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For Authors
Submit a ProposalPlasticity and Ductile Fracture
One Line Description
Master the critical intersection of plasticity and ductile fracture with this comprehensive guide, combining decades of global expertise and advanced numerical methods to ensure the structural safety and performance of metal designs.
Audience
Academics, researchers, engineers, and software developers in structural engineering, mechanical engineering, marine and offshore engineering, and materials science.
Academics, researchers, engineers, and software developers in structural engineering, mechanical engineering, marine and offshore engineering, and materials science.
Description
Plasticity and ductile fracture are two of the most critical subjects in the structural and mechanical behavior of materials, particularly for engineers involved in the design and safety assessment of metal structures. This book offers a unified and comprehensive treatment of both topics by integrating theoretical foundations, constitutive modeling, and practical case studies using advanced numerical methods. Starting with classical theories of plasticity, including stress tensors, yield criteria, hardening models, and constitutive equations, the text builds toward modern applications, including finite element formulations and real-world structural performance analysis. The text draws from the author’s extensive experience across China, Japan, Norway, and the U.S., making it a rich resource for graduate students, academic researchers, and practicing engineers in the structural, offshore, and mechanical engineering disciplines.
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Plasticity and ductile fracture are two of the most critical subjects in the structural and mechanical behavior of materials, particularly for engineers involved in the design and safety assessment of metal structures. This book offers a unified and comprehensive treatment of both topics by integrating theoretical foundations, constitutive modeling, and practical case studies using advanced numerical methods. Starting with classical theories of plasticity, including stress tensors, yield criteria, hardening models, and constitutive equations, the text builds toward modern applications, including finite element formulations and real-world structural performance analysis. The text draws from the author’s extensive experience across China, Japan, Norway, and the U.S., making it a rich resource for graduate students, academic researchers, and practicing engineers in the structural, offshore, and mechanical engineering disciplines.
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Author / Editor Details
Yong Bai, PhD is a Chair Professor at Zhejiang University and an internationally recognized expert in structural mechanics, plasticity, and ductile fracture. His research focuses on the nonlinear behavior and fracture response of metallic structures under complex loading conditions, with applications in offshore pipelines and energy infrastructure. He has authored 25 books and published more than 200 scientific papers, contributing significantly to the advancement of fracture mechanics and structural integrity analysis. His work has helped improve the safety and reliability of marine and offshore engineering systems.
Yong Bai, PhD is a Chair Professor at Zhejiang University and an internationally recognized expert in structural mechanics, plasticity, and ductile fracture. His research focuses on the nonlinear behavior and fracture response of metallic structures under complex loading conditions, with applications in offshore pipelines and energy infrastructure. He has authored 25 books and published more than 200 scientific papers, contributing significantly to the advancement of fracture mechanics and structural integrity analysis. His work has helped improve the safety and reliability of marine and offshore engineering systems.
