Materials science Books

Book SynopsisThe design of mechanical structures with improved and predictable durability cannot be achieved without a thorough understanding of the mechanisms of fatigue damage and more specifically the relationships between the microstructure of materials and their fatigue properties. Written by leading experts in the field, this book (which is complementary to Fatigue of Materials and Structures: Application to Damage and Design, also edited by Claude Bathias and André Pineau), provides an authoritative, comprehensive and unified treatment of the mechanics and micromechanisms of fatigue in metals, polymers and composites. Each chapter is devoted to one of the major classes of materials or to different types of fatigue damage, thereby providing overall coverage of the field. The book deals with crack initiation, crack growth, low-cycle fatigue, gigacycle fatigue, shorts cracks, fatigue micromechanisms and the local approach to fatigue damage, corrosion fatigue, environmental effects and variable amplitude loadings, and will be an important and much used reference for students, practicing engineers and researchers studying fracture and fatigue in numerous areas of mechanical, structural, civil, design, nuclear, and aerospace engineering as well as materials science.Table of ContentsForeword xi Stephen D. ANTOLOVICH Chapter 1. High Temperature Fatigue 1 Stephen D. ANTOLOVICH and Andre PINEAU 1.1. Introduction and overview 1 1.2. 9 to 12% Cr steels 7 1.3. Austenitic stainless steels 22 1.4. Fatigue of superalloys 40 1.5. Lifespan prediction in high-temperature fatigue 104 1.6. Conclusions 114 1.7. Acknowledgments 118 1.8. Bibliography 118 Chapter 2. Analysis of Elasto-plastic Strains and Stresses Near Notches Subjected to Monotonic and Cyclic Multiaxial Loading Paths 131 Gregory GLINKA 2.1. Introduction 131 2.2. Multiaxial fatigue parameters 134 2.3. Elasto-plastic notch-tip stress-strain calculation methods 146 2.4. Comparison of notch stress-strain calculations with numerical data 164 2.5. Conclusion 173 2.6. Bibliography 173 2.7. Symbols 176 Chapter 3. Fatigue of Composite Materials 179 Claude BATHIAS 3.1. Introduction 179 3.2. Drastic differences between the fatigue of composites and metals 183 3.3. Notch effect on fatigue strength 191 3.4. Effect of a stress on composite fatigue 193 3.5. Fatigue after impact 198 3.6. Fatigue damage criteria 199 3.7. Conclusion 202 3.8. Bibliography 203 Chapter 4. Fatigue of Polymers and Elastomers 205 Claude BATHIAS 4.1. Introduction 205 4.2. Life of polymers 206 4.3. Crack propagation within polymers 207 4.4. Damaging mechanisms of polymers 208 4.5. Specific case of the fatigue of elastomers 210 4.6. The life of natural rubbers 211 4.7. Crack propagation in natural rubber 213 4.8. Propagation mechanisms of cracks in natural rubber 217 4.9. Multiaxial fatigue of rubbers 219 4.10. Cavitation of rubbers 221 4.11. Conclusion 222 4.12. Bibliography 222 Chapter 5. Probabilistic Design of Structures Submitted to Fatigue 223 Bruno SUDRET 5.1. Introduction 223 5.2. Treatment of hazard in mechanical models 224 5.3. Plotting probabilistic S–N curves 229 5.4. Probabilistic design with respect to crack initiation 237 5.5. Probabilistic propagation models 245 5.6. Conclusion 252 5.7. Appendix A: probability theory reminder 253 5.8. Bibliography 259 Chapter 6. Prediction of Fatigue Crack Growth within Structures 265 Jean LEMAITRE 6.1. Prediction problems 265 6.2. Crack growth laws 268 6.3. Calculation of cracking variables 282 6.4. Resolution method of the cracking equations 289 6.5. New directions 296 6.6. Bibliography 296 List of Authors 299 Index 301

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Book SynopsisSelf-Compacting Concrete (SCC) is a relatively new building material. Nowadays, its use is progressively changing the method of concrete placement on building sites. However, the successful use of SCC requires a good understanding of the behavior of this material, which is vastly different from traditional concrete. For this purpose, a lot of research has been conducted on this area all over the world since 10 years. Intended for both practitioners and scientists, this book provides research results from the rheological behavior of fresh concrete to durability.Trade Review"This book provides research findings ranging from the rheological behaviour of fresh concrete to the durability of SSC." (Detail, 1 January 2012)Table of ContentsIntroduction ix Chapter 1. Design, Rheology and Casting of Self-Compacting Concretes 1 Sofiane AMZIANE, Christophe LANOS and Michel MOURET 1.1. Towards a fluid concrete 1 1.2. SCC formulation basics 7 1.3. SCC rheology 20 1.4. Industrial practices 42 1.5. Forces exerted by SCCs on formworks 50 1.6. Bibliography 59 Chapter 2. Early Age Behavior 67 Philippe TURCRY and Ahmed LOUKILI 2.1. Introduction 67 2.2. Hydration and its consequences 68 2.3. Early age desiccation and its consequences: different approaches to the problem 70 2.4. Plastic shrinkage and drop in capillary pressure 74 2.5. Comparison of plastic shrinkage for SCCs and conventional concretes 79 2.6. Influence of composition on free plastic shrinkage 86 2.7. Cracking due to early drying 89 2.8. Summary 93 2.9. Bibliography 95 Chapter 3. Mechanical Properties and Delayed Deformations 99 Thierry VIDAL, Philippe TURCRY, Stéphanie STAQUET and Ahmed LOUKILI 3.1. Introduction 99 3.2. Instantaneous mechanical properties 100 3.3. Differences in mechanical behavior 110 3.4. Behavior of steel-concrete bonding 122 3.5. Bibliography 130 Chapter 4. Durability of Self-Compacting Concrete 141 Emmanuel ROZIÈRE and Abdelhafid KHELIDJ 4.1. Introduction 141 4.2. Properties and parameters that influence durability 143 4.3. Transport phenomena 152 4.4. Degradation mechanisms 159 4.5. Conclusion 202 4.6. Bibliography 203 Chapter 5. High Temperature Behavior of Self-Compacting Concretes 215 Hana FARES, Sébastien RÉMOND, Albert NOUMOWÉ and Geert DE SCHUTTER 5.1. Introduction 215 5.2. Changes in SCC microstructure and physico-chemical properties with temperature 216 5.3. Mechanical behavior of SCCs at high temperature 240 5.4. Thermal stability 247 5.5. Conclusion 252 5.6. Bibliography 253 Glossary 259 List of Authors 261 Index 263

