Issue 38

D. Marhabi et alii, Frattura ed Integrità Strutturale, 38 (2016) 36-46; DOI: 10.3221/IGF-ESIS.38.05 40 Eq Rb Rb b a b m Rb Rb R R R b a u dud R R E E R a b a b R R E R R E I e 3 3 2 2 2 * * * * , 2 2 2 * * * 1 , 2 3 4 2 2 * * 1 2 2 cos cos sin 0 ) 8                                                                                                                  (7c) The Integral transformation in circular section evaluated by m Rb Rb u I c E E R m Rb Rb du d E E 2 2 1 1 , 3 (1 cos 2 ) (1 sin 2 ) 4 2 2 2 2 1 2 2 , 8 0 2                                       (7d) The over-energy (7a) under dissymmetrical rotating bending when a R * 1  , gives: m Rb Rb Rb Eq Rb Te Rb Rb d a b a b R R R R E b a E R R , , , 1 , 1 , 3 3 * * * * 2 2 2 2 ( 2 ) 2 2 2 4 * * 8 1                                                                                     (8) For us, this result is necessary to identify critical crack in the cylindrical specimen. An Asymptotic Method and over-Energy expressed by Critical Stress The basic concept in the influence area of no damage crack is expressed by * * W WRb,d Te  We allow writing two limits equations near the small half axis and the large half axis of the ellipse (Fig. 1). With this asymptotic method, we have: b For Eq Eq Rb R a For Eq Rb R 2* 2 * 2 0, ( ) , 2* 2 * 2 , ( ) 2                                      (9) The equality (8) and (9) are considered to define the critical stress Eq. (10). It can be deduced by the application of the postulate (Eq. 2b):     Eq Rb Eq Rb Rb d Te Rb B C A , 2 * 2 * 2 0          (10a)