numero25

J.T.P de Castro et alii, Frattura ed Integrità Strutturale, 25 (2013) 79-86; DOI: 10.3221/IGF-ESIS.25.12 80 Figure 1 : Classical data showing that non-propagating fatigue cracks are generated at the notch roots if S L /K t <  n < S L /K f [2, 7]. A NALYSIS OF N OTCH E FFECTS ON THE FCG B EHAVIOR OF S HORT C RACKS he generation of non-propagating fatigue cracks shown in Figure 1 indicates that whereas crack initiation by fatigue is controlled by the stresses acting at notch tips, the fatigue crack growth (FCG) behavior of short cracks emanating from them should be affected by the stress gradients around them too. It also indicates that notch sensitivity is caused by the existence of those non-propagating cracks. Indeed, to start a crack at a notch tip and then stop it after a short growth, its driving force must decrease in spite of its growing size. As the cracking driving force depends on the crack size and on the stress acting on it, the only mechanical explanation for such an apparently odd behavior is that the stresses ahead of the notch tip must decrease more than the crack growth contribution. Therefore, the stress gradients ahead of the notch tips must be as important as their SCF to understand the notch sensitivity behavior. Indeed, based on this sensible argument, even before developing its mechanics it could be claimed that, contrary to the traditional practice, for any given material the notch sensitivity value q should depend not only on the notch tip radius  , but also on its depth b , since both affect the stress gradients around notch tips. This means that shallow and elongated notches of same  may have quite different q . But before jumping to conclusions, let’s work out this mechanical model. First note that short fatigue cracks must behave differently from long cracks, since their FCG threshold must be smaller than the long crack threshold  K th (R) [11], otherwise the stress range  required to propagate them would be higher than the material fatigue limit  S L (R) . Indeed, assuming as usual that the FCG process is primarily controlled by the stress intensity factor (SIF) range,  K   (  a) , if short cracks with a  0 had the same  K th (R) threshold of long cracks, their propagation by fatigue would require    , clearly a nonsense. Note also that the word “short” is used here to mean “mechanical” and not “microstructural” small cracks, since material isotropy is assumed in their modeling, a simplified hypothesis corroborated by the tests. The FCG threshold of short fatigue cracks under pulsating loads  K th ( a, R  0 ) can be modeled using El Haddad-Topper-Smith (ETS) characteristic size a 0 [12], which is estimated from  S 0   S L (R  0) and  K 0   K th (R  0). This clever trick reproduces the Kitagawa-Takahashi plot trend [13], see Fig. 2, using a modified SIF range  K’ to describe the fatigue propagation conditions of any crack, short or long, defined by: 0 ( ) K a a       , where     2 0 0 0 1 a K S     (1) This  K’ has been deduced for the Griffith’s plate SIF,  K =  (  a) . To deal with other geometries it should be rewritten using the non-dimensional geometry factor g(a/w) of the cracked component: 0 ( ) ( ) K g a w a a        , where     2 0 0 0 1 ( ) a K g a w S          (2) But the tolerable stress range  under pulsating loads only tends to the fatigue limit  S 0 when a  0 if  is the notch root (instead of the nominal) stress range. However, most g(a/w) expressions found in tables include the notch SCF, thus they use  instead of  n as the nominal stress. A clearer way to define the short crack characteristic size a 0 when the short crack departs from a notch root is to explicitly recognize this practice, separating the geometry factor g(a/w) into two T