Jaroslav Pokluda Pavel Sandera Micromechanisms of fracture and Fatigue In a Multiscale Context Springer
Jaroslav Pokluda · Pavel Šandera Micromechanisms of Fracture and Fatigue 123 In a Multiscale Context
Preface Classical concepts and numerical methods of mechanical engineering such as, for example,fracture mechanics and finite element analysis focus on macro- scale problems where the microstructure is incorporated by using averag- ing constitutive laws.On the other hand,the domain of materials science and solid state physics focuses on investigation of atomic bonds,lattice de- fects,microstructural elements and their interactions at nano,micro and meso scales.However,a recent development in fracture and fatigue research clearly indicates that the most promising and effective concepts are based on cou- pling engineering mechanics with materials science within so-called multiscale fracture models.The objective of these approaches is to bridge the enormous gap between time and space scales and,therefore,they constitute a great challenge in the sense of scientific knowledge.Moreover,they still drive at psychological barriers of conservative mechanical engineers and/or material scientists.Therefore,an overwhelming majority of books about fracture and fatigue were written from the point of view of either mechanical engineers or material scientists.To our knowledge,a pioneering attempt to produce a successful integrated concept of fracture was made by Kelly and Macmil- lan [1].Since that time,however,many new methods and concepts have been developed which should be incorporated into advanced multiscale models of fracture and fatigue. This book was written as an overview of scientific results achieved by the authors during about 40 years of their research.However,another strong mo- tivation was to support advanced trends in fracture and fatigue which lead to the development of multiscale concepts for securing the integrity of engineer- ing components and structures.This second aim has always prevailed over the first.Therefore,the book is composed in a compact manner and provides a rather comprehensive survey of fracture micromechanisms and related mul- tiscale models.Although these models were predominantly proposed by the authors of this book,many passages devoted to models that were published by other authors are included in order to ensure a consistent presentation of the subject.A prevailing part of the book reflects the joint work of authors vii
Preface Classical concepts and numerical methods of mechanical engineering such as, for example, fracture mechanics and finite element analysis focus on macroscale problems where the microstructure is incorporated by using averaging constitutive laws. On the other hand, the domain of materials science and solid state physics focuses on investigation of atomic bonds, lattice defects, microstructural elements and their interactions at nano, micro and meso scales. However, a recent development in fracture and fatigue research clearly indicates that the most promising and effective concepts are based on coupling engineering mechanics with materials science within so-called multiscale fracture models. The objective of these approaches is to bridge the enormous gap between time and space scales and, therefore, they constitute a great challenge in the sense of scientific knowledge. Moreover, they still drive at psychological barriers of conservative mechanical engineers and/or material scientists. Therefore, an overwhelming majority of books about fracture and fatigue were written from the point of view of either mechanical engineers or material scientists. To our knowledge, a pioneering attempt to produce a successful integrated concept of fracture was made by Kelly and Macmillan [1]. Since that time, however, many new methods and concepts have been developed which should be incorporated into advanced multiscale models of fracture and fatigue. This book was written as an overview of scientific results achieved by the authors during about 40 years of their research. However, another strong motivation was to support advanced trends in fracture and fatigue which lead to the development of multiscale concepts for securing the integrity of engineering components and structures. This second aim has always prevailed over the first. Therefore, the book is composed in a compact manner and provides a rather comprehensive survey of fracture micromechanisms and related multiscale models. Although these models were predominantly proposed by the authors of this book, many passages devoted to models that were published by other authors are included in order to ensure a consistent presentation of the subject. A prevailing part of the book reflects the joint work of authors vii
