Models and Phenomena in Fracture Mechanics

Presenting the most important results, methods, and open questions, this book describes and compares advanced models in fracture mechanics. The author introduces the required mathematical technique, mainly the theory of analytical functions, from scratch.

Modern concepts of fracture mechanics are presented consecutively. Homogeneous and structured models, where microstructure plays an essential role, are considered for fracture and phase transition. Firstly, one-dimensional models are comprehensively studied allowing one to retrace the main phenomena without technical difficulties. More realistic models are then used as linear and nonlinear elastic mediums, such as elastic plates with crack closure, viscoelastic discrete lattices, chains and cohesive zone models. Also considered are, crack origination, equilibrium, slow and fast growth. Sub- and super critical crack speed regimes and transition from one regime to another are studied. Fourier transform and related topics, including a version of the Wiener-Hopf technique dealing with originals are presented, as well as required topics from wave theory. This book is targeted at researchers of materials and structures, also at lecturers and advanced students.

Describes and compares advanced models in fracture mechanics Presents the most improtant results, methods and open questions Introduces required mathematical technique, mainly the theory of analytical functions

Inhalt
1 Fundamentals and Basic Relations.- 1.1 Energy Release and Energy Criterion.- 1.2 Some Methods for Determination of Energy Release.- 1.3 Other Examples of the Energy Release Phenomenon.- 1.4 Stress Intensity Criterion.- 1.5 Some Fracture-Associated Phenomena.- 2 Fourier Transform and Related Topics.- 2.1 Continuous Fourier Transform.- 2.2 Wiener-Hopf Technique.- 2.3 Laplace and Fourier Transform.- 2.4 Discrete Fourier Transform.- 3 Waves.- 3.1 Waves of Sinusoidal and Exponential Types.- 3.2 Waves in Periodic Structures.- 3.3 Forced Waves.- 3.4 Waves in Homogeneous Space and Half-Space.- 3.5 Nonlinear Waves in a String.- 4 One-dimensional Models.- 4.1 String Model.- 4.2 Bending Beam Model.- 5 Static Cracks in a Linearly Elastic Body.- 5.1 Field Representations.- 5.2 KolosovMuskhelishvili Representation.- 5.3 Papkovich Representation.- 5.4 Crack in an Unbounded Plane.- 5.5 Asymptotes.- 5.6 Homogeneous Solutions.- 5.7 Integral Equations for a General Crack System.- 5.8 Crack Interaction.- 5.9 Energy Release Under Crack Kink.- 5.10 Cohesive Zone Model.- 5.11 Penny-Shaped Crack.- 5.12 Betti#x2019;s Theorem and the Weight Functions.- 6 Nonlinear Elastic Body.- 6.1 Some Data from Nonlinear Elasticity.- 6.2 Lagrangian and Eulerian Interpretation of Linear Elasticity.- 6.3 Strains in the Neighborhood of a Singular Point.- 6.4 Exact Relationships for the Energy Release and Some Consequences.- 7 Viscoelastic Fracture.- 7.1 Some Data from Viscoelasticity.- 7.2 Stationary Crack and Collinear Crack System.- 7.3 Growing Crack.- 7.4 Cohesive Zone for Viscoelastic Material.- 8 Elastic-Plastic Fracture.- 8.1 Elastic-Plastic Fields.- 8.2 Fixed Cracks.- 8.3 Growing Cracks.- 8.4 Elastic-Plastic Dynamic Fracture.- 9 Dynamic Fracture in a Homogeneous Elastic Medium.- 9.1 Some BasicRelations.- 9.2 Crack Tip Asymptotes and the Energy Release.- 9.3 Factorization of the Fundamental Solutions.- 9.4 Uniform Crack Propagation.- 9.5 Nonuniform Crack Speed Problem.- 9.6 Self-Similar Dynamic Problems.- 9.7 Dynamic Crack in a Plate Under Bending.- 9.8 Principle of Maximum Energy Dissipation Rate.- 10 Cracks in a Bending Plate.- 10.1 Asymptotic Solution for a Single Crack.- 10.2 Radial Cracking with Closure.- 10.3 Self-Similar Dynamic Problem.- 11 The Square-Cell Lattice.- 11.1 Preliminaries.- 11.2 Some Introductory Remarks.- 11.3 Elastic Lattice: Formulation and the Governing Equation.- 11.4 Factorization.- 11.5 Solutions.- 11.6 Viscoelastic Lattice.- 12 Triangular-Cell Elastic Lattice.- 12.1 Introductory Remarks.- 12.2 General Properties of Fundamental Solutions.- 12.3 Equations and General Solutions.- 12.4 Macrolevel-Associated Solution.- 12.5 Microlevel Solutions.- 12.6 Concluding Remarks.- 13 Phase Transition Waves.- 13.1 Introductory Remarks.- 13.2 Macrolevel Solution.- 13.3 Discrete Chain.- 13.4 Higher-Order-Derivative Model.- 13.5 Concluding Remarks.- 14 Dynamic Amplification Factor in Fracture and Phase Transition.- 14.1 Introductory Remarks.- 14.2 Line of Viscoelastic Oscillators.- 14.3 DOR and SAR Domains for Viscoelastic Oscillator.- 14.4 Viscoelastic Square-Cell Lattice.- 14.5 Slow Phase Transition Wave in a Chain.- 14.6 Triangular-Cell Lattice Irregularities in Fracture.- References.