This book perfects the theoretical system of fracture mechanics of nonhomogeneous materials through the establishment of the piecewise exponential model and expands the fracture research scope to nonhomogeneous materials containing complex interfaces through proposing the domain-independent interaction integral concept. The piecewise exponential model has overcome the problem of fracture mechanics of nonhomogeneous materials and clarified the doubt of traditional exponential models in recent 30 years. The domain-independent interaction integral method is not affected by material nonhomogeneity and discontinuity, which greatly facilitates its numerical implementation in the investigation of fracture behaviors of nonhomogeneous materials with complex interfaces.
Author(s): Licheng Guo, Yu Hongjun, Wu Linzhi
Publisher: Springer
Year: 2023
Language: English
Pages: 283
City: Singapore
Preface
Contents
1 Fundamental Theory of Fracture Mechanics of Nonhomogeneous Materials
1.1 Internal Crack
1.1.1 Basic Equations for Nonhomogeneous Materials
1.1.2 Crack-Tip Fields for Homogeneous Materials
1.1.3 Crack-Tip Fields for Nonhomogeneous Materials
1.1.4 Crack-Tip Fields for Nonhomogeneous Orthotropic Materials
1.2 Interface Crack
1.2.1 Crack-Tip Fields of an Interface Crack
1.2.2 Crack-Tip Fields of an Interface Crack Between Two Nonhomogeneous Media
1.3 Three-Dimensional Curved Crack
1.3.1 Internal Crack
1.3.2 Interface Crack
References
2 Exponential Models for Crack Problems in Nonhomogeneous Materials
2.1 Crack Model for Nonhomogeneous Materials with an Arbitrarily Oriented Crack
2.1.1 Basic Equations and Boundary Conditions
2.1.2 Full Field Solution for a Crack in the Nonhomogeneous Medium
2.1.3 Stress Intensity Factors (SIFs) and Strain Energy Release Rate (SERR)
2.2 Crack Problems in Nonhomogeneous Coating-Substrate or Double-Layered Structures
2.2.1 Interface Crack in Nonhomogeneous Coating-Substrate Structures
2.2.2 Cross -Interface Crack Parallel to the Gradient of Material Properties
2.2.3 Arbitrarily Oriented Crack in a Double-Layered Structure
2.3 Crack Problems in Orthotropic Nonhomogeneous Materials
2.3.1 Basic Equations and Boundary Conditions
2.3.2 Solutions to Stress and Displacement Fields
2.3.3 Crack-Tip SIFs
2.4 Transient Crack Problem of a Coating-Substrate Structure
2.4.1 Basic Equations and Boundary Conditions
2.4.2 Solutions to Stress and Displacement Fields
2.4.3 Crack-Tip SIFs
2.5 Representative Examples
2.5.1 Example 1: Arbitrarily Oriented Crack in an Infinite Nonhomogeneous Medium
2.5.2 Example 2: Interface Crack Between the Coating and the Substrate
2.5.3 Example 3: Cross-Interface Crack Perpendicular to the Interface in a Double-Layered Structure
2.5.4 Example 4: Inclined Crack Crossing the Interface
2.5.5 Example 5: Vertical Crack in a Nonhomogeneous Coating-Substrate Structure Subjected to Impact Loading
Appendix 2A
References
3 General Model for Nonhomogeneous Materials with General Elastic Properties
3.1 Piecewise-Exponential Model for the Mode I Crack Problem
3.1.1 Piecewise-Exponential Model (PE Model)
3.1.2 Solutions to Stress and Displacement Fields
3.1.3 Crack-Tip SIFs
3.2 PE Model for Mixed-Mode Crack Problem
3.2.1 Basic Equations and Boundary Conditions
3.2.2 Solutions to Stress and Displacement Fields
3.2.3 Crack-Tip SIFs
3.3 PE Model for Dynamic Crack Problem
3.3.1 Basic Equations and Boundary Conditions
3.3.2 Solutions to Stress and Displacement Fields
3.3.3 Crack-Tip SIFs
3.4 Representative Examples
3.4.1 Example 1: Mode I Crack Problem for Nonhomogeneous Materials with General Elastic Properties
3.4.2 Example 2: Mixed-Mode Crack Problem for Nonhomogeneous Materials with General Elastic Properties and an Arbitrarily Oriented Crack
3.4.3 Example 3: Dynamic Mode I Crack Problem for Nonhomogeneous Materials with General Elastic Properties
Appendix 3A
References