viii Preface at the Brno University of Technology.However,several results and models originate from the research of the first author,performed at the Military Institute of Material Science and Technology from 1973 to 1985.The oppor- tunity to present these results is much appreciated since,for obvious reasons, they were not allowed to be published in international scientific journals at that time. The book addresses students at graduate and postgraduate levels,lectur- ers,materials scientists and mechanical engineers,as well as materials physi- cists and chemists.Any kind of criticism or advice that can help to improve the text will be very welcome. Many results presented in this book were achieved either in the frame of international scientific collaboration or appeared as a consequence of stimu- lating discussions with colleagues from foreign universities and research in- stitutes.Our very special thanks go to Prof.R.Pippan from the Institute of Materials Science,Austrian Academy of Sciences,in Leoben,Austria,Prof. V.Vitek from the University of Pennsylvania in Philadelphia,Pennsylvania, USA and Prof.Y.Murakami from the Kyushu University in Fukuoka,Japan, for our stimulating discussions during our long-term collaboration.Our warm thanks go to Dr.A.Doig from the Military Academy in Shrivenham,Eng- land,and Dr.R.Groger from the Los Alamos National Laboratory,USA,for their fruitful comments on the scientific content and English language of this book.We are also deeply indebted to Prof.O.Kolednik,Prof.J.Janovec, Prof.M.Jenko,Prof.Y.Kondo,Dr.G.Chai,Prof.Y.Kitamura,Prof.C. Laird,Prof.S.Stanzel-Tschegg,Dr.M.Sauzay,Prof.M.Zehetbauer,Prof.A. Krasowski,Prof.E.Macha,Prof.A.Shaniavsky and Prof.L.Toth for helpful and friendly discussions associated with joint publications and/or scientific meetings and visits. There are also a number of Czech colleagues who directly or indirectly con- tributed to this book.Let us first mention a long-term collaboration,fruitful discussions and extended joint work with Prof.M.Sob from the Masaryk Uni- versity in Brno and Prof.P.Lejcek from the Institute of Physics,Academy of Sciences of the Czech Republic in Prague.Furthermore,Dr.P.Lukas from the Institute of Physics of Materials,Academy of Sciences of the Czech Re- public in Brno and Dr.F.Kroupa ()from the Institute of Plasma Physics, Academy of Sciences of the Czech Republic in Prague have helped us very much particularly during the first periods of our research activities.We are also grateful to Prof.J.Svejcar,Dr.I.Saxl ()Prof.I.Dlouhy,Prof.B. Vlach,Prof.M.Kotoul,Dr.P.Ponizil,Prof.K.Stransky,Prof.I.Dvorak, Dr.J.Siegl,Dr.L.Obdrzalek,Prof.J.Zeman,Prof.L.Kunz,Prof.Z.Knesl, Prof.P.Lukac,Dr.A.Machova,Dr.V.Paidar,Prof.V.Navratil,Prof.J. Polak,Dr.M.Holzmann,Prof.J.Kohout,Prof.R.Foret,Dr.P.Stanek,Dr. A.Buchal,Dr.K.Obrtlik,Prof.M.Slesar ()Prof.M.Bily,Dr.V.Oliva and Dr.H.Lauschmann for helpful discussions associated with joint publications and/or scientific meetings
viii Preface at the Brno University of Technology. However, several results and models originate from the research of the first author, performed at the Military Institute of Material Science and Technology from 1973 to 1985. The opportunity to present these results is much appreciated since, for obvious reasons, they were not allowed to be published in international scientific journals at that time. The book addresses students at graduate and postgraduate levels, lecturers, materials scientists and mechanical engineers, as well as materials physicists and chemists. Any kind of criticism or advice that can help to improve the text will be very welcome. Many results presented in this book were achieved either in the frame of international scientific collaboration or appeared as a consequence of stimulating discussions with colleagues from foreign