SOLUTIONS MANUAL
Basic Fracture Mechanics and its Applications | 1st Edition
By Ashok Saxena
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, TABLE OF CONTENT
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
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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
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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
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1.5 Summary
2. Early Theories of Fracture
2.1 Microscopic Aspects of Fracture
2.1.1 Intergranular and Transgranular Fracture
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
Basic Fracture Mechanics and its Applications | 1st Edition
By Ashok Saxena
LU
XE
LI
BR
AR
Y
, TABLE OF CONTENT
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
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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
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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
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1.5 Summary
2. Early Theories of Fracture
2.1 Microscopic Aspects of Fracture
2.1.1 Intergranular and Transgranular Fracture
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
