numero25

A. Spagnoli et alii Frattura ed Integrità Strutturale, 25 (2013) 94-101 ; DOI: 10.3221/IGF-ESIS.25.14 98 with I K  obtained from Eq. 9 (which includes the effect of the Bessel function 0 J ). No crack kinking occurs in such a case, but SIFs are not proportional to the square root of the crack length. Consequently, it can be shown that, in the bilogarithmic I dl / dN ΔK  plane, crack growth does not follow a linear relationship (e.g. see Barenblatt’s model to describe short fatigue crack growth in Ref. [19]). 0 10 20 30 40 Normalized projected crack length, l/d -40 -20 0 20 40 60 Slant angle,  [°] Figure 3 : Example of slant angle variation under nominally Mode I loading ( d = characteristic material length). Weighted average of effective stress intensity factor A weighted average value eq k  of the equivalent SIF range eq k  along the straight segments is introduced. Recognizing a repetitive pattern constituted by n segments in the crack profile, we have : n i i 1 eq,i i 1 eq n (s s ) k k s        (10) where eq,i k  (see Eq. 8) is the equivalent SIF value along the straight segment of length i i 1 (s s )   , s being the curvilinear coordinate along the crack path (Fig. 4). Figure 4 : Fatigue growth of the kinked crack. If the repetitive pattern is that of a zig-zag crack (this has been demonstrated to occur for remote/nominal Mode I load superimposed to any normal/shear microstress field), we have :   n eq,i i 1 ( ) ( ) ( ) i eq I a a n i 1 i k d 2 cos k K f , l d , , d 1 2 cos                          (11) 1 2 1    K I 3 l  s  K II  K II 0  K I