Issue 48

V. Giannella et alii, Frattura ed Integrità Strutturale, 48 (2019) 639-647; DOI: 10.3221/IGF-ESIS.48.61 643 Details of the procedures adopted numerically are illustrated in the followings. DBEM MODEL The portion of the cruciform specimen circumscribed by the dashed red line in Fig. 2b was considered as initial model for the DBEM analyses (Fig. 5). The initial notch with two cracks, initiated at 45° at the two opposite tips after the pre-cracking phase, was considered as the initial configuration for the DBEM simulations (Fig. 5c). The total length of the notch and cracks was equal to 2 mm, consistent with the specimen experimentally tested. (a) (b) (c) Figure 5 : (a)-(b) DBEM model with (c) close-up of the initial cracked configuration All the simulations considered a mission profile defined by means of two load cases built as in the following: A. static tensile load in X direction plus cyclic tensile load in Y direction (load case A); B. static tensile load in X direction plus cyclic compressive load in Y direction (load case B). Rings of internal points (J-paths) were introduced along the two crack fronts in order to compute the corresponding J- integral values. The J distributions were then used to compute K I , K II , and K III values along the crack front by means of the procedure developed in [20, 21]. The Yaoming-Mi formula (Eq. 1) [22] was used to combine the K values corresponding to the three basic modes into an equivalent K eq parameter, to be used in the Walker crack-growth law (Eq. 2) [23], whose coefficients are listed in Tab. 1. A crack-growth angle θ i was computed by means of the Minimum Strain Energy Density (MSED) [24, 25] criterion for each i-th load case (i.e. load cases “A” and “B”). MSED criterion considers as the growth angle, the one that minimize the strain energy density defined in terms of K (Eq. 4). Final kink angle was calculated by a weighted average of θ i by means of Eq. 5, whose weights are the K eq values for each load case. For some combinations of static and cyclic load magnitudes, load case “B” provided negative K I values, with no physical meaning since representative of mutual intersection of crack faces. To circumvent this drawback, a nonlinear contact condition, with allowance for friction (friction coefficient = 0.3), was applied to the crack face elements for such load cases. In this way, the resulting K I values became negligible and the related K II and K III decreased due to friction effects, with a corresponding impact on the K eq values and eventually on the final growth angle θ (Eq. 5).   2 2 2 eq I III II K K K K    (1)   m 1 w da / dN C K / 1 R eq         (2)