Fracture Mechanics

Fracture Mechanics covers classical and modern methods and introduce new/unique techniques, making this text an important resource for anyone involved in the study or application of fracture mechanics. Using insights from leading experts in fracture mechanics, it provides new approaches and new applications to advance the understanding of crack initiation and propagation. With a concise and easily understood mathematical treatment of crack tip fields, this book provides the basis for applying fracture mechanics in solving practical problems. It features a unique coverage of bi-material interfacial cracks, with applications to commercially important areas of composite materials, layered structures, and microelectronic packaging. A full chapter is devoted to the cohesive zone model approach, which has been extensively used in recent years to simulate crack propagation. A unified discussion of fracture criteria involving nonlinear/plastic deformations is also provided. The book is an invaluable resource for mechanical, aerospace, civil, and biomedical engineers in the field of mechanics as well as for graduate students and researchers studying mechanics. Concise and easily understood mathematical treatment of crack tip fields (chapter 3) provides the basis for applying fracture mechanics in solving practical problems Unique coverage of bi-material interfacial cracks (chapter 8), with applications to commercially important areas of composite materials, layered structures, and microelectronic packaging A full chapter (chapter 9) on the cohesive zone model approach, which has been extensively used in recent years to simulate crack propagation A unified discussion of fracture criteria involving nonlinear/plastic deformations 01-fm-i-iv-9780123850010......Page 2 02-ded-v-vi-9780123850010......Page 6 03-toc-vii-xii-9780123850010......Page 8 04-pre-xiii-xvi-9780123850010......Page 14 05-ata-xvii-xx-9780123850010......Page 18 1.1 Failure of Solids......Page 21 1.2 Fracture Mechanics Concepts......Page 22 1.3.1 Griffith Theory of Fracture......Page 25 1.3.2 Fracture Mechanics as an Engineering Science......Page 26 1.3.3 Recent Developments in Fracture Mechanics Research......Page 27 References......Page 28 2.1.1 An Atomistic Model......Page 31 2.1.2 The Energy Consideration......Page 33 2.2 The Griffith Theory of Fracture......Page 34 2.3 A Relation among Energies......Page 37 Problems......Page 42 3.1 Basic Modes of Fracture and Stress Intensity Factor......Page 45 3.2.1 Basic Equations of Plane Elasticity and Airy Stress Function......Page 47 3.2.2 Analytic Functions and Cauchy-Riemann Equations......Page 49 3.2.3 Complex Potential Representation of the Airy Stress Function......Page 50 3.2.4 Stress and Displacement......Page 52 3.3.1 Symmetric Problems (Mode I)......Page 54 3.3.2 Skew-Symmetric Problems (Mode II)......Page 56 3.4.1 Mode I Crack......Page 58 Solution of Stresses......Page 59 The Near-Tip Solution......Page 61 Crack Surface Displacement......Page 62 3.4.2 Mode II Crack......Page 63 3.4.3 Mode III Crack......Page 66 3.4.4 Complex Representation of Stress Intensity Factor......Page 68 3.5 Fundamental Solutions of Stress Intensity Factor......Page 70 3.5.1 A Finite Crack in an Infinite Plate......Page 71 3.5.2 Stress Intensity Factors for a Crack Subjected to Arbitrary Crack Face Loads......Page 73 3.5.3 A Semi-infinite Crack in an Infinite Medium......Page 74 3.6 Finite Specimen Size Effects......Page 75 3.7 Williams' Crack Tip Fields......Page 76 3.7.1 Williams' Crack Tip Stress and Displacement Fields: Mode I and II......Page 77 Mode I Case......Page 78 Mode II Case......Page 81 3.7.2 Williams' Crack Tip Stress and Displacement Fields: Mode III......Page 83 3.8 K-Dominance......Page 86 3.9 Irwin's K-Based Fracture Criterion......Page 88 References......Page 91 Problems......Page 92 4.1 The Concept of Energy Release Rate......Page 96 4.2 The Relations between G and K by the Crack Closure Method......Page 97 4.3 The J-Integral......Page 101 4.3.1 J as Energy Release Rate......Page 102 4.3.2 Path-Independence......Page 105 4.3.3 Relation between J and K......Page 106 4.3.4 Examples......Page 108 4.4.1 Direct Method......Page 111 4.4.2 Modified Crack Closure Technique......Page 112 4.5 Three-Dimensional Field near Crack Front......Page 113 4.5.1 Distribution of Stress Intensity Factor over Thickness......Page 114 4.5.2 Plane Strain Zone at the Crack Front......Page 118 References......Page 120 Problems......Page 121 5.1 A Simple Elliptical Model......Page 123 5.2 Maximum Tensile Stress Criterion(MS-Criterion)......Page 126 5.3 Strain Energy Density Criterion (S-Criterion)......Page 129 Mode I......Page 130 Mode II......Page 131 5.4 Maximum Energy Release Rate Criterion (ME-Criterion)......Page 133 5.5 Experimental Verifications......Page 135 References......Page 137 Problems......Page 138 6 Crack Tip Plasticity......Page 140 6.1.1 Tresca Yield Criterion......Page 141 6.2 Constitutive Relationships in Plasticity......Page 142 6.2.1 Flow Theory of Plasticity......Page 143 6.2.2 Deformation Theory of Plasticity......Page 145 6.3.1 Plastic Zone Size......Page 147 6.3.2 Effective Crack Length and Adjusted Stress Intensity Factor......Page 150 6.4 The Dugdale Model......Page 151 6.4.1 Small-Scale Yielding......Page 152 6.4.2 A Crack in an Infinite Plate......Page 154 6.5.1 Principal Stresses......Page 157 Plastic Zone Estimate Based on the von Mises Yield Criterion......Page 158 Plastic Zone Estimates Based on the von Mises Yield Criterion......Page 160 6.5.4 Antiplane Strain Case......Page 162 6.6 Plastic Zone Shape According to Finite Element Analyses......Page 163 6.7.1 Basic Equations......Page 165 6.7.2 Elastic-Plastic Solution and the Crack Tip Plastic Zone......Page 166 6.8 A Mode III Small-Scale Yielding Solution—Elastic Power-Law Hardening Materials......Page 169 6.8.1 Basic Equations......Page 170 6.8.2 Boundary Conditions of SSY......Page 173 6.8.3 Elastic-Plastic Solution......Page 175 6.9 HRR Field......Page 179 6.10 Energy Release Rate Concept in Elastic-Plastic Materials......Page 181 References......Page 184 Problems......Page 185 7.1 Irwin's Adjusted Stress Intensity Factor Approach......Page 187 7.2 K Resistance Curve Approach......Page 189 7.3 J-Integral as a Fracture Parameter......Page 193 7.4 Crack Tip Opening Displacement Criterion......Page 194 7.5 Crack Tip Opening Angle Criterion......Page 197 References......Page 201 Problems......Page 202 8.1.1 Asymptotic Stress and Displacement Fields......Page 204 8.1.2 Mode III Case......Page 209 8.2 Complex Function Method and Stress Intensity Factors......Page 212 8.2.1 Stress Intensity Factor Solutions for Two Typical Crack Problems......Page 213 8.2.2 Further Comments on the Stress Intensity Factor Definitions......Page 215 8.3.1 Crack Surface Contact Zone......Page 218 8.3.2 Stress Oscillation Zone......Page 220 8.4.1 Energy Release Rate......Page 222 8.4.2 Stress Intensity Factor Calculations......Page 224 8.5 Fracture Criterion......Page 227 8.6 Crack Kinking Out of the Interface......Page 228 8.7.1 Crack Tip Fields......Page 230 8.7.2 Finite Element Procedure for Energy Calculation......Page 233 8.7.3 Fracture Criterion......Page 235 References......Page 238 Problems......Page 239 9.1 The Barenblatt Model......Page 241 9.2 Cohesive Zone Concept in Continuum Mechanics and Cohesive Laws......Page 244 9.2.2 A Linear Softening Model......Page 247 9.2.4 An Exponential Model......Page 248 9.3 A Discussion on the Linear Hardening Law......Page 249 9.4 Cohesive Zone Modeling and LEFM......Page 252 9.5.1 Mixed Mode Cohesive Law......Page 254 9.5.2 Cohesive Energy Density......Page 255 9.5.3 Cohesive Zone Length......Page 257 Problems......Page 260 10.1 Fracture Mechanics of Anisotropic Solids......Page 261 10.1.1 Basic Plane Elasticity Equations of Anisotropic Solids......Page 262 10.1.2 A Mode I Crack in an Infinite Anisotropic Plate under Uniform Crack Surface Pressure......Page 264 10.1.3 A Mode II Crack in an Infinite Anisotropic Plate under Uniform Crack Surface Shear......Page 265 10.1.4 Energy Release Rate......Page 266 10.2 Fracture Mechanics of Nonhomogeneous Materials......Page 267 10.2.1 Basic Plane Elasticity Equations of Nonhomogenous Materials......Page 268 10.2.2 Crack Tip Stress and Displacement Fields......Page 270 10.2.3 Energy Release Rate......Page 274 10.2.4 Stress Intensity Factors for a Crack in a Graded Interlayer between Two Dissimilar Materials......Page 278 10.3.1 Basic Equations of Plane Elastodynamics......Page 280 10.3.2 Stationary Cracks under Dymanic Loading......Page 282 10.3.3 Dynamic Crack Propagation......Page 285 10.3.4 Yoffe Crack......Page 295 References......Page 298 Appendix: Stress Intensity Factors......Page 300