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Table of Contents
Preface
Acknowledgement
1. Stress and Strain
1.1 Plasticity in Structural Engineering
1.1.1 Introduction
1.1.2 History
1.1.3 Plasticity of Metals
1.1.4 Plasticity Theory
1.2 Tension and Compression 1
1.2.1 Uniform Loading
1.2.2 Loading Function
1.2.3 Opposite Loading
1.3 Stress Tensor and Deviatoric Stress Tensor
1.3.1 Principal Stress, Principal Shear Stress, and Invariants of Stress Tensor
1.3.2 Decomposition of Stress Tensor and Deviatoric Stress Tensor
1.3.3 Several Variables Related to J2
1.4 Stress Space, π Plane, and Lode Parameters
1.4.1 Principal Stress Space and Plane
1.4.2 Two-Dimensional Expression of Deviatoric Stress
1.5 Deviatoric Strain and Equivalent Strain
1.5.1 The Relationship between Displacement and Strain
1.5.2 Decomposition of the Strain Tensor and Deviatoric Strain
Bibliography
2. Yielding Conditions
2.1 Introduction
2.2 Yield Locus
2.3 Yield Surface
2.4 Yield Criterion
2.4.1 Geometrical Criterion
2.4.2 General Criterion
2.5 Common Yielding Conditions
2.5.1 Tresca Yield Condition
2.5.2 Mises Yield Condition
2.5.3 Anisotropic Yield Condition
2.5.3.1 Hill Yield Criterion
2.5.3.2 Hosford Yield Criterion
2.6 Hardening Rule
2.6.1 Isotropic Hardening Model
2.6.2 Kinematic Hardening Model
2.7 Loading and Unloading of Hardening Materials
2.8 Plastic Deformation
2.9 The Normality Rule
Bibliography
3. Constitutive Equations
3.1 Introduction
3.2 The Total Strain Theory
3.3 The Flow Rules
3.4 Drucker’s Stability Postulate
3.5 The Loading Criterion
3.6 Incremental Stress–Strain Relationships
3.6.1 Constitutive Relation for Perfectly Plastic Materials
3.6.2 Constitutive Relation for Work-Hardening Materials
Bibliography
4. Cyclic Loading and Shakedown
4.1 Introduction
4.2 Cycling Loading
4.3 Shakedown Theorem
4.3.1 Notion of Shakedown
4.3.2 An Intuitive Criterion of Shakedown
4.3.3 Example of Structural Behavior in the Case of Cyclic Loads
Bibliography
5. Some Application Problems
5.1 Torsion in Thin-Walled Tubes
5.2 Combined Tension and Torsion
5.3 Combined Tension, Torsion, and Bending
5.4 Bending in Thin-Walled Tubes
5.5 Combined Tension and Torsion in a Thin-Walled Tube
5.6 Bending in Rectangular Cross-Section
5.7 Internal Pressure in Thick-Walled Tubes
5.7.1 Elastic Analysis of Thick-Walled Cylinders
5.7.2 Plain Axial Symmetry Problem
5.8 Identification Problems
5.8.1 Upper-Bound Approach
5.8.2 Lower-Bound Approach
Bibliography
6. Plasticity in Finite Element Analysis
6.1 Introduction
6.2 Elastic Materials
6.2.1 Kirchhoff Material
6.2.2 Continuum Mechanics
6.2.3 Lagrangian Formulations
6.2.4 Hook’s Law
6.3 Thermo-Elastic Materials
6.4 Hypoelastic Materials
6.4.1 Cauchy Material
6.5 Hyperelastic Materials
6.5.1 Neo-Hookean Material
6.5.2 Modified Mooney-Rivlin Material
6.6 Viscoelastic Materials
6.7 Elastic–Plastic Materials
6.8 Hypoelastic–Plastic Materials
6.9 Hyperelastic–Plastic Materials
6.10 Viscoplastic Materials
6.11 Plastic Materials
Bibliography
7. Plasticity in Total Force Model
7.1 Introduction
7.2 Elastic Beam-Column with Large Displacements
7.3 The Plastic Node Method
7.3.1 History of the Plastic Node Method
7.3.2 Consistency Condition and Hardening Rates for Beam Cross-Sections
7.3.3 Plastic Displacement and Strain at Nodes
7.3.4 Elastic-Plastic Stiffness Equation for Elements
7.4 Transformation Matrix
7.5 Stress-Based Plasticity Constitutive Equations
7.5.1 General
7.5.2 Relationship between Stress and Strain in the Elastic Region
7.5.3 Yield Criterion
7.5.4 Plastic Strain Increment
7.5.4.1 Isotropic Hardening Rule
7.5.4.2 Kinematic Hardening Rule
7.5.5 Stress Increment–Strain Increment Relation in the Plastic Region
7.6 Deformation Matrix
Biblography
