1st Edition

Basic Fracture Mechanics and its Applications

By Ashok Saxena Copyright 2023
    342 Pages 202 B/W Illustrations
    by CRC Press

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    This textbook provides a comprehensive guide to fracture mechanics and its applications, providing an in-depth discussion of linear elastic fracture mechanics and a brief introduction to nonlinear fracture mechanics. It is an essential companion to the study of several disciplines such as aerospace, biomedical, civil, materials and mechanical engineering. This interdisciplinary textbook is also useful for professionals in several industries dealing with design and manufacturing of engineering materials and structures.

    Beginning with four foundational chapters, discussing the theory in depth, the book also presents specific aspects of how fracture mechanics is used to address fatigue crack growth, environment assisted cracking, and creep and creep-fatigue crack growth. Other topics include mixed-mode fracture and materials testing and selection for damage tolerant design, alongside in-depth discussions of ensuring structural integrity of components through real-world examples. There is a strong focus throughout the book on the practical applications of fracture mechanics. It provides a clear description of the theoretical aspects of fracture mechanics and also its limitations. Appendices provide additional background to ensure a comprehensive understanding and every chapter includes solved example problems and unsolved end of chapter problems. Additional instructor support materials are also available.

    1. Fracture in Structural Components

    1.1 Fracture in Engineering Materials and Structures: Societal Relevance

    1.1.1 Safety Assessments

    1.1.2 Environment and Health Hazards

    1.1.3 Optimizing Costs (Fuel economy, material costs, opportunity costs)

    1.1.4 Product Liability

    1.2 Examples of Prominent Fractures and the Underlying Causes

    1.2.1 Failures in Liberty Ships

    1.2.2 Failures of Comet Aircraft

    1.2.3 Cracks in A380 Aircrafts

    1.2.4 Crack in a Structural Member of an Interstate Highway Bridge

    1.2.5 Cracks in Human Bones

    1.2.6 Aneurysms in Human Abdominal Aortas

    1.3 Degradation Phenomena and Fracture in Engineering Materials and Structures

    1.3.1 Crack Initiation/Formation and Growth

    1.4 History of Developments in Understanding Fatigue and Fracture

    1.4.1 Developments in Understanding of Fatigue

    1.4.2 Understanding Brittle and Ductile Fracture

    1.4.3 Early Developments in Fracture Mechanics

    1.4.4 Developments in Elastic-Plastic Fracture Mechanics

    1.4.5 Environment Assisted Cracking

    1.4.6 Developments in Time Dependent Fracture Mechanics

    1.5 Summary

    2. Early Theories of Fracture

    2.1 Microscopic Aspects of Fracture

    2.1.1 Intergranular and Transgranular Fracture

    2.1.2 Equi-Cohesive Temperature

    2.1.3 Ductile and Brittle Fracture

    2.2 Models of Fracture at Atomic Scale

    2.3 Stress Concentration Effects of Flaws

    2.4 Griffith’s Theory of Brittle Fracture

    2.5 Orowan’s Modification to Griffith’s Theory

    2.6 The Concept of Crack Extension Force, G

    2.6.1 Estimation of Griffith’s Crack Extension Force for an Arbitrary Shaped Body

    2.7 Crack Growth Resistance, R

    2.8 Predicting Instability in Cracked Structures

    2.8.1 Predicting Instability Conditions for a General Case

    2.9 Summary

    Appendix 2A: Review of Solid Mechanics

    2A.1 Stress

    2A.2 Strain

    2A.3 Elasticity

    2A.4 Elastic Strain Energy

    2A.5 Stress Transformation Equations

    2A.6 Stress–Strain Behavior

    3. Theoretical Basis for Linear Elastic Fracture Mechanics

    3.1 Classification of Engineering Structural Materials and Defects

    3.2 Stress Analysis of Cracks

    3.2.1 Equations of Elasticity

    3.2.2 Compatibility Equations

    3.2.3 Application of Airy’s Stress Function to Crack Problems