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Book SynopsisThis book presents recent advances related to the following two topics: how mechanical fields close to material or geometrical singularities such as cracks can be determined; how failure criteria can be established according to the singularity degrees related to these discontinuities. Concerning the determination of mechanical fields close to a crack tip, the first part of the book presents most of the traditional methods in order to classify them into two major categories. The first is based on the stress field, such as the Airy function, and the second resolves the problem from functions related to displacement fields. Following this, a new method based on the Hamiltonian system is presented in great detail. Local and energetic approaches to fracture are used in order to determine the fracture parameters such as stress intensity factor and energy release rate. The second part of the book describes methodologies to establish the critical fracture loads and the crack growth criteria. Singular fields for homogeneous and non-homogeneous problems near crack tips, v-notches, interfaces, etc. associated with the crack initiation and propagation laws in elastic and elastic-plastic media, allow us to determine the basis of failure criteria. Each phenomenon studied is dealt with according to its conceptual and theoretical modeling, to its use in the criteria of fracture resistance; and finally to its implementation in terms of feasibility and numerical application. Contents 1. Introduction.Part 1: Stress Field Analysis Close to the Crack Tip2. Review of Continuum Mechanics and the Behavior Laws.3. Overview of Fracture Mechanics.4. Fracture Mechanics.5. Introduction to the Finite Element Analysis of Cracked Structures.Part 2: Crack Growth Criteria6. Crack Propagation.7. Crack Growth Prediction in Elements of Steel Structures Submitted to Fatigue.8. Potential Use of Crack Propagation Laws in Fatigue Life Design.Table of ContentsPreamble xiii Preface xv Notations xix Chapter 1 1 PART 1: STRESS FIELD ANALYSIS CLOSE TO THE CRACK TIP 5 Chapter 2. Review of Continuum Mechanics and the Behavior Laws 7 2.1. Kinematic equations 9 2.2. Equilibrium equations in a volume element 16 2.3. Behavior laws 20 2.4. Energy formalism 50 2.5. Solution of systems of equations of continuum mechanics and constitutive behavior law 63 2.6. Review of the finite element solution 72 Chapter 3. Overview of Fracture Mechanics 81 3.1. Fracture process 83 3.2. Basic modes of fracture 84 Chapter 4. Fracture Mechanics. 87 4.1. Determination of stress, strain and displacement fields around a crack in a homogeneous, isotropic and linearly elastic medium 90 4.2. Plastic analysis around a crack in an isotropic homogeneous medium 144 4.3. Case of a heterogeneous medium: elastic multimaterials 164 4.4. New modeling approach to singular fracture fields 165 Chapter 5. Introduction to the Finite Element Analysis of Cracked Structures 187 5.1. Modeling of a singular field close to the crack tip 188 5.2. Energetic methods 200 5.3. Nonlinear behavior 208 5.4. Specific finite elements for the calculation of cracked structures 213 5.5. Study of a finite elements program in a 2D linear elastic medium. 216 5.6. Application to the calculation of the J-integral in mixed mode 224 5.7. Different meshing fracture monitoring techniques by finite elements 229 PART 2: CRACK GROWTH CRITERIA 235 Chapter 6. Crack Propagation 237 6.1. Brittle fracture 239 6.2. Crack extension 265 6.3. Crack extension criterion in an elastic plastic medium 272 6.4. Crack-extension criterion from V-notches 275 6.5. Fracture following crack growth under high-cycle number fatigue 277 6.6. Crack propagation laws 279 6.7. Approaches used for the calculation of fatigue lifetime 286 6.8. Case of the variable amplitude loading 296 6.9. Crack retardation effect due to overloading 312 6.10. “Reliability–failure” in the presence of random variables 318 Chapter 7. Crack Growth Prediction in Elements of Steel Structures Submitted to Fatigue 331 7.1. Significance and analysis by calculation of stresses around the local effect 333 7.2. Crack initiation under fatigue 343 7.3. Localization and sensitivity to rupture of cracks 367 7.4. Extension of the initiated crack under fatigue 375 Chapter 8. Potential Use of Crack Propagation Laws in Fatigue Life Design 395 8.1. Calculation of the crack propagation fatigue life of a welded-joint 395 8.2. Study of the influence of different parameters on fatigue life 402 8.3. Statistical characterization of the initial crack size according to the welding procedure 404 8.4. Initiation/propagation coupled models: two phase models 410 8.5. Development of a damage model taking into account the crack growth phenomenon 419 8.6. Taking into account the presence of residual welding stresses on crack propagation 423 8.7. Consideration of initial crack length under variable amplitude loading 430 8.8. Propagation of short cracks in the presence of a stress gradient 433 8.9. Probabilistic approach to crack propagation fatigue life: reliability–failure 440 Conclusion 451 Bibliography 455 Index 477

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Book SynopsisThe main purpose of this book is to put forward the fundamental role of grain boundaries in the plasticity of crystalline materials. To understand this role requires a multi-scale approach to plasticity: starting from the atomic description of a grain boundary and its defects, moving on to the elemental interaction processes between dislocations and grain boundaries, and finally showing how the microscopic phenomena influence the macroscopic behaviors and constitutive laws. It involves bringing together physical, chemical and mechanical studies. The investigated properties are: deformation at low and high temperature, creep, fatigue and rupture.Table of ContentsPreface xi Chapter 1. Grain Boundary Structures and Defects 1 Jany THIBAULT-PENISSON and Louisette PRIESTER 1.1. Equilibrium structure of grain boundaries 1 1.2. Crystalline defects of grain boundaries 18 1.3. Conclusion 41 1.4. Bibliography 42 Chapter 2. Elementary Grain Boundary Deformation Mechanisms 47 Jean-Philippe COUZINIE and Louisette PRIESTER 2.1. Dislocation in close proximity to a grain boundary 48 2.2. Elastic interaction between dislocations and grain boundaries: image force 49 2.3. Short range (or core) interaction between dislocations and grain boundaries 52 2.4. Relaxation of stress fields associated with extrinsic dislocations 81 2.5. Relationships between elementary interface mechanisms and mechanical behaviors of materials 98 2.6. Bibliography 102 Chapter 3. Grain Boundaries in Cold Deformation 109 Colette REY, Denis SOLAS and Olivier FANDEUR 3.1. Introduction 109 3.2. Plastic compatibility and incompatibility of deformation at grain boundaries 111 3.3. Internal stresses in polycrystal grains 117 3.4. Modeling local mechanical fields using the finite element method (FEM)129 3.5. Hall-Petch’s law, geometrically necessary dislocations 139 3.6. Sub-grain boundaries and grain boundaries in deformation and recrystallization 145 3.7. Conclusion 155 3.8. Bibliography 156 Chapter 4. Creep and High Temperature Plasticity: Grain Boundary Dynamics 165 Sylvie LARTIGUE-KORINEK and Claude Paul CARRY 4.1. Introduction 165 4.2. Grain boundaries and grain growth 168 4.3. Grain boundaries and creep: mechanisms and phenomenological laws 174 4.4. Grain boundaries and superplasticity 197 4.5. Prospects: creep of nanograined materials 208 4.6. Bibliography 209 Chapter 5. Intergranular Fatigue 217 André PINEAU and Stephen ANTOLOVICH 5.1. Introduction 217 5.2. Low temperature intergranular fatigue 221 5.3. High temperature fatigue 252 5.4. Conclusion 271 5.5. Acknowledgements 272 5.6. Bibliography 272 Chapter 6. Intergranular Segregation and Crystalline Material Fracture 281 Anna FRACZKIEWICZ and Krzysztof WOLSKI 6.1. Grain boundaries and fracture 282 6.2. Intergranular segregation 286 6.3. Segregation and intergranular fracture 297 6.4. Intergranular fracture induced by liquid metals 308 6.5. General conclusion 320 6.6. Bibliography 321 APPENDICES 327 Appendix 1. Bicrystallography and Topological Characterization of Interfacial Defects 329 Sylvie LARTIGUE-KORINEK and Louisette PRIESTER Appendix 2. Appendices of Chapter 3 333 Colette REY, Denis SOLAS and Olivier FANDEUR List of Authors 341 Index 343

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Book SynopsisThis book addresses artificial materials including photonic crystals (PC) and metamaterials (MM). The first part is devoted to design concepts: negative permeability and permittivity for negative refraction, periodic structures, transformation optics. The second part concerns PC and MM in stop band regime: from cavities, guides to high impedance surfaces. Abnormal refraction, less than one and negative, in PC and MM are studied in a third part, addressing super-focusing and cloaking. Applications for telecommunications, lasers and imaging systems are also explored.Table of ContentsIntroduction xi PART 1. A FEW FUNDAMENTAL CONCEPTS 1 Chapter 1. Definitions and Concepts 3 1.1. Effective parameters of materials 3 1.2. Terminology of artificial materials 6 1.3. Negative refraction: stakes and consequences 8 1.4. Bibliography 11 Chapter 2. The Metamaterial Approach – Permeability and Permittivity Engineering 13 2.1. Background history 13 2.2. An imbricated lattice approach 17 2.3. Cell approach 23 2.4. Alternative approach: Mie resonances 31 2.5. Bibliography 33 Chapter 3. Photonic Crystal Approach – Band Gap Engineering 37 3.1. Historical background 37 3.2. Study tool: band structure 39 3.3. 2D ½ photonic crystals 44 3.4. A few words on three-dimensional photonic crystals 53 3.5. Conclusion: metamaterials or photonic crystals? 55 3.6. Bibliography 56 Chapter 4. Transformation Optics 59 4.1. Context 59 4.2. Method description 60 4.3. Bibliography 69 PART 2. MATERIALS USED IN A BAND GAP REGIME 71 Chapter 5. Point and Extended Defects in Photonic Crystals 73 5.1. Context 73 5.2. Defect zoology 74 5.3. Selectivity of photonic crystal microcavities 77 5.4. Waveguiding in photonic crystals 82 5.5. Slowing down light 90 5.6. Bibliography 92 Chapter 6. Routing Devices made from Photonic Crystals 95 6.1. The building brick: the add/drop filter 95 6.2. A few photonic crystal approaches 98 6.3. Interference-based couplers 100 6.4. Conclusion 117 6.5. Bibliography 117 Chapter 7. Single Negative Metamaterials 121 7.1. Context 121 7.2. ENGs: negative permittivity materials 122 7.3. MNGs: negative permeability materials 128 7.4. What of frequency-selective surfaces? 132 7.5. Bibliographyc 135 PART 3. MATERIALS IN AN ABNORMAL REFRACTION REGIME (N < 1 AND N < 0) 137 Chapter 8. Two-dimensional Microwave Balanced Composite Prism 139 8.1. Why use a microwave prism? 139 8.2. Conception and sizing of a balanced composite lattice 140 8.3. Two-dimensional prism 147 8.4. Bibliography 154 Chapter 9. Metal-dielectric Materials – from the Terahertz to the Visible 157 9.1. From the terahertz to the infrared 157 9.2. A backward propagation line at terahertz frequency 158 9.3. From “nano”-resonators to “fishnets” 163 9.4. Three-dimensional metamaterials 172 9.5. Bibliography 174 Chapter 10. Abnormal Refraction in Photonic Crystals 177 10.1. Context 177 10.2. (An)isotropy in photonic crystals 178 10.3. Exploiting anisotropy 185 10.4. Focalization and negative refraction: looking for isotropy 189 10.5. Bibliography 194 Chapter 11. A Photonic Crystal Flat Lens at Optical Wavelength 197 11.1. A bit of background 197 11.2. How to define a typical prototype at optical wavelengths 198 11.3. Lens optimization: impedance and resolution 201 11.4. Experiments 213 11.5. Reverse engineering: from a two-dimensional prototype to three-dimensional reality 218 11.6. Conclusion 221 11.7. Bibliography 222 Chapter 12. Wave-controlling Systems – Towards Bypass and Invisibility 225 12.1. “Transformation optics” or “dispersion engineering” 225 12.2. Component approaches for controlling waves 226 12.3. Invisibility at terahertz frequencies: Mie resonances 241 12.4. An alternative with the photonic crystal: the butterfly 246 12.5. Perspectives 250 12.6. Bibliography 250 PART 4. MOVING TOWARD APPLICATIONS 253 Chapter 13. Guiding, Filtering and Routing Electromagnetic Waves 255 13.1. Context 255 13.2. Guiding: propagation lines and tunable phase shifters 256 13.3. Filtering 266 13.4. Metamaterial-based routing 273 13.5. Conclusion 276 13.6. Bibliography 276 Chapter 14. Antennas 279 14.1. Towards the miniaturization of transmission/reception systems 279 14.2. Directivity engineering 280 14.3. Subwavelength sizing 293 14.4. Conclusion 298 14.5. Bibliography 299 Chapter 15. Optics: Fibers and Cavities 301 15.1. Optical issues: the privileged domain of photonic crystals 301 15.2. Microstructured optical fibers 302 15.3. Toward zero threshold lasers 310 15.4. Bibliography 318 Chapter 16. Detection, Imaging and Tomography Systems 321 16.1. From detection to imaging 321 16.2. Terahertz sensors 322 16.3. Direct approach for imaging 326 16.4. Detection and image reconstruction 328 16.5. A vast field to explore 337 16.6. Bibliography 339 Conclusion 341 Index 345

