Prediction of the critical stress to crack initiation associated to the investigation of fatigue small crack
Fatigue design is of vital importance to avoid fatigue small crack growth in engineering structures. This study shows that the critical fatigue design stress can be defined below the usual endurance limit, considered in
rules and codes. The material constitutive behaviour is using linear isotropic elasticity.
Lassere and Pallin-Luc [1-2] use the elastic energy and over-energy under uniaxial load (tension and rotating bending). The authors deduce the influencing critical stress value corresponding to sigma star. It’s a linear approach.
We propose an over-energy under dissymmetrical rotating bending and expressed in the ellipse axes. An asymptotic approach is transformed the over-energy in polynomial function of critical stress. Unknown depend on experimental service conditions, endurance limit of tension and rotating bending of specimen. The fatigue database of 30NCD16 steel studied by Froustey and Dubar [3-13] is used. Critical stresses are evaluated (Fig. 2).
The research done by Manning and all  has shown the small crack effect to be as large as 0.3 mm. Small crack and critical stress are illustrated here in as resulting from pure bending approach expressed by Bazant law . It’s reproduces well the Kitagawa diagram  (Fig. 3). When the short cracks are hidden in the material, we shows that the number cycles during small crack growth be significantly higher (Fig. 4) than the corresponding cycles of large cracks growth (ONI’s fatigue test) for the same physically crack size. Indeed its evolution can be blocked by a microstructural barrier (grain boundary, for example). Hence, the considerations of small crack growth are strongly influencing the fatigue life of a component or structure.
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