numero25

A. Spagnoli et alii, Frattura ed Integrità Strutturale, 25 (2013) 94-101; DOI: 10.3221/IGF-ESIS.25.14 99 where the function   ( ) ( ) a a f f , l d , ,               highlights the dependence of eq k  on the relevant parameters. Note that the kinking angle is itself a function of l d . Geometric effects of kinking on crack growth rate Considering the fact that, when the kinked crack spans a distance s , then the projected straight crack spans a distance l , the following relationship holds (between the crack growth rate, ds dN , for the kinked crack and the nominal crack growth rate, dl dN , for the projected straight crack) : ds s dl dN l dN  (12) Note that the crack rate dl dN is always smaller than ds dN . Now, for a zig-zag crack with slant angle  , we have : n i 1 i d 1 2 cos ds dl d dN dN n 2     (13) Kinetics of fatigue crack growth Now let us apply the Paris law to the periodically-kinked crack : m eq ds C k dN   (14) where C and m are material constants. By substituting Eqs 11 and 13 in Eq. 14, the following fatigue crack growth law in terms of the nominal quantities dl dN and I K  is determined for a zig-zag kinked crack : m eq n i 1 i dl n C k 1 dN cos      (15) and hence, by using Eq. 11, we get :   m n eq,i m m i 1 ( ) ( ) ( ) i a a I n n i 1 i 1 i i k cos dl n C C f , l d , , K 1 1 dN cos cos                                               (16) T WO APPLICATIONS OF THE KINKED CRACK MODEL TO EXPERIMENTAL EVIDENCES or illustrative purposes, the present model is applied to some fatigue experimental evidences demonstrating crack size effects. The aim is to discuss whether the present model is able to follow some trend of behavior observed in the experimental tests. The comparison is carried out by considering, in the theoretical model, nominally Mode I cracks (the acting remote fatigue load is ( )    ) under a shear microstress field with ( ) a       arbitrarily taken to be equal to 2. The first experimental data being analysed concern the fatigue threshold condition for mild steel [22]. Such data are related to ferritic and pearlitic steels with carbon content of 0.20% and grain size d of the ferritic phase equal to 7.8  m (small-size grain) and 55  m (large-size grain), respectively (see Ref. [12] for details of experimental data elaboration). For various values of the crack length (ranging from 6 to 1383  m), the threshold stress intensity factor range th K  was F