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Book SynopsisThe book, prepared in honor of the retirement of Professor J. Mazars, provides a wide overview of continuum damage modeling applied to cementitious materials. It starts from micro-nanoscale analyses, then follows on to continuum approaches and computational issues. The final part of the book presents industry-based case studies. The contents emphasize multiscale and coupled approaches toward the serviceability and the safety of concrete structures.Table of ContentsPreface xi Gilles PIJAUDIER-CABOT and Frédéric DUFOUR Chapter 1. Bottom–Up: From Atoms to Concrete Structures 1 Franz-Josef ULM and Roland J-M PELLENQ 1.1. Introduction 1 1.2. A realistic molecular model for calcium-silicatehydrates 2 1.3. Probing C-S-H microtexture by nanoindentation 9 1.4. Conclusions 15 1.5. Bibliography 16 Chapter 2. Poromechanics of Saturated Isotropic Nanoporous Materials 19 Romain VERMOREL, Gilles PIJAUDIER-CABOT,Christelle MIQUEU and Bruno MENDIBOURE 2.1. Introduction 20 2.2. Results from molecular simulations 22 2.3. Poromechanical model 24 2.4. Adsorption-induced swelling and permeability change in nanoporous materials 37 2.5. Discussion – interaction energy and entropy 42 2.6. Conclusions 46 2.7. Acknowledgments 47 2.8. Bibliography 48 Chapter 3. Stress-based Non-local Damage Model 51 Cédric GIRY and Frédéric DUFOUR 3.1. Introduction 52 3.2. Non-local damage models 57 3.3. Initiation of failure 67 3.4. Bar under traction 70 3.5. Description of the cracking evolution in a 3PBT of a concrete notched beam 79 3.6. Conclusions 82 3.7. Acknowledgments 84 3.8. Bibliography 84 Chapter 4. Discretization of Higher Order Gradient Damage Models Using Isogeometric Finite Elements 89 Clemens V. VERHOOSEL, Michael A. SCOTT, Michael J. BORDEN, Thomas J.R. HUGHES and René DE BORST 4.1. Introduction 89 4.2. Isotropic damage formulation 91 4.3. Isogeometric finite elements 97 4.4. Numerical simulations 103 4.5. Conclusions 115 4.6. Acknowledgments 116 4.7. Bibliography 116 Chapter 5. Macro and Mesoscale Models to Predict Concrete Failure and Size Effects 121 David GRÉGOIRE, Peter GRASSL, Laura B. ROJAS-SOLANO and Gilles PIJAUDIER-CABOT 5.1. Introduction 122 5.2. Experimental procedure 125 5.3. Numerical simulations 134 5.4. Conclusions 152 5.5. Acknowledgments 153 5.6. Bibliography 153 Chapter 6. Statistical Aspects of Quasi-Brittle Size Effect and Lifetime, with Consequences for Safety and Durability of Large Structures 161 Zdenìk P. BA?ANT, Jia-Liang LE and Qiang YU 6.1. Introduction 161 6.2. Type-I size effect derived from atomistic fracture mechanics 164 6.3. Size effect on structural lifetime 170 6.4. Consequences of ignoring Type-2 size effect 172 6.5. Conclusion 177 6.6. Acknowledgments 177 6.7. Bibliography 178 Chapter 7. Tertiary Creep: A Coupling Between Creep and Damage – Application to the Case of Radioactive Waste Disposal 183 J.M. TORRENTI, T. DE LARRARD and F. BENBOUDJEMA 7.1. Introduction to tertiary creep 184 7.2. Modeling of tertiary creep using a damage model coupled to creep 185 7.3. Comparison with experimental results 189 7.4. Application to the case of nuclear waste disposal 190 7.5. Conclusions 197 7.6. Bibliography 198 Chapter 8. Study of Damages and Risks Related to Complex Industrial Facilities 203 Bruno GÉRARD, Bruno CAPRA, Gaël THILLARD and Christophe BAILLIS 8.1. Context 203 8.2. Introduction to risk management 204 8.3. Case study: computation process 206 8.4. Application 212 8.5. Conclusion 219 8.6. Acknowledgment 220 8.7. Bibliography 220 Chapter 9. Measuring Earthquake Damages to a High Strength Concrete Structure 221 Patrick PAULTRE, Benedikt WEBER, Sébastian MOUSSEAU and Jean PROULX 9.1. Introduction 221 9.2. Overview of the selected testing methods 222 9.3. Two-storey HPC building 223 9.4. Inducing damage – pseudo-dynamic testing procedures 227 9.5. Evaluating damage – forced vibration testing procedures 236 9.6. Damage detection – analytical evaluation 239 9.7. Summary and conclusions 248 9.8. Bibliography 249 List of Authors 251 Index 253

