Fracture Mechanics

  1. Linear Elastic Fracture Mechanics
    1. Theoretical Foundations
      1. Basic Assumptions
        1. Linear Elastic Material Behavior
          1. Homogeneous and Isotropic Materials
            1. Small-Scale Yielding
              1. Quasi-Static Loading
              2. Applicability Criteria
                1. Material Requirements
                  1. Geometric Constraints
                    1. Loading Conditions
                    2. Limitations and Boundaries
                      1. Plastic Zone Size Restrictions
                        1. Specimen Size Requirements
                      2. Griffith Energy Approach
                        1. Energy Balance Concept
                          1. Surface Energy
                            1. Elastic Strain Energy
                              1. Work Done by External Forces
                              2. Critical Crack Length
                                1. Derivation and Significance
                                  1. Material Property Relationships
                                  2. Griffith Criterion
                                    1. Mathematical Formulation
                                      1. Physical Interpretation
                                      2. Extensions and Modifications
                                        1. Orowan Modification
                                          1. Plastic Work Considerations
                                        2. Stress Analysis Near Crack Tips
                                          1. Westergaard Stress Functions
                                            1. Mathematical Framework
                                              1. Complex Variable Approach
                                                1. Mode I Solutions
                                                2. Singular Stress Fields
                                                  1. Stress Singularity Nature
                                                    1. Displacement Fields
                                                      1. Strain Fields
                                                      2. Williams Series Expansion
                                                        1. Higher-Order Terms
                                                          1. Non-Singular Contributions
                                                            1. T-Stress Effects
                                                            2. Coordinate Systems
                                                              1. Crack Tip Coordinates
                                                                1. Global vs Local Systems
                                                              2. Stress Intensity Factor
                                                                1. Definition and Physical Meaning
                                                                  1. Mathematical Definition
                                                                    1. Units and Dimensions
                                                                      1. Physical Interpretation
                                                                      2. Mode-Specific Factors
                                                                        1. Mode I Stress Intensity Factor
                                                                          1. Mode II Stress Intensity Factor
                                                                            1. Mode III Stress Intensity Factor
                                                                            2. Relationship to Applied Loading
                                                                              1. Stress and Geometry Dependence
                                                                                1. Crack Size Effects
                                                                                  1. Loading Configuration Impact
                                                                                  2. Superposition Principles
                                                                                    1. Multiple Load Cases
                                                                                      1. Multiple Cracks
                                                                                        1. Linearity Considerations
                                                                                      2. Calculating Stress Intensity Factors
                                                                                        1. Analytical Solutions
                                                                                          1. Standard Crack Geometries
                                                                                            1. Infinite Plate Solutions
                                                                                              1. Semi-Infinite Plate Solutions
                                                                                                1. Finite Geometry Solutions
                                                                                                2. Handbook Solutions
                                                                                                  1. Correction Factors
                                                                                                    1. Geometric Functions
                                                                                                      1. Boundary Condition Effects
                                                                                                      2. Weight Function Method
                                                                                                        1. Theoretical Basis
                                                                                                          1. Application Procedures
                                                                                                            1. Advantages and Limitations
                                                                                                            2. Numerical Methods
                                                                                                              1. Finite Element Analysis
                                                                                                                1. Boundary Element Methods
                                                                                                                  1. Special Elements and Techniques
                                                                                                                  2. Experimental Methods
                                                                                                                    1. Photoelasticity
                                                                                                                      1. Strain Gauge Techniques
                                                                                                                        1. Compliance Methods
                                                                                                                      2. Fracture Toughness
                                                                                                                        1. Material Property Concept
                                                                                                                          1. Definition and Significance
                                                                                                                            1. Critical Stress Intensity Factor
                                                                                                                              1. Temperature Dependence
                                                                                                                                1. Rate Effects
                                                                                                                                2. Plane Stress vs Plane Strain
                                                                                                                                  1. Thickness Effects
                                                                                                                                    1. Constraint Conditions
                                                                                                                                      1. Transition Behavior
                                                                                                                                      2. Plane Strain Fracture Toughness
                                                                                                                                        1. KIc Measurement
                                                                                                                                          1. Specimen Requirements
                                                                                                                                            1. Validity Criteria
                                                                                                                                            2. Factors Affecting Toughness
                                                                                                                                              1. Microstructural Effects
                                                                                                                                                1. Temperature Influence
                                                                                                                                                  1. Loading Rate Effects
                                                                                                                                                    1. Environmental Conditions
                                                                                                                                                  2. Crack Tip Plasticity
                                                                                                                                                    1. Plastic Zone Development
                                                                                                                                                      1. Yielding Criteria
                                                                                                                                                        1. Zone Size Estimation
                                                                                                                                                          1. Shape Considerations
                                                                                                                                                          2. Irwin Plastic Zone Correction
                                                                                                                                                            1. Effective Crack Length
                                                                                                                                                              1. Modified Stress Intensity
                                                                                                                                                                1. Applicability Range
                                                                                                                                                                2. Dugdale Strip Yield Model
                                                                                                                                                                  1. Model Assumptions
                                                                                                                                                                    1. Crack Tip Opening Displacement
                                                                                                                                                                      1. Cohesive Stress Approach
                                                                                                                                                                      2. Plane Stress vs Plane Strain Plasticity
                                                                                                                                                                        1. Constraint Effects
                                                                                                                                                                          1. Zone Size Differences
                                                                                                                                                                            1. Shape Variations
                                                                                                                                                                            2. Small-Scale Yielding Validity
                                                                                                                                                                              1. Size Requirements
                                                                                                                                                                                1. Geometric Constraints
                                                                                                                                                                                  1. Material Considerations
                                                                                                                                                                                2. Energy Release Rate
                                                                                                                                                                                  1. Griffith Energy Criterion
                                                                                                                                                                                    1. Energy Balance Formulation
                                                                                                                                                                                      1. Critical Energy Release Rate
                                                                                                                                                                                        1. Crack Growth Resistance
                                                                                                                                                                                        2. Relationship to Stress Intensity
                                                                                                                                                                                          1. Mathematical Connections
                                                                                                                                                                                            1. Mode-Specific Relations
                                                                                                                                                                                              1. Elastic Constants Role
                                                                                                                                                                                              2. Path Independence
                                                                                                                                                                                                1. J-Integral Precursor
                                                                                                                                                                                                  1. Contour Integration
                                                                                                                                                                                                    1. Physical Significance
                                                                                                                                                                                                    2. R-Curve Behavior
                                                                                                                                                                                                      1. Rising Resistance
                                                                                                                                                                                                        1. Stable Crack Growth
                                                                                                                                                                                                          1. Toughening Mechanisms

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                                                                                                                                                                                                      1. Introduction to Fracture Mechanics

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                                                                                                                                                                                                      3. Elastic-Plastic Fracture Mechanics