CAMBRIDGE UNIVERSITY PRESS

Published by the Press Syndicate of the University of Cambridge The Pitt Building, Trumpington Street, Cambridge CB2 IRP 40 West 20th Street. New York, NY 10011-4211 USA 10 Stamford Road, Oakleigh, Melbourne 3166, Australia c Cambridge University Press 1975, 1993 First published 1975 Second edition 1993 A catalogue record of this book is available from the British Library Library of Congress cataloguing in publication data Lawn. Brian R fracture of brittle solids /Brian Lawn, -2nd edn cm-( Cambridge solid state science series) Includes bibliographical references and index ISBN0521401763.-ISBN0521409721(pbk) I. Fracture mechanics. 2. Brittleness. I. Title. Il. Series TA409L371993 620.l126dc2091-2619lCIP ISBN 0 521 401763 hard back ISBN 0 521 40972 I paperback Transferred tal printing 2004

Published by the Press Syndicate of the University of Cambridge The Pitt Building, Trumpington Street, Cambridge CB2 1RP 40 West 20th Street, New York, NY 10011-4211, USA 10 Stamford Road, Oakleigh, Melbourne 3166, Australia © Cambridge University Press 1975, 1993 First published 1975 Second edition 1993 A catalogue record of this book is available from the British Library Library of Congress cataloguing in publication data Lawn, Brian R. Fracture of brittle solids/Brian Lawn. - 2nd edn p. cm. - (Cambridge solid state science series) Includes bibliographical references and index. ISBN 0 521 40176 3. - ISBN 0 521 40972 1 (pbk.) 1. Fracture mechanics. 2. Brittleness. I. Title. II. Series. TA409.L37 1993 620.1'126-dc20 91-26191 CIP ISBN 0 521 40176 3 hardback ISBN 0 521 40972 1 paperback Transferred to digital printing 2004 UP

Contents Glossary of symbols and abbreviations The Griffith concept 1.1 Stress concentrators 1.2 Griffith energy-balance concept: equilibrium fracture 1.3 Crack in uniform tension 12579 1. 4 Obreimoff's experiment 1.5 Molecular theory of strength 12 1.6 Griffith flaws 1.7 Further considerations 2 Continuum aspects of crack propagation I: linear elastic crack-tip field 2. 1 Continuum approach to crack equilibrium: crack system as thermodynamic cycle 2.2 Mechanical-energy-release rate, G 20 2.3 Crack-tip field and stress-intensity factor, K 2. 4 Equivalence of G and K parameters 2.5 G and K for specific crack systems 2.6 Condition for equilibrium fracture: incorporation of the Griffith concept 7 Crack stability and additivity of K-fields 2.8 Crack paths 3 Continuum aspects of crack propagation I: nonlinear crack-tip field 3. 1 Nonlinearity and irreversibility of crack-tip processes 3.2 Irwin-Orowan extension of the Griffith concept 5269 3.3 Barenblatt cohesion-zone model

Contents Preface x Glossary of symbols and abbreviations xiii 1 The Griffith concept 1 1.1 Stress concentrators 2 1.2 Griffith energy-balance concept: equilibrium fracture 5 1.3 Crack in uniform tension 7 1.4 Obreimoff's experiment 9 1.5 Molecular theory of strength 12 1.6 Griffith flaws 13 1.7 Further considerations 14 2 Continuum aspects of crack propagation I: linear elastic crack-tip field 16 2.1 Continuum approach to crack equilibrium: crack system as thermodynamic cycle 17 2.2 Mechanical-energy-release rate, G 20 2.3 Crack-tip field and stress-intensity factor, K 23 2.4 Equivalence of G and K parameters 29 2.5 G and K for specific crack systems 30 2.6 Condition for equilibrium fracture: incorporation of the Griffith concept 39 2.7 Crack stability and additivity of ^-fields 41 2.8 Crack paths 44 3 Continuum aspects of crack propagation II: nonlinear crack-tip field 51 3.1 Nonlinearity and irreversibility of crack-tip processes 52 3.2 Irwin-Orowan extension of the Griffith concept 56 3.3 Barenblatt cohesion-zone model 59