    3.3 Stress Intensity Parameter, K, for Various Crack Geometries and Loading Configurations by the Westergaard Method

    3.4 Crack Tip Displacement Fields

    3.5 The Relationship between G and K

    3.6 Determining K for Other Loading and Crack Geometries

    3.7 Use of Linear Superposition Principle for Deriving K-Solutions

    3.8 K-Solutions for 3-D Cracks

    3.9 Summary

    Appendix 3A

    3A.1 Cauchy-Riemann Equations

    3A.2 Derivation of the Crack Tip Displacement Fields

    4. Crack Tip Plasticity

    4.1 Estimate of the Plastic Zone Size

    4.2 Plasticity Modified Crack Tip Stress Field for SSY

    4.3 Plastic Zone Shape

    4.4 Crack Tip Opening Displacement (CTOD)

    4.5 Summary

    Appendix 4A: Plastic Yielding Under Uniaxial and Multiaxial Conditions

    4A.1 Uniaxial Stress-Strain Curve

    4A.2 Von Mises Yield Criterion for Multiaxial Loading

    4A.3 Tresca Yield Criterion

    5. Fracture Toughness and Its Measurement

    5.1 Similitude and the Stress Intensity Parameter, K

    5.2 Fracture Toughness as a Function of Plate Thickness

    5.3 Ductile and Brittle Fracture and the LEFM Approach

    5.4 Measurement of Fracture Toughness

    5.4.1 Measurement of Plane Strain Fracture Toughness, KIc

    5.4.2 Fracture Toughness of Thin Panels

    5.5 Correlations between Charpy Energy and Fracture Toughness

    5.5.1 Charpy Energy versus Fracture Toughness Correlation for Lower-Shelf and Lower Transition Region

    5.5.2 Charpy Energy versus Fracture Toughness Correlation for Upper-Shelf Region

    5.6 Summary

    Appendix 5A: Compliance Relationships for C(T) and M(T) Specimens

    5A.1 Compliance Relationships for C(T) Specimen

    5A.2 Compliance and K - Relationships for M(T) Specimens

    6. Fatigue Crack Growth

    6.1 Introduction

    6.2 Fatigue Crack Growth (or Propagation) Rates

    6.2.1 Definitions

    6.2.2 Mechanisms of Fatigue Crack Growth

    6.2.3 Fatigue Crack Growth Life Estimation

    6.3 The Effect of Load Ratio, Temperature and Frequency on Fatigue Crack Growth Rate in the Paris Regime

    6.4 Wide Range Fatigue Crack Growth Behavior

    6.5 Crack Tip Plasticity during Cyclic Loading

    6.5.1 Cyclic Plastic Zone

    6.5.2 Crack Closure during Cyclic Loading

    6.6 Fatigue Cycles Involving Compressive Loading

    6.7 Models for Representing Load Ratio Effects on Fatigue Crack Growth Rates

    6.8 Fatigue Crack Growth Measurements (ASTM Standard E647)

    6.9 Behavior of Small or Short Cracks

    6.10 Fatigue Crack Growth Under Variable Amplitude Loading

    6.10.1 Effects of Single Overloads/Underloads on Fatigue Crack Growth Behavior

    6.10.2 Variable Amplitude Loading

    6.11 Summary

    7. Environment-Assisted Cracking

    7.1 Introduction

    7.2 Mechanisms of EAC

    7.3 Relationship between EAC and K under Static Loading

    7.4 Methods of Determining KIEAC

    7.5 Relationship betwee KIEAC and Yield Strength and Fracture Toughness

    7.6 Environment Assisted Fatigue Crack Growth

    7.7 Models for Environment Assisted Fatigue Crack Growth Behavior

    7.7.1 Linear Superposition Model

    7.7.2 A Model for Predicting the Effect of Hydrogen Pressure on the Fatigue Crack Growth Behavior

    7.8 Summary

    8. Fracture under Mixed-Mode Loading

    8.1 Introduction

    8.2 Stress Analysis of Cracks under Mixed-Mode Conditions

    8.3 Mixed Mode Considerations in Fracture of Isotropic Materials

    8.3.1 Fracture Criterion Based on Energy Available for Crack Extension

    8.3.2 Maximum Circumferential Stress Fracture Criterion

    8.3.3 Strain Energy Density (SED) as Mixed Mode Fracture Criterion

    8.4 Fracture Toughness Measurements Under Mixed-Mode Conditions

    8.4.1 Fracture in Bones

    8.4.2 Measurement of Fracture Toughness in Mode II (KIIc)

    8.4.3 Measurement of Interfacial Toughness in Laminate Composites

    8.5 Fatigue Crack Growth under Mixed-Mode Loading

    8.6 Summary

    9. Fracture and Crack Growth under Elastic/Plastic Loading

