Issue 38

D. Marhabi et alii, Frattura ed Integrità Strutturale, 38 (2016) 36-46; DOI: 10.3221/IGF-ESIS.38.05 39 The energy value corresponding to σ* for fatigue initiation crack is represented by: m Rb Te Rb Rb Uniax y r W E R E R E 2 2 2 2 2 2 * * , , 1 , 1 * * Rb,d 2( ) ( ) W 4 4 4                            (5c) The Iso-energy (Eq. 5c) is an ellipse on the cross-section of the specimen (Fig. 1). Eq. 5a Eq. 5c Figure 1 : Dissymmetrical rotating bending ( Eq. 5a ) and line Iso-energy *W ( Eq. 5c ). The large half axis a * and the small half axis b * defined by (Eq. 5c) are the ellipse axes: Te Rb Rb m Rb b R 2 2 2 * , 1 , 1 2 2 , 2                  (6a) Te Rb Rb a R 2 2 2 * , 1 , 1 2 2( ) ( )                (6b) Over-Energy under Dissymmetrical Rotating Bending (D.R.B) in the Ellipse Axes This part is dedicated to analyze the over-energy expressed in the ellipse support is: Rb d Te Rb RB d E b a R R R W ds I S ce WUniax S , , 1 , 1 , 2 2 2 * * 4 2 1 * * *                                  (7a) The member term I ce is given by: Rb d Rb d I W y r d dr W y r d dr I I y y Sc Se ce c e , , ( , ) ( , )       (7b) S c and S e are respectively the circular and the elliptical section (Fig. 1 (5c)) The Integral transformation in elliptical section gives