8. Metal Forming Processing Plasticity
8.1 Introduction
8.2 Classification
8.3 Forming Processes
8.3.1 Bulk-Forming Process
8.3.2 Sheet Metal Operations
8.4 Sheet Metal Formability
8.4.1 Uniform Strain Distribution in Sheet Metal Forming
8.4.2 Strain Diagram in Sheet Metal Forming
8.4.3 The Deformation Modes
8.5 Anisotropy of Sheet Metal
8.5.1 Uniaxial Anisotropy Coefficients
8.6 Metal Forming in the Carcass Layer of Flexible Pipes
8.6.1 Pre-Metal Forming
8.6.2 Metal Forming
8.6.3 Post-Metal Forming
8.7 Metal Forming Effect on Residual Stress of the Carcass Layer in Flexible Pipes
8.7.1 Experiments
8.7.2 Numerical Model
8.7.3 Results
8.7.4 Residual Stress in Carcass
References
9. Mechanical Behavior of Thin Cylindrical Shells Under Combined Axial Compression and Bending
9.1 Introduction
9.2 Experiments
9.2.1 Material Tests
9.2.2 Tensile Property Testing
9.2.3 Compressive Property Testing
9.2.4 Material Parameters
9.2.5 Combined Loading Tests
9.3 Numerical Studies
9.3.1 Model and Material Properties
9.3.2 Elastic Buckling Analysis
9.4 Validation
9.4.1 Induction of Initial Imperfections
9.4.2 Simulation Results
9.5 Buckling Behavior of Thin Tubes Under Combined Loads
9.6 Conclusions
Bibliography
10. Characterization of Ductile Fracture Criterion for API X80 Pipeline Steel Based on a Phenomenological Approach
10.1 Introduction
10.2 Overview of Damage Model
10.2.1 Descriptions of the Stress State
10.2.2 Gurson-Tvergaard-Needleman Model
10.2.3 Uncoupled Fracture Model
10.2.3.1 Modified Mohr-Coulomb (MMC) Criterion
10.2.3.2 Extended Rice-Tracey (ERT) Criterion
10.2.3.3 Damage Evolution Rule
10.3 Experimental Programs
10.3.1 Conventional Tensile Specimens
10.3.2 Notched Tensile Specimens
10.3.3 Compact Tension (CT) Test
10.4 Calibration Procedure
10.4.1 Finite Element Model
10.4.2 Parameter Identification for GTN Model
10.4.3 Parameter Identification for MMC and ERT Model
10.5 Comparison with Notched Tensile Specimen Test
10.6 Validation through CT Test
10.6.1 Finite Element Model
10.6.2 Mesh Size Sensitivity Analysis
10.6.3 Results and Discussions
10.7 Conclusions
Bibliography
11. Fracture Response of Steel Pipelines Under Combined Tension and Torsion
11.1 Introduction
11.2 Theoretical Equations
11.3 Finite Element Procedure
11.3.1 The Pipe Model
11.3.2 Finite Element Modeling
11.4 Results
11.5 Parametric Studies
11.5.1 Crack Depth
11.5.2 Crack Length
11.6 Conclusions
References
12. Fracture Response of Steel Pipelines Under Combined Tension and Bending
12.1 Introduction
12.2 Finite Element Procedure
12.2.1 The Pipe Model
12.2.2 Finite Element Modeling
12.3 Results
12.4 Parametric Studies
12.4.1 Crack Depth
12.4.2 Crack Length
12.5 Theoretical Models
12.6 Conclusions
Bibliography
13. Mechanical Behavior of Pipes with Crack under Combined Tension and Internal Pressure
13.1 Introduction
13.2 Finite Element Procedure
13.2.1 The Pipe Model
13.2.2 Finite Element Modeling
13.3 Results
13.4 Parametric Studies
13.4.1 Crack Depth
13.4.2 Crack Length
13.5 Theoretical Solutions
13.6 Analyzing a 21-Inch X80 Steel Pipe
13.6.1 Discussion
13.7 Conclusions
Bibliography
14. The Hoop Stress Failure Analysis of Defective X80 Steel Pipes
14.1 Introduction
14.2 Damage Mechanics Models
14.3 The Pipe Model
14.3.1 Standards
14.3.2 Numerical Model
14.3.3 Results
14.4 Parametric Studies
14.4.1 Burst Resistance of X80 Steel Pipe with Different Initial Defects
14.4.1.1 Crack Length
14.4.1.2 Crack Depth
14.4.2 Burst Resistance of X80 Steel Pipe under Combined Loading Conditions 418
14.4.2.1 Axial Loads
14.4.2.2 Bending
14.5 Conclusions
Bibliography
15. Fracture Study of X80 Steel Based on Phase Field Method
15.1 Introduction
15.2 Experiments
15.2.1 Uniaxial Tensile Test
15.2.2 Fracture Test of Notched Specimens
15.3 Finite Element Model
15.3.1 Implementation of Phase Field Method
15.3.2 Details of the Model