3.4 Path-independent integrals about crack tip 3.5 Equivalence of energy-balance and cohesion-zone 70 3.6 Crack-tip shielding: the R-curve or T-curve 3.7 Specific shielding configurations: bridged interfaces and frontal zones 4 Unstable crack propagation: dynamic fracture 86 4. 1 Mott extension of the Griffith concept 4.2 Running crack in tensile specimen 4.3 Dynamical effects near terminal velocity 4.4 Dynamical loading 4.5 Fracto-emission 5 Chemical processes in crack propagation: kinetic fracture 106 5.1 Orowan generalisation of the Grifith equilibrium concept: work of adhesion 5.2 Rice generalisation of the Griffith concept 5.3 Crack-tip chemistry and shielding 117 5.4 Crack velocity data 5 Models of kinetic crack propagation 5.6 Evaluation of crack velocity parameters 138 5.7 Thresholds and hysteresis in crack healing-repropagation 139 6 Atomic aspects of fracture 6. 1 Cohesive strength model 144 6.2 Lattice models and crack trapping: intrinsic bond rupture 6.3 Computer-simulation models 162 6.4 Chemistry: concentrated crack-tip reactions 6.5 Chemistry: surface for tates 6.6 Crack-tip plasticity l85 6.7 Fundamental atomic sharpness of brittle cracks: direc observations by transmission electron microscopy 7 Microstructure and toughness 7.1 Geometrical crack-front perturbations 7.2 Toughening by crack-tip shielding: general considerations 7.3 Frontal-zone shielding: dislocation and microcrack

viii Contents 3.4 Path-independent integrals about crack tip 66 3.5 Equivalence of energy-balance and cohesion-zone approaches 70 3.6 Crack-tip shielding: the incurve or T'-curve 72 3.7 Specific shielding configurations: bridged interfaces and frontal zones 80 4 Unstable crack propagation: dynamic fracture 86 4.1 Mott extension of the Griffith concept 87 4.2 Running crack in tensile specimen 88 4.3 Dynamical effects near terminal velocity 93 4.4 Dynamical loading 99 4.5 Fracto-emission 103 5 Chemical processes in crack propagation: kinetic fracture 106 5.1 Orowan generalisation of the Griffith equilibrium concept: work of adhesion 108 5.2 Rice generalisation of the Griffith concept 112 5.3 Crack-tip chemistry and shielding 117 5.4 Crack velocity data 119 5.5 Models of kinetic crack propagation 128 5.6 Evaluation of crack velocity parameters 138 5.7 Thresholds and hysteresis in crack healing-repropagation 139 6 Atomic aspects of fracture 143 6.1 Cohesive strength model 144 6.2 Lattice models and crack trapping: intrinsic bond rupture 149 6.3 Computer-simulation models 162 6.4 Chemistry: concentrated crack-tip reactions 165 6.5 Chemistry: surface forces and metastable crack-interface states 175 6.6 Crack-tip plasticity 185 6.7 Fundamental atomic sharpness of brittle cracks: direct observations by transmission electron microscopy 188 7 Microstructure and toughness 194 7.1 Geometrical crack-front perturbations 195 7.2 Toughening by crack-tip shielding: general considerations 208 7.3 Frontal-zone shielding: dislocation and microcrack clouds 211

7.4 Frontal-zone shielding: phase transformations in zirconia 7.5 Shielding by crack- interface bridg phase ceramIcs 7.6 Ceramic 8 Indentation fractu 8.1 Crack propagation in contact fields blunt and sharp indenters 8. 2 Ind toughness, and T-curves 8.3 Indentation cracks as controlled flaws: time-dependent strength and fatigue 276 8. 4 Subthreshold indentations: crack initiation 8.5 Subthreshold indentations: strength 8.6 Special applications of the indentation method 8.7 Contact damage: strength degradation, ero 8. 8 Surface forces and contact adhesion 9 Crack initiation: flaws 9.1 Crack nucleation at microcontacts 9.2 Crack nucleation at dislocation pile-ups 314 9.3 Flaws from chemical thermal. and radiant fields 9. 4 Processing flaws in ceramics 325 9.5 Stability of flaws: size effects in crack initiation 328 9.6 Stability of flaws: effect of grain size on strength 10 Strength and reliability 335 10.1 Strength and flaw statistics 10.2 Flaw statistics and lifetime 343 10.3 Flaw elimination 347 10.4 Flaw tolerance 350 10.5 Other design factors 357 References and reading list 363 372