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Book SynopsisThis book presents reviews of various aspects of radiation/matter interactions, be these instrumental developments, the application of the study of the interaction of X-rays and materials to a particular scientific field, or specific methodological approaches. The overall aim of the book is to provide reference summaries for a range of specific subject areas within a pedagogical framework. Each chapter is written by an author who is well known within their field and who has delivered an invited lecture on their subject area as part of the “RX2009 – X-rays and Materials” colloquium that took place in December 2009 at Orsay in France. The book consists of five chapters on the subject of X-ray diffraction, scattering and absorption. Chapter 1 gives a detailed presentation of the capabilities and potential of beam lines dedicated to condensed matter studies at the SOLEIL synchrotron radiation source. Chapter 2 focuses on the study of nanoparticles using small-angle X-ray scattering. Chapter 3 discusses the quantitative studies of this scattering signal used to analyze these characteristics in detail. Chapter 4 discusses relaxor materials, which are ceramics with a particularly complex microstructure. Chapter 5 discusses an approach enabling the in situ analysis of these phase transitions and their associated microstructural changes.Table of ContentsPreface xi Chapter 1. Synchrotron Radiation: Instrumentation in Condensed Matter 1 Jean-Paul ITIE, François BAUDELET, Valérie BRIOIS, Eric ELKAÏM, Amor NADJI and Dominique THIAUDIÈRE 1.1. Introduction 1 1.2. Light sources in the storage ring 2 1.3. Emittance and brilliance of a source 6 1.4. X-ray diffraction with synchrotron radiation 8 1.5. X-ray absorption spectroscopy usingsynchrotron radiation 13 1.6. SAMBA: the X-ray absorption spectroscopy beam line of SOLEIL for 4–40 keV 20 1.7. The DIFFABS beam line 27 1.8. CRISTAL beam line 34 1.9. The SOLEIL ODE line for dispersive EXAFS 38 1.10. Conclusion 43 1.11. Bibliography 44 Chapter 2. Nanoparticle Characterization using Central X-ray Diffraction 49 Olivier SPALLA 2.1. Introduction 49 2.2. Definition of scattered intensity 50 2.3. Invariance principle 52 2.4. Behavior for large q: the Porod regime 55 2.5. Particle-based systems 59 2.6. An absolute scale for measuring particle numbers 75 2.7. Conclusion 78 2.8. Bibliography 79 Chapter 3. X-ray Diffraction for Structural Studies of Carbon Nanotubes and their Insertion Compounds 81 Julien CAMBEDOUZOU and Pascale LAUNOIS 3.1. Introduction 81 3.2. Single-walled carbon nanotubes 85 3.3. Multi-walled carbon nanotubes 96 3.4. Hybrid nanotubes 102 3.5. Textured powder samples 110 3.6. Conclusion 121 3.7. Bibliography 122 Chapter 4. Dielectric Relaxation and Morphotropic Phases in Nanomaterials 129 Jean-Michel KIAT 4.1. Introduction 129 4.2. Dielectric relaxation and morphotropic region: definition and mechanism 130 4.3. Relaxation, morphotropic region and size reduction 163 4.4. Conclusion 174 4.5. Acknowledgements 175 4.6. Bibliography 175 Chapter 5. Evolution of Solid-state Microstructures in Polycrystalline Materials: Application of High-energy X-ray Diffraction to Kinetic and Phase Evolution Studies 181 Elisabeth AEBY-GAUTIER, Guillaume GEANDIER, Moukrane DEHMAS, Fabien BRUNESEAUX, Adeline BENETEAU, Patrick WEISBECKER, Benoît APPOLAIRE and Sabine DENIS 5.1. Introduction 181 5.2. Experimental methods 183 5.3. Results 195 5.4. Conclusion 213 5.5. Acknowledgements 214 5.6. Bibliography 214 List of Authors 221 Index 223

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Book SynopsisThe aim of this book is to summarize the current most effective methods for modeling, simulating, and optimizing metal forming processes, and to present the main features of new, innovative methods currently being developed which will no doubt be the industrial tools of tomorrow. It discusses damage (or defect) prediction in virtual metal forming, using advanced multiphysical and multiscale fully coupled constitutive equations. Theoretical formulation, numerical aspects as well as application to various sheet and bulk metal forming are presented in detail.Virtual metal forming is nowadays inescapable when looking to optimize numerically various metal forming processes in order to design advanced mechanical components. To do this, highly predictive constitutive equations accounting for the full coupling between various physical phenomena at various scales under large deformation including the ductile damage occurrence are required. In addition, fully 3D adaptive numerical methods related to time and space discretization are required in order to solve accurately the associated initial and boundary value problems. This book focuses on these two main and complementary aspects with application to a wide range of metal forming and machining processes. Contents 1. Elements of Continuum Mechanics and Thermodynamics.2. Thermomechanically-Consistent Modeling of the Metals Behavior with Ductile Damage.3. Numerical Methods for Solving Metal Forming Problems.4. Application to Virtual Metal Forming.Table of ContentsPreface xiii Principle of Mathematical Notations xix Chapter 1. Elements of Continuum Mechanics and Thermodynamics 1 1.1. Elements of kinematics and dynamics of materially simple continua 2 1.2. On the conservation laws for the materially simple continua. 33 1.3. Materially simple continuum thermodynamics and the necessity of constitutive equations 39 1.4. Mechanics of generalized continua. Micromorphic theory 55 Chapter 2. Thermomechanically-Consistent Modeling of the Metals Behavior with Ductile Damage 63 2.1. On the main schemes for modeling the behavior of materially simple continuous media 64 2.2. Behavior and fracture of metals and alloys: some physical and phenomenological aspects 69 2.3. Theoretical framework of modeling and main hypotheses 91 2.4. State potential: state relations 113 2.5. Dissipation analysis: evolution equations 139 2.6. Modeling of the damage-induced volume variation 194 2.7. Modeling of the contact and friction between deformable solids 200 2.8. Nonlocal modeling of damageable behavior of micromorphic continua 215 2.9. On the micro–macro modeling of inelastic flow with ductile damage 226 Chapter 3. Numerical Methods for Solving Metal Forming Problems 243 3.1. Initial and boundary value problem associated with virtual metal forming processes 244 3.2. Temporal and spatial discretization of the IBVP 259 3.3. On some global resolution scheme of the IBVP 270 3.4. Local integration scheme: state variables computation 304 3.5. Adaptive analysis of damageable elasto-inelastic structures 337 3.6. On other spatial discretization methods 347 Chapter 4. Application to Virtual Metal Forming 355 4.1. Why use virtual metal forming? 356 4.2. Model identification methodology 359 4.3. Some applications 431 4.4. Toward the optimization of forming and machining processes 484 Appendix: Legendre–Fenchel Transformation 493 Bibliography 499 Index 515

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Book SynopsisRecent advances into the wear of advanced materials In general, wear is currently defined as “the progressive loss of material from the operating surface of a body occurring as a result of relative motion at the surface”. It is related to surface interactions and more specifically to the form of contact due to relative motion. Wear is rarely catastrophic but does reduce the operating efficiency of machine components and structures. At this time of economic crisis, this is a very important field of study because of the huge impact the wear of materials has on the economy. The purpose of this book is to present a collection of examples illustrating the state of the art and research developments into the wear of advanced materials in several applications. It can be used as a research book for a final undergraduate engineering course (for example into materials, mechanics, etc.) or as the focus of the effect of wear on advanced materials at a postgraduate level. It can also serve as a useful reference for academics, biomaterials researchers, mechanical and materials engineers, and professionals in related spheres working with tribology and advanced materials.Table of ContentsPreface xi Chapter 1. Carbon Fabric-reinforced Polymer Composites and Parameters Controlling Tribological Performance 1 Jayashree BIJWE and Mohit SHARMA 1.1. Introduction to polymeric tribo-composites 3 1.2. Carbon fibers as reinforcement 6 1.3. Carbon fabric-reinforced composites 12 1.4. Tribo-performance of CFRCs: influential parameters 15 1.5. Concluding remarks 46 1.6. Bibliography 50 A1.1. Appendix I: Various techniques for developing CFRCs by compression molding 54 A2. Appendix II: Characterization methods for CFRCs 57 Chapter 2. Adhesive Wear Characteristics of Natural Fiber-reinforced Composites 61 Belal F. YOUSIF 2.1. Introduction 62 2.2. Preparation of polyester composites 67 2.3. Specifications of the fibers and composites 70 2.4. Tribo-experimental details 76 2.5. Summary 93 2.6. Bibliography 94 Chapter 3. Resistance to Cavitation Erosion: Material Selection 99 Jinjun LU, Zhen LI, Xue GONG, Jiesheng HAN and Junhu MENG 3.1. Cavitation erosion of materials – a brief review 99 3.2. Measuring the wear resistance of a material to cavitation erosionby using a vibratory cavitation erosion apparatus 101 3.3. Material selection 108 3.4. Conclusion 115 3.5. Acknowledgement 116 3.6. Bibliography 116 Chapter 4. Cavitation of Biofuel Applied in the Injection Nozzles of Diesel Engines 119 Hengzhou WO, Xianguo HU, Hu WANG and Yufu XU 4.1. Introduction 120 4.2. General understanding of cavitation erosion 122 4.3. Hydraulic characteristics of cavitation flow 131 4.4. Influence of fuel property on cavitation 139 4.5. Cavitation erosion of biofuel in the diesel injection nozzle 146 4.6. Conclusion 155 4.7. Acknowledgments 156 4.8. Bibliography 157 Chapter 5. Wear and Corrosion Damage of Medical-grade Metals and Alloys 163 Jae-Joong RYU and Pranav SHROTRIYA 5.1. Introduction 164 5.2. Clinical studies and mechanistic investigation into implant failure 173 5.3. Residual stress development by rough surface contact 184 5.4. Conclusion 192 5.5. Bibliography 193 List of Authors 197 Index 201

