Issue 38

D. Marhabi et alii, Frattura ed Integrità Strutturale, 38 (2016) 36-46; DOI: 10.3221/IGF-ESIS.38.05 38 W M W C S C S C C ds * * ( ( ) ( )) * ( ) ( ) 1 ( )     (1c) At the endurance limit, this quantity C ( )  is supposed to be constant. If we note D Uniax  as being its value at the endurance limit for any uniaxial stress our criterion is: D C Uniax ( )    (1d) Postulate: The quantity  is an intrinsic size in the material (noted Uniax  ) thus it does not depend on the loading type. We can identify their energy to satisfy the equation: Uniax Te Rb Pb Rb d W W W W W ,     (2a) D Uniax Te Rb Pb Rb d ,          (2b) Uniaxial Energy Associated to critical stress By reference to an homogenous fully reversed uniaxial stress and the energy analyses by Palin-Luc, Lasserre and Banvillet (Eqs. 1a and 1c). The authors deduce the influencing critical stress value corresponding to σ* in the fatigue initiation crack: Eq Eq Te Eq Rb * 2 2 , , 2      (3) From (Eqs. 1a and 1c) and value at the endurance limit for (Eq. 3) it easy to prove that * Uniax W is given by (4b); D Uniax  can be calculated by (4c). Eq Te Rb Te Rb Uniax Rb Te D Uniax W E E a b c * 2 2 , 1 , 1 2 2 , 1 , 1 * 2 2 , 1 , 1 2( ) ( ) 2( ) ( ) 4 ( ) ( ) 4 (4 ) (4 ) (4 )                              E NERGY UNDER DISSYMMETRICAL ROTATING BENDING he service stress (Fig. 1 (5a) (b)) on a straight section by a cylindrical specimen: y r t t Rb d m Rb Rb R R ( ) sin , ,        (5a) The energy density given to each elementary under dissymmetrical rotating bending is: m Rb Rb Rb d y r E R E R 2 2 2 2 , , W 4 4                 (5b) T (4a) (4b) (4c)