    9.1 Introduction

    9.2 Rice’s J-Integral

    9.3 J-Integral as a Fracture Parameter

    9.4 Equations for Determining J in C(T) Specimens

    9.5 Fatigue Crack Growth under Gross Plasticity Conditions

    9.5.1 Experimental Correlations between da/dN and ∆J

    9.6 Summary

    10. Creep and Creep-Fatigue Crack Growth

    10.1 Introduction

    10.2 Creep Crack Growth

    10.2.1 C*- Integral

    10.2.2 C(t) Integral and the Ct Parameter

    10.2.3 Creep Crack Growth in Creep-brittle Materials

    10.3 Crack Growth under Creep-Fatigue-Environment Conditions

    10.3.1 da/dN versus ∆K correlations

    10.3.2 Creep-Fatigue Crack Growth Rates for Long Cycle Times

    10.4 Summary

    11. Case Studies in Applications of Fracture Mechanics

    11.1 Introduction

    11.1.1 Integrity Assessment of Structures and Components

    11.1.2 Material and Process Selection

    11.1.3 Design of Remaining Life Prediction

    11.1.4 Inspection Criterion and Interval Determination

    11.1.5 Failure Analysis

    11.2 General Methodology for Fracture Mechanics Analysis

    11.3 Case Studies

    11.3.1 Optimizing Manufacturing Costs

    11.3.2 Reliability of Service-Degraded Steam Turbine Rotors

    11.3.3 Design of Vessels for Storing Gaseous Hydrogen at Very High Pressures

    11.4 Summary


    Dr. Ashok Saxena currently serves as President and CEO of WireTough Cylinders, a position he has held since January of 2018. Dr. Saxena also serves as Dean Emeritus and Distinguished Professor (Retired) in the Department of Mechanical Engineering at the University of Arkansas, Fayetteville and as Adjunct Professor in the School of Materials Science and Engineering at Georgia Institute of Technology. At University of Arkansas, he had previously served as the Provost and Vice-Chancellor of Academic Affairs, the Dean of Engineering, the Raymond and Irma Giffels’ Chair, the Head of Biomedical Engineering, and the Billingsley Endowed Chair. At Georgia Tech, he held the position of Regents’ Professor and Chair of the School of Materials Science and Engineering. Prior to that he was a Fellow Scientist at the Westinghouse Research and Development Center in Pittsburgh. He also served as the Vice-Chancellor of Galgotias University in Greater Noida, India from 2012-2014. Dr. Saxena served the American Board of Engineering and Technology (ABET) as Program Evaluator, member of the Engineering Accreditation Commission, and member of the ABET Board. He was a Director and the Vice-President of the International Congress on Fracture and the Executive Chair of the Fifteenth International Conference on Fracture in Atlanta, Georgia, during June 11 to 14, 2023. He is one of the founders of the Indian Structural Integrity Society (InSIS) and served as its President from 2015 – 2018. He has also been a Visiting Professor/ Visiting Scientist in several institutions/research organizations around the world over his professional career spanning five decades.

    Dr. Saxena received his MS and PhD degrees from University of Cincinnati in 1972 and 1974, respectively in Materials Science and Metallurgical Engineering and his B. Tech degree from the Indian Institute of Technology, Kanpur in 1970 in Mechanical Engineering. Dr. Saxena’s area of expertise is mechanical behavior of materials. He has published over 250 research papers, authored/edited 10 books. He is the recipient of numerous national and international awards and recognitions in the field of fracture research that include the George Irwin Medal, the Fracture Mechanics Medal from ASTM, the Wohler Fatigue Medal from the European Structural Integrity Society, Outstanding Research Author Award from Georgia Tech, Paul Paris Gold Medal from the International Congress on Fracture. He is a Fellow of American Society for Testing and Materials, ASM International, International Congress of Fracture, and the Indian Structural Integrity Society. He was an elected member of the European Academy of Sciences.