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Book SynopsisMachinability of Advanced Materials addresses the level of difficulty involved in machining a material, or multiple materials, with the appropriate tooling and cutting parameters. A variety of factors determine a material’s machinability, including tool life rate, cutting forces and power consumption, surface integrity, limiting rate of metal removal, and chip shape. These topics, among others, and multiple examples comprise this research resource for engineering students, academics, and practitioners.Table of ContentsPreface ix Chapter 1. Machinability: Existing and Advanced Concepts 1 Viktor P. Astakhov Chapter 2. Milling Burr Formation and Avoidance 57 Seyed A. Niknam, Walery Wygowski, Marek Balazinksi and Victor Songmene Chapter 3. Machinability of Titanium and Its Alloys 95 Ali Hosseini, Hossam A. Kishawy and Hussein M. Hussein Chapter 4. Effects of Alloying Elements on the Machinability of Near-Eutectic Al-Si Casting Alloys 119 Yasser Zedan, Saleh A. Alkahtani and Fawzy H. Samuel 5. The Machinability of Hard Materials – A Review 145 Paulo Campos, J. Paulo Davim, J. Roberto Ferreira, A. Paulo Paiva and P. Paulo Balestrassi Chapter 6. An Investigation of Ductile Regime Machining of Silicon Nitride Ceramics 175 Vijayan Krishnaraj and S. Senthil Kumar List of Authors 229 Index 233

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Book SynopsisMaking a decision, of any importance, is never simple. On the one hand, specialists in decision theory do not come within the reach of most policy makers and, secondly, there are very few books on pragmatic decision that are not purely anecdotal. In addition, there is virtually no book that provides a link between decision-making and action. This book provides a bridge between the latest results in artificial intelligence, neurobiology, psychology and decision-making for action. What is the role of intuition or emotion? What are the main psychological biases of which we must be wary? How can we avoid being manipulated? What is the proper use of planning? How can we remain rational even if one is not an expert in probabilities? Perhaps more importantly for managers, how does one go from decision to action? So many questions fundamental to the practice of decision-making are addressed. This book dissects all issues that arise almost daily for decision-makers, at least for major decisions. Drawing on numerous examples, this book answers, in plain language and imagery, all your questions. The final chapter takes the form of a brief reminder - everything you have to remember to be a good decision-maker.Table of ContentsIntroduction xi Chapter 1 What is a Decision, or What Does Decision Theory Have to Teach Us? 1 1.1 Actions and events 1 1.2 Probabilities 5 1.3 Expected utility 7 1.4 Subjective probabilities and rationality of the decision 12 1.5 Caveats and recommendations 14 Chapter 2 Scenarios and Conditional Probabilities 17 2.1 Scenarios 17 2.2 Compound probabilities 21 2.3 Scenarios and conditional probabilities 24 2.4 Decision tree 28 2.5 Scenarios, information and pragmatics 32 2.6 Pursuance of the scenarios and the "just one more push" 35 2.7 Conditional probabilities and accidents 39 2.8 Caveats and recommendations 41 Chapter 3 The Process of Decision-Making and its Rationality, or What Does Artificial Intelligence Have to Teach Us? 43 3.1 A decision as a problem 43 3.2 Decision table 45 3.3 The general process of decision-making 46 3.4 Case-based reasoning 48 3.5 The Olympian point-of-view, and H Simon’s view 51 3.6 Information 54 3.7 Limited rationality 57 3.8 Heuristics 60 3.9 Cognitive limitation 61 3.10 Feedback on rationality in decisions 62 3.11 Caveats and recommendations 64 Chapter 4 Intuition, Emotion, Recognition and Reasoning or, What Does the Neurobiology of Decision-Making Have to Teach Us? 67 4.1 Introduction 68 4.2 Animal "decision" 69 4.3 Recognition-primed decision 70 4.4 The brain and emotion 73 4.5 Short-term, long-term 78 4.6 The Bayesian brain 83 4.7 Caveats and recommendations 85 Chapter 5 Decision-Making in the Presence of Conflicting Criteria, or What Does a Multicriterion Decision Aid Have to Teach Us? 87 5.1 Preference structures 88 5.2 Multicriterion decision aid 91 5.3 Weighted sum aggregation 93 5.4 Other aggregation methods 100 5.5 Aggregation of votes 103 5.6 Social choice and collective decision 105 5.7 Individual reactions to multicriterion decision-making 109 5.8 Constraints and multicriterion decision-making in organizations 110 5.9 Caveats and recommendations 112 Chapter 6 The Decision-Maker’s Psychology, or What Does Psychology Have to Teach Us? 115 6.1 Introduction 116 6.2 The decision-maker’s rationality and utility function 117 6.3 Constructing the utility function 119 6.4 Utility function in the risk 120 6.5 Loss aversion and the endowment effect 125 6.6 Biases related to the probabilities 126 6.7 Self-confidence and the illusion of control 134 6.8 Biases linked to memory 136 6.9 Frame effect 140 6.10 Level of reference and anchoring 144 6.11 Rationalization and reinforcement 154 6.12 System 1 or System 2? 156 6.13 Biases or heuristics? 159 6.14 Caveats and recommendations 162 Chapter 7 Context of the Decision: Intention, Commitment, Trust, Fairness, Authority and Freedom 167 7.1 Intention and commitment 168 7.2 Trust and reciprocity 171 7.3 Fairness 177 7.4 Freedom and responsibility 180 7.5 Authority 182 7.6 "Leadership" in organizations 186 7.7 Rationality between logic and probabilities 189 7.8 Rationality and "good reasons" 192 7.9 Caveats and recommendations 197 Chapter 8 Action: Giving the Impetus or Managing 201 8.1 Deciding and acting 202 8.2 Quick or slow decision-makers 203 8.3 Consensual or imperative decision-makers 208 8.4 To act or to manage? That is the question 212 8.5 Reflect long, project long term: strategic planning and decision-making in organizations 217 8.6 Feedback and learning 221 8.7 Conclusion 226 8.8 Caveats and recommendations 226 Chapter 9 Vade Mecum of the Acting Decision-Maker 229 9.1 That which depends on you, and that which does not 229 9.2 That which depends on you: information, imagination and the process of decision-making 230 9.3 That which depends only on you: learning and planning 232 9.4 That which depends on nature: the pitfalls of probabilities 234 9.5 That which depends on our human nature: the pitfalls of the human brain 236 9.6 That which depends on other people: conflicts and manipulation 239 9.7 What the result depends on: your style and your action 241 9.8 And finally... 243 Bibliography 245 Index of Names 263 General Index 269

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Book SynopsisSince the middle of the 20th Century yield design approaches have been identified with the lower and upper bound theorem of limit analysis theory – a theory associated with perfect plasticity. This theory is very restrictive regarding the applicability of yield design approaches, which have been used for centuries for the stability of civil engineering structures. This book presents a theory of yield design within the original “equilibrium/resistance” framework rather than referring to the theories of plasticity or limit analysis; expressing the compatibility between the equilibrium of the considered structure and the resistance of its constituent material through simple mathematical arguments of duality and convex analysis results in a general formulation, which encompasses the many aspects of its implementation to various stability analysis problems. After a historic outline and an introductory example, the general theory is developed for the three-dimensional continuum model in a versatile form based upon simple arguments from the mathematical theory of convexity. It is then straightforwardly transposed to the one-dimensional curvilinear continuum, for the yield design analysis of beams, and the two-dimensional continuum model of plates and thin slabs subjected to bending. Field and laboratory observations of the collapse of mechanical systems are presented along with the defining concept of the multi-parameter loading mode. The compatibility of equilibrium and resistance is first expressed in its primal form, on the basis of the equilibrium equations and the strength domain of the material defined by a convex strength criterion along with the dual approach in the field of potentially safe loads, as is the highlighting of the role implicitly played by the theory of yield design as the fundamental basis of the implementation of the ultimate limit state design (ULSD) philosophy with the explicit introduction of resistance parameters. Contents 1. Origins and Topicality of a Concept. 2. An Introductory Example of the Yield Design Approach. 3. The Continuum Mechanics Framework. 4. Primal Approach of the Theory of Yield Design. 5. Dual Approach of the Theory of Yield Design. 6. Kinematic Exterior Approach. 7. Ultimate Limit State Design from the Theory of Yield Design. 8. Optimality and Probability Approaches of Yield Design. 9. Yield Design of Structures. 10. Yield Design of Plates: the Model. 11. Yield Design of Plates Subjected to Pure Bending. About the Authors Jean Salençon is Emeritus Professor at École polytechnique and École des ponts et chaussées, ParisTech, France. Since 2009 he has been a member of the Administrative Board of CNRS (Paris, France). He has received many awards including the Légion d’Honneur (Commander), Ordre National du Mérite (Officer) and Palmes Académiques (Commander). His research interests include structure analysis, soil mechanics and continuum mechanics.Table of ContentsPreface xi Chapter 1. Origins and Topicality of a Concept 1 1.1. Historical milestones 1 1.2. Topicality of the yield design approach 8 1.3. Bibliography 11 Chapter 2. An Introductory Example of the Yield Design Approach 19 2.1. Setting the problem 19 2.2. Potential stability of the structure 22 2.3. To what extent potential stability is a relevant concept? 24 2.4. Bibliography 28 Chapter 3. The Continuum Mechanics Framework 29 3.1. Modeling the continuum 29 3.2. Dynamics 34 3.3. The theory of virtual work 41 3.4. Statically and kinematically admissible fields 46 3.5. Bibliography 48 Chapter 4. Primal Approach of the Theory of Yield Design 51 4.1. Settlement of the problem 51 4.2. Potentially safe loads 57 4.3. Comments 60 4.4. Some usual isotropic strength criteria 66 4.5. Bibliography 70 Chapter 5. Dual Approach of the Theory of Yield Design 73 5.1. A static exterior approach 73 5.2. A kinematic necessary condition 76 5.3. The π functions 78 5.4. π functions for usual isotropic strength criteria 84 5.5. Bibliography 88 Chapter 6. Kinematic Exterior Approach 91 6.1. Equation of the kinematic exterior approach 91 6.2. Relevant virtual velocity fields 94 6.3. One domain, two approaches 100 6.4. Bibliography 107 Chapter 7. Ultimate Limit State Design from the Theory of Yield Design 111 7.1. Basic principles of ultimate limit state design 111 7.2. Revisiting the yield design theory in the context of ULSD 113 7.3. The yield design theory applied to ULSD 114 7.4. Conclusion 117 7.5. Bibliography 118 Chapter 8. Optimality and Probability Approaches of Yield Design 119 8.1. Optimal dimensioning and probabilistic approach 119 8.2. Domain of potential stability 120 8.3. Optimal dimensioning 130 8.4. Probabilistic approach of yield design 133 8.5. Bibliography 141 Chapter 9. Yield Design of Structures 145 9.1. The curvilinear one-dimensional continuum 145 9.2. Implementation of the yield design theory 157 9.3. Typical strength criteria 164 9.4. Final comments 172 9.5. Bibliography 174 Chapter 10. Yield Design of Plates: the Model 177 10.1. Modeling plates as two-dimensional continua 177 10.2. Dynamics 182 10.3. Theorem/principle of virtual work 191 10.4. Plate model derived from the three-dimensional continuum 198 10.5. Bibliography 204 Chapter 11. Yield Design of Plates Subjected to Pure Bending 205 11.1. The yield design problem 205 11.2. Implementation of the yield design theory 208 11.3. Strength criteria and π functions 213 11.4. Final comments 226 11.5. Bibliography 234 Index 237

