Fatigue and shakedown.. Duration : 20 hours

Fatigue and shakedown.

E. Charkaluk

Objectives:

This course offers an introduction to modern design approach in fatigue, based on the shakedown concept. Some elements on periodic loadings and cyclic plasticity are first given. Then, the shakedown concept, initially proposed by Melan, is introduced. Some high cycle fatigue criteria are presented, taking into account or not gradient effects. Finally, some numerical aspects of fatigue design are discussed.

Each lecture is illustrated with industrial problems and exercises.

Duration: 20 hours

Program:

1. Introduction in fatigue

· Fatigue phenomenon

· Classical macroscopic approach in fatigue

· Physical mechanisms

2. From uniaxial to multiaxial periodic loadings

· Generalities on periodic loadings

· Non proportional loadings

· General expression of amplitude and mean values on a periodic path

3. Cyclic plasticity and hardening under multiaxial loadings

· Plastic criteria

· Cyclic hardening laws

· Residual stresses

4. Shakedown concept

· Static bound of Melan

· Kinematic bound of Koiter

· Local theorem of Mandel

5. Multiaxial High Cycle Fatigue (HCF) criteria

· From physical mechanisms to crack initiation criteria

· Invariant-based approach (Crossland, Sines)

· Critical plane-based approach (Findley, Matake)

6. Dang Van’s multiscale and multiaxial HCF criterion

· Scale transition (Sachs, Taylor, Koiter)

· Shakedown-based fatigue criterion formulation

7. Gradient effects in fatigue

· Critical distance approach

· Gradient-based formulation of classical criteria

· Application in fretting-fatigue and notches

8. Some numerical aspects of fatigue design

· Shakedown, steady-state and direct cyclic algorithms

· Hypersphere problem and related topics