numero25

J.T.P de Castro et alii, Frattura ed Integrità Strutturale, 25 (2013) 79-86; DOI: 10.3221/IGF-ESIS.25.12 82 So, for circular holes  ( x  0)  3 and  ( x  )  1/1.1215  2  0.63 . Since to propagate by fatigue any crack its SIF must be larger than its threshold, then for pulsating loads:     1/ /2 0 0 ( ) 1 I th K a a K a K a a                       (10) Note that a 0 cannot depend on the stress gradient factor  (a/w) , otherwise it would not be a material property. The FCG criterion can thus be rewritten using two dimensionless functions, one related to the notch stress gradient  (a/w) , and the other g(  S 0 /  , a/  ,  K 0 /  S 0  ,  ) which includes the applied stress range  , and depends on the crack size, on the notch radius  , on the fatigue resistances  K 0 and  S 0 , and on the data fitting exponent  (if it is used):           0 0 0 0 0 1/ 0 0 0 , , , S K S S K a a g S a K S                                                    (11) Therefore, if x  a/  and    K 0 /  S 0    (  a 0 /  ) , a fatigue crack departing from a Kirsch hole under pulsating loads grows whenever  (x)/g(  S 0 /  , x,  ,  ) > 1 . Figure 3 plots some  /g functions for several fatigue strength to loading stress range ratios  S 0 /  as a function of the normalized crack length x , assuming a small notch root radius compared to the short crack characteristic size with  1.40a 0 , and a material with   1.5 and   6 [5]. Figure 3 : Cracks that can start from the border of a (small) circular hole may propagate by fatigue and then stop if their  /g  < 1 . For high applied stress ranges  , the strength to load ratio  S 0 /  is small, and the corresponding  /g curve is always higher than 1 , so cracks initiate and propagate from this Kirsch hole border without stopping during this process. Small stress ranges with load ratios  S 0 /   K t  3 have  /g < 1 , meaning that such loads cannot initiate a fatigue crack from this hole, and that small enough cracks introduced there by any other means will not propagate at such low loads. Intermediate load ranges can initiate and propagate a fatigue crack from this hole border, until the decreasing  /g ratio reaches 1 , where the crack stops because the stress gradient ahead of its small root is sharp enough to eventually force  K I (a) <  K th (a) . Finally, the curve is tangent to the  /g  1 line identifies the smallest pulsating stress range that can cause crack initiation and propagation (without arrest) from the notch border by fatigue alone. Hence, by definition, it is associated to this hole fatigue SCF K f . Moreover, the abscissa of its tangency point gives the largest non-propagating crack size that can arise from it by fatigue alone, a max . For any other  /a 0 ,  , and  combination, K f and a max can always be found by solving the system           max max max max , , , 1 0 , , , f f x g x K g g x x x g x K x                          (12) Kirsch holes induce relatively mild stress gradients. Larger holes compared with the short crack characteristic size, with radii  >> a 0 , are associated to small  values and do not induce short crack arrest. That is a nice way to mechanically