PSI - Issue 12

Venanzio Giannella et al. / Procedia Structural Integrity 12 (2018) 499–506 V. Giannella Structural Integrity Procedia 00 (2018) 000 – 000

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The initial notch with two cracks, initiated at the two opposite notch tips (Fig. 3) after the precracking phase, was considered as the initial configuration for the simulations; the total length of notch and cracks was 2 mm, consistently with experimental outcomes.

Figure 2: Drawings of the cruciform specimen used for the tests with highlight of the loading strategy and the initial notch; the red square define the portion of specimen considered from the numerical standpoint.

J-paths (rings of internal points) were introduced along the crack fronts in order to compute the corresponding J integral values; such J distributions were then used to compute KI, KII, and KIII values along the crack front by means of the procedure developed in (Rigby et al., 1993, 1998). The Yaoming-Mi formula (Eq. 1; Mi, 1995) was used to combine the K values corresponding to the three basic modes into an equivalent Keq parameter, to be used in the Walker crack-growth law (Eq. 2; Walker, 1970), whose coefficients are listed in Tab. 1. A crack- growth angle θi was computed by means of the Minimum Strain Energy Density (MSED; Sih, 1974) criterion for each load case (i.e. load cases “A” and “B”); then, the final kink angle was calculated by a weighted average of θi by means of Eq. 2, whose weights are the Keq values for each load case. K eq = √(K I + |K III |) 2 + 2K I 2 I (1) da⁄dN = C[∆K (1 − R) 1−w ⁄ ] m (2) θ = (θ A |K eA q | + θ B |K eB q |) (|K eA q | + |K eB q |) ⁄ (3) For some combinations of static and dynamic load magnitudes, load case “B” provided negative KI 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 modelled between the crack face elements for such loading conditions: as expected the resulting KI values became negligible and the related KII and KIII decreased due to friction, with a corresponding impact on the Keq values and, eventually, on the final growth angle θ (Eq. 3).