Mechanics and Physics of Fracture: Multiscale Modeling of the Failure Behavior of Solids

Description

The volume provides a comprehensive understanding of the macroscopic failure behavior of solids from the description of the microscopic failure processes and their coupling with the microstructure. Several fundamental questions were addressed: the relation between the microstructural features of materials and their fracture properties and crack trajectories; the role of damage mechanisms and non-linear deformations near the crack tip on the failure behavior of solids; and finally the role of dynamic inertial effects during fast fracture was more briefly evoked. The chapters provide a pedagogical overview of recently developed concepts and tools, that permit to perform the transition from small scales to large ones in fracture problems, thus introducing basic rules for the rational design of tough solids. Preface Contents Introduction to Mechanics of Fracture 1 Introduction 2 An Overview of the Griffith Theory of Fracture 2.1 How Strong is a Solid?—An Atomistic Point of View 2.2 How Strong is a Solid?—The Role of Defects 2.3 How Strong is a Solid?—Energy Balance and Continuum Aspects 2.4 Calculation of the Energy Release Rate 3 Linear Elastic Fracture Mechanics—The Local Approach to Fracture 3.1 Anti-plane Shear—Mode III 3.2 In-Plane Loading—Modes I and II 3.3 Out-of-Plane Components of Displacement, Stress and Strain Fields 3.4 The J-Integral 3.5 Linearly Elastic Fracture Mechanics (LEFM) 4 Mixed-Mode Fracture 4.1 In-Plane Mixed Mode Problem: Mixed-Modes I + II 4.2 Out-of-Plane Mixed Mode Problem: Mixed-Modes I + III 5 Dynamic Fracture 5.1 Dynamic Lifting and Peeling of an Inextensible, Flexible Tape 5.2 Local Stress Analysis in Linear Elastodynamics 6 Phase-Field Model for Linearly Elastic Fracture Problems 7 Summary References Perturbations of Cracks 1 General Introduction 2 2D Crack Perturbations in Mixed Mode I+II 2.1 Introduction 2.2 Hypotheses and Notations 2.3 Continuity of Mechanical Fields with Respect to the Crack Extension Length 2.4 The Stress Intensity Factors Just After the Kink 2.5 Practical Calculation of the Functions Fpq(α) 2.6 Higher-Order Terms of the Expansion of the Stress Intensity Factors 2.7 Extended Irwin Formula in the Presence of a Kink 2.8 Presentation of Classical Criteria of Prediction of the Kink Angle 2.9 Discussion of Criteria 2.10 Analysis of Directional Stability of a Mode I Crack 2.11 Application: Deviation of a Crack Propagating in a Quenched Plate 2.12 Concluding Summary 3 3D Coplanar Crack Perturbations 3.1 Introduction 3.2 ch2R85,ch2R89s Re-formulation of ch2B87s Theory of Weight Functions 3.3 Variations of the Mode I Stress Intensity Factor and the Fundamental Kernel: General Formulae 3.4 First- and Second-Order Perturbation of a Semi-infinite Mode I Crack in an Infinite Body 3.5 Perturbation of a Mode I Slit-Crack in an Infinite Body 3.6 Application 1: Configurational Stability of the Front of an Expanding Mode I Slit-Crack 3.7 First- and Second-Order Perturbation of a Semi-infinite Mode I Crack Lying on the Mid-Plane of a Plate 3.8 Application 2: Deformation of a Crack Front by a Hard Obstacle in a Plate 3.9 Perturbation of a Semi-infinite Interface Crack in an Infinite Body 3.10 Application 3: On the Interpretation of Some Experiments of Debonding of Plates Bonded onto Rigid Substrates 3.11 Concluding Summary 4 3D Out-of-Plane Crack Perturbations 4.1 Introduction 4.2 Crack Kinking in 3D 4.3 First-Order In-Plane and Out-of-Plane Perturbation of a Semi-infinite Crack in an Infinite Body 4.4 Linear Stability Analysis of a Semi-infinite Crack Loaded in Mixed-Mode I+III 4.5 Application of ch2CR80s Directional Stability Criterion to Cracks Propagating in Mode I+III 4.6 Extension of the Stability Analysis to the Case of a Mode-Dependent Critical Energy-release-rate 4.7 Further Extension to General Mixed-Mode I+II +III Situations 4.8 Concluding Summary 5 General Conclusion References Fracture Mechanics of Heterogeneous Materials: Effective Toughness and Fluctuations 1 Introduction 2 Effective Toughness of Heterogeneous Brittle Materials 2.1 Homogenization Procedure 2.2 Crack Evolution in Weakly Heterogeneous Brittle Solids 2.3 Comparison with Experiments: Crack Pinning by a Single Obstacle 2.4 Application: Failure by Design 2.5 Effective Toughness of Disordered Solids 2.6 Effective Toughness of Penny-Shaped Cracks: From Pinning to Fingering 2.7 Conclusion and Perspectives 3 Statistics of Fluctuations During the Tensile Failure of the Disordered Materials 3.1 Fluctuations in the Dynamics of Cracks 3.2 Statistics of Fluctuations in the Trajectory of Cracks 3.3 Conclusion and Perspectives References The Fracture Mechanics of Biological Materials 1 Introduction 2 Some General Construction Rules for Biological Materials 3 A Uniaxial Fiber Composite: Tendon 4 A Natural Composite Laminate: Fish Scale 5 A Rubber-Like Material: Skin 6 A Densely Mineralized Brick and Mortar Composite: Nacre 7 A Mineralized Cross-Ply: Tooth Enamel 8 A Complex Hierarchical Composite: Bone 9 Summary and Overview of Toughening Mechanisms in Natural Materials References