This book presents recent advances related to the following two topics:
- how mechanical fields close to material or geometrical singularities such as cracks can be determined;
- how failure criteria can be established according to the singularity degrees related to these discontinuities.
Concerning the determination of mechanical fields close to a crack tip, the first part of the book presents most of the traditional methods in order to classify them into two major categories. The first is based on the stress field, such as the Airy function, and the second resolves the problem from functions related to displacement fields. Following this, a new method based on the Hamiltonian system is presented in great detail. Local and energetic approaches to fracture are used in order to determine the fracture parameters such as stress intensity factor and energy release rate.
The second part of the book describes methodologies to establish the critical fracture loads and the crack growth criteria. Singular fields for homogeneous and non-homogeneous problems near crack tips, v-notches, interfaces, etc. associated with the crack initiation and propagation laws in elastic and elastic-plastic media, allow us to determine the basis of failure criteria.
Each phenomenon studied is dealt with according to its conceptual and theoretical modeling, to its use in the criteria of fracture resistance; and finally to its implementation in terms of feasibility and numerical application.
Part 1: Stress Field Analysis Close to the Crack Tip
2. Review of Continuum Mechanics and the Behavior Laws.
3. Overview of Fracture Mechanics.
4. Fracture Mechanics.
5. Introduction to the Finite Element Analysis of Cracked Structures.
Part 2: Crack Growth Criteria
6. Crack Propagation.
7. Crack Growth Prediction in Elements of Steel Structures Submitted to Fatigue.
8. Potential Use of Crack Propagation Laws in Fatigue Life Design.
Chapter 1 1
PART 1: STRESS FIELD ANALYSIS CLOSE TO THE CRACK TIP 5
Chapter 2. Review of Continuum Mechanics and the Behavior Laws 7
2.1. Kinematic equations 9
2.2. Equilibrium equations in a volume element 16
2.3. Behavior laws 20
2.4. Energy formalism 50
2.5. Solution of systems of equations of continuum mechanics and constitutive behavior law 63
2.6. Review of the finite element solution 72
Chapter 3. Overview of Fracture Mechanics 81
3.1. Fracture process 83
3.2. Basic modes of fracture 84
Chapter 4. Fracture Mechanics. 87
4.1. Determination of stress, strain and displacement fields around a crack in a homogeneous, isotropic and linearly elastic medium 90
4.2. Plastic analysis around a crack in an isotropic homogeneous medium 144
4.3. Case of a heterogeneous medium: elastic multimaterials 164
4.4. New modeling approach to singular fracture fields 165
Chapter 5. Introduction to the Finite Element Analysis of Cracked Structures 187
5.1. Modeling of a singular field close to the crack tip 188
5.2. Energetic methods 200
5.3. Nonlinear behavior 208
5.4. Specific finite elements for the calculation of cracked structures 213
5.5. Study of a finite elements program in a 2D linear elastic medium. 216
5.6. Application to the calculation of the J-integral in mixed mode 224
5.7. Different meshing fracture monitoring techniques by finite elements 229
PART 2: CRACK GROWTH CRITERIA 235
Chapter 6. Crack Propagation 237
6.1. Brittle fracture 239
6.2. Crack extension 265
6.3. Crack extension criterion in an elastic plastic medium 272
6.4. Crack-extension criterion from V-notches 275
6.5. Fracture following crack growth under high-cycle number fatigue 277
6.6. Crack propagation laws 279
6.7. Approaches used for the calculation of fatigue lifetime 286
6.8. Case of the variable amplitude loading 296
6.9. Crack retardation effect due to overloading 312
6.10. “Reliability–failure” in the presence of random variables 318
Chapter 7. Crack Growth Prediction in Elements of Steel Structures Submitted to Fatigue 331
7.1. Significance and analysis by calculation of stresses around the local effect 333
7.2. Crack initiation under fatigue 343
7.3. Localization and sensitivity to rupture of cracks 367
7.4. Extension of the initiated crack under fatigue 375
Chapter 8. Potential Use of Crack Propagation Laws in Fatigue Life Design 395
8.1. Calculation of the crack propagation fatigue life of a welded-joint 395
8.2. Study of the influence of different parameters on fatigue life 402
8.3. Statistical characterization of the initial crack size according to the welding procedure 404
8.4. Initiation/propagation coupled models: two phase models 410
8.5. Development of a damage model taking into account the crack growth phenomenon 419
8.6. Taking into account the presence of residual welding stresses on crack propagation 423
8.7. Consideration of initial crack length under variable amplitude loading 430
8.8. Propagation of short cracks in the presence of a stress gradient 433
8.9. Probabilistic approach to crack propagation fatigue life: reliability–failure 440