Fatigue and Rupture

Detection methods show that cracks can be present in large numbers in structures. Fracture mechanics is used to decide whether these cracks can be tolerated without risk, or whether the part should be repaired or scrapped. The aim of the course is to introduce the main concepts of fracture and fatigue which are necessary for the approaches used in damage-tolerant structural design. The main points covered are Brittle fracture (stress field singularity, KIc theory, energy theory of fracture, expression of G, equivalence of Irwin and Griffith theories), Fatigue (fatigue crack initiation, fatigue cracking laws, multiaxial fatigue).

* Fracture mechanics
- Singularity of the stress field
- Irwin's theory (KIc)
- Energy theory of fracture (expressions of G, equivalence of Irwin's and Griffith's theories, Rice integral)
- Supplements on : Mixed-mode crack propagation, Interface cracks, Three-dimensional aspects, Fracture mechanics tests, Dynamic aspects, Ductile fracture mechanics (the Gurson model), Fatigue crack propagation (Paris Law)


* Multiaxial fatigue crack initiation in metallic materials
- Introduction (Techno-economic issues)
- Basics and terminology (General notations, S-N curve, loading path, proportional and non-proportional loading)
- Fatigue testing (Methods of conducting and analyzing tests: staircase, cumulative frequencies)
- Physical basis of fatigue crack initiation in polycrystalline materials (Dislocations, persistent slip bands, intrusions, extrusions)
- Multiaxial fatigue criteria (Different families: empirical (for the record), critical plane (in stress, in energy), global (energetic, using invariants), 3 examples in detail: Crossland (macroscopic stress approach), Dang Van (meso-macro scaling approach), Lamefip (non-local energy approach)
- Factors influencing crack initiation (Which ones, how to take them into account in predictive calculations, how to take advantage of them (when possible)
- Some elements for variable amplitude (Cycle counting method (Rainflow), Notions of damage accumulation (Miner and Lemaitre et Chaboche rules - depending on time available)