15.3.3 Results and Discussions
15.4 Conclusions
References
About the Author
Index
Back to Top
Preface
Acknowledgement
1. Stress and Strain
1.1 Plasticity in Structural Engineering
1.1.1 Introduction
1.1.2 History
1.1.3 Plasticity of Metals
1.1.4 Plasticity Theory
1.2 Tension and Compression 1
1.2.1 Uniform Loading
1.2.2 Loading Function
1.2.3 Opposite Loading
1.3 Stress Tensor and Deviatoric Stress Tensor
1.3.1 Principal Stress, Principal Shear Stress, and Invariants of Stress Tensor
1.3.2 Decomposition of Stress Tensor and Deviatoric Stress Tensor
1.3.3 Several Variables Related to J2
1.4 Stress Space, π Plane, and Lode Parameters
1.4.1 Principal Stress Space and Plane
1.4.2 Two-Dimensional Expression of Deviatoric Stress
1.5 Deviatoric Strain and Equivalent Strain
1.5.1 The Relationship between Displacement and Strain
1.5.2 Decomposition of the Strain Tensor and Deviatoric Strain
Bibliography
2. Yielding Conditions
2.1 Introduction
2.2 Yield Locus
2.3 Yield Surface
2.4 Yield Criterion
2.4.1 Geometrical Criterion
2.4.2 General Criterion
2.5 Common Yielding Conditions
2.5.1 Tresca Yield Condition
2.5.2 Mises Yield Condition
2.5.3 Anisotropic Yield Condition
2.5.3.1 Hill Yield Criterion
2.5.3.2 Hosford Yield Criterion
2.6 Hardening Rule
2.6.1 Isotropic Hardening Model
2.6.2 Kinematic Hardening Model
2.7 Loading and Unloading of Hardening Materials
2.8 Plastic Deformation
2.9 The Normality Rule
Bibliography
3. Constitutive Equations
3.1 Introduction
3.2 The Total Strain Theory
3.3 The Flow Rules
3.4 Drucker’s Stability Postulate
3.5 The Loading Criterion
3.6 Incremental Stress–Strain Relationships
3.6.1 Constitutive Relation for Perfectly Plastic Materials
3.6.2 Constitutive Relation for Work-Hardening Materials
Bibliography
4. Cyclic Loading and Shakedown
4.1 Introduction
4.2 Cycling Loading
4.3 Shakedown Theorem
4.3.1 Notion of Shakedown
4.3.2 An Intuitive Criterion of Shakedown
4.3.3 Example of Structural Behavior in the Case of Cyclic Loads
Bibliography
5. Some Application Problems
5.1 Torsion in Thin-Walled Tubes
5.2 Combined Tension and Torsion
5.3 Combined Tension, Torsion, and Bending
5.4 Bending in Thin-Walled Tubes
5.5 Combined Tension and Torsion in a Thin-Walled Tube
5.6 Bending in Rectangular Cross-Section
5.7 Internal Pressure in Thick-Walled Tubes
5.7.1 Elastic Analysis of Thick-Walled Cylinders
5.7.2 Plain Axial Symmetry Problem
5.8 Identification Problems
5.8.1 Upper-Bound Approach
5.8.2 Lower-Bound Approach
Bibliography
6. Plasticity in Finite Element Analysis
6.1 Introduction
6.2 Elastic Materials
6.2.1 Kirchhoff Material
6.2.2 Continuum Mechanics
6.2.3 Lagrangian Formulations
6.2.4 Hook’s Law
6.3 Thermo-Elastic Materials
6.4 Hypoelastic Materials
6.4.1 Cauchy Material
6.5 Hyperelastic Materials
6.5.1 Neo-Hookean Material
6.5.2 Modified Mooney-Rivlin Material
6.6 Viscoelastic Materials
6.7 Elastic–Plastic Materials
6.8 Hypoelastic–Plastic Materials
6.9 Hyperelastic–Plastic Materials
6.10 Viscoplastic Materials
6.11 Plastic Materials
Bibliography
7. Plasticity in Total Force Model
7.1 Introduction
7.2 Elastic Beam-Column with Large Displacements
7.3 The Plastic Node Method
7.3.1 History of the Plastic Node Method
7.3.2 Consistency Condition and Hardening Rates for Beam Cross-Sections
7.3.3 Plastic Displacement and Strain at Nodes
7.3.4 Elastic-Plastic Stiffness Equation for Elements
7.4 Transformation Matrix
7.5 Stress-Based Plasticity Constitutive Equations
7.5.1 General
7.5.2 Relationship between Stress and Strain in the Elastic Region
7.5.3 Yield Criterion
7.5.4 Plastic Strain Increment
7.5.4.1 Isotropic Hardening Rule
7.5.4.2 Kinematic Hardening Rule
7.5.5 Stress Increment–Strain Increment Relation in the Plastic Region
7.6 Deformation Matrix
Biblography
8. Metal Forming Processing Plasticity
8.1 Introduction
8.2 Classification
8.3 Forming Processes
8.3.1 Bulk-Forming Process