Contents ix 7.4 Frontal-zone shielding: phase transformations in zirconia 221 7.5 Shielding by crack-interface bridging: monophase ceramics 230 7.6 Ceramic composites 242 8 Indentation fracture 249 8.1 Crack propagation in contact fields: blunt and sharp indenters 250 8.2 Indentation cracks as controlled flaws: inert strength, toughness, and T'-curves 263 8.3 Indentation cracks as controlled flaws: time-dependent strength and fatigue 276 8.4 Subthreshold indentations: crack initiation 282 8.5 Subthreshold indentations: strength 293 8.6 Special applications of the indentation method 296 8.7 Contact damage: strength degradation, erosion and wear 300 8.8 Surface forces and contact adhesion 304 9 Crack initiation: flaws 307 9.1 Crack nucleation at microcontacts 309 9.2 Crack nucleation at dislocation pile-ups 314 9.3 Flaws from chemical, thermal, and radiant fields 319 9.4 Processing flaws in ceramics 325 9.5 Stability of flaws: size effects in crack initiation 328 9.6 Stability of flaws: effect of grain size on strength 332 10 Strength and reliability 335 10.1 Strength and flaw statistics 337 10.2 Flaw statistics and lifetime 343 10.3 Flaw elimination 347 10.4 Flaw tolerance 350 10.5 Other design factors 357 References and reading list 363 Index 372

P1 rerace This book is a restructured version of a first edition published in 1975.As before, the objective is a text for higher degree students in materials science and researchers concerned with the strength and toughness of brittle solids More specifically, the aim is to present fracture mechanics in the context of the 'materials revolution, particularly in ceramics, that is now upon us Thus whereas some chapters from the original are barely changed, most are drastically rewritten, and still others are entirely new Our focus, therefore, is 'brittle ceramics. By brittle, we mean cracks of tomic sharpness that propagate essentially by bond rupture. By ceramics, we mean covalent-ionic materials of various persuasions, including glasse polycrystalline aggregates, minerals, and even composites. Since 1975, our knowledge of structural ceramics has equalled, some would insist sur- passed, that of metals and polymers. but it is brittleness that remains the singular limiting factor in the design of ceramic components. If one is to overcome this limitation, it is necessary first to understand the underlying mechanics and micromechanics of crack initiation and propagation Prominent among improvements in this understanding have been a continuing evolution in the theories of continuum fracture mechanics and new conceptions of fundamental crack-tip laws. Most significant, however, is the advent of 'microstructural shielding processes, as manifested in the so-called crack-resistance- or toughness-curve, with far-reaching con- sequences in relation to strength and toughness. This developing area promises to revolutionise traditional attitudes toward properties design The unifying theme of the book is the thermodynamic energy-balance oncept expounded by griffith in his classic 1920 paper. Griffith's concept leads naturally to classifications of crack systems as equilibrium or dynamic, stable or unstable, reversible or irreversible. His concept survives

Preface This book is a restructured version of a first edition published in 1975. As before, the objective is a text for higher degree students in materials science and researchers concerned with the strength and toughness of brittle solids. More specifically, the aim is to present fracture mechanics in the context of the 'materials revolution', particularly in ceramics, that is now upon us. Thus whereas some chapters from the original are barely changed, most are drastically rewritten, and still others are entirely new. Our focus, therefore, is 'brittle ceramics'. By brittle, we mean cracks of atomic sharpness that propagate essentially by bond rupture. By ceramics, we mean covalent-ionic materials of various persuasions, including glasses, polycrystalline aggregates, minerals, and even composites. Since 1975, our knowledge of structural ceramics has equalled, some would insist sur￾passed, that of metals and polymers. But it is brittleness that remains the singular limiting factor in the design of ceramic components. If one is to overcome this limitation, it is necessary first to understand the underlying mechanics and micromechanics of crack initiation and propagation. Prominent among improvements in this understanding have been a continuing evolution in the theories of continuum fracture mechanics and new conceptions of fundamental crack-tip laws. Most significant, however, is the advent of 'microstructural shielding' processes, as manifested in the so-called crack-resistance- or toughness-curve, with far-reaching con￾sequences in relation to strength and toughness. This developing area promises to revolutionise traditional attitudes toward properties design and processing strategies for ceramics. The unifying theme of the book is the thermodynamic energy-balance concept expounded by Griffith in his classic 1920 paper. Griffith's concept leads naturally to classifications of crack systems as equilibrium or dynamic, stable or unstable, reversible or irreversible. His concept survives