universities and research institutes. Our very special thanks go to Prof. R. Pippan from the Institute of Materials Science, Austrian Academy of Sciences, in Leoben, Austria, Prof. V. Vitek from the University of Pennsylvania in Philadelphia, Pennsylvania, USA and Prof. Y. Murakami from the Kyushu University in Fukuoka, Japan, for our stimulating discussions during our long-term collaboration. Our warm thanks go to Dr. A. Doig from the Military Academy in Shrivenham, England, and Dr. R. Gr¨oger from the Los Alamos National Laboratory, USA, for their fruitful comments on the scientific content and English language of this book. We are also deeply indebted to Prof. O. Kolednik, Prof. J. Janovec, Prof. M. Jenko, Prof. Y. Kondo, Dr. G. Chai, Prof. Y. Kitamura, Prof. C. Laird, Prof. S. Stanzel-Tschegg, Dr. M. Sauzay, Prof. M. Zehetbauer, Prof. A. Krasowski, Prof. E. Macha, Prof. A. Shaniavsky and Prof. L. T´oth for helpful and friendly discussions associated with joint publications and/or scientific meetings and visits. There are also a number of Czech colleagues who directly or indirectly contributed to this book. Let us first mention a long-term collaboration, fruitful discussions and extended joint work with Prof. M. Sob from the Masaryk Uni- ˇ versity in Brno and Prof. P. Lejˇcek from the Institute of Physics, Academy of Sciences of the Czech Republic in Prague. Furthermore, Dr. P. Luk´aˇs from the Institute of Physics of Materials, Academy of Sciences of the Czech Republic in Brno and Dr. F. Kroupa ( ) from the Institute of Plasma Physics, Academy of Sciences of the Czech Republic in Prague have helped us very much particularly during the first periods of our research activities. We are also grateful to Prof. J. Svejcar, Dr. I. Saxl ( ˇ ), Prof. I. Dlouh´y, Prof. B. Vlach, Prof. M. Kotoul, Dr. P. Pon´ıˇzil, Prof. K. Str´ansk´y, Prof. I. Dvoˇr´ak, Dr. J. Siegl, Dr. L. Obdrˇz´alek, Prof. J. Zeman, Prof. L. Kunz, Prof. Z. Kn´esl, Prof. P. Luk´aˇc, Dr. A. Machov´a, Dr. V. Paidar, Prof. V. Navr´atil, Prof. J. Pol´ak, Dr. M. Holzmann, Prof. J. Kohout, Prof. R. Foret, Dr. P. Stanˇek, Dr. A. Buchal, Dr. K. Obrtl´ık, Prof. M. Sles´ ˇ ar ( ), Prof. M. B´ıl´y, Dr. V. Oliva and Dr. H. Lauschmann for helpful discussions associated with joint publications and/or scientific meetings
Preface ix We are deeply grateful to our friends and colleagues from the Depart- ment of Materials Micromechanics and Applied Acoustics,especially to Dr. M.Cerny,who was our partner and consultant in most topics of the first chap- ter.We have also very much appreciated the help of Dr.J.Hornikova and Dr.K.Slamecka with experimental and theoretical investigations in mixed- mode fracture and fatigue as well as with the design and preparation of many figures.Finally,we would like to thank Anthony Doyle from Springer UK, who has offered us the opportunity to write this book. Brno, Jaroslav Pokluda December 2009 Pavel Sandera
Preface ix We are deeply grateful to our friends and colleagues from the Department of Materials Micromechanics and Applied Acoustics, especially to Dr. M. Cern´ ˇ y, who was our partner and consultant in most topics of the first chapter. We have also very much appreciated the help of Dr. J. Horn´ıkov´a and Dr. K. Sl´ameˇcka with experimental and theoretical investigations in mixedmode fracture and fatigue as well as with the design and preparation of many figures. Finally, we would like to thank Anthony Doyle from Springer UK, who has offered us the opportunity to write this book. Brno, Jaroslav Pokluda December 2009 Pavel Sandera ˇ
Contents 0 Introduction.…… 1 1 Deformation and Fracture of Perfect Crystals............. 9 1.1 Ideal Strength of Solids................................. 10 1.1.1 From Classics to Recent Concepts ................. 11 1.1.2 Calculation Principles............................. 16 1.1.3 Simple Loading Modes............................ 26 1.1.4 Multiaxial Loading............................... 36 1.l.5 Nanocomposites...…· 46 1.1.6 Influence of Crystal Defects and Temperature........ 52 1.2 Intrinsic Brittleness and Ductility 54 1.2.1 Fundamentals.........…· 55 1.2.2 Calibration of Crystals............................ 59 1.3 Multiscale Model of Nanoindentation Test................. 63 1.3.1 Description of Submodels.....