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Book SynopsisWall turbulence control is a major subject, the investigation of which involves significant industrial, environmental and fundamental consequences. Wall Turbulence Control addresses recent advances achieved in active and passive wall turbulence control over the past two decades. This valuable reference for scientists, researchers and engineers provides an updated view of the research into this topic, including passive control, optimal and suboptimal control methodology, linear control and control using adaptive methods (neural networks), polymer and bubble injection, electromagnetic control and recent advances in control by plasma.Table of ContentsPreface vii Notations ix Chapter 1. General Points 1 1.1. Introduction 1 1.2. Tools to analyze and develop control strategies 2 1.2.1. Numerical simulations 2 1.2.2. Sensors 3 1.2.3. Actuators 20 Chapter 2. Summary of the Main Characteristics of Wall Turbulence 23 2.1. Introduction 23 2.2. General equations 23 2.2.1. Eulerian relations 24 2.3. Notations 25 2.4. Reynolds equations 26 2.5. Exact relations and FIK identity 27 2.6. Equations for a turbulent boundary layer 32 2.7. Scales in a turbulent wall flow 34 2.8. Turbulent viscosity closures 35 2.9. Turbulent intensities of the velocity components 47 2.10. Vorticity and near wall coherent structures 51 Chapter 3. Passive Control 65 3.1. Introduction 65 3.2. Large eddy (outer layer) breakup devices, LEBUs (OLDs) 66 3.2.1. General 66 3.2.2. Alteration of the inner structure by outer layer devices 67 3.3. Riblets 72 3.3.1. General 72 3.3.2. Effect of the riblets on the fine structure of wall turbulence 76 3.3.3. Effect of the protrusion height 84 3.4. Superhydrophobic surfaces 93 Chapter 4. Active Control 99 4.1. Introduction 99 4.2. Local blowing 100 4.3. Ad-hoc control 107 4.4. Transverse wall oscillations 115 4.5. Alternated spanwise Lorenz forcing and electromagnetic (EM) control 123 4.6. Extensions of spanwise forcing 131 4.7. Reynolds number dependence 132 4.8. Suboptimal active control 134 4.9. Optimal active control 143 4.10. Optimal linear control 147 4.11. Neural networks 156 4.12. Stochastic synchronization of the wall turbulence and dual control 157 Bibliography 167 Index 185