Most design engineers are tasked to design against failure, and one of the biggest causes of product failure is failure of the material due to fatigue/fracture. From leading experts in fracture mechanics, this new text provides new approaches and new applications to advance the understanding of crack initiation and propagation. With applications in composite materials, layered structures, and microelectronic packaging, among others, this timely coverage is an important resource for anyone studying or applying concepts of fracture mechanics.

• Concise and easily understood mathematical treatment of crack tip fields (chapter 3) provides the basis for applying fracture mechanics in solving practical problems
• Unique coverage of bi-material interfacial cracks (chapter 8), with applications to commercially important areas of composite materials, layered structures, and microelectronic packaging
• A full chapter (chapter 9) on the cohesive zone model approach, which has been extensively used in recent years to simulate crack propagation
• A unified discussion of fracture criteria involving nonlinear/plastic deformations

"Most design engineers are tasked to design against failure, and one of the biggest causes of product failure is failure of the material due to fatigue/fracture. From leading experts in fracture mechanics, this new text provides new approaches and new applications to advance the understanding of crack initiation and propagation. With applications in composite materials, layered structures, and microelectronic packaging, among others, this timely coverage is an important resource for anyone studying or applying concepts of fracture mechanics. Concise and easily understood mathematical treatment of crack tip fields (chapter 3) provides the basis for applying fracture mechanics in solving practical problems. Unique coverage of bi-material interfacial cracks (chapter 8), with applications to commercially important areas of composite materials, layered structures, and microelectronic packaging. A full chapter (chapter 9) on the cohesive zone model approach, which has been extensively used in recent years to simulate crack propagation. A unified discussion of fracture criteria involving nonlinear/plastic deformations."--Provided by publisher Most design engineers are tasked to design against failure, and one of the biggest causes of product failure is failure of the material due to fatigue/fracture. This book provides approaches and applications to advance the understanding of crack initiation and propagation.