8.3.2 Sheet Metal Operations
8.4 Sheet Metal Formability
8.4.1 Uniform Strain Distribution in Sheet Metal Forming
8.4.2 Strain Diagram in Sheet Metal Forming
8.4.3 The Deformation Modes
8.5 Anisotropy of Sheet Metal
8.5.1 Uniaxial Anisotropy Coefficients
8.6 Metal Forming in the Carcass Layer of Flexible Pipes
8.6.1 Pre-Metal Forming
8.6.2 Metal Forming
8.6.3 Post-Metal Forming
8.7 Metal Forming Effect on Residual Stress of the Carcass Layer in Flexible Pipes
8.7.1 Experiments
8.7.2 Numerical Model
8.7.3 Results
8.7.4 Residual Stress in Carcass
References
9. Mechanical Behavior of Thin Cylindrical Shells Under Combined Axial Compression and Bending
9.1 Introduction
9.2 Experiments
9.2.1 Material Tests
9.2.2 Tensile Property Testing
9.2.3 Compressive Property Testing
9.2.4 Material Parameters
9.2.5 Combined Loading Tests
9.3 Numerical Studies
9.3.1 Model and Material Properties
9.3.2 Elastic Buckling Analysis
9.4 Validation
9.4.1 Induction of Initial Imperfections
9.4.2 Simulation Results
9.5 Buckling Behavior of Thin Tubes Under Combined Loads
9.6 Conclusions
Bibliography
10. Characterization of Ductile Fracture Criterion for API X80 Pipeline Steel Based on a Phenomenological Approach
10.1 Introduction
10.2 Overview of Damage Model
10.2.1 Descriptions of the Stress State
10.2.2 Gurson-Tvergaard-Needleman Model
10.2.3 Uncoupled Fracture Model
10.2.3.1 Modified Mohr-Coulomb (MMC) Criterion
10.2.3.2 Extended Rice-Tracey (ERT) Criterion
10.2.3.3 Damage Evolution Rule
10.3 Experimental Programs
10.3.1 Conventional Tensile Specimens
10.3.2 Notched Tensile Specimens
10.3.3 Compact Tension (CT) Test
10.4 Calibration Procedure
10.4.1 Finite Element Model
10.4.2 Parameter Identification for GTN Model
10.4.3 Parameter Identification for MMC and ERT Model
10.5 Comparison with Notched Tensile Specimen Test
10.6 Validation through CT Test
10.6.1 Finite Element Model
10.6.2 Mesh Size Sensitivity Analysis
10.6.3 Results and Discussions
10.7 Conclusions
Bibliography
11. Fracture Response of Steel Pipelines Under Combined Tension and Torsion
11.1 Introduction
11.2 Theoretical Equations
11.3 Finite Element Procedure
11.3.1 The Pipe Model
11.3.2 Finite Element Modeling
11.4 Results
11.5 Parametric Studies
11.5.1 Crack Depth
11.5.2 Crack Length
11.6 Conclusions
References
12. Fracture Response of Steel Pipelines Under Combined Tension and Bending
12.1 Introduction
12.2 Finite Element Procedure
12.2.1 The Pipe Model
12.2.2 Finite Element Modeling
12.3 Results
12.4 Parametric Studies
12.4.1 Crack Depth
12.4.2 Crack Length
12.5 Theoretical Models
12.6 Conclusions
Bibliography
13. Mechanical Behavior of Pipes with Crack under Combined Tension and Internal Pressure
13.1 Introduction
13.2 Finite Element Procedure
13.2.1 The Pipe Model
13.2.2 Finite Element Modeling
13.3 Results
13.4 Parametric Studies
13.4.1 Crack Depth
13.4.2 Crack Length
13.5 Theoretical Solutions
13.6 Analyzing a 21-Inch X80 Steel Pipe
13.6.1 Discussion
13.7 Conclusions
Bibliography
14. The Hoop Stress Failure Analysis of Defective X80 Steel Pipes
14.1 Introduction
14.2 Damage Mechanics Models
14.3 The Pipe Model
14.3.1 Standards
14.3.2 Numerical Model
14.3.3 Results
14.4 Parametric Studies
14.4.1 Burst Resistance of X80 Steel Pipe with Different Initial Defects
14.4.1.1 Crack Length
14.4.1.2 Crack Depth
14.4.2 Burst Resistance of X80 Steel Pipe under Combined Loading Conditions 418
14.4.2.1 Axial Loads
14.4.2.2 Bending
14.5 Conclusions
Bibliography
15. Fracture Study of X80 Steel Based on Phase Field Method
15.1 Introduction
15.2 Experiments
15.2.1 Uniaxial Tensile Test
15.2.2 Fracture Test of Notched Specimens
15.3 Finite Element Model
15.3.1 Implementation of Phase Field Method
15.3.2 Details of the Model
15.3.3 Results and Discussions
15.4 Conclusions
References
About the Author
Index
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