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Book SynopsisThis book presents a physical approach to the diffraction phenomenon and its applications in materials science. An historical background to the discovery of X-ray diffraction is first outlined. Next, Part 1 gives a description of the physical phenomenon of X-ray diffraction on perfect and imperfect crystals. Part 2 then provides a detailed analysis of the instruments used for the characterization of powdered materials or thin films. The description of the processing of measured signals and their results is also covered, as are recent developments relating to quantitative microstructural analysis of powders or epitaxial thin films on the basis of X-ray diffraction. Given the comprehensive coverage offered by this title, anyone involved in the field of X-ray diffraction and its applications will find this of great use.Table of ContentsPreface xi Acknowledgements xv An Historical Introduction: The Discovery of X-rays and the First Studies in X-ray Diffraction xvii Part 1. Basic Theoretical Elements, Instrumentation and Classical Interpretations of the Results 1 Chapter 1. Kinematic and Geometric Theories of X-ray Diffraction 3 1.1. Scattering by an atom 3 1.1.1. Scattering by a free electron 3 1.1.1.1. Coherent scattering: the Thomson formula 3 1.1.1.2. Incoherent scattering: Compton scattering [COM 23] 6 1.1.2. Scattering by a bound electron 8 1.1.3. Scattering by a multi-electron atom 11 1.2. Diffraction by an ideal crystal 14 1.2.1. A few elements of crystallography 14 1.2.1.1. Direct lattice 14 1.2.1.2. Reciprocal lattice 16 1.2.2. Kinematic theory of diffraction 17 1.2.2.1. Diffracted amplitude: structure factor and form factor 17 1.2.2.2. Diffracted intensity 18 1.2.2.3. Laue conditions [FRI 12] 22 1.2.3. Geometric theory of diffraction 23 1.2.3.1. Laue conditions 23 1.2.3.2. Bragg's law [BRA 13b, BRA 15] 24 1.2.3.3. The Ewald sphere 26 1.3. Diffraction by an ideally imperfect crystal 28 1.4. Diffraction by a polycrystalline sample 33 Chapter 2. Instrumentation used for X-ray Diffraction 39 2.1. The different elements of a diffractometer 39 2.1.1. X-ray sources 39 2.1.1.1. Crookes tubes 41 2.1.1.2. Coolidge tubes 42 2.1.1.3. High intensity tubes 47 2.1.1.4. Synchrotron radiation 49 2.1.2. Filters and monochromator crystals 52 2.1.2.1. Filters 52 2.1.2.2. Monochromator crystals 55 2.1.2.3. Multi-layered monochromators or mirrors 59 2.1.3. Detectors 62 2.1.3.1. Photographic film 62 2.1.3.2. Gas detectors 63 2.1.3.3. Solid detectors 68 2.2. Diffractometers designed for the study of powdered or bulk polycrystalline samples 72 2.2.1. The Debye-Scherrer and Hull diffractometer 73 2.2.1.1. The traditional Debye-Scherrer and Hull diffractometer 74 2.2.1.2. The modern Debye-Scherrer and Hill diffractometer: use of position sensitive detectors 76 2.2.2. Focusing diffractometers: Seeman and Bohlin diffractometers 87 2.2.2.1. Principle 87 2.2.2.2. The different configurations 88 2.2.3. Bragg-Brentano diffractometers 94 2.2.3.1. Principle 94 2.2.3.2. Description of the diffractometer; path of the X-ray beams 97 2.2.3.3. Depth and irradiated volume 103 2.2.4. Parallel geometry diffractometers 104 2.2.5. Diffractometers equipped with plane detectors 109 2.3. Diffractometers designed for the study of thin films 110 2.3.1. Fundamental problem 110 2.3.1.1. Introduction 110 2.3.1.2. Penetration depth and diffracted intensity 111 2.3.2. Conventional diffractometers designed for the study of polycrystalline films 116 2.3.3. Systems designed for the study of textured layers 118 2.3.4. High resolution diffractometers designed for the study of epitaxial films 120 2.3.5. Sample holder 123 2.4. An introduction to surface diffractometry 125 Chapter 3. Data Processing, Extracting Information 127 3.1. Peak profile: instrumental aberrations 129 3.1.1. X-ray source: g1(epsilon) 130 3.1.2. Slit: g2(epsilon) 130 3.1.3. Spectral width: g3(epsilon) 131 3.1.4. Axial divergence: g4(epsilon) 131 3.1.5. Transparency of the sample: g5(epsilon) 133 3.2. Instrumental resolution function 135 3.3. Fitting diffraction patterns 138 3.3.1. Fitting functions 138 3.3.1.1. Functions chosen a priori 138 3.3.1.2. Functions calculated from the physical characteristics of the diffractometer 143 3.3.2. Quality standards 144 3.3.3. Peak by peak fitting 145 3.3.4. Whole pattern fitting 147 3.3.4.1. Fitting with cell constraints 147 3.3.4.2. Structural simulation: the Rietveld method 147 3.4. The resulting characteristic values 150 3.4.1. Position 151 3.4.2. Integrated intensity 152 3.4.3. Intensity distribution: peak profiles 153 Chapter 4. Interpreting the Results 155 4.1. Phase identification 155 4.2. Quantitative phase analysis 158 4.2.1. Experimental problems 158 4.2.1.1. Number of diffracting grains and preferential orientation 158 4.2.1.2. Differential absorption 161 4.2.2. Methods for extracting the integrated intensity 162 4.2.2.1. Measurements based on peak by peak fitting 162 4.2.2.2. Measurements based on the whole fitting of the diagram 163 4.2.3. Quantitative analysis procedures 165 4.2.3.1. The direct method 165 4.2.3.2. External control samples 166 4.2.3.3. Internal control samples 166 4.3. Identification of the crystal system and refinement of the cell parameters 167 4.3.1. Identification of the crystal system: indexing 167 4.3.2. Refinement of the cell parameters 171 4.4. Introduction to structural analysis 172 4.4.1. General ideas and fundamental concepts 173 4.4.1.1. Relation between the integrated intensity and the electron density 173 4.4.1.2. Structural analysis 175 4.4.1.3. The Patterson function 177 4.4.1.4. Two-dimensional representations of the electron density distribution 180 4.4.2. Determining and refining structures based on diagrams produced with polycrystalline samples 183 4.4.2.1. Introduction 183 4.4.2.2. Measuring the integrated intensities and establishing a structural model 184 4.4.2.3. Structure refinement: the Rietveld method 185 Part 2. Microstructural Analysis 195 Chapter 5. Scattering and Diffraction on Imperfect Crystals 197 5.1. Punctual defects 197 5.1.1. Case of a crystal containing randomly placed vacancies causing no relaxation 198 5.1.2. Case of a crystal containing associated vacancies 201 5.1.3. Effects of atom position relaxations 203 5.2. Linear defects, dislocations 205 5.2.1. Comments on the displacement term 207 5.2.2. Comments on the contrast factor 210 5.2.3. Comments on the factor f(M) 212 5.3. Planar defects. 212 5.4. Volume defects 218 5.4.1. Size of the crystals 218 5.4.2. Microstrains 226 5.4.3. Effects of the grain size and of the microstrains on the peak profiles: Fourier analysis of the diffracted intensity distribution 231 Chapter 6. Microstructural Study of Randomly Oriented Polycrystalline Samples 235 6.1. Extracting the pure profile 236 6.1.1. Methods based on deconvolution 237 6.1.1.1. Constraint free deconvolution method: Stokes' method 238 6.1.1.2. Deconvolution by iteration 242 6.1.1.3. Stabilization methods 244 6.1.1.4. The maximum entropy or likelihood method, and the Bayesian method 244 6.1.1.5. Methods based on a priori assumptions on the profile 245 6.1.2. Convolutive methods 246 6.2. Microstructural study using the integral breadth method 247 6.2.1. The Williamson-Hall method 248 6.2.2. The modified Williamson-Hall method and Voigt function fitting 250 6.2.3. Study of size anisotropy 252 6.2.4. Measurement of stacking faults 255 6.2.5. Measurements of integral breadths by whole pattern fitting 257 6.3. Microstructural study by Fourier series analysis of the peak profiles 262 6.3.1. Direct analysis: the Bertaut-Warren-Averbach method 262 6.3.2. Indirect Fourier analysis 268 6.4. Microstructural study based on the modeling of the diffraction peak profiles 270 Chapter 7. Microstructural Study of Thin Films 275 7.1. Positioning and orienting the sample 276 7.2. Study of disoriented or textured polycrystalline films 279 7.2.1. Films comprised of randomly oriented crystals 279 7.2.2. Studying textured films 285 7.2.2.1. Determining the texture 285 7.2.2.2. Quantification of the crystallographic orientation: studying texture 289 7.3. Studying epitaxial films 292 7.3.1. Studying the crystallographic orientation and determining epitaxy relations 292 7.3.1.1. Measuring the normal orientation: rocking curves 293 7.3.1.2. Measuring the in-plane orientation: phi-scan 295 7.3.2. Microstructural studies of epitaxial films 300 7.3.2.1. Reciprocal space mapping and methodology 304 7.3.2.2. Quantitative microstructural study by fitting the intensity distributions with Voigt functions 307 7.3.2.3. Quantitative microstructural study by modeling of one-dimensional intensity distributions 312 Bibliography 319 Index 349

