Issue 38

D. Marhabi et alii, Frattura ed Integrità Strutturale, 38 (2016) 36-46; DOI: 10.3221/IGF-ESIS.38.05 37 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. K EYWORDS . Tensile; Dissymmetrical rotating bending; Over-energy; Critical stress; Small crack; Fatigue cycle. I NTRODUCTION ue to fatigue loading cracks can initiate in material. They can exist as a consequence of manufacturing process such as (deep machining marks, voids in welds) or of metallurgical and geometrical discontinuities. Small cracks have been thoroughly studied aerospace, nuclear, and the ground vehicle industries. In order to predict defects and/or transverse cracks under service conditions, different cracking process have to be noted and explained in terms of the fatigue small crack effect. The first part of this paper is dedicated to analyze the over-energy under dissymmetrical rotating bending and expressed in the ellipse support. An Asymptotic approach associated to critical stress function predict and evaluate the unknown stresses σ*. The second part proposes the small crack size effect using pure bending approach and Bazant law. We confirm that the curve trend reproduces well the Kitagawa diagram. The last part is considering the applicability of linear elastic fracture mechanics (LEFM) for physically small crack. The Integral calculus of number cycles required for small crack is determined. However, the small crack has faster growth rates than long crack. T HE INFLUENCING STRESS IN THE FATIGUE IN THE FATIGUE INITIATION CRACK s proposed by Palin-Luc, Lasserre and Banvillet [1-2] to predict the effect on the fatigue under a uniaxial load in the component. An area influencing fatigue crack initiation S* is considered. From fully reversed fatigue, these authors show that a stress σ* can be defined below the endurance limit σ -1 . The critical stress limit σ* is associated to no damage crack. The Elastic Energy and Over-Energy In this study we assume that the material’s behaviour law is linear isotropic elasticity. For a given elementary area of material, the energy density per loading cycle is: ij ij T M t M t dt T 1 1 W ( , ) ( , ) 2      (1a) The energy W Te and W Rb distributions are axisymmetric in tensile and rotating bending. These sinusoidal loadings are taking as a reference to identify the critical stress *  . S* is the area influencing fatigue crack initiation. S C P x y around C so that W P W C * * ( ) ( , ) ( ) ( )         (1b) The over-energy C ( )  allows initiating short cracks around the critical point C D A