4 Fracture Mechanics of Nonhomogeneous Materials Based on Piecewise-Exponential Model
4.1 Thermomechanical Crack Models of Nonhomogeneous Materials
4.1.1 Crack Model for Nonhomogeneous Materials Under Steady Thermal Loads
4.1.2 Crack Model for Nonhomogeneous Materials Under Thermal Shock Load
4.2 Viscoelastic Crack Model of Nonhomogeneous Materials
4.2.1 The Correspondence Principle for Viscoelastic FGMs
4.2.2 Viscoelastic Models for Nonhomogeneous Materials
4.2.3 PE Model for the Viscoelastic Nonhomogeneous Materials
4.3 Crack Model for Nonhomogeneous Materials with Stochastic Properties
4.3.1 Stochastic Micromechanics-Based Model for Effective Properties
4.3.2 Probabilistic Characteristics of Effective Properties at Transition Region
4.3.3 Crack in Nonhomogeneous Materials with Stochastic Mechanical Properties
4.4 Examples
4.4.1 Example 1: Steady Thermomechanical Crack Problem
4.4.2 Example 2: Viscoelastic Crack Problem
4.4.3 Example 3: Crack Problem in FGMs with Stochastic Mechanical Properties
References
5 Fracture of Nonhomogeneous Materials with Complex Interfaces
5.1 Interaction Integral (I-Integral)
5.1.1 J-integral
5.1.2 I-Integral
5.1.3 Auxiliary Field
5.1.4 Extraction of the SIFs
5.2 Domain-Independent I-integral (DII-Integral)
5.2.1 Domain Form of the I-Integral
5.2.2 DII-Integral
5.3 DII-Integral for Orthotropic Materials
5.4 Consideration of Dynamic Process
5.5 Calculation of the T-Stress
5.6 DII-Integral for 3D Problems
5.6.1 I-Integral
5.6.2 Auxiliary Fields
5.6.3 Extraction of the SIFs
5.6.4 Domain Form of the I-Integral
5.6.5 DII-Integral
5.7 Typical Fracture Problems
5.7.1 Stress Intensity Factor Evaluations
5.7.2 T-Stress Evaluations
5.7.3 Stress Intensity Factors of a Penny-Shaped Crack
5.7.4 Influences of the Material Continuity on the SIFs
References
6 Interfacial Fracture of Nonhomogeneous Materials with Complex Interfaces
6.1 I-integral for an Interface Crack
6.1.1 J-integral and I-integral
6.1.2 Auxiliary Field
6.1.3 Relation Between the I-integral and the SIFs
6.2 Domain-Independent I-integral (DII-Integral)
6.2.1 DII-Integral for Materials with Continuous Properties
6.2.2 DII-Integral for Materials with Complex Interfaces
6.2.3 DII-Integral for a Curved Interface Crack
6.2.4 Consideration of Dynamic Fracture Process
6.3 T-stress Evaluation
6.3.1 Auxiliary Field
6.3.2 Extraction of the T-stress
6.4 DII-Integral for 3D Interface Cracks
6.4.1 Definition of the I-integral on the Crack Front
6.4.2 Auxiliary Fields for 3D Interface Crack
6.4.3 Extraction of the SIFs
6.4.4 Domain Form of the I-integral
6.4.5 DII-Integral
6.5 Representative Interfacial Fracture Problems
6.5.1 Straight Interface Crack
6.5.2 A Circular-Arc Shaped Interface Crack
6.5.3 T-stress Evaluation of Biomaterial Strips
References
7 Thermal Fracture of Nonhomogeneous Materials with Complex Interfaces
7.1 Internal Crack Under Thermal Loading
7.1.1 Basic Equations of Thermoelasticity
7.1.2 I-integral for Thermoelasticity
7.1.3 Auxiliary Field
7.1.4 Extraction of the SIFs for Thermoelastic Media
7.1.5 Domain Form of the I-integral
7.2 Interface Crack Under Thermal Loading
7.2.1 Definition of the I-integral
7.2.2 Auxiliary Field
7.2.3 Extraction of Thermal SIFs
7.2.4 I-integral for a Thermoelastic Solid with Complex Interfaces
7.3 T-stress Evaluation for Nonhomogeneous Thermoelasticity
7.3.1 Auxiliary Field
7.3.2 Extraction of T-stress
7.4 Generalized DII-Integral for Elasticity
7.4.1 Requirements for the Establishment of the DII-Integral
7.4.2 Design of the Generalized Auxiliary Fields
7.4.3 Generalized DII-Integral
7.5 A New DII-Integral for Thermoelasticity
7.5.1 DII-Integral for an Internal Crack
7.5.2 DII-Integral for an Interface Crack
7.6 Typical Thermal Fracture Problems
7.6.1 Internal Crack Under Thermal Loading
7.6.2 Particulate Plate with an Internal Crack
7.6.3 Multi-interface Plate with an Interface Crack
References