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Book SynopsisThree aspects are developed in this book: modeling, a description of the phenomena and computation methods. A particular effort has been made to provide a clear understanding of the limits associated with each modeling approach. Examples of applications are used throughout the book to provide a better understanding of the material presented.Table of ContentsPreface 13 Chapter 1. Vibrations of Continuous Elastic Solid Media 17 1.1. Objective of the chapter 17 1.2. Equations of motion and boundary conditions of continuous media 18 1.2.1. Description of the movement of continuous media 18 1.2.2. Law of conservation 21 1.2.3. Conservation of mass 23 1.2.4. Conservation of momentum 23 1.2.5. Conservation of energy 25 1.2.6. Boundary conditions 26 1.3. Study of the vibrations: small movements around a position of static, stable equilibrium 28 1.3.1. Linearization around a configuration of reference 28 1.3.2. Elastic solid continuous media 32 1.3.3. Summary of the problem of small movements of an elastic continuous medium in adiabatic mode 33 1.3.4. Position of static equilibrium of an elastic solid medium 34 1.3.5. Vibrations of elastic solid media 35 1.3.6. Boundary conditions 37 1.3.7. Vibrations equations 38 1.3.8. Notes on the initial conditions of the problem of vibrations 39 1.3.9. Formulation in displacement 40 1.3.10. Vibration of viscoelastic solid media 40 1.4. Conclusion 44 Chapter 2. Variational Formulation for Vibrations of Elastic Continuous Media 45 2.1. Objective of the chapter 45 2.2. Concept of the functional, bases of the variational method 46 2.2.1. The problem 46 2.2.2. Fundamental lemma 46 2.2.3. Basis of variational formulation 47 2.2.4. Directional derivative 50 2.2.5. Extremum of a functional calculus 55 2.3. Reissner’s functional 56 2.3.1. Basic functional 56 2.3.2. Some particular cases of boundary conditions 59 2.3.3. Case of boundary conditions effects of rigidity and mass 60 2.4. Hamilton’s functional 61 2.4.1. The basic functional 61 2.4.2. Some particular cases of boundary conditions 62 2.5. Approximate solutions 63 2.6. Euler equations associated to the extremum of a functional 64 2.6.1. Introduction and first example 64 2.6.2. Second example: vibrations of plates 68 2.6.3. Some results 72 2.7. Conclusion 75 Chapter 3. Equation of Motion for Beams 77 3.1. Objective of the chapter 77 3.2. Hypotheses of condensation of straight beams 78 3.3. Equations of longitudinal vibrations of straight beams 80 3.3.1. Basic equations with mixed variables 80 3.3.2. Equations with displacement variables 85 3.3.3. Equations with displacement variables obtained by Hamilton’s functional 86 3.4. Equations of vibrations of torsion of straight beams 89 3.4.1. Basic equations with mixed variables 89 3.4.2. Equation with displacements 91 3.5. Equations of bending vibrations of straight beams 93 3.5.1. Basic equations with mixed variables: Timoshenko’s beam 93 3.5.2. Equations with displacement variables: Timoshenko’s beam 97 3.5.3. Basic equations with mixed variables: Euler-Bernoulli beam 101 3.5.4. Equations of the Euler-Bernoulli beam with displacement variable 102 3.6. Complex vibratory movements: sandwich beam with a flexible inside 104 3.7. Conclusion 109 Chapter 4. Equation of Vibration for Plates 111 4.1. Objective of the chapter 111 4.2. Thin plate hypotheses 112 4.2.1. General procedure 112 4.2.2. In plane vibrations 112 4.2.3. Transverse vibrations: Mindlin’s hypotheses 113 4.2.4. Transverse vibrations: Love-Kirchhoff hypotheses 114 4.2.5. Plates which are non-homogenous in thickness 115 4.3. Equations of motion and boundary conditions of in plane vibrations 116 4.4. Equations of motion and boundary conditions of transverse vibrations 121 4.4.1. Mindlin’s hypotheses: equations with mixed variables 121 4.4.2. Mindlin’s hypotheses: equations with displacement variables 123 4.4.3. Love-Kirchhoff hypotheses: equations with mixed variables 124 4.4.4. Love-Kirchhoff hypotheses: equations with displacement variables 127 4.4.5. Love-Kirchhoff hypotheses: equations with displacement variables obtained using Hamilton’s functional 129 4.4.6. Some comments on the formulations of transverse vibrations 130 4.5. Coupled movements 130 4.6. Equations with polar co-ordinates 133 4.6.1. Basic relations 133 4.6.2. Love-Kirchhoff equations of the transverse vibrations of plates 135 4.7. Conclusion 138 Chapter 5. Vibratory Phenomena Described by the Wave Equation 139 5.1. Introduction 139 5.2. Wave equation: presentation of the problem and uniqueness of the solution 140 5.2.1. The wave equation 140 5.2.2. Equation of energy and uniqueness of the solution 142 5.3. Resolution of the wave equation by the method of propagation (d’Alembert’s methodology) 145 5.3.1. General solution of the wave equation 145 5.3.2. Taking initial conditions into account 147 5.3.3. Taking into account boundary conditions: image source 151 5.4. Resolution of the wave equation by separation of variables 154 5.4.1. General solution of the wave equation in the form of separate variables 154 5.4.2. Taking boundary conditions into account 157 5.4.3. Taking initial conditions into account 163 5.4.4. Orthogonality of mode shapes 165 5.5. Applications 168 5.5.1. Longitudinal vibrations of a clamped-free beam 168 5.5.2. Torsion vibrations of a line of shafts with a reducer 172 5.6. Conclusion 178 Chapter 6. Free Bending Vibration of Beams 181 6.1. Introduction 181 6.2. The problem 182 6.3. Solution of the equation of the homogenous beam with a constant cross-section 184 6.3.1. Solution 184 6.3.2. Interpretation of the vibratory solution, traveling waves, vanishing waves 186 6.4. Propagation in infinite beams 189 6.4.1. Introduction 189 6.4.2. Propagation of a group of waves 191 6.5. Introduction of boundary conditions: vibration modes 197 6.5.1. Introduction 197 6.5.2. The case of the supported-supported beam 197 6.5.3. The case of the supported-clamped beam 201 6.5.4. The free-free beam 206 6.5.5. Summary table 209 6.6. Stress-displacement connection 210 6.7. Influence of secondary effects 211 6.7.1. Influence of rotational inertia 212 6.7.2. Influence of transverse shearing 215 6.7.3. Taking into account shearing and rotational inertia 221 6.8. Conclusion 227 Chapter 7. Bending Vibration of Plates 229 7.1. Introduction 229 7.2. Posing the problem: writing down boundary conditions 230 7.3. Solution of the equation of motion by separation of variables 234 7.3.1. Separation of the space and time variables 234 7.3.2. Solution of the equation of motion by separation of space variables 235 7.3.3. Solution of the equation of motion (second method) 237 7.4. Vibration modes of plates supported at two opposite edges 239 7.4.1. General case 239 7.4.2. Plate supported at its four edges 241 7.4.3. Physical interpretation of the vibration modes 244 7.4.4. The particular case of square plates 248 7.4.5. Second method of calculation 251 7.5. Vibration modes of rectangular plates: approximation by the edge effect method 254 7.5.1. General issues 254 7.5.2. Formulation of the method 255 7.5.3. The plate clamped at its four edges 259 7.5.4. Another type of boundary conditions 261 7.5.5. Approximation of the mode shapes 263 7.6. Calculation of the free vibratory response following the application of initial conditions 263 7.7. Circular plates 265 7.7.1. Equation of motion and solution by separation of variables 265 7.7.2. Vibration modes of the full circular plate clamped at the edge 272 7.7.3. Modal system of a ring-shaped plate 276 7.8. Conclusion 277 Chapter 8. Introduction to Damping: Example of the Wave Equation 279 8.1. Introduction 279 8.2. Wave equation with viscous damping 281 8.3. Damping by dissipative boundary conditions 287 8.3.1. Presentation of the problem 287 8.3.2. Solution of the problem 288 8.3.3. Calculation of the vibratory response 294 8.4. Viscoelastic beam 297 8.5. Properties of orthogonality of damped systems 303 8.6. Conclusion 308 Chapter 9. Calculation of Forced Vibrations by Modal Expansion 309 9.1. Objective of the chapter 309 9.2. Stages of the calculation of response by modal decomposition 310 9.2.1. Reference example 310 9.2.2. Overview 317 9.2.3. Taking damping into account 321 9.3. Examples of calculation of generalized mass and stiffness 322 9.3.1. Homogenous, isotropic beam in pure bending 322 9.3.2. Isotropic homogenous beam in pure bending with a rotational inertia effect 323 9.4. Solution of the modal equation 324 9.4.1. Solution of the modal equation for a harmonic excitation 324 9.4.2. Solution of the modal equation for an impulse excitation 330 9.4.3. Unspecified excitation, solution in frequency domain 332 9.4.4. Unspecified excitation, solution in time domain 333 9.5. Example response calculation 336 9.5.1. Response of a bending beam excited by a harmonic force 336 9.5.2. Response of a beam in longitudinal vibration excited by an impulse force (time domain calculation) 340 9.5.3. Response of a beam in longitudinal vibrations subjected to an impulse force (frequency domain calculation) 343 9.6. Convergence of modal series 347 9.6.1. Convergence of modal series in the case of harmonic excitations 347 9.6.2. Acceleration of the convergence of modal series of forced harmonic responses 350 9.7. Conclusion 353 Chapter 10. Calculation of Forced Vibrations by Forced Wave Decomposition 355 10.1. Introduction 355 10.2. Introduction to the method on the example of a beam in torsion 356 10.2.1. Example: homogenous beam in torsion 356 10.2.2. Forced waves 358 10.2.3. Calculation of the forced response 359 10.2.4. Heterogenous beam 361 10.2.5. Excitation by imposed displacement 363 10.3. Resolution of the problems of bending 365 10.3.1. Example of an excitation by force 365 10.3.2. Excitation by torque 368 10.4. Damped media (case of the longitudinal vibrations of beams) 369 10.4.1. Example 369 10.5. Generalization: distributed excitations and non-harmonic excitations 371 10.5.1. Distributed excitations 371 10.5.2. Non-harmonic excitations 375 10.5.3. Unspecified homogenous mono-dimensional medium 377 10.6 Forced vibrations of rectangular plates 379 10.7. Conclusion 385 Chapter 11. The Rayleigh-Ritz Method based on Reissner’s Functional 387 11.1. Introduction 387 11.2. Variational formulation of the vibrations of bending of beams 388 11.3. Generation of functional spaces 391 11.4. Approximation of the vibratory response 392 11.5. Formulation of the method 392 11.6. Application to the vibrations of a clamped-free beam 397 11.6.1. Construction of a polynomial base 397 11.6.2. Modeling with one degree of freedom 399 11.6.3. Model with two degrees of freedom 402 11.6.4. Model with one degree of freedom verifying the displacement and stress boundary conditions 404 11.7. Conclusion 406 Chapter 12. The Rayleigh-Ritz Method based on Hamilton’s Functional 409 12.1. Introduction 409 12.2. Reference example: bending vibrations of beams 409 12.2.1 Hamilton’s variational formulation 409 12.2.2. Formulation of the Rayleigh-Ritz method 411 12.2.3. Application: use of a polynomial base for the clamped-free beam 414 12.3. Functional base of the finite elements type: application to longitudinal vibrations of beams 415 12.4. Functional base of the modal type: application to plates equipped with heterogenities 420 12.5. Elastic boundary conditions 423 12.5.1. Introduction 423 12.5.2. The problem 423 12.5.3. Approximation with two terms 424 12.6. Convergence of the Rayleigh-Ritz method 426 12.6.1. Introduction 426 12.6.2. The Rayleigh quotient 426 12.6.3. Introduction to the modal system as an extremum of the Rayleigh quotient 428 12.6.4. Approximation of the normal angular frequencies by the Rayleigh quotient or the Rayleigh-Ritz method 431 12.7. Conclusion 432 Bibliography and Further Reading 435 Index 439

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