·:· 64 1.3.2 Simulation of Pop-in Effects....................... 66 2 Brittle and Ductile Fracture.............................. 69 21 Brittle Fracture.…… 73 2.1.1 Geometrically Induced Crack Tip Shielding.......... 74 2.1.2 Pyramidal Model of Tortuous Crack Front........... 78 2.1.3 Fracture Toughness of Particle Reinforced Glass Comp0site.… 80 2.2 Quasi-brittle Fracture................................... 88 2.2.1 Statistical Approach to Geometrical Shielding Based on Size Ratio Effect ............................. 90 2.2.2 Anomalous Fracture Behaviour of Ultra-high-strength Steels..... 93 2.2.3 Mixed Intergranular and Cleavage Fracture of Phosphorus-doped Fe-2.3%V Alloy ................ 98 2.3 Ductile Fracture..................108 xi
Contents 0 Introduction .............................................. 1 1 Deformation and Fracture of Perfect Crystals ............. 9 1.1 Ideal Strength of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.1.1 From Classics to Recent Concepts . . . . . . . . . . . . . . . . . . 11 1.1.2 Calculation Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.1.3 Simple Loading Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.1.4 Multiaxial Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.1.5 Nanocomposites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1.1.6 Influence of Crystal Defects and Temperature . . . . . . . . 52 1.2 Intrinsic Brittleness and Ductility . . . . . . . . . . . . . . . . . . . . . . . . 54 1.2.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 1.2.2 Calibration of Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 1.3 Multiscale Model of Nanoindentation Test . . . . . . . . . . . . . . . . . 63 1.3.1 Description of Submodels . . . . . . . . . . . . . . . . . . . . . . . . . . 64 1.3.2 Simulation of Pop-in Effects . . . . . . . . . . . . . . . . . . . . . . . 66 2 Brittle and Ductile Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 2.1 Brittle Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2.1.1 Geometrically Induced Crack Tip Shielding . . . . . . . . . . 74 2.1.2 Pyramidal Model of Tortuous Crack Front . . . . . . . . . . . 78 2.1.3 Fracture Toughness of Particle Reinforced Glass Composite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.2 Quasi-brittle Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 2.2.1 Statistical Approach to Geometrical Shielding Based on Size Ratio Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 2.2.2 Anomalous Fracture Behaviour of Ultra-high-strength Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 2.2.3 Mixed Intergranular and Cleavage Fracture of Phosphorus-doped Fe-2.3%V Alloy . . . . . . . . . . . . . . . . . 98 2.3 Ductile Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 xi
xii Contents 2.3.1 Kinetics of Plastic Deformation During Uniaxial Ductile Fracture:Modelling and Experiment.........111 2.3.2 Fracture Strain..................1l6 2.3.3 Assessment of Fracture Toughness from Basic Mechanical Characteristics........................121 3 Fatigue Fracture..........................................125 3.1 Quantitative Fractography...............................126 3.1.1 Topological Analysis..............................127 3.1.2 Morphological Patterns in Fatigue..................135 3.2 Opening Loading Mode.................................139 3.2.1 Discrete Dislocation Models of Mechanical Hysteresis 141 3.2.2 Nucleation and Growth of Short Cracks ............150 3.2.3 Discrete Dislocation Models of Mode I Growth of L0 ng Cracks............155 3.2.4 Crack Closure Mechanisms........................164 3.2.5 Unified Model of Crack-tip Shielding................175 3.2.6 Applications of the Unified Model..................179 3.2.7 Influence of Shielding on Crack Growth Rate .185 3.3 Shear and Mixed-mode Loading..........................188 3.3.1 Models of Shear-mode Crack Growth ..............189 3.3.2 Propagation of Cracks under Cyclic Torsion.........194 3.3.3 Propagation of Cracks under Cyclic Shear...........203 3.3.4 Crack Growth and Fatigue Life under Combined Bending-torsion Loading..........................217 3.3.5 Formation of Fish-eye Cracks under Combined Bending-torsion Loading..........................227 3.4 Failure Analysis........................................237 3.4.1 Theoretical Background...........................238 3.4.2 Case Study ....................................... 