Issue 48

V. Giannella et alii, Frattura ed Integrità Strutturale, 48 (2019) 639-647; DOI: 10.3221/IGF-ESIS.48.61 644 , , R K /K eq min eq max  (3)           2 2 2 11 13 22 33 I I II II III S a K a K K a K a K          (4) A A B B eq eq A B eq eq K K K K       (5) FEM MODEL The portion of the cruciform specimen circumscribed by the dashed red line in Fig. 2b was considered as initial model also for the FEM simulations (Fig. 6). No notch neither contacts between crack faces were considered and, as an alternative, a single crack with a total length of 2 mm was considered (Fig. 6c). The FEM simulations considered the same mission profile as for the DBEM analyses, thus cycling between load case A and load case B. (a) (b) (c) Figure 6 : (a)-(b) FEM model with (c) close-up of the initial cracked configuration. The M-integral formulation [26] was used to calculate the three single K values directly and, consequently, a K eq was derived with a sum of squares of the three K values (Eq. 6) to be used in the Walker crack-growth law (Eq. 2). A crack-growth angle θ i was computed by means of the Maximum Tensile Stress (MTS; Fig. 7) criterion for each load case, i.e. load cases A and B; MTS states that the crack kinks in the direction where tensile stress ahead of crack front points is maximized. A crack-growth rate i da / dN was computed for each load case with the Eq. 7, where da / dN is the crack-growth rate computed for any given crack front point and n is the number of load ranges in the spectrum. Finally, the corresponding predicted kink angle is a weighted average kink angle computed with Eq. 8, where θ i is the kink angle determined for load case i using the MTS. 2 2 2 eq I II III K K K K    (6)   1 , da / dN n i i i i da K R dN n     (7)