numero25
J.T.P de Castro et alii, Frattura ed Integrità Strutturale, 25 (2013) 79-86; DOI: 10.3221/IGF-ESIS.25.12 81 parts: g(a/w) = (a) , where (a) describes the stress gradient ahead of the notch tip, which tends to the SCF as the crack length a 0 , whereas encompasses all the remaining terms, such as the free surface correction: 0 ( ) ( ) K a a a , where 2 0 0 0 1 a K S (3) Figure 2 : Kitagawa-Takahashi plot describing the fatigue propagation of short and long cracks under pulsating loads ( R = 0) in HT80 steel with K 0 = 11.2 MPa m and S 0 = 575 MPa. Operationally, the short crack can be better treated by letting the SIF range retain its original form, while modifying the FCG threshold expression to become a function of the crack length a , namely K 0 (a) , resulting (under pulsating loads) in: 0 0 0 ( ) K a K a a a (4) The ETS equation can be seen as one possible asymptotic match between the short and long crack behaviors. Following Bazant’s idea [14], a more general equation can be used introducing an adjustable parameter to fit experimental data: 1 /2 0 0 0 ( ) 1 K a K a a (5) Equations (1) to (4) result from (5) if 2 . The bi-linear limit, (a a 0 ) S 0 for short cracks and K 0 (a a 0 ) K 0 for the long ones, is obtained if g(a/w) (a) 1 and . Most short crack FCP data is fitted by K 0 (a) curves with 1.5 8 , but 6 better reproduces classical q -plots based on data measured by testing semi-circular notched fatigue TS [3-5]. Using (5) as the FCP threshold, then any crack departing from a notch under pulsating loads should propagate if: 1 2 0 0 0 ( ) 1 K a a K a K a a (6) where 1.12 is the free surface correction . As fatigue depends on two driving forces, and max , (6) can be extended to consider max (indirectly modeled by the R -ratio) influence in short crack behavior. First, the short crack characteristic size should be defined using the fatigue limit S R and the FCP threshold for long cracks K R K th (a >> a R , R) , both measured or properly estimated at the desired R -ratio: 2 R R 1 1.12 R a K S (7) Likewise, the corresponding short crack FCP threshold should be re-written as: 1 /2 ( ) 1 R R R K a K a a (8) According to Tada [15], the SIF of a crack with size a that departs from a circular hole of radius given within 1% by: 2 3 6 1.1215 ( ), 0.2 0.3 1 ( ) 2 2.354 1.206 0.221 (1 ) (1 ) 1 1 1 I K a x x a x x x x x x x x x (9)
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