240 4 Final Reflections................ 243 4.1 Useful Results .........................................243 4.2 Open Tasks..................246 Appendixes A Ab initio Computational Methods........................ 249 A.1 TB-LMTO-ASA Code ................................. 251 A.2 Wien 95-w2k Codes .................................. 252 A.3 VAsp Code............................................253 B Mixed-mode Criteria of Crack Stability...................255 B.1 Energy Criterion ......................................255 B.2 Criterion of Linear Damage Accumulation.................256
xii Contents 2.3.1 Kinetics of Plastic Deformation During Uniaxial Ductile Fracture: Modelling and Experiment . . . . . . . . . 111 2.3.2 Fracture Strain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 2.3.3 Assessment of Fracture Toughness from Basic Mechanical Characteristics . . . . . . . . . . . . . . . . . . . . . . . . 121 3 Fatigue Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 3.1 Quantitative Fractography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 3.1.1 Topological Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 3.1.2 Morphological Patterns in Fatigue . . . . . . . . . . . . . . . . . . 135 3.2 Opening Loading Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 3.2.1 Discrete Dislocation Models of Mechanical Hysteresis . 141 3.2.2 Nucleation and Growth of Short Cracks . . . . . . . . . . . . . 150 3.2.3 Discrete Dislocation Models of Mode I Growth of Long Cracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 3.2.4 Crack Closure Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . 164 3.2.5 Unified Model of Crack-tip Shielding . . . . . . . . . . . . . . . . 175 3.2.6 Applications of the Unified Model . . . . . . . . . . . . . . . . . . 179 3.2.7 Influence of Shielding on Crack Growth Rate . . . . . . . . 185 3.3 Shear and Mixed-mode Loading . . . . . . . . . . . . . . . . . . . . . . . . . . 188 3.3.1 Models of Shear-mode Crack Growth . . . . . . . . . . . . . . . 189 3.3.2 Propagation of Cracks under Cyclic Torsion . . . . . . . . . 194 3.3.3 Propagation of Cracks under Cyclic Shear . . . . . . . . . . . 203 3.3.4 Crack Growth and Fatigue Life under Combined Bending-torsion Loading . . . . . . . . . . . . . . . . . . . . . . . . . . 217 3.3.5 Formation of Fish-eye Cracks under Combined Bending-torsion Loading . . . . . . . . . . . . . . . . . . . . . . . . . . 227 3.4 Failure Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 3.4.1 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 3.4.2 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 4 Final Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 4.1 Useful Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 4.2 Open Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 Appendixes A Ab initio Computational Methods . . . . . . . . . . . . . . . . . . . . . . . . 249 A.1 TB-LMTO-ASA Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 A.2 Wien 95 – w2k Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 A.3 VASP Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 B Mixed-mode Criteria of Crack Stability . . . . . . . . . . . . . . . . . . . 255 B.1 Energy Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 B.2 Criterion of Linear Damage Accumulation . . . . . . . . . . . . . . . . . 256
Contents xiii B.3 Criterion of Minimal Deformation Energy................. 256 B.4 Criterion of Maximal Principal Stress..................... 257 C Plastic Flow Rate Inside the Neck........................ 259 C.1 Ideal Model...............259 C.2 Real Model.....……… .....261 List of Reprinted Figures .................................... 265 References..................269 Index.........................................................283
Contents xiii B.4 Criterion of Maximal Principal Stress . . . . . . . . . . . . . . . . . . . . . 257 C Plastic Flow Rate Inside the Neck . . . . . . . . . . . . . . . . . . . . . . . . 259 C.1 Ideal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 C.2 Real Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 List of Reprinted Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 B.3 Criterion of Minimal Deformation Energy . . . . . . . . . . . . . . . . . 256
